%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET200+3 : TPTP v8.1.2. Released v2.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n029.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 15:24:17 EDT 2023 % Result : Theorem 4.46s 1.69s % Output : Proof 6.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET200+3 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n029.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sat Aug 26 14:34:40 EDT 2023 % 0.12/0.34 % 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 % 0.19/0.62 % 0.19/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.63 Running up to 7 provers in parallel. % 0.19/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.48/0.98 Prover 4: Preprocessing ... % 1.48/0.98 Prover 1: Preprocessing ... % 1.88/1.03 Prover 3: Preprocessing ... % 1.88/1.03 Prover 6: Preprocessing ... % 1.88/1.03 Prover 0: Preprocessing ... % 1.88/1.04 Prover 5: Preprocessing ... % 1.88/1.04 Prover 2: Preprocessing ... % 2.78/1.29 Prover 1: Warning: ignoring some quantifiers % 2.78/1.31 Prover 4: Warning: ignoring some quantifiers % 2.78/1.31 Prover 3: Warning: ignoring some quantifiers % 2.78/1.33 Prover 4: Constructing countermodel ... % 2.78/1.33 Prover 6: Proving ... % 2.78/1.33 Prover 5: Proving ... % 2.78/1.33 Prover 0: Proving ... % 2.78/1.33 Prover 2: Proving ... % 2.78/1.33 Prover 3: Constructing countermodel ... % 2.78/1.33 Prover 1: Constructing countermodel ... % 4.46/1.65 Prover 0: proved (1017ms) % 4.46/1.67 % 4.46/1.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.46/1.69 % 4.74/1.70 Prover 3: stopped % 4.74/1.71 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.74/1.71 Prover 6: stopped % 4.74/1.73 Prover 2: stopped % 4.74/1.74 Prover 5: stopped % 4.74/1.75 Prover 7: Preprocessing ... % 4.74/1.75 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.74/1.75 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.74/1.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.74/1.77 Prover 8: Preprocessing ... % 4.74/1.77 Prover 10: Preprocessing ... % 4.74/1.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.74/1.77 Prover 7: Warning: ignoring some quantifiers % 4.74/1.78 Prover 11: Preprocessing ... % 4.74/1.78 Prover 7: Constructing countermodel ... % 4.74/1.78 Prover 13: Preprocessing ... % 5.29/1.81 Prover 10: Warning: ignoring some quantifiers % 5.29/1.82 Prover 8: Warning: ignoring some quantifiers % 5.29/1.82 Prover 10: Constructing countermodel ... % 5.29/1.85 Prover 8: Constructing countermodel ... % 5.29/1.86 Prover 13: Warning: ignoring some quantifiers % 5.29/1.86 Prover 13: Constructing countermodel ... % 5.29/1.88 Prover 11: Warning: ignoring some quantifiers % 5.29/1.89 Prover 1: Found proof (size 38) % 5.29/1.89 Prover 4: Found proof (size 69) % 5.29/1.89 Prover 11: Constructing countermodel ... % 5.29/1.90 Prover 4: proved (1217ms) % 5.29/1.90 Prover 1: proved (1251ms) % 5.29/1.90 Prover 13: stopped % 5.29/1.90 Prover 8: stopped % 5.29/1.90 Prover 7: stopped % 5.29/1.90 Prover 10: gave up % 5.29/1.90 Prover 11: stopped % 5.29/1.90 % 5.29/1.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.29/1.90 % 5.74/1.92 % SZS output start Proof for theBenchmark % 5.74/1.92 Assumptions after simplification: % 5.74/1.92 --------------------------------- % 5.74/1.92 % 5.74/1.92 (commutativity_of_union) % 5.74/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v1, v0) = v2) | ~ $i(v1) % 5.74/1.96 | ~ $i(v0) | (union(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : % 5.74/1.96 ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (union(v1, v0) % 5.74/1.96 = v2 & $i(v2))) % 5.74/1.96 % 5.74/1.96 (prove_th34) % 5.74/1.96 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 5.74/1.96 $i] : ? [v6: int] : ( ~ (v6 = 0) & subset(v4, v5) = v6 & subset(v2, v3) = 0 % 5.74/1.96 & subset(v0, v1) = 0 & union(v1, v3) = v5 & union(v0, v2) = v4 & $i(v5) & % 5.74/1.96 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 5.74/1.96 % 5.74/1.96 (subset_defn) % 5.74/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 5.74/1.97 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 5.74/1.97 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] : % 5.74/1.97 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | % 5.74/1.97 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 & % 5.74/1.97 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 5.74/1.97 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | % 5.74/1.97 ~ $i(v0) | member(v2, v1) = 0) % 5.74/1.97 % 5.74/1.97 (union_defn) % 5.74/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 5.74/1.97 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 5.74/1.97 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & % 5.74/1.97 member(v2, v1) = v6 & member(v2, v0) = v5)) & ! [v0: $i] : ! [v1: $i] : % 5.74/1.97 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0) % 5.74/1.97 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 5.74/1.97 (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0))) % 5.74/1.97 % 5.74/1.97 (function-axioms) % 5.74/1.98 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 5.74/1.98 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 5.74/1.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.74/1.98 (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: MultipleValueBool] % 5.74/1.98 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.74/1.98 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 5.74/1.98 % 5.74/1.98 Further assumptions not needed in the proof: % 5.74/1.98 -------------------------------------------- % 5.74/1.98 equal_member_defn, reflexivity_of_subset % 5.74/1.98 % 5.74/1.98 Those formulas are unsatisfiable: % 5.74/1.98 --------------------------------- % 5.74/1.98 % 5.74/1.98 Begin of proof % 5.74/1.98 | % 5.74/1.98 | ALPHA: (union_defn) implies: % 6.05/1.99 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0, % 6.05/1.99 | v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 6.05/1.99 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v2, v1) = v5 & % 6.05/1.99 | member(v2, v0) = v4 & (v5 = 0 | v4 = 0))) % 6.05/1.99 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 6.05/1.99 | (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ % 6.05/1.99 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ % 6.05/1.99 | (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = % 6.05/1.99 | v5)) % 6.05/2.00 | % 6.05/2.00 | ALPHA: (subset_defn) implies: % 6.05/2.00 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 6.05/2.00 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 6.05/2.00 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 6.05/2.00 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 6.05/2.00 | (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ % 6.05/2.00 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = % 6.05/2.00 | v4)) % 6.05/2.00 | % 6.05/2.00 | ALPHA: (commutativity_of_union) implies: % 6.05/2.00 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v1, v0) = v2) | ~ % 6.05/2.00 | $i(v1) | ~ $i(v0) | (union(v0, v1) = v2 & $i(v2))) % 6.05/2.00 | % 6.05/2.00 | ALPHA: (function-axioms) implies: % 6.05/2.00 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 6.05/2.00 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 6.05/2.00 | = v0)) % 6.05/2.00 | % 6.05/2.00 | DELTA: instantiating (prove_th34) with fresh symbols all_8_0, all_8_1, % 6.05/2.00 | all_8_2, all_8_3, all_8_4, all_8_5, all_8_6 gives: % 6.05/2.01 | (7) ~ (all_8_0 = 0) & subset(all_8_2, all_8_1) = all_8_0 & subset(all_8_4, % 6.05/2.01 | all_8_3) = 0 & subset(all_8_6, all_8_5) = 0 & union(all_8_5, all_8_3) % 6.05/2.01 | = all_8_1 & union(all_8_6, all_8_4) = all_8_2 & $i(all_8_1) & % 6.05/2.01 | $i(all_8_2) & $i(all_8_3) & $i(all_8_4) & $i(all_8_5) & $i(all_8_6) % 6.05/2.01 | % 6.05/2.01 | ALPHA: (7) implies: % 6.05/2.01 | (8) ~ (all_8_0 = 0) % 6.05/2.01 | (9) $i(all_8_6) % 6.05/2.01 | (10) $i(all_8_5) % 6.05/2.01 | (11) $i(all_8_4) % 6.05/2.01 | (12) $i(all_8_3) % 6.05/2.01 | (13) union(all_8_6, all_8_4) = all_8_2 % 6.05/2.01 | (14) union(all_8_5, all_8_3) = all_8_1 % 6.05/2.01 | (15) subset(all_8_6, all_8_5) = 0 % 6.05/2.01 | (16) subset(all_8_4, all_8_3) = 0 % 6.05/2.01 | (17) subset(all_8_2, all_8_1) = all_8_0 % 6.05/2.01 | % 6.05/2.01 | GROUND_INST: instantiating (5) with all_8_4, all_8_6, all_8_2, simplifying % 6.05/2.01 | with (9), (11), (13) gives: % 6.05/2.01 | (18) union(all_8_4, all_8_6) = all_8_2 & $i(all_8_2) % 6.05/2.01 | % 6.05/2.01 | ALPHA: (18) implies: % 6.05/2.01 | (19) $i(all_8_2) % 6.05/2.01 | (20) union(all_8_4, all_8_6) = all_8_2 % 6.05/2.01 | % 6.05/2.01 | GROUND_INST: instantiating (5) with all_8_3, all_8_5, all_8_1, simplifying % 6.05/2.01 | with (10), (12), (14) gives: % 6.05/2.01 | (21) union(all_8_3, all_8_5) = all_8_1 & $i(all_8_1) % 6.05/2.01 | % 6.05/2.01 | ALPHA: (21) implies: % 6.05/2.01 | (22) $i(all_8_1) % 6.05/2.02 | (23) union(all_8_3, all_8_5) = all_8_1 % 6.05/2.02 | % 6.05/2.02 | GROUND_INST: instantiating (3) with all_8_2, all_8_1, all_8_0, simplifying % 6.05/2.02 | with (17), (19), (22) gives: % 6.05/2.02 | (24) all_8_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 6.05/2.02 | all_8_1) = v1 & member(v0, all_8_2) = 0 & $i(v0)) % 6.05/2.02 | % 6.05/2.02 | BETA: splitting (24) gives: % 6.05/2.02 | % 6.05/2.02 | Case 1: % 6.05/2.02 | | % 6.05/2.02 | | (25) all_8_0 = 0 % 6.05/2.02 | | % 6.05/2.02 | | REDUCE: (8), (25) imply: % 6.05/2.02 | | (26) $false % 6.05/2.02 | | % 6.05/2.02 | | CLOSE: (26) is inconsistent. % 6.05/2.02 | | % 6.05/2.02 | Case 2: % 6.05/2.02 | | % 6.05/2.02 | | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_8_1) = v1 % 6.05/2.02 | | & member(v0, all_8_2) = 0 & $i(v0)) % 6.05/2.02 | | % 6.05/2.02 | | DELTA: instantiating (27) with fresh symbols all_20_0, all_20_1 gives: % 6.05/2.02 | | (28) ~ (all_20_0 = 0) & member(all_20_1, all_8_1) = all_20_0 & % 6.05/2.02 | | member(all_20_1, all_8_2) = 0 & $i(all_20_1) % 6.05/2.02 | | % 6.05/2.02 | | ALPHA: (28) implies: % 6.05/2.02 | | (29) ~ (all_20_0 = 0) % 6.05/2.02 | | (30) $i(all_20_1) % 6.05/2.02 | | (31) member(all_20_1, all_8_2) = 0 % 6.05/2.02 | | (32) member(all_20_1, all_8_1) = all_20_0 % 6.05/2.02 | | % 6.05/2.02 | | GROUND_INST: instantiating (1) with all_8_6, all_8_4, all_20_1, all_8_2, % 6.05/2.02 | | simplifying with (9), (11), (13), (30), (31) gives: % 6.05/2.03 | | (33) ? [v0: any] : ? [v1: any] : (member(all_20_1, all_8_4) = v1 & % 6.05/2.03 | | member(all_20_1, all_8_6) = v0 & (v1 = 0 | v0 = 0)) % 6.05/2.03 | | % 6.05/2.03 | | GROUND_INST: instantiating (2) with all_8_5, all_8_3, all_20_1, all_8_1, % 6.05/2.03 | | all_20_0, simplifying with (10), (12), (14), (30), (32) gives: % 6.05/2.03 | | (34) all_20_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = % 6.05/2.03 | | 0) & member(all_20_1, all_8_3) = v1 & member(all_20_1, all_8_5) % 6.05/2.03 | | = v0) % 6.05/2.03 | | % 6.05/2.03 | | GROUND_INST: instantiating (1) with all_8_4, all_8_6, all_20_1, all_8_2, % 6.05/2.03 | | simplifying with (9), (11), (20), (30), (31) gives: % 6.05/2.03 | | (35) ? [v0: any] : ? [v1: any] : (member(all_20_1, all_8_4) = v0 & % 6.05/2.03 | | member(all_20_1, all_8_6) = v1 & (v1 = 0 | v0 = 0)) % 6.05/2.03 | | % 6.05/2.03 | | GROUND_INST: instantiating (2) with all_8_3, all_8_5, all_20_1, all_8_1, % 6.05/2.03 | | all_20_0, simplifying with (10), (12), (23), (30), (32) gives: % 6.05/2.03 | | (36) all_20_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = % 6.05/2.03 | | 0) & member(all_20_1, all_8_3) = v0 & member(all_20_1, all_8_5) % 6.05/2.03 | | = v1) % 6.05/2.03 | | % 6.05/2.03 | | DELTA: instantiating (35) with fresh symbols all_27_0, all_27_1 gives: % 6.05/2.03 | | (37) member(all_20_1, all_8_4) = all_27_1 & member(all_20_1, all_8_6) = % 6.05/2.03 | | all_27_0 & (all_27_0 = 0 | all_27_1 = 0) % 6.05/2.03 | | % 6.05/2.03 | | ALPHA: (37) implies: % 6.05/2.03 | | (38) member(all_20_1, all_8_6) = all_27_0 % 6.05/2.03 | | (39) member(all_20_1, all_8_4) = all_27_1 % 6.05/2.03 | | % 6.05/2.03 | | DELTA: instantiating (33) with fresh symbols all_29_0, all_29_1 gives: % 6.05/2.03 | | (40) member(all_20_1, all_8_4) = all_29_0 & member(all_20_1, all_8_6) = % 6.05/2.03 | | all_29_1 & (all_29_0 = 0 | all_29_1 = 0) % 6.05/2.03 | | % 6.05/2.03 | | ALPHA: (40) implies: % 6.05/2.03 | | (41) member(all_20_1, all_8_6) = all_29_1 % 6.05/2.03 | | (42) member(all_20_1, all_8_4) = all_29_0 % 6.05/2.03 | | (43) all_29_0 = 0 | all_29_1 = 0 % 6.05/2.03 | | % 6.05/2.03 | | BETA: splitting (36) gives: % 6.05/2.03 | | % 6.05/2.03 | | Case 1: % 6.05/2.03 | | | % 6.05/2.03 | | | (44) all_20_0 = 0 % 6.05/2.03 | | | % 6.05/2.04 | | | REDUCE: (29), (44) imply: % 6.05/2.04 | | | (45) $false % 6.05/2.04 | | | % 6.05/2.04 | | | CLOSE: (45) is inconsistent. % 6.05/2.04 | | | % 6.05/2.04 | | Case 2: % 6.05/2.04 | | | % 6.05/2.04 | | | (46) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 6.05/2.04 | | | member(all_20_1, all_8_3) = v0 & member(all_20_1, all_8_5) = v1) % 6.05/2.04 | | | % 6.05/2.04 | | | DELTA: instantiating (46) with fresh symbols all_35_0, all_35_1 gives: % 6.05/2.04 | | | (47) ~ (all_35_0 = 0) & ~ (all_35_1 = 0) & member(all_20_1, all_8_3) % 6.05/2.04 | | | = all_35_1 & member(all_20_1, all_8_5) = all_35_0 % 6.05/2.04 | | | % 6.05/2.04 | | | ALPHA: (47) implies: % 6.05/2.04 | | | (48) member(all_20_1, all_8_5) = all_35_0 % 6.05/2.04 | | | (49) member(all_20_1, all_8_3) = all_35_1 % 6.05/2.04 | | | % 6.05/2.04 | | | BETA: splitting (34) gives: % 6.05/2.04 | | | % 6.05/2.04 | | | Case 1: % 6.05/2.04 | | | | % 6.05/2.04 | | | | (50) all_20_0 = 0 % 6.05/2.04 | | | | % 6.05/2.04 | | | | REDUCE: (29), (50) imply: % 6.05/2.04 | | | | (51) $false % 6.05/2.04 | | | | % 6.05/2.04 | | | | CLOSE: (51) is inconsistent. % 6.05/2.04 | | | | % 6.05/2.04 | | | Case 2: % 6.05/2.04 | | | | % 6.05/2.04 | | | | (52) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 6.05/2.04 | | | | member(all_20_1, all_8_3) = v1 & member(all_20_1, all_8_5) = % 6.05/2.04 | | | | v0) % 6.05/2.04 | | | | % 6.05/2.04 | | | | DELTA: instantiating (52) with fresh symbols all_40_0, all_40_1 gives: % 6.05/2.06 | | | | (53) ~ (all_40_0 = 0) & ~ (all_40_1 = 0) & member(all_20_1, % 6.05/2.06 | | | | all_8_3) = all_40_0 & member(all_20_1, all_8_5) = all_40_1 % 6.05/2.06 | | | | % 6.05/2.06 | | | | ALPHA: (53) implies: % 6.05/2.06 | | | | (54) ~ (all_40_1 = 0) % 6.05/2.06 | | | | (55) ~ (all_40_0 = 0) % 6.05/2.06 | | | | (56) member(all_20_1, all_8_5) = all_40_1 % 6.05/2.06 | | | | (57) member(all_20_1, all_8_3) = all_40_0 % 6.05/2.06 | | | | % 6.05/2.06 | | | | GROUND_INST: instantiating (6) with all_27_0, all_29_1, all_8_6, % 6.05/2.06 | | | | all_20_1, simplifying with (38), (41) gives: % 6.05/2.06 | | | | (58) all_29_1 = all_27_0 % 6.05/2.06 | | | | % 6.05/2.06 | | | | GROUND_INST: instantiating (6) with all_35_0, all_40_1, all_8_5, % 6.05/2.06 | | | | all_20_1, simplifying with (48), (56) gives: % 6.05/2.06 | | | | (59) all_40_1 = all_35_0 % 6.05/2.06 | | | | % 6.05/2.06 | | | | GROUND_INST: instantiating (6) with all_27_1, all_29_0, all_8_4, % 6.05/2.06 | | | | all_20_1, simplifying with (39), (42) gives: % 6.05/2.06 | | | | (60) all_29_0 = all_27_1 % 6.05/2.06 | | | | % 6.05/2.06 | | | | GROUND_INST: instantiating (6) with all_35_1, all_40_0, all_8_3, % 6.05/2.06 | | | | all_20_1, simplifying with (49), (57) gives: % 6.05/2.06 | | | | (61) all_40_0 = all_35_1 % 6.05/2.06 | | | | % 6.05/2.06 | | | | REDUCE: (55), (61) imply: % 6.05/2.06 | | | | (62) ~ (all_35_1 = 0) % 6.05/2.06 | | | | % 6.05/2.06 | | | | REDUCE: (54), (59) imply: % 6.05/2.06 | | | | (63) ~ (all_35_0 = 0) % 6.05/2.06 | | | | % 6.05/2.06 | | | | GROUND_INST: instantiating (4) with all_8_6, all_8_5, all_20_1, % 6.05/2.06 | | | | all_35_0, simplifying with (9), (10), (15), (30), (48) % 6.05/2.06 | | | | gives: % 6.05/2.06 | | | | (64) all_35_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_20_1, % 6.05/2.06 | | | | all_8_6) = v0) % 6.05/2.06 | | | | % 6.05/2.06 | | | | GROUND_INST: instantiating (4) with all_8_4, all_8_3, all_20_1, % 6.05/2.06 | | | | all_35_1, simplifying with (11), (12), (16), (30), (49) % 6.05/2.06 | | | | gives: % 6.05/2.06 | | | | (65) all_35_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_20_1, % 6.05/2.06 | | | | all_8_4) = v0) % 6.05/2.06 | | | | % 6.05/2.06 | | | | BETA: splitting (65) gives: % 6.05/2.06 | | | | % 6.05/2.06 | | | | Case 1: % 6.05/2.06 | | | | | % 6.05/2.06 | | | | | (66) all_35_1 = 0 % 6.05/2.06 | | | | | % 6.05/2.06 | | | | | REDUCE: (62), (66) imply: % 6.05/2.06 | | | | | (67) $false % 6.05/2.06 | | | | | % 6.05/2.06 | | | | | CLOSE: (67) is inconsistent. % 6.05/2.06 | | | | | % 6.05/2.06 | | | | Case 2: % 6.05/2.06 | | | | | % 6.05/2.07 | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & member(all_20_1, all_8_4) = v0) % 6.05/2.07 | | | | | % 6.05/2.07 | | | | | DELTA: instantiating (68) with fresh symbol all_57_0 gives: % 6.05/2.07 | | | | | (69) ~ (all_57_0 = 0) & member(all_20_1, all_8_4) = all_57_0 % 6.05/2.07 | | | | | % 6.05/2.07 | | | | | ALPHA: (69) implies: % 6.05/2.07 | | | | | (70) ~ (all_57_0 = 0) % 6.05/2.07 | | | | | (71) member(all_20_1, all_8_4) = all_57_0 % 6.05/2.07 | | | | | % 6.05/2.07 | | | | | BETA: splitting (64) gives: % 6.05/2.07 | | | | | % 6.05/2.07 | | | | | Case 1: % 6.05/2.07 | | | | | | % 6.05/2.07 | | | | | | (72) all_35_0 = 0 % 6.05/2.07 | | | | | | % 6.05/2.07 | | | | | | REDUCE: (63), (72) imply: % 6.05/2.07 | | | | | | (73) $false % 6.05/2.07 | | | | | | % 6.05/2.07 | | | | | | CLOSE: (73) is inconsistent. % 6.05/2.07 | | | | | | % 6.05/2.07 | | | | | Case 2: % 6.05/2.07 | | | | | | % 6.05/2.07 | | | | | | (74) ? [v0: int] : ( ~ (v0 = 0) & member(all_20_1, all_8_6) = % 6.05/2.07 | | | | | | v0) % 6.05/2.07 | | | | | | % 6.05/2.07 | | | | | | DELTA: instantiating (74) with fresh symbol all_63_0 gives: % 6.05/2.07 | | | | | | (75) ~ (all_63_0 = 0) & member(all_20_1, all_8_6) = all_63_0 % 6.05/2.07 | | | | | | % 6.05/2.07 | | | | | | ALPHA: (75) implies: % 6.05/2.07 | | | | | | (76) ~ (all_63_0 = 0) % 6.05/2.07 | | | | | | (77) member(all_20_1, all_8_6) = all_63_0 % 6.05/2.07 | | | | | | % 6.05/2.07 | | | | | | GROUND_INST: instantiating (6) with all_27_0, all_63_0, all_8_6, % 6.05/2.07 | | | | | | all_20_1, simplifying with (38), (77) gives: % 6.05/2.07 | | | | | | (78) all_63_0 = all_27_0 % 6.05/2.07 | | | | | | % 6.05/2.07 | | | | | | GROUND_INST: instantiating (6) with all_27_1, all_57_0, all_8_4, % 6.05/2.07 | | | | | | all_20_1, simplifying with (39), (71) gives: % 6.05/2.07 | | | | | | (79) all_57_0 = all_27_1 % 6.05/2.07 | | | | | | % 6.05/2.07 | | | | | | REDUCE: (76), (78) imply: % 6.05/2.07 | | | | | | (80) ~ (all_27_0 = 0) % 6.05/2.07 | | | | | | % 6.05/2.07 | | | | | | REDUCE: (70), (79) imply: % 6.05/2.07 | | | | | | (81) ~ (all_27_1 = 0) % 6.05/2.07 | | | | | | % 6.05/2.07 | | | | | | BETA: splitting (43) gives: % 6.05/2.07 | | | | | | % 6.05/2.07 | | | | | | Case 1: % 6.05/2.07 | | | | | | | % 6.05/2.07 | | | | | | | (82) all_29_0 = 0 % 6.05/2.07 | | | | | | | % 6.05/2.07 | | | | | | | COMBINE_EQS: (60), (82) imply: % 6.05/2.07 | | | | | | | (83) all_27_1 = 0 % 6.05/2.07 | | | | | | | % 6.05/2.07 | | | | | | | SIMP: (83) implies: % 6.05/2.07 | | | | | | | (84) all_27_1 = 0 % 6.05/2.07 | | | | | | | % 6.05/2.07 | | | | | | | REDUCE: (81), (84) imply: % 6.05/2.07 | | | | | | | (85) $false % 6.05/2.07 | | | | | | | % 6.05/2.07 | | | | | | | CLOSE: (85) is inconsistent. % 6.05/2.07 | | | | | | | % 6.05/2.07 | | | | | | Case 2: % 6.05/2.07 | | | | | | | % 6.05/2.07 | | | | | | | (86) all_29_1 = 0 % 6.05/2.07 | | | | | | | % 6.05/2.07 | | | | | | | COMBINE_EQS: (58), (86) imply: % 6.05/2.07 | | | | | | | (87) all_27_0 = 0 % 6.05/2.07 | | | | | | | % 6.05/2.07 | | | | | | | REDUCE: (80), (87) imply: % 6.05/2.07 | | | | | | | (88) $false % 6.05/2.07 | | | | | | | % 6.05/2.07 | | | | | | | CLOSE: (88) is inconsistent. % 6.05/2.08 | | | | | | | % 6.05/2.08 | | | | | | End of split % 6.05/2.08 | | | | | | % 6.05/2.08 | | | | | End of split % 6.05/2.08 | | | | | % 6.05/2.08 | | | | End of split % 6.05/2.08 | | | | % 6.05/2.08 | | | End of split % 6.05/2.08 | | | % 6.05/2.08 | | End of split % 6.05/2.08 | | % 6.05/2.08 | End of split % 6.05/2.08 | % 6.05/2.08 End of proof % 6.05/2.08 % SZS output end Proof for theBenchmark % 6.05/2.08 % 6.05/2.08 1460ms %------------------------------------------------------------------------------