%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU170+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n018.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 17:43:01 EDT 2023 % Result : Theorem 22.79s 3.83s % Output : Proof 23.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU170+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.36 % Computer : n018.cluster.edu % 0.13/0.36 % Model : x86_64 x86_64 % 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.36 % Memory : 8042.1875MB % 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.36 % CPULimit : 300 % 0.13/0.36 % WCLimit : 300 % 0.13/0.36 % DateTime : Wed Aug 23 14:52:26 EDT 2023 % 0.13/0.36 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.42/1.06 Prover 4: Preprocessing ... % 2.68/1.08 Prover 1: Preprocessing ... % 2.68/1.11 Prover 3: Preprocessing ... % 2.68/1.11 Prover 2: Preprocessing ... % 2.68/1.11 Prover 5: Preprocessing ... % 2.68/1.11 Prover 6: Preprocessing ... % 2.68/1.11 Prover 0: Preprocessing ... % 4.87/1.48 Prover 1: Warning: ignoring some quantifiers % 4.87/1.50 Prover 6: Proving ... % 4.87/1.50 Prover 5: Proving ... % 4.87/1.50 Prover 2: Proving ... % 4.87/1.50 Prover 1: Constructing countermodel ... % 4.87/1.52 Prover 4: Warning: ignoring some quantifiers % 4.87/1.53 Prover 3: Warning: ignoring some quantifiers % 4.87/1.55 Prover 3: Constructing countermodel ... % 5.41/1.59 Prover 4: Constructing countermodel ... % 5.41/1.59 Prover 0: Proving ... % 9.08/2.01 Prover 3: gave up % 9.08/2.03 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.76/2.08 Prover 7: Preprocessing ... % 9.97/2.14 Prover 7: Warning: ignoring some quantifiers % 9.97/2.14 Prover 7: Constructing countermodel ... % 12.36/2.45 Prover 7: gave up % 12.36/2.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.36/2.48 Prover 8: Preprocessing ... % 12.36/2.48 Prover 1: gave up % 12.36/2.49 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 12.36/2.50 Prover 9: Preprocessing ... % 13.07/2.58 Prover 8: Warning: ignoring some quantifiers % 13.57/2.59 Prover 8: Constructing countermodel ... % 13.57/2.65 Prover 9: Warning: ignoring some quantifiers % 13.57/2.66 Prover 9: Constructing countermodel ... % 14.80/2.89 Prover 8: gave up % 14.80/2.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.80/2.93 Prover 10: Preprocessing ... % 16.22/3.00 Prover 10: Warning: ignoring some quantifiers % 16.22/3.01 Prover 10: Constructing countermodel ... % 17.13/3.09 Prover 10: gave up % 17.13/3.10 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 17.13/3.14 Prover 11: Preprocessing ... % 18.56/3.28 Prover 11: Warning: ignoring some quantifiers % 19.04/3.32 Prover 11: Constructing countermodel ... % 22.79/3.83 Prover 4: Found proof (size 185) % 22.79/3.83 Prover 4: proved (3196ms) % 22.79/3.83 Prover 11: stopped % 22.79/3.83 Prover 6: stopped % 22.79/3.83 Prover 0: stopped % 22.79/3.83 Prover 5: stopped % 22.79/3.83 Prover 9: stopped % 22.79/3.83 Prover 2: stopped % 22.79/3.83 % 22.79/3.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 22.79/3.83 % 22.79/3.85 % SZS output start Proof for theBenchmark % 22.79/3.85 Assumptions after simplification: % 22.79/3.85 --------------------------------- % 22.79/3.85 % 22.79/3.85 (d3_tarski) % 23.12/3.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 23.12/3.88 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 23.12/3.88 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 23.12/3.88 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 23.12/3.88 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 23.12/3.88 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 23.12/3.88 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 23.12/3.88 $i(v0) | in(v2, v1) = 0) % 23.12/3.88 % 23.12/3.88 (d4_xboole_0) % 23.12/3.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 23.12/3.89 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~ % 23.12/3.89 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1) = % 23.12/3.89 v6 & in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: % 23.12/3.89 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 23.12/3.89 (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) % 23.12/3.89 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v6 & % 23.12/3.89 in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : % 23.12/3.90 ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ (set_difference(v0, v1) = v2) | % 23.12/3.90 ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 23.12/3.90 [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) % 23.12/3.90 | (v6 = 0 & ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 23.12/3.90 ! [v3: $i] : ! [v4: any] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) % 23.12/3.90 = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? % 23.12/3.90 [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ % 23.12/3.90 (v6 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 23.12/3.90 ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 23.12/3.90 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = % 23.12/3.90 v4 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 23.12/3.90 $i] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | % 23.12/3.90 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v2) % 23.12/3.90 = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) & ? [v0: $i] : ! [v1: $i] : % 23.12/3.90 ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ~ % 23.12/3.90 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : % 23.12/3.90 ? [v7: any] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) % 23.12/3.90 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = % 23.12/3.90 0))))) % 23.12/3.90 % 23.12/3.90 (d5_subset_1) % 23.12/3.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v0) = v2) | ~ % 23.12/3.90 (element(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 23.12/3.90 (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3 & $i(v3))) & % 23.12/3.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2) % 23.12/3.90 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : % 23.12/3.90 (powerset(v0) = v3 & element(v1, v3) = v4 & set_difference(v0, v1) = v5 & % 23.12/3.90 $i(v5) & $i(v3) & ( ~ (v4 = 0) | v5 = v2))) & ! [v0: $i] : ! [v1: $i] : % 23.12/3.90 ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 23.12/3.90 [v3: $i] : ? [v4: any] : ? [v5: $i] : (powerset(v0) = v3 & element(v1, v3) % 23.12/3.90 = v4 & subset_complement(v0, v1) = v5 & $i(v5) & $i(v3) & ( ~ (v4 = 0) | % 23.12/3.90 v5 = v2))) % 23.12/3.90 % 23.12/3.90 (dt_k3_subset_1) % 23.12/3.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v0) = v2) | ~ % 23.12/3.90 (element(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (element(v3, % 23.12/3.90 v2) = 0 & subset_complement(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! % 23.12/3.90 [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2) | ~ $i(v1) | ~ % 23.12/3.90 $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : (powerset(v0) = v3 & % 23.12/3.90 element(v2, v3) = v5 & element(v1, v3) = v4 & $i(v3) & ( ~ (v4 = 0) | v5 = % 23.12/3.90 0))) % 23.12/3.90 % 23.12/3.90 (involutiveness_k3_subset_1) % 23.12/3.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v0) = v2) | ~ % 23.12/3.90 (element(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 23.12/3.90 (subset_complement(v0, v3) = v1 & subset_complement(v0, v1) = v3 & $i(v3))) % 23.12/3.90 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = % 23.12/3.90 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : % 23.12/3.90 (powerset(v0) = v3 & element(v1, v3) = v4 & subset_complement(v0, v2) = v5 & % 23.12/3.90 $i(v5) & $i(v3) & ( ~ (v4 = 0) | v5 = v1))) % 23.12/3.90 % 23.12/3.90 (rc1_subset_1) % 23.12/3.90 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 23.12/3.90 [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & empty(v3) = v4 & % 23.12/3.90 powerset(v0) = v2 & element(v3, v2) = 0 & $i(v3) & $i(v2))) & ! [v0: $i] % 23.12/3.91 : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: % 23.12/3.91 $i] : ? [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & % 23.12/3.91 empty(v3) = v5 & element(v3, v1) = 0) | (v2 = 0 & empty(v0) = 0)))) % 23.12/3.91 % 23.12/3.91 (rc2_subset_1) % 23.12/3.91 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] % 23.12/3.91 : (empty(v2) = 0 & element(v2, v1) = 0 & $i(v2))) % 23.12/3.91 % 23.12/3.91 (rc2_xboole_0) % 23.12/3.91 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & $i(v0)) % 23.12/3.91 % 23.12/3.91 (t3_boole) % 23.12/3.91 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (set_difference(v0, % 23.12/3.91 empty_set) = v1) | ~ $i(v0)) % 23.12/3.91 % 23.12/3.91 (t3_xboole_0) % 23.12/3.91 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, v1) = % 23.12/3.91 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (in(v3, v1) = 0 & in(v3, v0) = % 23.12/3.91 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (disjoint(v0, % 23.12/3.91 v1) = 0) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 23.12/3.91 [v3: int] : ( ~ (v3 = 0) & in(v2, v0) = v3)) & ! [v0: $i] : ! [v1: $i] : % 23.12/3.91 ! [v2: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ % 23.12/3.91 $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & in(v2, v1) = v3)) % 23.12/3.91 % 23.12/3.91 (t43_subset_1) % 23.12/3.91 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: % 23.12/3.91 $i] : ? [v6: any] : (disjoint(v1, v3) = v4 & powerset(v0) = v2 & % 23.12/3.91 element(v3, v2) = 0 & element(v1, v2) = 0 & subset_complement(v0, v3) = v5 & % 23.12/3.91 subset(v1, v5) = v6 & $i(v5) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v6 = 0 % 23.12/3.91 & ~ (v4 = 0)) | (v4 = 0 & ~ (v6 = 0)))) % 23.12/3.91 % 23.12/3.91 (t6_boole) % 23.12/3.91 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ % 23.12/3.91 $i(v0)) % 23.12/3.91 % 23.12/3.91 (function-axioms) % 23.12/3.91 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 23.12/3.91 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 23.12/3.91 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 23.12/3.91 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 23.12/3.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.12/3.91 (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! % 23.12/3.91 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.12/3.91 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 23.12/3.91 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 23.12/3.91 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 23.12/3.91 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 23.12/3.91 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 23.12/3.91 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 23.12/3.91 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 23.12/3.91 [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 23.12/3.91 % 23.12/3.91 Further assumptions not needed in the proof: % 23.12/3.91 -------------------------------------------- % 23.12/3.91 antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k4_xboole_0, % 23.12/3.91 dt_m1_subset_1, existence_m1_subset_1, fc1_subset_1, fc1_xboole_0, l3_subset_1, % 23.12/3.91 rc1_xboole_0, reflexivity_r1_tarski, symmetry_r1_xboole_0, t4_boole, t7_boole, % 23.12/3.91 t8_boole % 23.12/3.91 % 23.12/3.91 Those formulas are unsatisfiable: % 23.12/3.91 --------------------------------- % 23.12/3.91 % 23.12/3.91 Begin of proof % 23.12/3.91 | % 23.12/3.91 | ALPHA: (d3_tarski) implies: % 23.12/3.92 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~ % 23.12/3.92 | (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) = % 23.12/3.92 | 0) % 23.12/3.92 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 23.12/3.92 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 23.12/3.92 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 23.12/3.92 | % 23.12/3.92 | ALPHA: (d4_xboole_0) implies: % 23.12/3.92 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 23.12/3.92 | (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 23.12/3.92 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 23.12/3.92 | v1) = v4 & in(v3, v0) = 0)) % 23.12/3.92 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 23.12/3.92 | ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | % 23.12/3.92 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 23.12/3.92 | (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & ~ (v4 % 23.12/3.92 | = 0))))) % 23.12/3.92 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 23.12/3.92 | (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ % 23.12/3.92 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 23.12/3.92 | any] : (in(v3, v1) = v6 & in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = % 23.12/3.92 | 0))) % 23.12/3.92 | % 23.12/3.92 | ALPHA: (d5_subset_1) implies: % 23.12/3.92 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, % 23.12/3.92 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : % 23.12/3.92 | ? [v5: $i] : (powerset(v0) = v3 & element(v1, v3) = v4 & % 23.12/3.92 | set_difference(v0, v1) = v5 & $i(v5) & $i(v3) & ( ~ (v4 = 0) | v5 = % 23.12/3.92 | v2))) % 23.12/3.92 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v0) = v2) | ~ % 23.12/3.92 | (element(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 23.12/3.92 | (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3 & % 23.12/3.92 | $i(v3))) % 23.12/3.92 | % 23.12/3.92 | ALPHA: (dt_k3_subset_1) implies: % 23.12/3.92 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, % 23.12/3.92 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : % 23.12/3.92 | ? [v5: any] : (powerset(v0) = v3 & element(v2, v3) = v5 & element(v1, % 23.12/3.92 | v3) = v4 & $i(v3) & ( ~ (v4 = 0) | v5 = 0))) % 23.12/3.92 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v0) = v2) | ~ % 23.12/3.92 | (element(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 23.12/3.92 | (element(v3, v2) = 0 & subset_complement(v0, v1) = v3 & $i(v3))) % 23.12/3.92 | % 23.12/3.92 | ALPHA: (involutiveness_k3_subset_1) implies: % 23.12/3.92 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, % 23.12/3.92 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : % 23.12/3.92 | ? [v5: $i] : (powerset(v0) = v3 & element(v1, v3) = v4 & % 23.12/3.92 | subset_complement(v0, v2) = v5 & $i(v5) & $i(v3) & ( ~ (v4 = 0) | % 23.12/3.92 | v5 = v1))) % 23.12/3.92 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v0) = v2) | ~ % 23.12/3.92 | (element(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 23.12/3.92 | (subset_complement(v0, v3) = v1 & subset_complement(v0, v1) = v3 & % 23.12/3.92 | $i(v3))) % 23.12/3.92 | % 23.12/3.92 | ALPHA: (rc1_subset_1) implies: % 23.12/3.93 | (12) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) % 23.12/3.93 | | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 23.12/3.93 | empty(v3) = v4 & powerset(v0) = v2 & element(v3, v2) = 0 & $i(v3) % 23.12/3.93 | & $i(v2))) % 23.12/3.93 | % 23.12/3.93 | ALPHA: (t3_boole) implies: % 23.12/3.93 | (13) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (set_difference(v0, % 23.12/3.93 | empty_set) = v1) | ~ $i(v0)) % 23.12/3.93 | % 23.12/3.93 | ALPHA: (t3_xboole_0) implies: % 23.12/3.93 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (disjoint(v0, v1) = 0) | % 23.12/3.93 | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 23.12/3.93 | int] : ( ~ (v3 = 0) & in(v2, v1) = v3)) % 23.12/3.93 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, % 23.12/3.93 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (in(v3, v1) = % 23.12/3.93 | 0 & in(v3, v0) = 0 & $i(v3))) % 23.12/3.93 | % 23.12/3.93 | ALPHA: (t6_boole) implies: % 23.12/3.93 | (16) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0)) % 23.12/3.93 | % 23.12/3.93 | ALPHA: (function-axioms) implies: % 23.12/3.93 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) % 23.12/3.93 | = v1) | ~ (powerset(v2) = v0)) % 23.12/3.93 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 23.12/3.93 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 23.12/3.93 | v0)) % 23.12/3.93 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.12/3.93 | (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = % 23.12/3.93 | v0)) % 23.12/3.93 | (20) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 23.12/3.93 | : ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, % 23.12/3.93 | v2) = v0)) % 23.12/3.93 | % 23.12/3.93 | DELTA: instantiating (rc2_xboole_0) with fresh symbols all_24_0, all_24_1 % 23.12/3.93 | gives: % 23.12/3.93 | (21) ~ (all_24_0 = 0) & empty(all_24_1) = all_24_0 & $i(all_24_1) % 23.12/3.93 | % 23.12/3.93 | ALPHA: (21) implies: % 23.12/3.93 | (22) ~ (all_24_0 = 0) % 23.12/3.93 | (23) $i(all_24_1) % 23.12/3.93 | (24) empty(all_24_1) = all_24_0 % 23.12/3.93 | % 23.12/3.93 | DELTA: instantiating (t43_subset_1) with fresh symbols all_29_0, all_29_1, % 23.12/3.93 | all_29_2, all_29_3, all_29_4, all_29_5, all_29_6 gives: % 23.12/3.93 | (25) disjoint(all_29_5, all_29_3) = all_29_2 & powerset(all_29_6) = % 23.12/3.93 | all_29_4 & element(all_29_3, all_29_4) = 0 & element(all_29_5, % 23.12/3.93 | all_29_4) = 0 & subset_complement(all_29_6, all_29_3) = all_29_1 & % 23.12/3.93 | subset(all_29_5, all_29_1) = all_29_0 & $i(all_29_1) & $i(all_29_3) & % 23.12/3.93 | $i(all_29_4) & $i(all_29_5) & $i(all_29_6) & ((all_29_0 = 0 & ~ % 23.12/3.93 | (all_29_2 = 0)) | (all_29_2 = 0 & ~ (all_29_0 = 0))) % 23.12/3.93 | % 23.12/3.93 | ALPHA: (25) implies: % 23.12/3.93 | (26) $i(all_29_6) % 23.12/3.93 | (27) $i(all_29_5) % 23.12/3.93 | (28) $i(all_29_3) % 23.12/3.93 | (29) $i(all_29_1) % 23.12/3.93 | (30) subset(all_29_5, all_29_1) = all_29_0 % 23.12/3.93 | (31) subset_complement(all_29_6, all_29_3) = all_29_1 % 23.12/3.93 | (32) element(all_29_5, all_29_4) = 0 % 23.12/3.93 | (33) element(all_29_3, all_29_4) = 0 % 23.12/3.93 | (34) powerset(all_29_6) = all_29_4 % 23.12/3.93 | (35) disjoint(all_29_5, all_29_3) = all_29_2 % 23.12/3.93 | (36) (all_29_0 = 0 & ~ (all_29_2 = 0)) | (all_29_2 = 0 & ~ (all_29_0 = % 23.12/3.93 | 0)) % 23.12/3.93 | % 23.12/3.93 | GROUND_INST: instantiating (2) with all_29_5, all_29_1, all_29_0, simplifying % 23.12/3.93 | with (27), (29), (30) gives: % 23.12/3.94 | (37) all_29_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 23.12/3.94 | all_29_1) = v1 & in(v0, all_29_5) = 0 & $i(v0)) % 23.12/3.94 | % 23.12/3.94 | GROUND_INST: instantiating (8) with all_29_6, all_29_3, all_29_1, simplifying % 23.12/3.94 | with (26), (28), (31) gives: % 23.12/3.94 | (38) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (powerset(all_29_6) = v0 & % 23.12/3.94 | element(all_29_1, v0) = v2 & element(all_29_3, v0) = v1 & $i(v0) & ( % 23.12/3.94 | ~ (v1 = 0) | v2 = 0)) % 23.12/3.94 | % 23.12/3.94 | GROUND_INST: instantiating (10) with all_29_6, all_29_3, all_29_1, simplifying % 23.12/3.94 | with (26), (28), (31) gives: % 23.12/3.94 | (39) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : (powerset(all_29_6) = v0 & % 23.12/3.94 | element(all_29_3, v0) = v1 & subset_complement(all_29_6, all_29_1) = % 23.12/3.94 | v2 & $i(v2) & $i(v0) & ( ~ (v1 = 0) | v2 = all_29_3)) % 23.12/3.94 | % 23.12/3.94 | GROUND_INST: instantiating (6) with all_29_6, all_29_3, all_29_1, simplifying % 23.12/3.94 | with (26), (28), (31) gives: % 23.12/3.94 | (40) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : (powerset(all_29_6) = v0 & % 23.12/3.94 | element(all_29_3, v0) = v1 & set_difference(all_29_6, all_29_3) = v2 % 23.12/3.94 | & $i(v2) & $i(v0) & ( ~ (v1 = 0) | v2 = all_29_1)) % 23.12/3.94 | % 23.12/3.94 | GROUND_INST: instantiating (9) with all_29_6, all_29_3, all_29_4, simplifying % 23.12/3.94 | with (26), (28), (33), (34) gives: % 23.12/3.94 | (41) ? [v0: $i] : (element(v0, all_29_4) = 0 & subset_complement(all_29_6, % 23.12/3.94 | all_29_3) = v0 & $i(v0)) % 23.12/3.94 | % 23.12/3.94 | GROUND_INST: instantiating (11) with all_29_6, all_29_3, all_29_4, simplifying % 23.12/3.94 | with (26), (28), (33), (34) gives: % 23.12/3.94 | (42) ? [v0: $i] : (subset_complement(all_29_6, v0) = all_29_3 & % 23.12/3.94 | subset_complement(all_29_6, all_29_3) = v0 & $i(v0)) % 23.12/3.94 | % 23.12/3.94 | GROUND_INST: instantiating (7) with all_29_6, all_29_3, all_29_4, simplifying % 23.12/3.94 | with (26), (28), (33), (34) gives: % 23.12/3.94 | (43) ? [v0: $i] : (subset_complement(all_29_6, all_29_3) = v0 & % 23.12/3.94 | set_difference(all_29_6, all_29_3) = v0 & $i(v0)) % 23.12/3.94 | % 23.12/3.94 | GROUND_INST: instantiating (9) with all_29_6, all_29_5, all_29_4, simplifying % 23.12/3.94 | with (26), (27), (32), (34) gives: % 23.12/3.94 | (44) ? [v0: $i] : (element(v0, all_29_4) = 0 & subset_complement(all_29_6, % 23.12/3.94 | all_29_5) = v0 & $i(v0)) % 23.12/3.94 | % 23.12/3.94 | GROUND_INST: instantiating (11) with all_29_6, all_29_5, all_29_4, simplifying % 23.12/3.94 | with (26), (27), (32), (34) gives: % 23.12/3.94 | (45) ? [v0: $i] : (subset_complement(all_29_6, v0) = all_29_5 & % 23.12/3.94 | subset_complement(all_29_6, all_29_5) = v0 & $i(v0)) % 23.12/3.94 | % 23.12/3.94 | GROUND_INST: instantiating (7) with all_29_6, all_29_5, all_29_4, simplifying % 23.12/3.94 | with (26), (27), (32), (34) gives: % 23.12/3.94 | (46) ? [v0: $i] : (subset_complement(all_29_6, all_29_5) = v0 & % 23.12/3.94 | set_difference(all_29_6, all_29_5) = v0 & $i(v0)) % 23.12/3.94 | % 23.12/3.94 | GROUND_INST: instantiating (rc2_subset_1) with all_29_6, all_29_4, simplifying % 23.12/3.94 | with (26), (34) gives: % 23.12/3.94 | (47) ? [v0: $i] : (empty(v0) = 0 & element(v0, all_29_4) = 0 & $i(v0)) % 23.12/3.94 | % 23.12/3.94 | GROUND_INST: instantiating (12) with all_24_1, all_24_0, simplifying with % 23.12/3.94 | (23), (24) gives: % 23.12/3.94 | (48) all_24_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) % 23.12/3.94 | & empty(v1) = v2 & powerset(all_24_1) = v0 & element(v1, v0) = 0 & % 23.12/3.94 | $i(v1) & $i(v0)) % 23.12/3.94 | % 23.12/3.94 | GROUND_INST: instantiating (15) with all_29_5, all_29_3, all_29_2, simplifying % 23.12/3.94 | with (27), (28), (35) gives: % 23.12/3.94 | (49) all_29_2 = 0 | ? [v0: $i] : (in(v0, all_29_3) = 0 & in(v0, all_29_5) % 23.12/3.94 | = 0 & $i(v0)) % 23.12/3.94 | % 23.12/3.94 | DELTA: instantiating (42) with fresh symbol all_39_0 gives: % 23.12/3.95 | (50) subset_complement(all_29_6, all_39_0) = all_29_3 & % 23.12/3.95 | subset_complement(all_29_6, all_29_3) = all_39_0 & $i(all_39_0) % 23.12/3.95 | % 23.12/3.95 | ALPHA: (50) implies: % 23.12/3.95 | (51) $i(all_39_0) % 23.12/3.95 | (52) subset_complement(all_29_6, all_29_3) = all_39_0 % 23.12/3.95 | (53) subset_complement(all_29_6, all_39_0) = all_29_3 % 23.12/3.95 | % 23.12/3.95 | DELTA: instantiating (41) with fresh symbol all_41_0 gives: % 23.12/3.95 | (54) element(all_41_0, all_29_4) = 0 & subset_complement(all_29_6, % 23.12/3.95 | all_29_3) = all_41_0 & $i(all_41_0) % 23.12/3.95 | % 23.12/3.95 | ALPHA: (54) implies: % 23.12/3.95 | (55) subset_complement(all_29_6, all_29_3) = all_41_0 % 23.12/3.95 | (56) element(all_41_0, all_29_4) = 0 % 23.12/3.95 | % 23.12/3.95 | DELTA: instantiating (47) with fresh symbol all_43_0 gives: % 23.12/3.95 | (57) empty(all_43_0) = 0 & element(all_43_0, all_29_4) = 0 & $i(all_43_0) % 23.12/3.95 | % 23.12/3.95 | ALPHA: (57) implies: % 23.12/3.95 | (58) $i(all_43_0) % 23.12/3.95 | (59) element(all_43_0, all_29_4) = 0 % 23.12/3.95 | (60) empty(all_43_0) = 0 % 23.12/3.95 | % 23.12/3.95 | DELTA: instantiating (46) with fresh symbol all_45_0 gives: % 23.12/3.95 | (61) subset_complement(all_29_6, all_29_5) = all_45_0 & % 23.12/3.95 | set_difference(all_29_6, all_29_5) = all_45_0 & $i(all_45_0) % 23.12/3.95 | % 23.12/3.95 | ALPHA: (61) implies: % 23.12/3.95 | (62) set_difference(all_29_6, all_29_5) = all_45_0 % 23.12/3.95 | (63) subset_complement(all_29_6, all_29_5) = all_45_0 % 23.12/3.95 | % 23.12/3.95 | DELTA: instantiating (45) with fresh symbol all_47_0 gives: % 23.12/3.95 | (64) subset_complement(all_29_6, all_47_0) = all_29_5 & % 23.12/3.95 | subset_complement(all_29_6, all_29_5) = all_47_0 & $i(all_47_0) % 23.12/3.95 | % 23.12/3.95 | ALPHA: (64) implies: % 23.12/3.95 | (65) $i(all_47_0) % 23.12/3.95 | (66) subset_complement(all_29_6, all_29_5) = all_47_0 % 23.12/3.95 | (67) subset_complement(all_29_6, all_47_0) = all_29_5 % 23.12/3.95 | % 23.12/3.95 | DELTA: instantiating (44) with fresh symbol all_49_0 gives: % 23.12/3.95 | (68) element(all_49_0, all_29_4) = 0 & subset_complement(all_29_6, % 23.12/3.95 | all_29_5) = all_49_0 & $i(all_49_0) % 23.12/3.95 | % 23.12/3.95 | ALPHA: (68) implies: % 23.12/3.95 | (69) subset_complement(all_29_6, all_29_5) = all_49_0 % 23.12/3.95 | (70) element(all_49_0, all_29_4) = 0 % 23.12/3.95 | % 23.12/3.95 | DELTA: instantiating (43) with fresh symbol all_51_0 gives: % 23.12/3.95 | (71) subset_complement(all_29_6, all_29_3) = all_51_0 & % 23.12/3.95 | set_difference(all_29_6, all_29_3) = all_51_0 & $i(all_51_0) % 23.12/3.95 | % 23.12/3.95 | ALPHA: (71) implies: % 23.12/3.95 | (72) set_difference(all_29_6, all_29_3) = all_51_0 % 23.12/3.95 | (73) subset_complement(all_29_6, all_29_3) = all_51_0 % 23.12/3.95 | % 23.12/3.95 | DELTA: instantiating (38) with fresh symbols all_53_0, all_53_1, all_53_2 % 23.12/3.95 | gives: % 23.12/3.95 | (74) powerset(all_29_6) = all_53_2 & element(all_29_1, all_53_2) = all_53_0 % 23.12/3.95 | & element(all_29_3, all_53_2) = all_53_1 & $i(all_53_2) & ( ~ % 23.12/3.95 | (all_53_1 = 0) | all_53_0 = 0) % 23.12/3.95 | % 23.12/3.95 | ALPHA: (74) implies: % 23.12/3.95 | (75) element(all_29_1, all_53_2) = all_53_0 % 23.12/3.95 | (76) powerset(all_29_6) = all_53_2 % 23.12/3.95 | % 23.12/3.95 | DELTA: instantiating (40) with fresh symbols all_57_0, all_57_1, all_57_2 % 23.12/3.95 | gives: % 23.12/3.95 | (77) powerset(all_29_6) = all_57_2 & element(all_29_3, all_57_2) = all_57_1 % 23.12/3.95 | & set_difference(all_29_6, all_29_3) = all_57_0 & $i(all_57_0) & % 23.12/3.95 | $i(all_57_2) & ( ~ (all_57_1 = 0) | all_57_0 = all_29_1) % 23.12/3.95 | % 23.12/3.95 | ALPHA: (77) implies: % 23.12/3.95 | (78) powerset(all_29_6) = all_57_2 % 23.12/3.95 | % 23.12/3.95 | DELTA: instantiating (39) with fresh symbols all_59_0, all_59_1, all_59_2 % 23.12/3.95 | gives: % 23.12/3.95 | (79) powerset(all_29_6) = all_59_2 & element(all_29_3, all_59_2) = all_59_1 % 23.12/3.95 | & subset_complement(all_29_6, all_29_1) = all_59_0 & $i(all_59_0) & % 23.12/3.95 | $i(all_59_2) & ( ~ (all_59_1 = 0) | all_59_0 = all_29_3) % 23.12/3.95 | % 23.12/3.95 | ALPHA: (79) implies: % 23.12/3.95 | (80) subset_complement(all_29_6, all_29_1) = all_59_0 % 23.12/3.95 | (81) powerset(all_29_6) = all_59_2 % 23.12/3.95 | % 23.12/3.95 | BETA: splitting (48) gives: % 23.12/3.95 | % 23.54/3.95 | Case 1: % 23.54/3.95 | | % 23.54/3.95 | | (82) all_24_0 = 0 % 23.54/3.95 | | % 23.54/3.95 | | REDUCE: (22), (82) imply: % 23.54/3.95 | | (83) $false % 23.54/3.95 | | % 23.54/3.95 | | CLOSE: (83) is inconsistent. % 23.54/3.95 | | % 23.54/3.95 | Case 2: % 23.54/3.95 | | % 23.54/3.96 | | (84) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & empty(v1) % 23.54/3.96 | | = v2 & powerset(all_24_1) = v0 & element(v1, v0) = 0 & $i(v1) & % 23.54/3.96 | | $i(v0)) % 23.54/3.96 | | % 23.54/3.96 | | DELTA: instantiating (84) with fresh symbols all_65_0, all_65_1, all_65_2 % 23.54/3.96 | | gives: % 23.54/3.96 | | (85) ~ (all_65_0 = 0) & empty(all_65_1) = all_65_0 & powerset(all_24_1) % 23.54/3.96 | | = all_65_2 & element(all_65_1, all_65_2) = 0 & $i(all_65_1) & % 23.54/3.96 | | $i(all_65_2) % 23.54/3.96 | | % 23.54/3.96 | | ALPHA: (85) implies: % 23.54/3.96 | | (86) ~ (all_65_0 = 0) % 23.54/3.96 | | (87) $i(all_65_1) % 23.54/3.96 | | (88) empty(all_65_1) = all_65_0 % 23.54/3.96 | | % 23.54/3.96 | | GROUND_INST: instantiating (19) with all_47_0, all_49_0, all_29_5, all_29_6, % 23.54/3.96 | | simplifying with (66), (69) gives: % 23.54/3.96 | | (89) all_49_0 = all_47_0 % 23.54/3.96 | | % 23.54/3.96 | | GROUND_INST: instantiating (19) with all_45_0, all_49_0, all_29_5, all_29_6, % 23.54/3.96 | | simplifying with (63), (69) gives: % 23.54/3.96 | | (90) all_49_0 = all_45_0 % 23.54/3.96 | | % 23.54/3.96 | | GROUND_INST: instantiating (19) with all_39_0, all_41_0, all_29_3, all_29_6, % 23.54/3.96 | | simplifying with (52), (55) gives: % 23.54/3.96 | | (91) all_41_0 = all_39_0 % 23.54/3.96 | | % 23.54/3.96 | | GROUND_INST: instantiating (19) with all_29_1, all_51_0, all_29_3, all_29_6, % 23.54/3.96 | | simplifying with (31), (73) gives: % 23.54/3.96 | | (92) all_51_0 = all_29_1 % 23.54/3.96 | | % 23.54/3.96 | | GROUND_INST: instantiating (19) with all_41_0, all_51_0, all_29_3, all_29_6, % 23.54/3.96 | | simplifying with (55), (73) gives: % 23.54/3.96 | | (93) all_51_0 = all_41_0 % 23.54/3.96 | | % 23.54/3.96 | | GROUND_INST: instantiating (17) with all_29_4, all_57_2, all_29_6, % 23.54/3.96 | | simplifying with (34), (78) gives: % 23.54/3.96 | | (94) all_57_2 = all_29_4 % 23.54/3.96 | | % 23.54/3.96 | | GROUND_INST: instantiating (17) with all_57_2, all_59_2, all_29_6, % 23.54/3.96 | | simplifying with (78), (81) gives: % 23.54/3.96 | | (95) all_59_2 = all_57_2 % 23.54/3.96 | | % 23.54/3.96 | | GROUND_INST: instantiating (17) with all_53_2, all_59_2, all_29_6, % 23.54/3.96 | | simplifying with (76), (81) gives: % 23.54/3.96 | | (96) all_59_2 = all_53_2 % 23.54/3.96 | | % 23.54/3.96 | | COMBINE_EQS: (95), (96) imply: % 23.54/3.96 | | (97) all_57_2 = all_53_2 % 23.54/3.96 | | % 23.54/3.96 | | SIMP: (97) implies: % 23.54/3.96 | | (98) all_57_2 = all_53_2 % 23.54/3.96 | | % 23.54/3.96 | | COMBINE_EQS: (94), (98) imply: % 23.54/3.96 | | (99) all_53_2 = all_29_4 % 23.54/3.96 | | % 23.54/3.96 | | SIMP: (99) implies: % 23.54/3.96 | | (100) all_53_2 = all_29_4 % 23.54/3.96 | | % 23.54/3.96 | | COMBINE_EQS: (92), (93) imply: % 23.54/3.96 | | (101) all_41_0 = all_29_1 % 23.54/3.96 | | % 23.54/3.96 | | SIMP: (101) implies: % 23.54/3.96 | | (102) all_41_0 = all_29_1 % 23.54/3.96 | | % 23.54/3.96 | | COMBINE_EQS: (89), (90) imply: % 23.54/3.96 | | (103) all_47_0 = all_45_0 % 23.54/3.96 | | % 23.54/3.96 | | COMBINE_EQS: (91), (102) imply: % 23.54/3.96 | | (104) all_39_0 = all_29_1 % 23.54/3.96 | | % 23.54/3.96 | | SIMP: (104) implies: % 23.54/3.96 | | (105) all_39_0 = all_29_1 % 23.54/3.96 | | % 23.54/3.96 | | REDUCE: (70), (90) imply: % 23.54/3.96 | | (106) element(all_45_0, all_29_4) = 0 % 23.54/3.96 | | % 23.54/3.96 | | REDUCE: (56), (102) imply: % 23.54/3.96 | | (107) element(all_29_1, all_29_4) = 0 % 23.54/3.96 | | % 23.54/3.96 | | REDUCE: (75), (100) imply: % 23.54/3.96 | | (108) element(all_29_1, all_29_4) = all_53_0 % 23.54/3.96 | | % 23.54/3.96 | | REDUCE: (67), (103) imply: % 23.54/3.96 | | (109) subset_complement(all_29_6, all_45_0) = all_29_5 % 23.54/3.96 | | % 23.54/3.96 | | REDUCE: (53), (105) imply: % 23.54/3.96 | | (110) subset_complement(all_29_6, all_29_1) = all_29_3 % 23.54/3.96 | | % 23.54/3.96 | | REDUCE: (72), (92) imply: % 23.54/3.96 | | (111) set_difference(all_29_6, all_29_3) = all_29_1 % 23.54/3.96 | | % 23.54/3.96 | | REDUCE: (65), (103) imply: % 23.54/3.96 | | (112) $i(all_45_0) % 23.54/3.96 | | % 23.54/3.96 | | GROUND_INST: instantiating (19) with all_59_0, all_29_3, all_29_1, all_29_6, % 23.54/3.96 | | simplifying with (80), (110) gives: % 23.54/3.96 | | (113) all_59_0 = all_29_3 % 23.54/3.96 | | % 23.54/3.96 | | GROUND_INST: instantiating (20) with 0, all_53_0, all_29_4, all_29_1, % 23.54/3.96 | | simplifying with (107), (108) gives: % 23.54/3.96 | | (114) all_53_0 = 0 % 23.54/3.96 | | % 23.54/3.96 | | GROUND_INST: instantiating (7) with all_29_6, all_29_1, all_29_4, % 23.54/3.96 | | simplifying with (26), (29), (34), (107) gives: % 23.54/3.96 | | (115) ? [v0: $i] : (subset_complement(all_29_6, all_29_1) = v0 & % 23.54/3.96 | | set_difference(all_29_6, all_29_1) = v0 & $i(v0)) % 23.54/3.96 | | % 23.54/3.96 | | GROUND_INST: instantiating (9) with all_29_6, all_43_0, all_29_4, % 23.54/3.96 | | simplifying with (26), (34), (58), (59) gives: % 23.54/3.96 | | (116) ? [v0: $i] : (element(v0, all_29_4) = 0 & % 23.54/3.96 | | subset_complement(all_29_6, all_43_0) = v0 & $i(v0)) % 23.54/3.96 | | % 23.54/3.96 | | GROUND_INST: instantiating (11) with all_29_6, all_43_0, all_29_4, % 23.54/3.96 | | simplifying with (26), (34), (58), (59) gives: % 23.54/3.96 | | (117) ? [v0: $i] : (subset_complement(all_29_6, v0) = all_43_0 & % 23.54/3.96 | | subset_complement(all_29_6, all_43_0) = v0 & $i(v0)) % 23.54/3.96 | | % 23.54/3.97 | | GROUND_INST: instantiating (7) with all_29_6, all_43_0, all_29_4, % 23.54/3.97 | | simplifying with (26), (34), (58), (59) gives: % 23.54/3.97 | | (118) ? [v0: $i] : (subset_complement(all_29_6, all_43_0) = v0 & % 23.54/3.97 | | set_difference(all_29_6, all_43_0) = v0 & $i(v0)) % 23.54/3.97 | | % 23.54/3.97 | | GROUND_INST: instantiating (7) with all_29_6, all_45_0, all_29_4, % 23.54/3.97 | | simplifying with (26), (34), (106), (112) gives: % 23.54/3.97 | | (119) ? [v0: $i] : (subset_complement(all_29_6, all_45_0) = v0 & % 23.54/3.97 | | set_difference(all_29_6, all_45_0) = v0 & $i(v0)) % 23.54/3.97 | | % 23.54/3.97 | | GROUND_INST: instantiating (16) with all_43_0, simplifying with (58), (60) % 23.54/3.97 | | gives: % 23.54/3.97 | | (120) all_43_0 = empty_set % 23.54/3.97 | | % 23.54/3.97 | | GROUND_INST: instantiating (12) with all_65_1, all_65_0, simplifying with % 23.54/3.97 | | (87), (88) gives: % 23.54/3.97 | | (121) all_65_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = % 23.54/3.97 | | 0) & empty(v1) = v2 & powerset(all_65_1) = v0 & element(v1, v0) % 23.54/3.97 | | = 0 & $i(v1) & $i(v0)) % 23.54/3.97 | | % 23.54/3.97 | | DELTA: instantiating (118) with fresh symbol all_83_0 gives: % 23.54/3.97 | | (122) subset_complement(all_29_6, all_43_0) = all_83_0 & % 23.54/3.97 | | set_difference(all_29_6, all_43_0) = all_83_0 & $i(all_83_0) % 23.54/3.97 | | % 23.54/3.97 | | ALPHA: (122) implies: % 23.54/3.97 | | (123) set_difference(all_29_6, all_43_0) = all_83_0 % 23.54/3.97 | | (124) subset_complement(all_29_6, all_43_0) = all_83_0 % 23.54/3.97 | | % 23.54/3.97 | | DELTA: instantiating (117) with fresh symbol all_85_0 gives: % 23.54/3.97 | | (125) subset_complement(all_29_6, all_85_0) = all_43_0 & % 23.54/3.97 | | subset_complement(all_29_6, all_43_0) = all_85_0 & $i(all_85_0) % 23.54/3.97 | | % 23.54/3.97 | | ALPHA: (125) implies: % 23.54/3.97 | | (126) $i(all_85_0) % 23.54/3.97 | | (127) subset_complement(all_29_6, all_43_0) = all_85_0 % 23.54/3.97 | | % 23.54/3.97 | | DELTA: instantiating (119) with fresh symbol all_93_0 gives: % 23.54/3.97 | | (128) subset_complement(all_29_6, all_45_0) = all_93_0 & % 23.54/3.97 | | set_difference(all_29_6, all_45_0) = all_93_0 & $i(all_93_0) % 23.54/3.97 | | % 23.54/3.97 | | ALPHA: (128) implies: % 23.54/3.97 | | (129) $i(all_93_0) % 23.54/3.97 | | (130) set_difference(all_29_6, all_45_0) = all_93_0 % 23.54/3.97 | | (131) subset_complement(all_29_6, all_45_0) = all_93_0 % 23.54/3.97 | | % 23.54/3.97 | | DELTA: instantiating (116) with fresh symbol all_95_0 gives: % 23.54/3.97 | | (132) element(all_95_0, all_29_4) = 0 & subset_complement(all_29_6, % 23.54/3.97 | | all_43_0) = all_95_0 & $i(all_95_0) % 23.54/3.97 | | % 23.54/3.97 | | ALPHA: (132) implies: % 23.54/3.97 | | (133) subset_complement(all_29_6, all_43_0) = all_95_0 % 23.54/3.97 | | % 23.54/3.97 | | DELTA: instantiating (115) with fresh symbol all_97_0 gives: % 23.54/3.97 | | (134) subset_complement(all_29_6, all_29_1) = all_97_0 & % 23.54/3.97 | | set_difference(all_29_6, all_29_1) = all_97_0 & $i(all_97_0) % 23.54/3.97 | | % 23.54/3.97 | | ALPHA: (134) implies: % 23.54/3.97 | | (135) $i(all_97_0) % 23.54/3.97 | | (136) set_difference(all_29_6, all_29_1) = all_97_0 % 23.54/3.97 | | (137) subset_complement(all_29_6, all_29_1) = all_97_0 % 23.54/3.97 | | % 23.54/3.97 | | REDUCE: (120), (133) imply: % 23.54/3.97 | | (138) subset_complement(all_29_6, empty_set) = all_95_0 % 23.54/3.97 | | % 23.54/3.97 | | REDUCE: (120), (127) imply: % 23.54/3.97 | | (139) subset_complement(all_29_6, empty_set) = all_85_0 % 23.54/3.97 | | % 23.54/3.97 | | REDUCE: (120), (124) imply: % 23.54/3.97 | | (140) subset_complement(all_29_6, empty_set) = all_83_0 % 23.54/3.97 | | % 23.54/3.97 | | REDUCE: (120), (123) imply: % 23.54/3.97 | | (141) set_difference(all_29_6, empty_set) = all_83_0 % 23.54/3.97 | | % 23.54/3.97 | | BETA: splitting (121) gives: % 23.54/3.97 | | % 23.54/3.97 | | Case 1: % 23.54/3.97 | | | % 23.54/3.97 | | | (142) all_65_0 = 0 % 23.54/3.97 | | | % 23.54/3.97 | | | REDUCE: (86), (142) imply: % 23.54/3.97 | | | (143) $false % 23.54/3.97 | | | % 23.54/3.97 | | | CLOSE: (143) is inconsistent. % 23.54/3.97 | | | % 23.54/3.97 | | Case 2: % 23.54/3.97 | | | % 23.54/3.97 | | | % 23.54/3.97 | | | GROUND_INST: instantiating (19) with all_85_0, all_95_0, empty_set, % 23.54/3.97 | | | all_29_6, simplifying with (138), (139) gives: % 23.54/3.97 | | | (144) all_95_0 = all_85_0 % 23.54/3.97 | | | % 23.54/3.97 | | | GROUND_INST: instantiating (19) with all_83_0, all_95_0, empty_set, % 23.54/3.97 | | | all_29_6, simplifying with (138), (140) gives: % 23.54/3.97 | | | (145) all_95_0 = all_83_0 % 23.54/3.97 | | | % 23.54/3.97 | | | GROUND_INST: instantiating (19) with all_29_3, all_97_0, all_29_1, % 23.54/3.97 | | | all_29_6, simplifying with (110), (137) gives: % 23.54/3.97 | | | (146) all_97_0 = all_29_3 % 23.54/3.97 | | | % 23.54/3.97 | | | GROUND_INST: instantiating (19) with all_29_5, all_93_0, all_45_0, % 23.54/3.97 | | | all_29_6, simplifying with (109), (131) gives: % 23.54/3.97 | | | (147) all_93_0 = all_29_5 % 23.54/3.97 | | | % 23.54/3.97 | | | COMBINE_EQS: (144), (145) imply: % 23.54/3.97 | | | (148) all_85_0 = all_83_0 % 23.54/3.97 | | | % 23.54/3.97 | | | SIMP: (148) implies: % 23.54/3.97 | | | (149) all_85_0 = all_83_0 % 23.54/3.97 | | | % 23.54/3.97 | | | REDUCE: (130), (147) imply: % 23.54/3.97 | | | (150) set_difference(all_29_6, all_45_0) = all_29_5 % 23.54/3.97 | | | % 23.54/3.97 | | | REDUCE: (136), (146) imply: % 23.54/3.97 | | | (151) set_difference(all_29_6, all_29_1) = all_29_3 % 23.54/3.97 | | | % 23.54/3.97 | | | REDUCE: (126), (149) imply: % 23.54/3.97 | | | (152) $i(all_83_0) % 23.54/3.97 | | | % 23.54/3.97 | | | GROUND_INST: instantiating (13) with all_29_6, all_83_0, simplifying with % 23.54/3.97 | | | (26), (141) gives: % 23.54/3.97 | | | (153) all_83_0 = all_29_6 % 23.54/3.97 | | | % 23.54/3.97 | | | BETA: splitting (36) gives: % 23.54/3.97 | | | % 23.54/3.97 | | | Case 1: % 23.54/3.97 | | | | % 23.54/3.97 | | | | (154) all_29_0 = 0 & ~ (all_29_2 = 0) % 23.54/3.97 | | | | % 23.54/3.97 | | | | ALPHA: (154) implies: % 23.54/3.97 | | | | (155) all_29_0 = 0 % 23.54/3.97 | | | | (156) ~ (all_29_2 = 0) % 23.54/3.97 | | | | % 23.54/3.97 | | | | REDUCE: (30), (155) imply: % 23.54/3.97 | | | | (157) subset(all_29_5, all_29_1) = 0 % 23.54/3.97 | | | | % 23.54/3.97 | | | | BETA: splitting (49) gives: % 23.54/3.97 | | | | % 23.54/3.97 | | | | Case 1: % 23.54/3.97 | | | | | % 23.54/3.97 | | | | | (158) all_29_2 = 0 % 23.54/3.97 | | | | | % 23.54/3.97 | | | | | REDUCE: (156), (158) imply: % 23.54/3.97 | | | | | (159) $false % 23.54/3.97 | | | | | % 23.54/3.97 | | | | | CLOSE: (159) is inconsistent. % 23.54/3.97 | | | | | % 23.54/3.97 | | | | Case 2: % 23.54/3.97 | | | | | % 23.54/3.97 | | | | | (160) ? [v0: $i] : (in(v0, all_29_3) = 0 & in(v0, all_29_5) = 0 & % 23.54/3.97 | | | | | $i(v0)) % 23.54/3.97 | | | | | % 23.54/3.97 | | | | | DELTA: instantiating (160) with fresh symbol all_232_0 gives: % 23.54/3.97 | | | | | (161) in(all_232_0, all_29_3) = 0 & in(all_232_0, all_29_5) = 0 & % 23.54/3.97 | | | | | $i(all_232_0) % 23.54/3.97 | | | | | % 23.54/3.97 | | | | | ALPHA: (161) implies: % 23.54/3.98 | | | | | (162) $i(all_232_0) % 23.54/3.98 | | | | | (163) in(all_232_0, all_29_5) = 0 % 23.54/3.98 | | | | | (164) in(all_232_0, all_29_3) = 0 % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | GROUND_INST: instantiating (4) with all_29_6, all_29_3, all_29_1, % 23.54/3.98 | | | | | all_232_0, 0, simplifying with (26), (28), (29), (111), % 23.54/3.98 | | | | | (162), (164) gives: % 23.54/3.98 | | | | | (165) ? [v0: int] : ? [v1: MultipleValueBool] : ( ~ (v0 = 0) & % 23.54/3.98 | | | | | in(all_232_0, all_29_1) = v0 & in(all_232_0, all_29_6) = % 23.54/3.98 | | | | | v1) % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | GROUND_INST: instantiating (3) with all_29_6, all_29_1, all_29_3, % 23.54/3.98 | | | | | all_232_0, simplifying with (26), (28), (29), (151), % 23.54/3.98 | | | | | (162), (164) gives: % 23.54/3.98 | | | | | (166) ? [v0: int] : ( ~ (v0 = 0) & in(all_232_0, all_29_1) = v0 & % 23.54/3.98 | | | | | in(all_232_0, all_29_6) = 0) % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | GROUND_INST: instantiating (1) with all_29_5, all_29_1, all_232_0, % 23.54/3.98 | | | | | simplifying with (27), (29), (157), (162), (163) gives: % 23.54/3.98 | | | | | (167) in(all_232_0, all_29_1) = 0 % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | DELTA: instantiating (165) with fresh symbols all_263_0, all_263_1 % 23.54/3.98 | | | | | gives: % 23.54/3.98 | | | | | (168) ~ (all_263_1 = 0) & in(all_232_0, all_29_1) = all_263_1 & % 23.54/3.98 | | | | | in(all_232_0, all_29_6) = all_263_0 % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | ALPHA: (168) implies: % 23.54/3.98 | | | | | (169) ~ (all_263_1 = 0) % 23.54/3.98 | | | | | (170) in(all_232_0, all_29_1) = all_263_1 % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | DELTA: instantiating (166) with fresh symbol all_309_0 gives: % 23.54/3.98 | | | | | (171) ~ (all_309_0 = 0) & in(all_232_0, all_29_1) = all_309_0 & % 23.54/3.98 | | | | | in(all_232_0, all_29_6) = 0 % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | ALPHA: (171) implies: % 23.54/3.98 | | | | | (172) in(all_232_0, all_29_1) = all_309_0 % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | GROUND_INST: instantiating (18) with all_263_1, all_309_0, all_29_1, % 23.54/3.98 | | | | | all_232_0, simplifying with (170), (172) gives: % 23.54/3.98 | | | | | (173) all_309_0 = all_263_1 % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | GROUND_INST: instantiating (18) with 0, all_309_0, all_29_1, % 23.54/3.98 | | | | | all_232_0, simplifying with (167), (172) gives: % 23.54/3.98 | | | | | (174) all_309_0 = 0 % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | COMBINE_EQS: (173), (174) imply: % 23.54/3.98 | | | | | (175) all_263_1 = 0 % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | SIMP: (175) implies: % 23.54/3.98 | | | | | (176) all_263_1 = 0 % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | REDUCE: (169), (176) imply: % 23.54/3.98 | | | | | (177) $false % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | CLOSE: (177) is inconsistent. % 23.54/3.98 | | | | | % 23.54/3.98 | | | | End of split % 23.54/3.98 | | | | % 23.54/3.98 | | | Case 2: % 23.54/3.98 | | | | % 23.54/3.98 | | | | (178) all_29_2 = 0 & ~ (all_29_0 = 0) % 23.54/3.98 | | | | % 23.54/3.98 | | | | ALPHA: (178) implies: % 23.54/3.98 | | | | (179) all_29_2 = 0 % 23.54/3.98 | | | | (180) ~ (all_29_0 = 0) % 23.54/3.98 | | | | % 23.54/3.98 | | | | REDUCE: (35), (179) imply: % 23.54/3.98 | | | | (181) disjoint(all_29_5, all_29_3) = 0 % 23.54/3.98 | | | | % 23.54/3.98 | | | | BETA: splitting (37) gives: % 23.54/3.98 | | | | % 23.54/3.98 | | | | Case 1: % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | (182) all_29_0 = 0 % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | REDUCE: (180), (182) imply: % 23.54/3.98 | | | | | (183) $false % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | CLOSE: (183) is inconsistent. % 23.54/3.98 | | | | | % 23.54/3.98 | | | | Case 2: % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | (184) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_29_1) % 23.54/3.98 | | | | | = v1 & in(v0, all_29_5) = 0 & $i(v0)) % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | DELTA: instantiating (184) with fresh symbols all_232_0, all_232_1 % 23.54/3.98 | | | | | gives: % 23.54/3.98 | | | | | (185) ~ (all_232_0 = 0) & in(all_232_1, all_29_1) = all_232_0 & % 23.54/3.98 | | | | | in(all_232_1, all_29_5) = 0 & $i(all_232_1) % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | ALPHA: (185) implies: % 23.54/3.98 | | | | | (186) ~ (all_232_0 = 0) % 23.54/3.98 | | | | | (187) $i(all_232_1) % 23.54/3.98 | | | | | (188) in(all_232_1, all_29_5) = 0 % 23.54/3.98 | | | | | (189) in(all_232_1, all_29_1) = all_232_0 % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | GROUND_INST: instantiating (4) with all_29_6, all_29_5, all_45_0, % 23.54/3.98 | | | | | all_232_1, 0, simplifying with (26), (27), (62), (112), % 23.54/3.98 | | | | | (187), (188) gives: % 23.54/3.98 | | | | | (190) ? [v0: int] : ? [v1: MultipleValueBool] : ( ~ (v0 = 0) & % 23.54/3.98 | | | | | in(all_232_1, all_45_0) = v0 & in(all_232_1, all_29_6) = % 23.54/3.98 | | | | | v1) % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | GROUND_INST: instantiating (3) with all_29_6, all_45_0, all_29_5, % 23.54/3.98 | | | | | all_232_1, simplifying with (26), (27), (112), (150), % 23.54/3.98 | | | | | (187), (188) gives: % 23.54/3.98 | | | | | (191) ? [v0: int] : ( ~ (v0 = 0) & in(all_232_1, all_45_0) = v0 & % 23.54/3.98 | | | | | in(all_232_1, all_29_6) = 0) % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | GROUND_INST: instantiating (4) with all_29_6, all_29_1, all_29_3, % 23.54/3.98 | | | | | all_232_1, all_232_0, simplifying with (26), (28), (29), % 23.54/3.98 | | | | | (151), (187), (189) gives: % 23.54/3.98 | | | | | (192) ? [v0: any] : ? [v1: any] : (in(all_232_1, all_29_3) = v0 & % 23.54/3.98 | | | | | in(all_232_1, all_29_6) = v1 & ( ~ (v0 = 0) | (v1 = 0 & ~ % 23.54/3.98 | | | | | (all_232_0 = 0)))) % 23.54/3.98 | | | | | % 23.54/3.98 | | | | | GROUND_INST: instantiating (5) with all_29_6, all_29_3, all_29_1, % 23.54/3.98 | | | | | all_232_1, all_232_0, simplifying with (26), (28), (29), % 23.54/3.98 | | | | | (111), (187), (189) gives: % 23.68/3.98 | | | | | (193) all_232_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_232_1, % 23.68/3.98 | | | | | all_29_3) = v1 & in(all_232_1, all_29_6) = v0 & ( ~ (v0 = % 23.68/3.98 | | | | | 0) | v1 = 0)) % 23.68/3.98 | | | | | % 23.68/3.98 | | | | | GROUND_INST: instantiating (14) with all_29_5, all_29_3, all_232_1, % 23.68/3.98 | | | | | simplifying with (27), (28), (181), (187), (188) gives: % 23.68/3.98 | | | | | (194) ? [v0: int] : ( ~ (v0 = 0) & in(all_232_1, all_29_3) = v0) % 23.68/3.98 | | | | | % 23.68/3.98 | | | | | DELTA: instantiating (194) with fresh symbol all_250_0 gives: % 23.68/3.98 | | | | | (195) ~ (all_250_0 = 0) & in(all_232_1, all_29_3) = all_250_0 % 23.68/3.98 | | | | | % 23.68/3.98 | | | | | ALPHA: (195) implies: % 23.68/3.98 | | | | | (196) ~ (all_250_0 = 0) % 23.68/3.98 | | | | | (197) in(all_232_1, all_29_3) = all_250_0 % 23.68/3.98 | | | | | % 23.68/3.98 | | | | | DELTA: instantiating (191) with fresh symbol all_290_0 gives: % 23.68/3.98 | | | | | (198) ~ (all_290_0 = 0) & in(all_232_1, all_45_0) = all_290_0 & % 23.68/3.98 | | | | | in(all_232_1, all_29_6) = 0 % 23.68/3.98 | | | | | % 23.68/3.98 | | | | | ALPHA: (198) implies: % 23.68/3.98 | | | | | (199) in(all_232_1, all_29_6) = 0 % 23.68/3.98 | | | | | % 23.68/3.98 | | | | | DELTA: instantiating (190) with fresh symbols all_300_0, all_300_1 % 23.68/3.98 | | | | | gives: % 23.68/3.98 | | | | | (200) ~ (all_300_1 = 0) & in(all_232_1, all_45_0) = all_300_1 & % 23.68/3.98 | | | | | in(all_232_1, all_29_6) = all_300_0 % 23.68/3.98 | | | | | % 23.68/3.98 | | | | | ALPHA: (200) implies: % 23.68/3.98 | | | | | (201) in(all_232_1, all_29_6) = all_300_0 % 23.68/3.98 | | | | | % 23.68/3.98 | | | | | DELTA: instantiating (192) with fresh symbols all_322_0, all_322_1 % 23.68/3.98 | | | | | gives: % 23.68/3.98 | | | | | (202) in(all_232_1, all_29_3) = all_322_1 & in(all_232_1, all_29_6) % 23.68/3.98 | | | | | = all_322_0 & ( ~ (all_322_1 = 0) | (all_322_0 = 0 & ~ % 23.68/3.98 | | | | | (all_232_0 = 0))) % 23.68/3.98 | | | | | % 23.68/3.98 | | | | | ALPHA: (202) implies: % 23.68/3.98 | | | | | (203) in(all_232_1, all_29_6) = all_322_0 % 23.68/3.99 | | | | | (204) in(all_232_1, all_29_3) = all_322_1 % 23.68/3.99 | | | | | % 23.68/3.99 | | | | | GROUND_INST: instantiating (18) with all_300_0, all_322_0, all_29_6, % 23.68/3.99 | | | | | all_232_1, simplifying with (201), (203) gives: % 23.68/3.99 | | | | | (205) all_322_0 = all_300_0 % 23.68/3.99 | | | | | % 23.68/3.99 | | | | | GROUND_INST: instantiating (18) with 0, all_322_0, all_29_6, % 23.68/3.99 | | | | | all_232_1, simplifying with (199), (203) gives: % 23.68/3.99 | | | | | (206) all_322_0 = 0 % 23.68/3.99 | | | | | % 23.68/3.99 | | | | | GROUND_INST: instantiating (18) with all_250_0, all_322_1, all_29_3, % 23.68/3.99 | | | | | all_232_1, simplifying with (197), (204) gives: % 23.68/3.99 | | | | | (207) all_322_1 = all_250_0 % 23.68/3.99 | | | | | % 23.68/3.99 | | | | | COMBINE_EQS: (205), (206) imply: % 23.68/3.99 | | | | | (208) all_300_0 = 0 % 23.68/3.99 | | | | | % 23.68/3.99 | | | | | SIMP: (208) implies: % 23.68/3.99 | | | | | (209) all_300_0 = 0 % 23.68/3.99 | | | | | % 23.68/3.99 | | | | | BETA: splitting (193) gives: % 23.68/3.99 | | | | | % 23.68/3.99 | | | | | Case 1: % 23.68/3.99 | | | | | | % 23.68/3.99 | | | | | | (210) all_232_0 = 0 % 23.68/3.99 | | | | | | % 23.68/3.99 | | | | | | REDUCE: (186), (210) imply: % 23.68/3.99 | | | | | | (211) $false % 23.68/3.99 | | | | | | % 23.68/3.99 | | | | | | CLOSE: (211) is inconsistent. % 23.68/3.99 | | | | | | % 23.68/3.99 | | | | | Case 2: % 23.68/3.99 | | | | | | % 23.68/3.99 | | | | | | (212) ? [v0: any] : ? [v1: any] : (in(all_232_1, all_29_3) = v1 % 23.68/3.99 | | | | | | & in(all_232_1, all_29_6) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 23.68/3.99 | | | | | | % 23.68/3.99 | | | | | | DELTA: instantiating (212) with fresh symbols all_404_0, all_404_1 % 23.68/3.99 | | | | | | gives: % 23.68/3.99 | | | | | | (213) in(all_232_1, all_29_3) = all_404_0 & in(all_232_1, % 23.68/3.99 | | | | | | all_29_6) = all_404_1 & ( ~ (all_404_1 = 0) | all_404_0 = % 23.68/3.99 | | | | | | 0) % 23.68/3.99 | | | | | | % 23.68/3.99 | | | | | | ALPHA: (213) implies: % 23.68/3.99 | | | | | | (214) in(all_232_1, all_29_6) = all_404_1 % 23.68/3.99 | | | | | | (215) in(all_232_1, all_29_3) = all_404_0 % 23.68/3.99 | | | | | | (216) ~ (all_404_1 = 0) | all_404_0 = 0 % 23.68/3.99 | | | | | | % 23.68/3.99 | | | | | | GROUND_INST: instantiating (18) with 0, all_404_1, all_29_6, % 23.68/3.99 | | | | | | all_232_1, simplifying with (199), (214) gives: % 23.68/3.99 | | | | | | (217) all_404_1 = 0 % 23.68/3.99 | | | | | | % 23.68/3.99 | | | | | | GROUND_INST: instantiating (18) with all_250_0, all_404_0, all_29_3, % 23.68/3.99 | | | | | | all_232_1, simplifying with (197), (215) gives: % 23.68/3.99 | | | | | | (218) all_404_0 = all_250_0 % 23.68/3.99 | | | | | | % 23.68/3.99 | | | | | | BETA: splitting (216) gives: % 23.68/3.99 | | | | | | % 23.68/3.99 | | | | | | Case 1: % 23.68/3.99 | | | | | | | % 23.68/3.99 | | | | | | | (219) ~ (all_404_1 = 0) % 23.68/3.99 | | | | | | | % 23.68/3.99 | | | | | | | REDUCE: (217), (219) imply: % 23.68/3.99 | | | | | | | (220) $false % 23.68/3.99 | | | | | | | % 23.68/3.99 | | | | | | | CLOSE: (220) is inconsistent. % 23.68/3.99 | | | | | | | % 23.68/3.99 | | | | | | Case 2: % 23.68/3.99 | | | | | | | % 23.68/3.99 | | | | | | | (221) all_404_0 = 0 % 23.68/3.99 | | | | | | | % 23.68/3.99 | | | | | | | COMBINE_EQS: (218), (221) imply: % 23.68/3.99 | | | | | | | (222) all_250_0 = 0 % 23.68/3.99 | | | | | | | % 23.68/3.99 | | | | | | | REDUCE: (196), (222) imply: % 23.68/3.99 | | | | | | | (223) $false % 23.68/3.99 | | | | | | | % 23.68/3.99 | | | | | | | CLOSE: (223) is inconsistent. % 23.68/3.99 | | | | | | | % 23.68/3.99 | | | | | | End of split % 23.68/3.99 | | | | | | % 23.68/3.99 | | | | | End of split % 23.68/3.99 | | | | | % 23.68/3.99 | | | | End of split % 23.68/3.99 | | | | % 23.68/3.99 | | | End of split % 23.68/3.99 | | | % 23.68/3.99 | | End of split % 23.68/3.99 | | % 23.68/3.99 | End of split % 23.68/3.99 | % 23.68/3.99 End of proof % 23.68/3.99 % SZS output end Proof for theBenchmark % 23.68/3.99 % 23.68/3.99 3379ms %------------------------------------------------------------------------------