%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU227+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n023.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 17:43:28 EDT 2023 % Result : Theorem 12.29s 2.51s % Output : Proof 15.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SEU227+1 : TPTP v8.1.2. Released v3.3.0. % 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n023.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 : Wed Aug 23 18:51:43 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.64 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 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 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 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 % 2.94/1.11 Prover 1: Preprocessing ... % 2.94/1.11 Prover 4: Preprocessing ... % 2.94/1.15 Prover 5: Preprocessing ... % 2.94/1.15 Prover 3: Preprocessing ... % 2.94/1.15 Prover 0: Preprocessing ... % 2.94/1.15 Prover 2: Preprocessing ... % 2.94/1.15 Prover 6: Preprocessing ... % 7.45/1.76 Prover 1: Warning: ignoring some quantifiers % 7.76/1.80 Prover 5: Proving ... % 7.76/1.81 Prover 4: Warning: ignoring some quantifiers % 7.76/1.81 Prover 3: Warning: ignoring some quantifiers % 7.76/1.82 Prover 1: Constructing countermodel ... % 8.08/1.84 Prover 3: Constructing countermodel ... % 8.08/1.85 Prover 6: Proving ... % 8.08/1.88 Prover 4: Constructing countermodel ... % 8.08/1.89 Prover 2: Proving ... % 8.33/1.95 Prover 0: Proving ... % 12.29/2.51 Prover 3: proved (1853ms) % 12.29/2.51 % 12.29/2.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.29/2.51 % 12.29/2.52 Prover 2: stopped % 12.29/2.52 Prover 5: stopped % 12.29/2.52 Prover 6: stopped % 12.29/2.54 Prover 0: stopped % 12.90/2.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.90/2.54 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.90/2.54 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.90/2.54 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.90/2.54 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.90/2.58 Prover 8: Preprocessing ... % 12.90/2.58 Prover 7: Preprocessing ... % 12.90/2.59 Prover 10: Preprocessing ... % 12.90/2.60 Prover 13: Preprocessing ... % 12.90/2.60 Prover 11: Preprocessing ... % 13.76/2.69 Prover 7: Warning: ignoring some quantifiers % 13.76/2.70 Prover 7: Constructing countermodel ... % 13.76/2.71 Prover 8: Warning: ignoring some quantifiers % 13.76/2.71 Prover 13: Warning: ignoring some quantifiers % 13.76/2.72 Prover 10: Warning: ignoring some quantifiers % 14.46/2.73 Prover 8: Constructing countermodel ... % 14.46/2.74 Prover 1: Found proof (size 75) % 14.46/2.74 Prover 13: Constructing countermodel ... % 14.46/2.74 Prover 1: proved (2089ms) % 14.46/2.74 Prover 7: stopped % 14.46/2.74 Prover 4: stopped % 14.46/2.74 Prover 10: Constructing countermodel ... % 14.46/2.75 Prover 13: stopped % 14.46/2.75 Prover 10: stopped % 14.46/2.75 Prover 8: stopped % 14.80/2.81 Prover 11: Warning: ignoring some quantifiers % 14.80/2.82 Prover 11: Constructing countermodel ... % 14.80/2.83 Prover 11: stopped % 14.80/2.83 % 14.80/2.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.80/2.83 % 14.80/2.83 % SZS output start Proof for theBenchmark % 14.80/2.84 Assumptions after simplification: % 14.80/2.84 --------------------------------- % 14.80/2.84 % 14.80/2.84 (d13_relat_1) % 15.15/2.87 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ( ? [v1: $i] : ! [v2: $i] % 15.15/2.87 : ! [v3: $i] : (v3 = v1 | ~ (relation_image(v0, v2) = v3) | ~ $i(v2) | % 15.15/2.87 ~ $i(v1) | ? [v4: $i] : ? [v5: any] : (in(v4, v1) = v5 & $i(v4) & ( ~ % 15.15/2.87 (v5 = 0) | ! [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v6, v4) = % 15.15/2.87 v7) | ~ (in(v7, v0) = 0) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = % 15.15/2.87 0) & in(v6, v2) = v8))) & (v5 = 0 | ? [v6: $i] : ? [v7: $i] % 15.21/2.87 : (ordered_pair(v6, v4) = v7 & in(v7, v0) = 0 & in(v6, v2) = 0 & % 15.21/2.87 $i(v7) & $i(v6))))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 15.21/2.87 (relation_image(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ( ! [v3: $i] : % 15.21/2.87 ! [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | ! [v5: $i] % 15.21/2.87 : ! [v6: $i] : ( ~ (ordered_pair(v5, v3) = v6) | ~ (in(v6, v0) = % 15.21/2.87 0) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & in(v5, v1) = % 15.21/2.87 v7))) & ! [v3: $i] : ( ~ (in(v3, v2) = 0) | ~ $i(v3) | ? [v4: % 15.21/2.87 $i] : ? [v5: $i] : (ordered_pair(v4, v3) = v5 & in(v5, v0) = 0 & % 15.21/2.87 in(v4, v1) = 0 & $i(v5) & $i(v4))))))) % 15.21/2.87 % 15.21/2.87 (d14_relat_1) % 15.21/2.88 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ( ? [v1: $i] : ! [v2: $i] % 15.21/2.88 : ! [v3: $i] : (v3 = v1 | ~ (relation_inverse_image(v0, v2) = v3) | ~ % 15.21/2.88 $i(v2) | ~ $i(v1) | ? [v4: $i] : ? [v5: any] : (in(v4, v1) = v5 & % 15.21/2.88 $i(v4) & ( ~ (v5 = 0) | ! [v6: $i] : ! [v7: $i] : ( ~ % 15.21/2.88 (ordered_pair(v4, v6) = v7) | ~ (in(v7, v0) = 0) | ~ $i(v6) | ? % 15.21/2.88 [v8: int] : ( ~ (v8 = 0) & in(v6, v2) = v8))) & (v5 = 0 | ? [v6: % 15.21/2.88 $i] : ? [v7: $i] : (ordered_pair(v4, v6) = v7 & in(v7, v0) = 0 & % 15.21/2.88 in(v6, v2) = 0 & $i(v7) & $i(v6))))) & ! [v1: $i] : ! [v2: $i] : % 15.21/2.88 ( ~ (relation_inverse_image(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ( ! % 15.21/2.88 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | % 15.21/2.88 ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) = v6) | ~ % 15.21/2.88 (in(v6, v0) = 0) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & % 15.21/2.88 in(v5, v1) = v7))) & ! [v3: $i] : ( ~ (in(v3, v2) = 0) | ~ % 15.21/2.88 $i(v3) | ? [v4: $i] : ? [v5: $i] : (ordered_pair(v3, v4) = v5 & % 15.21/2.88 in(v5, v0) = 0 & in(v4, v1) = 0 & $i(v5) & $i(v4))))))) % 15.21/2.88 % 15.21/2.88 (d3_tarski) % 15.21/2.88 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 15.21/2.88 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 15.21/2.88 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 15.21/2.88 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 15.21/2.88 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 15.21/2.88 % 15.21/2.88 (d4_relat_1) % 15.21/2.89 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 15.21/2.89 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~ % 15.21/2.89 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~ % 15.21/2.89 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) = % 15.21/2.89 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i] % 15.21/2.89 : ? [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, v0) = 0 & $i(v6) % 15.21/2.89 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 % 15.21/2.89 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~ % 15.21/2.89 (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) & % 15.21/2.89 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: % 15.21/2.89 $i] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) & % 15.21/2.89 $i(v3))))))) % 15.21/2.89 % 15.21/2.89 (fc5_relat_1) % 15.21/2.89 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 15.21/2.89 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & empty(v1) = v4 & % 15.21/2.89 empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 15.21/2.89 % 15.21/2.89 (fc7_relat_1) % 15.21/2.89 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 15.21/2.89 any] : ? [v3: any] : ? [v4: any] : (relation(v1) = v4 & empty(v1) = v3 & % 15.21/2.89 empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) % 15.21/2.89 % 15.21/2.89 (t146_funct_1) % 15.21/2.89 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 15.21/2.89 int] : ( ~ (v5 = 0) & relation_dom(v1) = v2 & subset(v0, v4) = v5 & % 15.21/2.89 subset(v0, v2) = 0 & relation_inverse_image(v1, v3) = v4 & % 15.21/2.89 relation_image(v1, v0) = v3 & relation(v1) = 0 & $i(v4) & $i(v3) & $i(v2) & % 15.21/2.89 $i(v1) & $i(v0)) % 15.21/2.89 % 15.21/2.89 (t7_boole) % 15.21/2.89 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 15.21/2.89 [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2)) % 15.21/2.89 % 15.21/2.90 (function-axioms) % 15.21/2.90 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.21/2.90 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 15.21/2.90 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.21/2.90 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 15.21/2.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.21/2.90 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = % 15.21/2.90 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 15.21/2.90 ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & ! % 15.21/2.90 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.21/2.90 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] % 15.21/2.90 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, % 15.21/2.90 v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 15.21/2.90 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.21/2.90 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 15.21/2.90 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) % 15.21/2.90 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.21/2.90 $i] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ % 15.21/2.90 (relation_empty_yielding(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 15.21/2.90 $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! % 15.21/2.90 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | % 15.21/2.90 ~ (relation_dom(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.21/2.90 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ % 15.21/2.90 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.21/2.90 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 15.21/2.90 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.21/2.90 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~ % 15.21/2.90 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.21/2.90 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 15.21/2.90 (empty(v2) = v0)) % 15.21/2.90 % 15.21/2.90 Further assumptions not needed in the proof: % 15.21/2.90 -------------------------------------------- % 15.21/2.90 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, % 15.21/2.90 commutativity_k2_tarski, d5_tarski, dt_k10_relat_1, dt_k1_relat_1, dt_k1_tarski, % 15.21/2.90 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski, dt_k4_tarski, dt_k9_relat_1, % 15.21/2.90 dt_m1_subset_1, existence_m1_subset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0, % 15.21/2.90 fc1_zfmisc_1, fc2_subset_1, fc3_subset_1, fc4_relat_1, rc1_funct_1, rc1_relat_1, % 15.21/2.90 rc1_subset_1, rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_subset_1, % 15.21/2.90 rc2_xboole_0, rc3_funct_1, rc3_relat_1, reflexivity_r1_tarski, t1_subset, % 15.21/2.90 t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t8_boole % 15.21/2.90 % 15.21/2.90 Those formulas are unsatisfiable: % 15.21/2.90 --------------------------------- % 15.21/2.90 % 15.21/2.90 Begin of proof % 15.21/2.90 | % 15.21/2.90 | ALPHA: (d3_tarski) implies: % 15.21/2.91 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 15.21/2.91 | $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) = 0) | ~ $i(v2) | in(v2, v1) % 15.21/2.91 | = 0)) % 15.21/2.91 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 15.21/2.91 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 15.21/2.91 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 15.21/2.91 | % 15.21/2.91 | ALPHA: (function-axioms) implies: % 15.21/2.91 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.21/2.91 | (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 15.39/2.91 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.39/2.91 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 15.39/2.91 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.39/2.91 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 15.39/2.91 | % 15.39/2.91 | DELTA: instantiating (t146_funct_1) with fresh symbols all_49_0, all_49_1, % 15.39/2.91 | all_49_2, all_49_3, all_49_4, all_49_5 gives: % 15.39/2.91 | (6) ~ (all_49_0 = 0) & relation_dom(all_49_4) = all_49_3 & % 15.39/2.91 | subset(all_49_5, all_49_1) = all_49_0 & subset(all_49_5, all_49_3) = 0 % 15.39/2.91 | & relation_inverse_image(all_49_4, all_49_2) = all_49_1 & % 15.39/2.91 | relation_image(all_49_4, all_49_5) = all_49_2 & relation(all_49_4) = 0 % 15.39/2.91 | & $i(all_49_1) & $i(all_49_2) & $i(all_49_3) & $i(all_49_4) & % 15.39/2.91 | $i(all_49_5) % 15.39/2.91 | % 15.39/2.91 | ALPHA: (6) implies: % 15.39/2.91 | (7) ~ (all_49_0 = 0) % 15.39/2.91 | (8) $i(all_49_5) % 15.39/2.91 | (9) $i(all_49_4) % 15.39/2.91 | (10) $i(all_49_3) % 15.39/2.91 | (11) $i(all_49_2) % 15.39/2.91 | (12) $i(all_49_1) % 15.39/2.91 | (13) relation(all_49_4) = 0 % 15.39/2.91 | (14) relation_image(all_49_4, all_49_5) = all_49_2 % 15.39/2.91 | (15) relation_inverse_image(all_49_4, all_49_2) = all_49_1 % 15.39/2.91 | (16) subset(all_49_5, all_49_3) = 0 % 15.39/2.91 | (17) subset(all_49_5, all_49_1) = all_49_0 % 15.39/2.91 | (18) relation_dom(all_49_4) = all_49_3 % 15.39/2.91 | % 15.39/2.91 | GROUND_INST: instantiating (d14_relat_1) with all_49_4, simplifying with (9), % 15.39/2.91 | (13) gives: % 15.39/2.92 | (19) ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 15.39/2.92 | (relation_inverse_image(all_49_4, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 15.39/2.92 | | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = % 15.39/2.92 | 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) = % 15.39/2.92 | v6) | ~ (in(v6, all_49_4) = 0) | ~ $i(v5) | ? [v7: int] : % 15.39/2.92 | ( ~ (v7 = 0) & in(v5, v1) = v7))) & (v4 = 0 | ? [v5: $i] : ? % 15.39/2.92 | [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, all_49_4) = 0 & % 15.39/2.92 | in(v5, v1) = 0 & $i(v6) & $i(v5))))) & ! [v0: $i] : ! [v1: % 15.39/2.92 | $i] : ( ~ (relation_inverse_image(all_49_4, v0) = v1) | ~ $i(v1) | % 15.39/2.92 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2, v1) = % 15.39/2.92 | v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~ % 15.39/2.92 | (ordered_pair(v2, v4) = v5) | ~ (in(v5, all_49_4) = 0) | ~ % 15.39/2.92 | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & in(v4, v0) = v6))) & ! % 15.39/2.92 | [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? % 15.39/2.92 | [v4: $i] : (ordered_pair(v2, v3) = v4 & in(v4, all_49_4) = 0 & % 15.39/2.92 | in(v3, v0) = 0 & $i(v4) & $i(v3))))) % 15.39/2.92 | % 15.39/2.92 | ALPHA: (19) implies: % 15.39/2.92 | (20) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_inverse_image(all_49_4, v0) % 15.39/2.92 | = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 % 15.39/2.92 | = 0 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: % 15.39/2.92 | $i] : ( ~ (ordered_pair(v2, v4) = v5) | ~ (in(v5, all_49_4) = % 15.39/2.92 | 0) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & in(v4, v0) = % 15.39/2.92 | v6))) & ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? % 15.39/2.92 | [v3: $i] : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & in(v4, % 15.39/2.92 | all_49_4) = 0 & in(v3, v0) = 0 & $i(v4) & $i(v3))))) % 15.39/2.92 | % 15.39/2.92 | GROUND_INST: instantiating (d13_relat_1) with all_49_4, simplifying with (9), % 15.39/2.92 | (13) gives: % 15.39/2.92 | (21) ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 15.39/2.92 | (relation_image(all_49_4, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 15.39/2.92 | [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = 0) | % 15.39/2.92 | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v3) = v6) | ~ % 15.39/2.92 | (in(v6, all_49_4) = 0) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = % 15.39/2.92 | 0) & in(v5, v1) = v7))) & (v4 = 0 | ? [v5: $i] : ? [v6: % 15.39/2.92 | $i] : (ordered_pair(v5, v3) = v6 & in(v6, all_49_4) = 0 & % 15.39/2.92 | in(v5, v1) = 0 & $i(v6) & $i(v5))))) & ! [v0: $i] : ! [v1: % 15.39/2.92 | $i] : ( ~ (relation_image(all_49_4, v0) = v1) | ~ $i(v1) | ~ % 15.39/2.92 | $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2, v1) = % 15.39/2.92 | v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~ % 15.39/2.92 | (ordered_pair(v4, v2) = v5) | ~ (in(v5, all_49_4) = 0) | ~ % 15.39/2.92 | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & in(v4, v0) = v6))) & ! % 15.39/2.92 | [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? % 15.39/2.92 | [v4: $i] : (ordered_pair(v3, v2) = v4 & in(v4, all_49_4) = 0 & % 15.39/2.92 | in(v3, v0) = 0 & $i(v4) & $i(v3))))) % 15.39/2.92 | % 15.39/2.92 | ALPHA: (21) implies: % 15.39/2.92 | (22) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_image(all_49_4, v0) = v1) | % 15.39/2.92 | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 15.39/2.92 | (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~ % 15.39/2.92 | (ordered_pair(v4, v2) = v5) | ~ (in(v5, all_49_4) = 0) | ~ % 15.39/2.92 | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & in(v4, v0) = v6))) & ! % 15.39/2.92 | [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? % 15.39/2.92 | [v4: $i] : (ordered_pair(v3, v2) = v4 & in(v4, all_49_4) = 0 & % 15.39/2.92 | in(v3, v0) = 0 & $i(v4) & $i(v3))))) % 15.39/2.92 | % 15.39/2.92 | GROUND_INST: instantiating (1) with all_49_5, all_49_3, simplifying with (8), % 15.39/2.92 | (10), (16) gives: % 15.39/2.92 | (23) ! [v0: $i] : ( ~ (in(v0, all_49_5) = 0) | ~ $i(v0) | in(v0, % 15.39/2.92 | all_49_3) = 0) % 15.39/2.92 | % 15.39/2.93 | GROUND_INST: instantiating (2) with all_49_5, all_49_1, all_49_0, simplifying % 15.39/2.93 | with (8), (12), (17) gives: % 15.39/2.93 | (24) all_49_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 15.39/2.93 | all_49_1) = v1 & in(v0, all_49_5) = 0 & $i(v0)) % 15.39/2.93 | % 15.39/2.93 | GROUND_INST: instantiating (fc7_relat_1) with all_49_4, all_49_3, simplifying % 15.39/2.93 | with (9), (18) gives: % 15.39/2.93 | (25) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_49_3) = v2 % 15.39/2.93 | & empty(all_49_3) = v1 & empty(all_49_4) = v0 & ( ~ (v0 = 0) | (v2 = % 15.39/2.93 | 0 & v1 = 0))) % 15.39/2.93 | % 15.39/2.93 | GROUND_INST: instantiating (fc5_relat_1) with all_49_4, all_49_3, simplifying % 15.39/2.93 | with (9), (18) gives: % 15.39/2.93 | (26) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_49_4) = v1 % 15.39/2.93 | & empty(all_49_3) = v2 & empty(all_49_4) = v0 & ( ~ (v2 = 0) | ~ % 15.39/2.93 | (v1 = 0) | v0 = 0)) % 15.39/2.93 | % 15.39/2.93 | GROUND_INST: instantiating (d4_relat_1) with all_49_4, all_49_3, simplifying % 15.39/2.93 | with (9), (18) gives: % 15.39/2.93 | (27) ? [v0: int] : ( ~ (v0 = 0) & relation(all_49_4) = v0) | ( ? [v0: any] % 15.39/2.93 | : (v0 = all_49_3 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1, % 15.39/2.93 | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] : % 15.39/2.93 | ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4, all_49_4) = 0) | % 15.39/2.93 | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] : % 15.39/2.93 | (ordered_pair(v1, v3) = v4 & in(v4, all_49_4) = 0 & $i(v4) & % 15.39/2.93 | $i(v3))))) & ( ~ $i(all_49_3) | ( ! [v0: $i] : ! [v1: int] % 15.39/2.93 | : (v1 = 0 | ~ (in(v0, all_49_3) = v1) | ~ $i(v0) | ! [v2: $i] % 15.39/2.93 | : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, % 15.39/2.93 | all_49_4) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, % 15.39/2.93 | all_49_3) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 15.39/2.93 | (ordered_pair(v0, v1) = v2 & in(v2, all_49_4) = 0 & $i(v2) & % 15.39/2.93 | $i(v1)))))) % 15.39/2.93 | % 15.39/2.93 | GROUND_INST: instantiating (22) with all_49_5, all_49_2, simplifying with (8), % 15.39/2.93 | (11), (14) gives: % 15.39/2.93 | (28) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_49_2) = v1) | ~ % 15.39/2.93 | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) % 15.39/2.93 | | ~ (in(v3, all_49_4) = 0) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = % 15.39/2.93 | 0) & in(v2, all_49_5) = v4))) & ! [v0: $i] : ( ~ (in(v0, % 15.39/2.93 | all_49_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 15.39/2.93 | (ordered_pair(v1, v0) = v2 & in(v2, all_49_4) = 0 & in(v1, all_49_5) % 15.39/2.93 | = 0 & $i(v2) & $i(v1))) % 15.39/2.93 | % 15.39/2.93 | ALPHA: (28) implies: % 15.39/2.93 | (29) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_49_2) = v1) | ~ % 15.39/2.93 | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) % 15.39/2.93 | | ~ (in(v3, all_49_4) = 0) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = % 15.39/2.93 | 0) & in(v2, all_49_5) = v4))) % 15.39/2.93 | % 15.39/2.93 | GROUND_INST: instantiating (20) with all_49_2, all_49_1, simplifying with % 15.39/2.93 | (11), (12), (15) gives: % 15.52/2.93 | (30) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_49_1) = v1) | ~ % 15.52/2.93 | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) % 15.52/2.93 | | ~ (in(v3, all_49_4) = 0) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = % 15.52/2.94 | 0) & in(v2, all_49_2) = v4))) & ! [v0: $i] : ( ~ (in(v0, % 15.52/2.94 | all_49_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 15.52/2.94 | (ordered_pair(v0, v1) = v2 & in(v2, all_49_4) = 0 & in(v1, all_49_2) % 15.52/2.94 | = 0 & $i(v2) & $i(v1))) % 15.52/2.94 | % 15.52/2.94 | ALPHA: (30) implies: % 15.52/2.94 | (31) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_49_1) = v1) | ~ % 15.52/2.94 | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) % 15.52/2.94 | | ~ (in(v3, all_49_4) = 0) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = % 15.52/2.94 | 0) & in(v2, all_49_2) = v4))) % 15.52/2.94 | % 15.52/2.94 | DELTA: instantiating (26) with fresh symbols all_78_0, all_78_1, all_78_2 % 15.52/2.94 | gives: % 15.52/2.94 | (32) relation(all_49_4) = all_78_1 & empty(all_49_3) = all_78_0 & % 15.52/2.94 | empty(all_49_4) = all_78_2 & ( ~ (all_78_0 = 0) | ~ (all_78_1 = 0) | % 15.52/2.94 | all_78_2 = 0) % 15.52/2.94 | % 15.52/2.94 | ALPHA: (32) implies: % 15.52/2.94 | (33) empty(all_49_3) = all_78_0 % 15.52/2.94 | (34) relation(all_49_4) = all_78_1 % 15.52/2.94 | % 15.52/2.94 | DELTA: instantiating (25) with fresh symbols all_80_0, all_80_1, all_80_2 % 15.52/2.94 | gives: % 15.52/2.94 | (35) relation(all_49_3) = all_80_0 & empty(all_49_3) = all_80_1 & % 15.52/2.94 | empty(all_49_4) = all_80_2 & ( ~ (all_80_2 = 0) | (all_80_0 = 0 & % 15.52/2.94 | all_80_1 = 0)) % 15.52/2.94 | % 15.52/2.94 | ALPHA: (35) implies: % 15.52/2.94 | (36) empty(all_49_3) = all_80_1 % 15.52/2.94 | (37) ~ (all_80_2 = 0) | (all_80_0 = 0 & all_80_1 = 0) % 15.52/2.94 | % 15.52/2.94 | BETA: splitting (24) gives: % 15.52/2.94 | % 15.52/2.94 | Case 1: % 15.52/2.94 | | % 15.52/2.94 | | (38) all_49_0 = 0 % 15.52/2.94 | | % 15.52/2.94 | | REDUCE: (7), (38) imply: % 15.52/2.94 | | (39) $false % 15.52/2.94 | | % 15.52/2.94 | | CLOSE: (39) is inconsistent. % 15.52/2.94 | | % 15.52/2.94 | Case 2: % 15.52/2.94 | | % 15.52/2.94 | | (40) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_49_1) = v1 & % 15.52/2.94 | | in(v0, all_49_5) = 0 & $i(v0)) % 15.52/2.94 | | % 15.52/2.94 | | DELTA: instantiating (40) with fresh symbols all_118_0, all_118_1 gives: % 15.52/2.94 | | (41) ~ (all_118_0 = 0) & in(all_118_1, all_49_1) = all_118_0 & % 15.52/2.94 | | in(all_118_1, all_49_5) = 0 & $i(all_118_1) % 15.52/2.94 | | % 15.52/2.94 | | ALPHA: (41) implies: % 15.52/2.94 | | (42) ~ (all_118_0 = 0) % 15.52/2.94 | | (43) $i(all_118_1) % 15.52/2.94 | | (44) in(all_118_1, all_49_5) = 0 % 15.52/2.94 | | (45) in(all_118_1, all_49_1) = all_118_0 % 15.52/2.94 | | % 15.52/2.94 | | GROUND_INST: instantiating (3) with all_78_0, all_80_1, all_49_3, % 15.52/2.94 | | simplifying with (33), (36) gives: % 15.52/2.94 | | (46) all_80_1 = all_78_0 % 15.52/2.94 | | % 15.52/2.94 | | GROUND_INST: instantiating (4) with 0, all_78_1, all_49_4, simplifying with % 15.52/2.94 | | (13), (34) gives: % 15.52/2.94 | | (47) all_78_1 = 0 % 15.52/2.94 | | % 15.52/2.94 | | BETA: splitting (27) gives: % 15.52/2.94 | | % 15.52/2.94 | | Case 1: % 15.52/2.94 | | | % 15.52/2.94 | | | (48) ? [v0: int] : ( ~ (v0 = 0) & relation(all_49_4) = v0) % 15.52/2.94 | | | % 15.52/2.94 | | | DELTA: instantiating (48) with fresh symbol all_127_0 gives: % 15.52/2.94 | | | (49) ~ (all_127_0 = 0) & relation(all_49_4) = all_127_0 % 15.52/2.94 | | | % 15.52/2.94 | | | ALPHA: (49) implies: % 15.52/2.94 | | | (50) ~ (all_127_0 = 0) % 15.52/2.94 | | | (51) relation(all_49_4) = all_127_0 % 15.52/2.94 | | | % 15.52/2.94 | | | GROUND_INST: instantiating (4) with 0, all_127_0, all_49_4, simplifying % 15.52/2.94 | | | with (13), (51) gives: % 15.52/2.94 | | | (52) all_127_0 = 0 % 15.52/2.94 | | | % 15.52/2.94 | | | REDUCE: (50), (52) imply: % 15.52/2.94 | | | (53) $false % 15.52/2.94 | | | % 15.52/2.94 | | | CLOSE: (53) is inconsistent. % 15.52/2.94 | | | % 15.52/2.94 | | Case 2: % 15.52/2.94 | | | % 15.52/2.95 | | | (54) ? [v0: any] : (v0 = all_49_3 | ~ $i(v0) | ? [v1: $i] : ? [v2: % 15.52/2.95 | | | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] % 15.52/2.95 | | | : ! [v4: $i] : ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4, % 15.52/2.95 | | | all_49_4) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : % 15.52/2.95 | | | ? [v4: $i] : (ordered_pair(v1, v3) = v4 & in(v4, all_49_4) % 15.52/2.95 | | | = 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_49_3) | ( ! [v0: % 15.52/2.95 | | | $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_49_3) = v1) | % 15.52/2.95 | | | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, % 15.52/2.95 | | | v2) = v3) | ~ (in(v3, all_49_4) = 0) | ~ $i(v2))) & % 15.52/2.95 | | | ! [v0: $i] : ( ~ (in(v0, all_49_3) = 0) | ~ $i(v0) | ? [v1: % 15.52/2.95 | | | $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2, % 15.52/2.95 | | | all_49_4) = 0 & $i(v2) & $i(v1))))) % 15.52/2.95 | | | % 15.52/2.95 | | | ALPHA: (54) implies: % 15.52/2.95 | | | (55) ~ $i(all_49_3) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 15.52/2.95 | | | (in(v0, all_49_3) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: % 15.52/2.95 | | | $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_49_4) % 15.52/2.95 | | | = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_49_3) = % 15.52/2.95 | | | 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 15.52/2.95 | | | (ordered_pair(v0, v1) = v2 & in(v2, all_49_4) = 0 & $i(v2) & % 15.52/2.95 | | | $i(v1)))) % 15.52/2.95 | | | % 15.52/2.95 | | | BETA: splitting (55) gives: % 15.52/2.95 | | | % 15.52/2.95 | | | Case 1: % 15.52/2.95 | | | | % 15.52/2.95 | | | | (56) ~ $i(all_49_3) % 15.52/2.95 | | | | % 15.52/2.95 | | | | PRED_UNIFY: (10), (56) imply: % 15.52/2.95 | | | | (57) $false % 15.52/2.95 | | | | % 15.52/2.95 | | | | CLOSE: (57) is inconsistent. % 15.52/2.95 | | | | % 15.52/2.95 | | | Case 2: % 15.52/2.95 | | | | % 15.52/2.95 | | | | (58) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_49_3) = % 15.52/2.95 | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ % 15.52/2.95 | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_49_4) = 0) | ~ % 15.52/2.95 | | | | $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_49_3) = 0) | ~ % 15.52/2.95 | | | | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = % 15.52/2.95 | | | | v2 & in(v2, all_49_4) = 0 & $i(v2) & $i(v1))) % 15.52/2.95 | | | | % 15.52/2.95 | | | | ALPHA: (58) implies: % 15.52/2.95 | | | | (59) ! [v0: $i] : ( ~ (in(v0, all_49_3) = 0) | ~ $i(v0) | ? [v1: % 15.52/2.95 | | | | $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2, % 15.52/2.95 | | | | all_49_4) = 0 & $i(v2) & $i(v1))) % 15.52/2.95 | | | | % 15.52/2.95 | | | | GROUND_INST: instantiating (23) with all_118_1, simplifying with (43), % 15.52/2.95 | | | | (44) gives: % 15.52/2.95 | | | | (60) in(all_118_1, all_49_3) = 0 % 15.52/2.95 | | | | % 15.52/2.95 | | | | GROUND_INST: instantiating (31) with all_118_1, all_118_0, simplifying % 15.52/2.95 | | | | with (43), (45) gives: % 15.52/2.95 | | | | (61) all_118_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ % 15.52/2.95 | | | | (ordered_pair(all_118_1, v0) = v1) | ~ (in(v1, all_49_4) = 0) % 15.52/2.95 | | | | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, all_49_2) = % 15.52/2.95 | | | | v2)) % 15.52/2.95 | | | | % 15.52/2.95 | | | | BETA: splitting (61) gives: % 15.52/2.95 | | | | % 15.52/2.95 | | | | Case 1: % 15.52/2.95 | | | | | % 15.52/2.95 | | | | | (62) all_118_0 = 0 % 15.52/2.95 | | | | | % 15.52/2.95 | | | | | REDUCE: (42), (62) imply: % 15.52/2.95 | | | | | (63) $false % 15.52/2.95 | | | | | % 15.52/2.95 | | | | | CLOSE: (63) is inconsistent. % 15.52/2.95 | | | | | % 15.52/2.95 | | | | Case 2: % 15.52/2.95 | | | | | % 15.52/2.95 | | | | | (64) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(all_118_1, v0) = % 15.52/2.95 | | | | | v1) | ~ (in(v1, all_49_4) = 0) | ~ $i(v0) | ? [v2: int] % 15.52/2.95 | | | | | : ( ~ (v2 = 0) & in(v0, all_49_2) = v2)) % 15.52/2.95 | | | | | % 15.52/2.95 | | | | | GROUND_INST: instantiating (59) with all_118_1, simplifying with (43), % 15.52/2.95 | | | | | (60) gives: % 15.52/2.95 | | | | | (65) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_118_1, v0) = v1 % 15.52/2.95 | | | | | & in(v1, all_49_4) = 0 & $i(v1) & $i(v0)) % 15.52/2.95 | | | | | % 15.52/2.96 | | | | | GROUND_INST: instantiating (t7_boole) with all_118_1, all_49_3, % 15.52/2.96 | | | | | simplifying with (10), (43), (60) gives: % 15.52/2.96 | | | | | (66) ? [v0: int] : ( ~ (v0 = 0) & empty(all_49_3) = v0) % 15.52/2.96 | | | | | % 15.52/2.96 | | | | | DELTA: instantiating (66) with fresh symbol all_162_0 gives: % 15.52/2.96 | | | | | (67) ~ (all_162_0 = 0) & empty(all_49_3) = all_162_0 % 15.52/2.96 | | | | | % 15.52/2.96 | | | | | ALPHA: (67) implies: % 15.52/2.96 | | | | | (68) ~ (all_162_0 = 0) % 15.52/2.96 | | | | | (69) empty(all_49_3) = all_162_0 % 15.52/2.96 | | | | | % 15.52/2.96 | | | | | DELTA: instantiating (65) with fresh symbols all_164_0, all_164_1 % 15.52/2.96 | | | | | gives: % 15.52/2.96 | | | | | (70) ordered_pair(all_118_1, all_164_1) = all_164_0 & in(all_164_0, % 15.52/2.96 | | | | | all_49_4) = 0 & $i(all_164_0) & $i(all_164_1) % 15.52/2.96 | | | | | % 15.52/2.96 | | | | | ALPHA: (70) implies: % 15.52/2.96 | | | | | (71) $i(all_164_1) % 15.52/2.96 | | | | | (72) in(all_164_0, all_49_4) = 0 % 15.52/2.96 | | | | | (73) ordered_pair(all_118_1, all_164_1) = all_164_0 % 15.52/2.96 | | | | | % 15.52/2.96 | | | | | GROUND_INST: instantiating (3) with all_78_0, all_162_0, all_49_3, % 15.52/2.96 | | | | | simplifying with (33), (69) gives: % 15.52/2.96 | | | | | (74) all_162_0 = all_78_0 % 15.52/2.96 | | | | | % 15.52/2.96 | | | | | REDUCE: (68), (74) imply: % 15.52/2.96 | | | | | (75) ~ (all_78_0 = 0) % 15.52/2.96 | | | | | % 15.52/2.96 | | | | | BETA: splitting (37) gives: % 15.52/2.96 | | | | | % 15.52/2.96 | | | | | Case 1: % 15.52/2.96 | | | | | | % 15.52/2.96 | | | | | | % 15.52/2.96 | | | | | | GROUND_INST: instantiating (64) with all_164_1, all_164_0, % 15.52/2.96 | | | | | | simplifying with (71), (72), (73) gives: % 15.52/2.96 | | | | | | (76) ? [v0: int] : ( ~ (v0 = 0) & in(all_164_1, all_49_2) = v0) % 15.52/2.96 | | | | | | % 15.52/2.96 | | | | | | DELTA: instantiating (76) with fresh symbol all_183_0 gives: % 15.52/2.96 | | | | | | (77) ~ (all_183_0 = 0) & in(all_164_1, all_49_2) = all_183_0 % 15.52/2.96 | | | | | | % 15.52/2.96 | | | | | | ALPHA: (77) implies: % 15.52/2.96 | | | | | | (78) ~ (all_183_0 = 0) % 15.52/2.96 | | | | | | (79) in(all_164_1, all_49_2) = all_183_0 % 15.52/2.96 | | | | | | % 15.52/2.96 | | | | | | GROUND_INST: instantiating (29) with all_164_1, all_183_0, % 15.52/2.96 | | | | | | simplifying with (71), (79) gives: % 15.52/2.96 | | | | | | (80) all_183_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ % 15.52/2.96 | | | | | | (ordered_pair(v0, all_164_1) = v1) | ~ (in(v1, all_49_4) % 15.52/2.96 | | | | | | = 0) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, % 15.52/2.96 | | | | | | all_49_5) = v2)) % 15.52/2.96 | | | | | | % 15.52/2.96 | | | | | | BETA: splitting (80) gives: % 15.52/2.96 | | | | | | % 15.52/2.96 | | | | | | Case 1: % 15.52/2.96 | | | | | | | % 15.52/2.96 | | | | | | | (81) all_183_0 = 0 % 15.52/2.96 | | | | | | | % 15.52/2.96 | | | | | | | REDUCE: (78), (81) imply: % 15.52/2.96 | | | | | | | (82) $false % 15.52/2.96 | | | | | | | % 15.52/2.96 | | | | | | | CLOSE: (82) is inconsistent. % 15.52/2.96 | | | | | | | % 15.52/2.96 | | | | | | Case 2: % 15.52/2.96 | | | | | | | % 15.52/2.96 | | | | | | | (83) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, % 15.52/2.96 | | | | | | | all_164_1) = v1) | ~ (in(v1, all_49_4) = 0) | ~ % 15.52/2.96 | | | | | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, all_49_5) % 15.52/2.96 | | | | | | | = v2)) % 15.52/2.96 | | | | | | | % 15.52/2.96 | | | | | | | GROUND_INST: instantiating (83) with all_118_1, all_164_0, % 15.52/2.96 | | | | | | | simplifying with (43), (72), (73) gives: % 15.52/2.96 | | | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & in(all_118_1, all_49_5) = % 15.52/2.96 | | | | | | | v0) % 15.52/2.96 | | | | | | | % 15.52/2.96 | | | | | | | DELTA: instantiating (84) with fresh symbol all_199_0 gives: % 15.52/2.96 | | | | | | | (85) ~ (all_199_0 = 0) & in(all_118_1, all_49_5) = all_199_0 % 15.52/2.96 | | | | | | | % 15.52/2.96 | | | | | | | ALPHA: (85) implies: % 15.52/2.96 | | | | | | | (86) ~ (all_199_0 = 0) % 15.52/2.96 | | | | | | | (87) in(all_118_1, all_49_5) = all_199_0 % 15.52/2.96 | | | | | | | % 15.52/2.96 | | | | | | | GROUND_INST: instantiating (5) with 0, all_199_0, all_49_5, % 15.52/2.96 | | | | | | | all_118_1, simplifying with (44), (87) gives: % 15.52/2.96 | | | | | | | (88) all_199_0 = 0 % 15.52/2.96 | | | | | | | % 15.52/2.96 | | | | | | | REDUCE: (86), (88) imply: % 15.52/2.96 | | | | | | | (89) $false % 15.52/2.96 | | | | | | | % 15.52/2.96 | | | | | | | CLOSE: (89) is inconsistent. % 15.52/2.96 | | | | | | | % 15.52/2.96 | | | | | | End of split % 15.52/2.96 | | | | | | % 15.52/2.96 | | | | | Case 2: % 15.52/2.96 | | | | | | % 15.52/2.96 | | | | | | (90) all_80_0 = 0 & all_80_1 = 0 % 15.52/2.96 | | | | | | % 15.52/2.96 | | | | | | ALPHA: (90) implies: % 15.52/2.96 | | | | | | (91) all_80_1 = 0 % 15.52/2.96 | | | | | | % 15.52/2.96 | | | | | | COMBINE_EQS: (46), (91) imply: % 15.52/2.96 | | | | | | (92) all_78_0 = 0 % 15.52/2.96 | | | | | | % 15.52/2.96 | | | | | | SIMP: (92) implies: % 15.52/2.96 | | | | | | (93) all_78_0 = 0 % 15.52/2.96 | | | | | | % 15.52/2.96 | | | | | | REDUCE: (75), (93) imply: % 15.52/2.96 | | | | | | (94) $false % 15.52/2.96 | | | | | | % 15.52/2.96 | | | | | | CLOSE: (94) is inconsistent. % 15.52/2.96 | | | | | | % 15.52/2.96 | | | | | End of split % 15.52/2.96 | | | | | % 15.52/2.96 | | | | End of split % 15.52/2.96 | | | | % 15.52/2.96 | | | End of split % 15.52/2.96 | | | % 15.52/2.96 | | End of split % 15.52/2.96 | | % 15.52/2.96 | End of split % 15.52/2.96 | % 15.52/2.96 End of proof % 15.52/2.96 % SZS output end Proof for theBenchmark % 15.52/2.96 % 15.52/2.96 2333ms %------------------------------------------------------------------------------