%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU129+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 : n009.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 17:42:39 EDT 2023 % Result : Theorem 7.09s 1.70s % Output : Proof 8.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU129+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n009.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 : Wed Aug 23 16:28:06 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. % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.73/0.98 Prover 1: Preprocessing ... % 1.73/0.98 Prover 4: Preprocessing ... % 2.41/1.02 Prover 2: Preprocessing ... % 2.41/1.02 Prover 3: Preprocessing ... % 2.41/1.02 Prover 6: Preprocessing ... % 2.41/1.02 Prover 5: Preprocessing ... % 2.41/1.02 Prover 0: Preprocessing ... % 3.71/1.30 Prover 5: Proving ... % 4.43/1.33 Prover 3: Warning: ignoring some quantifiers % 4.43/1.33 Prover 1: Warning: ignoring some quantifiers % 4.43/1.34 Prover 6: Proving ... % 4.43/1.34 Prover 2: Proving ... % 4.43/1.35 Prover 4: Warning: ignoring some quantifiers % 4.43/1.35 Prover 3: Constructing countermodel ... % 4.43/1.35 Prover 1: Constructing countermodel ... % 4.43/1.36 Prover 4: Constructing countermodel ... % 4.43/1.37 Prover 0: Proving ... % 5.77/1.63 Prover 1: gave up % 5.77/1.63 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.77/1.66 Prover 7: Preprocessing ... % 7.09/1.70 Prover 0: proved (1071ms) % 7.09/1.70 % 7.09/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.09/1.70 % 7.09/1.70 Prover 6: stopped % 7.09/1.70 Prover 5: stopped % 7.09/1.70 Prover 2: stopped % 7.12/1.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.12/1.71 Prover 3: stopped % 7.12/1.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.12/1.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.12/1.71 Prover 7: Warning: ignoring some quantifiers % 7.12/1.71 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.12/1.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.12/1.73 Prover 7: Constructing countermodel ... % 7.12/1.73 Prover 11: Preprocessing ... % 7.12/1.74 Prover 8: Preprocessing ... % 7.12/1.74 Prover 13: Preprocessing ... % 7.12/1.74 Prover 10: Preprocessing ... % 7.12/1.76 Prover 16: Preprocessing ... % 7.12/1.78 Prover 4: Found proof (size 43) % 7.12/1.78 Prover 4: proved (1145ms) % 7.12/1.78 Prover 7: stopped % 7.12/1.78 Prover 11: stopped % 7.12/1.79 Prover 13: Warning: ignoring some quantifiers % 7.12/1.79 Prover 16: stopped % 7.12/1.79 Prover 13: Constructing countermodel ... % 7.12/1.80 Prover 13: stopped % 7.83/1.80 Prover 10: Warning: ignoring some quantifiers % 7.83/1.81 Prover 10: Constructing countermodel ... % 7.83/1.81 Prover 8: Warning: ignoring some quantifiers % 7.83/1.81 Prover 10: stopped % 7.83/1.82 Prover 8: Constructing countermodel ... % 7.83/1.82 Prover 8: stopped % 7.83/1.82 % 7.83/1.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.83/1.82 % 7.83/1.83 % SZS output start Proof for theBenchmark % 7.83/1.83 Assumptions after simplification: % 7.83/1.83 --------------------------------- % 7.83/1.83 % 7.83/1.83 (commutativity_k3_xboole_0) % 7.83/1.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2) % 7.83/1.86 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) & ! % 7.83/1.86 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | % 7.83/1.86 ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) % 7.83/1.86 % 7.83/1.86 (d3_tarski) % 7.83/1.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 7.83/1.86 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 7.83/1.86 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 7.83/1.86 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 7.83/1.86 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 7.83/1.86 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 7.83/1.86 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 7.83/1.86 $i(v0) | in(v2, v1) = 0) % 7.83/1.86 % 7.83/1.86 (d3_xboole_0) % 7.83/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 7.83/1.87 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | % 7.83/1.87 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1) % 7.83/1.87 = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 7.83/1.87 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 7.83/1.87 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 7.83/1.87 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = % 7.83/1.87 v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] : % 7.83/1.87 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 7.83/1.87 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ % 7.83/1.87 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = % 7.83/1.87 v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] : % 7.83/1.87 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) % 7.83/1.87 | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 7.83/1.87 (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 7.83/1.87 : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | % 7.83/1.87 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 7.83/1.87 (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i] % 7.83/1.87 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = % 7.83/1.87 v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 7.83/1.87 | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 % 7.83/1.87 = 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 7.83/1.87 $i] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 7.83/1.87 | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 7.83/1.87 (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0) % 7.83/1.87 | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) % 7.83/1.88 % 7.83/1.88 (t26_xboole_1) % 7.83/1.88 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 7.83/1.88 int] : ( ~ (v5 = 0) & subset(v3, v4) = v5 & subset(v0, v1) = 0 & % 7.83/1.88 set_intersection2(v1, v2) = v4 & set_intersection2(v0, v2) = v3 & $i(v4) & % 7.83/1.88 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 7.83/1.88 % 7.83/1.88 (function-axioms) % 7.83/1.88 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 7.83/1.88 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 7.83/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.83/1.88 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 7.83/1.88 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 7.83/1.88 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 7.83/1.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 7.83/1.88 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 7.83/1.88 % 7.83/1.88 Further assumptions not needed in the proof: % 7.83/1.88 -------------------------------------------- % 7.83/1.88 antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k3_xboole_0, fc1_xboole_0, % 7.83/1.88 idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, % 7.83/1.88 t2_boole, t6_boole, t7_boole, t8_boole % 7.83/1.88 % 7.83/1.88 Those formulas are unsatisfiable: % 7.83/1.88 --------------------------------- % 7.83/1.88 % 7.83/1.88 Begin of proof % 7.83/1.88 | % 7.83/1.88 | ALPHA: (commutativity_k3_xboole_0) implies: % 7.83/1.88 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, % 7.83/1.88 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = % 7.83/1.88 | v2 & $i(v2))) % 7.83/1.88 | % 7.83/1.88 | ALPHA: (d3_tarski) implies: % 7.83/1.88 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~ % 7.83/1.88 | (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) = % 7.83/1.88 | 0) % 7.83/1.88 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 7.83/1.88 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 7.83/1.88 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 7.83/1.88 | % 7.83/1.88 | ALPHA: (d3_xboole_0) implies: % 7.83/1.89 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 7.83/1.89 | (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | % 7.83/1.89 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v3, v1) = 0 & in(v3, v0) = 0)) % 7.83/1.89 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 7.83/1.89 | (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | % 7.83/1.89 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 7.83/1.89 | any] : (in(v3, v1) = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 7.83/1.89 | 0)))) % 7.83/1.89 | % 7.83/1.89 | ALPHA: (function-axioms) implies: % 7.83/1.89 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 7.83/1.89 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 7.83/1.89 | % 7.83/1.89 | DELTA: instantiating (t26_xboole_1) with fresh symbols all_18_0, all_18_1, % 7.83/1.89 | all_18_2, all_18_3, all_18_4, all_18_5 gives: % 7.83/1.89 | (7) ~ (all_18_0 = 0) & subset(all_18_2, all_18_1) = all_18_0 & % 7.83/1.89 | subset(all_18_5, all_18_4) = 0 & set_intersection2(all_18_4, all_18_3) % 7.83/1.89 | = all_18_1 & set_intersection2(all_18_5, all_18_3) = all_18_2 & % 7.83/1.89 | $i(all_18_1) & $i(all_18_2) & $i(all_18_3) & $i(all_18_4) & % 7.83/1.89 | $i(all_18_5) % 7.83/1.89 | % 7.83/1.89 | ALPHA: (7) implies: % 7.83/1.89 | (8) ~ (all_18_0 = 0) % 7.83/1.89 | (9) $i(all_18_5) % 7.83/1.89 | (10) $i(all_18_4) % 7.83/1.89 | (11) $i(all_18_3) % 7.83/1.89 | (12) set_intersection2(all_18_5, all_18_3) = all_18_2 % 7.83/1.89 | (13) set_intersection2(all_18_4, all_18_3) = all_18_1 % 7.83/1.89 | (14) subset(all_18_5, all_18_4) = 0 % 7.83/1.89 | (15) subset(all_18_2, all_18_1) = all_18_0 % 7.83/1.89 | % 7.83/1.89 | GROUND_INST: instantiating (1) with all_18_3, all_18_5, all_18_2, simplifying % 7.83/1.89 | with (9), (11), (12) gives: % 7.83/1.89 | (16) set_intersection2(all_18_3, all_18_5) = all_18_2 & $i(all_18_2) % 7.83/1.89 | % 7.83/1.89 | ALPHA: (16) implies: % 7.83/1.89 | (17) $i(all_18_2) % 7.83/1.89 | (18) set_intersection2(all_18_3, all_18_5) = all_18_2 % 7.83/1.89 | % 7.83/1.89 | GROUND_INST: instantiating (1) with all_18_3, all_18_4, all_18_1, simplifying % 7.83/1.89 | with (10), (11), (13) gives: % 8.29/1.89 | (19) set_intersection2(all_18_3, all_18_4) = all_18_1 & $i(all_18_1) % 8.29/1.89 | % 8.29/1.89 | ALPHA: (19) implies: % 8.29/1.89 | (20) $i(all_18_1) % 8.29/1.89 | (21) set_intersection2(all_18_3, all_18_4) = all_18_1 % 8.29/1.89 | % 8.29/1.89 | GROUND_INST: instantiating (3) with all_18_2, all_18_1, all_18_0, simplifying % 8.29/1.89 | with (15), (17), (20) gives: % 8.29/1.90 | (22) all_18_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 8.29/1.90 | all_18_1) = v1 & in(v0, all_18_2) = 0 & $i(v0)) % 8.29/1.90 | % 8.29/1.90 | BETA: splitting (22) gives: % 8.29/1.90 | % 8.29/1.90 | Case 1: % 8.29/1.90 | | % 8.29/1.90 | | (23) all_18_0 = 0 % 8.29/1.90 | | % 8.29/1.90 | | REDUCE: (8), (23) imply: % 8.29/1.90 | | (24) $false % 8.29/1.90 | | % 8.29/1.90 | | CLOSE: (24) is inconsistent. % 8.29/1.90 | | % 8.29/1.90 | Case 2: % 8.29/1.90 | | % 8.29/1.90 | | (25) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_18_1) = v1 & % 8.29/1.90 | | in(v0, all_18_2) = 0 & $i(v0)) % 8.29/1.90 | | % 8.29/1.90 | | DELTA: instantiating (25) with fresh symbols all_32_0, all_32_1 gives: % 8.29/1.90 | | (26) ~ (all_32_0 = 0) & in(all_32_1, all_18_1) = all_32_0 & in(all_32_1, % 8.29/1.90 | | all_18_2) = 0 & $i(all_32_1) % 8.29/1.90 | | % 8.29/1.90 | | ALPHA: (26) implies: % 8.29/1.90 | | (27) ~ (all_32_0 = 0) % 8.29/1.90 | | (28) $i(all_32_1) % 8.29/1.90 | | (29) in(all_32_1, all_18_2) = 0 % 8.29/1.90 | | (30) in(all_32_1, all_18_1) = all_32_0 % 8.29/1.90 | | % 8.29/1.90 | | GROUND_INST: instantiating (5) with all_18_4, all_18_3, all_18_1, all_32_1, % 8.29/1.90 | | all_32_0, simplifying with (10), (11), (13), (20), (28), (30) % 8.29/1.90 | | gives: % 8.29/1.90 | | (31) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_32_1, all_18_3) % 8.29/1.90 | | = v1 & in(all_32_1, all_18_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.29/1.90 | | % 8.29/1.90 | | GROUND_INST: instantiating (4) with all_18_3, all_18_5, all_18_2, all_32_1, % 8.29/1.90 | | simplifying with (9), (11), (17), (18), (28), (29) gives: % 8.29/1.90 | | (32) in(all_32_1, all_18_3) = 0 & in(all_32_1, all_18_5) = 0 % 8.29/1.90 | | % 8.29/1.90 | | ALPHA: (32) implies: % 8.29/1.90 | | (33) in(all_32_1, all_18_5) = 0 % 8.29/1.90 | | (34) in(all_32_1, all_18_3) = 0 % 8.29/1.90 | | % 8.29/1.90 | | GROUND_INST: instantiating (5) with all_18_3, all_18_4, all_18_1, all_32_1, % 8.29/1.90 | | all_32_0, simplifying with (10), (11), (20), (21), (28), (30) % 8.29/1.90 | | gives: % 8.29/1.90 | | (35) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_32_1, all_18_3) % 8.29/1.91 | | = v0 & in(all_32_1, all_18_4) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.29/1.91 | | % 8.29/1.91 | | BETA: splitting (31) gives: % 8.29/1.91 | | % 8.29/1.91 | | Case 1: % 8.29/1.91 | | | % 8.29/1.91 | | | (36) all_32_0 = 0 % 8.29/1.91 | | | % 8.29/1.91 | | | REDUCE: (27), (36) imply: % 8.29/1.91 | | | (37) $false % 8.29/1.91 | | | % 8.29/1.91 | | | CLOSE: (37) is inconsistent. % 8.29/1.91 | | | % 8.29/1.91 | | Case 2: % 8.29/1.91 | | | % 8.29/1.91 | | | (38) ? [v0: any] : ? [v1: any] : (in(all_32_1, all_18_3) = v1 & % 8.29/1.91 | | | in(all_32_1, all_18_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.29/1.91 | | | % 8.29/1.91 | | | DELTA: instantiating (38) with fresh symbols all_48_0, all_48_1 gives: % 8.29/1.91 | | | (39) in(all_32_1, all_18_3) = all_48_0 & in(all_32_1, all_18_4) = % 8.29/1.91 | | | all_48_1 & ( ~ (all_48_0 = 0) | ~ (all_48_1 = 0)) % 8.29/1.91 | | | % 8.29/1.91 | | | ALPHA: (39) implies: % 8.29/1.91 | | | (40) in(all_32_1, all_18_4) = all_48_1 % 8.29/1.91 | | | (41) in(all_32_1, all_18_3) = all_48_0 % 8.29/1.91 | | | (42) ~ (all_48_0 = 0) | ~ (all_48_1 = 0) % 8.29/1.91 | | | % 8.29/1.91 | | | BETA: splitting (35) gives: % 8.29/1.91 | | | % 8.29/1.91 | | | Case 1: % 8.29/1.91 | | | | % 8.29/1.91 | | | | (43) all_32_0 = 0 % 8.29/1.91 | | | | % 8.29/1.91 | | | | REDUCE: (27), (43) imply: % 8.29/1.91 | | | | (44) $false % 8.29/1.91 | | | | % 8.29/1.91 | | | | CLOSE: (44) is inconsistent. % 8.29/1.91 | | | | % 8.29/1.91 | | | Case 2: % 8.29/1.91 | | | | % 8.29/1.91 | | | | (45) ? [v0: any] : ? [v1: any] : (in(all_32_1, all_18_3) = v0 & % 8.29/1.91 | | | | in(all_32_1, all_18_4) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.29/1.91 | | | | % 8.29/1.91 | | | | DELTA: instantiating (45) with fresh symbols all_53_0, all_53_1 gives: % 8.29/1.91 | | | | (46) in(all_32_1, all_18_3) = all_53_1 & in(all_32_1, all_18_4) = % 8.29/1.91 | | | | all_53_0 & ( ~ (all_53_0 = 0) | ~ (all_53_1 = 0)) % 8.29/1.91 | | | | % 8.29/1.91 | | | | ALPHA: (46) implies: % 8.29/1.91 | | | | (47) in(all_32_1, all_18_4) = all_53_0 % 8.29/1.91 | | | | (48) in(all_32_1, all_18_3) = all_53_1 % 8.29/1.91 | | | | % 8.29/1.91 | | | | GROUND_INST: instantiating (6) with all_48_1, all_53_0, all_18_4, % 8.29/1.91 | | | | all_32_1, simplifying with (40), (47) gives: % 8.29/1.91 | | | | (49) all_53_0 = all_48_1 % 8.29/1.91 | | | | % 8.29/1.91 | | | | GROUND_INST: instantiating (6) with all_48_0, all_53_1, all_18_3, % 8.29/1.91 | | | | all_32_1, simplifying with (41), (48) gives: % 8.29/1.91 | | | | (50) all_53_1 = all_48_0 % 8.29/1.91 | | | | % 8.29/1.91 | | | | GROUND_INST: instantiating (6) with 0, all_53_1, all_18_3, all_32_1, % 8.29/1.91 | | | | simplifying with (34), (48) gives: % 8.29/1.91 | | | | (51) all_53_1 = 0 % 8.29/1.91 | | | | % 8.29/1.91 | | | | COMBINE_EQS: (50), (51) imply: % 8.29/1.91 | | | | (52) all_48_0 = 0 % 8.29/1.91 | | | | % 8.29/1.91 | | | | BETA: splitting (42) gives: % 8.29/1.91 | | | | % 8.29/1.91 | | | | Case 1: % 8.29/1.91 | | | | | % 8.29/1.91 | | | | | (53) ~ (all_48_0 = 0) % 8.29/1.91 | | | | | % 8.29/1.91 | | | | | REDUCE: (52), (53) imply: % 8.29/1.91 | | | | | (54) $false % 8.29/1.91 | | | | | % 8.29/1.91 | | | | | CLOSE: (54) is inconsistent. % 8.29/1.91 | | | | | % 8.29/1.91 | | | | Case 2: % 8.29/1.91 | | | | | % 8.29/1.91 | | | | | (55) ~ (all_48_1 = 0) % 8.29/1.91 | | | | | % 8.29/1.91 | | | | | GROUND_INST: instantiating (2) with all_18_5, all_18_4, all_32_1, % 8.29/1.91 | | | | | simplifying with (9), (10), (14), (28), (33) gives: % 8.29/1.91 | | | | | (56) in(all_32_1, all_18_4) = 0 % 8.29/1.91 | | | | | % 8.29/1.91 | | | | | GROUND_INST: instantiating (6) with all_48_1, 0, all_18_4, all_32_1, % 8.29/1.91 | | | | | simplifying with (40), (56) gives: % 8.29/1.91 | | | | | (57) all_48_1 = 0 % 8.29/1.91 | | | | | % 8.29/1.91 | | | | | REDUCE: (55), (57) imply: % 8.29/1.91 | | | | | (58) $false % 8.29/1.91 | | | | | % 8.29/1.91 | | | | | CLOSE: (58) is inconsistent. % 8.29/1.91 | | | | | % 8.29/1.91 | | | | End of split % 8.29/1.91 | | | | % 8.29/1.91 | | | End of split % 8.29/1.91 | | | % 8.29/1.91 | | End of split % 8.29/1.91 | | % 8.29/1.91 | End of split % 8.29/1.91 | % 8.29/1.91 End of proof % 8.29/1.91 % SZS output end Proof for theBenchmark % 8.29/1.91 % 8.29/1.91 1305ms %------------------------------------------------------------------------------