%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU145+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 : n015.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 17:42:45 EDT 2023 % Result : Theorem 5.15s 1.45s % Output : Proof 6.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU145+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 : n015.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 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Wed Aug 23 15:41:04 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.00/0.97 Prover 1: Preprocessing ... % 2.00/0.97 Prover 4: Preprocessing ... % 2.00/1.02 Prover 6: Preprocessing ... % 2.00/1.02 Prover 5: Preprocessing ... % 2.00/1.02 Prover 3: Preprocessing ... % 2.00/1.02 Prover 0: Preprocessing ... % 2.00/1.02 Prover 2: Preprocessing ... % 3.77/1.21 Prover 1: Warning: ignoring some quantifiers % 3.77/1.22 Prover 3: Warning: ignoring some quantifiers % 3.77/1.24 Prover 6: Proving ... % 3.77/1.24 Prover 5: Proving ... % 3.77/1.24 Prover 3: Constructing countermodel ... % 3.77/1.24 Prover 1: Constructing countermodel ... % 4.09/1.27 Prover 2: Proving ... % 4.09/1.28 Prover 4: Warning: ignoring some quantifiers % 4.09/1.28 Prover 0: Proving ... % 4.09/1.30 Prover 4: Constructing countermodel ... % 5.15/1.45 Prover 3: proved (809ms) % 5.15/1.45 % 5.15/1.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.15/1.45 % 5.15/1.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.15/1.47 Prover 2: stopped % 5.15/1.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.15/1.48 Prover 5: stopped % 5.15/1.48 Prover 0: stopped % 5.15/1.50 Prover 6: stopped % 5.15/1.50 Prover 8: Preprocessing ... % 5.15/1.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.15/1.50 Prover 7: Preprocessing ... % 5.15/1.50 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.15/1.50 Prover 10: Preprocessing ... % 5.15/1.51 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.15/1.51 Prover 11: Preprocessing ... % 5.15/1.52 Prover 13: Preprocessing ... % 5.15/1.52 Prover 7: Warning: ignoring some quantifiers % 5.15/1.53 Prover 7: Constructing countermodel ... % 5.15/1.54 Prover 10: Warning: ignoring some quantifiers % 5.15/1.54 Prover 10: Constructing countermodel ... % 5.15/1.56 Prover 4: Found proof (size 29) % 5.15/1.56 Prover 4: proved (922ms) % 5.15/1.56 Prover 1: stopped % 5.15/1.56 Prover 11: stopped % 5.15/1.56 Prover 10: stopped % 5.15/1.56 Prover 7: stopped % 5.15/1.57 Prover 13: stopped % 5.15/1.57 Prover 8: Warning: ignoring some quantifiers % 5.15/1.58 Prover 8: Constructing countermodel ... % 5.15/1.58 Prover 8: stopped % 5.15/1.58 % 5.15/1.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.15/1.58 % 5.15/1.58 % SZS output start Proof for theBenchmark % 5.15/1.59 Assumptions after simplification: % 5.15/1.59 --------------------------------- % 5.15/1.59 % 5.15/1.59 (d1_tarski) % 6.43/1.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) | % 6.43/1.62 ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! % 6.43/1.62 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = % 6.43/1.62 v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 6.43/1.62 (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 6.43/1.62 [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = % 6.43/1.62 0 | v3 = v1))) % 6.43/1.62 % 6.43/1.62 (d3_tarski) % 6.43/1.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 6.43/1.63 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 6.43/1.63 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 6.43/1.63 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 6.43/1.63 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 6.43/1.63 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 6.43/1.63 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 6.43/1.63 $i(v0) | in(v2, v1) = 0) % 6.43/1.63 % 6.43/1.63 (d4_xboole_0) % 6.67/1.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 6.67/1.65 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~ % 6.67/1.65 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1) = % 6.67/1.65 v6 & in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: % 6.67/1.65 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 6.67/1.65 (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) % 6.67/1.65 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v6 & % 6.67/1.65 in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : % 6.67/1.65 ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ (set_difference(v0, v1) = v2) | % 6.67/1.65 ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 6.67/1.65 [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) % 6.67/1.65 | (v6 = 0 & ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 6.67/1.65 ! [v3: $i] : ! [v4: any] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) % 6.67/1.65 = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? % 6.67/1.65 [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ % 6.67/1.65 (v6 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 6.67/1.65 ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 6.67/1.65 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = % 6.67/1.65 v4 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 6.67/1.65 $i] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | % 6.67/1.65 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v2) % 6.67/1.65 = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) & ? [v0: $i] : ! [v1: $i] : % 6.67/1.65 ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ~ % 6.67/1.65 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : % 6.67/1.65 ? [v7: any] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) % 6.67/1.65 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = % 6.67/1.65 0))))) % 6.67/1.65 % 6.67/1.65 (l3_zfmisc_1) % 6.67/1.65 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: $i] : ? [v5: % 6.67/1.65 $i] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v3 = 0) & set_difference(v1, v4) = % 6.67/1.65 v5 & subset(v0, v5) = v6 & subset(v0, v1) = 0 & singleton(v2) = v4 & in(v2, % 6.67/1.65 v0) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v1) & $i(v0)) % 6.67/1.65 % 6.67/1.65 (function-axioms) % 6.67/1.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 6.67/1.66 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 6.67/1.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 6.67/1.66 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 6.67/1.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 6.67/1.66 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 6.67/1.66 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 6.67/1.66 (singleton(v2) = v0)) % 6.67/1.66 % 6.67/1.66 Further assumptions not needed in the proof: % 6.67/1.66 -------------------------------------------- % 6.67/1.66 antisymmetry_r2_hidden, dt_k1_tarski, dt_k4_xboole_0, reflexivity_r1_tarski % 6.67/1.66 % 6.67/1.66 Those formulas are unsatisfiable: % 6.67/1.66 --------------------------------- % 6.67/1.66 % 6.67/1.66 Begin of proof % 6.67/1.66 | % 6.67/1.66 | ALPHA: (d1_tarski) implies: % 6.67/1.66 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) % 6.67/1.66 | = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 6.67/1.66 | % 6.67/1.66 | ALPHA: (d3_tarski) implies: % 6.67/1.66 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~ % 6.67/1.66 | (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) = % 6.67/1.66 | 0) % 6.67/1.66 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 6.67/1.66 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 6.67/1.66 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 6.67/1.66 | % 6.67/1.66 | ALPHA: (d4_xboole_0) implies: % 6.67/1.66 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 6.67/1.66 | (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ % 6.67/1.66 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 6.67/1.66 | any] : (in(v3, v1) = v6 & in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = % 6.67/1.66 | 0))) % 6.67/1.66 | % 6.67/1.66 | ALPHA: (function-axioms) implies: % 6.67/1.66 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 6.67/1.66 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 6.67/1.67 | % 6.67/1.67 | DELTA: instantiating (l3_zfmisc_1) with fresh symbols all_10_0, all_10_1, % 6.67/1.67 | all_10_2, all_10_3, all_10_4, all_10_5, all_10_6 gives: % 6.67/1.67 | (6) ~ (all_10_0 = 0) & ~ (all_10_3 = 0) & set_difference(all_10_5, % 6.67/1.67 | all_10_2) = all_10_1 & subset(all_10_6, all_10_1) = all_10_0 & % 6.67/1.67 | subset(all_10_6, all_10_5) = 0 & singleton(all_10_4) = all_10_2 & % 6.67/1.67 | in(all_10_4, all_10_6) = all_10_3 & $i(all_10_1) & $i(all_10_2) & % 6.67/1.67 | $i(all_10_4) & $i(all_10_5) & $i(all_10_6) % 6.67/1.67 | % 6.67/1.67 | ALPHA: (6) implies: % 6.67/1.67 | (7) ~ (all_10_3 = 0) % 6.67/1.67 | (8) ~ (all_10_0 = 0) % 6.67/1.67 | (9) $i(all_10_6) % 6.67/1.67 | (10) $i(all_10_5) % 6.67/1.67 | (11) $i(all_10_4) % 6.67/1.67 | (12) $i(all_10_2) % 6.67/1.67 | (13) $i(all_10_1) % 6.67/1.67 | (14) in(all_10_4, all_10_6) = all_10_3 % 6.67/1.67 | (15) singleton(all_10_4) = all_10_2 % 6.67/1.67 | (16) subset(all_10_6, all_10_5) = 0 % 6.67/1.67 | (17) subset(all_10_6, all_10_1) = all_10_0 % 6.67/1.67 | (18) set_difference(all_10_5, all_10_2) = all_10_1 % 6.67/1.67 | % 6.67/1.67 | GROUND_INST: instantiating (3) with all_10_6, all_10_1, all_10_0, simplifying % 6.67/1.67 | with (9), (13), (17) gives: % 6.67/1.67 | (19) all_10_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 6.67/1.67 | all_10_1) = v1 & in(v0, all_10_6) = 0 & $i(v0)) % 6.67/1.67 | % 6.67/1.67 | BETA: splitting (19) gives: % 6.67/1.67 | % 6.67/1.67 | Case 1: % 6.67/1.67 | | % 6.67/1.67 | | (20) all_10_0 = 0 % 6.67/1.67 | | % 6.67/1.67 | | REDUCE: (8), (20) imply: % 6.67/1.67 | | (21) $false % 6.67/1.67 | | % 6.67/1.67 | | CLOSE: (21) is inconsistent. % 6.67/1.67 | | % 6.67/1.67 | Case 2: % 6.67/1.67 | | % 6.67/1.68 | | (22) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_10_1) = v1 & % 6.67/1.68 | | in(v0, all_10_6) = 0 & $i(v0)) % 6.67/1.68 | | % 6.67/1.68 | | DELTA: instantiating (22) with fresh symbols all_21_0, all_21_1 gives: % 6.67/1.68 | | (23) ~ (all_21_0 = 0) & in(all_21_1, all_10_1) = all_21_0 & in(all_21_1, % 6.67/1.68 | | all_10_6) = 0 & $i(all_21_1) % 6.67/1.68 | | % 6.67/1.68 | | ALPHA: (23) implies: % 6.67/1.68 | | (24) ~ (all_21_0 = 0) % 6.67/1.68 | | (25) $i(all_21_1) % 6.67/1.68 | | (26) in(all_21_1, all_10_6) = 0 % 6.67/1.68 | | (27) in(all_21_1, all_10_1) = all_21_0 % 6.67/1.68 | | % 6.67/1.68 | | GROUND_INST: instantiating (2) with all_10_6, all_10_5, all_21_1, % 6.67/1.68 | | simplifying with (9), (10), (16), (25), (26) gives: % 6.67/1.68 | | (28) in(all_21_1, all_10_5) = 0 % 6.67/1.68 | | % 6.67/1.68 | | GROUND_INST: instantiating (4) with all_10_5, all_10_2, all_10_1, all_21_1, % 6.67/1.68 | | all_21_0, simplifying with (10), (12), (13), (18), (25), (27) % 6.67/1.68 | | gives: % 6.67/1.68 | | (29) all_21_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_21_1, all_10_2) % 6.67/1.68 | | = v1 & in(all_21_1, all_10_5) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 6.67/1.68 | | % 6.67/1.68 | | BETA: splitting (29) gives: % 6.67/1.68 | | % 6.67/1.68 | | Case 1: % 6.67/1.68 | | | % 6.67/1.68 | | | (30) all_21_0 = 0 % 6.67/1.68 | | | % 6.67/1.68 | | | REDUCE: (24), (30) imply: % 6.67/1.68 | | | (31) $false % 6.67/1.68 | | | % 6.67/1.68 | | | CLOSE: (31) is inconsistent. % 6.67/1.68 | | | % 6.67/1.68 | | Case 2: % 6.67/1.68 | | | % 6.67/1.68 | | | (32) ? [v0: any] : ? [v1: any] : (in(all_21_1, all_10_2) = v1 & % 6.67/1.68 | | | in(all_21_1, all_10_5) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 6.67/1.68 | | | % 6.67/1.68 | | | DELTA: instantiating (32) with fresh symbols all_35_0, all_35_1 gives: % 6.67/1.68 | | | (33) in(all_21_1, all_10_2) = all_35_0 & in(all_21_1, all_10_5) = % 6.67/1.68 | | | all_35_1 & ( ~ (all_35_1 = 0) | all_35_0 = 0) % 6.67/1.68 | | | % 6.67/1.68 | | | ALPHA: (33) implies: % 6.67/1.68 | | | (34) in(all_21_1, all_10_5) = all_35_1 % 6.67/1.68 | | | (35) in(all_21_1, all_10_2) = all_35_0 % 6.67/1.68 | | | (36) ~ (all_35_1 = 0) | all_35_0 = 0 % 6.67/1.68 | | | % 6.67/1.68 | | | GROUND_INST: instantiating (5) with 0, all_35_1, all_10_5, all_21_1, % 6.67/1.68 | | | simplifying with (28), (34) gives: % 6.67/1.68 | | | (37) all_35_1 = 0 % 6.67/1.68 | | | % 6.67/1.68 | | | BETA: splitting (36) gives: % 6.67/1.68 | | | % 6.67/1.68 | | | Case 1: % 6.67/1.68 | | | | % 6.67/1.68 | | | | (38) ~ (all_35_1 = 0) % 6.67/1.68 | | | | % 6.67/1.68 | | | | REDUCE: (37), (38) imply: % 6.67/1.68 | | | | (39) $false % 6.67/1.68 | | | | % 6.67/1.68 | | | | CLOSE: (39) is inconsistent. % 6.67/1.68 | | | | % 6.67/1.68 | | | Case 2: % 6.67/1.68 | | | | % 6.67/1.68 | | | | (40) all_35_0 = 0 % 6.67/1.68 | | | | % 6.67/1.68 | | | | REDUCE: (35), (40) imply: % 6.67/1.68 | | | | (41) in(all_21_1, all_10_2) = 0 % 6.67/1.68 | | | | % 6.67/1.69 | | | | GROUND_INST: instantiating (1) with all_10_4, all_10_2, all_21_1, % 6.67/1.69 | | | | simplifying with (11), (12), (15), (25), (41) gives: % 6.67/1.69 | | | | (42) all_21_1 = all_10_4 % 6.67/1.69 | | | | % 6.67/1.69 | | | | REDUCE: (26), (42) imply: % 6.67/1.69 | | | | (43) in(all_10_4, all_10_6) = 0 % 6.67/1.69 | | | | % 6.67/1.69 | | | | GROUND_INST: instantiating (5) with all_10_3, 0, all_10_6, all_10_4, % 6.67/1.69 | | | | simplifying with (14), (43) gives: % 6.67/1.69 | | | | (44) all_10_3 = 0 % 6.67/1.69 | | | | % 6.67/1.69 | | | | REDUCE: (7), (44) imply: % 6.67/1.69 | | | | (45) $false % 6.67/1.69 | | | | % 6.67/1.69 | | | | CLOSE: (45) is inconsistent. % 6.67/1.69 | | | | % 6.67/1.69 | | | End of split % 6.67/1.69 | | | % 6.67/1.69 | | End of split % 6.67/1.69 | | % 6.67/1.69 | End of split % 6.67/1.69 | % 6.67/1.69 End of proof % 6.67/1.69 % SZS output end Proof for theBenchmark % 6.67/1.69 % 6.67/1.69 1076ms %------------------------------------------------------------------------------