%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET619+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 : n005.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 15:25:40 EDT 2023 % Result : Theorem 7.76s 1.87s % Output : Proof 12.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SET619+3 : TPTP v8.1.2. Released v2.2.0. % 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n005.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Sat Aug 26 13:51:08 EDT 2023 % 0.14/0.35 % CPUTime : % 0.22/0.62 ________ _____ % 0.22/0.62 ___ __ \_________(_)________________________________ % 0.22/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.62 % 0.22/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.62 (2023-06-19) % 0.22/0.62 % 0.22/0.62 (c) Philipp Rümmer, 2009-2023 % 0.22/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.62 Amanda Stjerna. % 0.22/0.62 Free software under BSD-3-Clause. % 0.22/0.62 % 0.22/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.62 % 0.22/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.22/0.63 Running up to 7 provers in parallel. % 0.22/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.22/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.02/1.02 Prover 4: Preprocessing ... % 2.02/1.02 Prover 1: Preprocessing ... % 2.59/1.07 Prover 6: Preprocessing ... % 2.59/1.07 Prover 5: Preprocessing ... % 2.59/1.07 Prover 2: Preprocessing ... % 2.59/1.07 Prover 0: Preprocessing ... % 2.59/1.08 Prover 3: Preprocessing ... % 5.00/1.43 Prover 1: Warning: ignoring some quantifiers % 5.00/1.44 Prover 3: Warning: ignoring some quantifiers % 5.00/1.46 Prover 2: Proving ... % 5.00/1.46 Prover 6: Proving ... % 5.00/1.46 Prover 1: Constructing countermodel ... % 5.00/1.46 Prover 3: Constructing countermodel ... % 5.00/1.46 Prover 5: Proving ... % 5.00/1.47 Prover 0: Proving ... % 5.00/1.47 Prover 4: Warning: ignoring some quantifiers % 5.00/1.49 Prover 4: Constructing countermodel ... % 6.16/1.63 Prover 3: gave up % 6.16/1.63 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.16/1.63 Prover 1: gave up % 6.16/1.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.16/1.67 Prover 8: Preprocessing ... % 6.16/1.67 Prover 7: Preprocessing ... % 7.20/1.76 Prover 8: Warning: ignoring some quantifiers % 7.20/1.77 Prover 7: Warning: ignoring some quantifiers % 7.20/1.77 Prover 8: Constructing countermodel ... % 7.20/1.78 Prover 7: Constructing countermodel ... % 7.76/1.87 Prover 0: proved (1228ms) % 7.76/1.87 % 7.76/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.76/1.87 % 7.76/1.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.76/1.88 Prover 6: stopped % 7.76/1.89 Prover 5: stopped % 7.76/1.89 Prover 2: stopped % 7.76/1.90 Prover 10: Preprocessing ... % 7.76/1.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.76/1.90 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.76/1.90 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.76/1.91 Prover 8: gave up % 7.76/1.91 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 7.76/1.93 Prover 11: Preprocessing ... % 7.76/1.94 Prover 16: Preprocessing ... % 7.76/1.94 Prover 13: Preprocessing ... % 7.76/1.95 Prover 19: Preprocessing ... % 8.56/1.96 Prover 10: Warning: ignoring some quantifiers % 8.56/1.96 Prover 10: Constructing countermodel ... % 8.56/2.00 Prover 16: Warning: ignoring some quantifiers % 8.56/2.01 Prover 16: Constructing countermodel ... % 9.43/2.05 Prover 13: Warning: ignoring some quantifiers % 9.43/2.07 Prover 13: Constructing countermodel ... % 9.59/2.09 Prover 11: Warning: ignoring some quantifiers % 9.59/2.10 Prover 10: gave up % 9.59/2.10 Prover 11: Constructing countermodel ... % 9.95/2.12 Prover 19: Warning: ignoring some quantifiers % 10.15/2.14 Prover 19: Constructing countermodel ... % 10.69/2.24 Prover 13: gave up % 11.09/2.30 Prover 19: gave up % 12.12/2.42 Prover 4: Found proof (size 150) % 12.12/2.42 Prover 4: proved (1765ms) % 12.12/2.42 Prover 11: stopped % 12.12/2.42 Prover 7: stopped % 12.12/2.42 Prover 16: stopped % 12.12/2.42 % 12.12/2.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.12/2.42 % 12.26/2.46 % SZS output start Proof for theBenchmark % 12.26/2.46 Assumptions after simplification: % 12.26/2.46 --------------------------------- % 12.26/2.46 % 12.26/2.46 (associativity_of_union) % 12.26/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 12.26/2.49 (union(v3, v2) = v4) | ~ (union(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 12.26/2.49 $i(v0) | ? [v5: $i] : (union(v1, v2) = v5 & union(v0, v5) = v4 & $i(v5) & % 12.26/2.49 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 12.26/2.49 $i] : ( ~ (union(v1, v2) = v3) | ~ (union(v0, v3) = v4) | ~ $i(v2) | ~ % 12.26/2.49 $i(v1) | ~ $i(v0) | ? [v5: $i] : (union(v5, v2) = v4 & union(v0, v1) = v5 % 12.26/2.49 & $i(v5) & $i(v4))) % 12.26/2.49 % 12.26/2.49 (commutativity_of_intersection) % 12.26/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) = v2) | ~ % 12.26/2.49 $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : % 12.26/2.49 ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~ $i(v1) | ~ % 12.26/2.49 $i(v0) | (intersection(v1, v0) = v2 & $i(v2))) % 12.26/2.49 % 12.26/2.49 (commutativity_of_symmetric_difference) % 12.26/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v1, v0) = % 12.26/2.50 v2) | ~ $i(v1) | ~ $i(v0) | (symmetric_difference(v0, v1) = v2 & % 12.26/2.50 $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 12.26/2.50 (symmetric_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 12.26/2.50 (symmetric_difference(v1, v0) = v2 & $i(v2))) % 12.26/2.50 % 12.26/2.50 (commutativity_of_union) % 12.26/2.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v1, v0) = v2) | ~ $i(v1) % 12.26/2.50 | ~ $i(v0) | (union(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : % 12.26/2.50 ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (union(v1, v0) % 12.26/2.50 = v2 & $i(v2))) % 12.26/2.50 % 12.26/2.50 (prove_th95) % 12.26/2.50 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 12.26/2.50 $i] : ( ~ (v5 = v2) & intersection(v0, v1) = v4 & symmetric_difference(v0, % 12.26/2.50 v1) = v3 & union(v3, v4) = v5 & union(v0, v1) = v2 & $i(v5) & $i(v4) & % 12.26/2.50 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 12.26/2.50 % 12.26/2.50 (symmetric_difference_defn) % 12.26/2.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0, v1) = % 12.26/2.51 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (difference(v1, % 12.26/2.51 v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2 & $i(v4) & % 12.26/2.51 $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 12.26/2.51 (difference(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 12.26/2.51 $i] : (symmetric_difference(v0, v1) = v3 & difference(v0, v1) = v4 & % 12.26/2.51 union(v4, v2) = v3 & $i(v4) & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 12.26/2.51 [v2: $i] : ( ~ (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] % 12.26/2.51 : ? [v4: $i] : (symmetric_difference(v0, v1) = v3 & difference(v1, v0) = v4 % 12.26/2.51 & union(v2, v4) = v3 & $i(v4) & $i(v3))) % 12.26/2.51 % 12.26/2.51 (union_intersection) % 12.26/2.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~ % 12.26/2.51 $i(v1) | ~ $i(v0) | union(v0, v2) = v0) % 12.26/2.51 % 12.26/2.51 (union_intersection_difference) % 12.26/2.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~ % 12.26/2.51 $i(v1) | ~ $i(v0) | ? [v3: $i] : (difference(v0, v1) = v3 & union(v2, v3) % 12.26/2.51 = v0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 12.26/2.51 (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 12.26/2.51 (intersection(v0, v1) = v3 & union(v3, v2) = v0 & $i(v3))) % 12.26/2.51 % 12.26/2.51 (function-axioms) % 12.26/2.51 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 12.26/2.51 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 12.26/2.51 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 12.26/2.51 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! % 12.26/2.51 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.26/2.51 (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0: $i] % 12.26/2.51 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.26/2.51 (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = % 12.26/2.51 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 12.26/2.51 ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : % 12.26/2.51 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | % 12.26/2.51 ~ (union(v3, v2) = v0)) % 12.26/2.51 % 12.26/2.51 Further assumptions not needed in the proof: % 12.26/2.51 -------------------------------------------- % 12.26/2.52 equal_defn, equal_member_defn, intersection_defn, reflexivity_of_subset, % 12.26/2.52 subset_defn, union_defn % 12.26/2.52 % 12.26/2.52 Those formulas are unsatisfiable: % 12.26/2.52 --------------------------------- % 12.26/2.52 % 12.26/2.52 Begin of proof % 12.26/2.52 | % 12.26/2.52 | ALPHA: (symmetric_difference_defn) implies: % 12.26/2.52 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (difference(v0, v1) = v2) % 12.26/2.52 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 12.26/2.52 | (symmetric_difference(v0, v1) = v3 & difference(v1, v0) = v4 & % 12.26/2.52 | union(v2, v4) = v3 & $i(v4) & $i(v3))) % 12.26/2.52 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (difference(v1, v0) = v2) % 12.26/2.52 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 12.26/2.52 | (symmetric_difference(v0, v1) = v3 & difference(v0, v1) = v4 & % 12.26/2.52 | union(v4, v2) = v3 & $i(v4) & $i(v3))) % 12.26/2.52 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0, % 12.26/2.52 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 12.26/2.52 | (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = % 12.26/2.52 | v2 & $i(v4) & $i(v3) & $i(v2))) % 12.26/2.52 | % 12.26/2.52 | ALPHA: (associativity_of_union) implies: % 12.26/2.52 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 12.26/2.52 | ~ (union(v1, v2) = v3) | ~ (union(v0, v3) = v4) | ~ $i(v2) | ~ % 12.26/2.52 | $i(v1) | ~ $i(v0) | ? [v5: $i] : (union(v5, v2) = v4 & union(v0, % 12.26/2.52 | v1) = v5 & $i(v5) & $i(v4))) % 12.26/2.53 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 12.26/2.53 | ~ (union(v3, v2) = v4) | ~ (union(v0, v1) = v3) | ~ $i(v2) | ~ % 12.26/2.53 | $i(v1) | ~ $i(v0) | ? [v5: $i] : (union(v1, v2) = v5 & union(v0, % 12.26/2.53 | v5) = v4 & $i(v5) & $i(v4))) % 12.26/2.53 | % 12.26/2.53 | ALPHA: (union_intersection_difference) implies: % 12.26/2.53 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (difference(v0, v1) = v2) % 12.26/2.53 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (intersection(v0, v1) = v3 & % 12.26/2.53 | union(v3, v2) = v0 & $i(v3))) % 12.26/2.53 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = % 12.26/2.53 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (difference(v0, v1) = % 12.26/2.53 | v3 & union(v2, v3) = v0 & $i(v3))) % 12.26/2.53 | % 12.26/2.53 | ALPHA: (commutativity_of_union) implies: % 12.26/2.53 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v1, v0) = v2) | ~ % 12.26/2.53 | $i(v1) | ~ $i(v0) | (union(v0, v1) = v2 & $i(v2))) % 12.26/2.53 | % 12.26/2.53 | ALPHA: (commutativity_of_intersection) implies: % 12.26/2.53 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) = % 12.26/2.53 | v2) | ~ $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2))) % 12.26/2.53 | % 12.26/2.53 | ALPHA: (commutativity_of_symmetric_difference) implies: % 12.26/2.53 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 12.26/2.53 | (symmetric_difference(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | % 12.26/2.53 | (symmetric_difference(v0, v1) = v2 & $i(v2))) % 12.26/2.53 | % 12.26/2.53 | ALPHA: (function-axioms) implies: % 12.26/2.53 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.26/2.53 | (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 12.26/2.53 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.26/2.53 | (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 12.26/2.53 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.26/2.53 | (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, % 12.26/2.53 | v2) = v0)) % 12.26/2.54 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.26/2.54 | (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 12.26/2.54 | % 12.26/2.54 | DELTA: instantiating (prove_th95) with fresh symbols all_16_0, all_16_1, % 12.26/2.54 | all_16_2, all_16_3, all_16_4, all_16_5 gives: % 12.26/2.54 | (15) ~ (all_16_0 = all_16_3) & intersection(all_16_5, all_16_4) = all_16_1 % 12.26/2.54 | & symmetric_difference(all_16_5, all_16_4) = all_16_2 & % 12.26/2.54 | union(all_16_2, all_16_1) = all_16_0 & union(all_16_5, all_16_4) = % 12.26/2.54 | all_16_3 & $i(all_16_0) & $i(all_16_1) & $i(all_16_2) & $i(all_16_3) & % 12.26/2.54 | $i(all_16_4) & $i(all_16_5) % 12.26/2.54 | % 12.26/2.54 | ALPHA: (15) implies: % 12.26/2.54 | (16) ~ (all_16_0 = all_16_3) % 12.26/2.54 | (17) $i(all_16_5) % 12.26/2.54 | (18) $i(all_16_4) % 12.26/2.54 | (19) $i(all_16_2) % 12.26/2.54 | (20) $i(all_16_1) % 12.26/2.54 | (21) union(all_16_5, all_16_4) = all_16_3 % 12.26/2.54 | (22) union(all_16_2, all_16_1) = all_16_0 % 12.26/2.54 | (23) symmetric_difference(all_16_5, all_16_4) = all_16_2 % 12.26/2.54 | (24) intersection(all_16_5, all_16_4) = all_16_1 % 12.26/2.54 | % 12.26/2.54 | GROUND_INST: instantiating (8) with all_16_4, all_16_5, all_16_3, simplifying % 12.26/2.54 | with (17), (18), (21) gives: % 12.26/2.54 | (25) union(all_16_4, all_16_5) = all_16_3 & $i(all_16_3) % 12.26/2.54 | % 12.26/2.54 | ALPHA: (25) implies: % 12.26/2.54 | (26) union(all_16_4, all_16_5) = all_16_3 % 12.26/2.54 | % 12.26/2.54 | GROUND_INST: instantiating (8) with all_16_1, all_16_2, all_16_0, simplifying % 12.26/2.54 | with (19), (20), (22) gives: % 12.26/2.54 | (27) union(all_16_1, all_16_2) = all_16_0 & $i(all_16_0) % 12.26/2.54 | % 12.26/2.54 | ALPHA: (27) implies: % 12.26/2.54 | (28) union(all_16_1, all_16_2) = all_16_0 % 12.26/2.54 | % 12.26/2.54 | GROUND_INST: instantiating (10) with all_16_4, all_16_5, all_16_2, simplifying % 12.26/2.54 | with (17), (18), (23) gives: % 12.26/2.54 | (29) symmetric_difference(all_16_4, all_16_5) = all_16_2 & $i(all_16_2) % 12.26/2.54 | % 12.26/2.54 | ALPHA: (29) implies: % 12.26/2.54 | (30) symmetric_difference(all_16_4, all_16_5) = all_16_2 % 12.26/2.54 | % 12.26/2.54 | GROUND_INST: instantiating (3) with all_16_5, all_16_4, all_16_2, simplifying % 12.26/2.54 | with (17), (18), (23) gives: % 12.26/2.55 | (31) ? [v0: $i] : ? [v1: $i] : (difference(all_16_4, all_16_5) = v1 & % 12.26/2.55 | difference(all_16_5, all_16_4) = v0 & union(v0, v1) = all_16_2 & % 12.26/2.55 | $i(v1) & $i(v0) & $i(all_16_2)) % 12.26/2.55 | % 12.26/2.55 | GROUND_INST: instantiating (9) with all_16_4, all_16_5, all_16_1, simplifying % 12.26/2.55 | with (17), (18), (24) gives: % 12.26/2.55 | (32) intersection(all_16_4, all_16_5) = all_16_1 & $i(all_16_1) % 12.26/2.55 | % 12.26/2.55 | ALPHA: (32) implies: % 12.26/2.55 | (33) intersection(all_16_4, all_16_5) = all_16_1 % 12.26/2.55 | % 12.26/2.55 | GROUND_INST: instantiating (union_intersection) with all_16_5, all_16_4, % 12.26/2.55 | all_16_1, simplifying with (17), (18), (24) gives: % 12.26/2.55 | (34) union(all_16_5, all_16_1) = all_16_5 % 12.26/2.55 | % 12.26/2.55 | GROUND_INST: instantiating (7) with all_16_5, all_16_4, all_16_1, simplifying % 12.26/2.55 | with (17), (18), (24) gives: % 12.26/2.55 | (35) ? [v0: $i] : (difference(all_16_5, all_16_4) = v0 & union(all_16_1, % 12.26/2.55 | v0) = all_16_5 & $i(v0)) % 12.26/2.55 | % 12.26/2.55 | DELTA: instantiating (35) with fresh symbol all_24_0 gives: % 12.26/2.55 | (36) difference(all_16_5, all_16_4) = all_24_0 & union(all_16_1, all_24_0) % 12.26/2.55 | = all_16_5 & $i(all_24_0) % 12.26/2.55 | % 12.26/2.55 | ALPHA: (36) implies: % 12.26/2.55 | (37) union(all_16_1, all_24_0) = all_16_5 % 12.26/2.55 | (38) difference(all_16_5, all_16_4) = all_24_0 % 12.26/2.55 | % 12.26/2.55 | DELTA: instantiating (31) with fresh symbols all_26_0, all_26_1 gives: % 12.26/2.55 | (39) difference(all_16_4, all_16_5) = all_26_0 & difference(all_16_5, % 12.26/2.55 | all_16_4) = all_26_1 & union(all_26_1, all_26_0) = all_16_2 & % 12.26/2.55 | $i(all_26_0) & $i(all_26_1) & $i(all_16_2) % 12.26/2.55 | % 12.26/2.55 | ALPHA: (39) implies: % 12.26/2.55 | (40) $i(all_26_1) % 12.26/2.55 | (41) $i(all_26_0) % 12.26/2.55 | (42) union(all_26_1, all_26_0) = all_16_2 % 12.26/2.55 | (43) difference(all_16_5, all_16_4) = all_26_1 % 12.26/2.55 | (44) difference(all_16_4, all_16_5) = all_26_0 % 12.26/2.55 | % 12.26/2.55 | GROUND_INST: instantiating (12) with all_24_0, all_26_1, all_16_4, all_16_5, % 12.26/2.55 | simplifying with (38), (43) gives: % 12.26/2.55 | (45) all_26_1 = all_24_0 % 12.26/2.55 | % 12.26/2.55 | REDUCE: (42), (45) imply: % 12.26/2.55 | (46) union(all_24_0, all_26_0) = all_16_2 % 12.26/2.55 | % 12.26/2.55 | REDUCE: (40), (45) imply: % 12.26/2.55 | (47) $i(all_24_0) % 12.26/2.55 | % 12.26/2.55 | GROUND_INST: instantiating (5) with all_16_5, all_16_1, all_16_4, all_16_5, % 12.26/2.55 | all_16_3, simplifying with (17), (18), (20), (21), (34) gives: % 12.26/2.55 | (48) ? [v0: $i] : (union(all_16_1, all_16_4) = v0 & union(all_16_5, v0) = % 12.26/2.55 | all_16_3 & $i(v0) & $i(all_16_3)) % 12.26/2.55 | % 12.26/2.56 | GROUND_INST: instantiating (5) with all_16_1, all_24_0, all_16_4, all_16_5, % 12.26/2.56 | all_16_3, simplifying with (18), (20), (21), (37), (47) gives: % 12.26/2.56 | (49) ? [v0: $i] : (union(all_24_0, all_16_4) = v0 & union(all_16_1, v0) = % 12.26/2.56 | all_16_3 & $i(v0) & $i(all_16_3)) % 12.26/2.56 | % 12.26/2.56 | GROUND_INST: instantiating (4) with all_16_4, all_16_1, all_24_0, all_16_5, % 12.26/2.56 | all_16_3, simplifying with (18), (20), (26), (37), (47) gives: % 12.26/2.56 | (50) ? [v0: $i] : (union(v0, all_24_0) = all_16_3 & union(all_16_4, % 12.26/2.56 | all_16_1) = v0 & $i(v0) & $i(all_16_3)) % 12.26/2.56 | % 12.26/2.56 | GROUND_INST: instantiating (5) with all_16_1, all_24_0, all_16_1, all_16_5, % 12.26/2.56 | all_16_5, simplifying with (20), (34), (37), (47) gives: % 12.26/2.56 | (51) ? [v0: $i] : (union(all_24_0, all_16_1) = v0 & union(all_16_1, v0) = % 12.26/2.56 | all_16_5 & $i(v0) & $i(all_16_5)) % 12.26/2.56 | % 12.26/2.56 | GROUND_INST: instantiating (8) with all_24_0, all_16_1, all_16_5, simplifying % 12.26/2.56 | with (20), (37), (47) gives: % 12.26/2.56 | (52) union(all_24_0, all_16_1) = all_16_5 & $i(all_16_5) % 12.26/2.56 | % 12.26/2.56 | ALPHA: (52) implies: % 12.26/2.56 | (53) union(all_24_0, all_16_1) = all_16_5 % 12.26/2.56 | % 12.26/2.56 | GROUND_INST: instantiating (5) with all_24_0, all_26_0, all_16_1, all_16_2, % 12.26/2.56 | all_16_0, simplifying with (20), (22), (41), (46), (47) gives: % 12.26/2.56 | (54) ? [v0: $i] : (union(all_26_0, all_16_1) = v0 & union(all_24_0, v0) = % 12.26/2.56 | all_16_0 & $i(v0) & $i(all_16_0)) % 12.26/2.56 | % 12.26/2.56 | GROUND_INST: instantiating (4) with all_16_1, all_24_0, all_26_0, all_16_2, % 12.26/2.56 | all_16_0, simplifying with (20), (28), (41), (46), (47) gives: % 12.26/2.56 | (55) ? [v0: $i] : (union(v0, all_26_0) = all_16_0 & union(all_16_1, % 12.26/2.56 | all_24_0) = v0 & $i(v0) & $i(all_16_0)) % 12.26/2.56 | % 12.26/2.56 | GROUND_INST: instantiating (2) with all_16_4, all_16_5, all_24_0, simplifying % 12.26/2.56 | with (17), (18), (38) gives: % 12.26/2.56 | (56) ? [v0: $i] : ? [v1: $i] : (symmetric_difference(all_16_4, all_16_5) % 12.26/2.56 | = v0 & difference(all_16_4, all_16_5) = v1 & union(v1, all_24_0) = % 12.26/2.56 | v0 & $i(v1) & $i(v0)) % 12.26/2.56 | % 12.26/2.57 | GROUND_INST: instantiating (1) with all_16_4, all_16_5, all_26_0, simplifying % 12.26/2.57 | with (17), (18), (44) gives: % 12.26/2.57 | (57) ? [v0: $i] : ? [v1: $i] : (symmetric_difference(all_16_4, all_16_5) % 12.26/2.57 | = v0 & difference(all_16_5, all_16_4) = v1 & union(all_26_0, v1) = % 12.26/2.57 | v0 & $i(v1) & $i(v0)) % 12.26/2.57 | % 12.26/2.57 | GROUND_INST: instantiating (6) with all_16_4, all_16_5, all_26_0, simplifying % 12.26/2.57 | with (17), (18), (44) gives: % 12.26/2.57 | (58) ? [v0: $i] : (intersection(all_16_4, all_16_5) = v0 & union(v0, % 12.26/2.57 | all_26_0) = all_16_4 & $i(v0)) % 12.26/2.57 | % 12.26/2.57 | GROUND_INST: instantiating (3) with all_16_4, all_16_5, all_16_2, simplifying % 12.26/2.57 | with (17), (18), (30) gives: % 12.26/2.57 | (59) ? [v0: $i] : ? [v1: $i] : (difference(all_16_4, all_16_5) = v0 & % 12.26/2.57 | difference(all_16_5, all_16_4) = v1 & union(v0, v1) = all_16_2 & % 12.26/2.57 | $i(v1) & $i(v0) & $i(all_16_2)) % 12.26/2.57 | % 12.26/2.57 | GROUND_INST: instantiating (union_intersection) with all_16_4, all_16_5, % 12.26/2.57 | all_16_1, simplifying with (17), (18), (33) gives: % 12.26/2.57 | (60) union(all_16_4, all_16_1) = all_16_4 % 12.26/2.57 | % 12.26/2.57 | GROUND_INST: instantiating (7) with all_16_4, all_16_5, all_16_1, simplifying % 12.26/2.57 | with (17), (18), (33) gives: % 12.26/2.57 | (61) ? [v0: $i] : (difference(all_16_4, all_16_5) = v0 & union(all_16_1, % 12.26/2.57 | v0) = all_16_4 & $i(v0)) % 12.26/2.57 | % 12.26/2.57 | DELTA: instantiating (58) with fresh symbol all_38_0 gives: % 12.26/2.57 | (62) intersection(all_16_4, all_16_5) = all_38_0 & union(all_38_0, % 12.26/2.57 | all_26_0) = all_16_4 & $i(all_38_0) % 12.26/2.57 | % 12.26/2.57 | ALPHA: (62) implies: % 12.26/2.57 | (63) $i(all_38_0) % 12.26/2.57 | (64) intersection(all_16_4, all_16_5) = all_38_0 % 12.26/2.57 | % 12.26/2.57 | DELTA: instantiating (61) with fresh symbol all_42_0 gives: % 12.26/2.57 | (65) difference(all_16_4, all_16_5) = all_42_0 & union(all_16_1, all_42_0) % 12.26/2.57 | = all_16_4 & $i(all_42_0) % 12.26/2.57 | % 12.26/2.57 | ALPHA: (65) implies: % 12.26/2.57 | (66) $i(all_42_0) % 12.26/2.57 | (67) union(all_16_1, all_42_0) = all_16_4 % 12.26/2.57 | (68) difference(all_16_4, all_16_5) = all_42_0 % 12.26/2.57 | % 12.26/2.57 | DELTA: instantiating (55) with fresh symbol all_44_0 gives: % 12.26/2.57 | (69) union(all_44_0, all_26_0) = all_16_0 & union(all_16_1, all_24_0) = % 12.26/2.57 | all_44_0 & $i(all_44_0) & $i(all_16_0) % 12.26/2.57 | % 12.26/2.57 | ALPHA: (69) implies: % 12.26/2.57 | (70) $i(all_44_0) % 12.26/2.57 | (71) union(all_16_1, all_24_0) = all_44_0 % 12.26/2.57 | (72) union(all_44_0, all_26_0) = all_16_0 % 12.26/2.57 | % 12.26/2.57 | DELTA: instantiating (54) with fresh symbol all_46_0 gives: % 12.26/2.58 | (73) union(all_26_0, all_16_1) = all_46_0 & union(all_24_0, all_46_0) = % 12.26/2.58 | all_16_0 & $i(all_46_0) & $i(all_16_0) % 12.26/2.58 | % 12.26/2.58 | ALPHA: (73) implies: % 12.26/2.58 | (74) union(all_24_0, all_46_0) = all_16_0 % 12.26/2.58 | (75) union(all_26_0, all_16_1) = all_46_0 % 12.26/2.58 | % 12.26/2.58 | DELTA: instantiating (51) with fresh symbol all_48_0 gives: % 12.26/2.58 | (76) union(all_24_0, all_16_1) = all_48_0 & union(all_16_1, all_48_0) = % 12.26/2.58 | all_16_5 & $i(all_48_0) & $i(all_16_5) % 12.26/2.58 | % 12.26/2.58 | ALPHA: (76) implies: % 12.26/2.58 | (77) union(all_24_0, all_16_1) = all_48_0 % 12.26/2.58 | % 12.26/2.58 | DELTA: instantiating (49) with fresh symbol all_50_0 gives: % 12.26/2.58 | (78) union(all_24_0, all_16_4) = all_50_0 & union(all_16_1, all_50_0) = % 12.26/2.58 | all_16_3 & $i(all_50_0) & $i(all_16_3) % 12.26/2.58 | % 12.26/2.58 | ALPHA: (78) implies: % 12.26/2.58 | (79) union(all_24_0, all_16_4) = all_50_0 % 12.26/2.58 | % 12.26/2.58 | DELTA: instantiating (50) with fresh symbol all_54_0 gives: % 12.26/2.58 | (80) union(all_54_0, all_24_0) = all_16_3 & union(all_16_4, all_16_1) = % 12.26/2.58 | all_54_0 & $i(all_54_0) & $i(all_16_3) % 12.26/2.58 | % 12.26/2.58 | ALPHA: (80) implies: % 12.26/2.58 | (81) $i(all_54_0) % 12.26/2.58 | (82) union(all_16_4, all_16_1) = all_54_0 % 12.26/2.58 | (83) union(all_54_0, all_24_0) = all_16_3 % 12.26/2.58 | % 12.26/2.58 | DELTA: instantiating (48) with fresh symbol all_56_0 gives: % 12.26/2.58 | (84) union(all_16_1, all_16_4) = all_56_0 & union(all_16_5, all_56_0) = % 12.26/2.58 | all_16_3 & $i(all_56_0) & $i(all_16_3) % 12.26/2.58 | % 12.26/2.58 | ALPHA: (84) implies: % 12.26/2.58 | (85) $i(all_56_0) % 12.26/2.58 | (86) union(all_16_5, all_56_0) = all_16_3 % 12.26/2.58 | (87) union(all_16_1, all_16_4) = all_56_0 % 12.26/2.58 | % 12.26/2.58 | DELTA: instantiating (57) with fresh symbols all_58_0, all_58_1 gives: % 12.26/2.58 | (88) symmetric_difference(all_16_4, all_16_5) = all_58_1 & % 12.26/2.58 | difference(all_16_5, all_16_4) = all_58_0 & union(all_26_0, all_58_0) % 12.26/2.58 | = all_58_1 & $i(all_58_0) & $i(all_58_1) % 12.26/2.58 | % 12.26/2.58 | ALPHA: (88) implies: % 12.26/2.58 | (89) $i(all_58_0) % 12.26/2.58 | (90) union(all_26_0, all_58_0) = all_58_1 % 12.26/2.58 | (91) difference(all_16_5, all_16_4) = all_58_0 % 12.26/2.58 | (92) symmetric_difference(all_16_4, all_16_5) = all_58_1 % 12.26/2.58 | % 12.26/2.58 | DELTA: instantiating (56) with fresh symbols all_60_0, all_60_1 gives: % 12.26/2.58 | (93) symmetric_difference(all_16_4, all_16_5) = all_60_1 & % 12.26/2.58 | difference(all_16_4, all_16_5) = all_60_0 & union(all_60_0, all_24_0) % 12.26/2.58 | = all_60_1 & $i(all_60_0) & $i(all_60_1) % 12.26/2.58 | % 12.26/2.58 | ALPHA: (93) implies: % 12.26/2.58 | (94) difference(all_16_4, all_16_5) = all_60_0 % 12.26/2.58 | (95) symmetric_difference(all_16_4, all_16_5) = all_60_1 % 12.26/2.58 | % 12.26/2.58 | DELTA: instantiating (59) with fresh symbols all_62_0, all_62_1 gives: % 12.26/2.58 | (96) difference(all_16_4, all_16_5) = all_62_1 & difference(all_16_5, % 12.26/2.59 | all_16_4) = all_62_0 & union(all_62_1, all_62_0) = all_16_2 & % 12.26/2.59 | $i(all_62_0) & $i(all_62_1) & $i(all_16_2) % 12.26/2.59 | % 12.26/2.59 | ALPHA: (96) implies: % 12.26/2.59 | (97) difference(all_16_5, all_16_4) = all_62_0 % 12.26/2.59 | (98) difference(all_16_4, all_16_5) = all_62_1 % 12.26/2.59 | % 12.26/2.59 | GROUND_INST: instantiating (11) with all_16_4, all_54_0, all_16_1, all_16_4, % 12.26/2.59 | simplifying with (60), (82) gives: % 12.26/2.59 | (99) all_54_0 = all_16_4 % 12.26/2.59 | % 12.26/2.59 | GROUND_INST: instantiating (11) with all_16_5, all_44_0, all_24_0, all_16_1, % 12.26/2.59 | simplifying with (37), (71) gives: % 12.26/2.59 | (100) all_44_0 = all_16_5 % 12.26/2.59 | % 12.26/2.59 | GROUND_INST: instantiating (11) with all_16_5, all_48_0, all_16_1, all_24_0, % 12.26/2.59 | simplifying with (53), (77) gives: % 12.26/2.59 | (101) all_48_0 = all_16_5 % 12.26/2.59 | % 12.26/2.59 | GROUND_INST: instantiating (12) with all_24_0, all_62_0, all_16_4, all_16_5, % 12.26/2.59 | simplifying with (38), (97) gives: % 12.26/2.59 | (102) all_62_0 = all_24_0 % 12.26/2.59 | % 12.77/2.59 | GROUND_INST: instantiating (12) with all_58_0, all_62_0, all_16_4, all_16_5, % 12.77/2.59 | simplifying with (91), (97) gives: % 12.77/2.59 | (103) all_62_0 = all_58_0 % 12.77/2.59 | % 12.77/2.59 | GROUND_INST: instantiating (12) with all_26_0, all_62_1, all_16_5, all_16_4, % 12.77/2.59 | simplifying with (44), (98) gives: % 12.77/2.59 | (104) all_62_1 = all_26_0 % 12.77/2.59 | % 12.77/2.59 | GROUND_INST: instantiating (12) with all_60_0, all_62_1, all_16_5, all_16_4, % 12.77/2.59 | simplifying with (94), (98) gives: % 12.77/2.59 | (105) all_62_1 = all_60_0 % 12.77/2.59 | % 12.77/2.59 | GROUND_INST: instantiating (12) with all_42_0, all_62_1, all_16_5, all_16_4, % 12.77/2.59 | simplifying with (68), (98) gives: % 12.77/2.59 | (106) all_62_1 = all_42_0 % 12.77/2.59 | % 12.77/2.59 | GROUND_INST: instantiating (13) with all_16_2, all_60_1, all_16_5, all_16_4, % 12.77/2.59 | simplifying with (30), (95) gives: % 12.77/2.59 | (107) all_60_1 = all_16_2 % 12.77/2.59 | % 12.77/2.59 | GROUND_INST: instantiating (13) with all_58_1, all_60_1, all_16_5, all_16_4, % 12.77/2.59 | simplifying with (92), (95) gives: % 12.77/2.59 | (108) all_60_1 = all_58_1 % 12.77/2.59 | % 12.77/2.59 | GROUND_INST: instantiating (14) with all_16_1, all_38_0, all_16_5, all_16_4, % 12.77/2.59 | simplifying with (33), (64) gives: % 12.77/2.59 | (109) all_38_0 = all_16_1 % 12.77/2.59 | % 12.77/2.59 | COMBINE_EQS: (102), (103) imply: % 12.77/2.59 | (110) all_58_0 = all_24_0 % 12.77/2.59 | % 12.77/2.59 | SIMP: (110) implies: % 12.77/2.59 | (111) all_58_0 = all_24_0 % 12.77/2.59 | % 12.77/2.59 | COMBINE_EQS: (104), (105) imply: % 12.77/2.59 | (112) all_60_0 = all_26_0 % 12.77/2.59 | % 12.77/2.59 | COMBINE_EQS: (105), (106) imply: % 12.77/2.59 | (113) all_60_0 = all_42_0 % 12.77/2.59 | % 12.77/2.59 | COMBINE_EQS: (112), (113) imply: % 12.77/2.59 | (114) all_42_0 = all_26_0 % 12.77/2.59 | % 12.77/2.59 | SIMP: (114) implies: % 12.77/2.59 | (115) all_42_0 = all_26_0 % 12.77/2.59 | % 12.77/2.59 | COMBINE_EQS: (107), (108) imply: % 12.77/2.59 | (116) all_58_1 = all_16_2 % 12.77/2.59 | % 12.77/2.59 | REDUCE: (83), (99) imply: % 12.77/2.60 | (117) union(all_16_4, all_24_0) = all_16_3 % 12.77/2.60 | % 12.77/2.60 | REDUCE: (72), (100) imply: % 12.77/2.60 | (118) union(all_16_5, all_26_0) = all_16_0 % 12.77/2.60 | % 12.77/2.60 | REDUCE: (90), (111), (116) imply: % 12.77/2.60 | (119) union(all_26_0, all_24_0) = all_16_2 % 12.77/2.60 | % 12.77/2.60 | REDUCE: (67), (115) imply: % 12.77/2.60 | (120) union(all_16_1, all_26_0) = all_16_4 % 12.77/2.60 | % 12.77/2.60 | GROUND_INST: instantiating (5) with all_16_5, all_16_1, all_26_0, all_16_5, % 12.77/2.60 | all_16_0, simplifying with (17), (20), (34), (41), (118) gives: % 12.77/2.60 | (121) ? [v0: $i] : (union(all_16_1, all_26_0) = v0 & union(all_16_5, v0) = % 12.77/2.60 | all_16_0 & $i(v0) & $i(all_16_0)) % 12.77/2.60 | % 12.77/2.60 | GROUND_INST: instantiating (5) with all_16_1, all_24_0, all_56_0, all_16_5, % 12.77/2.60 | all_16_3, simplifying with (20), (37), (47), (85), (86) gives: % 12.77/2.60 | (122) ? [v0: $i] : (union(all_24_0, all_56_0) = v0 & union(all_16_1, v0) = % 12.77/2.60 | all_16_3 & $i(v0) & $i(all_16_3)) % 12.77/2.60 | % 12.77/2.60 | GROUND_INST: instantiating (8) with all_16_1, all_16_4, all_16_4, simplifying % 12.77/2.60 | with (18), (20), (60) gives: % 12.77/2.60 | (123) union(all_16_1, all_16_4) = all_16_4 % 12.77/2.60 | % 12.77/2.60 | GROUND_INST: instantiating (8) with all_24_0, all_16_4, all_16_3, simplifying % 12.77/2.60 | with (18), (47), (117) gives: % 12.77/2.60 | (124) union(all_24_0, all_16_4) = all_16_3 & $i(all_16_3) % 12.77/2.60 | % 12.77/2.60 | ALPHA: (124) implies: % 12.77/2.60 | (125) union(all_24_0, all_16_4) = all_16_3 % 12.77/2.60 | % 12.77/2.60 | GROUND_INST: instantiating (4) with all_16_1, all_16_4, all_16_1, all_16_4, % 12.77/2.60 | all_56_0, simplifying with (18), (20), (60), (87) gives: % 12.77/2.60 | (126) ? [v0: $i] : (union(v0, all_16_1) = all_56_0 & union(all_16_1, % 12.77/2.60 | all_16_4) = v0 & $i(v0) & $i(all_56_0)) % 12.77/2.60 | % 12.77/2.60 | GROUND_INST: instantiating (8) with all_26_0, all_16_1, all_16_4, simplifying % 12.77/2.60 | with (20), (41), (120) gives: % 12.77/2.60 | (127) union(all_26_0, all_16_1) = all_16_4 & $i(all_16_4) % 12.77/2.60 | % 12.77/2.60 | GROUND_INST: instantiating (4) with all_24_0, all_16_4, all_16_1, all_16_4, % 12.77/2.60 | all_50_0, simplifying with (18), (20), (47), (60), (79) gives: % 12.77/2.60 | (128) ? [v0: $i] : (union(v0, all_16_1) = all_50_0 & union(all_24_0, % 12.77/2.60 | all_16_4) = v0 & $i(v0) & $i(all_50_0)) % 12.77/2.60 | % 12.77/2.60 | GROUND_INST: instantiating (5) with all_24_0, all_16_1, all_16_4, all_16_5, % 12.77/2.60 | all_16_3, simplifying with (18), (20), (21), (47), (53) gives: % 12.77/2.61 | (129) ? [v0: $i] : (union(all_24_0, v0) = all_16_3 & union(all_16_1, % 12.77/2.61 | all_16_4) = v0 & $i(v0) & $i(all_16_3)) % 12.77/2.61 | % 12.77/2.61 | GROUND_INST: instantiating (5) with all_24_0, all_16_1, all_26_0, all_16_5, % 12.77/2.61 | all_16_0, simplifying with (20), (41), (47), (53), (118) gives: % 12.77/2.61 | (130) ? [v0: $i] : (union(all_24_0, v0) = all_16_0 & union(all_16_1, % 12.77/2.61 | all_26_0) = v0 & $i(v0) & $i(all_16_0)) % 12.77/2.61 | % 12.77/2.61 | GROUND_INST: instantiating (8) with all_16_1, all_26_0, all_46_0, simplifying % 12.77/2.61 | with (20), (41), (75) gives: % 12.77/2.61 | (131) union(all_16_1, all_26_0) = all_46_0 & $i(all_46_0) % 12.77/2.61 | % 12.77/2.61 | ALPHA: (131) implies: % 12.77/2.61 | (132) union(all_16_1, all_26_0) = all_46_0 % 12.77/2.61 | % 12.77/2.61 | GROUND_INST: instantiating (4) with all_16_1, all_26_0, all_24_0, all_16_2, % 12.77/2.61 | all_16_0, simplifying with (20), (28), (41), (47), (119) gives: % 12.77/2.61 | (133) ? [v0: $i] : (union(v0, all_24_0) = all_16_0 & union(all_16_1, % 12.77/2.61 | all_26_0) = v0 & $i(v0) & $i(all_16_0)) % 12.77/2.61 | % 12.77/2.61 | DELTA: instantiating (121) with fresh symbol all_88_0 gives: % 12.77/2.61 | (134) union(all_16_1, all_26_0) = all_88_0 & union(all_16_5, all_88_0) = % 12.77/2.61 | all_16_0 & $i(all_88_0) & $i(all_16_0) % 12.77/2.61 | % 12.77/2.61 | ALPHA: (134) implies: % 12.77/2.61 | (135) union(all_16_1, all_26_0) = all_88_0 % 12.77/2.61 | % 12.77/2.61 | DELTA: instantiating (126) with fresh symbol all_98_0 gives: % 12.77/2.61 | (136) union(all_98_0, all_16_1) = all_56_0 & union(all_16_1, all_16_4) = % 12.77/2.61 | all_98_0 & $i(all_98_0) & $i(all_56_0) % 12.77/2.61 | % 12.77/2.61 | ALPHA: (136) implies: % 12.77/2.61 | (137) union(all_16_1, all_16_4) = all_98_0 % 12.77/2.61 | % 12.77/2.61 | DELTA: instantiating (133) with fresh symbol all_102_0 gives: % 12.77/2.61 | (138) union(all_102_0, all_24_0) = all_16_0 & union(all_16_1, all_26_0) = % 12.77/2.61 | all_102_0 & $i(all_102_0) & $i(all_16_0) % 12.77/2.61 | % 12.77/2.61 | ALPHA: (138) implies: % 12.77/2.61 | (139) union(all_16_1, all_26_0) = all_102_0 % 12.77/2.61 | % 12.77/2.61 | DELTA: instantiating (130) with fresh symbol all_108_0 gives: % 12.77/2.61 | (140) union(all_24_0, all_108_0) = all_16_0 & union(all_16_1, all_26_0) = % 12.77/2.61 | all_108_0 & $i(all_108_0) & $i(all_16_0) % 12.77/2.61 | % 12.77/2.61 | ALPHA: (140) implies: % 12.77/2.61 | (141) union(all_16_1, all_26_0) = all_108_0 % 12.77/2.61 | % 12.77/2.61 | DELTA: instantiating (129) with fresh symbol all_118_0 gives: % 12.77/2.61 | (142) union(all_24_0, all_118_0) = all_16_3 & union(all_16_1, all_16_4) = % 12.77/2.61 | all_118_0 & $i(all_118_0) & $i(all_16_3) % 12.77/2.61 | % 12.77/2.61 | ALPHA: (142) implies: % 12.77/2.61 | (143) union(all_16_1, all_16_4) = all_118_0 % 12.77/2.61 | % 12.77/2.61 | DELTA: instantiating (128) with fresh symbol all_122_0 gives: % 12.77/2.61 | (144) union(all_122_0, all_16_1) = all_50_0 & union(all_24_0, all_16_4) = % 12.77/2.61 | all_122_0 & $i(all_122_0) & $i(all_50_0) % 12.77/2.61 | % 12.77/2.61 | ALPHA: (144) implies: % 12.77/2.61 | (145) union(all_24_0, all_16_4) = all_122_0 % 12.77/2.61 | % 12.77/2.61 | DELTA: instantiating (122) with fresh symbol all_132_0 gives: % 12.77/2.61 | (146) union(all_24_0, all_56_0) = all_132_0 & union(all_16_1, all_132_0) = % 12.77/2.61 | all_16_3 & $i(all_132_0) & $i(all_16_3) % 12.77/2.61 | % 12.77/2.61 | ALPHA: (146) implies: % 12.77/2.61 | (147) union(all_24_0, all_56_0) = all_132_0 % 12.77/2.61 | % 12.77/2.61 | GROUND_INST: instantiating (11) with all_56_0, all_118_0, all_16_4, all_16_1, % 12.77/2.61 | simplifying with (87), (143) gives: % 12.77/2.61 | (148) all_118_0 = all_56_0 % 12.77/2.61 | % 12.77/2.61 | GROUND_INST: instantiating (11) with all_98_0, all_118_0, all_16_4, all_16_1, % 12.77/2.61 | simplifying with (137), (143) gives: % 12.77/2.61 | (149) all_118_0 = all_98_0 % 12.77/2.61 | % 12.77/2.62 | GROUND_INST: instantiating (11) with all_16_4, all_118_0, all_16_4, all_16_1, % 12.77/2.62 | simplifying with (123), (143) gives: % 12.77/2.62 | (150) all_118_0 = all_16_4 % 12.77/2.62 | % 12.77/2.62 | GROUND_INST: instantiating (11) with all_88_0, all_102_0, all_26_0, all_16_1, % 12.77/2.62 | simplifying with (135), (139) gives: % 12.77/2.62 | (151) all_102_0 = all_88_0 % 12.77/2.62 | % 12.77/2.62 | GROUND_INST: instantiating (11) with all_46_0, all_102_0, all_26_0, all_16_1, % 12.77/2.62 | simplifying with (132), (139) gives: % 12.77/2.62 | (152) all_102_0 = all_46_0 % 12.77/2.62 | % 12.77/2.62 | GROUND_INST: instantiating (11) with all_16_4, all_108_0, all_26_0, all_16_1, % 12.77/2.62 | simplifying with (120), (141) gives: % 12.77/2.62 | (153) all_108_0 = all_16_4 % 12.77/2.62 | % 12.77/2.62 | GROUND_INST: instantiating (11) with all_88_0, all_108_0, all_26_0, all_16_1, % 12.77/2.62 | simplifying with (135), (141) gives: % 12.77/2.62 | (154) all_108_0 = all_88_0 % 12.77/2.62 | % 12.77/2.62 | GROUND_INST: instantiating (11) with all_50_0, all_122_0, all_16_4, all_24_0, % 12.77/2.62 | simplifying with (79), (145) gives: % 12.77/2.62 | (155) all_122_0 = all_50_0 % 12.77/2.62 | % 12.77/2.62 | GROUND_INST: instantiating (11) with all_16_3, all_122_0, all_16_4, all_24_0, % 12.77/2.62 | simplifying with (125), (145) gives: % 12.77/2.62 | (156) all_122_0 = all_16_3 % 12.77/2.62 | % 12.77/2.62 | COMBINE_EQS: (155), (156) imply: % 12.77/2.62 | (157) all_50_0 = all_16_3 % 12.77/2.62 | % 12.77/2.62 | SIMP: (157) implies: % 12.77/2.62 | (158) all_50_0 = all_16_3 % 12.77/2.62 | % 12.77/2.62 | COMBINE_EQS: (148), (149) imply: % 12.77/2.62 | (159) all_98_0 = all_56_0 % 12.77/2.62 | % 12.77/2.62 | COMBINE_EQS: (149), (150) imply: % 12.77/2.62 | (160) all_98_0 = all_16_4 % 12.77/2.62 | % 12.77/2.62 | COMBINE_EQS: (153), (154) imply: % 12.77/2.62 | (161) all_88_0 = all_16_4 % 12.77/2.62 | % 12.77/2.62 | SIMP: (161) implies: % 12.77/2.62 | (162) all_88_0 = all_16_4 % 12.77/2.62 | % 12.77/2.62 | COMBINE_EQS: (151), (152) imply: % 12.77/2.62 | (163) all_88_0 = all_46_0 % 12.77/2.62 | % 12.77/2.62 | SIMP: (163) implies: % 12.77/2.62 | (164) all_88_0 = all_46_0 % 12.77/2.62 | % 12.77/2.62 | COMBINE_EQS: (159), (160) imply: % 12.77/2.62 | (165) all_56_0 = all_16_4 % 12.77/2.62 | % 12.77/2.62 | SIMP: (165) implies: % 12.77/2.62 | (166) all_56_0 = all_16_4 % 12.77/2.62 | % 12.77/2.62 | COMBINE_EQS: (162), (164) imply: % 12.77/2.62 | (167) all_46_0 = all_16_4 % 12.77/2.62 | % 12.77/2.62 | REDUCE: (147), (166) imply: % 12.77/2.62 | (168) union(all_24_0, all_16_4) = all_132_0 % 12.77/2.62 | % 12.77/2.62 | REDUCE: (74), (167) imply: % 12.77/2.62 | (169) union(all_24_0, all_16_4) = all_16_0 % 12.77/2.62 | % 12.77/2.62 | GROUND_INST: instantiating (11) with all_16_3, all_132_0, all_16_4, all_24_0, % 12.77/2.62 | simplifying with (125), (168) gives: % 12.77/2.62 | (170) all_132_0 = all_16_3 % 12.77/2.62 | % 12.77/2.62 | GROUND_INST: instantiating (11) with all_16_0, all_132_0, all_16_4, all_24_0, % 12.77/2.62 | simplifying with (168), (169) gives: % 12.77/2.62 | (171) all_132_0 = all_16_0 % 12.77/2.62 | % 12.77/2.62 | COMBINE_EQS: (170), (171) imply: % 12.77/2.62 | (172) all_16_0 = all_16_3 % 12.77/2.62 | % 12.77/2.62 | REDUCE: (16), (172) imply: % 12.77/2.62 | (173) $false % 12.77/2.62 | % 12.77/2.62 | CLOSE: (173) is inconsistent. % 12.77/2.62 | % 12.77/2.62 End of proof % 12.77/2.62 % SZS output end Proof for theBenchmark % 12.77/2.62 % 12.77/2.62 2003ms %------------------------------------------------------------------------------