%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET997+1 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n026.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 15:27:19 EDT 2023 % Result : Theorem 9.28s 2.17s % Output : Proof 17.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.14 % Problem : SET997+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.36 % Computer : n026.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.37 % DateTime : Sat Aug 26 09:09:03 EDT 2023 % 0.14/0.37 % CPUTime : % 0.21/0.64 ________ _____ % 0.21/0.64 ___ __ \_________(_)________________________________ % 0.21/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.64 % 0.21/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.64 (2023-06-19) % 0.21/0.64 % 0.21/0.64 (c) Philipp Rümmer, 2009-2023 % 0.21/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.64 Amanda Stjerna. % 0.21/0.64 Free software under BSD-3-Clause. % 0.21/0.64 % 0.21/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.64 % 0.21/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.65 Running up to 7 provers in parallel. % 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.67 Prover 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 % 2.54/1.15 Prover 4: Preprocessing ... % 2.54/1.15 Prover 1: Preprocessing ... % 3.17/1.20 Prover 0: Preprocessing ... % 3.17/1.20 Prover 6: Preprocessing ... % 3.17/1.20 Prover 2: Preprocessing ... % 3.17/1.20 Prover 3: Preprocessing ... % 3.17/1.20 Prover 5: Preprocessing ... % 6.39/1.69 Prover 1: Warning: ignoring some quantifiers % 6.39/1.77 Prover 1: Constructing countermodel ... % 6.39/1.77 Prover 5: Proving ... % 7.32/1.82 Prover 2: Proving ... % 7.32/1.84 Prover 6: Proving ... % 7.32/1.84 Prover 3: Warning: ignoring some quantifiers % 7.32/1.87 Prover 3: Constructing countermodel ... % 8.04/1.99 Prover 4: Warning: ignoring some quantifiers % 8.66/2.04 Prover 0: Proving ... % 8.66/2.04 Prover 4: Constructing countermodel ... % 9.28/2.17 Prover 3: proved (1502ms) % 9.28/2.17 % 9.28/2.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.28/2.17 % 9.28/2.17 Prover 2: stopped % 9.28/2.17 Prover 5: stopped % 9.28/2.18 Prover 6: stopped % 9.28/2.19 Prover 0: stopped % 9.28/2.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.28/2.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.28/2.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.28/2.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.28/2.21 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.31/2.27 Prover 8: Preprocessing ... % 10.31/2.27 Prover 10: Preprocessing ... % 10.31/2.28 Prover 11: Preprocessing ... % 10.31/2.28 Prover 13: Preprocessing ... % 10.31/2.29 Prover 7: Preprocessing ... % 11.01/2.37 Prover 10: Warning: ignoring some quantifiers % 11.01/2.37 Prover 13: Warning: ignoring some quantifiers % 11.01/2.38 Prover 13: Constructing countermodel ... % 11.01/2.39 Prover 10: Constructing countermodel ... % 11.39/2.40 Prover 8: Warning: ignoring some quantifiers % 11.39/2.40 Prover 7: Warning: ignoring some quantifiers % 11.39/2.42 Prover 8: Constructing countermodel ... % 11.39/2.42 Prover 7: Constructing countermodel ... % 11.76/2.54 Prover 10: gave up % 12.51/2.56 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 12.90/2.60 Prover 11: Warning: ignoring some quantifiers % 12.90/2.60 Prover 16: Preprocessing ... % 12.90/2.63 Prover 11: Constructing countermodel ... % 13.27/2.68 Prover 16: Warning: ignoring some quantifiers % 13.27/2.69 Prover 16: Constructing countermodel ... % 17.00/3.21 Prover 8: Found proof (size 104) % 17.00/3.21 Prover 8: proved (1039ms) % 17.00/3.21 Prover 4: stopped % 17.00/3.21 Prover 13: stopped % 17.00/3.21 Prover 1: stopped % 17.00/3.21 Prover 7: stopped % 17.00/3.22 Prover 16: stopped % 17.00/3.22 Prover 11: stopped % 17.00/3.22 % 17.00/3.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.00/3.22 % 17.00/3.23 % SZS output start Proof for theBenchmark % 17.00/3.23 Assumptions after simplification: % 17.00/3.23 --------------------------------- % 17.00/3.23 % 17.00/3.23 (d3_tarski) % 17.49/3.26 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 17.49/3.26 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 17.49/3.26 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 17.49/3.26 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 17.49/3.26 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 17.49/3.26 % 17.49/3.26 (d5_funct_1) % 17.49/3.27 ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] % 17.49/3.27 : ? [v3: $i] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 & % 17.49/3.27 relation(v0) = v1 & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ( ! [v4: $i] : ! % 17.49/3.27 [v5: int] : (v5 = 0 | ~ (in(v4, v2) = v5) | ~ $i(v4) | ! [v6: $i] : % 17.49/3.27 ( ~ (in(v6, v3) = 0) | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v4) & % 17.49/3.27 apply(v0, v6) = v7 & $i(v7)))) & ! [v4: $i] : ( ~ (in(v4, v2) = % 17.49/3.27 0) | ~ $i(v4) | ? [v5: $i] : (apply(v0, v5) = v4 & in(v5, v3) = % 17.49/3.27 0 & $i(v5))) & ? [v4: $i] : (v4 = v2 | ~ $i(v4) | ? [v5: $i] : % 17.49/3.27 ? [v6: any] : (in(v5, v4) = v6 & $i(v5) & ( ~ (v6 = 0) | ! [v7: $i] % 17.49/3.27 : ( ~ (in(v7, v3) = 0) | ~ $i(v7) | ? [v8: $i] : ( ~ (v8 = v5) % 17.49/3.27 & apply(v0, v7) = v8 & $i(v8)))) & (v6 = 0 | ? [v7: $i] : % 17.49/3.27 (apply(v0, v7) = v5 & in(v7, v3) = 0 & $i(v7))))))))) % 17.49/3.27 % 17.61/3.27 (fc5_relat_1) % 17.61/3.27 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 17.61/3.27 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & empty(v1) = v4 & % 17.61/3.27 empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 17.61/3.27 % 17.61/3.27 (fc6_relat_1) % 17.61/3.28 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 17.61/3.28 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & empty(v1) = v4 & % 17.61/3.28 empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 17.61/3.28 % 17.61/3.28 (fc7_relat_1) % 17.61/3.28 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 17.61/3.28 any] : ? [v3: any] : ? [v4: any] : (relation(v1) = v4 & empty(v1) = v3 & % 17.61/3.28 empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) % 17.61/3.28 % 17.61/3.28 (fc8_relat_1) % 17.61/3.28 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 17.61/3.28 any] : ? [v3: any] : ? [v4: any] : (relation(v1) = v4 & empty(v1) = v3 & % 17.61/3.28 empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) % 17.61/3.28 % 17.61/3.28 (rc1_funct_1) % 17.61/3.28 ? [v0: $i] : (relation(v0) = 0 & function(v0) = 0 & $i(v0)) % 17.61/3.28 % 17.61/3.28 (t19_funct_1) % 17.61/3.28 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 17.61/3.28 = 0) & relation_rng(v1) = v3 & relation_dom(v1) = v2 & subset(v0, v3) = v4 % 17.61/3.28 & relation(v1) = 0 & function(v1) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 17.61/3.28 ! [v5: $i] : ( ~ (in(v5, v0) = 0) | ~ $i(v5) | ? [v6: $i] : (apply(v1, v6) % 17.61/3.28 = v5 & in(v6, v2) = 0 & $i(v6)))) % 17.61/3.28 % 17.61/3.28 (function-axioms) % 17.61/3.29 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 17.61/3.29 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 17.61/3.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.61/3.29 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: MultipleValueBool] % 17.61/3.29 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.61/3.29 (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 17.61/3.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.61/3.29 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 17.61/3.29 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) % 17.61/3.29 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 17.61/3.29 $i] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ % 17.61/3.29 (relation_empty_yielding(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.61/3.29 $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & % 17.61/3.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) % 17.61/3.29 | ~ (relation_dom(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 17.61/3.29 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 17.61/3.29 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 17.61/3.29 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~ % 17.61/3.29 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 17.61/3.29 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 17.61/3.29 (empty(v2) = v0)) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : % 17.61/3.29 (element(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 17.61/3.29 MultipleValueBool] : (subset(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 17.61/3.29 [v2: MultipleValueBool] : (in(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 17.61/3.29 [v2: $i] : (apply(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: % 17.61/3.29 MultipleValueBool] : (relation_empty_yielding(v0) = v1) & ? [v0: $i] : ? % 17.61/3.29 [v1: MultipleValueBool] : (relation(v0) = v1) & ? [v0: $i] : ? [v1: % 17.61/3.29 MultipleValueBool] : (function(v0) = v1) & ? [v0: $i] : ? [v1: % 17.61/3.29 MultipleValueBool] : (empty(v0) = v1) & ? [v0: $i] : ? [v1: $i] : % 17.61/3.29 (powerset(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (relation_rng(v0) = % 17.61/3.29 v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (relation_dom(v0) = v1 & $i(v1)) % 17.61/3.29 % 17.61/3.29 Further assumptions not needed in the proof: % 17.61/3.29 -------------------------------------------- % 17.61/3.29 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, existence_m1_subset_1, % 17.61/3.29 fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1, rc1_relat_1, % 17.61/3.29 rc1_subset_1, rc1_xboole_0, rc2_relat_1, rc2_subset_1, rc2_xboole_0, % 17.61/3.29 rc3_relat_1, reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, % 17.61/3.29 t5_subset, t6_boole, t7_boole, t8_boole % 17.61/3.29 % 17.61/3.29 Those formulas are unsatisfiable: % 17.61/3.29 --------------------------------- % 17.61/3.29 % 17.61/3.29 Begin of proof % 17.61/3.30 | % 17.61/3.30 | ALPHA: (d3_tarski) implies: % 17.61/3.30 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 17.61/3.30 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 17.61/3.30 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 17.61/3.30 | % 17.61/3.30 | ALPHA: (function-axioms) implies: % 17.61/3.30 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.61/3.30 | (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 17.61/3.30 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.61/3.30 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 17.61/3.30 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 17.61/3.30 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 17.61/3.30 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 17.61/3.30 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 17.61/3.30 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.61/3.30 | (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 17.61/3.30 | % 17.61/3.30 | DELTA: instantiating (rc1_funct_1) with fresh symbol all_49_0 gives: % 17.61/3.30 | (7) relation(all_49_0) = 0 & function(all_49_0) = 0 & $i(all_49_0) % 17.61/3.30 | % 17.61/3.30 | ALPHA: (7) implies: % 17.61/3.30 | (8) $i(all_49_0) % 17.61/3.30 | (9) function(all_49_0) = 0 % 17.61/3.30 | (10) relation(all_49_0) = 0 % 17.61/3.30 | % 17.61/3.30 | DELTA: instantiating (t19_funct_1) with fresh symbols all_61_0, all_61_1, % 17.61/3.30 | all_61_2, all_61_3, all_61_4 gives: % 17.61/3.30 | (11) ~ (all_61_0 = 0) & relation_rng(all_61_3) = all_61_1 & % 17.61/3.30 | relation_dom(all_61_3) = all_61_2 & subset(all_61_4, all_61_1) = % 17.61/3.30 | all_61_0 & relation(all_61_3) = 0 & function(all_61_3) = 0 & % 17.61/3.30 | $i(all_61_1) & $i(all_61_2) & $i(all_61_3) & $i(all_61_4) & ! [v0: % 17.61/3.30 | $i] : ( ~ (in(v0, all_61_4) = 0) | ~ $i(v0) | ? [v1: $i] : % 17.61/3.30 | (apply(all_61_3, v1) = v0 & in(v1, all_61_2) = 0 & $i(v1))) % 17.61/3.30 | % 17.61/3.30 | ALPHA: (11) implies: % 17.61/3.31 | (12) ~ (all_61_0 = 0) % 17.61/3.31 | (13) $i(all_61_4) % 17.61/3.31 | (14) $i(all_61_3) % 17.61/3.31 | (15) $i(all_61_1) % 17.61/3.31 | (16) function(all_61_3) = 0 % 17.61/3.31 | (17) relation(all_61_3) = 0 % 17.61/3.31 | (18) subset(all_61_4, all_61_1) = all_61_0 % 17.61/3.31 | (19) relation_dom(all_61_3) = all_61_2 % 17.61/3.31 | (20) relation_rng(all_61_3) = all_61_1 % 17.61/3.31 | (21) ! [v0: $i] : ( ~ (in(v0, all_61_4) = 0) | ~ $i(v0) | ? [v1: $i] : % 17.61/3.31 | (apply(all_61_3, v1) = v0 & in(v1, all_61_2) = 0 & $i(v1))) % 17.61/3.31 | % 17.61/3.31 | GROUND_INST: instantiating (d5_funct_1) with all_49_0, simplifying with (8), % 17.61/3.31 | (9) gives: % 17.61/3.31 | (22) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (relation_rng(all_49_0) = % 17.61/3.31 | v1 & relation_dom(all_49_0) = v2 & relation(all_49_0) = v0 & $i(v2) % 17.61/3.31 | & $i(v1) & ( ~ (v0 = 0) | ( ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 17.61/3.31 | (in(v3, v1) = v4) | ~ $i(v3) | ! [v5: $i] : ( ~ (in(v5, v2) % 17.61/3.31 | = 0) | ~ $i(v5) | ? [v6: $i] : ( ~ (v6 = v3) & % 17.61/3.31 | apply(all_49_0, v5) = v6 & $i(v6)))) & ! [v3: $i] : ( ~ % 17.61/3.31 | (in(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(all_49_0, % 17.61/3.31 | v4) = v3 & in(v4, v2) = 0 & $i(v4))) & ? [v3: $i] : (v3 = % 17.61/3.31 | v1 | ~ $i(v3) | ? [v4: $i] : ? [v5: any] : (in(v4, v3) = v5 % 17.61/3.31 | & $i(v4) & ( ~ (v5 = 0) | ! [v6: $i] : ( ~ (in(v6, v2) = 0) % 17.61/3.31 | | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v4) & % 17.61/3.31 | apply(all_49_0, v6) = v7 & $i(v7)))) & (v5 = 0 | ? % 17.61/3.31 | [v6: $i] : (apply(all_49_0, v6) = v4 & in(v6, v2) = 0 & % 17.61/3.31 | $i(v6)))))))) % 17.61/3.31 | % 17.61/3.31 | GROUND_INST: instantiating (d5_funct_1) with all_61_3, simplifying with (14), % 17.61/3.31 | (16) gives: % 17.61/3.32 | (23) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (relation_rng(all_61_3) = % 17.61/3.32 | v1 & relation_dom(all_61_3) = v2 & relation(all_61_3) = v0 & $i(v2) % 17.61/3.32 | & $i(v1) & ( ~ (v0 = 0) | ( ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 17.61/3.32 | (in(v3, v1) = v4) | ~ $i(v3) | ! [v5: $i] : ( ~ (in(v5, v2) % 17.61/3.32 | = 0) | ~ $i(v5) | ? [v6: $i] : ( ~ (v6 = v3) & % 17.61/3.32 | apply(all_61_3, v5) = v6 & $i(v6)))) & ! [v3: $i] : ( ~ % 17.61/3.32 | (in(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(all_61_3, % 17.61/3.32 | v4) = v3 & in(v4, v2) = 0 & $i(v4))) & ? [v3: $i] : (v3 = % 17.61/3.32 | v1 | ~ $i(v3) | ? [v4: $i] : ? [v5: any] : (in(v4, v3) = v5 % 17.61/3.32 | & $i(v4) & ( ~ (v5 = 0) | ! [v6: $i] : ( ~ (in(v6, v2) = 0) % 17.61/3.32 | | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v4) & % 17.61/3.32 | apply(all_61_3, v6) = v7 & $i(v7)))) & (v5 = 0 | ? % 17.61/3.32 | [v6: $i] : (apply(all_61_3, v6) = v4 & in(v6, v2) = 0 & % 17.61/3.32 | $i(v6)))))))) % 17.61/3.32 | % 17.61/3.32 | GROUND_INST: instantiating (1) with all_61_4, all_61_1, all_61_0, simplifying % 17.61/3.32 | with (13), (15), (18) gives: % 17.61/3.32 | (24) all_61_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 17.61/3.32 | all_61_1) = v1 & in(v0, all_61_4) = 0 & $i(v0)) % 17.61/3.32 | % 17.61/3.32 | GROUND_INST: instantiating (fc5_relat_1) with all_61_3, all_61_2, simplifying % 17.61/3.32 | with (14), (19) gives: % 17.61/3.32 | (25) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_61_3) = v1 % 17.61/3.32 | & empty(all_61_2) = v2 & empty(all_61_3) = v0 & ( ~ (v2 = 0) | ~ % 17.61/3.32 | (v1 = 0) | v0 = 0)) % 17.61/3.32 | % 17.61/3.32 | GROUND_INST: instantiating (fc6_relat_1) with all_61_3, all_61_1, simplifying % 17.61/3.32 | with (14), (20) gives: % 17.61/3.32 | (26) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_61_3) = v1 % 17.61/3.32 | & empty(all_61_1) = v2 & empty(all_61_3) = v0 & ( ~ (v2 = 0) | ~ % 17.61/3.32 | (v1 = 0) | v0 = 0)) % 17.61/3.32 | % 17.61/3.32 | DELTA: instantiating (26) with fresh symbols all_70_0, all_70_1, all_70_2 % 17.61/3.32 | gives: % 17.61/3.32 | (27) relation(all_61_3) = all_70_1 & empty(all_61_1) = all_70_0 & % 17.61/3.32 | empty(all_61_3) = all_70_2 & ( ~ (all_70_0 = 0) | ~ (all_70_1 = 0) | % 17.61/3.32 | all_70_2 = 0) % 17.61/3.32 | % 17.61/3.32 | ALPHA: (27) implies: % 17.61/3.32 | (28) relation(all_61_3) = all_70_1 % 17.87/3.32 | % 17.87/3.32 | DELTA: instantiating (25) with fresh symbols all_72_0, all_72_1, all_72_2 % 17.87/3.32 | gives: % 17.87/3.32 | (29) relation(all_61_3) = all_72_1 & empty(all_61_2) = all_72_0 & % 17.87/3.32 | empty(all_61_3) = all_72_2 & ( ~ (all_72_0 = 0) | ~ (all_72_1 = 0) | % 17.87/3.32 | all_72_2 = 0) % 17.87/3.32 | % 17.87/3.32 | ALPHA: (29) implies: % 17.87/3.32 | (30) relation(all_61_3) = all_72_1 % 17.87/3.32 | % 17.87/3.32 | DELTA: instantiating (23) with fresh symbols all_78_0, all_78_1, all_78_2 % 17.87/3.32 | gives: % 17.87/3.33 | (31) relation_rng(all_61_3) = all_78_1 & relation_dom(all_61_3) = all_78_0 % 17.87/3.33 | & relation(all_61_3) = all_78_2 & $i(all_78_0) & $i(all_78_1) & ( ~ % 17.87/3.33 | (all_78_2 = 0) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, % 17.87/3.33 | all_78_1) = v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, % 17.87/3.33 | all_78_0) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ (v3 = v0) & % 17.87/3.33 | apply(all_61_3, v2) = v3 & $i(v3)))) & ! [v0: $i] : ( ~ % 17.87/3.33 | (in(v0, all_78_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 17.87/3.33 | (apply(all_61_3, v1) = v0 & in(v1, all_78_0) = 0 & $i(v1))) & ? % 17.87/3.33 | [v0: any] : (v0 = all_78_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: % 17.87/3.33 | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] % 17.87/3.33 | : ( ~ (in(v3, all_78_0) = 0) | ~ $i(v3) | ? [v4: $i] : ( ~ % 17.87/3.33 | (v4 = v1) & apply(all_61_3, v3) = v4 & $i(v4)))) & (v2 = % 17.87/3.33 | 0 | ? [v3: $i] : (apply(all_61_3, v3) = v1 & in(v3, % 17.87/3.33 | all_78_0) = 0 & $i(v3))))))) % 17.87/3.33 | % 17.87/3.33 | ALPHA: (31) implies: % 17.87/3.33 | (32) relation(all_61_3) = all_78_2 % 17.87/3.33 | (33) relation_dom(all_61_3) = all_78_0 % 17.87/3.33 | (34) relation_rng(all_61_3) = all_78_1 % 17.87/3.33 | (35) ~ (all_78_2 = 0) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, % 17.87/3.33 | all_78_1) = v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, % 17.87/3.33 | all_78_0) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ (v3 = v0) & % 17.87/3.33 | apply(all_61_3, v2) = v3 & $i(v3)))) & ! [v0: $i] : ( ~ % 17.87/3.33 | (in(v0, all_78_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 17.87/3.33 | (apply(all_61_3, v1) = v0 & in(v1, all_78_0) = 0 & $i(v1))) & ? % 17.87/3.33 | [v0: any] : (v0 = all_78_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] % 17.87/3.33 | : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ( ~ % 17.87/3.33 | (in(v3, all_78_0) = 0) | ~ $i(v3) | ? [v4: $i] : ( ~ (v4 = % 17.87/3.33 | v1) & apply(all_61_3, v3) = v4 & $i(v4)))) & (v2 = 0 | % 17.87/3.33 | ? [v3: $i] : (apply(all_61_3, v3) = v1 & in(v3, all_78_0) = 0 % 17.87/3.33 | & $i(v3)))))) % 17.87/3.33 | % 17.87/3.33 | DELTA: instantiating (22) with fresh symbols all_80_0, all_80_1, all_80_2 % 17.87/3.33 | gives: % 17.87/3.33 | (36) relation_rng(all_49_0) = all_80_1 & relation_dom(all_49_0) = all_80_0 % 17.87/3.33 | & relation(all_49_0) = all_80_2 & $i(all_80_0) & $i(all_80_1) & ( ~ % 17.87/3.33 | (all_80_2 = 0) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, % 17.87/3.33 | all_80_1) = v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, % 17.87/3.33 | all_80_0) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ (v3 = v0) & % 17.87/3.33 | apply(all_49_0, v2) = v3 & $i(v3)))) & ! [v0: $i] : ( ~ % 17.87/3.34 | (in(v0, all_80_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 17.87/3.34 | (apply(all_49_0, v1) = v0 & in(v1, all_80_0) = 0 & $i(v1))) & ? % 17.87/3.34 | [v0: any] : (v0 = all_80_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: % 17.87/3.34 | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] % 17.87/3.34 | : ( ~ (in(v3, all_80_0) = 0) | ~ $i(v3) | ? [v4: $i] : ( ~ % 17.87/3.34 | (v4 = v1) & apply(all_49_0, v3) = v4 & $i(v4)))) & (v2 = % 17.87/3.34 | 0 | ? [v3: $i] : (apply(all_49_0, v3) = v1 & in(v3, % 17.87/3.34 | all_80_0) = 0 & $i(v3))))))) % 17.87/3.34 | % 17.87/3.34 | ALPHA: (36) implies: % 17.87/3.34 | (37) relation(all_49_0) = all_80_2 % 17.87/3.34 | (38) relation_dom(all_49_0) = all_80_0 % 17.87/3.34 | (39) relation_rng(all_49_0) = all_80_1 % 17.87/3.34 | % 17.87/3.34 | BETA: splitting (24) gives: % 17.87/3.34 | % 17.87/3.34 | Case 1: % 17.87/3.34 | | % 17.87/3.34 | | (40) all_61_0 = 0 % 17.87/3.34 | | % 17.87/3.34 | | REDUCE: (12), (40) imply: % 17.87/3.34 | | (41) $false % 17.87/3.34 | | % 17.87/3.34 | | CLOSE: (41) is inconsistent. % 17.87/3.34 | | % 17.87/3.34 | Case 2: % 17.87/3.34 | | % 17.87/3.34 | | (42) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_61_1) = v1 & % 17.87/3.34 | | in(v0, all_61_4) = 0 & $i(v0)) % 17.87/3.34 | | % 17.87/3.34 | | DELTA: instantiating (42) with fresh symbols all_86_0, all_86_1 gives: % 17.87/3.34 | | (43) ~ (all_86_0 = 0) & in(all_86_1, all_61_1) = all_86_0 & in(all_86_1, % 17.87/3.34 | | all_61_4) = 0 & $i(all_86_1) % 17.87/3.34 | | % 17.87/3.34 | | ALPHA: (43) implies: % 17.87/3.34 | | (44) ~ (all_86_0 = 0) % 17.87/3.34 | | (45) $i(all_86_1) % 17.87/3.34 | | (46) in(all_86_1, all_61_4) = 0 % 17.87/3.34 | | (47) in(all_86_1, all_61_1) = all_86_0 % 17.87/3.34 | | % 17.87/3.34 | | GROUND_INST: instantiating (3) with 0, all_80_2, all_49_0, simplifying with % 17.87/3.34 | | (10), (37) gives: % 17.87/3.34 | | (48) all_80_2 = 0 % 17.87/3.34 | | % 17.87/3.34 | | GROUND_INST: instantiating (3) with 0, all_72_1, all_61_3, simplifying with % 17.87/3.34 | | (17), (30) gives: % 17.87/3.34 | | (49) all_72_1 = 0 % 17.87/3.34 | | % 17.87/3.34 | | GROUND_INST: instantiating (3) with all_72_1, all_78_2, all_61_3, % 17.87/3.34 | | simplifying with (30), (32) gives: % 17.87/3.34 | | (50) all_78_2 = all_72_1 % 17.87/3.34 | | % 17.87/3.34 | | GROUND_INST: instantiating (3) with all_70_1, all_78_2, all_61_3, % 17.87/3.34 | | simplifying with (28), (32) gives: % 17.87/3.34 | | (51) all_78_2 = all_70_1 % 17.87/3.34 | | % 17.87/3.34 | | GROUND_INST: instantiating (4) with all_61_2, all_78_0, all_61_3, % 17.87/3.34 | | simplifying with (19), (33) gives: % 17.87/3.34 | | (52) all_78_0 = all_61_2 % 17.87/3.34 | | % 17.87/3.34 | | GROUND_INST: instantiating (5) with all_61_1, all_78_1, all_61_3, % 17.87/3.34 | | simplifying with (20), (34) gives: % 17.87/3.34 | | (53) all_78_1 = all_61_1 % 17.87/3.34 | | % 17.87/3.34 | | COMBINE_EQS: (50), (51) imply: % 17.87/3.34 | | (54) all_72_1 = all_70_1 % 17.87/3.34 | | % 17.87/3.34 | | SIMP: (54) implies: % 17.87/3.34 | | (55) all_72_1 = all_70_1 % 17.87/3.34 | | % 17.87/3.34 | | COMBINE_EQS: (49), (55) imply: % 17.87/3.34 | | (56) all_70_1 = 0 % 17.87/3.34 | | % 17.87/3.34 | | COMBINE_EQS: (51), (56) imply: % 17.87/3.34 | | (57) all_78_2 = 0 % 17.87/3.34 | | % 17.87/3.34 | | BETA: splitting (35) gives: % 17.87/3.34 | | % 17.87/3.34 | | Case 1: % 17.87/3.34 | | | % 17.87/3.35 | | | (58) ~ (all_78_2 = 0) % 17.87/3.35 | | | % 17.87/3.35 | | | REDUCE: (57), (58) imply: % 17.87/3.35 | | | (59) $false % 17.87/3.35 | | | % 17.87/3.35 | | | CLOSE: (59) is inconsistent. % 17.87/3.35 | | | % 17.87/3.35 | | Case 2: % 17.87/3.35 | | | % 17.98/3.35 | | | (60) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_78_1) = v1) % 17.98/3.35 | | | | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, all_78_0) = 0) | ~ % 17.98/3.35 | | | $i(v2) | ? [v3: $i] : ( ~ (v3 = v0) & apply(all_61_3, v2) = % 17.98/3.35 | | | v3 & $i(v3)))) & ! [v0: $i] : ( ~ (in(v0, all_78_1) = 0) | % 17.98/3.35 | | | ~ $i(v0) | ? [v1: $i] : (apply(all_61_3, v1) = v0 & in(v1, % 17.98/3.35 | | | all_78_0) = 0 & $i(v1))) & ? [v0: any] : (v0 = all_78_1 | % 17.98/3.35 | | | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1, v0) = v2 & % 17.98/3.35 | | | $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ( ~ (in(v3, all_78_0) = % 17.98/3.35 | | | 0) | ~ $i(v3) | ? [v4: $i] : ( ~ (v4 = v1) & % 17.98/3.35 | | | apply(all_61_3, v3) = v4 & $i(v4)))) & (v2 = 0 | ? [v3: % 17.98/3.35 | | | $i] : (apply(all_61_3, v3) = v1 & in(v3, all_78_0) = 0 & % 17.98/3.35 | | | $i(v3))))) % 17.98/3.35 | | | % 17.98/3.35 | | | ALPHA: (60) implies: % 17.98/3.35 | | | (61) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_78_1) = v1) % 17.98/3.35 | | | | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, all_78_0) = 0) | ~ % 17.98/3.35 | | | $i(v2) | ? [v3: $i] : ( ~ (v3 = v0) & apply(all_61_3, v2) = % 17.98/3.35 | | | v3 & $i(v3)))) % 17.98/3.35 | | | % 17.98/3.35 | | | GROUND_INST: instantiating (21) with all_86_1, simplifying with (45), (46) % 17.98/3.35 | | | gives: % 17.98/3.35 | | | (62) ? [v0: $i] : (apply(all_61_3, v0) = all_86_1 & in(v0, all_61_2) = % 17.98/3.35 | | | 0 & $i(v0)) % 17.98/3.35 | | | % 17.98/3.35 | | | GROUND_INST: instantiating (fc7_relat_1) with all_49_0, all_80_0, % 17.98/3.35 | | | simplifying with (8), (38) gives: % 17.98/3.35 | | | (63) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_80_0) = % 17.98/3.35 | | | v2 & empty(all_80_0) = v1 & empty(all_49_0) = v0 & ( ~ (v0 = 0) % 17.98/3.35 | | | | (v2 = 0 & v1 = 0))) % 17.98/3.35 | | | % 17.98/3.35 | | | GROUND_INST: instantiating (fc8_relat_1) with all_49_0, all_80_1, % 17.98/3.35 | | | simplifying with (8), (39) gives: % 17.98/3.35 | | | (64) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_80_1) = % 17.98/3.35 | | | v2 & empty(all_80_1) = v1 & empty(all_49_0) = v0 & ( ~ (v0 = 0) % 17.98/3.35 | | | | (v2 = 0 & v1 = 0))) % 17.98/3.35 | | | % 17.98/3.35 | | | GROUND_INST: instantiating (fc6_relat_1) with all_49_0, all_80_1, % 17.98/3.35 | | | simplifying with (8), (39) gives: % 17.98/3.35 | | | (65) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_49_0) = % 17.98/3.35 | | | v1 & empty(all_80_1) = v2 & empty(all_49_0) = v0 & ( ~ (v2 = 0) % 17.98/3.35 | | | | ~ (v1 = 0) | v0 = 0)) % 17.98/3.35 | | | % 17.98/3.35 | | | DELTA: instantiating (62) with fresh symbol all_112_0 gives: % 17.98/3.35 | | | (66) apply(all_61_3, all_112_0) = all_86_1 & in(all_112_0, all_61_2) = % 17.98/3.35 | | | 0 & $i(all_112_0) % 17.98/3.35 | | | % 17.98/3.35 | | | ALPHA: (66) implies: % 17.98/3.35 | | | (67) $i(all_112_0) % 17.98/3.35 | | | (68) in(all_112_0, all_61_2) = 0 % 17.98/3.35 | | | (69) apply(all_61_3, all_112_0) = all_86_1 % 17.98/3.35 | | | % 17.98/3.35 | | | DELTA: instantiating (64) with fresh symbols all_114_0, all_114_1, % 17.98/3.35 | | | all_114_2 gives: % 17.98/3.35 | | | (70) relation(all_80_1) = all_114_0 & empty(all_80_1) = all_114_1 & % 17.98/3.35 | | | empty(all_49_0) = all_114_2 & ( ~ (all_114_2 = 0) | (all_114_0 = 0 % 17.98/3.35 | | | & all_114_1 = 0)) % 17.98/3.35 | | | % 17.98/3.35 | | | ALPHA: (70) implies: % 17.98/3.36 | | | (71) empty(all_49_0) = all_114_2 % 17.98/3.36 | | | (72) ~ (all_114_2 = 0) | (all_114_0 = 0 & all_114_1 = 0) % 17.98/3.36 | | | % 17.98/3.36 | | | DELTA: instantiating (65) with fresh symbols all_118_0, all_118_1, % 17.98/3.36 | | | all_118_2 gives: % 17.98/3.36 | | | (73) relation(all_49_0) = all_118_1 & empty(all_80_1) = all_118_0 & % 17.98/3.36 | | | empty(all_49_0) = all_118_2 & ( ~ (all_118_0 = 0) | ~ (all_118_1 % 17.98/3.36 | | | = 0) | all_118_2 = 0) % 17.98/3.36 | | | % 17.98/3.36 | | | ALPHA: (73) implies: % 17.98/3.36 | | | (74) empty(all_49_0) = all_118_2 % 17.98/3.36 | | | (75) relation(all_49_0) = all_118_1 % 17.98/3.36 | | | (76) ~ (all_118_0 = 0) | ~ (all_118_1 = 0) | all_118_2 = 0 % 17.98/3.36 | | | % 17.98/3.36 | | | DELTA: instantiating (63) with fresh symbols all_120_0, all_120_1, % 17.98/3.36 | | | all_120_2 gives: % 17.98/3.36 | | | (77) relation(all_80_0) = all_120_0 & empty(all_80_0) = all_120_1 & % 17.98/3.36 | | | empty(all_49_0) = all_120_2 & ( ~ (all_120_2 = 0) | (all_120_0 = 0 % 17.98/3.36 | | | & all_120_1 = 0)) % 17.98/3.36 | | | % 17.98/3.36 | | | ALPHA: (77) implies: % 17.98/3.36 | | | (78) empty(all_49_0) = all_120_2 % 17.98/3.36 | | | % 17.98/3.36 | | | GROUND_INST: instantiating (2) with all_118_2, all_120_2, all_49_0, % 17.98/3.36 | | | simplifying with (74), (78) gives: % 17.98/3.36 | | | (79) all_120_2 = all_118_2 % 17.98/3.36 | | | % 17.98/3.36 | | | GROUND_INST: instantiating (2) with all_114_2, all_120_2, all_49_0, % 17.98/3.36 | | | simplifying with (71), (78) gives: % 17.98/3.36 | | | (80) all_120_2 = all_114_2 % 17.98/3.36 | | | % 17.98/3.36 | | | GROUND_INST: instantiating (3) with 0, all_118_1, all_49_0, simplifying % 17.98/3.36 | | | with (10), (75) gives: % 17.98/3.36 | | | (81) all_118_1 = 0 % 17.98/3.36 | | | % 17.98/3.36 | | | COMBINE_EQS: (79), (80) imply: % 17.98/3.36 | | | (82) all_118_2 = all_114_2 % 17.98/3.36 | | | % 17.98/3.36 | | | BETA: splitting (72) gives: % 17.98/3.36 | | | % 17.98/3.36 | | | Case 1: % 17.98/3.36 | | | | % 17.98/3.36 | | | | (83) ~ (all_114_2 = 0) % 17.98/3.36 | | | | % 17.98/3.36 | | | | BETA: splitting (76) gives: % 17.98/3.36 | | | | % 17.98/3.36 | | | | Case 1: % 17.98/3.36 | | | | | % 17.98/3.36 | | | | | % 17.98/3.36 | | | | | GROUND_INST: instantiating (61) with all_86_1, all_86_0, simplifying % 17.98/3.36 | | | | | with (45) gives: % 17.98/3.36 | | | | | (84) all_86_0 = 0 | ~ (in(all_86_1, all_78_1) = all_86_0) | ! % 17.98/3.36 | | | | | [v0: $i] : ( ~ (in(v0, all_78_0) = 0) | ~ $i(v0) | ? [v1: % 17.98/3.36 | | | | | any] : ( ~ (v1 = all_86_1) & apply(all_61_3, v0) = v1 & % 17.98/3.36 | | | | | $i(v1))) % 17.98/3.36 | | | | | % 17.98/3.36 | | | | | REF_CLOSE: (6), (44), (47), (52), (53), (67), (68), (69), (84) are % 17.98/3.36 | | | | | inconsistent by sub-proof #1. % 17.98/3.36 | | | | | % 17.98/3.36 | | | | Case 2: % 17.98/3.36 | | | | | % 17.98/3.36 | | | | | (85) ~ (all_118_1 = 0) | all_118_2 = 0 % 17.98/3.36 | | | | | % 17.98/3.36 | | | | | BETA: splitting (85) gives: % 17.98/3.36 | | | | | % 17.98/3.36 | | | | | Case 1: % 17.98/3.36 | | | | | | % 17.98/3.36 | | | | | | (86) ~ (all_118_1 = 0) % 17.98/3.36 | | | | | | % 17.98/3.36 | | | | | | REDUCE: (81), (86) imply: % 17.98/3.36 | | | | | | (87) $false % 17.98/3.36 | | | | | | % 17.98/3.36 | | | | | | CLOSE: (87) is inconsistent. % 17.98/3.36 | | | | | | % 17.98/3.36 | | | | | Case 2: % 17.98/3.36 | | | | | | % 17.98/3.36 | | | | | | (88) all_118_2 = 0 % 17.98/3.36 | | | | | | % 17.98/3.36 | | | | | | COMBINE_EQS: (82), (88) imply: % 17.98/3.36 | | | | | | (89) all_114_2 = 0 % 17.98/3.36 | | | | | | % 17.98/3.36 | | | | | | SIMP: (89) implies: % 17.98/3.36 | | | | | | (90) all_114_2 = 0 % 17.98/3.36 | | | | | | % 17.98/3.36 | | | | | | REDUCE: (83), (90) imply: % 17.98/3.36 | | | | | | (91) $false % 17.98/3.36 | | | | | | % 17.98/3.36 | | | | | | CLOSE: (91) is inconsistent. % 17.98/3.36 | | | | | | % 17.98/3.36 | | | | | End of split % 17.98/3.36 | | | | | % 17.98/3.36 | | | | End of split % 17.98/3.36 | | | | % 17.98/3.36 | | | Case 2: % 17.98/3.36 | | | | % 17.98/3.36 | | | | % 17.98/3.36 | | | | GROUND_INST: instantiating (61) with all_86_1, all_86_0, simplifying % 17.98/3.36 | | | | with (45) gives: % 17.98/3.36 | | | | (92) all_86_0 = 0 | ~ (in(all_86_1, all_78_1) = all_86_0) | ! [v0: % 17.98/3.36 | | | | $i] : ( ~ (in(v0, all_78_0) = 0) | ~ $i(v0) | ? [v1: any] : % 17.98/3.36 | | | | ( ~ (v1 = all_86_1) & apply(all_61_3, v0) = v1 & $i(v1))) % 17.98/3.36 | | | | % 17.98/3.36 | | | | REF_CLOSE: (6), (44), (47), (52), (53), (67), (68), (69), (92) are % 17.98/3.36 | | | | inconsistent by sub-proof #1. % 17.98/3.36 | | | | % 17.98/3.36 | | | End of split % 17.98/3.36 | | | % 17.98/3.36 | | End of split % 17.98/3.36 | | % 17.98/3.36 | End of split % 17.98/3.36 | % 17.98/3.36 End of proof % 17.98/3.37 % 17.98/3.37 Sub-proof #1 shows that the following formulas are inconsistent: % 17.98/3.37 ---------------------------------------------------------------- % 17.98/3.37 (1) $i(all_112_0) % 17.98/3.37 (2) all_78_0 = all_61_2 % 17.98/3.37 (3) all_78_1 = all_61_1 % 17.98/3.37 (4) in(all_86_1, all_61_1) = all_86_0 % 17.98/3.37 (5) all_86_0 = 0 | ~ (in(all_86_1, all_78_1) = all_86_0) | ! [v0: $i] : ( ~ % 17.98/3.37 (in(v0, all_78_0) = 0) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_86_1) % 17.98/3.37 & apply(all_61_3, v0) = v1 & $i(v1))) % 17.98/3.37 (6) ~ (all_86_0 = 0) % 17.98/3.37 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.98/3.37 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 17.98/3.37 (8) in(all_112_0, all_61_2) = 0 % 17.98/3.37 (9) apply(all_61_3, all_112_0) = all_86_1 % 17.98/3.37 % 17.98/3.37 Begin of proof % 17.98/3.37 | % 17.98/3.37 | BETA: splitting (5) gives: % 17.98/3.37 | % 17.98/3.37 | Case 1: % 17.98/3.37 | | % 17.98/3.37 | | (10) ~ (in(all_86_1, all_78_1) = all_86_0) % 17.98/3.37 | | % 17.98/3.37 | | REDUCE: (3), (10) imply: % 17.98/3.37 | | (11) ~ (in(all_86_1, all_61_1) = all_86_0) % 17.98/3.37 | | % 17.98/3.37 | | PRED_UNIFY: (4), (11) imply: % 17.98/3.37 | | (12) $false % 17.98/3.37 | | % 17.98/3.37 | | CLOSE: (12) is inconsistent. % 17.98/3.37 | | % 17.98/3.37 | Case 2: % 17.98/3.37 | | % 17.98/3.37 | | (13) all_86_0 = 0 | ! [v0: $i] : ( ~ (in(v0, all_78_0) = 0) | ~ $i(v0) % 17.98/3.37 | | | ? [v1: any] : ( ~ (v1 = all_86_1) & apply(all_61_3, v0) = v1 & % 17.98/3.37 | | $i(v1))) % 17.98/3.37 | | % 17.98/3.37 | | BETA: splitting (13) gives: % 17.98/3.37 | | % 17.98/3.37 | | Case 1: % 17.98/3.37 | | | % 17.98/3.37 | | | (14) all_86_0 = 0 % 17.98/3.37 | | | % 17.98/3.37 | | | REDUCE: (6), (14) imply: % 17.98/3.37 | | | (15) $false % 17.98/3.37 | | | % 17.98/3.37 | | | CLOSE: (15) is inconsistent. % 17.98/3.37 | | | % 17.98/3.37 | | Case 2: % 17.98/3.37 | | | % 17.98/3.37 | | | (16) ! [v0: $i] : ( ~ (in(v0, all_78_0) = 0) | ~ $i(v0) | ? [v1: % 17.98/3.37 | | | any] : ( ~ (v1 = all_86_1) & apply(all_61_3, v0) = v1 & % 17.98/3.37 | | | $i(v1))) % 17.98/3.37 | | | % 17.98/3.37 | | | GROUND_INST: instantiating (16) with all_112_0, simplifying with (1) % 17.98/3.37 | | | gives: % 17.98/3.37 | | | (17) ~ (in(all_112_0, all_78_0) = 0) | ? [v0: any] : ( ~ (v0 = % 17.98/3.37 | | | all_86_1) & apply(all_61_3, all_112_0) = v0 & $i(v0)) % 17.98/3.37 | | | % 17.98/3.37 | | | BETA: splitting (17) gives: % 17.98/3.37 | | | % 17.98/3.37 | | | Case 1: % 17.98/3.37 | | | | % 17.98/3.37 | | | | (18) ~ (in(all_112_0, all_78_0) = 0) % 17.98/3.37 | | | | % 17.98/3.37 | | | | REDUCE: (2), (18) imply: % 17.98/3.37 | | | | (19) ~ (in(all_112_0, all_61_2) = 0) % 17.98/3.37 | | | | % 17.98/3.37 | | | | PRED_UNIFY: (8), (19) imply: % 17.98/3.37 | | | | (20) $false % 17.98/3.37 | | | | % 17.98/3.37 | | | | CLOSE: (20) is inconsistent. % 17.98/3.37 | | | | % 17.98/3.37 | | | Case 2: % 17.98/3.37 | | | | % 17.98/3.37 | | | | (21) ? [v0: any] : ( ~ (v0 = all_86_1) & apply(all_61_3, all_112_0) % 17.98/3.37 | | | | = v0 & $i(v0)) % 17.98/3.37 | | | | % 17.98/3.37 | | | | DELTA: instantiating (21) with fresh symbol all_291_0 gives: % 17.98/3.37 | | | | (22) ~ (all_291_0 = all_86_1) & apply(all_61_3, all_112_0) = % 17.98/3.37 | | | | all_291_0 & $i(all_291_0) % 17.98/3.37 | | | | % 17.98/3.37 | | | | ALPHA: (22) implies: % 17.98/3.37 | | | | (23) ~ (all_291_0 = all_86_1) % 17.98/3.37 | | | | (24) apply(all_61_3, all_112_0) = all_291_0 % 17.98/3.37 | | | | % 17.98/3.37 | | | | GROUND_INST: instantiating (7) with all_86_1, all_291_0, all_112_0, % 17.98/3.37 | | | | all_61_3, simplifying with (9), (24) gives: % 17.98/3.37 | | | | (25) all_291_0 = all_86_1 % 17.98/3.37 | | | | % 17.98/3.37 | | | | REDUCE: (23), (25) imply: % 17.98/3.37 | | | | (26) $false % 17.98/3.37 | | | | % 17.98/3.37 | | | | CLOSE: (26) is inconsistent. % 17.98/3.37 | | | | % 17.98/3.37 | | | End of split % 17.98/3.37 | | | % 17.98/3.37 | | End of split % 17.98/3.37 | | % 17.98/3.37 | End of split % 17.98/3.37 | % 17.98/3.37 End of proof % 17.98/3.37 % SZS output end Proof for theBenchmark % 17.98/3.37 % 17.98/3.37 2733ms %------------------------------------------------------------------------------