%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET047+1 : TPTP v8.1.2. Released v2.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n014.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 15:23:25 EDT 2023 % Result : Theorem 4.21s 1.36s % Output : Proof 5.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.14 % Problem : SET047+1 : TPTP v8.1.2. Released v2.0.0. % 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.36 % Computer : n014.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Sat Aug 26 13:17:17 EDT 2023 % 0.15/0.36 % CPUTime : % 0.21/0.64 ________ _____ % 0.21/0.64 ___ __ \_________(_)________________________________ % 0.21/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.64 % 0.21/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.64 (2023-06-19) % 0.21/0.64 % 0.21/0.64 (c) Philipp Rümmer, 2009-2023 % 0.21/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.64 Amanda Stjerna. % 0.21/0.64 Free software under BSD-3-Clause. % 0.21/0.64 % 0.21/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.64 % 0.21/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.65 Running up to 7 provers in parallel. % 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.82/1.01 Prover 4: Preprocessing ... % 1.82/1.01 Prover 1: Preprocessing ... % 2.18/1.06 Prover 0: Preprocessing ... % 2.18/1.06 Prover 2: Preprocessing ... % 2.18/1.06 Prover 3: Preprocessing ... % 2.27/1.06 Prover 6: Preprocessing ... % 2.27/1.06 Prover 5: Preprocessing ... % 2.70/1.15 Prover 5: Proving ... % 2.70/1.15 Prover 2: Proving ... % 2.97/1.16 Prover 6: Proving ... % 2.97/1.16 Prover 3: Constructing countermodel ... % 2.97/1.17 Prover 1: Constructing countermodel ... % 2.97/1.19 Prover 0: Proving ... % 2.97/1.20 Prover 4: Constructing countermodel ... % 4.21/1.36 Prover 3: proved (695ms) % 4.21/1.36 % 4.21/1.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.21/1.36 % 4.21/1.37 Prover 2: stopped % 4.21/1.37 Prover 6: stopped % 4.21/1.37 Prover 0: stopped % 4.21/1.37 Prover 5: stopped % 4.21/1.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.21/1.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.21/1.38 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.21/1.38 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.21/1.38 Prover 10: Preprocessing ... % 4.21/1.38 Prover 7: Preprocessing ... % 4.21/1.38 Prover 8: Preprocessing ... % 4.21/1.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.21/1.38 Prover 11: Preprocessing ... % 4.21/1.39 Prover 13: Preprocessing ... % 4.21/1.41 Prover 10: Warning: ignoring some quantifiers % 4.21/1.41 Prover 10: Constructing countermodel ... % 4.21/1.41 Prover 13: Warning: ignoring some quantifiers % 4.21/1.41 Prover 7: Warning: ignoring some quantifiers % 4.21/1.41 Prover 13: Constructing countermodel ... % 4.21/1.42 Prover 7: Constructing countermodel ... % 4.21/1.43 Prover 13: gave up % 4.21/1.43 Prover 10: gave up % 4.21/1.45 Prover 8: Warning: ignoring some quantifiers % 4.21/1.45 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 4.21/1.45 Prover 8: Constructing countermodel ... % 4.21/1.45 Prover 16: Preprocessing ... % 4.21/1.45 Prover 7: gave up % 4.21/1.45 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 4.21/1.45 Prover 11: Constructing countermodel ... % 4.21/1.45 Prover 19: Preprocessing ... % 4.21/1.47 Prover 1: Found proof (size 63) % 4.21/1.47 Prover 1: proved (811ms) % 4.21/1.47 Prover 8: stopped % 4.21/1.47 Prover 11: stopped % 4.21/1.47 Prover 4: Found proof (size 69) % 4.21/1.47 Prover 4: proved (806ms) % 4.21/1.47 Prover 16: Warning: ignoring some quantifiers % 4.21/1.47 Prover 16: Constructing countermodel ... % 4.21/1.47 Prover 16: stopped % 4.59/1.51 Prover 19: Warning: ignoring some quantifiers % 4.59/1.51 Prover 19: Constructing countermodel ... % 4.59/1.51 Prover 19: stopped % 4.59/1.51 % 4.59/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.59/1.51 % 4.59/1.52 % SZS output start Proof for theBenchmark % 4.59/1.52 Assumptions after simplification: % 4.59/1.52 --------------------------------- % 4.59/1.52 % 4.59/1.52 (pel43) % 5.41/1.55 ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : (set_equal(v1, v0) = % 5.41/1.55 v3 & set_equal(v0, v1) = v2 & $i(v1) & $i(v0) & ((v3 = 0 & ~ (v2 = 0)) | % 5.41/1.55 (v2 = 0 & ~ (v3 = 0)))) % 5.41/1.55 % 5.41/1.55 (pel43_1) % 5.41/1.56 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (set_equal(v0, v1) = % 5.41/1.56 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 5.41/1.56 (element(v3, v1) = v5 & element(v3, v0) = v4 & $i(v3) & ( ~ (v5 = 0) | ~ % 5.41/1.56 (v4 = 0)) & (v5 = 0 | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 5.41/1.56 (set_equal(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: % 5.41/1.56 int] : (v3 = 0 | ~ (element(v2, v0) = v3) | ~ $i(v2) | ? [v4: int] : % 5.41/1.56 ( ~ (v4 = 0) & element(v2, v1) = v4)) & ! [v2: $i] : ( ~ (element(v2, % 5.41/1.56 v0) = 0) | ~ $i(v2) | element(v2, v1) = 0))) % 5.41/1.56 % 5.41/1.56 (function-axioms) % 5.41/1.56 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 5.41/1.56 [v3: $i] : (v1 = v0 | ~ (set_equal(v3, v2) = v1) | ~ (set_equal(v3, v2) = % 5.41/1.56 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 5.41/1.56 $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, % 5.41/1.56 v2) = v0)) % 5.41/1.56 % 5.41/1.56 Those formulas are unsatisfiable: % 5.41/1.56 --------------------------------- % 5.41/1.56 % 5.41/1.56 Begin of proof % 5.41/1.56 | % 5.41/1.56 | ALPHA: (pel43_1) implies: % 5.41/1.57 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (set_equal(v0, v1) = 0) | ~ $i(v1) | % 5.41/1.57 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (element(v2, % 5.41/1.57 | v0) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & % 5.41/1.57 | element(v2, v1) = v4)) & ! [v2: $i] : ( ~ (element(v2, v0) = % 5.41/1.57 | 0) | ~ $i(v2) | element(v2, v1) = 0))) % 5.41/1.57 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (set_equal(v0, % 5.41/1.57 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : % 5.41/1.57 | ? [v5: any] : (element(v3, v1) = v5 & element(v3, v0) = v4 & $i(v3) & % 5.41/1.57 | ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) % 5.41/1.57 | % 5.41/1.57 | ALPHA: (function-axioms) implies: % 5.41/1.57 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 5.41/1.57 | ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, % 5.41/1.57 | v2) = v0)) % 5.41/1.57 | % 5.41/1.57 | DELTA: instantiating (pel43) with fresh symbols all_4_0, all_4_1, all_4_2, % 5.41/1.57 | all_4_3 gives: % 5.41/1.57 | (4) set_equal(all_4_2, all_4_3) = all_4_0 & set_equal(all_4_3, all_4_2) = % 5.41/1.57 | all_4_1 & $i(all_4_2) & $i(all_4_3) & ((all_4_0 = 0 & ~ (all_4_1 = 0)) % 5.41/1.57 | | (all_4_1 = 0 & ~ (all_4_0 = 0))) % 5.41/1.57 | % 5.41/1.57 | ALPHA: (4) implies: % 5.41/1.57 | (5) $i(all_4_3) % 5.41/1.58 | (6) $i(all_4_2) % 5.41/1.58 | (7) set_equal(all_4_3, all_4_2) = all_4_1 % 5.41/1.58 | (8) set_equal(all_4_2, all_4_3) = all_4_0 % 5.41/1.58 | (9) (all_4_0 = 0 & ~ (all_4_1 = 0)) | (all_4_1 = 0 & ~ (all_4_0 = 0)) % 5.41/1.58 | % 5.41/1.58 | GROUND_INST: instantiating (2) with all_4_3, all_4_2, all_4_1, simplifying % 5.41/1.58 | with (5), (6), (7) gives: % 5.41/1.58 | (10) all_4_1 = 0 | ? [v0: $i] : ? [v1: any] : ? [v2: any] : (element(v0, % 5.41/1.58 | all_4_2) = v2 & element(v0, all_4_3) = v1 & $i(v0) & ( ~ (v2 = 0) % 5.41/1.58 | | ~ (v1 = 0)) & (v2 = 0 | v1 = 0)) % 5.41/1.58 | % 5.41/1.58 | GROUND_INST: instantiating (2) with all_4_2, all_4_3, all_4_0, simplifying % 5.41/1.58 | with (5), (6), (8) gives: % 5.41/1.58 | (11) all_4_0 = 0 | ? [v0: $i] : ? [v1: any] : ? [v2: any] : (element(v0, % 5.41/1.58 | all_4_2) = v1 & element(v0, all_4_3) = v2 & $i(v0) & ( ~ (v2 = 0) % 5.41/1.58 | | ~ (v1 = 0)) & (v2 = 0 | v1 = 0)) % 5.41/1.58 | % 5.41/1.58 | BETA: splitting (9) gives: % 5.41/1.58 | % 5.41/1.58 | Case 1: % 5.41/1.58 | | % 5.41/1.58 | | (12) all_4_0 = 0 & ~ (all_4_1 = 0) % 5.41/1.58 | | % 5.41/1.58 | | ALPHA: (12) implies: % 5.58/1.58 | | (13) all_4_0 = 0 % 5.58/1.58 | | (14) ~ (all_4_1 = 0) % 5.58/1.58 | | % 5.58/1.58 | | REDUCE: (8), (13) imply: % 5.58/1.58 | | (15) set_equal(all_4_2, all_4_3) = 0 % 5.58/1.58 | | % 5.58/1.58 | | BETA: splitting (10) gives: % 5.58/1.58 | | % 5.58/1.58 | | Case 1: % 5.58/1.58 | | | % 5.58/1.58 | | | (16) all_4_1 = 0 % 5.58/1.58 | | | % 5.58/1.58 | | | REDUCE: (14), (16) imply: % 5.58/1.58 | | | (17) $false % 5.58/1.59 | | | % 5.58/1.59 | | | CLOSE: (17) is inconsistent. % 5.58/1.59 | | | % 5.58/1.59 | | Case 2: % 5.58/1.59 | | | % 5.58/1.59 | | | (18) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (element(v0, all_4_2) % 5.58/1.59 | | | = v2 & element(v0, all_4_3) = v1 & $i(v0) & ( ~ (v2 = 0) | ~ % 5.58/1.59 | | | (v1 = 0)) & (v2 = 0 | v1 = 0)) % 5.58/1.59 | | | % 5.58/1.59 | | | DELTA: instantiating (18) with fresh symbols all_17_0, all_17_1, all_17_2 % 5.58/1.59 | | | gives: % 5.58/1.59 | | | (19) element(all_17_2, all_4_2) = all_17_0 & element(all_17_2, all_4_3) % 5.58/1.59 | | | = all_17_1 & $i(all_17_2) & ( ~ (all_17_0 = 0) | ~ (all_17_1 = % 5.58/1.59 | | | 0)) & (all_17_0 = 0 | all_17_1 = 0) % 5.58/1.59 | | | % 5.58/1.59 | | | ALPHA: (19) implies: % 5.58/1.59 | | | (20) $i(all_17_2) % 5.58/1.59 | | | (21) element(all_17_2, all_4_3) = all_17_1 % 5.58/1.59 | | | (22) element(all_17_2, all_4_2) = all_17_0 % 5.58/1.59 | | | (23) all_17_0 = 0 | all_17_1 = 0 % 5.58/1.59 | | | (24) ~ (all_17_0 = 0) | ~ (all_17_1 = 0) % 5.58/1.59 | | | % 5.58/1.59 | | | GROUND_INST: instantiating (1) with all_4_2, all_4_3, simplifying with % 5.58/1.59 | | | (5), (6), (15) gives: % 5.58/1.59 | | | (25) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (element(v0, all_4_2) = % 5.58/1.59 | | | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & element(v0, % 5.58/1.59 | | | all_4_3) = v2)) & ! [v0: $i] : ( ~ (element(v0, all_4_2) = % 5.58/1.59 | | | 0) | ~ $i(v0) | element(v0, all_4_3) = 0) % 5.58/1.59 | | | % 5.58/1.59 | | | ALPHA: (25) implies: % 5.58/1.59 | | | (26) ! [v0: $i] : ( ~ (element(v0, all_4_2) = 0) | ~ $i(v0) | % 5.58/1.59 | | | element(v0, all_4_3) = 0) % 5.58/1.59 | | | (27) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (element(v0, all_4_2) = % 5.58/1.59 | | | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & element(v0, % 5.58/1.59 | | | all_4_3) = v2)) % 5.58/1.59 | | | % 5.58/1.59 | | | GROUND_INST: instantiating (27) with all_17_2, all_17_0, simplifying with % 5.58/1.59 | | | (20), (22) gives: % 5.58/1.59 | | | (28) all_17_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & element(all_17_2, % 5.58/1.59 | | | all_4_3) = v0) % 5.58/1.59 | | | % 5.58/1.59 | | | BETA: splitting (23) gives: % 5.58/1.59 | | | % 5.58/1.59 | | | Case 1: % 5.58/1.59 | | | | % 5.58/1.59 | | | | (29) all_17_0 = 0 % 5.58/1.59 | | | | % 5.58/1.59 | | | | REDUCE: (22), (29) imply: % 5.58/1.60 | | | | (30) element(all_17_2, all_4_2) = 0 % 5.58/1.60 | | | | % 5.58/1.60 | | | | BETA: splitting (24) gives: % 5.58/1.60 | | | | % 5.58/1.60 | | | | Case 1: % 5.58/1.60 | | | | | % 5.58/1.60 | | | | | (31) ~ (all_17_0 = 0) % 5.58/1.60 | | | | | % 5.58/1.60 | | | | | REDUCE: (29), (31) imply: % 5.58/1.60 | | | | | (32) $false % 5.58/1.60 | | | | | % 5.58/1.60 | | | | | CLOSE: (32) is inconsistent. % 5.58/1.60 | | | | | % 5.58/1.60 | | | | Case 2: % 5.58/1.60 | | | | | % 5.58/1.60 | | | | | (33) ~ (all_17_1 = 0) % 5.58/1.60 | | | | | % 5.58/1.60 | | | | | GROUND_INST: instantiating (26) with all_17_2, simplifying with (20), % 5.58/1.60 | | | | | (30) gives: % 5.58/1.60 | | | | | (34) element(all_17_2, all_4_3) = 0 % 5.58/1.60 | | | | | % 5.58/1.60 | | | | | GROUND_INST: instantiating (3) with all_17_1, 0, all_4_3, all_17_2, % 5.58/1.60 | | | | | simplifying with (21), (34) gives: % 5.58/1.60 | | | | | (35) all_17_1 = 0 % 5.58/1.60 | | | | | % 5.58/1.60 | | | | | REDUCE: (33), (35) imply: % 5.58/1.60 | | | | | (36) $false % 5.58/1.60 | | | | | % 5.58/1.60 | | | | | CLOSE: (36) is inconsistent. % 5.58/1.60 | | | | | % 5.58/1.60 | | | | End of split % 5.58/1.60 | | | | % 5.58/1.60 | | | Case 2: % 5.58/1.60 | | | | % 5.58/1.60 | | | | (37) all_17_1 = 0 % 5.58/1.60 | | | | (38) ~ (all_17_0 = 0) % 5.58/1.60 | | | | % 5.58/1.60 | | | | REDUCE: (21), (37) imply: % 5.58/1.60 | | | | (39) element(all_17_2, all_4_3) = 0 % 5.58/1.60 | | | | % 5.58/1.60 | | | | BETA: splitting (28) gives: % 5.58/1.60 | | | | % 5.58/1.60 | | | | Case 1: % 5.58/1.60 | | | | | % 5.58/1.60 | | | | | (40) all_17_0 = 0 % 5.58/1.60 | | | | | % 5.58/1.60 | | | | | REDUCE: (38), (40) imply: % 5.58/1.60 | | | | | (41) $false % 5.58/1.60 | | | | | % 5.58/1.60 | | | | | CLOSE: (41) is inconsistent. % 5.58/1.60 | | | | | % 5.58/1.60 | | | | Case 2: % 5.58/1.60 | | | | | % 5.58/1.60 | | | | | (42) ? [v0: int] : ( ~ (v0 = 0) & element(all_17_2, all_4_3) = v0) % 5.58/1.60 | | | | | % 5.58/1.60 | | | | | DELTA: instantiating (42) with fresh symbol all_33_0 gives: % 5.58/1.60 | | | | | (43) ~ (all_33_0 = 0) & element(all_17_2, all_4_3) = all_33_0 % 5.58/1.60 | | | | | % 5.58/1.60 | | | | | ALPHA: (43) implies: % 5.58/1.60 | | | | | (44) ~ (all_33_0 = 0) % 5.58/1.60 | | | | | (45) element(all_17_2, all_4_3) = all_33_0 % 5.58/1.60 | | | | | % 5.58/1.60 | | | | | GROUND_INST: instantiating (3) with 0, all_33_0, all_4_3, all_17_2, % 5.58/1.60 | | | | | simplifying with (39), (45) gives: % 5.58/1.60 | | | | | (46) all_33_0 = 0 % 5.58/1.60 | | | | | % 5.58/1.60 | | | | | REDUCE: (44), (46) imply: % 5.58/1.60 | | | | | (47) $false % 5.58/1.60 | | | | | % 5.58/1.60 | | | | | CLOSE: (47) is inconsistent. % 5.58/1.60 | | | | | % 5.58/1.60 | | | | End of split % 5.58/1.60 | | | | % 5.58/1.60 | | | End of split % 5.58/1.60 | | | % 5.58/1.60 | | End of split % 5.58/1.60 | | % 5.58/1.60 | Case 2: % 5.58/1.60 | | % 5.58/1.60 | | (48) all_4_1 = 0 & ~ (all_4_0 = 0) % 5.58/1.60 | | % 5.58/1.60 | | ALPHA: (48) implies: % 5.58/1.60 | | (49) all_4_1 = 0 % 5.58/1.60 | | (50) ~ (all_4_0 = 0) % 5.58/1.60 | | % 5.58/1.60 | | REDUCE: (7), (49) imply: % 5.58/1.60 | | (51) set_equal(all_4_3, all_4_2) = 0 % 5.58/1.60 | | % 5.58/1.60 | | BETA: splitting (11) gives: % 5.58/1.60 | | % 5.58/1.60 | | Case 1: % 5.58/1.60 | | | % 5.58/1.60 | | | (52) all_4_0 = 0 % 5.58/1.60 | | | % 5.58/1.60 | | | REDUCE: (50), (52) imply: % 5.58/1.60 | | | (53) $false % 5.58/1.60 | | | % 5.58/1.60 | | | CLOSE: (53) is inconsistent. % 5.58/1.60 | | | % 5.58/1.60 | | Case 2: % 5.58/1.60 | | | % 5.58/1.60 | | | (54) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (element(v0, all_4_2) % 5.58/1.60 | | | = v1 & element(v0, all_4_3) = v2 & $i(v0) & ( ~ (v2 = 0) | ~ % 5.58/1.60 | | | (v1 = 0)) & (v2 = 0 | v1 = 0)) % 5.58/1.60 | | | % 5.58/1.60 | | | DELTA: instantiating (54) with fresh symbols all_17_0, all_17_1, all_17_2 % 5.58/1.60 | | | gives: % 5.58/1.61 | | | (55) element(all_17_2, all_4_2) = all_17_1 & element(all_17_2, all_4_3) % 5.58/1.61 | | | = all_17_0 & $i(all_17_2) & ( ~ (all_17_0 = 0) | ~ (all_17_1 = % 5.58/1.61 | | | 0)) & (all_17_0 = 0 | all_17_1 = 0) % 5.58/1.61 | | | % 5.58/1.61 | | | ALPHA: (55) implies: % 5.58/1.61 | | | (56) $i(all_17_2) % 5.58/1.61 | | | (57) element(all_17_2, all_4_3) = all_17_0 % 5.58/1.61 | | | (58) element(all_17_2, all_4_2) = all_17_1 % 5.58/1.61 | | | (59) all_17_0 = 0 | all_17_1 = 0 % 5.58/1.61 | | | (60) ~ (all_17_0 = 0) | ~ (all_17_1 = 0) % 5.58/1.61 | | | % 5.58/1.61 | | | GROUND_INST: instantiating (1) with all_4_3, all_4_2, simplifying with % 5.58/1.61 | | | (5), (6), (51) gives: % 5.58/1.61 | | | (61) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (element(v0, all_4_3) = % 5.58/1.61 | | | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & element(v0, % 5.58/1.61 | | | all_4_2) = v2)) & ! [v0: $i] : ( ~ (element(v0, all_4_3) = % 5.58/1.61 | | | 0) | ~ $i(v0) | element(v0, all_4_2) = 0) % 5.58/1.61 | | | % 5.58/1.61 | | | ALPHA: (61) implies: % 5.58/1.61 | | | (62) ! [v0: $i] : ( ~ (element(v0, all_4_3) = 0) | ~ $i(v0) | % 5.58/1.61 | | | element(v0, all_4_2) = 0) % 5.58/1.61 | | | (63) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (element(v0, all_4_3) = % 5.58/1.61 | | | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & element(v0, % 5.58/1.61 | | | all_4_2) = v2)) % 5.58/1.61 | | | % 5.58/1.61 | | | GROUND_INST: instantiating (63) with all_17_2, all_17_0, simplifying with % 5.58/1.61 | | | (56), (57) gives: % 5.58/1.61 | | | (64) all_17_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & element(all_17_2, % 5.58/1.61 | | | all_4_2) = v0) % 5.58/1.61 | | | % 5.58/1.61 | | | BETA: splitting (59) gives: % 5.58/1.61 | | | % 5.58/1.61 | | | Case 1: % 5.58/1.61 | | | | % 5.58/1.61 | | | | (65) all_17_0 = 0 % 5.58/1.61 | | | | % 5.58/1.61 | | | | REDUCE: (57), (65) imply: % 5.58/1.61 | | | | (66) element(all_17_2, all_4_3) = 0 % 5.58/1.61 | | | | % 5.58/1.61 | | | | BETA: splitting (60) gives: % 5.58/1.61 | | | | % 5.58/1.61 | | | | Case 1: % 5.58/1.61 | | | | | % 5.58/1.61 | | | | | (67) ~ (all_17_0 = 0) % 5.58/1.61 | | | | | % 5.58/1.61 | | | | | REDUCE: (65), (67) imply: % 5.58/1.61 | | | | | (68) $false % 5.58/1.61 | | | | | % 5.58/1.61 | | | | | CLOSE: (68) is inconsistent. % 5.58/1.61 | | | | | % 5.58/1.61 | | | | Case 2: % 5.58/1.61 | | | | | % 5.58/1.61 | | | | | (69) ~ (all_17_1 = 0) % 5.58/1.61 | | | | | % 5.58/1.61 | | | | | GROUND_INST: instantiating (62) with all_17_2, simplifying with (56), % 5.58/1.61 | | | | | (66) gives: % 5.58/1.61 | | | | | (70) element(all_17_2, all_4_2) = 0 % 5.58/1.61 | | | | | % 5.58/1.61 | | | | | GROUND_INST: instantiating (3) with all_17_1, 0, all_4_2, all_17_2, % 5.58/1.61 | | | | | simplifying with (58), (70) gives: % 5.58/1.61 | | | | | (71) all_17_1 = 0 % 5.58/1.61 | | | | | % 5.58/1.61 | | | | | REDUCE: (69), (71) imply: % 5.58/1.61 | | | | | (72) $false % 5.58/1.61 | | | | | % 5.58/1.61 | | | | | CLOSE: (72) is inconsistent. % 5.58/1.61 | | | | | % 5.58/1.61 | | | | End of split % 5.58/1.61 | | | | % 5.58/1.61 | | | Case 2: % 5.58/1.61 | | | | % 5.58/1.61 | | | | (73) all_17_1 = 0 % 5.58/1.61 | | | | (74) ~ (all_17_0 = 0) % 5.58/1.61 | | | | % 5.58/1.61 | | | | REDUCE: (58), (73) imply: % 5.58/1.61 | | | | (75) element(all_17_2, all_4_2) = 0 % 5.58/1.61 | | | | % 5.58/1.61 | | | | BETA: splitting (64) gives: % 5.58/1.61 | | | | % 5.58/1.61 | | | | Case 1: % 5.58/1.61 | | | | | % 5.58/1.61 | | | | | (76) all_17_0 = 0 % 5.58/1.61 | | | | | % 5.58/1.61 | | | | | REDUCE: (74), (76) imply: % 5.58/1.61 | | | | | (77) $false % 5.58/1.61 | | | | | % 5.58/1.61 | | | | | CLOSE: (77) is inconsistent. % 5.58/1.61 | | | | | % 5.58/1.61 | | | | Case 2: % 5.58/1.61 | | | | | % 5.58/1.61 | | | | | (78) ? [v0: int] : ( ~ (v0 = 0) & element(all_17_2, all_4_2) = v0) % 5.58/1.61 | | | | | % 5.58/1.61 | | | | | DELTA: instantiating (78) with fresh symbol all_33_0 gives: % 5.58/1.61 | | | | | (79) ~ (all_33_0 = 0) & element(all_17_2, all_4_2) = all_33_0 % 5.58/1.61 | | | | | % 5.58/1.61 | | | | | ALPHA: (79) implies: % 5.58/1.61 | | | | | (80) ~ (all_33_0 = 0) % 5.58/1.62 | | | | | (81) element(all_17_2, all_4_2) = all_33_0 % 5.58/1.62 | | | | | % 5.58/1.62 | | | | | GROUND_INST: instantiating (3) with 0, all_33_0, all_4_2, all_17_2, % 5.58/1.62 | | | | | simplifying with (75), (81) gives: % 5.58/1.62 | | | | | (82) all_33_0 = 0 % 5.58/1.62 | | | | | % 5.58/1.62 | | | | | REDUCE: (80), (82) imply: % 5.58/1.62 | | | | | (83) $false % 5.58/1.62 | | | | | % 5.58/1.62 | | | | | CLOSE: (83) is inconsistent. % 5.58/1.62 | | | | | % 5.58/1.62 | | | | End of split % 5.58/1.62 | | | | % 5.58/1.62 | | | End of split % 5.58/1.62 | | | % 5.58/1.62 | | End of split % 5.58/1.62 | | % 5.58/1.62 | End of split % 5.58/1.62 | % 5.58/1.62 End of proof % 5.58/1.62 % SZS output end Proof for theBenchmark % 5.58/1.62 % 5.58/1.62 979ms %------------------------------------------------------------------------------