%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU178+2 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n009.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 17:43:04 EDT 2023 % Result : Theorem 23.90s 3.96s % Output : Proof 61.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU178+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.34 % Computer : n009.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Wed Aug 23 20:55:21 EDT 2023 % 0.16/0.34 % CPUTime : % 0.19/0.66 ________ _____ % 0.19/0.66 ___ __ \_________(_)________________________________ % 0.19/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.66 % 0.19/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.66 (2023-06-19) % 0.19/0.66 % 0.19/0.66 (c) Philipp Rümmer, 2009-2023 % 0.19/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.66 Amanda Stjerna. % 0.19/0.66 Free software under BSD-3-Clause. % 0.19/0.66 % 0.19/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.66 % 0.19/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.68 Running up to 7 provers in parallel. % 0.19/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 4.65/1.43 Prover 4: Preprocessing ... % 4.65/1.43 Prover 1: Preprocessing ... % 4.65/1.46 Prover 5: Preprocessing ... % 4.65/1.46 Prover 0: Preprocessing ... % 4.65/1.46 Prover 6: Preprocessing ... % 4.65/1.46 Prover 2: Preprocessing ... % 4.65/1.46 Prover 3: Preprocessing ... % 13.56/2.66 Prover 1: Warning: ignoring some quantifiers % 14.29/2.73 Prover 3: Warning: ignoring some quantifiers % 14.29/2.75 Prover 5: Proving ... % 14.29/2.80 Prover 1: Constructing countermodel ... % 15.08/2.80 Prover 3: Constructing countermodel ... % 15.32/2.82 Prover 6: Proving ... % 15.37/2.83 Prover 4: Warning: ignoring some quantifiers % 15.93/2.92 Prover 4: Constructing countermodel ... % 16.48/2.99 Prover 0: Proving ... % 16.48/3.03 Prover 2: Proving ... % 23.68/3.95 Prover 0: proved (3262ms) % 23.90/3.96 % 23.90/3.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 23.90/3.96 % 23.90/3.96 Prover 6: stopped % 23.90/3.96 Prover 5: stopped % 23.90/3.96 Prover 2: stopped % 23.90/3.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 23.90/3.97 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 23.90/3.97 Prover 3: stopped % 23.90/3.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 23.90/3.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 23.90/3.98 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 25.54/4.23 Prover 7: Preprocessing ... % 26.40/4.32 Prover 11: Preprocessing ... % 26.40/4.32 Prover 10: Preprocessing ... % 26.40/4.33 Prover 13: Preprocessing ... % 26.40/4.33 Prover 8: Preprocessing ... % 28.42/4.56 Prover 7: Warning: ignoring some quantifiers % 28.42/4.58 Prover 10: Warning: ignoring some quantifiers % 28.42/4.59 Prover 7: Constructing countermodel ... % 28.72/4.60 Prover 10: Constructing countermodel ... % 28.72/4.62 Prover 8: Warning: ignoring some quantifiers % 28.72/4.64 Prover 8: Constructing countermodel ... % 28.72/4.67 Prover 13: Warning: ignoring some quantifiers % 28.72/4.70 Prover 13: Constructing countermodel ... % 31.41/4.98 Prover 11: Warning: ignoring some quantifiers % 31.77/5.04 Prover 11: Constructing countermodel ... % 34.09/5.45 Prover 10: gave up % 34.09/5.47 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 36.28/5.60 Prover 16: Preprocessing ... % 38.20/5.88 Prover 16: Warning: ignoring some quantifiers % 38.62/5.91 Prover 16: Constructing countermodel ... % 61.12/8.83 Prover 1: Found proof (size 215) % 61.12/8.83 Prover 1: proved (8150ms) % 61.12/8.84 Prover 13: stopped % 61.12/8.84 Prover 16: stopped % 61.12/8.84 Prover 8: stopped % 61.12/8.84 Prover 7: stopped % 61.12/8.84 Prover 11: stopped % 61.12/8.85 Prover 4: stopped % 61.12/8.85 % 61.12/8.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 61.12/8.85 % 61.12/8.86 % SZS output start Proof for theBenchmark % 61.12/8.87 Assumptions after simplification: % 61.12/8.87 --------------------------------- % 61.12/8.87 % 61.12/8.87 (d1_relat_1) % 61.45/8.89 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (relation(v0) = v1) | ~ $i(v0) | ? % 61.45/8.89 [v2: $i] : (in(v2, v0) = 0 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~ % 61.45/8.89 (ordered_pair(v3, v4) = v2) | ~ $i(v4) | ~ $i(v3)))) & ! [v0: $i] : ( % 61.45/8.89 ~ (relation(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ % 61.45/8.89 $i(v1) | ? [v2: $i] : ? [v3: $i] : (ordered_pair(v2, v3) = v1 & $i(v3) & % 61.45/8.89 $i(v2)))) % 61.45/8.89 % 61.45/8.89 (d2_subset_1) % 61.45/8.90 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (element(v1, v0) = v2) | ~ % 61.45/8.90 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v0) = v3 & in(v1, % 61.45/8.90 v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = % 61.45/8.90 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (empty(v1) = % 61.45/8.90 v2) | ~ (empty(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 61.45/8.90 (element(v1, v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0))) % 61.45/8.90 % 61.45/8.90 (d2_zfmisc_1) % 61.45/8.90 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 61.45/8.90 (cartesian_product2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 61.45/8.90 [v4: $i] : ? [v5: any] : (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ! [v6: % 61.45/8.90 $i] : ! [v7: $i] : ( ~ (ordered_pair(v6, v7) = v4) | ~ $i(v7) | ~ % 61.45/8.90 $i(v6) | ? [v8: any] : ? [v9: any] : (in(v7, v2) = v9 & in(v6, v1) = % 61.45/8.90 v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) & (v5 = 0 | ? [v6: $i] : ? % 61.45/8.90 [v7: $i] : (ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0 % 61.45/8.90 & $i(v7) & $i(v6))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 61.45/8.90 (cartesian_product2(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! % 61.45/8.90 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | ! % 61.45/8.90 [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v6) = v3) | ~ $i(v6) | % 61.45/8.90 ~ $i(v5) | ? [v7: any] : ? [v8: any] : (in(v6, v1) = v8 & in(v5, v0) % 61.45/8.90 = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))) & ! [v3: $i] : ( ~ (in(v3, % 61.45/8.90 v2) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: $i] : (ordered_pair(v4, % 61.45/8.90 v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0 & $i(v5) & $i(v4))))) % 61.45/8.90 % 61.45/8.90 (d3_tarski) % 61.45/8.91 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 61.45/8.91 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 61.45/8.91 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 61.45/8.91 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 61.45/8.91 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 61.45/8.91 % 61.45/8.91 (d4_relat_1) % 61.45/8.91 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 61.45/8.91 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~ % 61.45/8.91 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~ % 61.45/8.91 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) = % 61.45/8.91 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i] % 61.45/8.91 : ? [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, v0) = 0 & $i(v6) % 61.45/8.91 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 % 61.45/8.91 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~ % 61.45/8.91 (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) & % 61.45/8.91 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: % 61.45/8.91 $i] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) & % 61.45/8.91 $i(v3))))))) % 61.45/8.91 % 61.45/8.91 (d4_xboole_0) % 61.45/8.91 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 61.45/8.91 (set_difference(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 61.45/8.91 $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, v2) = v7 & % 61.45/8.91 in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v6 = 0) | ~ (v5 = 0) | % 61.45/8.91 v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) & ! [v0: $i] : ! [v1: % 61.45/8.91 $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) | ~ $i(v2) | ~ % 61.45/8.91 $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: any] : ( ~ (in(v3, v0) = v4) | % 61.45/8.91 ~ $i(v3) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = % 61.45/8.91 v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0))))) & ! [v3: $i] : ( ~ % 61.45/8.91 (in(v3, v0) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) % 61.45/8.91 = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))))) % 61.45/8.91 % 61.45/8.91 (d5_subset_1) % 61.45/8.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (element(v1, v2) = 0) | ~ % 61.45/8.91 (powerset(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 61.45/8.91 (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3 & $i(v3))) % 61.45/8.91 % 61.45/8.91 (fc1_subset_1) % 61.45/8.91 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] % 61.45/8.91 : ( ~ (v2 = 0) & empty(v1) = v2)) % 61.45/8.91 % 61.45/8.91 (fc4_subset_1) % 61.45/8.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0, v1) = % 61.45/8.91 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 61.45/8.91 (empty(v2) = v5 & empty(v1) = v4 & empty(v0) = v3 & ( ~ (v5 = 0) | v4 = 0 | % 61.45/8.91 v3 = 0))) % 61.45/8.91 % 61.45/8.91 (rc1_relat_1) % 61.45/8.92 ? [v0: $i] : (empty(v0) = 0 & relation(v0) = 0 & $i(v0)) % 61.45/8.92 % 61.45/8.92 (rc1_subset_1) % 61.45/8.92 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 61.45/8.92 [v2: $i] : (powerset(v0) = v2 & $i(v2) & ? [v3: $i] : ? [v4: int] : ( ~ % 61.45/8.92 (v4 = 0) & element(v3, v2) = 0 & empty(v3) = v4 & $i(v3)))) % 61.45/8.92 % 61.45/8.92 (rc1_xboole_0) % 61.45/8.92 ? [v0: $i] : (empty(v0) = 0 & $i(v0)) % 61.45/8.92 % 61.45/8.92 (rc2_subset_1) % 61.45/8.92 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] % 61.45/8.92 : (element(v2, v1) = 0 & empty(v2) = 0 & $i(v2))) % 61.45/8.92 % 61.45/8.92 (rc2_xboole_0) % 61.45/8.92 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & $i(v0)) % 61.45/8.92 % 61.45/8.92 (redefinition_k6_subset_1) % 61.45/8.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (element(v2, v3) = % 61.45/8.92 0) | ~ (element(v1, v3) = 0) | ~ (powerset(v0) = v3) | ~ $i(v2) | ~ % 61.45/8.92 $i(v1) | ~ $i(v0) | ? [v4: $i] : (subset_difference(v0, v1, v2) = v4 & % 61.45/8.92 set_difference(v1, v2) = v4 & $i(v4))) % 61.45/8.92 % 61.45/8.92 (t1_subset) % 61.45/8.92 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (element(v0, v1) = v2) % 61.45/8.92 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 61.45/8.92 % 61.45/8.92 (t1_zfmisc_1) % 61.45/8.92 $i(empty_set) & ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) % 61.45/8.92 = v0 & $i(v0)) % 61.45/8.92 % 61.45/8.92 (t20_relat_1) % 61.45/8.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ! [v5: % 61.45/8.92 $i] : ! [v6: any] : ( ~ (relation_rng(v2) = v5) | ~ (relation_dom(v2) = % 61.45/8.92 v3) | ~ (in(v1, v5) = v6) | ~ (in(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 61.45/8.92 | ~ $i(v0) | ? [v7: any] : ? [v8: $i] : ? [v9: any] : (relation(v2) = v7 % 61.45/8.92 & ordered_pair(v0, v1) = v8 & in(v8, v2) = v9 & $i(v8) & ( ~ (v9 = 0) | ~ % 61.45/8.92 (v7 = 0))) | (v6 = 0 & v4 = 0)) % 61.45/8.92 % 61.45/8.92 (t21_relat_1) % 61.45/8.92 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 61.45/8.92 = 0) & relation_rng(v0) = v2 & relation_dom(v0) = v1 & % 61.45/8.92 cartesian_product2(v1, v2) = v3 & relation(v0) = 0 & subset(v0, v3) = v4 & % 61.45/8.92 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 61.45/8.92 % 61.45/8.92 (t2_subset) % 61.45/8.92 ! [v0: $i] : ! [v1: $i] : ( ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) % 61.45/8.92 | ? [v2: any] : ? [v3: any] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 % 61.45/8.92 | v2 = 0))) % 61.45/8.92 % 61.45/8.92 (t3_boole) % 61.45/8.92 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (set_difference(v0, % 61.45/8.92 empty_set) = v1) | ~ $i(v0)) % 61.45/8.92 % 61.45/8.92 (t6_boole) % 61.45/8.92 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ % 61.45/8.92 $i(v0)) % 61.45/8.92 % 61.45/8.92 (t8_boole) % 61.45/8.93 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0) % 61.45/8.93 | ~ $i(v1) | ~ $i(v0)) % 61.45/8.93 % 61.45/8.93 (function-axioms) % 61.45/8.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 61.45/8.93 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, % 61.45/8.93 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 61.45/8.93 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ % 61.45/8.93 (are_equipotent(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 61.45/8.93 ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ % 61.45/8.93 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 61.45/8.93 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ % 61.45/8.93 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 61.45/8.93 ! [v3: $i] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ % 61.45/8.93 (complements_of_subsets(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 61.45/8.93 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 61.45/8.93 (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! % 61.45/8.93 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, % 61.45/8.93 v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 61.45/8.93 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = % 61.45/8.93 v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 61.45/8.93 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ % 61.45/8.93 (cartesian_product2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 61.45/8.93 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3, % 61.45/8.93 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 61.45/8.93 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ % 61.45/8.93 (ordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 61.45/8.93 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 61.45/8.93 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 61.45/8.93 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ % 61.45/8.93 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 61.45/8.93 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, % 61.45/8.93 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 61.45/8.93 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 61.45/8.93 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 61.45/8.93 [v3: $i] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, % 61.45/8.93 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 61.45/8.93 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 61.45/8.93 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 61.45/8.93 (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! % 61.45/8.93 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) % 61.45/8.93 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cast_to_subset(v2) % 61.45/8.93 = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 61.45/8.93 [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 61.45/8.93 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 61.45/8.93 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: % 61.45/8.93 $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = % 61.45/8.93 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 61.45/8.93 (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 61.45/8.93 : ! [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & % 61.45/8.93 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 61.45/8.93 v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 61.45/8.93 % 61.45/8.93 Further assumptions not needed in the proof: % 61.45/8.93 -------------------------------------------- % 61.45/8.94 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski, % 61.45/8.94 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_setfam_1, % 61.45/8.94 d1_tarski, d1_xboole_0, d1_zfmisc_1, d2_tarski, d2_xboole_0, d3_xboole_0, % 61.45/8.94 d4_subset_1, d4_tarski, d5_relat_1, d5_tarski, d7_xboole_0, d8_setfam_1, % 61.45/8.94 d8_xboole_0, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, dt_k1_xboole_0, % 61.45/8.94 dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, dt_k2_xboole_0, % 61.45/8.94 dt_k2_zfmisc_1, dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0, dt_k4_tarski, % 61.45/8.94 dt_k4_xboole_0, dt_k5_setfam_1, dt_k6_setfam_1, dt_k6_subset_1, dt_k7_setfam_1, % 61.45/8.94 dt_m1_subset_1, existence_m1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_subset_1, % 61.45/8.94 fc2_xboole_0, fc3_subset_1, fc3_xboole_0, idempotence_k2_xboole_0, % 61.45/8.94 idempotence_k3_xboole_0, involutiveness_k3_subset_1, involutiveness_k7_setfam_1, % 61.45/8.94 irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1, % 61.45/8.94 l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, % 61.45/8.94 l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, redefinition_k5_setfam_1, % 61.45/8.94 redefinition_k6_setfam_1, reflexivity_r1_tarski, symmetry_r1_xboole_0, % 61.45/8.94 t106_zfmisc_1, t10_zfmisc_1, t118_zfmisc_1, t119_zfmisc_1, t12_xboole_1, % 61.45/8.94 t136_zfmisc_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_xboole_1, t26_xboole_1, % 61.45/8.94 t28_xboole_1, t2_boole, t2_tarski, t2_xboole_1, t33_xboole_1, t33_zfmisc_1, % 61.45/8.94 t36_xboole_1, t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1, % 61.45/8.94 t39_zfmisc_1, t3_subset, t3_xboole_0, t3_xboole_1, t40_xboole_1, t43_subset_1, % 61.45/8.94 t45_xboole_1, t46_setfam_1, t46_zfmisc_1, t47_setfam_1, t48_setfam_1, % 61.45/8.94 t48_xboole_1, t4_boole, t4_subset, t4_xboole_0, t50_subset_1, t54_subset_1, % 61.45/8.94 t5_subset, t60_xboole_1, t63_xboole_1, t65_zfmisc_1, t69_enumset1, t6_zfmisc_1, % 61.45/8.94 t7_boole, t7_xboole_1, t83_xboole_1, t8_xboole_1, t8_zfmisc_1, t92_zfmisc_1, % 61.45/8.94 t99_zfmisc_1, t9_tarski, t9_zfmisc_1 % 61.45/8.94 % 61.45/8.94 Those formulas are unsatisfiable: % 61.45/8.94 --------------------------------- % 61.45/8.94 % 61.45/8.94 Begin of proof % 61.45/8.94 | % 61.45/8.94 | ALPHA: (d1_relat_1) implies: % 61.45/8.94 | (1) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 61.45/8.94 | (in(v1, v0) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: $i] : % 61.45/8.94 | (ordered_pair(v2, v3) = v1 & $i(v3) & $i(v2)))) % 61.45/8.94 | % 61.45/8.94 | ALPHA: (d2_subset_1) implies: % 61.45/8.94 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (empty(v1) = v2) | ~ % 61.45/8.94 | (empty(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : (element(v1, % 61.45/8.94 | v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0))) % 61.45/8.94 | % 61.45/8.94 | ALPHA: (d2_zfmisc_1) implies: % 61.45/8.94 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0, % 61.45/8.94 | v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! % 61.45/8.94 | [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | ! [v5: % 61.45/8.94 | $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v6) = v3) | ~ $i(v6) % 61.45/8.94 | | ~ $i(v5) | ? [v7: any] : ? [v8: any] : (in(v6, v1) = v8 & % 61.45/8.94 | in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))) & ! [v3: % 61.45/8.94 | $i] : ( ~ (in(v3, v2) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: % 61.45/8.94 | $i] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) % 61.45/8.94 | = 0 & $i(v5) & $i(v4))))) % 61.45/8.94 | % 61.45/8.94 | ALPHA: (d3_tarski) implies: % 61.45/8.94 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 61.45/8.94 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 61.45/8.94 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 61.45/8.94 | % 61.45/8.94 | ALPHA: (d4_xboole_0) implies: % 61.45/8.94 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = % 61.45/8.94 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: % 61.45/8.94 | any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: % 61.45/8.94 | any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 % 61.45/8.94 | = 0 & ~ (v6 = 0))))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) % 61.45/8.94 | | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & % 61.45/8.94 | in(v3, v1) = v4 & (v5 = 0 | v4 = 0))))) % 61.45/8.94 | % 61.45/8.94 | ALPHA: (t1_zfmisc_1) implies: % 61.45/8.94 | (6) ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) = v0 & % 61.45/8.94 | $i(v0)) % 61.45/8.94 | % 61.45/8.94 | ALPHA: (t3_boole) implies: % 61.45/8.95 | (7) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (set_difference(v0, % 61.45/8.95 | empty_set) = v1) | ~ $i(v0)) % 61.45/8.95 | % 61.45/8.95 | ALPHA: (t6_boole) implies: % 61.45/8.95 | (8) $i(empty_set) % 61.45/8.95 | (9) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0)) % 61.45/8.95 | % 61.45/8.95 | ALPHA: (function-axioms) implies: % 61.45/8.95 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 61.45/8.95 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 61.45/8.95 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 61.45/8.95 | : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 61.45/8.95 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 61.45/8.95 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 61.45/8.95 | v0)) % 61.45/8.95 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 61.45/8.95 | (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 61.45/8.95 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 61.45/8.95 | : ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, % 61.45/8.95 | v2) = v0)) % 61.45/8.95 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 61.45/8.95 | (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 61.45/8.95 | % 61.45/8.95 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_120_0 gives: % 61.45/8.95 | (16) empty(all_120_0) = 0 & $i(all_120_0) % 61.45/8.95 | % 61.45/8.95 | ALPHA: (16) implies: % 61.45/8.95 | (17) $i(all_120_0) % 61.45/8.95 | (18) empty(all_120_0) = 0 % 61.45/8.95 | % 61.45/8.95 | DELTA: instantiating (6) with fresh symbol all_122_0 gives: % 61.45/8.95 | (19) powerset(empty_set) = all_122_0 & singleton(empty_set) = all_122_0 & % 61.45/8.95 | $i(all_122_0) % 61.45/8.95 | % 61.45/8.95 | ALPHA: (19) implies: % 61.45/8.95 | (20) $i(all_122_0) % 61.45/8.95 | (21) powerset(empty_set) = all_122_0 % 61.45/8.95 | % 61.45/8.95 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_126_0 gives: % 61.45/8.95 | (22) empty(all_126_0) = 0 & relation(all_126_0) = 0 & $i(all_126_0) % 61.45/8.95 | % 61.45/8.95 | ALPHA: (22) implies: % 61.45/8.95 | (23) $i(all_126_0) % 61.45/8.95 | (24) empty(all_126_0) = 0 % 61.45/8.95 | % 61.45/8.95 | DELTA: instantiating (rc2_xboole_0) with fresh symbols all_129_0, all_129_1 % 61.45/8.95 | gives: % 61.45/8.95 | (25) ~ (all_129_0 = 0) & empty(all_129_1) = all_129_0 & $i(all_129_1) % 61.45/8.95 | % 61.45/8.95 | ALPHA: (25) implies: % 61.45/8.95 | (26) ~ (all_129_0 = 0) % 61.45/8.95 | (27) $i(all_129_1) % 61.45/8.95 | (28) empty(all_129_1) = all_129_0 % 61.45/8.95 | % 61.45/8.95 | DELTA: instantiating (t21_relat_1) with fresh symbols all_143_0, all_143_1, % 61.45/8.95 | all_143_2, all_143_3, all_143_4 gives: % 61.45/8.95 | (29) ~ (all_143_0 = 0) & relation_rng(all_143_4) = all_143_2 & % 61.45/8.95 | relation_dom(all_143_4) = all_143_3 & cartesian_product2(all_143_3, % 61.45/8.95 | all_143_2) = all_143_1 & relation(all_143_4) = 0 & subset(all_143_4, % 61.45/8.95 | all_143_1) = all_143_0 & $i(all_143_1) & $i(all_143_2) & % 61.45/8.95 | $i(all_143_3) & $i(all_143_4) % 61.45/8.95 | % 61.45/8.95 | ALPHA: (29) implies: % 61.45/8.95 | (30) ~ (all_143_0 = 0) % 61.45/8.95 | (31) $i(all_143_4) % 61.45/8.95 | (32) $i(all_143_3) % 61.45/8.96 | (33) $i(all_143_2) % 61.45/8.96 | (34) $i(all_143_1) % 61.45/8.96 | (35) subset(all_143_4, all_143_1) = all_143_0 % 61.45/8.96 | (36) relation(all_143_4) = 0 % 61.45/8.96 | (37) cartesian_product2(all_143_3, all_143_2) = all_143_1 % 61.45/8.96 | (38) relation_dom(all_143_4) = all_143_3 % 61.45/8.96 | (39) relation_rng(all_143_4) = all_143_2 % 61.45/8.96 | % 61.45/8.96 | GROUND_INST: instantiating (4) with all_143_4, all_143_1, all_143_0, % 61.45/8.96 | simplifying with (31), (34), (35) gives: % 61.45/8.96 | (40) all_143_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 61.45/8.96 | all_143_1) = v1 & in(v0, all_143_4) = 0 & $i(v0)) % 61.45/8.96 | % 61.45/8.96 | GROUND_INST: instantiating (1) with all_143_4, simplifying with (31), (36) % 61.45/8.96 | gives: % 61.45/8.96 | (41) ! [v0: $i] : ( ~ (in(v0, all_143_4) = 0) | ~ $i(v0) | ? [v1: $i] : % 61.45/8.96 | ? [v2: $i] : (ordered_pair(v1, v2) = v0 & $i(v2) & $i(v1))) % 61.45/8.96 | % 61.45/8.96 | GROUND_INST: instantiating (fc1_subset_1) with empty_set, all_122_0, % 61.45/8.96 | simplifying with (8), (21) gives: % 61.45/8.96 | (42) ? [v0: int] : ( ~ (v0 = 0) & empty(all_122_0) = v0) % 61.45/8.96 | % 61.45/8.96 | GROUND_INST: instantiating (rc2_subset_1) with empty_set, all_122_0, % 61.45/8.96 | simplifying with (8), (21) gives: % 61.45/8.96 | (43) ? [v0: $i] : (element(v0, all_122_0) = 0 & empty(v0) = 0 & $i(v0)) % 61.45/8.96 | % 61.45/8.96 | GROUND_INST: instantiating (t8_boole) with all_120_0, all_126_0, simplifying % 61.45/8.96 | with (17), (18), (23), (24) gives: % 61.45/8.96 | (44) all_126_0 = all_120_0 % 61.45/8.96 | % 61.45/8.96 | GROUND_INST: instantiating (9) with all_126_0, simplifying with (23), (24) % 61.45/8.96 | gives: % 61.45/8.96 | (45) all_126_0 = empty_set % 61.45/8.96 | % 61.45/8.96 | GROUND_INST: instantiating (rc1_subset_1) with all_129_1, all_129_0, % 61.45/8.96 | simplifying with (27), (28) gives: % 61.45/8.96 | (46) all_129_0 = 0 | ? [v0: $i] : (powerset(all_129_1) = v0 & $i(v0) & ? % 61.45/8.96 | [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 & % 61.45/8.96 | empty(v1) = v2 & $i(v1))) % 61.45/8.96 | % 61.45/8.96 | GROUND_INST: instantiating (3) with all_143_3, all_143_2, all_143_1, % 61.45/8.96 | simplifying with (32), (33), (34), (37) gives: % 61.45/8.96 | (47) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_143_1) = v1) | % 61.45/8.96 | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v3) = % 61.45/8.96 | v0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : % 61.45/8.96 | (in(v3, all_143_2) = v5 & in(v2, all_143_3) = v4 & ( ~ (v5 = 0) | % 61.45/8.96 | ~ (v4 = 0))))) & ! [v0: $i] : ( ~ (in(v0, all_143_1) = 0) | % 61.45/8.96 | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v2) = v0 & % 61.45/8.96 | in(v2, all_143_2) = 0 & in(v1, all_143_3) = 0 & $i(v2) & $i(v1))) % 61.45/8.96 | % 61.45/8.96 | ALPHA: (47) implies: % 61.45/8.96 | (48) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_143_1) = v1) | % 61.45/8.96 | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v3) = % 61.45/8.96 | v0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : % 61.45/8.96 | (in(v3, all_143_2) = v5 & in(v2, all_143_3) = v4 & ( ~ (v5 = 0) | % 61.45/8.96 | ~ (v4 = 0))))) % 61.45/8.96 | % 61.45/8.96 | GROUND_INST: instantiating (fc4_subset_1) with all_143_3, all_143_2, % 61.45/8.96 | all_143_1, simplifying with (32), (33), (37) gives: % 61.45/8.96 | (49) ? [v0: any] : ? [v1: any] : ? [v2: any] : (empty(all_143_1) = v2 & % 61.45/8.96 | empty(all_143_2) = v1 & empty(all_143_3) = v0 & ( ~ (v2 = 0) | v1 = % 61.45/8.96 | 0 | v0 = 0)) % 61.45/8.96 | % 61.45/8.96 | GROUND_INST: instantiating (d4_relat_1) with all_143_4, all_143_3, simplifying % 61.45/8.96 | with (31), (38) gives: % 61.45/8.97 | (50) ? [v0: int] : ( ~ (v0 = 0) & relation(all_143_4) = v0) | ( ? [v0: % 61.45/8.97 | any] : (v0 = all_143_3 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : % 61.45/8.97 | (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: % 61.45/8.97 | $i] : ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4, % 61.45/8.97 | all_143_4) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : % 61.45/8.97 | ? [v4: $i] : (ordered_pair(v1, v3) = v4 & in(v4, all_143_4) = % 61.45/8.97 | 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_143_3) | ( ! [v0: $i] : % 61.45/8.97 | ! [v1: int] : (v1 = 0 | ~ (in(v0, all_143_3) = v1) | ~ $i(v0) % 61.45/8.97 | | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) % 61.45/8.97 | | ~ (in(v3, all_143_4) = 0) | ~ $i(v2))) & ! [v0: $i] : ( % 61.45/8.97 | ~ (in(v0, all_143_3) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 61.45/8.97 | $i] : (ordered_pair(v0, v1) = v2 & in(v2, all_143_4) = 0 & % 61.45/8.97 | $i(v2) & $i(v1)))))) % 61.45/8.97 | % 61.45/8.97 | COMBINE_EQS: (44), (45) imply: % 61.45/8.97 | (51) all_120_0 = empty_set % 61.45/8.97 | % 61.45/8.97 | SIMP: (51) implies: % 61.45/8.97 | (52) all_120_0 = empty_set % 61.45/8.97 | % 61.45/8.97 | DELTA: instantiating (42) with fresh symbol all_174_0 gives: % 61.45/8.97 | (53) ~ (all_174_0 = 0) & empty(all_122_0) = all_174_0 % 61.45/8.97 | % 61.45/8.97 | ALPHA: (53) implies: % 61.45/8.97 | (54) ~ (all_174_0 = 0) % 61.45/8.97 | (55) empty(all_122_0) = all_174_0 % 61.45/8.97 | % 61.45/8.97 | DELTA: instantiating (43) with fresh symbol all_176_0 gives: % 61.45/8.97 | (56) element(all_176_0, all_122_0) = 0 & empty(all_176_0) = 0 & % 61.45/8.97 | $i(all_176_0) % 61.45/8.97 | % 61.45/8.97 | ALPHA: (56) implies: % 61.45/8.97 | (57) $i(all_176_0) % 61.45/8.97 | (58) empty(all_176_0) = 0 % 61.45/8.97 | (59) element(all_176_0, all_122_0) = 0 % 61.45/8.97 | % 61.45/8.97 | DELTA: instantiating (49) with fresh symbols all_184_0, all_184_1, all_184_2 % 61.45/8.97 | gives: % 61.45/8.97 | (60) empty(all_143_1) = all_184_0 & empty(all_143_2) = all_184_1 & % 61.45/8.97 | empty(all_143_3) = all_184_2 & ( ~ (all_184_0 = 0) | all_184_1 = 0 | % 61.45/8.97 | all_184_2 = 0) % 61.45/8.97 | % 61.45/8.97 | ALPHA: (60) implies: % 61.45/8.97 | (61) empty(all_143_2) = all_184_1 % 61.45/8.97 | % 61.45/8.97 | REDUCE: (18), (52) imply: % 61.45/8.97 | (62) empty(empty_set) = 0 % 61.45/8.97 | % 61.45/8.97 | BETA: splitting (50) gives: % 61.45/8.97 | % 61.45/8.97 | Case 1: % 61.45/8.97 | | % 61.45/8.97 | | (63) ? [v0: int] : ( ~ (v0 = 0) & relation(all_143_4) = v0) % 61.45/8.97 | | % 61.45/8.97 | | DELTA: instantiating (63) with fresh symbol all_192_0 gives: % 61.45/8.97 | | (64) ~ (all_192_0 = 0) & relation(all_143_4) = all_192_0 % 61.45/8.97 | | % 61.45/8.97 | | ALPHA: (64) implies: % 61.45/8.97 | | (65) ~ (all_192_0 = 0) % 61.45/8.97 | | (66) relation(all_143_4) = all_192_0 % 61.45/8.97 | | % 61.45/8.97 | | GROUND_INST: instantiating (10) with 0, all_192_0, all_143_4, simplifying % 61.45/8.97 | | with (36), (66) gives: % 61.45/8.97 | | (67) all_192_0 = 0 % 61.45/8.97 | | % 61.45/8.97 | | REDUCE: (65), (67) imply: % 61.45/8.97 | | (68) $false % 61.45/8.97 | | % 61.45/8.97 | | CLOSE: (68) is inconsistent. % 61.45/8.97 | | % 61.45/8.97 | Case 2: % 61.45/8.97 | | % 61.45/8.97 | | (69) ? [v0: any] : (v0 = all_143_3 | ~ $i(v0) | ? [v1: $i] : ? [v2: % 61.45/8.97 | | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : % 61.45/8.97 | | ! [v4: $i] : ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4, % 61.45/8.97 | | all_143_4) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : % 61.45/8.97 | | ? [v4: $i] : (ordered_pair(v1, v3) = v4 & in(v4, all_143_4) = % 61.45/8.97 | | 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_143_3) | ( ! [v0: $i] : % 61.45/8.97 | | ! [v1: int] : (v1 = 0 | ~ (in(v0, all_143_3) = v1) | ~ $i(v0) % 61.45/8.97 | | | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) % 61.45/8.97 | | | ~ (in(v3, all_143_4) = 0) | ~ $i(v2))) & ! [v0: $i] : ( % 61.45/8.97 | | ~ (in(v0, all_143_3) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 61.45/8.97 | | $i] : (ordered_pair(v0, v1) = v2 & in(v2, all_143_4) = 0 & % 61.45/8.97 | | $i(v2) & $i(v1))))) % 61.45/8.97 | | % 61.45/8.97 | | ALPHA: (69) implies: % 61.45/8.97 | | (70) ~ $i(all_143_3) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 61.45/8.97 | | (in(v0, all_143_3) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] % 61.45/8.97 | | : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_143_4) = 0) | % 61.45/8.97 | | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_143_3) = 0) | ~ % 61.45/8.97 | | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2 % 61.45/8.97 | | & in(v2, all_143_4) = 0 & $i(v2) & $i(v1)))) % 61.45/8.97 | | % 61.45/8.97 | | BETA: splitting (40) gives: % 61.45/8.97 | | % 61.45/8.97 | | Case 1: % 61.45/8.97 | | | % 61.45/8.98 | | | (71) all_143_0 = 0 % 61.45/8.98 | | | % 61.45/8.98 | | | REDUCE: (30), (71) imply: % 61.45/8.98 | | | (72) $false % 61.45/8.98 | | | % 61.45/8.98 | | | CLOSE: (72) is inconsistent. % 61.45/8.98 | | | % 61.45/8.98 | | Case 2: % 61.45/8.98 | | | % 61.45/8.98 | | | (73) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_143_1) = v1 % 61.45/8.98 | | | & in(v0, all_143_4) = 0 & $i(v0)) % 61.45/8.98 | | | % 61.45/8.98 | | | DELTA: instantiating (73) with fresh symbols all_201_0, all_201_1 gives: % 61.45/8.98 | | | (74) ~ (all_201_0 = 0) & in(all_201_1, all_143_1) = all_201_0 & % 61.45/8.98 | | | in(all_201_1, all_143_4) = 0 & $i(all_201_1) % 61.45/8.98 | | | % 61.45/8.98 | | | ALPHA: (74) implies: % 61.45/8.98 | | | (75) ~ (all_201_0 = 0) % 61.45/8.98 | | | (76) $i(all_201_1) % 61.45/8.98 | | | (77) in(all_201_1, all_143_4) = 0 % 61.45/8.98 | | | (78) in(all_201_1, all_143_1) = all_201_0 % 61.45/8.98 | | | % 61.45/8.98 | | | BETA: splitting (46) gives: % 61.45/8.98 | | | % 61.45/8.98 | | | Case 1: % 61.45/8.98 | | | | % 61.45/8.98 | | | | (79) all_129_0 = 0 % 61.45/8.98 | | | | % 61.45/8.98 | | | | REDUCE: (26), (79) imply: % 61.45/8.98 | | | | (80) $false % 61.45/8.98 | | | | % 61.45/8.98 | | | | CLOSE: (80) is inconsistent. % 61.45/8.98 | | | | % 61.45/8.98 | | | Case 2: % 61.45/8.98 | | | | % 61.45/8.98 | | | | (81) ? [v0: $i] : (powerset(all_129_1) = v0 & $i(v0) & ? [v1: $i] : % 61.45/8.98 | | | | ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 & empty(v1) % 61.45/8.98 | | | | = v2 & $i(v1))) % 61.45/8.98 | | | | % 61.45/8.98 | | | | DELTA: instantiating (81) with fresh symbol all_206_0 gives: % 61.45/8.98 | | | | (82) powerset(all_129_1) = all_206_0 & $i(all_206_0) & ? [v0: $i] : % 61.45/8.98 | | | | ? [v1: int] : ( ~ (v1 = 0) & element(v0, all_206_0) = 0 & % 61.45/8.98 | | | | empty(v0) = v1 & $i(v0)) % 61.45/8.98 | | | | % 61.45/8.98 | | | | ALPHA: (82) implies: % 61.45/8.98 | | | | (83) $i(all_206_0) % 61.45/8.98 | | | | (84) powerset(all_129_1) = all_206_0 % 61.45/8.98 | | | | (85) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0, % 61.45/8.98 | | | | all_206_0) = 0 & empty(v0) = v1 & $i(v0)) % 61.45/8.98 | | | | % 61.45/8.98 | | | | DELTA: instantiating (85) with fresh symbols all_208_0, all_208_1 gives: % 61.45/8.98 | | | | (86) ~ (all_208_0 = 0) & element(all_208_1, all_206_0) = 0 & % 61.45/8.98 | | | | empty(all_208_1) = all_208_0 & $i(all_208_1) % 61.45/8.98 | | | | % 61.45/8.98 | | | | ALPHA: (86) implies: % 61.45/8.98 | | | | (87) ~ (all_208_0 = 0) % 61.45/8.98 | | | | (88) $i(all_208_1) % 61.45/8.98 | | | | (89) empty(all_208_1) = all_208_0 % 61.45/8.98 | | | | (90) element(all_208_1, all_206_0) = 0 % 61.45/8.98 | | | | % 61.45/8.98 | | | | BETA: splitting (70) gives: % 61.45/8.98 | | | | % 61.45/8.98 | | | | Case 1: % 61.45/8.98 | | | | | % 61.45/8.98 | | | | | (91) ~ $i(all_143_3) % 61.45/8.98 | | | | | % 61.45/8.98 | | | | | PRED_UNIFY: (32), (91) imply: % 61.45/8.98 | | | | | (92) $false % 61.45/8.98 | | | | | % 61.45/8.98 | | | | | CLOSE: (92) is inconsistent. % 61.45/8.98 | | | | | % 61.45/8.98 | | | | Case 2: % 61.45/8.98 | | | | | % 61.45/8.98 | | | | | % 61.45/8.98 | | | | | GROUND_INST: instantiating (41) with all_201_1, simplifying with (76), % 61.45/8.98 | | | | | (77) gives: % 61.45/8.98 | | | | | (93) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_201_1 % 61.45/8.98 | | | | | & $i(v1) & $i(v0)) % 61.45/8.98 | | | | | % 61.45/8.98 | | | | | GROUND_INST: instantiating (48) with all_201_1, all_201_0, simplifying % 61.45/8.98 | | | | | with (76), (78) gives: % 61.45/8.98 | | | | | (94) all_201_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ % 61.45/8.98 | | | | | (ordered_pair(v0, v1) = all_201_1) | ~ $i(v1) | ~ $i(v0) | % 61.45/8.98 | | | | | ? [v2: any] : ? [v3: any] : (in(v1, all_143_2) = v3 & % 61.45/8.98 | | | | | in(v0, all_143_3) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 61.45/8.98 | | | | | % 61.45/8.98 | | | | | GROUND_INST: instantiating (fc1_subset_1) with all_129_1, all_206_0, % 61.45/8.98 | | | | | simplifying with (27), (84) gives: % 61.45/8.98 | | | | | (95) ? [v0: int] : ( ~ (v0 = 0) & empty(all_206_0) = v0) % 61.45/8.98 | | | | | % 61.45/8.98 | | | | | GROUND_INST: instantiating (rc2_subset_1) with all_129_1, all_206_0, % 61.45/8.98 | | | | | simplifying with (27), (84) gives: % 61.45/8.98 | | | | | (96) ? [v0: $i] : (element(v0, all_206_0) = 0 & empty(v0) = 0 & % 61.45/8.98 | | | | | $i(v0)) % 61.45/8.98 | | | | | % 61.45/8.98 | | | | | GROUND_INST: instantiating (rc1_subset_1) with all_122_0, all_174_0, % 61.45/8.98 | | | | | simplifying with (20), (55) gives: % 61.45/8.98 | | | | | (97) all_174_0 = 0 | ? [v0: $i] : (powerset(all_122_0) = v0 & % 61.45/8.98 | | | | | $i(v0) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 61.45/8.98 | | | | | element(v1, v0) = 0 & empty(v1) = v2 & $i(v1))) % 61.45/8.98 | | | | | % 61.45/8.98 | | | | | GROUND_INST: instantiating (2) with empty_set, all_143_2, all_184_1, % 61.45/8.98 | | | | | simplifying with (8), (33), (61), (62) gives: % 61.45/8.98 | | | | | (98) ? [v0: any] : (element(all_143_2, empty_set) = v0 & ( ~ (v0 = % 61.45/8.98 | | | | | 0) | all_184_1 = 0) & ( ~ (all_184_1 = 0) | v0 = 0)) % 61.45/8.98 | | | | | % 61.45/8.98 | | | | | GROUND_INST: instantiating (rc1_subset_1) with all_143_2, all_184_1, % 61.45/8.98 | | | | | simplifying with (33), (61) gives: % 61.45/8.98 | | | | | (99) all_184_1 = 0 | ? [v0: $i] : (powerset(all_143_2) = v0 & % 61.45/8.98 | | | | | $i(v0) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 61.45/8.98 | | | | | element(v1, v0) = 0 & empty(v1) = v2 & $i(v1))) % 61.45/8.98 | | | | | % 61.45/8.98 | | | | | GROUND_INST: instantiating (2) with all_176_0, all_143_2, all_184_1, % 61.45/8.98 | | | | | simplifying with (33), (57), (58), (61) gives: % 61.45/8.99 | | | | | (100) ? [v0: any] : (element(all_143_2, all_176_0) = v0 & ( ~ (v0 % 61.45/8.99 | | | | | = 0) | all_184_1 = 0) & ( ~ (all_184_1 = 0) | v0 = 0)) % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | GROUND_INST: instantiating (9) with all_176_0, simplifying with (57), % 61.45/8.99 | | | | | (58) gives: % 61.45/8.99 | | | | | (101) all_176_0 = empty_set % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | GROUND_INST: instantiating (rc1_subset_1) with all_208_1, all_208_0, % 61.45/8.99 | | | | | simplifying with (88), (89) gives: % 61.45/8.99 | | | | | (102) all_208_0 = 0 | ? [v0: $i] : (powerset(all_208_1) = v0 & % 61.45/8.99 | | | | | $i(v0) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 61.45/8.99 | | | | | element(v1, v0) = 0 & empty(v1) = v2 & $i(v1))) % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | GROUND_INST: instantiating (redefinition_k6_subset_1) with empty_set, % 61.45/8.99 | | | | | all_176_0, all_176_0, all_122_0, simplifying with (8), % 61.45/8.99 | | | | | (21), (57), (59) gives: % 61.45/8.99 | | | | | (103) ? [v0: $i] : (subset_difference(empty_set, all_176_0, % 61.45/8.99 | | | | | all_176_0) = v0 & set_difference(all_176_0, all_176_0) = % 61.45/8.99 | | | | | v0 & $i(v0)) % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | GROUND_INST: instantiating (d5_subset_1) with empty_set, all_176_0, % 61.45/8.99 | | | | | all_122_0, simplifying with (8), (21), (57), (59) gives: % 61.45/8.99 | | | | | (104) ? [v0: $i] : (subset_complement(empty_set, all_176_0) = v0 & % 61.45/8.99 | | | | | set_difference(empty_set, all_176_0) = v0 & $i(v0)) % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | GROUND_INST: instantiating (t2_subset) with all_208_1, all_206_0, % 61.45/8.99 | | | | | simplifying with (83), (88), (90) gives: % 61.45/8.99 | | | | | (105) ? [v0: any] : ? [v1: any] : (empty(all_206_0) = v0 & % 61.45/8.99 | | | | | in(all_208_1, all_206_0) = v1 & (v1 = 0 | v0 = 0)) % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | DELTA: instantiating (95) with fresh symbol all_239_0 gives: % 61.45/8.99 | | | | | (106) ~ (all_239_0 = 0) & empty(all_206_0) = all_239_0 % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | ALPHA: (106) implies: % 61.45/8.99 | | | | | (107) ~ (all_239_0 = 0) % 61.45/8.99 | | | | | (108) empty(all_206_0) = all_239_0 % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | DELTA: instantiating (104) with fresh symbol all_247_0 gives: % 61.45/8.99 | | | | | (109) subset_complement(empty_set, all_176_0) = all_247_0 & % 61.45/8.99 | | | | | set_difference(empty_set, all_176_0) = all_247_0 & % 61.45/8.99 | | | | | $i(all_247_0) % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | ALPHA: (109) implies: % 61.45/8.99 | | | | | (110) set_difference(empty_set, all_176_0) = all_247_0 % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | DELTA: instantiating (93) with fresh symbols all_251_0, all_251_1 % 61.45/8.99 | | | | | gives: % 61.45/8.99 | | | | | (111) ordered_pair(all_251_1, all_251_0) = all_201_1 & % 61.45/8.99 | | | | | $i(all_251_0) & $i(all_251_1) % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | ALPHA: (111) implies: % 61.45/8.99 | | | | | (112) $i(all_251_1) % 61.45/8.99 | | | | | (113) $i(all_251_0) % 61.45/8.99 | | | | | (114) ordered_pair(all_251_1, all_251_0) = all_201_1 % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | DELTA: instantiating (103) with fresh symbol all_253_0 gives: % 61.45/8.99 | | | | | (115) subset_difference(empty_set, all_176_0, all_176_0) = % 61.45/8.99 | | | | | all_253_0 & set_difference(all_176_0, all_176_0) = all_253_0 % 61.45/8.99 | | | | | & $i(all_253_0) % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | ALPHA: (115) implies: % 61.45/8.99 | | | | | (116) $i(all_253_0) % 61.45/8.99 | | | | | (117) set_difference(all_176_0, all_176_0) = all_253_0 % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | DELTA: instantiating (96) with fresh symbol all_255_0 gives: % 61.45/8.99 | | | | | (118) element(all_255_0, all_206_0) = 0 & empty(all_255_0) = 0 & % 61.45/8.99 | | | | | $i(all_255_0) % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | ALPHA: (118) implies: % 61.45/8.99 | | | | | (119) $i(all_255_0) % 61.45/8.99 | | | | | (120) empty(all_255_0) = 0 % 61.45/8.99 | | | | | (121) element(all_255_0, all_206_0) = 0 % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | DELTA: instantiating (105) with fresh symbols all_257_0, all_257_1 % 61.45/8.99 | | | | | gives: % 61.45/8.99 | | | | | (122) empty(all_206_0) = all_257_1 & in(all_208_1, all_206_0) = % 61.45/8.99 | | | | | all_257_0 & (all_257_0 = 0 | all_257_1 = 0) % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | ALPHA: (122) implies: % 61.45/8.99 | | | | | (123) empty(all_206_0) = all_257_1 % 61.45/8.99 | | | | | (124) all_257_0 = 0 | all_257_1 = 0 % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | DELTA: instantiating (100) with fresh symbol all_267_0 gives: % 61.45/8.99 | | | | | (125) element(all_143_2, all_176_0) = all_267_0 & ( ~ (all_267_0 = % 61.45/8.99 | | | | | 0) | all_184_1 = 0) & ( ~ (all_184_1 = 0) | all_267_0 = % 61.45/8.99 | | | | | 0) % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | ALPHA: (125) implies: % 61.45/8.99 | | | | | (126) element(all_143_2, all_176_0) = all_267_0 % 61.45/8.99 | | | | | (127) ~ (all_267_0 = 0) | all_184_1 = 0 % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | DELTA: instantiating (98) with fresh symbol all_279_0 gives: % 61.45/8.99 | | | | | (128) element(all_143_2, empty_set) = all_279_0 & ( ~ (all_279_0 = % 61.45/8.99 | | | | | 0) | all_184_1 = 0) & ( ~ (all_184_1 = 0) | all_279_0 = % 61.45/8.99 | | | | | 0) % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | ALPHA: (128) implies: % 61.45/8.99 | | | | | (129) element(all_143_2, empty_set) = all_279_0 % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | REDUCE: (101), (117) imply: % 61.45/8.99 | | | | | (130) set_difference(empty_set, empty_set) = all_253_0 % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | REDUCE: (101), (110) imply: % 61.45/8.99 | | | | | (131) set_difference(empty_set, empty_set) = all_247_0 % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | REDUCE: (101), (126) imply: % 61.45/8.99 | | | | | (132) element(all_143_2, empty_set) = all_267_0 % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | BETA: splitting (102) gives: % 61.45/8.99 | | | | | % 61.45/8.99 | | | | | Case 1: % 61.45/8.99 | | | | | | % 61.45/8.99 | | | | | | (133) all_208_0 = 0 % 61.45/8.99 | | | | | | % 61.45/8.99 | | | | | | REDUCE: (87), (133) imply: % 61.45/8.99 | | | | | | (134) $false % 61.45/8.99 | | | | | | % 61.45/8.99 | | | | | | CLOSE: (134) is inconsistent. % 61.45/8.99 | | | | | | % 61.45/8.99 | | | | | Case 2: % 61.45/8.99 | | | | | | % 61.45/8.99 | | | | | | (135) ? [v0: $i] : (powerset(all_208_1) = v0 & $i(v0) & ? [v1: % 61.45/8.99 | | | | | | $i] : ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 % 61.45/8.99 | | | | | | & empty(v1) = v2 & $i(v1))) % 61.45/8.99 | | | | | | % 61.45/8.99 | | | | | | DELTA: instantiating (135) with fresh symbol all_294_0 gives: % 61.45/8.99 | | | | | | (136) powerset(all_208_1) = all_294_0 & $i(all_294_0) & ? [v0: % 61.45/8.99 | | | | | | $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0, % 61.45/8.99 | | | | | | all_294_0) = 0 & empty(v0) = v1 & $i(v0)) % 61.45/8.99 | | | | | | % 61.45/8.99 | | | | | | ALPHA: (136) implies: % 61.45/8.99 | | | | | | (137) powerset(all_208_1) = all_294_0 % 61.45/8.99 | | | | | | % 61.45/8.99 | | | | | | BETA: splitting (94) gives: % 61.45/8.99 | | | | | | % 61.45/8.99 | | | | | | Case 1: % 61.45/8.99 | | | | | | | % 61.45/9.00 | | | | | | | (138) all_201_0 = 0 % 61.45/9.00 | | | | | | | % 61.45/9.00 | | | | | | | REDUCE: (75), (138) imply: % 61.45/9.00 | | | | | | | (139) $false % 61.45/9.00 | | | | | | | % 61.45/9.00 | | | | | | | CLOSE: (139) is inconsistent. % 61.45/9.00 | | | | | | | % 61.45/9.00 | | | | | | Case 2: % 61.45/9.00 | | | | | | | % 61.45/9.00 | | | | | | | (140) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v1) = % 61.45/9.00 | | | | | | | all_201_1) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : % 61.45/9.00 | | | | | | | ? [v3: any] : (in(v1, all_143_2) = v3 & in(v0, % 61.45/9.00 | | | | | | | all_143_3) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 61.45/9.00 | | | | | | | % 61.45/9.00 | | | | | | | BETA: splitting (97) gives: % 61.45/9.00 | | | | | | | % 61.45/9.00 | | | | | | | Case 1: % 61.45/9.00 | | | | | | | | % 61.45/9.00 | | | | | | | | (141) all_174_0 = 0 % 61.45/9.00 | | | | | | | | % 61.45/9.00 | | | | | | | | REDUCE: (54), (141) imply: % 61.45/9.00 | | | | | | | | (142) $false % 61.45/9.00 | | | | | | | | % 61.45/9.00 | | | | | | | | CLOSE: (142) is inconsistent. % 61.45/9.00 | | | | | | | | % 61.45/9.00 | | | | | | | Case 2: % 61.45/9.00 | | | | | | | | % 61.45/9.00 | | | | | | | | (143) ? [v0: $i] : (powerset(all_122_0) = v0 & $i(v0) & ? % 61.45/9.00 | | | | | | | | [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & element(v1, % 61.45/9.00 | | | | | | | | v0) = 0 & empty(v1) = v2 & $i(v1))) % 61.45/9.00 | | | | | | | | % 61.45/9.00 | | | | | | | | DELTA: instantiating (143) with fresh symbol all_319_0 gives: % 61.45/9.00 | | | | | | | | (144) powerset(all_122_0) = all_319_0 & $i(all_319_0) & ? % 61.45/9.00 | | | | | | | | [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0, % 61.45/9.00 | | | | | | | | all_319_0) = 0 & empty(v0) = v1 & $i(v0)) % 61.45/9.00 | | | | | | | | % 61.45/9.00 | | | | | | | | ALPHA: (144) implies: % 61.45/9.00 | | | | | | | | (145) $i(all_319_0) % 61.45/9.00 | | | | | | | | (146) powerset(all_122_0) = all_319_0 % 61.45/9.00 | | | | | | | | % 61.45/9.00 | | | | | | | | GROUND_INST: instantiating (11) with all_239_0, all_257_1, % 61.45/9.00 | | | | | | | | all_206_0, simplifying with (108), (123) gives: % 61.45/9.00 | | | | | | | | (147) all_257_1 = all_239_0 % 61.45/9.00 | | | | | | | | % 61.45/9.00 | | | | | | | | GROUND_INST: instantiating (14) with all_267_0, all_279_0, % 61.45/9.00 | | | | | | | | empty_set, all_143_2, simplifying with (129), (132) % 61.45/9.00 | | | | | | | | gives: % 61.45/9.00 | | | | | | | | (148) all_279_0 = all_267_0 % 61.45/9.00 | | | | | | | | % 61.45/9.00 | | | | | | | | GROUND_INST: instantiating (15) with all_247_0, all_253_0, % 61.45/9.00 | | | | | | | | empty_set, empty_set, simplifying with (130), (131) % 61.45/9.00 | | | | | | | | gives: % 61.45/9.00 | | | | | | | | (149) all_253_0 = all_247_0 % 61.45/9.00 | | | | | | | | % 61.45/9.00 | | | | | | | | REDUCE: (116), (149) imply: % 61.45/9.00 | | | | | | | | (150) $i(all_247_0) % 61.45/9.00 | | | | | | | | % 61.45/9.00 | | | | | | | | BETA: splitting (124) gives: % 61.45/9.00 | | | | | | | | % 61.45/9.00 | | | | | | | | Case 1: % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | GROUND_INST: instantiating (140) with all_251_1, all_251_0, % 61.45/9.00 | | | | | | | | | simplifying with (112), (113), (114) gives: % 61.45/9.00 | | | | | | | | | (151) ? [v0: any] : ? [v1: any] : (in(all_251_0, % 61.45/9.00 | | | | | | | | | all_143_2) = v1 & in(all_251_1, all_143_3) = v0 & % 61.45/9.00 | | | | | | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | GROUND_INST: instantiating (fc1_subset_1) with all_122_0, % 61.45/9.00 | | | | | | | | | all_319_0, simplifying with (20), (146) gives: % 61.45/9.00 | | | | | | | | | (152) ? [v0: int] : ( ~ (v0 = 0) & empty(all_319_0) = v0) % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | GROUND_INST: instantiating (rc2_subset_1) with all_208_1, % 61.45/9.00 | | | | | | | | | all_294_0, simplifying with (88), (137) gives: % 61.45/9.00 | | | | | | | | | (153) ? [v0: $i] : (element(v0, all_294_0) = 0 & empty(v0) % 61.45/9.00 | | | | | | | | | = 0 & $i(v0)) % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | GROUND_INST: instantiating (9) with all_255_0, simplifying with % 61.45/9.00 | | | | | | | | | (119), (120) gives: % 61.45/9.00 | | | | | | | | | (154) all_255_0 = empty_set % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | GROUND_INST: instantiating (t1_subset) with all_143_2, % 61.45/9.00 | | | | | | | | | empty_set, all_267_0, simplifying with (8), (33), % 61.45/9.00 | | | | | | | | | (132) gives: % 61.45/9.00 | | | | | | | | | (155) all_267_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 61.45/9.00 | | | | | | | | | in(all_143_2, empty_set) = v0) % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | GROUND_INST: instantiating (redefinition_k6_subset_1) with % 61.45/9.00 | | | | | | | | | all_129_1, all_255_0, all_208_1, all_206_0, % 61.45/9.00 | | | | | | | | | simplifying with (27), (84), (88), (90), (119), % 61.45/9.00 | | | | | | | | | (121) gives: % 61.45/9.00 | | | | | | | | | (156) ? [v0: $i] : (subset_difference(all_129_1, % 61.45/9.00 | | | | | | | | | all_255_0, all_208_1) = v0 & % 61.45/9.00 | | | | | | | | | set_difference(all_255_0, all_208_1) = v0 & $i(v0)) % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | GROUND_INST: instantiating (7) with empty_set, all_247_0, % 61.45/9.00 | | | | | | | | | simplifying with (8), (131) gives: % 61.45/9.00 | | | | | | | | | (157) all_247_0 = empty_set % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | DELTA: instantiating (152) with fresh symbol all_370_0 gives: % 61.45/9.00 | | | | | | | | | (158) ~ (all_370_0 = 0) & empty(all_319_0) = all_370_0 % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | ALPHA: (158) implies: % 61.45/9.00 | | | | | | | | | (159) ~ (all_370_0 = 0) % 61.45/9.00 | | | | | | | | | (160) empty(all_319_0) = all_370_0 % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | DELTA: instantiating (156) with fresh symbol all_392_0 gives: % 61.45/9.00 | | | | | | | | | (161) subset_difference(all_129_1, all_255_0, all_208_1) = % 61.45/9.00 | | | | | | | | | all_392_0 & set_difference(all_255_0, all_208_1) = % 61.45/9.00 | | | | | | | | | all_392_0 & $i(all_392_0) % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | ALPHA: (161) implies: % 61.45/9.00 | | | | | | | | | (162) $i(all_392_0) % 61.45/9.00 | | | | | | | | | (163) set_difference(all_255_0, all_208_1) = all_392_0 % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | DELTA: instantiating (153) with fresh symbol all_398_0 gives: % 61.45/9.00 | | | | | | | | | (164) element(all_398_0, all_294_0) = 0 & empty(all_398_0) % 61.45/9.00 | | | | | | | | | = 0 & $i(all_398_0) % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | ALPHA: (164) implies: % 61.45/9.00 | | | | | | | | | (165) $i(all_398_0) % 61.45/9.00 | | | | | | | | | (166) empty(all_398_0) = 0 % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | DELTA: instantiating (151) with fresh symbols all_404_0, % 61.45/9.00 | | | | | | | | | all_404_1 gives: % 61.45/9.00 | | | | | | | | | (167) in(all_251_0, all_143_2) = all_404_0 & in(all_251_1, % 61.45/9.00 | | | | | | | | | all_143_3) = all_404_1 & ( ~ (all_404_0 = 0) | ~ % 61.45/9.00 | | | | | | | | | (all_404_1 = 0)) % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | ALPHA: (167) implies: % 61.45/9.00 | | | | | | | | | (168) in(all_251_1, all_143_3) = all_404_1 % 61.45/9.00 | | | | | | | | | (169) in(all_251_0, all_143_2) = all_404_0 % 61.45/9.00 | | | | | | | | | (170) ~ (all_404_0 = 0) | ~ (all_404_1 = 0) % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | REDUCE: (154), (163) imply: % 61.45/9.00 | | | | | | | | | (171) set_difference(empty_set, all_208_1) = all_392_0 % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | BETA: splitting (99) gives: % 61.45/9.00 | | | | | | | | | % 61.45/9.00 | | | | | | | | | Case 1: % 61.45/9.00 | | | | | | | | | | % 61.45/9.00 | | | | | | | | | | % 61.45/9.00 | | | | | | | | | | GROUND_INST: instantiating (t20_relat_1) with all_251_1, % 61.45/9.00 | | | | | | | | | | all_251_0, all_143_4, all_143_3, all_404_1, % 61.45/9.00 | | | | | | | | | | all_143_2, all_404_0, simplifying with (31), (38), % 61.45/9.00 | | | | | | | | | | (39), (112), (113), (168), (169) gives: % 61.45/9.01 | | | | | | | | | | (172) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 61.45/9.01 | | | | | | | | | | (relation(all_143_4) = v0 & ordered_pair(all_251_1, % 61.45/9.01 | | | | | | | | | | all_251_0) = v1 & in(v1, all_143_4) = v2 & % 61.45/9.01 | | | | | | | | | | $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0))) | % 61.45/9.01 | | | | | | | | | | (all_404_0 = 0 & all_404_1 = 0) % 61.45/9.01 | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | GROUND_INST: instantiating (2) with all_398_0, all_319_0, % 61.45/9.01 | | | | | | | | | | all_370_0, simplifying with (145), (160), (165), % 61.45/9.01 | | | | | | | | | | (166) gives: % 61.45/9.01 | | | | | | | | | | (173) ? [v0: any] : (element(all_319_0, all_398_0) = v0 % 61.45/9.01 | | | | | | | | | | & ( ~ (v0 = 0) | all_370_0 = 0) & ( ~ (all_370_0 % 61.45/9.01 | | | | | | | | | | = 0) | v0 = 0)) % 61.45/9.01 | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | DELTA: instantiating (173) with fresh symbol all_980_0 % 61.45/9.01 | | | | | | | | | | gives: % 61.45/9.01 | | | | | | | | | | (174) element(all_319_0, all_398_0) = all_980_0 & ( ~ % 61.45/9.01 | | | | | | | | | | (all_980_0 = 0) | all_370_0 = 0) & ( ~ (all_370_0 % 61.45/9.01 | | | | | | | | | | = 0) | all_980_0 = 0) % 61.45/9.01 | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | ALPHA: (174) implies: % 61.45/9.01 | | | | | | | | | | (175) ~ (all_980_0 = 0) | all_370_0 = 0 % 61.45/9.01 | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | BETA: splitting (172) gives: % 61.45/9.01 | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | Case 1: % 61.45/9.01 | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | (176) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 61.45/9.01 | | | | | | | | | | | (relation(all_143_4) = v0 & % 61.45/9.01 | | | | | | | | | | | ordered_pair(all_251_1, all_251_0) = v1 & in(v1, % 61.45/9.01 | | | | | | | | | | | all_143_4) = v2 & $i(v1) & ( ~ (v2 = 0) | ~ % 61.45/9.01 | | | | | | | | | | | (v0 = 0))) % 61.45/9.01 | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | DELTA: instantiating (176) with fresh symbols all_1281_0, % 61.45/9.01 | | | | | | | | | | | all_1281_1, all_1281_2 gives: % 61.45/9.01 | | | | | | | | | | | (177) relation(all_143_4) = all_1281_2 & % 61.45/9.01 | | | | | | | | | | | ordered_pair(all_251_1, all_251_0) = all_1281_1 & % 61.45/9.01 | | | | | | | | | | | in(all_1281_1, all_143_4) = all_1281_0 & % 61.45/9.01 | | | | | | | | | | | $i(all_1281_1) & ( ~ (all_1281_0 = 0) | ~ % 61.45/9.01 | | | | | | | | | | | (all_1281_2 = 0)) % 61.45/9.01 | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | ALPHA: (177) implies: % 61.45/9.01 | | | | | | | | | | | (178) in(all_1281_1, all_143_4) = all_1281_0 % 61.45/9.01 | | | | | | | | | | | (179) ordered_pair(all_251_1, all_251_0) = all_1281_1 % 61.45/9.01 | | | | | | | | | | | (180) relation(all_143_4) = all_1281_2 % 61.45/9.01 | | | | | | | | | | | (181) ~ (all_1281_0 = 0) | ~ (all_1281_2 = 0) % 61.45/9.01 | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | BETA: splitting (175) gives: % 61.45/9.01 | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | Case 1: % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_201_1, all_1281_1, % 61.45/9.01 | | | | | | | | | | | | all_251_0, all_251_1, simplifying with (114), % 61.45/9.01 | | | | | | | | | | | | (179) gives: % 61.45/9.01 | | | | | | | | | | | | (182) all_1281_1 = all_201_1 % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_1281_2, all_143_4, % 61.45/9.01 | | | | | | | | | | | | simplifying with (36), (180) gives: % 61.45/9.01 | | | | | | | | | | | | (183) all_1281_2 = 0 % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | REDUCE: (178), (182) imply: % 61.45/9.01 | | | | | | | | | | | | (184) in(all_201_1, all_143_4) = all_1281_0 % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | BETA: splitting (181) gives: % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | Case 1: % 61.45/9.01 | | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | | (185) ~ (all_1281_0 = 0) % 61.45/9.01 | | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_1281_0, all_143_4, % 61.45/9.01 | | | | | | | | | | | | | all_201_1, simplifying with (77), (184) gives: % 61.45/9.01 | | | | | | | | | | | | | (186) all_1281_0 = 0 % 61.45/9.01 | | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | | REDUCE: (185), (186) imply: % 61.45/9.01 | | | | | | | | | | | | | (187) $false % 61.45/9.01 | | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | | CLOSE: (187) is inconsistent. % 61.45/9.01 | | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | Case 2: % 61.45/9.01 | | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | | (188) ~ (all_1281_2 = 0) % 61.45/9.01 | | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | | REDUCE: (183), (188) imply: % 61.45/9.01 | | | | | | | | | | | | | (189) $false % 61.45/9.01 | | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | | CLOSE: (189) is inconsistent. % 61.45/9.01 | | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | End of split % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | Case 2: % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | (190) all_370_0 = 0 % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | REDUCE: (159), (190) imply: % 61.45/9.01 | | | | | | | | | | | | (191) $false % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | CLOSE: (191) is inconsistent. % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | End of split % 61.45/9.01 | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | Case 2: % 61.45/9.01 | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | (192) all_404_0 = 0 & all_404_1 = 0 % 61.45/9.01 | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | ALPHA: (192) implies: % 61.45/9.01 | | | | | | | | | | | (193) all_404_1 = 0 % 61.45/9.01 | | | | | | | | | | | (194) all_404_0 = 0 % 61.45/9.01 | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | REF_CLOSE: (170), (193), (194) are inconsistent by sub-proof % 61.45/9.01 | | | | | | | | | | | #1. % 61.45/9.01 | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | End of split % 61.45/9.01 | | | | | | | | | | % 61.45/9.01 | | | | | | | | | Case 2: % 61.45/9.01 | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | (195) ~ (all_184_1 = 0) % 61.45/9.01 | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | BETA: splitting (127) gives: % 61.45/9.01 | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | Case 1: % 61.45/9.01 | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | (196) ~ (all_267_0 = 0) % 61.45/9.01 | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | BETA: splitting (155) gives: % 61.45/9.01 | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | Case 1: % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | (197) all_267_0 = 0 % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | REDUCE: (196), (197) imply: % 61.45/9.01 | | | | | | | | | | | | (198) $false % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | CLOSE: (198) is inconsistent. % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | Case 2: % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | (199) ? [v0: int] : ( ~ (v0 = 0) & in(all_143_2, % 61.45/9.01 | | | | | | | | | | | | empty_set) = v0) % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | DELTA: instantiating (199) with fresh symbol all_708_0 % 61.45/9.01 | | | | | | | | | | | | gives: % 61.45/9.01 | | | | | | | | | | | | (200) ~ (all_708_0 = 0) & in(all_143_2, empty_set) = % 61.45/9.01 | | | | | | | | | | | | all_708_0 % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | ALPHA: (200) implies: % 61.45/9.01 | | | | | | | | | | | | (201) ~ (all_708_0 = 0) % 61.45/9.01 | | | | | | | | | | | | (202) in(all_143_2, empty_set) = all_708_0 % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | GROUND_INST: instantiating (t20_relat_1) with all_251_1, % 61.45/9.01 | | | | | | | | | | | | all_251_0, all_143_4, all_143_3, all_404_1, % 61.45/9.01 | | | | | | | | | | | | all_143_2, all_404_0, simplifying with (31), (38), % 61.45/9.01 | | | | | | | | | | | | (39), (112), (113), (168), (169) gives: % 61.45/9.01 | | | | | | | | | | | | (203) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 61.45/9.01 | | | | | | | | | | | | (relation(all_143_4) = v0 & % 61.45/9.01 | | | | | | | | | | | | ordered_pair(all_251_1, all_251_0) = v1 & in(v1, % 61.45/9.01 | | | | | | | | | | | | all_143_4) = v2 & $i(v1) & ( ~ (v2 = 0) | ~ % 61.45/9.01 | | | | | | | | | | | | (v0 = 0))) | (all_404_0 = 0 & all_404_1 = 0) % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | GROUND_INST: instantiating (5) with empty_set, all_208_1, % 61.45/9.01 | | | | | | | | | | | | all_392_0, simplifying with (8), (88), (162), % 61.45/9.01 | | | | | | | | | | | | (171) gives: % 61.45/9.01 | | | | | | | | | | | | (204) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, % 61.45/9.01 | | | | | | | | | | | | empty_set) = v1) | ~ $i(v0) | ? [v2: any] % 61.45/9.01 | | | | | | | | | | | | : ? [v3: any] : (in(v0, all_392_0) = v2 & % 61.45/9.01 | | | | | | | | | | | | in(v0, all_208_1) = v3 & ( ~ (v2 = 0) | (v1 = % 61.45/9.01 | | | | | | | | | | | | 0 & ~ (v3 = 0))))) & ! [v0: $i] : ( ~ % 61.45/9.01 | | | | | | | | | | | | (in(v0, empty_set) = 0) | ~ $i(v0) | ? [v1: % 61.45/9.01 | | | | | | | | | | | | any] : ? [v2: any] : (in(v0, all_392_0) = v2 % 61.45/9.01 | | | | | | | | | | | | & in(v0, all_208_1) = v1 & (v2 = 0 | v1 = 0))) % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | ALPHA: (204) implies: % 61.45/9.01 | | | | | | | | | | | | (205) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, % 61.45/9.01 | | | | | | | | | | | | empty_set) = v1) | ~ $i(v0) | ? [v2: any] % 61.45/9.01 | | | | | | | | | | | | : ? [v3: any] : (in(v0, all_392_0) = v2 & % 61.45/9.01 | | | | | | | | | | | | in(v0, all_208_1) = v3 & ( ~ (v2 = 0) | (v1 = % 61.45/9.01 | | | | | | | | | | | | 0 & ~ (v3 = 0))))) % 61.45/9.01 | | | | | | | | | | | | % 61.45/9.01 | | | | | | | | | | | | GROUND_INST: instantiating (205) with all_143_2, all_708_0, % 61.45/9.01 | | | | | | | | | | | | simplifying with (33), (202) gives: % 61.45/9.02 | | | | | | | | | | | | (206) ? [v0: any] : ? [v1: any] : (in(all_143_2, % 61.45/9.02 | | | | | | | | | | | | all_392_0) = v0 & in(all_143_2, all_208_1) = % 61.45/9.02 | | | | | | | | | | | | v1 & ( ~ (v0 = 0) | (all_708_0 = 0 & ~ (v1 = % 61.45/9.02 | | | | | | | | | | | | 0)))) % 61.45/9.02 | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | DELTA: instantiating (206) with fresh symbols all_1012_0, % 61.45/9.02 | | | | | | | | | | | | all_1012_1 gives: % 61.45/9.02 | | | | | | | | | | | | (207) in(all_143_2, all_392_0) = all_1012_1 & % 61.45/9.02 | | | | | | | | | | | | in(all_143_2, all_208_1) = all_1012_0 & ( ~ % 61.45/9.02 | | | | | | | | | | | | (all_1012_1 = 0) | (all_708_0 = 0 & ~ % 61.45/9.02 | | | | | | | | | | | | (all_1012_0 = 0))) % 61.45/9.02 | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | ALPHA: (207) implies: % 61.45/9.02 | | | | | | | | | | | | (208) ~ (all_1012_1 = 0) | (all_708_0 = 0 & ~ % 61.45/9.02 | | | | | | | | | | | | (all_1012_0 = 0)) % 61.45/9.02 | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | BETA: splitting (203) gives: % 61.45/9.02 | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | Case 1: % 61.45/9.02 | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | (209) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 61.45/9.02 | | | | | | | | | | | | | (relation(all_143_4) = v0 & % 61.45/9.02 | | | | | | | | | | | | | ordered_pair(all_251_1, all_251_0) = v1 & in(v1, % 61.45/9.02 | | | | | | | | | | | | | all_143_4) = v2 & $i(v1) & ( ~ (v2 = 0) | ~ % 61.45/9.02 | | | | | | | | | | | | | (v0 = 0))) % 61.45/9.02 | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | DELTA: instantiating (209) with fresh symbols all_1142_0, % 61.45/9.02 | | | | | | | | | | | | | all_1142_1, all_1142_2 gives: % 61.45/9.02 | | | | | | | | | | | | | (210) relation(all_143_4) = all_1142_2 & % 61.45/9.02 | | | | | | | | | | | | | ordered_pair(all_251_1, all_251_0) = all_1142_1 & % 61.45/9.02 | | | | | | | | | | | | | in(all_1142_1, all_143_4) = all_1142_0 & % 61.45/9.02 | | | | | | | | | | | | | $i(all_1142_1) & ( ~ (all_1142_0 = 0) | ~ % 61.45/9.02 | | | | | | | | | | | | | (all_1142_2 = 0)) % 61.45/9.02 | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | ALPHA: (210) implies: % 61.45/9.02 | | | | | | | | | | | | | (211) in(all_1142_1, all_143_4) = all_1142_0 % 61.45/9.02 | | | | | | | | | | | | | (212) ordered_pair(all_251_1, all_251_0) = all_1142_1 % 61.45/9.02 | | | | | | | | | | | | | (213) relation(all_143_4) = all_1142_2 % 61.45/9.02 | | | | | | | | | | | | | (214) ~ (all_1142_0 = 0) | ~ (all_1142_2 = 0) % 61.45/9.02 | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | BETA: splitting (208) gives: % 61.45/9.02 | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | Case 1: % 61.45/9.02 | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_201_1, all_1142_1, % 61.45/9.02 | | | | | | | | | | | | | | all_251_0, all_251_1, simplifying with (114), % 61.45/9.02 | | | | | | | | | | | | | | (212) gives: % 61.45/9.02 | | | | | | | | | | | | | | (215) all_1142_1 = all_201_1 % 61.45/9.02 | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_1142_2, all_143_4, % 61.45/9.02 | | | | | | | | | | | | | | simplifying with (36), (213) gives: % 61.45/9.02 | | | | | | | | | | | | | | (216) all_1142_2 = 0 % 61.45/9.02 | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | REDUCE: (211), (215) imply: % 61.45/9.02 | | | | | | | | | | | | | | (217) in(all_201_1, all_143_4) = all_1142_0 % 61.45/9.02 | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | BETA: splitting (214) gives: % 61.45/9.02 | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | Case 1: % 61.45/9.02 | | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | | (218) ~ (all_1142_0 = 0) % 61.45/9.02 | | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_1142_0, all_143_4, % 61.45/9.02 | | | | | | | | | | | | | | | all_201_1, simplifying with (77), (217) gives: % 61.45/9.02 | | | | | | | | | | | | | | | (219) all_1142_0 = 0 % 61.45/9.02 | | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | | REDUCE: (218), (219) imply: % 61.45/9.02 | | | | | | | | | | | | | | | (220) $false % 61.45/9.02 | | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | | CLOSE: (220) is inconsistent. % 61.45/9.02 | | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | Case 2: % 61.45/9.02 | | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | | (221) ~ (all_1142_2 = 0) % 61.45/9.02 | | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | | REDUCE: (216), (221) imply: % 61.45/9.02 | | | | | | | | | | | | | | | (222) $false % 61.45/9.02 | | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | | CLOSE: (222) is inconsistent. % 61.45/9.02 | | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | End of split % 61.45/9.02 | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | Case 2: % 61.45/9.02 | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | (223) all_708_0 = 0 & ~ (all_1012_0 = 0) % 61.45/9.02 | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | ALPHA: (223) implies: % 61.45/9.02 | | | | | | | | | | | | | | (224) all_708_0 = 0 % 61.45/9.02 | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | REDUCE: (201), (224) imply: % 61.45/9.02 | | | | | | | | | | | | | | (225) $false % 61.45/9.02 | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | | CLOSE: (225) is inconsistent. % 61.45/9.02 | | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | End of split % 61.45/9.02 | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | Case 2: % 61.45/9.02 | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | (226) all_404_0 = 0 & all_404_1 = 0 % 61.45/9.02 | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | ALPHA: (226) implies: % 61.45/9.02 | | | | | | | | | | | | | (227) all_404_1 = 0 % 61.45/9.02 | | | | | | | | | | | | | (228) all_404_0 = 0 % 61.45/9.02 | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | | REF_CLOSE: (170), (227), (228) are inconsistent by sub-proof % 61.45/9.02 | | | | | | | | | | | | | #1. % 61.45/9.02 | | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | | End of split % 61.45/9.02 | | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | End of split % 61.45/9.02 | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | Case 2: % 61.45/9.02 | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | (229) all_184_1 = 0 % 61.45/9.02 | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | REDUCE: (195), (229) imply: % 61.45/9.02 | | | | | | | | | | | (230) $false % 61.45/9.02 | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | | CLOSE: (230) is inconsistent. % 61.45/9.02 | | | | | | | | | | | % 61.45/9.02 | | | | | | | | | | End of split % 61.45/9.02 | | | | | | | | | | % 61.45/9.02 | | | | | | | | | End of split % 61.45/9.02 | | | | | | | | | % 61.45/9.02 | | | | | | | | Case 2: % 61.45/9.02 | | | | | | | | | % 61.45/9.02 | | | | | | | | | (231) all_257_1 = 0 % 61.45/9.02 | | | | | | | | | % 61.45/9.02 | | | | | | | | | COMBINE_EQS: (147), (231) imply: % 61.45/9.02 | | | | | | | | | (232) all_239_0 = 0 % 61.45/9.02 | | | | | | | | | % 61.45/9.02 | | | | | | | | | SIMP: (232) implies: % 61.45/9.02 | | | | | | | | | (233) all_239_0 = 0 % 61.45/9.02 | | | | | | | | | % 61.45/9.02 | | | | | | | | | REDUCE: (107), (233) imply: % 61.45/9.02 | | | | | | | | | (234) $false % 61.45/9.02 | | | | | | | | | % 61.45/9.02 | | | | | | | | | CLOSE: (234) is inconsistent. % 61.45/9.02 | | | | | | | | | % 61.45/9.02 | | | | | | | | End of split % 61.45/9.02 | | | | | | | | % 61.45/9.02 | | | | | | | End of split % 61.45/9.02 | | | | | | | % 61.45/9.02 | | | | | | End of split % 61.45/9.02 | | | | | | % 61.45/9.02 | | | | | End of split % 61.45/9.02 | | | | | % 61.45/9.02 | | | | End of split % 61.45/9.02 | | | | % 61.45/9.02 | | | End of split % 61.45/9.02 | | | % 61.45/9.02 | | End of split % 61.45/9.02 | | % 61.45/9.02 | End of split % 61.45/9.02 | % 61.45/9.02 End of proof % 61.45/9.02 % 61.45/9.02 Sub-proof #1 shows that the following formulas are inconsistent: % 61.45/9.02 ---------------------------------------------------------------- % 61.45/9.02 (1) ~ (all_404_0 = 0) | ~ (all_404_1 = 0) % 61.45/9.02 (2) all_404_0 = 0 % 61.45/9.02 (3) all_404_1 = 0 % 61.45/9.02 % 61.45/9.02 Begin of proof % 61.45/9.02 | % 61.45/9.02 | BETA: splitting (1) gives: % 61.45/9.02 | % 61.45/9.02 | Case 1: % 61.45/9.02 | | % 61.45/9.02 | | (4) ~ (all_404_0 = 0) % 61.45/9.02 | | % 61.45/9.02 | | REDUCE: (2), (4) imply: % 61.45/9.02 | | (5) $false % 61.45/9.02 | | % 61.45/9.02 | | CLOSE: (5) is inconsistent. % 61.45/9.02 | | % 61.45/9.02 | Case 2: % 61.45/9.02 | | % 61.45/9.02 | | (6) ~ (all_404_1 = 0) % 61.45/9.02 | | % 61.45/9.02 | | REDUCE: (3), (6) imply: % 61.45/9.02 | | (7) $false % 61.45/9.02 | | % 61.45/9.02 | | CLOSE: (7) is inconsistent. % 61.45/9.02 | | % 61.45/9.02 | End of split % 61.45/9.02 | % 61.45/9.02 End of proof % 61.45/9.02 % SZS output end Proof for theBenchmark % 61.45/9.02 % 61.45/9.02 8358ms %------------------------------------------------------------------------------