%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU262+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 : n023.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 17:43:43 EDT 2023 % Result : Theorem 11.41s 2.29s % Output : Proof 15.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SEU262+1 : TPTP v8.1.2. Released v3.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n023.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.33 % CPULimit : 300 % 0.18/0.33 % WCLimit : 300 % 0.18/0.33 % DateTime : Thu Aug 24 01:44:57 EDT 2023 % 0.18/0.33 % CPUTime : % 0.61/0.60 ________ _____ % 0.61/0.60 ___ __ \_________(_)________________________________ % 0.61/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.61/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.61/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.61/0.60 % 0.61/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.61/0.60 (2023-06-19) % 0.61/0.60 % 0.61/0.60 (c) Philipp Rümmer, 2009-2023 % 0.61/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.61/0.60 Amanda Stjerna. % 0.61/0.60 Free software under BSD-3-Clause. % 0.61/0.60 % 0.61/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.61/0.60 % 0.61/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.61/0.61 Running up to 7 provers in parallel. % 0.61/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.61/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.61/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.61/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.61/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.61/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.61/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.31/1.06 Prover 1: Preprocessing ... % 2.31/1.06 Prover 4: Preprocessing ... % 2.83/1.10 Prover 5: Preprocessing ... % 2.83/1.10 Prover 6: Preprocessing ... % 2.83/1.10 Prover 3: Preprocessing ... % 2.83/1.10 Prover 0: Preprocessing ... % 2.83/1.10 Prover 2: Preprocessing ... % 6.31/1.54 Prover 1: Warning: ignoring some quantifiers % 6.31/1.57 Prover 3: Warning: ignoring some quantifiers % 6.31/1.58 Prover 1: Constructing countermodel ... % 6.31/1.59 Prover 5: Proving ... % 6.31/1.59 Prover 3: Constructing countermodel ... % 6.31/1.59 Prover 4: Warning: ignoring some quantifiers % 6.31/1.61 Prover 2: Proving ... % 7.02/1.63 Prover 6: Proving ... % 7.02/1.65 Prover 4: Constructing countermodel ... % 7.02/1.68 Prover 0: Proving ... % 9.24/1.94 Prover 3: gave up % 9.24/1.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.24/1.98 Prover 1: gave up % 9.70/2.00 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.70/2.03 Prover 7: Preprocessing ... % 9.70/2.04 Prover 8: Preprocessing ... % 10.54/2.12 Prover 7: Warning: ignoring some quantifiers % 10.65/2.13 Prover 7: Constructing countermodel ... % 10.65/2.19 Prover 8: Warning: ignoring some quantifiers % 10.65/2.21 Prover 8: Constructing countermodel ... % 11.41/2.27 Prover 7: gave up % 11.41/2.28 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 11.41/2.28 Prover 0: proved (1668ms) % 11.41/2.29 % 11.41/2.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.41/2.29 % 11.41/2.29 Prover 2: stopped % 11.41/2.29 Prover 6: stopped % 11.41/2.29 Prover 5: stopped % 11.41/2.29 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.41/2.29 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.41/2.29 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 11.41/2.29 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.01/2.32 Prover 9: Preprocessing ... % 12.01/2.32 Prover 11: Preprocessing ... % 12.01/2.33 Prover 13: Preprocessing ... % 12.01/2.34 Prover 16: Preprocessing ... % 12.01/2.34 Prover 10: Preprocessing ... % 12.68/2.39 Prover 10: Warning: ignoring some quantifiers % 12.68/2.40 Prover 10: Constructing countermodel ... % 12.68/2.42 Prover 16: Warning: ignoring some quantifiers % 12.68/2.43 Prover 13: Warning: ignoring some quantifiers % 12.68/2.45 Prover 13: Constructing countermodel ... % 12.68/2.47 Prover 16: Constructing countermodel ... % 12.68/2.48 Prover 10: gave up % 12.68/2.48 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 13.54/2.50 Prover 9: Warning: ignoring some quantifiers % 13.67/2.51 Prover 9: Constructing countermodel ... % 13.67/2.51 Prover 19: Preprocessing ... % 13.70/2.52 Prover 9: stopped % 13.70/2.55 Prover 11: Warning: ignoring some quantifiers % 13.70/2.56 Prover 8: gave up % 13.70/2.58 Prover 11: Constructing countermodel ... % 14.35/2.62 Prover 19: Warning: ignoring some quantifiers % 14.35/2.63 Prover 19: Constructing countermodel ... % 14.35/2.67 Prover 4: Found proof (size 112) % 14.35/2.67 Prover 4: proved (2053ms) % 14.35/2.67 Prover 19: stopped % 14.35/2.67 Prover 16: stopped % 14.35/2.67 Prover 11: stopped % 14.35/2.67 Prover 13: stopped % 14.35/2.67 % 14.35/2.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.35/2.67 % 14.93/2.69 % SZS output start Proof for theBenchmark % 14.93/2.70 Assumptions after simplification: % 14.93/2.70 --------------------------------- % 14.93/2.70 % 14.93/2.70 (antisymmetry_r2_hidden) % 14.93/2.72 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 14.93/2.72 [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0: $i] : ! [v1: $i] : ( % 14.93/2.72 ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 14.93/2.72 in(v1, v0) = v2)) % 14.93/2.72 % 14.93/2.72 (cc1_relset_1) % 14.93/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 14.93/2.72 (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, % 14.93/2.72 v4) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | relation(v2) = 0) % 14.93/2.72 % 14.93/2.72 (d3_tarski) % 14.93/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 14.93/2.72 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 14.93/2.72 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 14.93/2.73 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 14.93/2.73 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 14.93/2.73 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 14.93/2.73 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 14.93/2.73 $i(v0) | in(v2, v1) = 0) % 14.93/2.73 % 14.93/2.73 (d4_relat_1) % 14.93/2.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : ! [v5: % 14.93/2.74 $i] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v4) = v5) % 14.93/2.74 | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 14.93/2.74 [v6: int] : (( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) = % 14.93/2.74 v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0) % 14.93/2.74 = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 14.93/2.74 int] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ($i(v4) & ((v6 = 0 & % 14.93/2.74 ordered_pair(v2, v4) = v5 & in(v5, v0) = 0 & $i(v5)) | ( ~ (v3 = 0) & % 14.93/2.74 relation(v0) = v3)))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 % 14.93/2.74 = v0 | ~ (relation_dom(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : % 14.93/2.74 ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : % 14.93/2.74 ($i(v6) & $i(v4) & (( ~ (v3 = 0) & relation(v1) = v3) | (in(v4, v0) = v5 & ( % 14.93/2.74 ~ (v5 = 0) | ! [v9: $i] : ! [v10: $i] : ( ~ (ordered_pair(v4, v9) % 14.93/2.74 = v10) | ~ $i(v9) | ? [v11: int] : ( ~ (v11 = 0) & in(v10, v1) % 14.93/2.74 = v11))) & (v5 = 0 | (v8 = 0 & ordered_pair(v4, v6) = v7 & % 14.93/2.74 in(v7, v1) = 0 & $i(v7))))))) & ! [v0: $i] : ( ~ (relation(v0) = % 14.93/2.74 0) | ~ $i(v0) | ? [v1: $i] : (relation_dom(v0) = v1 & $i(v1) & ! [v2: % 14.93/2.74 $i] : ! [v3: int] : ! [v4: $i] : ! [v5: $i] : (v3 = 0 | ~ % 14.93/2.74 (ordered_pair(v2, v4) = v5) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ % 14.93/2.74 $i(v2) | ? [v6: int] : ( ~ (v6 = 0) & in(v5, v0) = v6)) & ! [v2: $i] : % 14.93/2.74 ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : % 14.93/2.74 (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) & $i(v3))) & ? % 14.93/2.74 [v2: $i] : (v2 = v1 | ~ $i(v2) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] % 14.93/2.74 : ? [v6: $i] : ? [v7: int] : (in(v3, v2) = v4 & $i(v5) & $i(v3) & ( ~ % 14.93/2.74 (v4 = 0) | ! [v8: $i] : ! [v9: $i] : ( ~ (ordered_pair(v3, v8) = % 14.93/2.74 v9) | ~ $i(v8) | ? [v10: int] : ( ~ (v10 = 0) & in(v9, v0) = % 14.93/2.74 v10))) & (v4 = 0 | (v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, % 14.93/2.74 v0) = 0 & $i(v6))))))) % 14.93/2.74 % 14.93/2.74 (d5_relat_1) % 14.93/2.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : ! [v5: % 14.93/2.75 $i] : (v3 = 0 | ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v4, v2) = v5) % 14.93/2.75 | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 14.93/2.75 [v6: int] : (( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) = % 14.93/2.75 v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v0) % 14.93/2.75 = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 14.93/2.75 int] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ($i(v4) & ((v6 = 0 & % 14.93/2.75 ordered_pair(v4, v2) = v5 & in(v5, v0) = 0 & $i(v5)) | ( ~ (v3 = 0) & % 14.93/2.75 relation(v0) = v3)))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 % 14.93/2.75 = v0 | ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : % 14.93/2.75 ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : % 14.93/2.75 ($i(v6) & $i(v4) & (( ~ (v3 = 0) & relation(v1) = v3) | (in(v4, v0) = v5 & ( % 14.93/2.75 ~ (v5 = 0) | ! [v9: $i] : ! [v10: $i] : ( ~ (ordered_pair(v9, v4) % 14.93/2.75 = v10) | ~ $i(v9) | ? [v11: int] : ( ~ (v11 = 0) & in(v10, v1) % 14.93/2.75 = v11))) & (v5 = 0 | (v8 = 0 & ordered_pair(v6, v4) = v7 & % 14.93/2.75 in(v7, v1) = 0 & $i(v7))))))) & ! [v0: $i] : ( ~ (relation(v0) = % 14.93/2.75 0) | ~ $i(v0) | ? [v1: $i] : (relation_rng(v0) = v1 & $i(v1) & ! [v2: % 14.93/2.75 $i] : ! [v3: int] : ! [v4: $i] : ! [v5: $i] : (v3 = 0 | ~ % 14.93/2.75 (ordered_pair(v4, v2) = v5) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ % 14.93/2.75 $i(v2) | ? [v6: int] : ( ~ (v6 = 0) & in(v5, v0) = v6)) & ! [v2: $i] : % 14.93/2.75 ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : % 14.93/2.75 (ordered_pair(v3, v2) = v4 & in(v4, v0) = 0 & $i(v4) & $i(v3))) & ? % 14.93/2.75 [v2: $i] : (v2 = v1 | ~ $i(v2) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] % 14.93/2.75 : ? [v6: $i] : ? [v7: int] : (in(v3, v2) = v4 & $i(v5) & $i(v3) & ( ~ % 14.93/2.75 (v4 = 0) | ! [v8: $i] : ! [v9: $i] : ( ~ (ordered_pair(v8, v3) = % 14.93/2.75 v9) | ~ $i(v8) | ? [v10: int] : ( ~ (v10 = 0) & in(v9, v0) = % 14.93/2.75 v10))) & (v4 = 0 | (v7 = 0 & ordered_pair(v5, v3) = v6 & in(v6, % 14.93/2.75 v0) = 0 & $i(v6))))))) % 14.93/2.75 % 14.93/2.75 (dt_m2_relset_1) % 14.93/2.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 14.93/2.75 int] : (v5 = 0 | ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = % 14.93/2.75 v4) | ~ (element(v2, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 14.93/2.75 [v6: int] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6)) & ! % 14.93/2.75 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2_as_subset(v2, v0, v1) % 14.93/2.75 = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 14.93/2.75 (cartesian_product2(v0, v1) = v3 & powerset(v3) = v4 & element(v2, v4) = 0 & % 14.93/2.75 $i(v4) & $i(v3))) % 14.93/2.75 % 14.93/2.75 (t106_zfmisc_1) % 14.93/2.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 14.93/2.75 $i] : ! [v6: int] : (v6 = 0 | ~ (ordered_pair(v0, v1) = v4) | ~ % 14.93/2.75 (cartesian_product2(v2, v3) = v5) | ~ (in(v4, v5) = v6) | ~ $i(v3) | ~ % 14.93/2.75 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : (in(v1, v3) = % 14.93/2.75 v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! % 14.93/2.75 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 14.93/2.75 (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, v3) = v5) | ~ % 14.93/2.75 (in(v4, v5) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1, % 14.93/2.75 v3) = 0 & in(v0, v2) = 0)) % 14.93/2.75 % 14.93/2.75 (t12_relset_1) % 14.93/2.75 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: % 14.93/2.75 $i] : ? [v6: any] : (relation_of2_as_subset(v2, v0, v1) = 0 & % 14.93/2.75 relation_rng(v2) = v5 & relation_dom(v2) = v3 & subset(v5, v1) = v6 & % 14.93/2.75 subset(v3, v0) = v4 & $i(v5) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v6 = % 14.93/2.75 0) | ~ (v4 = 0))) % 14.93/2.75 % 14.93/2.75 (t1_subset) % 14.93/2.75 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (element(v0, v1) = v2) % 14.93/2.75 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & % 14.93/2.75 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 14.93/2.75 element(v0, v1) = 0) % 14.93/2.75 % 14.93/2.75 (t2_subset) % 14.93/2.75 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~ % 14.93/2.75 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v1) = v4 & % 14.93/2.75 element(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: % 14.93/2.75 $i] : ( ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? % 14.93/2.75 [v3: any] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) % 14.93/2.75 % 14.93/2.75 (t3_subset) % 14.93/2.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 14.93/2.76 (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 14.93/2.76 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] % 14.93/2.76 : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 14.93/2.76 ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, % 14.93/2.76 v3) = v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 14.93/2.76 (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | % 14.93/2.76 subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | % 14.93/2.76 ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) = % 14.93/2.76 0 & $i(v2))) % 14.93/2.76 % 14.93/2.76 (function-axioms) % 14.93/2.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 14.93/2.76 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ % 14.93/2.76 (relation_of2(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.93/2.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 14.93/2.76 (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, % 14.93/2.76 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 14.93/2.76 (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & % 14.93/2.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 14.93/2.76 $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! % 14.93/2.76 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.93/2.76 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 14.93/2.76 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.93/2.76 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & % 14.93/2.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 14.93/2.76 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! % 14.93/2.76 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 14.93/2.76 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 14.93/2.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 14.93/2.76 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 14.93/2.76 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! % 14.93/2.76 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | % 14.93/2.76 ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 14.93/2.76 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: % 14.93/2.76 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 14.93/2.76 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.93/2.76 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 14.93/2.76 (relation(v2) = v0)) % 14.93/2.76 % 14.93/2.76 Further assumptions not needed in the proof: % 14.93/2.76 -------------------------------------------- % 14.93/2.76 commutativity_k2_tarski, d5_tarski, dt_k1_relat_1, dt_k1_tarski, dt_k1_xboole_0, % 14.93/2.76 dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_tarski, dt_k2_zfmisc_1, dt_k4_tarski, % 14.93/2.76 dt_m1_relset_1, dt_m1_subset_1, existence_m1_relset_1, existence_m1_subset_1, % 14.93/2.76 existence_m2_relset_1, fc1_xboole_0, fc1_zfmisc_1, rc1_xboole_0, rc2_xboole_0, % 14.93/2.76 redefinition_m2_relset_1, reflexivity_r1_tarski, t4_subset, t5_subset, t6_boole, % 14.93/2.76 t7_boole, t8_boole % 14.93/2.76 % 14.93/2.76 Those formulas are unsatisfiable: % 14.93/2.76 --------------------------------- % 14.93/2.76 % 14.93/2.76 Begin of proof % 14.93/2.76 | % 14.93/2.76 | ALPHA: (antisymmetry_r2_hidden) implies: % 14.93/2.76 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ % 14.93/2.76 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 14.93/2.76 | % 14.93/2.76 | ALPHA: (d3_tarski) implies: % 14.93/2.76 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~ % 14.93/2.76 | (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) = % 14.93/2.76 | 0) % 14.93/2.77 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 14.93/2.77 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 14.93/2.77 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 14.93/2.77 | % 14.93/2.77 | ALPHA: (d4_relat_1) implies: % 14.93/2.77 | (4) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 14.93/2.77 | (relation_dom(v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: int] : ! % 14.93/2.77 | [v4: $i] : ! [v5: $i] : (v3 = 0 | ~ (ordered_pair(v2, v4) = v5) | % 14.93/2.77 | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ? [v6: int] : ( ~ % 14.93/2.77 | (v6 = 0) & in(v5, v0) = v6)) & ! [v2: $i] : ( ~ (in(v2, v1) = % 14.93/2.77 | 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v2, % 14.93/2.77 | v3) = v4 & in(v4, v0) = 0 & $i(v4) & $i(v3))) & ? [v2: $i] : % 14.93/2.77 | (v2 = v1 | ~ $i(v2) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : % 14.93/2.77 | ? [v6: $i] : ? [v7: int] : (in(v3, v2) = v4 & $i(v5) & $i(v3) & % 14.93/2.77 | ( ~ (v4 = 0) | ! [v8: $i] : ! [v9: $i] : ( ~ % 14.93/2.77 | (ordered_pair(v3, v8) = v9) | ~ $i(v8) | ? [v10: int] : ( % 14.93/2.77 | ~ (v10 = 0) & in(v9, v0) = v10))) & (v4 = 0 | (v7 = 0 & % 14.93/2.77 | ordered_pair(v3, v5) = v6 & in(v6, v0) = 0 & $i(v6))))))) % 14.93/2.77 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0) = v1) | % 14.93/2.77 | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 14.93/2.77 | int] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ($i(v4) & ((v6 = % 14.93/2.77 | 0 & ordered_pair(v2, v4) = v5 & in(v5, v0) = 0 & $i(v5)) | ( ~ % 14.93/2.77 | (v3 = 0) & relation(v0) = v3)))) % 14.93/2.77 | % 14.93/2.77 | ALPHA: (d5_relat_1) implies: % 14.93/2.77 | (6) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 14.93/2.77 | (relation_rng(v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: int] : ! % 14.93/2.77 | [v4: $i] : ! [v5: $i] : (v3 = 0 | ~ (ordered_pair(v4, v2) = v5) | % 14.93/2.77 | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ? [v6: int] : ( ~ % 14.93/2.77 | (v6 = 0) & in(v5, v0) = v6)) & ! [v2: $i] : ( ~ (in(v2, v1) = % 14.93/2.77 | 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v3, % 14.93/2.77 | v2) = v4 & in(v4, v0) = 0 & $i(v4) & $i(v3))) & ? [v2: $i] : % 14.93/2.77 | (v2 = v1 | ~ $i(v2) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : % 14.93/2.77 | ? [v6: $i] : ? [v7: int] : (in(v3, v2) = v4 & $i(v5) & $i(v3) & % 14.93/2.77 | ( ~ (v4 = 0) | ! [v8: $i] : ! [v9: $i] : ( ~ % 14.93/2.77 | (ordered_pair(v8, v3) = v9) | ~ $i(v8) | ? [v10: int] : ( % 14.93/2.77 | ~ (v10 = 0) & in(v9, v0) = v10))) & (v4 = 0 | (v7 = 0 & % 14.93/2.77 | ordered_pair(v5, v3) = v6 & in(v6, v0) = 0 & $i(v6))))))) % 14.93/2.77 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v0) = v1) | % 14.93/2.77 | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 14.93/2.77 | int] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ($i(v4) & ((v6 = % 14.93/2.77 | 0 & ordered_pair(v4, v2) = v5 & in(v5, v0) = 0 & $i(v5)) | ( ~ % 14.93/2.77 | (v3 = 0) & relation(v0) = v3)))) % 14.93/2.77 | % 14.93/2.77 | ALPHA: (dt_m2_relset_1) implies: % 14.93/2.77 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 14.93/2.77 | (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 14.93/2.77 | $i(v0) | ? [v3: $i] : ? [v4: $i] : (cartesian_product2(v0, v1) = v3 % 14.93/2.77 | & powerset(v3) = v4 & element(v2, v4) = 0 & $i(v4) & $i(v3))) % 14.93/2.77 | % 14.93/2.77 | ALPHA: (t106_zfmisc_1) implies: % 14.93/2.77 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 14.93/2.77 | ! [v5: $i] : ( ~ (ordered_pair(v0, v1) = v4) | ~ % 14.93/2.77 | (cartesian_product2(v2, v3) = v5) | ~ (in(v4, v5) = 0) | ~ $i(v3) | % 14.93/2.77 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1, v3) = 0 & in(v0, v2) = % 14.93/2.77 | 0)) % 14.93/2.77 | % 14.93/2.77 | ALPHA: (t1_subset) implies: % 14.93/2.78 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (element(v0, % 14.93/2.78 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) % 14.93/2.78 | & in(v0, v1) = v3)) % 14.93/2.78 | % 14.93/2.78 | ALPHA: (t2_subset) implies: % 14.93/2.78 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = % 14.93/2.78 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 14.93/2.78 | (empty(v1) = v4 & element(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 14.93/2.78 | % 14.93/2.78 | ALPHA: (t3_subset) implies: % 14.93/2.78 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ % 14.93/2.78 | (element(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | subset(v0, v1) = 0) % 14.93/2.78 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, % 14.93/2.78 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : % 14.93/2.78 | ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4 & $i(v3))) % 14.93/2.78 | % 14.93/2.78 | ALPHA: (function-axioms) implies: % 14.93/2.78 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 14.93/2.78 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 14.93/2.78 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 14.93/2.78 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 14.93/2.78 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 14.93/2.78 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 14.93/2.78 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 14.93/2.78 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 15.40/2.78 | v0)) % 15.40/2.78 | % 15.40/2.78 | DELTA: instantiating (t12_relset_1) with fresh symbols all_31_0, all_31_1, % 15.40/2.78 | all_31_2, all_31_3, all_31_4, all_31_5, all_31_6 gives: % 15.40/2.78 | (18) relation_of2_as_subset(all_31_4, all_31_6, all_31_5) = 0 & % 15.40/2.78 | relation_rng(all_31_4) = all_31_1 & relation_dom(all_31_4) = all_31_3 % 15.40/2.78 | & subset(all_31_1, all_31_5) = all_31_0 & subset(all_31_3, all_31_6) = % 15.40/2.78 | all_31_2 & $i(all_31_1) & $i(all_31_3) & $i(all_31_4) & $i(all_31_5) & % 15.40/2.78 | $i(all_31_6) & ( ~ (all_31_0 = 0) | ~ (all_31_2 = 0)) % 15.40/2.78 | % 15.40/2.78 | ALPHA: (18) implies: % 15.40/2.78 | (19) $i(all_31_6) % 15.40/2.78 | (20) $i(all_31_5) % 15.40/2.78 | (21) $i(all_31_4) % 15.40/2.78 | (22) $i(all_31_3) % 15.40/2.78 | (23) $i(all_31_1) % 15.40/2.78 | (24) subset(all_31_3, all_31_6) = all_31_2 % 15.40/2.78 | (25) subset(all_31_1, all_31_5) = all_31_0 % 15.40/2.78 | (26) relation_dom(all_31_4) = all_31_3 % 15.40/2.78 | (27) relation_rng(all_31_4) = all_31_1 % 15.40/2.78 | (28) relation_of2_as_subset(all_31_4, all_31_6, all_31_5) = 0 % 15.40/2.78 | (29) ~ (all_31_0 = 0) | ~ (all_31_2 = 0) % 15.40/2.78 | % 15.40/2.78 | GROUND_INST: instantiating (13) with all_31_3, all_31_6, all_31_2, simplifying % 15.40/2.78 | with (19), (22), (24) gives: % 15.40/2.78 | (30) all_31_2 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 15.40/2.78 | powerset(all_31_6) = v0 & element(all_31_3, v0) = v1 & $i(v0)) % 15.40/2.78 | % 15.40/2.78 | GROUND_INST: instantiating (3) with all_31_3, all_31_6, all_31_2, simplifying % 15.40/2.78 | with (19), (22), (24) gives: % 15.40/2.79 | (31) all_31_2 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 15.40/2.79 | all_31_3) = 0 & in(v0, all_31_6) = v1 & $i(v0)) % 15.40/2.79 | % 15.40/2.79 | GROUND_INST: instantiating (13) with all_31_1, all_31_5, all_31_0, simplifying % 15.40/2.79 | with (20), (23), (25) gives: % 15.40/2.79 | (32) all_31_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 15.40/2.79 | powerset(all_31_5) = v0 & element(all_31_1, v0) = v1 & $i(v0)) % 15.40/2.79 | % 15.40/2.79 | GROUND_INST: instantiating (3) with all_31_1, all_31_5, all_31_0, simplifying % 15.40/2.79 | with (20), (23), (25) gives: % 15.40/2.79 | (33) all_31_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 15.40/2.79 | all_31_1) = 0 & in(v0, all_31_5) = v1 & $i(v0)) % 15.40/2.79 | % 15.40/2.79 | GROUND_INST: instantiating (8) with all_31_6, all_31_5, all_31_4, simplifying % 15.40/2.79 | with (19), (20), (21), (28) gives: % 15.40/2.79 | (34) ? [v0: $i] : ? [v1: $i] : (cartesian_product2(all_31_6, all_31_5) = % 15.40/2.79 | v0 & powerset(v0) = v1 & element(all_31_4, v1) = 0 & $i(v1) & % 15.40/2.79 | $i(v0)) % 15.40/2.79 | % 15.40/2.79 | DELTA: instantiating (34) with fresh symbols all_43_0, all_43_1 gives: % 15.40/2.79 | (35) cartesian_product2(all_31_6, all_31_5) = all_43_1 & powerset(all_43_1) % 15.40/2.79 | = all_43_0 & element(all_31_4, all_43_0) = 0 & $i(all_43_0) & % 15.40/2.79 | $i(all_43_1) % 15.40/2.79 | % 15.40/2.79 | ALPHA: (35) implies: % 15.40/2.79 | (36) $i(all_43_1) % 15.40/2.79 | (37) element(all_31_4, all_43_0) = 0 % 15.40/2.79 | (38) powerset(all_43_1) = all_43_0 % 15.40/2.79 | (39) cartesian_product2(all_31_6, all_31_5) = all_43_1 % 15.40/2.79 | % 15.40/2.79 | GROUND_INST: instantiating (12) with all_31_4, all_43_1, all_43_0, simplifying % 15.40/2.79 | with (21), (36), (37), (38) gives: % 15.40/2.79 | (40) subset(all_31_4, all_43_1) = 0 % 15.40/2.79 | % 15.40/2.79 | GROUND_INST: instantiating (cc1_relset_1) with all_31_6, all_31_5, all_31_4, % 15.40/2.79 | all_43_1, all_43_0, simplifying with (19), (20), (21), (37), % 15.40/2.79 | (38), (39) gives: % 15.40/2.79 | (41) relation(all_31_4) = 0 % 15.40/2.79 | % 15.40/2.79 | GROUND_INST: instantiating (6) with all_31_4, simplifying with (21), (41) % 15.40/2.79 | gives: % 15.46/2.79 | (42) ? [v0: $i] : (relation_rng(all_31_4) = v0 & $i(v0) & ! [v1: $i] : ! % 15.46/2.79 | [v2: int] : ! [v3: $i] : ! [v4: $i] : (v2 = 0 | ~ % 15.46/2.79 | (ordered_pair(v3, v1) = v4) | ~ (in(v1, v0) = v2) | ~ $i(v3) | % 15.46/2.79 | ~ $i(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v4, all_31_4) = v5)) & % 15.46/2.79 | ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ? [v2: $i] : ? % 15.46/2.79 | [v3: $i] : (ordered_pair(v2, v1) = v3 & in(v3, all_31_4) = 0 & % 15.46/2.79 | $i(v3) & $i(v2))) & ? [v1: $i] : (v1 = v0 | ~ $i(v1) | ? [v2: % 15.46/2.79 | $i] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : % 15.46/2.79 | (in(v2, v1) = v3 & $i(v4) & $i(v2) & ( ~ (v3 = 0) | ! [v7: $i] : % 15.46/2.79 | ! [v8: $i] : ( ~ (ordered_pair(v7, v2) = v8) | ~ $i(v7) | ? % 15.46/2.79 | [v9: int] : ( ~ (v9 = 0) & in(v8, all_31_4) = v9))) & (v3 = % 15.46/2.79 | 0 | (v6 = 0 & ordered_pair(v4, v2) = v5 & in(v5, all_31_4) = 0 % 15.46/2.79 | & $i(v5)))))) % 15.46/2.79 | % 15.46/2.79 | GROUND_INST: instantiating (4) with all_31_4, simplifying with (21), (41) % 15.46/2.79 | gives: % 15.46/2.79 | (43) ? [v0: $i] : (relation_dom(all_31_4) = v0 & $i(v0) & ! [v1: $i] : ! % 15.46/2.79 | [v2: int] : ! [v3: $i] : ! [v4: $i] : (v2 = 0 | ~ % 15.46/2.80 | (ordered_pair(v1, v3) = v4) | ~ (in(v1, v0) = v2) | ~ $i(v3) | % 15.46/2.80 | ~ $i(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v4, all_31_4) = v5)) & % 15.46/2.80 | ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ? [v2: $i] : ? % 15.46/2.80 | [v3: $i] : (ordered_pair(v1, v2) = v3 & in(v3, all_31_4) = 0 & % 15.46/2.80 | $i(v3) & $i(v2))) & ? [v1: $i] : (v1 = v0 | ~ $i(v1) | ? [v2: % 15.46/2.80 | $i] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : % 15.46/2.80 | (in(v2, v1) = v3 & $i(v4) & $i(v2) & ( ~ (v3 = 0) | ! [v7: $i] : % 15.46/2.80 | ! [v8: $i] : ( ~ (ordered_pair(v2, v7) = v8) | ~ $i(v7) | ? % 15.46/2.80 | [v9: int] : ( ~ (v9 = 0) & in(v8, all_31_4) = v9))) & (v3 = % 15.46/2.80 | 0 | (v6 = 0 & ordered_pair(v2, v4) = v5 & in(v5, all_31_4) = 0 % 15.46/2.80 | & $i(v5)))))) % 15.46/2.80 | % 15.46/2.80 | DELTA: instantiating (43) with fresh symbol all_58_0 gives: % 15.46/2.80 | (44) relation_dom(all_31_4) = all_58_0 & $i(all_58_0) & ! [v0: $i] : ! % 15.46/2.80 | [v1: int] : ! [v2: $i] : ! [v3: $i] : (v1 = 0 | ~ (ordered_pair(v0, % 15.46/2.80 | v2) = v3) | ~ (in(v0, all_58_0) = v1) | ~ $i(v2) | ~ $i(v0) | % 15.46/2.80 | ? [v4: int] : ( ~ (v4 = 0) & in(v3, all_31_4) = v4)) & ! [v0: $i] % 15.46/2.80 | : ( ~ (in(v0, all_58_0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 15.46/2.80 | (ordered_pair(v0, v1) = v2 & in(v2, all_31_4) = 0 & $i(v2) & % 15.46/2.80 | $i(v1))) & ? [v0: any] : (v0 = all_58_0 | ~ $i(v0) | ? [v1: $i] % 15.46/2.80 | : ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: int] : (in(v1, % 15.46/2.80 | v0) = v2 & $i(v3) & $i(v1) & ( ~ (v2 = 0) | ! [v6: $i] : ! % 15.46/2.80 | [v7: $i] : ( ~ (ordered_pair(v1, v6) = v7) | ~ $i(v6) | ? [v8: % 15.46/2.80 | int] : ( ~ (v8 = 0) & in(v7, all_31_4) = v8))) & (v2 = 0 | % 15.46/2.80 | (v5 = 0 & ordered_pair(v1, v3) = v4 & in(v4, all_31_4) = 0 & % 15.46/2.80 | $i(v4))))) % 15.46/2.80 | % 15.46/2.80 | ALPHA: (44) implies: % 15.46/2.80 | (45) $i(all_58_0) % 15.46/2.80 | (46) relation_dom(all_31_4) = all_58_0 % 15.46/2.80 | % 15.46/2.80 | DELTA: instantiating (42) with fresh symbol all_62_0 gives: % 15.46/2.80 | (47) relation_rng(all_31_4) = all_62_0 & $i(all_62_0) & ! [v0: $i] : ! % 15.46/2.80 | [v1: int] : ! [v2: $i] : ! [v3: $i] : (v1 = 0 | ~ (ordered_pair(v2, % 15.46/2.80 | v0) = v3) | ~ (in(v0, all_62_0) = v1) | ~ $i(v2) | ~ $i(v0) | % 15.46/2.80 | ? [v4: int] : ( ~ (v4 = 0) & in(v3, all_31_4) = v4)) & ! [v0: $i] % 15.46/2.80 | : ( ~ (in(v0, all_62_0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 15.46/2.80 | (ordered_pair(v1, v0) = v2 & in(v2, all_31_4) = 0 & $i(v2) & % 15.46/2.80 | $i(v1))) & ? [v0: any] : (v0 = all_62_0 | ~ $i(v0) | ? [v1: $i] % 15.46/2.80 | : ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: int] : (in(v1, % 15.46/2.80 | v0) = v2 & $i(v3) & $i(v1) & ( ~ (v2 = 0) | ! [v6: $i] : ! % 15.46/2.80 | [v7: $i] : ( ~ (ordered_pair(v6, v1) = v7) | ~ $i(v6) | ? [v8: % 15.46/2.80 | int] : ( ~ (v8 = 0) & in(v7, all_31_4) = v8))) & (v2 = 0 | % 15.46/2.80 | (v5 = 0 & ordered_pair(v3, v1) = v4 & in(v4, all_31_4) = 0 & % 15.46/2.80 | $i(v4))))) % 15.46/2.80 | % 15.46/2.80 | ALPHA: (47) implies: % 15.46/2.80 | (48) $i(all_62_0) % 15.46/2.80 | (49) relation_rng(all_31_4) = all_62_0 % 15.46/2.80 | % 15.46/2.80 | GROUND_INST: instantiating (15) with all_31_3, all_58_0, all_31_4, simplifying % 15.46/2.80 | with (26), (46) gives: % 15.46/2.80 | (50) all_58_0 = all_31_3 % 15.46/2.80 | % 15.46/2.80 | GROUND_INST: instantiating (16) with all_31_1, all_62_0, all_31_4, simplifying % 15.46/2.80 | with (27), (49) gives: % 15.46/2.80 | (51) all_62_0 = all_31_1 % 15.46/2.80 | % 15.46/2.80 | BETA: splitting (29) gives: % 15.46/2.80 | % 15.46/2.80 | Case 1: % 15.46/2.80 | | % 15.46/2.80 | | (52) ~ (all_31_0 = 0) % 15.46/2.80 | | % 15.46/2.80 | | BETA: splitting (33) gives: % 15.46/2.80 | | % 15.46/2.80 | | Case 1: % 15.46/2.80 | | | % 15.46/2.80 | | | (53) all_31_0 = 0 % 15.46/2.80 | | | % 15.46/2.80 | | | REDUCE: (52), (53) imply: % 15.46/2.80 | | | (54) $false % 15.46/2.80 | | | % 15.46/2.80 | | | CLOSE: (54) is inconsistent. % 15.46/2.80 | | | % 15.46/2.80 | | Case 2: % 15.46/2.80 | | | % 15.46/2.80 | | | (55) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_31_1) = 0 & % 15.46/2.80 | | | in(v0, all_31_5) = v1 & $i(v0)) % 15.46/2.80 | | | % 15.46/2.80 | | | DELTA: instantiating (55) with fresh symbols all_111_0, all_111_1 gives: % 15.46/2.80 | | | (56) ~ (all_111_0 = 0) & in(all_111_1, all_31_1) = 0 & in(all_111_1, % 15.46/2.80 | | | all_31_5) = all_111_0 & $i(all_111_1) % 15.46/2.80 | | | % 15.46/2.80 | | | ALPHA: (56) implies: % 15.46/2.80 | | | (57) ~ (all_111_0 = 0) % 15.46/2.80 | | | (58) $i(all_111_1) % 15.46/2.80 | | | (59) in(all_111_1, all_31_5) = all_111_0 % 15.46/2.80 | | | (60) in(all_111_1, all_31_1) = 0 % 15.46/2.80 | | | % 15.46/2.80 | | | BETA: splitting (32) gives: % 15.46/2.80 | | | % 15.46/2.80 | | | Case 1: % 15.46/2.80 | | | | % 15.46/2.80 | | | | (61) all_31_0 = 0 % 15.46/2.80 | | | | % 15.46/2.80 | | | | REDUCE: (52), (61) imply: % 15.46/2.80 | | | | (62) $false % 15.46/2.80 | | | | % 15.46/2.80 | | | | CLOSE: (62) is inconsistent. % 15.46/2.80 | | | | % 15.46/2.80 | | | Case 2: % 15.46/2.80 | | | | % 15.46/2.80 | | | | (63) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & powerset(all_31_5) = % 15.46/2.80 | | | | v0 & element(all_31_1, v0) = v1 & $i(v0)) % 15.46/2.81 | | | | % 15.46/2.81 | | | | DELTA: instantiating (63) with fresh symbols all_116_0, all_116_1 gives: % 15.46/2.81 | | | | (64) ~ (all_116_0 = 0) & powerset(all_31_5) = all_116_1 & % 15.46/2.81 | | | | element(all_31_1, all_116_1) = all_116_0 & $i(all_116_1) % 15.46/2.81 | | | | % 15.46/2.81 | | | | ALPHA: (64) implies: % 15.46/2.81 | | | | (65) ~ (all_116_0 = 0) % 15.46/2.81 | | | | (66) $i(all_116_1) % 15.46/2.81 | | | | (67) element(all_31_1, all_116_1) = all_116_0 % 15.46/2.81 | | | | % 15.46/2.81 | | | | GROUND_INST: instantiating (7) with all_31_4, all_31_1, all_111_1, % 15.46/2.81 | | | | simplifying with (21), (23), (27), (58), (60) gives: % 15.46/2.81 | | | | (68) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : % 15.46/2.81 | | | | ($i(v1) & ((v3 = 0 & ordered_pair(v1, all_111_1) = v2 & in(v2, % 15.46/2.81 | | | | all_31_4) = 0 & $i(v2)) | ( ~ (v0 = 0) & % 15.46/2.81 | | | | relation(all_31_4) = v0))) % 15.46/2.81 | | | | % 15.46/2.81 | | | | GROUND_INST: instantiating (10) with all_31_1, all_116_1, all_116_0, % 15.46/2.81 | | | | simplifying with (23), (66), (67) gives: % 15.46/2.81 | | | | (69) all_116_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_31_1, % 15.46/2.81 | | | | all_116_1) = v0) % 15.46/2.81 | | | | % 15.46/2.81 | | | | DELTA: instantiating (68) with fresh symbols all_130_0, all_130_1, % 15.46/2.81 | | | | all_130_2, all_130_3 gives: % 15.46/2.81 | | | | (70) $i(all_130_2) & ((all_130_0 = 0 & ordered_pair(all_130_2, % 15.46/2.81 | | | | all_111_1) = all_130_1 & in(all_130_1, all_31_4) = 0 & % 15.46/2.81 | | | | $i(all_130_1)) | ( ~ (all_130_3 = 0) & relation(all_31_4) = % 15.46/2.81 | | | | all_130_3)) % 15.46/2.81 | | | | % 15.46/2.81 | | | | ALPHA: (70) implies: % 15.46/2.81 | | | | (71) $i(all_130_2) % 15.46/2.81 | | | | (72) (all_130_0 = 0 & ordered_pair(all_130_2, all_111_1) = all_130_1 % 15.46/2.81 | | | | & in(all_130_1, all_31_4) = 0 & $i(all_130_1)) | ( ~ % 15.46/2.81 | | | | (all_130_3 = 0) & relation(all_31_4) = all_130_3) % 15.46/2.81 | | | | % 15.46/2.81 | | | | BETA: splitting (72) gives: % 15.46/2.81 | | | | % 15.46/2.81 | | | | Case 1: % 15.46/2.81 | | | | | % 15.46/2.81 | | | | | (73) all_130_0 = 0 & ordered_pair(all_130_2, all_111_1) = all_130_1 % 15.46/2.81 | | | | | & in(all_130_1, all_31_4) = 0 & $i(all_130_1) % 15.46/2.81 | | | | | % 15.46/2.81 | | | | | ALPHA: (73) implies: % 15.46/2.81 | | | | | (74) $i(all_130_1) % 15.46/2.81 | | | | | (75) in(all_130_1, all_31_4) = 0 % 15.46/2.81 | | | | | (76) ordered_pair(all_130_2, all_111_1) = all_130_1 % 15.46/2.81 | | | | | % 15.46/2.81 | | | | | BETA: splitting (69) gives: % 15.46/2.81 | | | | | % 15.46/2.81 | | | | | Case 1: % 15.46/2.81 | | | | | | % 15.46/2.81 | | | | | | (77) all_116_0 = 0 % 15.46/2.81 | | | | | | % 15.46/2.81 | | | | | | REDUCE: (65), (77) imply: % 15.46/2.81 | | | | | | (78) $false % 15.46/2.81 | | | | | | % 15.46/2.81 | | | | | | CLOSE: (78) is inconsistent. % 15.46/2.81 | | | | | | % 15.46/2.81 | | | | | Case 2: % 15.46/2.81 | | | | | | % 15.46/2.81 | | | | | | (79) ? [v0: int] : ( ~ (v0 = 0) & in(all_31_1, all_116_1) = v0) % 15.46/2.81 | | | | | | % 15.46/2.81 | | | | | | DELTA: instantiating (79) with fresh symbol all_139_0 gives: % 15.46/2.81 | | | | | | (80) ~ (all_139_0 = 0) & in(all_31_1, all_116_1) = all_139_0 % 15.46/2.81 | | | | | | % 15.46/2.81 | | | | | | ALPHA: (80) implies: % 15.46/2.81 | | | | | | (81) ~ (all_139_0 = 0) % 15.46/2.81 | | | | | | (82) in(all_31_1, all_116_1) = all_139_0 % 15.46/2.81 | | | | | | % 15.46/2.81 | | | | | | GROUND_INST: instantiating (11) with all_31_1, all_116_1, all_139_0, % 15.46/2.81 | | | | | | simplifying with (23), (66), (82) gives: % 15.46/2.81 | | | | | | (83) all_139_0 = 0 | ? [v0: any] : ? [v1: any] : % 15.46/2.81 | | | | | | (empty(all_116_1) = v1 & element(all_31_1, all_116_1) = v0 & % 15.46/2.81 | | | | | | ( ~ (v0 = 0) | v1 = 0)) % 15.46/2.81 | | | | | | % 15.46/2.81 | | | | | | GROUND_INST: instantiating (2) with all_31_4, all_43_1, all_130_1, % 15.46/2.81 | | | | | | simplifying with (21), (36), (40), (74), (75) gives: % 15.46/2.81 | | | | | | (84) in(all_130_1, all_43_1) = 0 % 15.46/2.81 | | | | | | % 15.46/2.81 | | | | | | BETA: splitting (83) gives: % 15.46/2.81 | | | | | | % 15.46/2.81 | | | | | | Case 1: % 15.46/2.81 | | | | | | | % 15.46/2.81 | | | | | | | (85) all_139_0 = 0 % 15.46/2.81 | | | | | | | % 15.46/2.81 | | | | | | | REDUCE: (81), (85) imply: % 15.46/2.81 | | | | | | | (86) $false % 15.46/2.81 | | | | | | | % 15.46/2.81 | | | | | | | CLOSE: (86) is inconsistent. % 15.46/2.81 | | | | | | | % 15.46/2.81 | | | | | | Case 2: % 15.46/2.81 | | | | | | | % 15.46/2.81 | | | | | | | % 15.46/2.81 | | | | | | | GROUND_INST: instantiating (9) with all_130_2, all_111_1, % 15.46/2.81 | | | | | | | all_31_6, all_31_5, all_130_1, all_43_1, simplifying % 15.46/2.81 | | | | | | | with (19), (20), (39), (58), (71), (76), (84) gives: % 15.46/2.81 | | | | | | | (87) in(all_130_2, all_31_6) = 0 & in(all_111_1, all_31_5) = 0 % 15.46/2.81 | | | | | | | % 15.46/2.81 | | | | | | | ALPHA: (87) implies: % 15.46/2.81 | | | | | | | (88) in(all_111_1, all_31_5) = 0 % 15.46/2.81 | | | | | | | % 15.46/2.81 | | | | | | | GROUND_INST: instantiating (17) with all_111_0, 0, all_31_5, % 15.46/2.81 | | | | | | | all_111_1, simplifying with (59), (88) gives: % 15.46/2.81 | | | | | | | (89) all_111_0 = 0 % 15.46/2.81 | | | | | | | % 15.46/2.81 | | | | | | | REDUCE: (57), (89) imply: % 15.46/2.81 | | | | | | | (90) $false % 15.46/2.81 | | | | | | | % 15.46/2.81 | | | | | | | CLOSE: (90) is inconsistent. % 15.46/2.81 | | | | | | | % 15.46/2.81 | | | | | | End of split % 15.46/2.81 | | | | | | % 15.46/2.81 | | | | | End of split % 15.46/2.81 | | | | | % 15.46/2.81 | | | | Case 2: % 15.46/2.81 | | | | | % 15.46/2.81 | | | | | (91) ~ (all_130_3 = 0) & relation(all_31_4) = all_130_3 % 15.46/2.81 | | | | | % 15.46/2.81 | | | | | ALPHA: (91) implies: % 15.46/2.81 | | | | | (92) ~ (all_130_3 = 0) % 15.46/2.81 | | | | | (93) relation(all_31_4) = all_130_3 % 15.46/2.81 | | | | | % 15.46/2.81 | | | | | GROUND_INST: instantiating (14) with 0, all_130_3, all_31_4, % 15.46/2.81 | | | | | simplifying with (41), (93) gives: % 15.46/2.81 | | | | | (94) all_130_3 = 0 % 15.46/2.81 | | | | | % 15.46/2.81 | | | | | REDUCE: (92), (94) imply: % 15.46/2.81 | | | | | (95) $false % 15.46/2.81 | | | | | % 15.46/2.81 | | | | | CLOSE: (95) is inconsistent. % 15.46/2.81 | | | | | % 15.46/2.82 | | | | End of split % 15.46/2.82 | | | | % 15.46/2.82 | | | End of split % 15.46/2.82 | | | % 15.46/2.82 | | End of split % 15.46/2.82 | | % 15.46/2.82 | Case 2: % 15.46/2.82 | | % 15.46/2.82 | | (96) ~ (all_31_2 = 0) % 15.46/2.82 | | % 15.46/2.82 | | BETA: splitting (31) gives: % 15.46/2.82 | | % 15.46/2.82 | | Case 1: % 15.46/2.82 | | | % 15.46/2.82 | | | (97) all_31_2 = 0 % 15.46/2.82 | | | % 15.46/2.82 | | | REDUCE: (96), (97) imply: % 15.46/2.82 | | | (98) $false % 15.46/2.82 | | | % 15.46/2.82 | | | CLOSE: (98) is inconsistent. % 15.46/2.82 | | | % 15.46/2.82 | | Case 2: % 15.46/2.82 | | | % 15.46/2.82 | | | (99) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_31_3) = 0 & % 15.46/2.82 | | | in(v0, all_31_6) = v1 & $i(v0)) % 15.46/2.82 | | | % 15.46/2.82 | | | DELTA: instantiating (99) with fresh symbols all_111_0, all_111_1 gives: % 15.46/2.82 | | | (100) ~ (all_111_0 = 0) & in(all_111_1, all_31_3) = 0 & in(all_111_1, % 15.46/2.82 | | | all_31_6) = all_111_0 & $i(all_111_1) % 15.46/2.82 | | | % 15.46/2.82 | | | ALPHA: (100) implies: % 15.46/2.82 | | | (101) ~ (all_111_0 = 0) % 15.46/2.82 | | | (102) $i(all_111_1) % 15.46/2.82 | | | (103) in(all_111_1, all_31_6) = all_111_0 % 15.46/2.82 | | | (104) in(all_111_1, all_31_3) = 0 % 15.46/2.82 | | | % 15.46/2.82 | | | BETA: splitting (30) gives: % 15.46/2.82 | | | % 15.46/2.82 | | | Case 1: % 15.46/2.82 | | | | % 15.46/2.82 | | | | (105) all_31_2 = 0 % 15.46/2.82 | | | | % 15.46/2.82 | | | | REDUCE: (96), (105) imply: % 15.46/2.82 | | | | (106) $false % 15.46/2.82 | | | | % 15.46/2.82 | | | | CLOSE: (106) is inconsistent. % 15.46/2.82 | | | | % 15.46/2.82 | | | Case 2: % 15.46/2.82 | | | | % 15.46/2.82 | | | | (107) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & powerset(all_31_6) % 15.46/2.82 | | | | = v0 & element(all_31_3, v0) = v1 & $i(v0)) % 15.46/2.82 | | | | % 15.46/2.82 | | | | DELTA: instantiating (107) with fresh symbols all_116_0, all_116_1 % 15.46/2.82 | | | | gives: % 15.46/2.82 | | | | (108) ~ (all_116_0 = 0) & powerset(all_31_6) = all_116_1 & % 15.46/2.82 | | | | element(all_31_3, all_116_1) = all_116_0 & $i(all_116_1) % 15.46/2.82 | | | | % 15.46/2.82 | | | | ALPHA: (108) implies: % 15.46/2.82 | | | | (109) ~ (all_116_0 = 0) % 15.46/2.82 | | | | (110) $i(all_116_1) % 15.46/2.82 | | | | (111) element(all_31_3, all_116_1) = all_116_0 % 15.46/2.82 | | | | % 15.46/2.82 | | | | GROUND_INST: instantiating (5) with all_31_4, all_31_3, all_111_1, % 15.46/2.82 | | | | simplifying with (21), (22), (26), (102), (104) gives: % 15.46/2.82 | | | | (112) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : % 15.46/2.82 | | | | ($i(v1) & ((v3 = 0 & ordered_pair(all_111_1, v1) = v2 & in(v2, % 15.46/2.82 | | | | all_31_4) = 0 & $i(v2)) | ( ~ (v0 = 0) & % 15.46/2.82 | | | | relation(all_31_4) = v0))) % 15.58/2.82 | | | | % 15.58/2.82 | | | | GROUND_INST: instantiating (1) with all_31_3, all_111_1, simplifying % 15.58/2.82 | | | | with (22), (102), (104) gives: % 15.58/2.82 | | | | (113) ? [v0: int] : ( ~ (v0 = 0) & in(all_31_3, all_111_1) = v0) % 15.58/2.82 | | | | % 15.58/2.82 | | | | GROUND_INST: instantiating (10) with all_31_3, all_116_1, all_116_0, % 15.58/2.82 | | | | simplifying with (22), (110), (111) gives: % 15.58/2.82 | | | | (114) all_116_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_31_3, % 15.58/2.82 | | | | all_116_1) = v0) % 15.58/2.82 | | | | % 15.58/2.82 | | | | DELTA: instantiating (113) with fresh symbol all_126_0 gives: % 15.58/2.82 | | | | (115) ~ (all_126_0 = 0) & in(all_31_3, all_111_1) = all_126_0 % 15.58/2.82 | | | | % 15.58/2.82 | | | | ALPHA: (115) implies: % 15.58/2.82 | | | | (116) ~ (all_126_0 = 0) % 15.58/2.82 | | | | (117) in(all_31_3, all_111_1) = all_126_0 % 15.58/2.82 | | | | % 15.58/2.82 | | | | DELTA: instantiating (112) with fresh symbols all_132_0, all_132_1, % 15.58/2.82 | | | | all_132_2, all_132_3 gives: % 15.58/2.82 | | | | (118) $i(all_132_2) & ((all_132_0 = 0 & ordered_pair(all_111_1, % 15.58/2.82 | | | | all_132_2) = all_132_1 & in(all_132_1, all_31_4) = 0 & % 15.58/2.82 | | | | $i(all_132_1)) | ( ~ (all_132_3 = 0) & relation(all_31_4) = % 15.58/2.82 | | | | all_132_3)) % 15.58/2.82 | | | | % 15.58/2.82 | | | | ALPHA: (118) implies: % 15.58/2.82 | | | | (119) $i(all_132_2) % 15.58/2.82 | | | | (120) (all_132_0 = 0 & ordered_pair(all_111_1, all_132_2) = all_132_1 % 15.58/2.82 | | | | & in(all_132_1, all_31_4) = 0 & $i(all_132_1)) | ( ~ % 15.58/2.82 | | | | (all_132_3 = 0) & relation(all_31_4) = all_132_3) % 15.58/2.82 | | | | % 15.58/2.82 | | | | BETA: splitting (120) gives: % 15.58/2.82 | | | | % 15.58/2.82 | | | | Case 1: % 15.58/2.82 | | | | | % 15.58/2.82 | | | | | (121) all_132_0 = 0 & ordered_pair(all_111_1, all_132_2) = % 15.58/2.82 | | | | | all_132_1 & in(all_132_1, all_31_4) = 0 & $i(all_132_1) % 15.58/2.82 | | | | | % 15.58/2.82 | | | | | ALPHA: (121) implies: % 15.58/2.82 | | | | | (122) $i(all_132_1) % 15.58/2.82 | | | | | (123) in(all_132_1, all_31_4) = 0 % 15.58/2.82 | | | | | (124) ordered_pair(all_111_1, all_132_2) = all_132_1 % 15.58/2.82 | | | | | % 15.58/2.82 | | | | | BETA: splitting (114) gives: % 15.58/2.82 | | | | | % 15.58/2.82 | | | | | Case 1: % 15.58/2.82 | | | | | | % 15.58/2.82 | | | | | | (125) all_116_0 = 0 % 15.58/2.82 | | | | | | % 15.58/2.82 | | | | | | REDUCE: (109), (125) imply: % 15.58/2.82 | | | | | | (126) $false % 15.58/2.82 | | | | | | % 15.58/2.82 | | | | | | CLOSE: (126) is inconsistent. % 15.58/2.82 | | | | | | % 15.58/2.82 | | | | | Case 2: % 15.58/2.82 | | | | | | % 15.58/2.82 | | | | | | % 15.58/2.82 | | | | | | GROUND_INST: instantiating (11) with all_31_3, all_111_1, all_126_0, % 15.58/2.82 | | | | | | simplifying with (22), (102), (117) gives: % 15.58/2.82 | | | | | | (127) all_126_0 = 0 | ? [v0: any] : ? [v1: any] : % 15.58/2.82 | | | | | | (empty(all_111_1) = v1 & element(all_31_3, all_111_1) = v0 % 15.58/2.82 | | | | | | & ( ~ (v0 = 0) | v1 = 0)) % 15.58/2.82 | | | | | | % 15.61/2.82 | | | | | | GROUND_INST: instantiating (2) with all_31_4, all_43_1, all_132_1, % 15.61/2.82 | | | | | | simplifying with (21), (36), (40), (122), (123) gives: % 15.61/2.82 | | | | | | (128) in(all_132_1, all_43_1) = 0 % 15.61/2.82 | | | | | | % 15.61/2.82 | | | | | | BETA: splitting (127) gives: % 15.61/2.82 | | | | | | % 15.61/2.82 | | | | | | Case 1: % 15.61/2.82 | | | | | | | % 15.61/2.82 | | | | | | | (129) all_126_0 = 0 % 15.61/2.82 | | | | | | | % 15.61/2.82 | | | | | | | REDUCE: (116), (129) imply: % 15.61/2.82 | | | | | | | (130) $false % 15.61/2.82 | | | | | | | % 15.61/2.82 | | | | | | | CLOSE: (130) is inconsistent. % 15.61/2.82 | | | | | | | % 15.61/2.82 | | | | | | Case 2: % 15.61/2.82 | | | | | | | % 15.61/2.82 | | | | | | | % 15.61/2.83 | | | | | | | GROUND_INST: instantiating (9) with all_111_1, all_132_2, % 15.61/2.83 | | | | | | | all_31_6, all_31_5, all_132_1, all_43_1, simplifying % 15.61/2.83 | | | | | | | with (19), (20), (39), (102), (119), (124), (128) % 15.61/2.83 | | | | | | | gives: % 15.61/2.83 | | | | | | | (131) in(all_132_2, all_31_5) = 0 & in(all_111_1, all_31_6) = 0 % 15.61/2.83 | | | | | | | % 15.61/2.83 | | | | | | | ALPHA: (131) implies: % 15.61/2.83 | | | | | | | (132) in(all_111_1, all_31_6) = 0 % 15.61/2.83 | | | | | | | % 15.61/2.83 | | | | | | | GROUND_INST: instantiating (17) with all_111_0, 0, all_31_6, % 15.61/2.83 | | | | | | | all_111_1, simplifying with (103), (132) gives: % 15.61/2.83 | | | | | | | (133) all_111_0 = 0 % 15.61/2.83 | | | | | | | % 15.61/2.83 | | | | | | | REDUCE: (101), (133) imply: % 15.61/2.83 | | | | | | | (134) $false % 15.61/2.83 | | | | | | | % 15.61/2.83 | | | | | | | CLOSE: (134) is inconsistent. % 15.61/2.83 | | | | | | | % 15.61/2.83 | | | | | | End of split % 15.61/2.83 | | | | | | % 15.61/2.83 | | | | | End of split % 15.61/2.83 | | | | | % 15.61/2.83 | | | | Case 2: % 15.61/2.83 | | | | | % 15.61/2.83 | | | | | (135) ~ (all_132_3 = 0) & relation(all_31_4) = all_132_3 % 15.61/2.83 | | | | | % 15.61/2.83 | | | | | ALPHA: (135) implies: % 15.61/2.83 | | | | | (136) ~ (all_132_3 = 0) % 15.61/2.83 | | | | | (137) relation(all_31_4) = all_132_3 % 15.61/2.83 | | | | | % 15.61/2.83 | | | | | GROUND_INST: instantiating (14) with 0, all_132_3, all_31_4, % 15.61/2.83 | | | | | simplifying with (41), (137) gives: % 15.61/2.83 | | | | | (138) all_132_3 = 0 % 15.61/2.83 | | | | | % 15.61/2.83 | | | | | REDUCE: (136), (138) imply: % 15.61/2.83 | | | | | (139) $false % 15.61/2.83 | | | | | % 15.61/2.83 | | | | | CLOSE: (139) is inconsistent. % 15.61/2.83 | | | | | % 15.61/2.83 | | | | End of split % 15.61/2.83 | | | | % 15.61/2.83 | | | End of split % 15.61/2.83 | | | % 15.61/2.83 | | End of split % 15.61/2.83 | | % 15.61/2.83 | End of split % 15.61/2.83 | % 15.61/2.83 End of proof % 15.61/2.83 % SZS output end Proof for theBenchmark % 15.61/2.83 % 15.61/2.83 2231ms %------------------------------------------------------------------------------