%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU212+3 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n022.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 17:43:18 EDT 2023 % Result : Theorem 11.49s 2.31s % Output : Proof 13.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU212+3 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n022.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Wed Aug 23 17:14:56 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.66 ________ _____ % 0.21/0.66 ___ __ \_________(_)________________________________ % 0.21/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.66 % 0.21/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.66 (2023-06-19) % 0.21/0.66 % 0.21/0.66 (c) Philipp Rümmer, 2009-2023 % 0.21/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.66 Amanda Stjerna. % 0.21/0.66 Free software under BSD-3-Clause. % 0.21/0.66 % 0.21/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.66 % 0.21/0.66 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.67 Running up to 7 provers in parallel. % 0.21/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.88/1.10 Prover 4: Preprocessing ... % 2.88/1.10 Prover 1: Preprocessing ... % 2.88/1.14 Prover 6: Preprocessing ... % 2.88/1.14 Prover 2: Preprocessing ... % 2.88/1.14 Prover 5: Preprocessing ... % 2.88/1.14 Prover 0: Preprocessing ... % 2.88/1.15 Prover 3: Preprocessing ... % 6.31/1.61 Prover 1: Warning: ignoring some quantifiers % 6.84/1.65 Prover 1: Constructing countermodel ... % 6.84/1.66 Prover 5: Proving ... % 6.84/1.66 Prover 3: Warning: ignoring some quantifiers % 7.00/1.68 Prover 3: Constructing countermodel ... % 7.00/1.69 Prover 2: Proving ... % 7.00/1.69 Prover 6: Proving ... % 7.00/1.70 Prover 4: Warning: ignoring some quantifiers % 7.60/1.76 Prover 4: Constructing countermodel ... % 8.17/1.84 Prover 0: Proving ... % 11.05/2.30 Prover 3: proved (1605ms) % 11.05/2.30 % 11.49/2.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.49/2.31 % 11.49/2.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.49/2.31 Prover 6: stopped % 11.49/2.31 Prover 0: stopped % 11.49/2.31 Prover 5: stopped % 11.49/2.32 Prover 2: stopped % 11.49/2.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.49/2.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.49/2.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.49/2.34 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.94/2.36 Prover 8: Preprocessing ... % 11.94/2.38 Prover 11: Preprocessing ... % 11.94/2.38 Prover 13: Preprocessing ... % 11.94/2.38 Prover 10: Preprocessing ... % 11.94/2.38 Prover 7: Preprocessing ... % 12.67/2.46 Prover 1: Found proof (size 81) % 12.67/2.46 Prover 1: proved (1789ms) % 12.67/2.46 Prover 4: stopped % 12.67/2.48 Prover 7: Warning: ignoring some quantifiers % 12.93/2.49 Prover 13: Warning: ignoring some quantifiers % 12.93/2.49 Prover 7: Constructing countermodel ... % 12.93/2.50 Prover 10: Warning: ignoring some quantifiers % 12.93/2.50 Prover 7: stopped % 12.93/2.51 Prover 13: Constructing countermodel ... % 12.93/2.52 Prover 8: Warning: ignoring some quantifiers % 12.93/2.52 Prover 10: Constructing countermodel ... % 12.93/2.52 Prover 13: stopped % 12.93/2.53 Prover 10: stopped % 12.93/2.53 Prover 8: Constructing countermodel ... % 13.23/2.54 Prover 8: stopped % 13.23/2.56 Prover 11: Warning: ignoring some quantifiers % 13.23/2.58 Prover 11: Constructing countermodel ... % 13.23/2.59 Prover 11: stopped % 13.23/2.59 % 13.23/2.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.23/2.59 % 13.23/2.60 % SZS output start Proof for theBenchmark % 13.23/2.61 Assumptions after simplification: % 13.23/2.61 --------------------------------- % 13.23/2.61 % 13.23/2.61 (d4_funct_1) % 13.23/2.64 $i(empty_set) & ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: % 13.23/2.64 any] : ? [v2: $i] : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & % 13.23/2.64 ( ~ (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( % 13.23/2.64 ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = v6) | ~ $i(v4) | % 13.23/2.64 ~ $i(v3) | ? [v7: any] : ? [v8: $i] : (apply(v0, v3) = v8 & in(v3, % 13.23/2.64 v2) = v7 & $i(v8) & ( ~ (v7 = 0) | (( ~ (v8 = v4) | v6 = 0) & ( % 13.23/2.64 ~ (v6 = 0) | v8 = v4))))) & ? [v3: $i] : ! [v4: $i] : ! % 13.23/2.64 [v5: int] : (v5 = 0 | ~ (in(v4, v2) = v5) | ~ $i(v4) | ~ $i(v3) | % 13.23/2.64 ? [v6: $i] : (apply(v0, v4) = v6 & $i(v6) & ( ~ (v6 = v3) | v3 = % 13.23/2.64 empty_set) & ( ~ (v3 = empty_set) | v6 = empty_set))))))) % 13.23/2.64 % 13.23/2.64 (d4_relat_1) % 13.23/2.64 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 13.23/2.64 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~ % 13.23/2.64 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~ % 13.23/2.64 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) = % 13.23/2.65 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i] % 13.23/2.65 : ? [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, v0) = 0 & $i(v6) % 13.23/2.65 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 % 13.23/2.65 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~ % 13.23/2.65 (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) & % 13.23/2.65 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: % 13.23/2.65 $i] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) & % 13.23/2.65 $i(v3))))))) % 13.23/2.65 % 13.23/2.65 (fc5_relat_1) % 13.23/2.65 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 13.23/2.65 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & empty(v1) = v4 & % 13.23/2.65 empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 13.23/2.65 % 13.23/2.65 (t8_funct_1) % 13.23/2.65 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: % 13.23/2.65 $i] : ? [v6: any] : ? [v7: $i] : (relation_dom(v2) = v5 & ordered_pair(v0, % 13.23/2.65 v1) = v3 & apply(v2, v0) = v7 & relation(v2) = 0 & function(v2) = 0 & % 13.23/2.65 in(v3, v2) = v4 & in(v0, v5) = v6 & $i(v7) & $i(v5) & $i(v3) & $i(v2) & % 13.23/2.65 $i(v1) & $i(v0) & ((v7 = v1 & v6 = 0 & ~ (v4 = 0)) | (v4 = 0 & ( ~ (v7 = % 13.23/2.65 v1) | ~ (v6 = 0))))) % 13.23/2.65 % 13.23/2.65 (function-axioms) % 13.23/2.65 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.23/2.65 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 13.23/2.65 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 13.23/2.65 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! % 13.23/2.65 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.23/2.65 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] % 13.23/2.65 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) = v1) % 13.23/2.65 | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 13.23/2.65 [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ % 13.23/2.65 (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.23/2.65 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = % 13.23/2.65 v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 13.23/2.65 (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: % 13.23/2.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 13.23/2.65 ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = % 13.23/2.65 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 13.23/2.65 (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 13.23/2.65 : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = % 13.23/2.65 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.23/2.65 $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: % 13.23/2.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 13.23/2.65 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] % 13.23/2.65 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | % 13.23/2.65 ~ (empty(v2) = v0)) % 13.23/2.65 % 13.23/2.65 Further assumptions not needed in the proof: % 13.23/2.65 -------------------------------------------- % 13.23/2.66 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, commutativity_k2_tarski, % 13.23/2.66 d5_tarski, existence_m1_subset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0, % 13.23/2.66 fc1_zfmisc_1, fc2_subset_1, fc3_subset_1, fc4_relat_1, fc7_relat_1, rc1_funct_1, % 13.23/2.66 rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_relat_1, rc2_subset_1, % 13.23/2.66 rc2_xboole_0, rc3_relat_1, reflexivity_r1_tarski, t1_subset, t2_subset, % 13.23/2.66 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole % 13.23/2.66 % 13.23/2.66 Those formulas are unsatisfiable: % 13.23/2.66 --------------------------------- % 13.23/2.66 % 13.23/2.66 Begin of proof % 13.23/2.66 | % 13.23/2.66 | ALPHA: (d4_funct_1) implies: % 13.23/2.66 | (1) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 13.23/2.66 | [v2: $i] : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~ % 13.23/2.66 | (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 13.23/2.66 | any] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = v6) % 13.23/2.66 | | ~ $i(v4) | ~ $i(v3) | ? [v7: any] : ? [v8: $i] : % 13.23/2.66 | (apply(v0, v3) = v8 & in(v3, v2) = v7 & $i(v8) & ( ~ (v7 = 0) % 13.23/2.66 | | (( ~ (v8 = v4) | v6 = 0) & ( ~ (v6 = 0) | v8 = v4))))) % 13.23/2.66 | & ? [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 13.23/2.66 | (in(v4, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : % 13.23/2.66 | (apply(v0, v4) = v6 & $i(v6) & ( ~ (v6 = v3) | v3 = % 13.23/2.66 | empty_set) & ( ~ (v3 = empty_set) | v6 = empty_set))))))) % 13.23/2.66 | % 13.23/2.66 | ALPHA: (function-axioms) implies: % 13.23/2.66 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.23/2.66 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 13.23/2.66 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 13.23/2.66 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 13.23/2.66 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.23/2.66 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 13.23/2.66 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.23/2.66 | (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 13.23/2.66 | % 13.23/2.66 | DELTA: instantiating (t8_funct_1) with fresh symbols all_42_0, all_42_1, % 13.23/2.66 | all_42_2, all_42_3, all_42_4, all_42_5, all_42_6, all_42_7 gives: % 13.23/2.66 | (6) relation_dom(all_42_5) = all_42_2 & ordered_pair(all_42_7, all_42_6) = % 13.23/2.66 | all_42_4 & apply(all_42_5, all_42_7) = all_42_0 & relation(all_42_5) = % 13.23/2.66 | 0 & function(all_42_5) = 0 & in(all_42_4, all_42_5) = all_42_3 & % 13.23/2.66 | in(all_42_7, all_42_2) = all_42_1 & $i(all_42_0) & $i(all_42_2) & % 13.23/2.66 | $i(all_42_4) & $i(all_42_5) & $i(all_42_6) & $i(all_42_7) & ((all_42_0 % 13.23/2.66 | = all_42_6 & all_42_1 = 0 & ~ (all_42_3 = 0)) | (all_42_3 = 0 & ( % 13.23/2.66 | ~ (all_42_0 = all_42_6) | ~ (all_42_1 = 0)))) % 13.23/2.66 | % 13.23/2.66 | ALPHA: (6) implies: % 13.23/2.67 | (7) $i(all_42_7) % 13.23/2.67 | (8) $i(all_42_6) % 13.23/2.67 | (9) $i(all_42_5) % 13.23/2.67 | (10) in(all_42_7, all_42_2) = all_42_1 % 13.23/2.67 | (11) in(all_42_4, all_42_5) = all_42_3 % 13.23/2.67 | (12) function(all_42_5) = 0 % 13.23/2.67 | (13) relation(all_42_5) = 0 % 13.23/2.67 | (14) apply(all_42_5, all_42_7) = all_42_0 % 13.23/2.67 | (15) ordered_pair(all_42_7, all_42_6) = all_42_4 % 13.23/2.67 | (16) relation_dom(all_42_5) = all_42_2 % 13.23/2.67 | (17) (all_42_0 = all_42_6 & all_42_1 = 0 & ~ (all_42_3 = 0)) | (all_42_3 = % 13.23/2.67 | 0 & ( ~ (all_42_0 = all_42_6) | ~ (all_42_1 = 0))) % 13.23/2.67 | % 13.23/2.67 | GROUND_INST: instantiating (1) with all_42_5, simplifying with (9), (12) % 13.23/2.67 | gives: % 13.23/2.67 | (18) ? [v0: any] : ? [v1: $i] : (relation_dom(all_42_5) = v1 & % 13.23/2.67 | relation(all_42_5) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : ! % 13.23/2.67 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (ordered_pair(v2, % 13.23/2.67 | v3) = v4) | ~ (in(v4, all_42_5) = v5) | ~ $i(v3) | ~ % 13.23/2.67 | $i(v2) | ? [v6: any] : ? [v7: $i] : (apply(all_42_5, v2) = % 13.23/2.67 | v7 & in(v2, v1) = v6 & $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 = % 13.23/2.67 | v3) | v5 = 0) & ( ~ (v5 = 0) | v7 = v3))))) & ? % 13.23/2.67 | [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v1) % 13.23/2.67 | = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] : % 13.23/2.67 | (apply(all_42_5, v3) = v5 & $i(v5) & ( ~ (v5 = v2) | v2 = % 13.23/2.67 | empty_set) & ( ~ (v2 = empty_set) | v5 = empty_set)))))) % 13.23/2.67 | % 13.23/2.67 | GROUND_INST: instantiating (fc5_relat_1) with all_42_5, all_42_2, simplifying % 13.23/2.67 | with (9), (16) gives: % 13.23/2.67 | (19) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_42_5) = v1 % 13.23/2.67 | & empty(all_42_2) = v2 & empty(all_42_5) = v0 & ( ~ (v2 = 0) | ~ % 13.23/2.67 | (v1 = 0) | v0 = 0)) % 13.23/2.67 | % 13.23/2.67 | GROUND_INST: instantiating (d4_relat_1) with all_42_5, all_42_2, simplifying % 13.23/2.67 | with (9), (16) gives: % 13.23/2.67 | (20) ? [v0: int] : ( ~ (v0 = 0) & relation(all_42_5) = v0) | ( ? [v0: any] % 13.23/2.67 | : (v0 = all_42_2 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1, % 13.23/2.67 | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] : % 13.23/2.67 | ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4, all_42_5) = 0) | % 13.23/2.67 | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] : % 13.23/2.67 | (ordered_pair(v1, v3) = v4 & in(v4, all_42_5) = 0 & $i(v4) & % 13.23/2.67 | $i(v3))))) & ( ~ $i(all_42_2) | ( ! [v0: $i] : ! [v1: int] % 13.23/2.67 | : (v1 = 0 | ~ (in(v0, all_42_2) = v1) | ~ $i(v0) | ! [v2: $i] % 13.23/2.67 | : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, % 13.23/2.67 | all_42_5) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, % 13.23/2.67 | all_42_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 13.23/2.67 | (ordered_pair(v0, v1) = v2 & in(v2, all_42_5) = 0 & $i(v2) & % 13.23/2.67 | $i(v1)))))) % 13.23/2.67 | % 13.23/2.67 | DELTA: instantiating (19) with fresh symbols all_52_0, all_52_1, all_52_2 % 13.23/2.67 | gives: % 13.23/2.68 | (21) relation(all_42_5) = all_52_1 & empty(all_42_2) = all_52_0 & % 13.23/2.68 | empty(all_42_5) = all_52_2 & ( ~ (all_52_0 = 0) | ~ (all_52_1 = 0) | % 13.23/2.68 | all_52_2 = 0) % 13.23/2.68 | % 13.23/2.68 | ALPHA: (21) implies: % 13.23/2.68 | (22) relation(all_42_5) = all_52_1 % 13.23/2.68 | % 13.23/2.68 | DELTA: instantiating (18) with fresh symbols all_56_0, all_56_1 gives: % 13.23/2.68 | (23) relation_dom(all_42_5) = all_56_0 & relation(all_42_5) = all_56_1 & % 13.23/2.68 | $i(all_56_0) & ( ~ (all_56_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! % 13.23/2.68 | [v2: $i] : ! [v3: any] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 13.23/2.68 | (in(v2, all_42_5) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : % 13.23/2.68 | ? [v5: $i] : (apply(all_42_5, v0) = v5 & in(v0, all_56_0) = v4 % 13.23/2.68 | & $i(v5) & ( ~ (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~ (v3 = % 13.23/2.68 | 0) | v5 = v1))))) & ? [v0: $i] : ! [v1: $i] : ! % 13.23/2.68 | [v2: int] : (v2 = 0 | ~ (in(v1, all_56_0) = v2) | ~ $i(v1) | ~ % 13.23/2.68 | $i(v0) | ? [v3: $i] : (apply(all_42_5, v1) = v3 & $i(v3) & ( ~ % 13.23/2.68 | (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 = % 13.23/2.68 | empty_set))))) % 13.23/2.68 | % 13.23/2.68 | ALPHA: (23) implies: % 13.23/2.68 | (24) $i(all_56_0) % 13.23/2.68 | (25) relation(all_42_5) = all_56_1 % 13.23/2.68 | (26) relation_dom(all_42_5) = all_56_0 % 13.23/2.68 | (27) ~ (all_56_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 13.23/2.68 | any] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_42_5) = % 13.23/2.68 | v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : % 13.23/2.68 | (apply(all_42_5, v0) = v5 & in(v0, all_56_0) = v4 & $i(v5) & ( ~ % 13.23/2.68 | (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~ (v3 = 0) | v5 = % 13.23/2.68 | v1))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = % 13.23/2.68 | 0 | ~ (in(v1, all_56_0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 13.23/2.68 | $i] : (apply(all_42_5, v1) = v3 & $i(v3) & ( ~ (v3 = v0) | v0 = % 13.23/2.68 | empty_set) & ( ~ (v0 = empty_set) | v3 = empty_set)))) % 13.23/2.68 | % 13.23/2.68 | GROUND_INST: instantiating (2) with 0, all_56_1, all_42_5, simplifying with % 13.23/2.68 | (13), (25) gives: % 13.23/2.68 | (28) all_56_1 = 0 % 13.23/2.68 | % 13.23/2.68 | GROUND_INST: instantiating (2) with all_52_1, all_56_1, all_42_5, simplifying % 13.23/2.68 | with (22), (25) gives: % 13.23/2.68 | (29) all_56_1 = all_52_1 % 13.23/2.68 | % 13.23/2.68 | GROUND_INST: instantiating (3) with all_42_2, all_56_0, all_42_5, simplifying % 13.23/2.68 | with (16), (26) gives: % 13.23/2.68 | (30) all_56_0 = all_42_2 % 13.23/2.68 | % 13.23/2.68 | COMBINE_EQS: (28), (29) imply: % 13.23/2.68 | (31) all_52_1 = 0 % 13.23/2.68 | % 13.23/2.68 | REDUCE: (24), (30) imply: % 13.23/2.68 | (32) $i(all_42_2) % 13.23/2.68 | % 13.23/2.68 | BETA: splitting (20) gives: % 13.23/2.68 | % 13.23/2.68 | Case 1: % 13.23/2.68 | | % 13.23/2.68 | | (33) ? [v0: int] : ( ~ (v0 = 0) & relation(all_42_5) = v0) % 13.23/2.68 | | % 13.23/2.68 | | DELTA: instantiating (33) with fresh symbol all_74_0 gives: % 13.23/2.68 | | (34) ~ (all_74_0 = 0) & relation(all_42_5) = all_74_0 % 13.23/2.68 | | % 13.23/2.68 | | ALPHA: (34) implies: % 13.23/2.68 | | (35) ~ (all_74_0 = 0) % 13.23/2.68 | | (36) relation(all_42_5) = all_74_0 % 13.23/2.68 | | % 13.23/2.68 | | GROUND_INST: instantiating (2) with 0, all_74_0, all_42_5, simplifying with % 13.23/2.68 | | (13), (36) gives: % 13.23/2.68 | | (37) all_74_0 = 0 % 13.23/2.68 | | % 13.23/2.68 | | REDUCE: (35), (37) imply: % 13.23/2.68 | | (38) $false % 13.23/2.69 | | % 13.23/2.69 | | CLOSE: (38) is inconsistent. % 13.23/2.69 | | % 13.23/2.69 | Case 2: % 13.23/2.69 | | % 13.23/2.69 | | (39) ? [v0: any] : (v0 = all_42_2 | ~ $i(v0) | ? [v1: $i] : ? [v2: % 13.23/2.69 | | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : % 13.23/2.69 | | ! [v4: $i] : ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4, % 13.23/2.69 | | all_42_5) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : % 13.23/2.69 | | ? [v4: $i] : (ordered_pair(v1, v3) = v4 & in(v4, all_42_5) = 0 % 13.23/2.69 | | & $i(v4) & $i(v3))))) & ( ~ $i(all_42_2) | ( ! [v0: $i] : ! % 13.23/2.69 | | [v1: int] : (v1 = 0 | ~ (in(v0, all_42_2) = v1) | ~ $i(v0) | % 13.23/2.69 | | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | % 13.23/2.69 | | ~ (in(v3, all_42_5) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ % 13.23/2.69 | | (in(v0, all_42_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] % 13.23/2.69 | | : (ordered_pair(v0, v1) = v2 & in(v2, all_42_5) = 0 & $i(v2) & % 13.23/2.69 | | $i(v1))))) % 13.23/2.69 | | % 13.23/2.69 | | ALPHA: (39) implies: % 13.23/2.69 | | (40) ~ $i(all_42_2) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, % 13.23/2.69 | | all_42_2) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( % 13.23/2.69 | | ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_42_5) = 0) | ~ % 13.23/2.69 | | $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_42_2) = 0) | ~ % 13.23/2.69 | | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2 % 13.23/2.69 | | & in(v2, all_42_5) = 0 & $i(v2) & $i(v1)))) % 13.23/2.69 | | % 13.23/2.69 | | BETA: splitting (27) gives: % 13.23/2.69 | | % 13.23/2.69 | | Case 1: % 13.23/2.69 | | | % 13.23/2.69 | | | (41) ~ (all_56_1 = 0) % 13.23/2.69 | | | % 13.23/2.69 | | | REDUCE: (28), (41) imply: % 13.23/2.69 | | | (42) $false % 13.23/2.69 | | | % 13.23/2.69 | | | CLOSE: (42) is inconsistent. % 13.23/2.69 | | | % 13.23/2.69 | | Case 2: % 13.23/2.69 | | | % 13.23/2.69 | | | (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 13.23/2.69 | | | (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_42_5) = v3) | ~ % 13.23/2.69 | | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : % 13.23/2.69 | | | (apply(all_42_5, v0) = v5 & in(v0, all_56_0) = v4 & $i(v5) & ( ~ % 13.23/2.69 | | | (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~ (v3 = 0) | v5 = % 13.23/2.69 | | | v1))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 % 13.23/2.69 | | | = 0 | ~ (in(v1, all_56_0) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 13.23/2.69 | | | [v3: $i] : (apply(all_42_5, v1) = v3 & $i(v3) & ( ~ (v3 = v0) | % 13.23/2.69 | | | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 = empty_set))) % 13.23/2.69 | | | % 13.23/2.69 | | | ALPHA: (43) implies: % 13.23/2.69 | | | (44) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 13.23/2.69 | | | (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_42_5) = v3) | ~ % 13.23/2.69 | | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : % 13.23/2.69 | | | (apply(all_42_5, v0) = v5 & in(v0, all_56_0) = v4 & $i(v5) & ( ~ % 13.23/2.69 | | | (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~ (v3 = 0) | v5 = % 13.23/2.69 | | | v1))))) % 13.23/2.69 | | | % 13.23/2.69 | | | GROUND_INST: instantiating (44) with all_42_7, all_42_6, all_42_4, % 13.23/2.69 | | | all_42_3, simplifying with (7), (8), (11), (15) gives: % 13.23/2.70 | | | (45) ? [v0: any] : ? [v1: $i] : (apply(all_42_5, all_42_7) = v1 & % 13.23/2.70 | | | in(all_42_7, all_56_0) = v0 & $i(v1) & ( ~ (v0 = 0) | (( ~ (v1 = % 13.23/2.70 | | | all_42_6) | all_42_3 = 0) & ( ~ (all_42_3 = 0) | v1 = % 13.23/2.70 | | | all_42_6)))) % 13.23/2.70 | | | % 13.23/2.70 | | | DELTA: instantiating (45) with fresh symbols all_74_0, all_74_1 gives: % 13.23/2.70 | | | (46) apply(all_42_5, all_42_7) = all_74_0 & in(all_42_7, all_56_0) = % 13.23/2.70 | | | all_74_1 & $i(all_74_0) & ( ~ (all_74_1 = 0) | (( ~ (all_74_0 = % 13.23/2.70 | | | all_42_6) | all_42_3 = 0) & ( ~ (all_42_3 = 0) | all_74_0 % 13.23/2.70 | | | = all_42_6))) % 13.23/2.70 | | | % 13.23/2.70 | | | ALPHA: (46) implies: % 13.23/2.70 | | | (47) in(all_42_7, all_56_0) = all_74_1 % 13.23/2.70 | | | (48) apply(all_42_5, all_42_7) = all_74_0 % 13.23/2.70 | | | (49) ~ (all_74_1 = 0) | (( ~ (all_74_0 = all_42_6) | all_42_3 = 0) & ( % 13.23/2.70 | | | ~ (all_42_3 = 0) | all_74_0 = all_42_6)) % 13.23/2.70 | | | % 13.23/2.70 | | | REDUCE: (30), (47) imply: % 13.23/2.70 | | | (50) in(all_42_7, all_42_2) = all_74_1 % 13.23/2.70 | | | % 13.23/2.70 | | | BETA: splitting (40) gives: % 13.23/2.70 | | | % 13.23/2.70 | | | Case 1: % 13.23/2.70 | | | | % 13.23/2.70 | | | | (51) ~ $i(all_42_2) % 13.23/2.70 | | | | % 13.23/2.70 | | | | PRED_UNIFY: (32), (51) imply: % 13.23/2.70 | | | | (52) $false % 13.23/2.70 | | | | % 13.23/2.70 | | | | CLOSE: (52) is inconsistent. % 13.23/2.70 | | | | % 13.23/2.70 | | | Case 2: % 13.23/2.70 | | | | % 13.23/2.70 | | | | (53) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_42_2) = % 13.23/2.70 | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ % 13.23/2.70 | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_42_5) = 0) | ~ % 13.23/2.70 | | | | $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_42_2) = 0) | ~ % 13.23/2.70 | | | | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = % 13.23/2.70 | | | | v2 & in(v2, all_42_5) = 0 & $i(v2) & $i(v1))) % 13.23/2.70 | | | | % 13.23/2.70 | | | | ALPHA: (53) implies: % 13.23/2.70 | | | | (54) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_42_2) = % 13.23/2.70 | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ % 13.23/2.70 | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_42_5) = 0) | ~ % 13.23/2.70 | | | | $i(v2))) % 13.23/2.70 | | | | % 13.23/2.70 | | | | GROUND_INST: instantiating (54) with all_42_7, all_42_1, simplifying % 13.23/2.70 | | | | with (7), (10) gives: % 13.23/2.70 | | | | (55) all_42_1 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ % 13.23/2.70 | | | | (ordered_pair(all_42_7, v0) = v1) | ~ (in(v1, all_42_5) = 0) % 13.23/2.70 | | | | | ~ $i(v0)) % 13.23/2.70 | | | | % 13.23/2.70 | | | | GROUND_INST: instantiating (4) with all_42_1, all_74_1, all_42_2, % 13.23/2.70 | | | | all_42_7, simplifying with (10), (50) gives: % 13.23/2.70 | | | | (56) all_74_1 = all_42_1 % 13.23/2.70 | | | | % 13.23/2.70 | | | | GROUND_INST: instantiating (5) with all_42_0, all_74_0, all_42_7, % 13.23/2.70 | | | | all_42_5, simplifying with (14), (48) gives: % 13.23/2.70 | | | | (57) all_74_0 = all_42_0 % 13.23/2.70 | | | | % 13.23/2.70 | | | | BETA: splitting (17) gives: % 13.23/2.70 | | | | % 13.23/2.70 | | | | Case 1: % 13.23/2.70 | | | | | % 13.23/2.70 | | | | | (58) all_42_0 = all_42_6 & all_42_1 = 0 & ~ (all_42_3 = 0) % 13.23/2.70 | | | | | % 13.23/2.70 | | | | | ALPHA: (58) implies: % 13.23/2.70 | | | | | (59) all_42_1 = 0 % 13.23/2.70 | | | | | (60) all_42_0 = all_42_6 % 13.23/2.70 | | | | | (61) ~ (all_42_3 = 0) % 13.23/2.70 | | | | | % 13.23/2.70 | | | | | COMBINE_EQS: (56), (59) imply: % 13.23/2.70 | | | | | (62) all_74_1 = 0 % 13.23/2.70 | | | | | % 13.23/2.70 | | | | | COMBINE_EQS: (57), (60) imply: % 13.23/2.70 | | | | | (63) all_74_0 = all_42_6 % 13.23/2.70 | | | | | % 13.23/2.70 | | | | | BETA: splitting (49) gives: % 13.23/2.70 | | | | | % 13.23/2.70 | | | | | Case 1: % 13.23/2.70 | | | | | | % 13.23/2.70 | | | | | | (64) ~ (all_74_1 = 0) % 13.23/2.70 | | | | | | % 13.23/2.70 | | | | | | REDUCE: (62), (64) imply: % 13.23/2.70 | | | | | | (65) $false % 13.23/2.70 | | | | | | % 13.23/2.70 | | | | | | CLOSE: (65) is inconsistent. % 13.23/2.70 | | | | | | % 13.23/2.70 | | | | | Case 2: % 13.23/2.70 | | | | | | % 13.23/2.71 | | | | | | (66) ( ~ (all_74_0 = all_42_6) | all_42_3 = 0) & ( ~ (all_42_3 = % 13.23/2.71 | | | | | | 0) | all_74_0 = all_42_6) % 13.23/2.71 | | | | | | % 13.23/2.71 | | | | | | ALPHA: (66) implies: % 13.23/2.71 | | | | | | (67) ~ (all_74_0 = all_42_6) | all_42_3 = 0 % 13.23/2.71 | | | | | | % 13.23/2.71 | | | | | | BETA: splitting (67) gives: % 13.23/2.71 | | | | | | % 13.23/2.71 | | | | | | Case 1: % 13.23/2.71 | | | | | | | % 13.23/2.71 | | | | | | | (68) ~ (all_74_0 = all_42_6) % 13.23/2.71 | | | | | | | % 13.23/2.71 | | | | | | | REDUCE: (63), (68) imply: % 13.23/2.71 | | | | | | | (69) $false % 13.23/2.71 | | | | | | | % 13.23/2.71 | | | | | | | CLOSE: (69) is inconsistent. % 13.23/2.71 | | | | | | | % 13.23/2.71 | | | | | | Case 2: % 13.23/2.71 | | | | | | | % 13.23/2.71 | | | | | | | (70) all_42_3 = 0 % 13.23/2.71 | | | | | | | % 13.23/2.71 | | | | | | | REDUCE: (61), (70) imply: % 13.23/2.71 | | | | | | | (71) $false % 13.23/2.71 | | | | | | | % 13.23/2.71 | | | | | | | CLOSE: (71) is inconsistent. % 13.23/2.71 | | | | | | | % 13.23/2.71 | | | | | | End of split % 13.23/2.71 | | | | | | % 13.23/2.71 | | | | | End of split % 13.23/2.71 | | | | | % 13.23/2.71 | | | | Case 2: % 13.23/2.71 | | | | | % 13.23/2.71 | | | | | (72) all_42_3 = 0 & ( ~ (all_42_0 = all_42_6) | ~ (all_42_1 = 0)) % 13.23/2.71 | | | | | % 13.23/2.71 | | | | | ALPHA: (72) implies: % 13.23/2.71 | | | | | (73) all_42_3 = 0 % 13.23/2.71 | | | | | (74) ~ (all_42_0 = all_42_6) | ~ (all_42_1 = 0) % 13.23/2.71 | | | | | % 13.23/2.71 | | | | | REDUCE: (11), (73) imply: % 13.23/2.71 | | | | | (75) in(all_42_4, all_42_5) = 0 % 13.23/2.71 | | | | | % 13.23/2.71 | | | | | GROUND_INST: instantiating (44) with all_42_7, all_42_6, all_42_4, 0, % 13.23/2.71 | | | | | simplifying with (7), (8), (15), (75) gives: % 13.23/2.71 | | | | | (76) ? [v0: any] : ? [v1: $i] : (apply(all_42_5, all_42_7) = v1 & % 13.23/2.71 | | | | | in(all_42_7, all_56_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 13.23/2.71 | | | | | all_42_6)) % 13.23/2.71 | | | | | % 13.23/2.71 | | | | | DELTA: instantiating (76) with fresh symbols all_134_0, all_134_1 % 13.23/2.71 | | | | | gives: % 13.23/2.71 | | | | | (77) apply(all_42_5, all_42_7) = all_134_0 & in(all_42_7, all_56_0) % 13.23/2.71 | | | | | = all_134_1 & $i(all_134_0) & ( ~ (all_134_1 = 0) | all_134_0 % 13.23/2.71 | | | | | = all_42_6) % 13.23/2.71 | | | | | % 13.23/2.71 | | | | | ALPHA: (77) implies: % 13.23/2.71 | | | | | (78) in(all_42_7, all_56_0) = all_134_1 % 13.23/2.71 | | | | | (79) apply(all_42_5, all_42_7) = all_134_0 % 13.23/2.71 | | | | | (80) ~ (all_134_1 = 0) | all_134_0 = all_42_6 % 13.23/2.71 | | | | | % 13.23/2.71 | | | | | REDUCE: (30), (78) imply: % 13.23/2.71 | | | | | (81) in(all_42_7, all_42_2) = all_134_1 % 13.23/2.71 | | | | | % 13.23/2.71 | | | | | GROUND_INST: instantiating (4) with all_42_1, all_134_1, all_42_2, % 13.23/2.71 | | | | | all_42_7, simplifying with (10), (81) gives: % 13.23/2.71 | | | | | (82) all_134_1 = all_42_1 % 13.23/2.71 | | | | | % 13.23/2.71 | | | | | GROUND_INST: instantiating (5) with all_42_0, all_134_0, all_42_7, % 13.23/2.71 | | | | | all_42_5, simplifying with (14), (79) gives: % 13.23/2.71 | | | | | (83) all_134_0 = all_42_0 % 13.23/2.71 | | | | | % 13.23/2.71 | | | | | BETA: splitting (55) gives: % 13.23/2.71 | | | | | % 13.23/2.71 | | | | | Case 1: % 13.23/2.71 | | | | | | % 13.23/2.71 | | | | | | (84) all_42_1 = 0 % 13.23/2.71 | | | | | | % 13.23/2.71 | | | | | | COMBINE_EQS: (82), (84) imply: % 13.23/2.71 | | | | | | (85) all_134_1 = 0 % 13.23/2.71 | | | | | | % 13.23/2.71 | | | | | | BETA: splitting (74) gives: % 13.23/2.71 | | | | | | % 13.23/2.71 | | | | | | Case 1: % 13.23/2.71 | | | | | | | % 13.23/2.71 | | | | | | | (86) ~ (all_42_1 = 0) % 13.23/2.71 | | | | | | | % 13.23/2.71 | | | | | | | REDUCE: (84), (86) imply: % 13.23/2.71 | | | | | | | (87) $false % 13.23/2.71 | | | | | | | % 13.23/2.71 | | | | | | | CLOSE: (87) is inconsistent. % 13.23/2.71 | | | | | | | % 13.23/2.71 | | | | | | Case 2: % 13.23/2.71 | | | | | | | % 13.23/2.71 | | | | | | | (88) ~ (all_42_0 = all_42_6) % 13.23/2.71 | | | | | | | % 13.23/2.71 | | | | | | | BETA: splitting (80) gives: % 13.23/2.71 | | | | | | | % 13.23/2.71 | | | | | | | Case 1: % 13.23/2.71 | | | | | | | | % 13.23/2.71 | | | | | | | | (89) ~ (all_134_1 = 0) % 13.23/2.71 | | | | | | | | % 13.23/2.71 | | | | | | | | REDUCE: (85), (89) imply: % 13.23/2.71 | | | | | | | | (90) $false % 13.23/2.71 | | | | | | | | % 13.23/2.71 | | | | | | | | CLOSE: (90) is inconsistent. % 13.23/2.71 | | | | | | | | % 13.23/2.71 | | | | | | | Case 2: % 13.23/2.71 | | | | | | | | % 13.23/2.71 | | | | | | | | (91) all_134_0 = all_42_6 % 13.23/2.71 | | | | | | | | % 13.23/2.71 | | | | | | | | COMBINE_EQS: (83), (91) imply: % 13.23/2.71 | | | | | | | | (92) all_42_0 = all_42_6 % 13.23/2.71 | | | | | | | | % 13.23/2.71 | | | | | | | | REDUCE: (88), (92) imply: % 13.23/2.71 | | | | | | | | (93) $false % 13.23/2.71 | | | | | | | | % 13.23/2.71 | | | | | | | | CLOSE: (93) is inconsistent. % 13.23/2.71 | | | | | | | | % 13.23/2.71 | | | | | | | End of split % 13.23/2.71 | | | | | | | % 13.23/2.71 | | | | | | End of split % 13.23/2.71 | | | | | | % 13.23/2.71 | | | | | Case 2: % 13.23/2.71 | | | | | | % 13.23/2.71 | | | | | | (94) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(all_42_7, v0) % 13.23/2.71 | | | | | | = v1) | ~ (in(v1, all_42_5) = 0) | ~ $i(v0)) % 13.23/2.71 | | | | | | % 13.23/2.71 | | | | | | GROUND_INST: instantiating (94) with all_42_6, all_42_4, simplifying % 13.23/2.71 | | | | | | with (8), (15), (75) gives: % 13.23/2.71 | | | | | | (95) $false % 13.23/2.71 | | | | | | % 13.23/2.71 | | | | | | CLOSE: (95) is inconsistent. % 13.23/2.71 | | | | | | % 13.23/2.71 | | | | | End of split % 13.23/2.71 | | | | | % 13.23/2.71 | | | | End of split % 13.23/2.71 | | | | % 13.23/2.71 | | | End of split % 13.23/2.71 | | | % 13.23/2.71 | | End of split % 13.23/2.71 | | % 13.23/2.71 | End of split % 13.23/2.71 | % 13.23/2.71 End of proof % 13.23/2.71 % SZS output end Proof for theBenchmark % 13.23/2.71 % 13.23/2.71 2057ms %------------------------------------------------------------------------------