%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET792+4 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n020.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 15:26:28 EDT 2023 % Result : Theorem 7.32s 1.72s % Output : Proof 9.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET792+4 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n020.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 : Sat Aug 26 10:52:14 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.83/1.13 Prover 4: Preprocessing ... % 2.83/1.13 Prover 1: Preprocessing ... % 2.83/1.16 Prover 3: Preprocessing ... % 2.83/1.16 Prover 2: Preprocessing ... % 2.83/1.16 Prover 6: Preprocessing ... % 2.83/1.16 Prover 5: Preprocessing ... % 2.83/1.16 Prover 0: Preprocessing ... % 5.12/1.49 Prover 5: Proving ... % 5.12/1.49 Prover 2: Proving ... % 6.37/1.61 Prover 6: Proving ... % 6.37/1.63 Prover 3: Constructing countermodel ... % 6.37/1.67 Prover 1: Constructing countermodel ... % 7.32/1.71 Prover 3: proved (1077ms) % 7.32/1.72 % 7.32/1.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.32/1.72 % 7.32/1.72 Prover 2: stopped % 7.32/1.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.38/1.72 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.38/1.72 Prover 6: stopped % 7.38/1.72 Prover 5: stopped % 7.38/1.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.38/1.73 Prover 4: Constructing countermodel ... % 7.38/1.73 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.38/1.74 Prover 0: Proving ... % 7.38/1.76 Prover 0: stopped % 7.38/1.76 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.38/1.77 Prover 7: Preprocessing ... % 7.38/1.78 Prover 10: Preprocessing ... % 7.38/1.78 Prover 11: Preprocessing ... % 7.38/1.79 Prover 8: Preprocessing ... % 8.01/1.84 Prover 13: Preprocessing ... % 8.01/1.86 Prover 7: Warning: ignoring some quantifiers % 8.01/1.87 Prover 10: Warning: ignoring some quantifiers % 8.01/1.88 Prover 7: Constructing countermodel ... % 8.01/1.88 Prover 10: Constructing countermodel ... % 8.55/1.91 Prover 13: Warning: ignoring some quantifiers % 8.55/1.91 Prover 1: Found proof (size 46) % 8.55/1.92 Prover 1: proved (1277ms) % 8.55/1.92 Prover 4: stopped % 8.55/1.92 Prover 11: stopped % 8.55/1.92 Prover 10: stopped % 8.55/1.92 Prover 7: stopped % 8.55/1.92 Prover 13: Constructing countermodel ... % 8.55/1.93 Prover 13: stopped % 9.10/1.98 Prover 8: Warning: ignoring some quantifiers % 9.10/1.99 Prover 8: Constructing countermodel ... % 9.10/2.00 Prover 8: stopped % 9.10/2.00 % 9.10/2.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.10/2.00 % 9.10/2.01 % SZS output start Proof for theBenchmark % 9.10/2.01 Assumptions after simplification: % 9.10/2.01 --------------------------------- % 9.10/2.01 % 9.10/2.01 (least) % 9.10/2.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 9.10/2.04 (least(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 9.10/2.04 ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 & member(v4, v1) = 0 & % 9.10/2.04 $i(v4)) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0: % 9.10/2.04 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (least(v2, v0, v1) = 0) | ~ $i(v2) | % 9.10/2.04 ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & ! [v3: $i] : ! [v4: int] : % 9.10/2.04 (v4 = 0 | ~ (apply(v0, v2, v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 % 9.10/2.04 = 0) & member(v3, v1) = v5)))) % 9.10/2.04 % 9.10/2.04 (min) % 9.10/2.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (min(v2, % 9.10/2.05 v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ( ~ % 9.10/2.05 (v4 = v2) & apply(v0, v4, v2) = 0 & member(v4, v1) = 0 & $i(v4)) | ? [v4: % 9.10/2.05 int] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : % 9.10/2.05 ! [v2: $i] : ( ~ (min(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 9.10/2.05 (member(v2, v1) = 0 & ! [v3: $i] : (v3 = v2 | ~ (apply(v0, v3, v2) = 0) | % 9.10/2.05 ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4)))) % 9.10/2.05 % 9.10/2.05 (order) % 9.10/2.06 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (order(v0, v1) = v2) | % 9.10/2.06 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 9.10/2.06 int] : ( ~ (v6 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v6 & % 9.10/2.06 apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & % 9.10/2.06 member(v3, v1) = 0 & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] % 9.10/2.06 : ( ~ (v4 = v3) & apply(v0, v4, v3) = 0 & apply(v0, v3, v4) = 0 & member(v4, % 9.10/2.06 v1) = 0 & member(v3, v1) = 0 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: % 9.10/2.06 int] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0 & % 9.10/2.06 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (order(v0, v1) = 0) | ~ $i(v1) % 9.10/2.06 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 % 9.10/2.06 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ~ % 9.10/2.06 $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: % 9.10/2.06 any] : ? [v9: any] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 & % 9.10/2.06 member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) % 9.10/2.06 | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v2: $i] : ! [v3: $i] : (v3 = % 9.10/2.06 v2 | ~ (apply(v0, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : % 9.10/2.06 ? [v5: any] : ? [v6: any] : (apply(v0, v3, v2) = v6 & member(v3, v1) = % 9.10/2.06 v5 & member(v2, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) % 9.10/2.06 & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v0, v2, v2) = v3) | ~ % 9.10/2.06 $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4)))) % 9.10/2.06 % 9.10/2.06 (thIV4) % 9.10/2.06 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 9.10/2.06 min(v2, v0, v1) = v3 & least(v2, v0, v1) = 0 & order(v0, v1) = 0 & $i(v2) & % 9.10/2.06 $i(v1) & $i(v0)) % 9.10/2.06 % 9.10/2.06 (function-axioms) % 9.10/2.06 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 9.10/2.06 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (greatest_lower_bound(v5, % 9.10/2.06 v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) & ! % 9.10/2.06 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 9.10/2.06 $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (least_upper_bound(v5, v4, % 9.10/2.06 v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0)) & ! [v0: % 9.10/2.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.10/2.06 : ! [v4: $i] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) = % 9.10/2.06 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.10/2.06 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~ % 9.10/2.06 (max(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.10/2.06 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 9.10/2.06 (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0: % 9.10/2.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.10/2.06 : ! [v4: $i] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4, % 9.10/2.06 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 9.10/2.06 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (lower_bound(v4, v3, % 9.10/2.06 v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0)) & ! [v0: % 9.10/2.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.10/2.06 : ! [v4: $i] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~ % 9.10/2.06 (upper_bound(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.10/2.06 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 9.10/2.06 (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0: % 9.10/2.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.10/2.06 : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0)) & % 9.10/2.06 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 9.10/2.06 $i] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0)) & ! % 9.10/2.06 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 9.10/2.06 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 9.10/2.06 % 9.10/2.06 Further assumptions not needed in the proof: % 9.10/2.06 -------------------------------------------- % 9.10/2.06 greatest, greatest_lower_bound, least_upper_bound, lower_bound, max, % 9.10/2.06 total_order, upper_bound % 9.10/2.06 % 9.10/2.06 Those formulas are unsatisfiable: % 9.10/2.06 --------------------------------- % 9.10/2.06 % 9.10/2.06 Begin of proof % 9.10/2.06 | % 9.10/2.06 | ALPHA: (order) implies: % 9.10/2.07 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (order(v0, v1) = 0) | ~ $i(v1) | ~ % 9.10/2.07 | $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : % 9.10/2.07 | (v5 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) % 9.10/2.07 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] % 9.10/2.07 | : ? [v8: any] : ? [v9: any] : (apply(v0, v3, v4) = v9 & % 9.10/2.07 | member(v4, v1) = v8 & member(v3, v1) = v7 & member(v2, v1) = v6 % 9.10/2.07 | & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & % 9.10/2.07 | ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (apply(v0, v2, v3) = 0) | % 9.10/2.07 | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6: any] % 9.10/2.07 | : (apply(v0, v3, v2) = v6 & member(v3, v1) = v5 & member(v2, v1) % 9.10/2.07 | = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v2: % 9.10/2.07 | $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v0, v2, v2) = v3) | ~ % 9.10/2.07 | $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4)))) % 9.10/2.07 | % 9.10/2.07 | ALPHA: (least) implies: % 9.10/2.07 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (least(v2, v0, v1) = 0) | % 9.10/2.07 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & ! [v3: $i] % 9.10/2.07 | : ! [v4: int] : (v4 = 0 | ~ (apply(v0, v2, v3) = v4) | ~ $i(v3) % 9.10/2.07 | | ? [v5: int] : ( ~ (v5 = 0) & member(v3, v1) = v5)))) % 9.10/2.07 | % 9.10/2.07 | ALPHA: (min) implies: % 9.10/2.07 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 9.10/2.07 | (min(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 9.10/2.07 | $i] : ( ~ (v4 = v2) & apply(v0, v4, v2) = 0 & member(v4, v1) = 0 & % 9.10/2.07 | $i(v4)) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4)) % 9.10/2.07 | % 9.10/2.07 | ALPHA: (function-axioms) implies: % 9.10/2.07 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.10/2.07 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 9.10/2.07 | = v0)) % 9.10/2.07 | % 9.10/2.07 | DELTA: instantiating (thIV4) with fresh symbols all_13_0, all_13_1, all_13_2, % 9.10/2.07 | all_13_3 gives: % 9.10/2.07 | (5) ~ (all_13_0 = 0) & min(all_13_1, all_13_3, all_13_2) = all_13_0 & % 9.10/2.07 | least(all_13_1, all_13_3, all_13_2) = 0 & order(all_13_3, all_13_2) = 0 % 9.10/2.07 | & $i(all_13_1) & $i(all_13_2) & $i(all_13_3) % 9.10/2.07 | % 9.10/2.07 | ALPHA: (5) implies: % 9.10/2.07 | (6) ~ (all_13_0 = 0) % 9.10/2.07 | (7) $i(all_13_3) % 9.10/2.07 | (8) $i(all_13_2) % 9.10/2.07 | (9) $i(all_13_1) % 9.10/2.07 | (10) order(all_13_3, all_13_2) = 0 % 9.10/2.07 | (11) least(all_13_1, all_13_3, all_13_2) = 0 % 9.10/2.07 | (12) min(all_13_1, all_13_3, all_13_2) = all_13_0 % 9.10/2.07 | % 9.10/2.08 | GROUND_INST: instantiating (1) with all_13_3, all_13_2, simplifying with (7), % 9.10/2.08 | (8), (10) gives: % 9.10/2.08 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 9.10/2.08 | (apply(all_13_3, v0, v2) = v3) | ~ (apply(all_13_3, v0, v1) = 0) | % 9.10/2.08 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? % 9.10/2.08 | [v6: any] : ? [v7: any] : (apply(all_13_3, v1, v2) = v7 & % 9.10/2.08 | member(v2, all_13_2) = v6 & member(v1, all_13_2) = v5 & member(v0, % 9.10/2.08 | all_13_2) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ % 9.10/2.08 | (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 9.10/2.08 | (apply(all_13_3, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] % 9.10/2.08 | : ? [v3: any] : ? [v4: any] : (apply(all_13_3, v1, v0) = v4 & % 9.10/2.08 | member(v1, all_13_2) = v3 & member(v0, all_13_2) = v2 & ( ~ (v4 = % 9.10/2.08 | 0) | ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: int] % 9.10/2.08 | : (v1 = 0 | ~ (apply(all_13_3, v0, v0) = v1) | ~ $i(v0) | ? [v2: % 9.10/2.08 | int] : ( ~ (v2 = 0) & member(v0, all_13_2) = v2)) % 9.10/2.08 | % 9.10/2.08 | ALPHA: (13) implies: % 9.10/2.08 | (14) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (apply(all_13_3, v0, v1) = % 9.10/2.08 | 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: % 9.10/2.08 | any] : (apply(all_13_3, v1, v0) = v4 & member(v1, all_13_2) = v3 & % 9.10/2.08 | member(v0, all_13_2) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = % 9.10/2.08 | 0)))) % 9.10/2.08 | % 9.10/2.08 | GROUND_INST: instantiating (2) with all_13_3, all_13_2, all_13_1, simplifying % 9.10/2.08 | with (7), (8), (9), (11) gives: % 9.10/2.08 | (15) member(all_13_1, all_13_2) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 % 9.10/2.08 | | ~ (apply(all_13_3, all_13_1, v0) = v1) | ~ $i(v0) | ? [v2: int] % 9.10/2.08 | : ( ~ (v2 = 0) & member(v0, all_13_2) = v2)) % 9.10/2.08 | % 9.10/2.08 | ALPHA: (15) implies: % 9.10/2.08 | (16) member(all_13_1, all_13_2) = 0 % 9.10/2.08 | (17) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_13_3, all_13_1, % 9.10/2.08 | v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & member(v0, % 9.10/2.08 | all_13_2) = v2)) % 9.10/2.08 | % 9.10/2.08 | GROUND_INST: instantiating (3) with all_13_3, all_13_2, all_13_1, all_13_0, % 9.10/2.08 | simplifying with (7), (8), (9), (12) gives: % 9.10/2.08 | (18) all_13_0 = 0 | ? [v0: any] : ( ~ (v0 = all_13_1) & apply(all_13_3, % 9.10/2.08 | v0, all_13_1) = 0 & member(v0, all_13_2) = 0 & $i(v0)) | ? [v0: % 9.10/2.08 | int] : ( ~ (v0 = 0) & member(all_13_1, all_13_2) = v0) % 9.10/2.08 | % 9.10/2.08 | BETA: splitting (18) gives: % 9.10/2.08 | % 9.10/2.08 | Case 1: % 9.10/2.08 | | % 9.10/2.08 | | (19) all_13_0 = 0 % 9.10/2.08 | | % 9.10/2.08 | | REDUCE: (6), (19) imply: % 9.10/2.08 | | (20) $false % 9.10/2.08 | | % 9.10/2.08 | | CLOSE: (20) is inconsistent. % 9.10/2.08 | | % 9.10/2.08 | Case 2: % 9.10/2.08 | | % 9.10/2.09 | | (21) ? [v0: any] : ( ~ (v0 = all_13_1) & apply(all_13_3, v0, all_13_1) = % 9.10/2.09 | | 0 & member(v0, all_13_2) = 0 & $i(v0)) | ? [v0: int] : ( ~ (v0 = % 9.10/2.09 | | 0) & member(all_13_1, all_13_2) = v0) % 9.10/2.09 | | % 9.10/2.09 | | BETA: splitting (21) gives: % 9.10/2.09 | | % 9.10/2.09 | | Case 1: % 9.10/2.09 | | | % 9.10/2.09 | | | (22) ? [v0: any] : ( ~ (v0 = all_13_1) & apply(all_13_3, v0, all_13_1) % 9.10/2.09 | | | = 0 & member(v0, all_13_2) = 0 & $i(v0)) % 9.10/2.09 | | | % 9.10/2.09 | | | DELTA: instantiating (22) with fresh symbol all_30_0 gives: % 9.10/2.09 | | | (23) ~ (all_30_0 = all_13_1) & apply(all_13_3, all_30_0, all_13_1) = 0 % 9.10/2.09 | | | & member(all_30_0, all_13_2) = 0 & $i(all_30_0) % 9.10/2.09 | | | % 9.10/2.09 | | | ALPHA: (23) implies: % 9.10/2.09 | | | (24) ~ (all_30_0 = all_13_1) % 9.10/2.09 | | | (25) $i(all_30_0) % 9.10/2.09 | | | (26) member(all_30_0, all_13_2) = 0 % 9.10/2.09 | | | (27) apply(all_13_3, all_30_0, all_13_1) = 0 % 9.10/2.09 | | | % 9.10/2.09 | | | GROUND_INST: instantiating (14) with all_30_0, all_13_1, simplifying with % 9.10/2.09 | | | (9), (25), (27) gives: % 9.10/2.09 | | | (28) all_30_0 = all_13_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 9.10/2.09 | | | (apply(all_13_3, all_13_1, all_30_0) = v2 & member(all_30_0, % 9.10/2.09 | | | all_13_2) = v0 & member(all_13_1, all_13_2) = v1 & ( ~ (v2 = % 9.10/2.09 | | | 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 9.10/2.09 | | | % 9.10/2.09 | | | BETA: splitting (28) gives: % 9.10/2.09 | | | % 9.10/2.09 | | | Case 1: % 9.10/2.09 | | | | % 9.10/2.09 | | | | (29) all_30_0 = all_13_1 % 9.10/2.09 | | | | % 9.10/2.09 | | | | REDUCE: (24), (29) imply: % 9.10/2.09 | | | | (30) $false % 9.10/2.09 | | | | % 9.10/2.09 | | | | CLOSE: (30) is inconsistent. % 9.10/2.09 | | | | % 9.10/2.09 | | | Case 2: % 9.10/2.09 | | | | % 9.10/2.09 | | | | (31) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_13_3, % 9.10/2.09 | | | | all_13_1, all_30_0) = v2 & member(all_30_0, all_13_2) = v0 & % 9.10/2.09 | | | | member(all_13_1, all_13_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | % 9.10/2.09 | | | | ~ (v0 = 0))) % 9.10/2.09 | | | | % 9.10/2.09 | | | | DELTA: instantiating (31) with fresh symbols all_39_0, all_39_1, % 9.10/2.09 | | | | all_39_2 gives: % 9.10/2.09 | | | | (32) apply(all_13_3, all_13_1, all_30_0) = all_39_0 & % 9.10/2.09 | | | | member(all_30_0, all_13_2) = all_39_2 & member(all_13_1, % 9.10/2.09 | | | | all_13_2) = all_39_1 & ( ~ (all_39_0 = 0) | ~ (all_39_1 = 0) % 9.10/2.09 | | | | | ~ (all_39_2 = 0)) % 9.10/2.09 | | | | % 9.10/2.09 | | | | ALPHA: (32) implies: % 9.10/2.09 | | | | (33) member(all_13_1, all_13_2) = all_39_1 % 9.10/2.09 | | | | (34) member(all_30_0, all_13_2) = all_39_2 % 9.10/2.09 | | | | (35) apply(all_13_3, all_13_1, all_30_0) = all_39_0 % 9.10/2.09 | | | | (36) ~ (all_39_0 = 0) | ~ (all_39_1 = 0) | ~ (all_39_2 = 0) % 9.10/2.09 | | | | % 9.10/2.09 | | | | GROUND_INST: instantiating (4) with 0, all_39_1, all_13_2, all_13_1, % 9.10/2.09 | | | | simplifying with (16), (33) gives: % 9.10/2.09 | | | | (37) all_39_1 = 0 % 9.10/2.09 | | | | % 9.10/2.09 | | | | GROUND_INST: instantiating (4) with 0, all_39_2, all_13_2, all_30_0, % 9.10/2.09 | | | | simplifying with (26), (34) gives: % 9.10/2.09 | | | | (38) all_39_2 = 0 % 9.10/2.09 | | | | % 9.10/2.09 | | | | BETA: splitting (36) gives: % 9.10/2.09 | | | | % 9.10/2.09 | | | | Case 1: % 9.10/2.09 | | | | | % 9.10/2.09 | | | | | (39) ~ (all_39_0 = 0) % 9.10/2.09 | | | | | % 9.10/2.09 | | | | | GROUND_INST: instantiating (17) with all_30_0, all_39_0, simplifying % 9.10/2.09 | | | | | with (25), (35) gives: % 9.10/2.09 | | | | | (40) all_39_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_30_0, % 9.10/2.09 | | | | | all_13_2) = v0) % 9.10/2.09 | | | | | % 9.10/2.09 | | | | | BETA: splitting (40) gives: % 9.10/2.09 | | | | | % 9.10/2.09 | | | | | Case 1: % 9.10/2.09 | | | | | | % 9.10/2.09 | | | | | | (41) all_39_0 = 0 % 9.10/2.09 | | | | | | % 9.10/2.09 | | | | | | REDUCE: (39), (41) imply: % 9.10/2.09 | | | | | | (42) $false % 9.10/2.09 | | | | | | % 9.10/2.09 | | | | | | CLOSE: (42) is inconsistent. % 9.10/2.09 | | | | | | % 9.10/2.09 | | | | | Case 2: % 9.10/2.09 | | | | | | % 9.10/2.09 | | | | | | (43) ? [v0: int] : ( ~ (v0 = 0) & member(all_30_0, all_13_2) = % 9.10/2.09 | | | | | | v0) % 9.10/2.09 | | | | | | % 9.10/2.09 | | | | | | DELTA: instantiating (43) with fresh symbol all_56_0 gives: % 9.10/2.10 | | | | | | (44) ~ (all_56_0 = 0) & member(all_30_0, all_13_2) = all_56_0 % 9.10/2.10 | | | | | | % 9.10/2.10 | | | | | | ALPHA: (44) implies: % 9.10/2.10 | | | | | | (45) ~ (all_56_0 = 0) % 9.10/2.10 | | | | | | (46) member(all_30_0, all_13_2) = all_56_0 % 9.10/2.10 | | | | | | % 9.10/2.10 | | | | | | GROUND_INST: instantiating (4) with 0, all_56_0, all_13_2, all_30_0, % 9.10/2.10 | | | | | | simplifying with (26), (46) gives: % 9.10/2.10 | | | | | | (47) all_56_0 = 0 % 9.10/2.10 | | | | | | % 9.10/2.10 | | | | | | REDUCE: (45), (47) imply: % 9.10/2.10 | | | | | | (48) $false % 9.10/2.10 | | | | | | % 9.10/2.10 | | | | | | CLOSE: (48) is inconsistent. % 9.10/2.10 | | | | | | % 9.10/2.10 | | | | | End of split % 9.10/2.10 | | | | | % 9.10/2.10 | | | | Case 2: % 9.10/2.10 | | | | | % 9.10/2.10 | | | | | (49) ~ (all_39_1 = 0) | ~ (all_39_2 = 0) % 9.10/2.10 | | | | | % 9.10/2.10 | | | | | BETA: splitting (49) gives: % 9.10/2.10 | | | | | % 9.10/2.10 | | | | | Case 1: % 9.10/2.10 | | | | | | % 9.10/2.10 | | | | | | (50) ~ (all_39_1 = 0) % 9.10/2.10 | | | | | | % 9.10/2.10 | | | | | | REDUCE: (37), (50) imply: % 9.10/2.10 | | | | | | (51) $false % 9.10/2.10 | | | | | | % 9.10/2.10 | | | | | | CLOSE: (51) is inconsistent. % 9.10/2.10 | | | | | | % 9.10/2.10 | | | | | Case 2: % 9.10/2.10 | | | | | | % 9.10/2.10 | | | | | | (52) ~ (all_39_2 = 0) % 9.10/2.10 | | | | | | % 9.10/2.10 | | | | | | REDUCE: (38), (52) imply: % 9.10/2.10 | | | | | | (53) $false % 9.10/2.10 | | | | | | % 9.10/2.10 | | | | | | CLOSE: (53) is inconsistent. % 9.10/2.10 | | | | | | % 9.10/2.10 | | | | | End of split % 9.10/2.10 | | | | | % 9.10/2.10 | | | | End of split % 9.10/2.10 | | | | % 9.10/2.10 | | | End of split % 9.10/2.10 | | | % 9.10/2.10 | | Case 2: % 9.10/2.10 | | | % 9.10/2.10 | | | (54) ? [v0: int] : ( ~ (v0 = 0) & member(all_13_1, all_13_2) = v0) % 9.10/2.10 | | | % 9.10/2.10 | | | DELTA: instantiating (54) with fresh symbol all_30_0 gives: % 9.10/2.10 | | | (55) ~ (all_30_0 = 0) & member(all_13_1, all_13_2) = all_30_0 % 9.10/2.10 | | | % 9.10/2.10 | | | ALPHA: (55) implies: % 9.10/2.10 | | | (56) ~ (all_30_0 = 0) % 9.10/2.10 | | | (57) member(all_13_1, all_13_2) = all_30_0 % 9.10/2.10 | | | % 9.10/2.10 | | | GROUND_INST: instantiating (4) with 0, all_30_0, all_13_2, all_13_1, % 9.10/2.10 | | | simplifying with (16), (57) gives: % 9.10/2.10 | | | (58) all_30_0 = 0 % 9.10/2.10 | | | % 9.10/2.10 | | | REDUCE: (56), (58) imply: % 9.10/2.10 | | | (59) $false % 9.62/2.10 | | | % 9.62/2.10 | | | CLOSE: (59) is inconsistent. % 9.62/2.10 | | | % 9.62/2.10 | | End of split % 9.62/2.10 | | % 9.62/2.10 | End of split % 9.62/2.10 | % 9.62/2.10 End of proof % 9.62/2.10 % SZS output end Proof for theBenchmark % 9.62/2.10 % 9.62/2.10 1499ms %------------------------------------------------------------------------------