%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU077+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 : n024.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 17:42:28 EDT 2023 % Result : Theorem 11.79s 2.27s % Output : Proof 15.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU077+1 : TPTP v8.1.2. Released v3.2.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n024.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Aug 23 18:13:24 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.42/1.07 Prover 1: Preprocessing ... % 2.42/1.07 Prover 4: Preprocessing ... % 3.16/1.11 Prover 3: Preprocessing ... % 3.16/1.11 Prover 2: Preprocessing ... % 3.16/1.11 Prover 6: Preprocessing ... % 3.16/1.11 Prover 0: Preprocessing ... % 3.16/1.11 Prover 5: Preprocessing ... % 6.64/1.59 Prover 1: Warning: ignoring some quantifiers % 7.10/1.65 Prover 1: Constructing countermodel ... % 7.10/1.65 Prover 5: Proving ... % 7.10/1.69 Prover 6: Proving ... % 7.10/1.69 Prover 3: Warning: ignoring some quantifiers % 7.10/1.71 Prover 3: Constructing countermodel ... % 8.26/1.80 Prover 2: Proving ... % 9.37/1.93 Prover 4: Warning: ignoring some quantifiers % 9.37/1.99 Prover 4: Constructing countermodel ... % 9.37/2.03 Prover 0: Proving ... % 11.50/2.26 Prover 3: proved (1628ms) % 11.50/2.27 % 11.79/2.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.79/2.27 % 11.79/2.27 Prover 2: stopped % 11.79/2.27 Prover 0: stopped % 11.79/2.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.79/2.27 Prover 6: stopped % 11.79/2.27 Prover 5: stopped % 11.79/2.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.79/2.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.79/2.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.79/2.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.79/2.34 Prover 10: Preprocessing ... % 11.79/2.34 Prover 7: Preprocessing ... % 12.27/2.34 Prover 13: Preprocessing ... % 12.27/2.36 Prover 11: Preprocessing ... % 12.27/2.36 Prover 8: Preprocessing ... % 12.50/2.42 Prover 10: Warning: ignoring some quantifiers % 12.91/2.44 Prover 10: Constructing countermodel ... % 13.13/2.46 Prover 13: Warning: ignoring some quantifiers % 13.13/2.46 Prover 7: Warning: ignoring some quantifiers % 13.13/2.50 Prover 7: Constructing countermodel ... % 13.13/2.51 Prover 8: Warning: ignoring some quantifiers % 13.13/2.52 Prover 13: Constructing countermodel ... % 13.13/2.52 Prover 8: Constructing countermodel ... % 14.54/2.67 Prover 1: Found proof (size 91) % 14.54/2.67 Prover 1: proved (2045ms) % 14.54/2.68 Prover 10: stopped % 14.54/2.68 Prover 4: stopped % 14.54/2.68 Prover 8: stopped % 14.54/2.68 Prover 7: stopped % 14.54/2.68 Prover 13: stopped % 14.54/2.69 Prover 11: Warning: ignoring some quantifiers % 14.54/2.70 Prover 11: Constructing countermodel ... % 14.54/2.71 Prover 11: stopped % 14.54/2.71 % 14.54/2.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.54/2.71 % 14.54/2.72 % SZS output start Proof for theBenchmark % 14.86/2.73 Assumptions after simplification: % 14.86/2.73 --------------------------------- % 14.86/2.73 % 14.86/2.73 (d13_funct_1) % 14.86/2.76 ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] % 14.86/2.76 : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~ (v1 = 0) | ( ? % 14.86/2.76 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~ % 14.86/2.76 (relation_inverse_image(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ? % 14.86/2.76 [v6: $i] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: any] % 14.86/2.76 : (apply(v0, v6) = v9 & in(v9, v4) = v10 & in(v6, v3) = v7 & in(v6, % 14.86/2.76 v2) = v8 & $i(v9) & $i(v6) & ( ~ (v10 = 0) | ~ (v8 = 0) | ~ % 14.86/2.76 (v7 = 0)) & (v7 = 0 | (v10 = 0 & v8 = 0)))) & ! [v3: $i] : ! % 14.86/2.76 [v4: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ $i(v4) | ~ % 14.86/2.76 $i(v3) | ( ! [v5: $i] : ! [v6: $i] : ! [v7: any] : ( ~ (apply(v0, % 14.86/2.76 v5) = v6) | ~ (in(v6, v3) = v7) | ~ $i(v5) | ? [v8: any] % 14.86/2.76 : ? [v9: any] : (in(v5, v4) = v8 & in(v5, v2) = v9 & ( ~ (v8 = % 14.86/2.76 0) | (v9 = 0 & v7 = 0)))) & ! [v5: $i] : ! [v6: $i] : ( % 14.86/2.76 ~ (apply(v0, v5) = v6) | ~ (in(v6, v3) = 0) | ~ $i(v5) | ? % 14.86/2.76 [v7: any] : ? [v8: any] : (in(v5, v4) = v8 & in(v5, v2) = v7 & % 14.86/2.76 ( ~ (v7 = 0) | v8 = 0))))))))) % 14.86/2.76 % 14.86/2.76 (d3_tarski) % 14.86/2.76 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 14.86/2.76 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 14.86/2.76 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 14.86/2.76 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 14.86/2.76 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 14.86/2.76 % 14.86/2.76 (d5_funct_1) % 14.86/2.77 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 14.86/2.77 any] : ? [v3: any] : ? [v4: $i] : (relation_dom(v0) = v4 & relation(v0) % 14.86/2.77 = v2 & function(v0) = v3 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | ( ? [v5: % 14.86/2.77 $i] : (v5 = v1 | ~ $i(v5) | ? [v6: $i] : ? [v7: any] : (in(v6, % 14.86/2.77 v5) = v7 & $i(v6) & ( ~ (v7 = 0) | ! [v8: $i] : ( ~ (in(v8, v4) % 14.86/2.77 = 0) | ~ $i(v8) | ? [v9: $i] : ( ~ (v9 = v6) & apply(v0, % 14.86/2.77 v8) = v9 & $i(v9)))) & (v7 = 0 | ? [v8: $i] : (apply(v0, % 14.86/2.77 v8) = v6 & in(v8, v4) = 0 & $i(v8))))) & ( ~ $i(v1) | ( ! % 14.86/2.77 [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (in(v5, v1) = v6) | ~ % 14.86/2.77 $i(v5) | ! [v7: $i] : ( ~ (in(v7, v4) = 0) | ~ $i(v7) | ? % 14.86/2.77 [v8: $i] : ( ~ (v8 = v5) & apply(v0, v7) = v8 & $i(v8)))) & ! % 14.86/2.77 [v5: $i] : ( ~ (in(v5, v1) = 0) | ~ $i(v5) | ? [v6: $i] : % 14.86/2.77 (apply(v0, v6) = v5 & in(v6, v4) = 0 & $i(v6))))))))) % 14.86/2.77 % 14.86/2.77 (fc6_relat_1) % 14.86/2.77 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 14.86/2.77 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & empty(v1) = v4 & % 14.86/2.77 empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 14.86/2.77 % 14.86/2.77 (t158_funct_1) % 14.86/2.77 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 14.86/2.77 $i] : ? [v6: int] : ( ~ (v6 = 0) & relation_rng(v2) = v5 & subset(v3, v4) = % 14.86/2.77 0 & subset(v0, v5) = 0 & subset(v0, v1) = v6 & relation_inverse_image(v2, % 14.86/2.77 v1) = v4 & relation_inverse_image(v2, v0) = v3 & relation(v2) = 0 & % 14.86/2.77 function(v2) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 14.86/2.77 % 14.86/2.77 (function-axioms) % 14.86/2.77 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 14.86/2.77 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 14.86/2.77 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 14.86/2.77 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 14.86/2.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.86/2.77 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = % 14.86/2.77 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 14.86/2.77 ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: % 14.86/2.77 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.86/2.77 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 14.86/2.77 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) % 14.86/2.77 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.86/2.77 $i] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ % 14.86/2.77 (relation_empty_yielding(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 14.86/2.77 $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & % 14.86/2.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) % 14.86/2.77 | ~ (relation_dom(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.77 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ % 14.86/2.77 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.77 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 14.86/2.77 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.77 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~ % 14.86/2.77 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.77 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 14.86/2.77 (empty(v2) = v0)) % 14.86/2.77 % 14.86/2.77 Further assumptions not needed in the proof: % 14.86/2.77 -------------------------------------------- % 14.86/2.77 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, % 14.86/2.77 existence_m1_subset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1, % 14.86/2.77 fc5_relat_1, fc7_relat_1, fc8_relat_1, rc1_funct_1, rc1_relat_1, rc1_subset_1, % 14.86/2.77 rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1, % 14.86/2.77 rc3_relat_1, reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, % 14.86/2.77 t5_subset, t6_boole, t7_boole, t8_boole % 14.86/2.77 % 14.86/2.77 Those formulas are unsatisfiable: % 14.86/2.77 --------------------------------- % 14.86/2.77 % 14.86/2.77 Begin of proof % 14.86/2.77 | % 14.86/2.77 | ALPHA: (d3_tarski) implies: % 14.86/2.78 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 14.86/2.78 | $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) = 0) | ~ $i(v2) | in(v2, v1) % 14.86/2.78 | = 0)) % 14.86/2.78 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 14.86/2.78 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 14.86/2.78 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 14.86/2.78 | % 14.86/2.78 | ALPHA: (function-axioms) implies: % 14.86/2.78 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.86/2.78 | (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 14.86/2.78 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.86/2.78 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 14.86/2.78 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 14.86/2.78 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 14.86/2.78 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.86/2.78 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 14.86/2.78 | % 14.86/2.78 | DELTA: instantiating (t158_funct_1) with fresh symbols all_45_0, all_45_1, % 14.86/2.78 | all_45_2, all_45_3, all_45_4, all_45_5, all_45_6 gives: % 14.86/2.78 | (7) ~ (all_45_0 = 0) & relation_rng(all_45_4) = all_45_1 & % 15.30/2.78 | subset(all_45_3, all_45_2) = 0 & subset(all_45_6, all_45_1) = 0 & % 15.30/2.78 | subset(all_45_6, all_45_5) = all_45_0 & % 15.30/2.78 | relation_inverse_image(all_45_4, all_45_5) = all_45_2 & % 15.30/2.78 | relation_inverse_image(all_45_4, all_45_6) = all_45_3 & % 15.30/2.78 | relation(all_45_4) = 0 & function(all_45_4) = 0 & $i(all_45_1) & % 15.30/2.78 | $i(all_45_2) & $i(all_45_3) & $i(all_45_4) & $i(all_45_5) & % 15.30/2.78 | $i(all_45_6) % 15.30/2.78 | % 15.30/2.78 | ALPHA: (7) implies: % 15.30/2.78 | (8) ~ (all_45_0 = 0) % 15.30/2.78 | (9) $i(all_45_6) % 15.30/2.78 | (10) $i(all_45_5) % 15.30/2.78 | (11) $i(all_45_4) % 15.30/2.78 | (12) $i(all_45_3) % 15.30/2.78 | (13) $i(all_45_2) % 15.30/2.78 | (14) $i(all_45_1) % 15.30/2.78 | (15) function(all_45_4) = 0 % 15.30/2.78 | (16) relation(all_45_4) = 0 % 15.30/2.78 | (17) relation_inverse_image(all_45_4, all_45_6) = all_45_3 % 15.30/2.78 | (18) relation_inverse_image(all_45_4, all_45_5) = all_45_2 % 15.30/2.78 | (19) subset(all_45_6, all_45_5) = all_45_0 % 15.30/2.78 | (20) subset(all_45_6, all_45_1) = 0 % 15.30/2.78 | (21) subset(all_45_3, all_45_2) = 0 % 15.30/2.78 | (22) relation_rng(all_45_4) = all_45_1 % 15.30/2.78 | % 15.30/2.78 | GROUND_INST: instantiating (d13_funct_1) with all_45_4, simplifying with (11), % 15.30/2.78 | (15) gives: % 15.30/2.79 | (23) ? [v0: any] : ? [v1: $i] : (relation_dom(all_45_4) = v1 & % 15.30/2.79 | relation(all_45_4) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : ! % 15.30/2.79 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ % 15.30/2.79 | (relation_inverse_image(all_45_4, v3) = v4) | ~ $i(v3) | ~ % 15.30/2.79 | $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: % 15.30/2.79 | $i] : ? [v9: any] : (apply(all_45_4, v5) = v8 & in(v8, v3) % 15.30/2.79 | = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & $i(v5) & % 15.30/2.79 | ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 | (v9 = % 15.30/2.79 | 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 15.30/2.79 | (relation_inverse_image(all_45_4, v2) = v3) | ~ $i(v3) | ~ % 15.30/2.79 | $i(v2) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~ % 15.30/2.79 | (apply(all_45_4, v4) = v5) | ~ (in(v5, v2) = v6) | ~ % 15.30/2.79 | $i(v4) | ? [v7: any] : ? [v8: any] : (in(v4, v3) = v7 & % 15.30/2.79 | in(v4, v1) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) & % 15.30/2.79 | ! [v4: $i] : ! [v5: $i] : ( ~ (apply(all_45_4, v4) = v5) | % 15.30/2.79 | ~ (in(v5, v2) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7: % 15.30/2.79 | any] : (in(v4, v3) = v7 & in(v4, v1) = v6 & ( ~ (v6 = 0) % 15.30/2.79 | | v7 = 0)))))))) % 15.30/2.79 | % 15.30/2.79 | GROUND_INST: instantiating (2) with all_45_6, all_45_5, all_45_0, simplifying % 15.30/2.79 | with (9), (10), (19) gives: % 15.30/2.79 | (24) all_45_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 15.30/2.79 | all_45_5) = v1 & in(v0, all_45_6) = 0 & $i(v0)) % 15.30/2.79 | % 15.30/2.79 | GROUND_INST: instantiating (1) with all_45_6, all_45_1, simplifying with (9), % 15.30/2.79 | (14), (20) gives: % 15.30/2.79 | (25) ! [v0: $i] : ( ~ (in(v0, all_45_6) = 0) | ~ $i(v0) | in(v0, % 15.30/2.79 | all_45_1) = 0) % 15.30/2.79 | % 15.30/2.79 | GROUND_INST: instantiating (1) with all_45_3, all_45_2, simplifying with (12), % 15.30/2.79 | (13), (21) gives: % 15.30/2.79 | (26) ! [v0: $i] : ( ~ (in(v0, all_45_3) = 0) | ~ $i(v0) | in(v0, % 15.30/2.79 | all_45_2) = 0) % 15.30/2.79 | % 15.30/2.79 | GROUND_INST: instantiating (d5_funct_1) with all_45_4, all_45_1, simplifying % 15.30/2.79 | with (11), (22) gives: % 15.30/2.79 | (27) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (relation_dom(all_45_4) = % 15.30/2.79 | v2 & relation(all_45_4) = v0 & function(all_45_4) = v1 & $i(v2) & ( % 15.30/2.79 | ~ (v1 = 0) | ~ (v0 = 0) | ( ? [v3: any] : (v3 = all_45_1 | ~ % 15.30/2.79 | $i(v3) | ? [v4: $i] : ? [v5: any] : (in(v4, v3) = v5 & % 15.30/2.79 | $i(v4) & ( ~ (v5 = 0) | ! [v6: $i] : ( ~ (in(v6, v2) = 0) | % 15.30/2.79 | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v4) & % 15.30/2.79 | apply(all_45_4, v6) = v7 & $i(v7)))) & (v5 = 0 | ? % 15.30/2.79 | [v6: $i] : (apply(all_45_4, v6) = v4 & in(v6, v2) = 0 & % 15.30/2.79 | $i(v6))))) & ( ~ $i(all_45_1) | ( ! [v3: $i] : ! [v4: % 15.30/2.79 | int] : (v4 = 0 | ~ (in(v3, all_45_1) = v4) | ~ $i(v3) | % 15.30/2.79 | ! [v5: $i] : ( ~ (in(v5, v2) = 0) | ~ $i(v5) | ? [v6: % 15.30/2.79 | $i] : ( ~ (v6 = v3) & apply(all_45_4, v5) = v6 & % 15.30/2.79 | $i(v6)))) & ! [v3: $i] : ( ~ (in(v3, all_45_1) = 0) | % 15.30/2.79 | ~ $i(v3) | ? [v4: $i] : (apply(all_45_4, v4) = v3 & % 15.30/2.79 | in(v4, v2) = 0 & $i(v4)))))))) % 15.30/2.79 | % 15.30/2.79 | GROUND_INST: instantiating (fc6_relat_1) with all_45_4, all_45_1, simplifying % 15.30/2.79 | with (11), (22) gives: % 15.30/2.79 | (28) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_45_4) = v1 % 15.30/2.79 | & empty(all_45_1) = v2 & empty(all_45_4) = v0 & ( ~ (v2 = 0) | ~ % 15.30/2.79 | (v1 = 0) | v0 = 0)) % 15.30/2.79 | % 15.30/2.79 | DELTA: instantiating (28) with fresh symbols all_57_0, all_57_1, all_57_2 % 15.30/2.79 | gives: % 15.30/2.79 | (29) relation(all_45_4) = all_57_1 & empty(all_45_1) = all_57_0 & % 15.30/2.79 | empty(all_45_4) = all_57_2 & ( ~ (all_57_0 = 0) | ~ (all_57_1 = 0) | % 15.30/2.79 | all_57_2 = 0) % 15.30/2.79 | % 15.30/2.79 | ALPHA: (29) implies: % 15.30/2.79 | (30) relation(all_45_4) = all_57_1 % 15.30/2.79 | % 15.30/2.79 | DELTA: instantiating (27) with fresh symbols all_61_0, all_61_1, all_61_2 % 15.30/2.79 | gives: % 15.30/2.80 | (31) relation_dom(all_45_4) = all_61_0 & relation(all_45_4) = all_61_2 & % 15.30/2.80 | function(all_45_4) = all_61_1 & $i(all_61_0) & ( ~ (all_61_1 = 0) | ~ % 15.30/2.80 | (all_61_2 = 0) | ( ? [v0: any] : (v0 = all_45_1 | ~ $i(v0) | ? % 15.30/2.80 | [v1: $i] : ? [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = % 15.30/2.80 | 0) | ! [v3: $i] : ( ~ (in(v3, all_61_0) = 0) | ~ $i(v3) % 15.30/2.80 | | ? [v4: $i] : ( ~ (v4 = v1) & apply(all_45_4, v3) = v4 & % 15.30/2.80 | $i(v4)))) & (v2 = 0 | ? [v3: $i] : (apply(all_45_4, v3) % 15.30/2.80 | = v1 & in(v3, all_61_0) = 0 & $i(v3))))) & ( ~ % 15.30/2.80 | $i(all_45_1) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 15.30/2.80 | (in(v0, all_45_1) = v1) | ~ $i(v0) | ! [v2: $i] : ( ~ % 15.30/2.80 | (in(v2, all_61_0) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ (v3 % 15.30/2.80 | = v0) & apply(all_45_4, v2) = v3 & $i(v3)))) & ! [v0: % 15.30/2.80 | $i] : ( ~ (in(v0, all_45_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 15.30/2.80 | (apply(all_45_4, v1) = v0 & in(v1, all_61_0) = 0 & % 15.30/2.80 | $i(v1))))))) % 15.30/2.80 | % 15.30/2.80 | ALPHA: (31) implies: % 15.30/2.80 | (32) function(all_45_4) = all_61_1 % 15.30/2.80 | (33) relation(all_45_4) = all_61_2 % 15.30/2.80 | (34) relation_dom(all_45_4) = all_61_0 % 15.30/2.80 | (35) ~ (all_61_1 = 0) | ~ (all_61_2 = 0) | ( ? [v0: any] : (v0 = all_45_1 % 15.30/2.80 | | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1, v0) = v2 & % 15.30/2.80 | $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ( ~ (in(v3, all_61_0) = 0) % 15.30/2.80 | | ~ $i(v3) | ? [v4: $i] : ( ~ (v4 = v1) & apply(all_45_4, % 15.30/2.80 | v3) = v4 & $i(v4)))) & (v2 = 0 | ? [v3: $i] : % 15.30/2.80 | (apply(all_45_4, v3) = v1 & in(v3, all_61_0) = 0 & $i(v3))))) % 15.30/2.80 | & ( ~ $i(all_45_1) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 15.30/2.80 | (in(v0, all_45_1) = v1) | ~ $i(v0) | ! [v2: $i] : ( ~ % 15.30/2.80 | (in(v2, all_61_0) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ (v3 = % 15.30/2.80 | v0) & apply(all_45_4, v2) = v3 & $i(v3)))) & ! [v0: $i] % 15.30/2.80 | : ( ~ (in(v0, all_45_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 15.30/2.80 | (apply(all_45_4, v1) = v0 & in(v1, all_61_0) = 0 & $i(v1)))))) % 15.30/2.80 | % 15.30/2.80 | DELTA: instantiating (23) with fresh symbols all_63_0, all_63_1 gives: % 15.30/2.80 | (36) relation_dom(all_45_4) = all_63_0 & relation(all_45_4) = all_63_1 & % 15.30/2.80 | $i(all_63_0) & ( ~ (all_63_1 = 0) | ( ? [v0: $i] : ! [v1: $i] : ! % 15.30/2.80 | [v2: $i] : (v2 = v0 | ~ (relation_inverse_image(all_45_4, v1) = % 15.30/2.80 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? % 15.30/2.80 | [v5: any] : ? [v6: $i] : ? [v7: any] : (apply(all_45_4, v3) = % 15.30/2.80 | v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_63_0) = v5 % 15.30/2.80 | & $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) % 15.30/2.80 | & (v4 = 0 | (v7 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 15.30/2.80 | ( ~ (relation_inverse_image(all_45_4, v0) = v1) | ~ $i(v1) | ~ % 15.30/2.80 | $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 15.30/2.80 | (apply(all_45_4, v2) = v3) | ~ (in(v3, v0) = v4) | ~ % 15.30/2.80 | $i(v2) | ? [v5: any] : ? [v6: any] : (in(v2, v1) = v5 & % 15.30/2.80 | in(v2, all_63_0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = % 15.30/2.80 | 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 15.30/2.80 | (apply(all_45_4, v2) = v3) | ~ (in(v3, v0) = 0) | ~ $i(v2) % 15.30/2.80 | | ? [v4: any] : ? [v5: any] : (in(v2, v1) = v5 & in(v2, % 15.30/2.80 | all_63_0) = v4 & ( ~ (v4 = 0) | v5 = 0))))))) % 15.30/2.80 | % 15.30/2.80 | ALPHA: (36) implies: % 15.30/2.80 | (37) relation(all_45_4) = all_63_1 % 15.30/2.80 | (38) relation_dom(all_45_4) = all_63_0 % 15.30/2.81 | (39) ~ (all_63_1 = 0) | ( ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = % 15.30/2.81 | v0 | ~ (relation_inverse_image(all_45_4, v1) = v2) | ~ $i(v1) | % 15.30/2.81 | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : ? [v6: $i] % 15.30/2.81 | : ? [v7: any] : (apply(all_45_4, v3) = v6 & in(v6, v1) = v7 & % 15.30/2.81 | in(v3, v0) = v4 & in(v3, all_63_0) = v5 & $i(v6) & $i(v3) & ( ~ % 15.30/2.81 | (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 % 15.30/2.81 | = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 15.30/2.81 | (relation_inverse_image(all_45_4, v0) = v1) | ~ $i(v1) | ~ % 15.30/2.81 | $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 15.30/2.81 | (apply(all_45_4, v2) = v3) | ~ (in(v3, v0) = v4) | ~ $i(v2) % 15.30/2.81 | | ? [v5: any] : ? [v6: any] : (in(v2, v1) = v5 & in(v2, % 15.30/2.81 | all_63_0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! % 15.30/2.81 | [v2: $i] : ! [v3: $i] : ( ~ (apply(all_45_4, v2) = v3) | ~ % 15.30/2.81 | (in(v3, v0) = 0) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : % 15.30/2.81 | (in(v2, v1) = v5 & in(v2, all_63_0) = v4 & ( ~ (v4 = 0) | v5 = % 15.30/2.81 | 0)))))) % 15.30/2.81 | % 15.30/2.81 | BETA: splitting (24) gives: % 15.30/2.81 | % 15.30/2.81 | Case 1: % 15.30/2.81 | | % 15.30/2.81 | | (40) all_45_0 = 0 % 15.30/2.81 | | % 15.30/2.81 | | REDUCE: (8), (40) imply: % 15.30/2.81 | | (41) $false % 15.43/2.81 | | % 15.43/2.81 | | CLOSE: (41) is inconsistent. % 15.43/2.81 | | % 15.43/2.81 | Case 2: % 15.43/2.81 | | % 15.43/2.81 | | (42) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_45_5) = v1 & % 15.43/2.81 | | in(v0, all_45_6) = 0 & $i(v0)) % 15.43/2.81 | | % 15.43/2.81 | | DELTA: instantiating (42) with fresh symbols all_75_0, all_75_1 gives: % 15.43/2.81 | | (43) ~ (all_75_0 = 0) & in(all_75_1, all_45_5) = all_75_0 & in(all_75_1, % 15.43/2.81 | | all_45_6) = 0 & $i(all_75_1) % 15.43/2.81 | | % 15.43/2.81 | | ALPHA: (43) implies: % 15.43/2.81 | | (44) ~ (all_75_0 = 0) % 15.43/2.81 | | (45) $i(all_75_1) % 15.43/2.81 | | (46) in(all_75_1, all_45_6) = 0 % 15.43/2.81 | | (47) in(all_75_1, all_45_5) = all_75_0 % 15.43/2.81 | | % 15.43/2.81 | | GROUND_INST: instantiating (3) with 0, all_61_1, all_45_4, simplifying with % 15.43/2.81 | | (15), (32) gives: % 15.43/2.81 | | (48) all_61_1 = 0 % 15.43/2.81 | | % 15.43/2.81 | | GROUND_INST: instantiating (4) with 0, all_61_2, all_45_4, simplifying with % 15.43/2.81 | | (16), (33) gives: % 15.43/2.81 | | (49) all_61_2 = 0 % 15.43/2.81 | | % 15.43/2.81 | | GROUND_INST: instantiating (4) with all_61_2, all_63_1, all_45_4, % 15.43/2.81 | | simplifying with (33), (37) gives: % 15.43/2.81 | | (50) all_63_1 = all_61_2 % 15.43/2.81 | | % 15.43/2.81 | | GROUND_INST: instantiating (4) with all_57_1, all_63_1, all_45_4, % 15.43/2.81 | | simplifying with (30), (37) gives: % 15.43/2.81 | | (51) all_63_1 = all_57_1 % 15.43/2.81 | | % 15.43/2.81 | | GROUND_INST: instantiating (5) with all_61_0, all_63_0, all_45_4, % 15.43/2.81 | | simplifying with (34), (38) gives: % 15.43/2.81 | | (52) all_63_0 = all_61_0 % 15.43/2.81 | | % 15.43/2.81 | | COMBINE_EQS: (50), (51) imply: % 15.43/2.81 | | (53) all_61_2 = all_57_1 % 15.43/2.81 | | % 15.43/2.81 | | SIMP: (53) implies: % 15.43/2.81 | | (54) all_61_2 = all_57_1 % 15.43/2.81 | | % 15.43/2.81 | | COMBINE_EQS: (49), (54) imply: % 15.43/2.81 | | (55) all_57_1 = 0 % 15.43/2.81 | | % 15.43/2.81 | | SIMP: (55) implies: % 15.43/2.81 | | (56) all_57_1 = 0 % 15.43/2.81 | | % 15.43/2.81 | | COMBINE_EQS: (51), (56) imply: % 15.43/2.81 | | (57) all_63_1 = 0 % 15.43/2.81 | | % 15.43/2.81 | | BETA: splitting (39) gives: % 15.43/2.81 | | % 15.43/2.81 | | Case 1: % 15.43/2.81 | | | % 15.43/2.81 | | | (58) ~ (all_63_1 = 0) % 15.43/2.81 | | | % 15.43/2.81 | | | REDUCE: (57), (58) imply: % 15.43/2.81 | | | (59) $false % 15.43/2.81 | | | % 15.43/2.81 | | | CLOSE: (59) is inconsistent. % 15.43/2.81 | | | % 15.43/2.81 | | Case 2: % 15.43/2.81 | | | % 15.43/2.82 | | | (60) ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 15.43/2.82 | | | (relation_inverse_image(all_45_4, v1) = v2) | ~ $i(v1) | ~ % 15.43/2.82 | | | $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : ? [v6: $i] % 15.43/2.82 | | | : ? [v7: any] : (apply(all_45_4, v3) = v6 & in(v6, v1) = v7 & % 15.43/2.82 | | | in(v3, v0) = v4 & in(v3, all_63_0) = v5 & $i(v6) & $i(v3) & ( % 15.43/2.82 | | | ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 % 15.43/2.82 | | | & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 15.43/2.82 | | | (relation_inverse_image(all_45_4, v0) = v1) | ~ $i(v1) | ~ % 15.43/2.82 | | | $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 15.43/2.82 | | | (apply(all_45_4, v2) = v3) | ~ (in(v3, v0) = v4) | ~ % 15.43/2.82 | | | $i(v2) | ? [v5: any] : ? [v6: any] : (in(v2, v1) = v5 & % 15.43/2.82 | | | in(v2, all_63_0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = % 15.43/2.82 | | | 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 15.43/2.82 | | | (apply(all_45_4, v2) = v3) | ~ (in(v3, v0) = 0) | ~ $i(v2) % 15.43/2.82 | | | | ? [v4: any] : ? [v5: any] : (in(v2, v1) = v5 & in(v2, % 15.43/2.82 | | | all_63_0) = v4 & ( ~ (v4 = 0) | v5 = 0))))) % 15.43/2.82 | | | % 15.43/2.82 | | | ALPHA: (60) implies: % 15.43/2.82 | | | (61) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_inverse_image(all_45_4, % 15.43/2.82 | | | v0) = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: % 15.43/2.82 | | | $i] : ! [v4: any] : ( ~ (apply(all_45_4, v2) = v3) | ~ % 15.43/2.82 | | | (in(v3, v0) = v4) | ~ $i(v2) | ? [v5: any] : ? [v6: any] % 15.43/2.82 | | | : (in(v2, v1) = v5 & in(v2, all_63_0) = v6 & ( ~ (v5 = 0) | % 15.43/2.82 | | | (v6 = 0 & v4 = 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 15.43/2.82 | | | (apply(all_45_4, v2) = v3) | ~ (in(v3, v0) = 0) | ~ $i(v2) % 15.43/2.82 | | | | ? [v4: any] : ? [v5: any] : (in(v2, v1) = v5 & in(v2, % 15.43/2.82 | | | all_63_0) = v4 & ( ~ (v4 = 0) | v5 = 0))))) % 15.43/2.82 | | | % 15.43/2.82 | | | GROUND_INST: instantiating (61) with all_45_6, all_45_3, simplifying with % 15.43/2.82 | | | (9), (12), (17) gives: % 15.43/2.82 | | | (62) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (apply(all_45_4, % 15.43/2.82 | | | v0) = v1) | ~ (in(v1, all_45_6) = v2) | ~ $i(v0) | ? [v3: % 15.43/2.82 | | | any] : ? [v4: any] : (in(v0, all_63_0) = v4 & in(v0, % 15.43/2.82 | | | all_45_3) = v3 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! % 15.43/2.82 | | | [v0: $i] : ! [v1: $i] : ( ~ (apply(all_45_4, v0) = v1) | ~ % 15.43/2.82 | | | (in(v1, all_45_6) = 0) | ~ $i(v0) | ? [v2: any] : ? [v3: any] % 15.43/2.82 | | | : (in(v0, all_63_0) = v2 & in(v0, all_45_3) = v3 & ( ~ (v2 = 0) % 15.43/2.82 | | | | v3 = 0))) % 15.43/2.82 | | | % 15.43/2.82 | | | ALPHA: (62) implies: % 15.43/2.82 | | | (63) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_45_4, v0) = v1) | ~ % 15.43/2.82 | | | (in(v1, all_45_6) = 0) | ~ $i(v0) | ? [v2: any] : ? [v3: any] % 15.43/2.82 | | | : (in(v0, all_63_0) = v2 & in(v0, all_45_3) = v3 & ( ~ (v2 = 0) % 15.43/2.82 | | | | v3 = 0))) % 15.43/2.82 | | | (64) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (apply(all_45_4, % 15.43/2.82 | | | v0) = v1) | ~ (in(v1, all_45_6) = v2) | ~ $i(v0) | ? [v3: % 15.43/2.82 | | | any] : ? [v4: any] : (in(v0, all_63_0) = v4 & in(v0, % 15.43/2.82 | | | all_45_3) = v3 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) % 15.43/2.82 | | | % 15.43/2.82 | | | GROUND_INST: instantiating (61) with all_45_5, all_45_2, simplifying with % 15.43/2.82 | | | (10), (13), (18) gives: % 15.43/2.82 | | | (65) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (apply(all_45_4, % 15.43/2.82 | | | v0) = v1) | ~ (in(v1, all_45_5) = v2) | ~ $i(v0) | ? [v3: % 15.43/2.82 | | | any] : ? [v4: any] : (in(v0, all_63_0) = v4 & in(v0, % 15.43/2.82 | | | all_45_2) = v3 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! % 15.43/2.82 | | | [v0: $i] : ! [v1: $i] : ( ~ (apply(all_45_4, v0) = v1) | ~ % 15.51/2.82 | | | (in(v1, all_45_5) = 0) | ~ $i(v0) | ? [v2: any] : ? [v3: any] % 15.51/2.82 | | | : (in(v0, all_63_0) = v2 & in(v0, all_45_2) = v3 & ( ~ (v2 = 0) % 15.51/2.82 | | | | v3 = 0))) % 15.51/2.82 | | | % 15.51/2.82 | | | ALPHA: (65) implies: % 15.51/2.82 | | | (66) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (apply(all_45_4, % 15.51/2.82 | | | v0) = v1) | ~ (in(v1, all_45_5) = v2) | ~ $i(v0) | ? [v3: % 15.51/2.82 | | | any] : ? [v4: any] : (in(v0, all_63_0) = v4 & in(v0, % 15.51/2.82 | | | all_45_2) = v3 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) % 15.51/2.82 | | | % 15.51/2.82 | | | BETA: splitting (35) gives: % 15.51/2.82 | | | % 15.51/2.82 | | | Case 1: % 15.51/2.82 | | | | % 15.51/2.82 | | | | (67) ~ (all_61_1 = 0) % 15.51/2.82 | | | | % 15.51/2.82 | | | | REDUCE: (48), (67) imply: % 15.51/2.82 | | | | (68) $false % 15.51/2.82 | | | | % 15.51/2.82 | | | | CLOSE: (68) is inconsistent. % 15.51/2.82 | | | | % 15.51/2.82 | | | Case 2: % 15.51/2.82 | | | | % 15.51/2.83 | | | | (69) ~ (all_61_2 = 0) | ( ? [v0: any] : (v0 = all_45_1 | ~ $i(v0) | % 15.51/2.83 | | | | ? [v1: $i] : ? [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ % 15.51/2.83 | | | | (v2 = 0) | ! [v3: $i] : ( ~ (in(v3, all_61_0) = 0) | ~ % 15.51/2.83 | | | | $i(v3) | ? [v4: $i] : ( ~ (v4 = v1) & apply(all_45_4, % 15.51/2.83 | | | | v3) = v4 & $i(v4)))) & (v2 = 0 | ? [v3: $i] : % 15.51/2.83 | | | | (apply(all_45_4, v3) = v1 & in(v3, all_61_0) = 0 & % 15.51/2.83 | | | | $i(v3))))) & ( ~ $i(all_45_1) | ( ! [v0: $i] : ! [v1: % 15.51/2.83 | | | | int] : (v1 = 0 | ~ (in(v0, all_45_1) = v1) | ~ $i(v0) % 15.51/2.83 | | | | | ! [v2: $i] : ( ~ (in(v2, all_61_0) = 0) | ~ $i(v2) | % 15.51/2.83 | | | | ? [v3: $i] : ( ~ (v3 = v0) & apply(all_45_4, v2) = v3 % 15.51/2.83 | | | | & $i(v3)))) & ! [v0: $i] : ( ~ (in(v0, all_45_1) = % 15.51/2.83 | | | | 0) | ~ $i(v0) | ? [v1: $i] : (apply(all_45_4, v1) = % 15.51/2.83 | | | | v0 & in(v1, all_61_0) = 0 & $i(v1)))))) % 15.51/2.83 | | | | % 15.51/2.83 | | | | BETA: splitting (69) gives: % 15.51/2.83 | | | | % 15.51/2.83 | | | | Case 1: % 15.51/2.83 | | | | | % 15.51/2.83 | | | | | (70) ~ (all_61_2 = 0) % 15.51/2.83 | | | | | % 15.51/2.83 | | | | | REDUCE: (49), (70) imply: % 15.51/2.83 | | | | | (71) $false % 15.51/2.83 | | | | | % 15.51/2.83 | | | | | CLOSE: (71) is inconsistent. % 15.51/2.83 | | | | | % 15.51/2.83 | | | | Case 2: % 15.51/2.83 | | | | | % 15.51/2.83 | | | | | (72) ? [v0: any] : (v0 = all_45_1 | ~ $i(v0) | ? [v1: $i] : ? % 15.51/2.83 | | | | | [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! % 15.51/2.83 | | | | | [v3: $i] : ( ~ (in(v3, all_61_0) = 0) | ~ $i(v3) | ? % 15.51/2.83 | | | | | [v4: $i] : ( ~ (v4 = v1) & apply(all_45_4, v3) = v4 & % 15.51/2.83 | | | | | $i(v4)))) & (v2 = 0 | ? [v3: $i] : (apply(all_45_4, % 15.51/2.83 | | | | | v3) = v1 & in(v3, all_61_0) = 0 & $i(v3))))) & ( ~ % 15.51/2.83 | | | | | $i(all_45_1) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 15.51/2.83 | | | | | (in(v0, all_45_1) = v1) | ~ $i(v0) | ! [v2: $i] : ( ~ % 15.51/2.83 | | | | | (in(v2, all_61_0) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ % 15.51/2.83 | | | | | (v3 = v0) & apply(all_45_4, v2) = v3 & $i(v3)))) & % 15.51/2.83 | | | | | ! [v0: $i] : ( ~ (in(v0, all_45_1) = 0) | ~ $i(v0) | ? % 15.51/2.83 | | | | | [v1: $i] : (apply(all_45_4, v1) = v0 & in(v1, all_61_0) % 15.51/2.83 | | | | | = 0 & $i(v1))))) % 15.51/2.83 | | | | | % 15.51/2.83 | | | | | ALPHA: (72) implies: % 15.51/2.83 | | | | | (73) ~ $i(all_45_1) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 15.51/2.83 | | | | | (in(v0, all_45_1) = v1) | ~ $i(v0) | ! [v2: $i] : ( ~ % 15.51/2.83 | | | | | (in(v2, all_61_0) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ % 15.51/2.83 | | | | | (v3 = v0) & apply(all_45_4, v2) = v3 & $i(v3)))) & ! % 15.51/2.83 | | | | | [v0: $i] : ( ~ (in(v0, all_45_1) = 0) | ~ $i(v0) | ? [v1: % 15.51/2.83 | | | | | $i] : (apply(all_45_4, v1) = v0 & in(v1, all_61_0) = 0 & % 15.51/2.83 | | | | | $i(v1)))) % 15.51/2.83 | | | | | % 15.51/2.83 | | | | | BETA: splitting (73) gives: % 15.51/2.83 | | | | | % 15.51/2.83 | | | | | Case 1: % 15.51/2.83 | | | | | | % 15.51/2.83 | | | | | | (74) ~ $i(all_45_1) % 15.51/2.83 | | | | | | % 15.51/2.83 | | | | | | PRED_UNIFY: (14), (74) imply: % 15.51/2.83 | | | | | | (75) $false % 15.51/2.83 | | | | | | % 15.51/2.83 | | | | | | CLOSE: (75) is inconsistent. % 15.51/2.83 | | | | | | % 15.51/2.83 | | | | | Case 2: % 15.51/2.83 | | | | | | % 15.51/2.83 | | | | | | (76) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_45_1) % 15.51/2.83 | | | | | | = v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, all_61_0) % 15.51/2.83 | | | | | | = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ (v3 = v0) & % 15.51/2.83 | | | | | | apply(all_45_4, v2) = v3 & $i(v3)))) & ! [v0: $i] : ( % 15.51/2.83 | | | | | | ~ (in(v0, all_45_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 15.51/2.83 | | | | | | (apply(all_45_4, v1) = v0 & in(v1, all_61_0) = 0 & % 15.51/2.83 | | | | | | $i(v1))) % 15.51/2.83 | | | | | | % 15.51/2.83 | | | | | | ALPHA: (76) implies: % 15.51/2.83 | | | | | | (77) ! [v0: $i] : ( ~ (in(v0, all_45_1) = 0) | ~ $i(v0) | ? % 15.51/2.83 | | | | | | [v1: $i] : (apply(all_45_4, v1) = v0 & in(v1, all_61_0) = % 15.51/2.83 | | | | | | 0 & $i(v1))) % 15.51/2.83 | | | | | | % 15.51/2.83 | | | | | | GROUND_INST: instantiating (25) with all_75_1, simplifying with % 15.51/2.83 | | | | | | (45), (46) gives: % 15.51/2.83 | | | | | | (78) in(all_75_1, all_45_1) = 0 % 15.51/2.83 | | | | | | % 15.51/2.83 | | | | | | GROUND_INST: instantiating (77) with all_75_1, simplifying with % 15.51/2.83 | | | | | | (45), (78) gives: % 15.51/2.83 | | | | | | (79) ? [v0: $i] : (apply(all_45_4, v0) = all_75_1 & in(v0, % 15.51/2.83 | | | | | | all_61_0) = 0 & $i(v0)) % 15.51/2.83 | | | | | | % 15.51/2.83 | | | | | | DELTA: instantiating (79) with fresh symbol all_173_0 gives: % 15.51/2.83 | | | | | | (80) apply(all_45_4, all_173_0) = all_75_1 & in(all_173_0, % 15.51/2.83 | | | | | | all_61_0) = 0 & $i(all_173_0) % 15.51/2.83 | | | | | | % 15.51/2.83 | | | | | | ALPHA: (80) implies: % 15.51/2.83 | | | | | | (81) $i(all_173_0) % 15.51/2.83 | | | | | | (82) in(all_173_0, all_61_0) = 0 % 15.51/2.83 | | | | | | (83) apply(all_45_4, all_173_0) = all_75_1 % 15.51/2.83 | | | | | | % 15.51/2.83 | | | | | | GROUND_INST: instantiating (66) with all_173_0, all_75_1, all_75_0, % 15.51/2.83 | | | | | | simplifying with (47), (81), (83) gives: % 15.51/2.83 | | | | | | (84) ? [v0: any] : ? [v1: any] : (in(all_173_0, all_63_0) = v1 % 15.51/2.83 | | | | | | & in(all_173_0, all_45_2) = v0 & ( ~ (v0 = 0) | (v1 = 0 & % 15.51/2.83 | | | | | | all_75_0 = 0))) % 15.51/2.83 | | | | | | % 15.51/2.83 | | | | | | GROUND_INST: instantiating (63) with all_173_0, all_75_1, % 15.51/2.83 | | | | | | simplifying with (46), (81), (83) gives: % 15.51/2.84 | | | | | | (85) ? [v0: any] : ? [v1: any] : (in(all_173_0, all_63_0) = v0 % 15.51/2.84 | | | | | | & in(all_173_0, all_45_3) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 15.51/2.84 | | | | | | % 15.51/2.84 | | | | | | GROUND_INST: instantiating (64) with all_173_0, all_75_1, 0, % 15.51/2.84 | | | | | | simplifying with (46), (81), (83) gives: % 15.51/2.84 | | | | | | (86) ? [v0: any] : ? [v1: any] : (in(all_173_0, all_63_0) = v1 % 15.51/2.84 | | | | | | & in(all_173_0, all_45_3) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 15.51/2.84 | | | | | | % 15.51/2.84 | | | | | | DELTA: instantiating (86) with fresh symbols all_196_0, all_196_1 % 15.51/2.84 | | | | | | gives: % 15.51/2.84 | | | | | | (87) in(all_173_0, all_63_0) = all_196_0 & in(all_173_0, % 15.51/2.84 | | | | | | all_45_3) = all_196_1 & ( ~ (all_196_1 = 0) | all_196_0 = % 15.51/2.84 | | | | | | 0) % 15.51/2.84 | | | | | | % 15.51/2.84 | | | | | | ALPHA: (87) implies: % 15.51/2.84 | | | | | | (88) in(all_173_0, all_45_3) = all_196_1 % 15.51/2.84 | | | | | | (89) in(all_173_0, all_63_0) = all_196_0 % 15.51/2.84 | | | | | | % 15.51/2.84 | | | | | | DELTA: instantiating (85) with fresh symbols all_198_0, all_198_1 % 15.51/2.84 | | | | | | gives: % 15.51/2.84 | | | | | | (90) in(all_173_0, all_63_0) = all_198_1 & in(all_173_0, % 15.51/2.84 | | | | | | all_45_3) = all_198_0 & ( ~ (all_198_1 = 0) | all_198_0 = % 15.51/2.84 | | | | | | 0) % 15.51/2.84 | | | | | | % 15.51/2.84 | | | | | | ALPHA: (90) implies: % 15.51/2.84 | | | | | | (91) in(all_173_0, all_45_3) = all_198_0 % 15.51/2.84 | | | | | | (92) in(all_173_0, all_63_0) = all_198_1 % 15.51/2.84 | | | | | | (93) ~ (all_198_1 = 0) | all_198_0 = 0 % 15.51/2.84 | | | | | | % 15.51/2.84 | | | | | | DELTA: instantiating (84) with fresh symbols all_200_0, all_200_1 % 15.51/2.84 | | | | | | gives: % 15.51/2.84 | | | | | | (94) in(all_173_0, all_63_0) = all_200_0 & in(all_173_0, % 15.51/2.84 | | | | | | all_45_2) = all_200_1 & ( ~ (all_200_1 = 0) | (all_200_0 = % 15.51/2.84 | | | | | | 0 & all_75_0 = 0)) % 15.51/2.84 | | | | | | % 15.51/2.84 | | | | | | ALPHA: (94) implies: % 15.51/2.84 | | | | | | (95) in(all_173_0, all_45_2) = all_200_1 % 15.51/2.84 | | | | | | (96) in(all_173_0, all_63_0) = all_200_0 % 15.51/2.84 | | | | | | (97) ~ (all_200_1 = 0) | (all_200_0 = 0 & all_75_0 = 0) % 15.51/2.84 | | | | | | % 15.51/2.84 | | | | | | REDUCE: (52), (96) imply: % 15.51/2.84 | | | | | | (98) in(all_173_0, all_61_0) = all_200_0 % 15.51/2.84 | | | | | | % 15.51/2.84 | | | | | | REDUCE: (52), (92) imply: % 15.51/2.84 | | | | | | (99) in(all_173_0, all_61_0) = all_198_1 % 15.51/2.84 | | | | | | % 15.51/2.84 | | | | | | REDUCE: (52), (89) imply: % 15.51/2.84 | | | | | | (100) in(all_173_0, all_61_0) = all_196_0 % 15.51/2.84 | | | | | | % 15.51/2.84 | | | | | | BETA: splitting (97) gives: % 15.51/2.84 | | | | | | % 15.51/2.84 | | | | | | Case 1: % 15.51/2.84 | | | | | | | % 15.51/2.84 | | | | | | | (101) ~ (all_200_1 = 0) % 15.51/2.84 | | | | | | | % 15.51/2.84 | | | | | | | GROUND_INST: instantiating (6) with all_196_1, all_198_0, % 15.51/2.84 | | | | | | | all_45_3, all_173_0, simplifying with (88), (91) % 15.51/2.84 | | | | | | | gives: % 15.51/2.84 | | | | | | | (102) all_198_0 = all_196_1 % 15.51/2.84 | | | | | | | % 15.51/2.84 | | | | | | | GROUND_INST: instantiating (6) with 0, all_198_1, all_61_0, % 15.51/2.84 | | | | | | | all_173_0, simplifying with (82), (99) gives: % 15.51/2.84 | | | | | | | (103) all_198_1 = 0 % 15.51/2.84 | | | | | | | % 15.51/2.84 | | | | | | | GROUND_INST: instantiating (6) with all_198_1, all_200_0, % 15.51/2.84 | | | | | | | all_61_0, all_173_0, simplifying with (98), (99) % 15.51/2.84 | | | | | | | gives: % 15.51/2.84 | | | | | | | (104) all_200_0 = all_198_1 % 15.51/2.84 | | | | | | | % 15.51/2.84 | | | | | | | GROUND_INST: instantiating (6) with all_196_0, all_200_0, % 15.51/2.84 | | | | | | | all_61_0, all_173_0, simplifying with (98), (100) % 15.51/2.84 | | | | | | | gives: % 15.51/2.84 | | | | | | | (105) all_200_0 = all_196_0 % 15.51/2.84 | | | | | | | % 15.51/2.84 | | | | | | | COMBINE_EQS: (104), (105) imply: % 15.51/2.84 | | | | | | | (106) all_198_1 = all_196_0 % 15.51/2.84 | | | | | | | % 15.51/2.84 | | | | | | | SIMP: (106) implies: % 15.51/2.84 | | | | | | | (107) all_198_1 = all_196_0 % 15.51/2.84 | | | | | | | % 15.51/2.84 | | | | | | | COMBINE_EQS: (103), (107) imply: % 15.51/2.84 | | | | | | | (108) all_196_0 = 0 % 15.51/2.84 | | | | | | | % 15.51/2.84 | | | | | | | BETA: splitting (93) gives: % 15.51/2.84 | | | | | | | % 15.51/2.84 | | | | | | | Case 1: % 15.51/2.84 | | | | | | | | % 15.51/2.84 | | | | | | | | (109) ~ (all_198_1 = 0) % 15.51/2.84 | | | | | | | | % 15.51/2.84 | | | | | | | | REDUCE: (103), (109) imply: % 15.51/2.84 | | | | | | | | (110) $false % 15.51/2.84 | | | | | | | | % 15.51/2.84 | | | | | | | | CLOSE: (110) is inconsistent. % 15.51/2.84 | | | | | | | | % 15.51/2.84 | | | | | | | Case 2: % 15.51/2.84 | | | | | | | | % 15.51/2.84 | | | | | | | | (111) all_198_0 = 0 % 15.51/2.84 | | | | | | | | % 15.51/2.84 | | | | | | | | COMBINE_EQS: (102), (111) imply: % 15.51/2.84 | | | | | | | | (112) all_196_1 = 0 % 15.51/2.84 | | | | | | | | % 15.51/2.84 | | | | | | | | REDUCE: (88), (112) imply: % 15.51/2.84 | | | | | | | | (113) in(all_173_0, all_45_3) = 0 % 15.51/2.84 | | | | | | | | % 15.51/2.84 | | | | | | | | GROUND_INST: instantiating (26) with all_173_0, simplifying with % 15.51/2.84 | | | | | | | | (81), (113) gives: % 15.51/2.84 | | | | | | | | (114) in(all_173_0, all_45_2) = 0 % 15.51/2.84 | | | | | | | | % 15.51/2.84 | | | | | | | | GROUND_INST: instantiating (6) with all_200_1, 0, all_45_2, % 15.51/2.84 | | | | | | | | all_173_0, simplifying with (95), (114) gives: % 15.51/2.84 | | | | | | | | (115) all_200_1 = 0 % 15.51/2.84 | | | | | | | | % 15.51/2.84 | | | | | | | | REDUCE: (101), (115) imply: % 15.51/2.84 | | | | | | | | (116) $false % 15.51/2.84 | | | | | | | | % 15.51/2.84 | | | | | | | | CLOSE: (116) is inconsistent. % 15.51/2.84 | | | | | | | | % 15.51/2.84 | | | | | | | End of split % 15.51/2.84 | | | | | | | % 15.51/2.84 | | | | | | Case 2: % 15.51/2.84 | | | | | | | % 15.51/2.84 | | | | | | | (117) all_200_0 = 0 & all_75_0 = 0 % 15.51/2.84 | | | | | | | % 15.51/2.84 | | | | | | | ALPHA: (117) implies: % 15.51/2.84 | | | | | | | (118) all_75_0 = 0 % 15.51/2.84 | | | | | | | % 15.51/2.84 | | | | | | | REDUCE: (44), (118) imply: % 15.51/2.84 | | | | | | | (119) $false % 15.51/2.84 | | | | | | | % 15.51/2.84 | | | | | | | CLOSE: (119) is inconsistent. % 15.51/2.84 | | | | | | | % 15.51/2.84 | | | | | | End of split % 15.51/2.84 | | | | | | % 15.51/2.84 | | | | | End of split % 15.51/2.84 | | | | | % 15.51/2.84 | | | | End of split % 15.51/2.84 | | | | % 15.51/2.84 | | | End of split % 15.51/2.84 | | | % 15.51/2.84 | | End of split % 15.51/2.84 | | % 15.51/2.84 | End of split % 15.51/2.84 | % 15.51/2.84 End of proof % 15.51/2.84 % SZS output end Proof for theBenchmark % 15.51/2.84 % 15.51/2.84 2237ms %------------------------------------------------------------------------------