%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYN966+1 : TPTP v8.1.2. Released v3.1.0. % 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 : Fri Sep 1 03:29:23 EDT 2023 % Result : Theorem 3.69s 1.19s % Output : Proof 4.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN966+1 : TPTP v8.1.2. Released v3.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n014.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 18:39:47 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 ... % 0.19/0.63 Running up to 7 provers in parallel. % 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 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 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 % 1.92/0.93 Prover 4: Preprocessing ... % 1.92/0.93 Prover 1: Preprocessing ... % 1.95/0.97 Prover 3: Preprocessing ... % 1.95/0.97 Prover 0: Preprocessing ... % 1.95/0.97 Prover 2: Preprocessing ... % 1.95/0.97 Prover 6: Preprocessing ... % 1.95/0.97 Prover 5: Preprocessing ... % 2.37/1.06 Prover 1: Constructing countermodel ... % 2.37/1.06 Prover 3: Constructing countermodel ... % 2.84/1.07 Prover 5: Proving ... % 2.84/1.07 Prover 2: Proving ... % 2.84/1.07 Prover 6: Proving ... % 2.84/1.08 Prover 4: Constructing countermodel ... % 2.84/1.09 Prover 0: Proving ... % 3.69/1.19 Prover 3: proved (557ms) % 3.69/1.19 % 3.69/1.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.69/1.19 % 3.69/1.19 Prover 0: stopped % 3.69/1.19 Prover 6: stopped % 3.69/1.19 Prover 2: stopped % 3.69/1.20 Prover 5: stopped % 3.69/1.20 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.69/1.20 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.69/1.20 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.69/1.20 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.69/1.20 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.69/1.21 Prover 8: Preprocessing ... % 3.69/1.21 Prover 10: Preprocessing ... % 3.69/1.21 Prover 13: Preprocessing ... % 3.69/1.21 Prover 11: Preprocessing ... % 3.69/1.21 Prover 7: Preprocessing ... % 3.69/1.22 Prover 10: Warning: ignoring some quantifiers % 3.69/1.22 Prover 10: Constructing countermodel ... % 3.97/1.23 Prover 7: Warning: ignoring some quantifiers % 4.04/1.23 Prover 7: Constructing countermodel ... % 4.04/1.24 Prover 13: Warning: ignoring some quantifiers % 4.04/1.24 Prover 13: Constructing countermodel ... % 4.04/1.25 Prover 10: gave up % 4.04/1.25 Prover 8: Warning: ignoring some quantifiers % 4.04/1.25 Prover 8: Constructing countermodel ... % 4.04/1.25 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 4.04/1.26 Prover 4: Found proof (size 33) % 4.04/1.26 Prover 4: proved (620ms) % 4.04/1.26 Prover 8: stopped % 4.04/1.26 Prover 13: stopped % 4.04/1.26 Prover 1: Found proof (size 31) % 4.04/1.26 Prover 1: proved (625ms) % 4.04/1.26 Prover 7: stopped % 4.04/1.26 Prover 16: Preprocessing ... % 4.04/1.27 Prover 16: Warning: ignoring some quantifiers % 4.04/1.27 Prover 16: Constructing countermodel ... % 4.04/1.28 Prover 16: stopped % 4.04/1.28 Prover 11: Constructing countermodel ... % 4.04/1.28 Prover 11: stopped % 4.04/1.28 % 4.04/1.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.04/1.28 % 4.04/1.29 % SZS output start Proof for theBenchmark % 4.04/1.29 Assumptions after simplification: % 4.04/1.29 --------------------------------- % 4.04/1.29 % 4.04/1.29 (prove_this) % 4.47/1.33 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & eq(v1, v0) = v2 & % 4.47/1.33 eq(v0, v1) = 0 & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 4.47/1.33 ! [v6: int] : (v6 = 0 | ~ (eq(v3, v4) = 0) | ~ (a_member_of(v5, v4) = v6) % 4.47/1.33 | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v7: int] : ( ~ (v7 = 0) & % 4.47/1.33 a_member_of(v5, v3) = v7)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 4.47/1.33 ! [v6: int] : (v6 = 0 | ~ (eq(v3, v4) = 0) | ~ (a_member_of(v5, v3) = v6) % 4.47/1.33 | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v7: int] : ( ~ (v7 = 0) & % 4.47/1.33 a_member_of(v5, v4) = v7)) & ! [v3: $i] : ! [v4: $i] : ! [v5: int] : % 4.47/1.33 (v5 = 0 | ~ (eq(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : ? % 4.47/1.33 [v7: any] : ? [v8: any] : (a_member_of(v6, v4) = v8 & a_member_of(v6, v3) % 4.47/1.33 = v7 & $i(v6) & ( ~ (v8 = 0) | ~ (v7 = 0)) & (v8 = 0 | v7 = 0))) & ! % 4.47/1.33 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (eq(v3, v4) = 0) | ~ % 4.47/1.33 (a_member_of(v5, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | % 4.47/1.33 a_member_of(v5, v3) = 0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 4.47/1.33 (eq(v3, v4) = 0) | ~ (a_member_of(v5, v3) = 0) | ~ $i(v5) | ~ $i(v4) | % 4.47/1.33 ~ $i(v3) | a_member_of(v5, v4) = 0)) % 4.47/1.33 % 4.47/1.33 (function-axioms) % 4.47/1.33 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 4.47/1.33 [v3: $i] : (v1 = v0 | ~ (eq(v3, v2) = v1) | ~ (eq(v3, v2) = v0)) & ! [v0: % 4.47/1.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 4.47/1.34 : (v1 = v0 | ~ (a_member_of(v3, v2) = v1) | ~ (a_member_of(v3, v2) = v0)) % 4.47/1.34 % 4.47/1.34 Those formulas are unsatisfiable: % 4.47/1.34 --------------------------------- % 4.47/1.34 % 4.47/1.34 Begin of proof % 4.47/1.34 | % 4.47/1.34 | ALPHA: (function-axioms) implies: % 4.47/1.34 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.47/1.34 | ! [v3: $i] : (v1 = v0 | ~ (a_member_of(v3, v2) = v1) | ~ % 4.47/1.34 | (a_member_of(v3, v2) = v0)) % 4.47/1.34 | % 4.47/1.34 | DELTA: instantiating (prove_this) with fresh symbols all_3_0, all_3_1, all_3_2 % 4.47/1.34 | gives: % 4.47/1.35 | (2) ~ (all_3_0 = 0) & eq(all_3_1, all_3_2) = all_3_0 & eq(all_3_2, % 4.47/1.35 | all_3_1) = 0 & $i(all_3_1) & $i(all_3_2) & ! [v0: $i] : ! [v1: $i] % 4.47/1.35 | : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (eq(v0, v1) = 0) | ~ % 4.47/1.35 | (a_member_of(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 4.47/1.35 | [v4: int] : ( ~ (v4 = 0) & a_member_of(v2, v0) = v4)) & ! [v0: $i] : % 4.47/1.35 | ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (eq(v0, v1) = % 4.47/1.35 | 0) | ~ (a_member_of(v2, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 4.47/1.35 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & a_member_of(v2, v1) = v4)) & % 4.47/1.35 | ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (eq(v0, v1) = % 4.47/1.35 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: % 4.47/1.35 | any] : (a_member_of(v3, v1) = v5 & a_member_of(v3, v0) = v4 & % 4.47/1.35 | $i(v3) & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) & ! % 4.47/1.35 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (eq(v0, v1) = 0) | ~ % 4.47/1.35 | (a_member_of(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 4.47/1.35 | a_member_of(v2, v0) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 4.47/1.35 | ( ~ (eq(v0, v1) = 0) | ~ (a_member_of(v2, v0) = 0) | ~ $i(v2) | ~ % 4.47/1.35 | $i(v1) | ~ $i(v0) | a_member_of(v2, v1) = 0) % 4.47/1.35 | % 4.47/1.35 | ALPHA: (2) implies: % 4.47/1.35 | (3) ~ (all_3_0 = 0) % 4.47/1.35 | (4) $i(all_3_2) % 4.47/1.35 | (5) $i(all_3_1) % 4.47/1.35 | (6) eq(all_3_2, all_3_1) = 0 % 4.47/1.35 | (7) eq(all_3_1, all_3_2) = all_3_0 % 4.47/1.35 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (eq(v0, v1) = % 4.47/1.35 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: % 4.47/1.35 | any] : (a_member_of(v3, v1) = v5 & a_member_of(v3, v0) = v4 & % 4.47/1.35 | $i(v3) & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) % 4.47/1.35 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 4.47/1.35 | (eq(v0, v1) = 0) | ~ (a_member_of(v2, v0) = v3) | ~ $i(v2) | ~ % 4.47/1.35 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & a_member_of(v2, % 4.47/1.35 | v1) = v4)) % 4.47/1.35 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 4.47/1.35 | (eq(v0, v1) = 0) | ~ (a_member_of(v2, v1) = v3) | ~ $i(v2) | ~ % 4.47/1.35 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & a_member_of(v2, % 4.47/1.35 | v0) = v4)) % 4.47/1.36 | % 4.47/1.36 | GROUND_INST: instantiating (8) with all_3_1, all_3_2, all_3_0, simplifying % 4.47/1.36 | with (4), (5), (7) gives: % 4.47/1.36 | (11) all_3_0 = 0 | ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 4.47/1.36 | (a_member_of(v0, all_3_1) = v1 & a_member_of(v0, all_3_2) = v2 & % 4.47/1.36 | $i(v0) & ( ~ (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0)) % 4.47/1.36 | % 4.47/1.36 | BETA: splitting (11) gives: % 4.47/1.36 | % 4.47/1.36 | Case 1: % 4.47/1.36 | | % 4.47/1.36 | | (12) all_3_0 = 0 % 4.47/1.36 | | % 4.47/1.36 | | REDUCE: (3), (12) imply: % 4.47/1.36 | | (13) $false % 4.47/1.36 | | % 4.47/1.36 | | CLOSE: (13) is inconsistent. % 4.47/1.36 | | % 4.47/1.36 | Case 2: % 4.47/1.36 | | % 4.47/1.36 | | (14) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (a_member_of(v0, % 4.47/1.36 | | all_3_1) = v1 & a_member_of(v0, all_3_2) = v2 & $i(v0) & ( ~ (v2 % 4.47/1.36 | | = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0)) % 4.47/1.36 | | % 4.47/1.36 | | DELTA: instantiating (14) with fresh symbols all_13_0, all_13_1, all_13_2 % 4.47/1.36 | | gives: % 4.47/1.36 | | (15) a_member_of(all_13_2, all_3_1) = all_13_1 & a_member_of(all_13_2, % 4.47/1.36 | | all_3_2) = all_13_0 & $i(all_13_2) & ( ~ (all_13_0 = 0) | ~ % 4.47/1.36 | | (all_13_1 = 0)) & (all_13_0 = 0 | all_13_1 = 0) % 4.47/1.36 | | % 4.47/1.36 | | ALPHA: (15) implies: % 4.47/1.36 | | (16) $i(all_13_2) % 4.47/1.36 | | (17) a_member_of(all_13_2, all_3_2) = all_13_0 % 4.47/1.36 | | (18) a_member_of(all_13_2, all_3_1) = all_13_1 % 4.47/1.36 | | (19) all_13_0 = 0 | all_13_1 = 0 % 4.47/1.36 | | (20) ~ (all_13_0 = 0) | ~ (all_13_1 = 0) % 4.47/1.36 | | % 4.47/1.36 | | GROUND_INST: instantiating (9) with all_3_2, all_3_1, all_13_2, all_13_0, % 4.47/1.36 | | simplifying with (4), (5), (6), (16), (17) gives: % 4.47/1.36 | | (21) all_13_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_13_2, % 4.47/1.36 | | all_3_1) = v0) % 4.47/1.36 | | % 4.47/1.37 | | GROUND_INST: instantiating (10) with all_3_2, all_3_1, all_13_2, all_13_1, % 4.47/1.37 | | simplifying with (4), (5), (6), (16), (18) gives: % 4.47/1.37 | | (22) all_13_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_13_2, % 4.47/1.37 | | all_3_2) = v0) % 4.47/1.37 | | % 4.76/1.37 | | BETA: splitting (19) gives: % 4.76/1.37 | | % 4.76/1.37 | | Case 1: % 4.76/1.37 | | | % 4.76/1.37 | | | (23) all_13_0 = 0 % 4.76/1.37 | | | % 4.76/1.37 | | | REDUCE: (17), (23) imply: % 4.76/1.37 | | | (24) a_member_of(all_13_2, all_3_2) = 0 % 4.76/1.37 | | | % 4.76/1.37 | | | BETA: splitting (20) gives: % 4.76/1.37 | | | % 4.76/1.37 | | | Case 1: % 4.76/1.37 | | | | % 4.76/1.37 | | | | (25) ~ (all_13_0 = 0) % 4.76/1.37 | | | | % 4.76/1.37 | | | | REDUCE: (23), (25) imply: % 4.76/1.37 | | | | (26) $false % 4.76/1.37 | | | | % 4.76/1.37 | | | | CLOSE: (26) is inconsistent. % 4.76/1.37 | | | | % 4.76/1.37 | | | Case 2: % 4.76/1.37 | | | | % 4.76/1.37 | | | | (27) ~ (all_13_1 = 0) % 4.76/1.37 | | | | % 4.76/1.37 | | | | BETA: splitting (22) gives: % 4.76/1.37 | | | | % 4.76/1.37 | | | | Case 1: % 4.76/1.37 | | | | | % 4.76/1.37 | | | | | (28) all_13_1 = 0 % 4.76/1.37 | | | | | % 4.76/1.37 | | | | | REDUCE: (27), (28) imply: % 4.76/1.37 | | | | | (29) $false % 4.76/1.37 | | | | | % 4.76/1.37 | | | | | CLOSE: (29) is inconsistent. % 4.76/1.37 | | | | | % 4.76/1.37 | | | | Case 2: % 4.76/1.37 | | | | | % 4.76/1.37 | | | | | (30) ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_13_2, all_3_2) = % 4.76/1.37 | | | | | v0) % 4.76/1.37 | | | | | % 4.76/1.37 | | | | | DELTA: instantiating (30) with fresh symbol all_30_0 gives: % 4.76/1.37 | | | | | (31) ~ (all_30_0 = 0) & a_member_of(all_13_2, all_3_2) = all_30_0 % 4.76/1.37 | | | | | % 4.76/1.37 | | | | | ALPHA: (31) implies: % 4.76/1.37 | | | | | (32) ~ (all_30_0 = 0) % 4.76/1.37 | | | | | (33) a_member_of(all_13_2, all_3_2) = all_30_0 % 4.76/1.37 | | | | | % 4.76/1.37 | | | | | GROUND_INST: instantiating (1) with 0, all_30_0, all_3_2, all_13_2, % 4.76/1.37 | | | | | simplifying with (24), (33) gives: % 4.76/1.37 | | | | | (34) all_30_0 = 0 % 4.76/1.37 | | | | | % 4.76/1.37 | | | | | REDUCE: (32), (34) imply: % 4.76/1.37 | | | | | (35) $false % 4.76/1.37 | | | | | % 4.76/1.37 | | | | | CLOSE: (35) is inconsistent. % 4.76/1.37 | | | | | % 4.76/1.37 | | | | End of split % 4.76/1.37 | | | | % 4.76/1.37 | | | End of split % 4.76/1.37 | | | % 4.76/1.37 | | Case 2: % 4.76/1.37 | | | % 4.76/1.37 | | | (36) all_13_1 = 0 % 4.76/1.37 | | | (37) ~ (all_13_0 = 0) % 4.76/1.37 | | | % 4.76/1.37 | | | REDUCE: (18), (36) imply: % 4.76/1.37 | | | (38) a_member_of(all_13_2, all_3_1) = 0 % 4.76/1.37 | | | % 4.76/1.37 | | | BETA: splitting (21) gives: % 4.76/1.37 | | | % 4.76/1.37 | | | Case 1: % 4.76/1.37 | | | | % 4.76/1.37 | | | | (39) all_13_0 = 0 % 4.76/1.37 | | | | % 4.76/1.37 | | | | REDUCE: (37), (39) imply: % 4.76/1.37 | | | | (40) $false % 4.76/1.37 | | | | % 4.76/1.37 | | | | CLOSE: (40) is inconsistent. % 4.76/1.37 | | | | % 4.76/1.37 | | | Case 2: % 4.76/1.37 | | | | % 4.76/1.37 | | | | (41) ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_13_2, all_3_1) = % 4.76/1.37 | | | | v0) % 4.76/1.37 | | | | % 4.76/1.37 | | | | DELTA: instantiating (41) with fresh symbol all_26_0 gives: % 4.76/1.37 | | | | (42) ~ (all_26_0 = 0) & a_member_of(all_13_2, all_3_1) = all_26_0 % 4.76/1.37 | | | | % 4.76/1.37 | | | | ALPHA: (42) implies: % 4.76/1.37 | | | | (43) ~ (all_26_0 = 0) % 4.76/1.37 | | | | (44) a_member_of(all_13_2, all_3_1) = all_26_0 % 4.76/1.37 | | | | % 4.76/1.37 | | | | GROUND_INST: instantiating (1) with 0, all_26_0, all_3_1, all_13_2, % 4.76/1.37 | | | | simplifying with (38), (44) gives: % 4.76/1.37 | | | | (45) all_26_0 = 0 % 4.76/1.37 | | | | % 4.76/1.37 | | | | REDUCE: (43), (45) imply: % 4.76/1.37 | | | | (46) $false % 4.76/1.37 | | | | % 4.76/1.37 | | | | CLOSE: (46) is inconsistent. % 4.76/1.37 | | | | % 4.76/1.37 | | | End of split % 4.76/1.37 | | | % 4.76/1.37 | | End of split % 4.76/1.37 | | % 4.76/1.37 | End of split % 4.76/1.37 | % 4.76/1.37 End of proof % 4.76/1.38 % SZS output end Proof for theBenchmark % 4.76/1.38 % 4.76/1.38 761ms %------------------------------------------------------------------------------