%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU245+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 : n009.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 17:43:37 EDT 2023 % Result : Theorem 8.15s 1.83s % Output : Proof 14.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU245+1 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n009.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Aug 24 00:51:21 EDT 2023 % 0.12/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.24/1.01 Prover 4: Preprocessing ... % 2.24/1.01 Prover 1: Preprocessing ... % 2.84/1.05 Prover 3: Preprocessing ... % 2.84/1.05 Prover 6: Preprocessing ... % 2.84/1.05 Prover 2: Preprocessing ... % 2.84/1.05 Prover 0: Preprocessing ... % 2.84/1.05 Prover 5: Preprocessing ... % 4.74/1.37 Prover 1: Warning: ignoring some quantifiers % 4.74/1.39 Prover 5: Proving ... % 4.74/1.40 Prover 3: Warning: ignoring some quantifiers % 4.74/1.41 Prover 2: Proving ... % 4.74/1.41 Prover 3: Constructing countermodel ... % 5.39/1.42 Prover 4: Warning: ignoring some quantifiers % 5.39/1.42 Prover 1: Constructing countermodel ... % 5.39/1.42 Prover 6: Proving ... % 5.39/1.44 Prover 4: Constructing countermodel ... % 5.39/1.47 Prover 0: Proving ... % 7.58/1.72 Prover 3: gave up % 7.58/1.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.58/1.75 Prover 7: Preprocessing ... % 8.15/1.79 Prover 1: gave up % 8.15/1.79 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.15/1.81 Prover 8: Preprocessing ... % 8.15/1.83 Prover 5: proved (1193ms) % 8.15/1.83 % 8.15/1.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.15/1.83 % 8.15/1.83 Prover 2: stopped % 8.15/1.83 Prover 0: stopped % 8.15/1.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.15/1.84 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.15/1.84 Prover 7: Warning: ignoring some quantifiers % 8.15/1.84 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.15/1.84 Prover 6: stopped % 8.15/1.85 Prover 7: Constructing countermodel ... % 8.15/1.85 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.15/1.86 Prover 11: Preprocessing ... % 8.82/1.88 Prover 10: Preprocessing ... % 8.82/1.88 Prover 16: Preprocessing ... % 8.82/1.88 Prover 13: Preprocessing ... % 8.82/1.91 Prover 8: Warning: ignoring some quantifiers % 8.82/1.93 Prover 8: Constructing countermodel ... % 9.21/1.95 Prover 16: Warning: ignoring some quantifiers % 9.21/1.96 Prover 16: Constructing countermodel ... % 9.21/1.96 Prover 13: Warning: ignoring some quantifiers % 9.21/1.96 Prover 13: Constructing countermodel ... % 9.21/1.96 Prover 10: Warning: ignoring some quantifiers % 9.65/1.99 Prover 10: Constructing countermodel ... % 9.90/2.06 Prover 11: Warning: ignoring some quantifiers % 9.90/2.07 Prover 11: Constructing countermodel ... % 9.90/2.08 Prover 10: gave up % 9.90/2.08 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 9.90/2.10 Prover 19: Preprocessing ... % 10.56/2.18 Prover 8: gave up % 11.12/2.20 Prover 19: Warning: ignoring some quantifiers % 11.12/2.21 Prover 19: Constructing countermodel ... % 12.24/2.39 Prover 19: gave up % 13.14/2.47 Prover 4: Found proof (size 174) % 13.14/2.47 Prover 4: proved (1840ms) % 13.14/2.47 Prover 7: stopped % 13.14/2.47 Prover 13: stopped % 13.14/2.47 Prover 16: stopped % 13.14/2.47 Prover 11: stopped % 13.14/2.47 % 13.14/2.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.14/2.47 % 13.14/2.50 % SZS output start Proof for theBenchmark % 13.14/2.50 Assumptions after simplification: % 13.14/2.50 --------------------------------- % 13.14/2.50 % 13.14/2.50 (cc2_funct_1) % 13.14/2.53 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2: % 13.14/2.53 any] : ? [v3: any] : ? [v4: any] : (empty(v0) = v3 & relation(v0) = v2 & % 13.14/2.53 function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) & % 13.14/2.53 ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : % 13.14/2.53 ? [v3: any] : (relation(v0) = v1 & function(v0) = v2 & one_to_one(v0) = v3 & % 13.14/2.53 ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (relation(v0) = % 13.14/2.53 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] : (empty(v0) = % 13.14/2.53 v1 & function(v0) = v2 & one_to_one(v0) = v3 & ( ~ (v2 = 0) | ~ (v1 = 0) % 13.14/2.53 | v3 = 0))) & ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: % 13.14/2.53 any] : ? [v2: any] : ? [v3: any] : (empty(v0) = v2 & relation(v0) = v1 & % 13.14/2.53 one_to_one(v0) = v3 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 13.14/2.53 % 13.14/2.53 (commutativity_k3_xboole_0) % 13.64/2.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2) % 13.64/2.54 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) & ! % 13.64/2.54 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | % 13.64/2.54 ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) % 13.64/2.54 % 13.64/2.54 (d3_xboole_0) % 13.64/2.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 13.64/2.55 | ~ (in(v3, v2) = v4) | ~ (set_intersection2(v0, v1) = v2) | ~ $i(v3) | % 13.64/2.55 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1) % 13.64/2.55 = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 13.64/2.55 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ (in(v3, v1) = v4) | % 13.64/2.55 ~ (set_intersection2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 13.64/2.55 $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v0) = v6 & % 13.64/2.55 ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 13.64/2.55 $i] : ! [v3: $i] : ! [v4: any] : ( ~ (in(v3, v0) = v4) | ~ % 13.64/2.55 (set_intersection2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 13.64/2.55 $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & % 13.64/2.55 ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 13.64/2.55 $i] : ! [v3: $i] : ( ~ (in(v3, v2) = 0) | ~ (set_intersection2(v0, v1) = % 13.64/2.55 v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v3, v1) = 0 & % 13.64/2.55 in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 13.64/2.55 ( ~ (in(v3, v1) = 0) | ~ (set_intersection2(v0, v1) = v2) | ~ $i(v3) | ~ % 13.64/2.55 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = % 13.64/2.55 v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: % 13.64/2.55 $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (in(v3, v0) = 0) | ~ % 13.64/2.55 (set_intersection2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 13.64/2.55 $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3, v1) = v4 & % 13.64/2.55 ( ~ (v4 = 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 13.64/2.55 [v3: $i] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ % 13.64/2.55 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: % 13.64/2.55 any] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ % 13.64/2.55 (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) % 13.64/2.55 % 13.64/2.55 (d6_wellord1) % 13.64/2.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v1, v1) = % 13.64/2.55 v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 13.64/2.55 (relation_restriction(v0, v1) = v3 & set_intersection2(v0, v2) = v3 & % 13.64/2.55 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 13.64/2.55 (relation_restriction(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~ % 13.64/2.55 $i(v0) | ? [v3: $i] : (cartesian_product2(v1, v1) = v3 & % 13.64/2.55 set_intersection2(v0, v3) = v2 & $i(v3) & $i(v2))) % 13.64/2.55 % 13.64/2.55 (dt_k2_wellord1) % 13.64/2.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0, v1) = % 13.64/2.55 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (relation(v2) % 13.64/2.55 = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 13.64/2.55 % 13.64/2.55 (rc1_funct_1) % 13.64/2.55 ? [v0: $i] : (relation(v0) = 0 & function(v0) = 0 & $i(v0)) % 13.64/2.55 % 13.64/2.55 (rc1_xboole_0) % 13.64/2.55 ? [v0: $i] : (empty(v0) = 0 & $i(v0)) % 13.64/2.55 % 13.64/2.55 (rc2_funct_1) % 13.64/2.55 ? [v0: $i] : (empty(v0) = 0 & relation(v0) = 0 & function(v0) = 0 & $i(v0)) % 13.64/2.55 % 13.64/2.55 (rc3_funct_1) % 13.64/2.55 ? [v0: $i] : (relation(v0) = 0 & function(v0) = 0 & one_to_one(v0) = 0 & % 13.64/2.55 $i(v0)) % 13.64/2.55 % 13.64/2.55 (t16_wellord1) % 13.64/2.56 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: % 13.64/2.56 any] : ? [v6: $i] : ? [v7: any] : (cartesian_product2(v1, v1) = v6 & % 13.64/2.56 relation_restriction(v2, v1) = v3 & in(v0, v6) = v7 & in(v0, v3) = v4 & % 13.64/2.56 in(v0, v2) = v5 & relation(v2) = 0 & $i(v6) & $i(v3) & $i(v2) & $i(v1) & % 13.64/2.56 $i(v0) & ((v7 = 0 & v5 = 0 & ~ (v4 = 0)) | (v4 = 0 & ( ~ (v7 = 0) | ~ (v5 % 13.64/2.56 = 0))))) % 13.64/2.56 % 13.64/2.56 (t6_boole) % 13.64/2.56 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ % 13.64/2.56 $i(v0)) % 13.64/2.56 % 13.64/2.56 (t8_boole) % 13.64/2.56 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0) % 13.64/2.56 | ~ $i(v1) | ~ $i(v0)) % 13.64/2.56 % 13.64/2.56 (function-axioms) % 13.64/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.64/2.56 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & % 13.64/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.64/2.56 (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) = % 13.64/2.56 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.64/2.56 $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 13.64/2.56 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.64/2.56 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 13.64/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.64/2.56 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 13.64/2.56 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 13.64/2.56 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: MultipleValueBool] : % 13.64/2.56 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | % 13.64/2.56 ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.64/2.56 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~ % 13.64/2.56 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.64/2.56 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ % 13.64/2.56 (one_to_one(v2) = v0)) % 13.64/2.56 % 13.64/2.56 Further assumptions not needed in the proof: % 13.64/2.56 -------------------------------------------- % 13.64/2.56 antisymmetry_r2_hidden, cc1_funct_1, dt_k1_xboole_0, dt_k2_zfmisc_1, % 13.64/2.56 dt_k3_xboole_0, dt_m1_subset_1, existence_m1_subset_1, fc1_xboole_0, % 13.64/2.56 idempotence_k3_xboole_0, rc2_xboole_0, t1_subset, t2_boole, t2_subset, t7_boole % 13.64/2.56 % 13.64/2.56 Those formulas are unsatisfiable: % 13.64/2.56 --------------------------------- % 13.64/2.56 % 13.64/2.56 Begin of proof % 13.64/2.56 | % 13.64/2.56 | ALPHA: (cc2_funct_1) implies: % 13.64/2.56 | (1) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 13.64/2.56 | [v2: any] : ? [v3: any] : (empty(v0) = v2 & relation(v0) = v1 & % 13.64/2.56 | one_to_one(v0) = v3 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 13.64/2.56 | (2) ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? % 13.64/2.56 | [v2: any] : ? [v3: any] : ? [v4: any] : (empty(v0) = v3 & % 13.64/2.57 | relation(v0) = v2 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) % 13.64/2.57 | | ~ (v2 = 0) | v1 = 0))) % 13.64/2.57 | % 13.64/2.57 | ALPHA: (t6_boole) implies: % 13.64/2.57 | (3) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0)) % 13.64/2.57 | % 13.64/2.57 | ALPHA: (commutativity_k3_xboole_0) implies: % 13.64/2.57 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, % 13.64/2.57 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = % 13.64/2.57 | v2 & $i(v2))) % 13.64/2.57 | % 13.64/2.57 | ALPHA: (d6_wellord1) implies: % 13.64/2.57 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0, % 13.64/2.57 | v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 13.64/2.57 | [v3: $i] : (cartesian_product2(v1, v1) = v3 & set_intersection2(v0, % 13.64/2.57 | v3) = v2 & $i(v3) & $i(v2))) % 13.64/2.57 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v1, % 13.64/2.57 | v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 13.64/2.57 | [v3: $i] : (relation_restriction(v0, v1) = v3 & set_intersection2(v0, % 13.64/2.57 | v2) = v3 & $i(v3))) % 13.64/2.57 | % 13.64/2.57 | ALPHA: (d3_xboole_0) implies: % 13.64/2.57 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 13.64/2.57 | ( ~ (in(v3, v0) = v4) | ~ (set_intersection2(v0, v1) = v2) | ~ $i(v3) % 13.64/2.57 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 13.64/2.57 | (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = % 13.64/2.57 | 0)))) % 13.64/2.57 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 13.64/2.57 | ( ~ (in(v3, v1) = v4) | ~ (set_intersection2(v0, v1) = v2) | ~ $i(v3) % 13.64/2.57 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 13.64/2.57 | (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = % 13.64/2.57 | 0)))) % 13.64/2.57 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 13.64/2.57 | (v4 = 0 | ~ (in(v3, v2) = v4) | ~ (set_intersection2(v0, v1) = v2) | % 13.64/2.57 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 13.64/2.57 | any] : (in(v3, v1) = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 13.64/2.57 | 0)))) % 13.64/2.57 | % 13.64/2.57 | ALPHA: (function-axioms) implies: % 13.64/2.57 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 13.64/2.57 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 13.64/2.57 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 13.64/2.57 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 13.64/2.57 | v0)) % 13.64/2.57 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.64/2.57 | (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, % 13.64/2.58 | v2) = v0)) % 13.64/2.58 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.64/2.58 | (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = % 13.64/2.58 | v0)) % 13.64/2.58 | % 13.64/2.58 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_18_0 gives: % 13.64/2.58 | (14) empty(all_18_0) = 0 & $i(all_18_0) % 13.64/2.58 | % 13.64/2.58 | ALPHA: (14) implies: % 13.64/2.58 | (15) $i(all_18_0) % 13.64/2.58 | (16) empty(all_18_0) = 0 % 13.64/2.58 | % 13.64/2.58 | DELTA: instantiating (rc1_funct_1) with fresh symbol all_22_0 gives: % 13.64/2.58 | (17) relation(all_22_0) = 0 & function(all_22_0) = 0 & $i(all_22_0) % 13.64/2.58 | % 13.64/2.58 | ALPHA: (17) implies: % 13.64/2.58 | (18) $i(all_22_0) % 13.64/2.58 | (19) relation(all_22_0) = 0 % 13.64/2.58 | % 13.64/2.58 | DELTA: instantiating (rc2_funct_1) with fresh symbol all_25_0 gives: % 13.64/2.58 | (20) empty(all_25_0) = 0 & relation(all_25_0) = 0 & function(all_25_0) = 0 % 13.64/2.58 | & $i(all_25_0) % 13.64/2.58 | % 13.64/2.58 | ALPHA: (20) implies: % 13.64/2.58 | (21) $i(all_25_0) % 13.64/2.58 | (22) relation(all_25_0) = 0 % 13.64/2.58 | (23) empty(all_25_0) = 0 % 13.64/2.58 | % 13.64/2.58 | DELTA: instantiating (rc3_funct_1) with fresh symbol all_27_0 gives: % 13.64/2.58 | (24) relation(all_27_0) = 0 & function(all_27_0) = 0 & one_to_one(all_27_0) % 13.64/2.58 | = 0 & $i(all_27_0) % 13.64/2.58 | % 13.64/2.58 | ALPHA: (24) implies: % 13.64/2.58 | (25) $i(all_27_0) % 13.64/2.58 | (26) one_to_one(all_27_0) = 0 % 13.64/2.58 | (27) function(all_27_0) = 0 % 13.64/2.58 | (28) relation(all_27_0) = 0 % 13.64/2.58 | % 13.64/2.58 | DELTA: instantiating (t16_wellord1) with fresh symbols all_31_0, all_31_1, % 13.64/2.58 | all_31_2, all_31_3, all_31_4, all_31_5, all_31_6, all_31_7 gives: % 13.64/2.58 | (29) cartesian_product2(all_31_6, all_31_6) = all_31_1 & % 13.64/2.58 | relation_restriction(all_31_5, all_31_6) = all_31_4 & in(all_31_7, % 13.64/2.58 | all_31_1) = all_31_0 & in(all_31_7, all_31_4) = all_31_3 & % 13.64/2.58 | in(all_31_7, all_31_5) = all_31_2 & relation(all_31_5) = 0 & % 13.64/2.58 | $i(all_31_1) & $i(all_31_4) & $i(all_31_5) & $i(all_31_6) & % 13.64/2.58 | $i(all_31_7) & ((all_31_0 = 0 & all_31_2 = 0 & ~ (all_31_3 = 0)) | % 13.64/2.58 | (all_31_3 = 0 & ( ~ (all_31_0 = 0) | ~ (all_31_2 = 0)))) % 13.64/2.58 | % 13.64/2.58 | ALPHA: (29) implies: % 13.64/2.58 | (30) $i(all_31_7) % 13.64/2.58 | (31) $i(all_31_6) % 13.64/2.58 | (32) $i(all_31_5) % 13.64/2.58 | (33) relation(all_31_5) = 0 % 13.64/2.58 | (34) in(all_31_7, all_31_5) = all_31_2 % 13.64/2.58 | (35) in(all_31_7, all_31_4) = all_31_3 % 13.64/2.58 | (36) in(all_31_7, all_31_1) = all_31_0 % 13.64/2.58 | (37) relation_restriction(all_31_5, all_31_6) = all_31_4 % 13.64/2.58 | (38) cartesian_product2(all_31_6, all_31_6) = all_31_1 % 13.64/2.58 | (39) (all_31_0 = 0 & all_31_2 = 0 & ~ (all_31_3 = 0)) | (all_31_3 = 0 & ( % 13.64/2.58 | ~ (all_31_0 = 0) | ~ (all_31_2 = 0))) % 13.64/2.58 | % 13.64/2.58 | GROUND_INST: instantiating (2) with all_27_0, 0, simplifying with (25), (26) % 13.64/2.58 | gives: % 13.64/2.59 | (40) ? [v0: MultipleValueBool] : ? [v1: MultipleValueBool] : ? [v2: % 13.64/2.59 | MultipleValueBool] : (empty(all_27_0) = v1 & relation(all_27_0) = v0 % 13.64/2.59 | & function(all_27_0) = v2) % 13.64/2.59 | % 13.64/2.59 | GROUND_INST: instantiating (1) with all_27_0, simplifying with (25), (27) % 13.64/2.59 | gives: % 13.64/2.59 | (41) ? [v0: any] : ? [v1: any] : ? [v2: any] : (empty(all_27_0) = v1 & % 13.64/2.59 | relation(all_27_0) = v0 & one_to_one(all_27_0) = v2 & ( ~ (v1 = 0) | % 13.64/2.59 | ~ (v0 = 0) | v2 = 0)) % 13.64/2.59 | % 13.64/2.59 | GROUND_INST: instantiating (t8_boole) with all_18_0, all_25_0, simplifying % 13.64/2.59 | with (15), (16), (21), (23) gives: % 13.64/2.59 | (42) all_25_0 = all_18_0 % 13.64/2.59 | % 13.64/2.59 | GROUND_INST: instantiating (3) with all_25_0, simplifying with (21), (23) % 13.64/2.59 | gives: % 13.64/2.59 | (43) all_25_0 = empty_set % 13.64/2.59 | % 13.64/2.59 | GROUND_INST: instantiating (5) with all_31_5, all_31_6, all_31_4, simplifying % 13.64/2.59 | with (31), (32), (33), (37) gives: % 13.64/2.59 | (44) ? [v0: $i] : (cartesian_product2(all_31_6, all_31_6) = v0 & % 13.64/2.59 | set_intersection2(all_31_5, v0) = all_31_4 & $i(v0) & $i(all_31_4)) % 13.64/2.59 | % 13.64/2.59 | GROUND_INST: instantiating (dt_k2_wellord1) with all_31_5, all_31_6, all_31_4, % 13.64/2.59 | simplifying with (31), (32), (37) gives: % 13.64/2.59 | (45) ? [v0: any] : ? [v1: any] : (relation(all_31_4) = v1 & % 13.64/2.59 | relation(all_31_5) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 13.64/2.59 | % 13.64/2.59 | GROUND_INST: instantiating (6) with all_31_5, all_31_6, all_31_1, simplifying % 13.64/2.59 | with (31), (32), (33), (38) gives: % 13.64/2.59 | (46) ? [v0: $i] : (relation_restriction(all_31_5, all_31_6) = v0 & % 13.64/2.59 | set_intersection2(all_31_5, all_31_1) = v0 & $i(v0)) % 13.64/2.59 | % 13.64/2.59 | GROUND_INST: instantiating (6) with all_27_0, all_31_6, all_31_1, simplifying % 13.64/2.59 | with (25), (28), (31), (38) gives: % 13.64/2.59 | (47) ? [v0: $i] : (relation_restriction(all_27_0, all_31_6) = v0 & % 13.64/2.59 | set_intersection2(all_27_0, all_31_1) = v0 & $i(v0)) % 13.64/2.59 | % 13.64/2.59 | GROUND_INST: instantiating (6) with all_25_0, all_31_6, all_31_1, simplifying % 13.64/2.59 | with (21), (22), (31), (38) gives: % 13.64/2.59 | (48) ? [v0: $i] : (relation_restriction(all_25_0, all_31_6) = v0 & % 13.64/2.59 | set_intersection2(all_25_0, all_31_1) = v0 & $i(v0)) % 13.64/2.59 | % 13.64/2.59 | GROUND_INST: instantiating (6) with all_22_0, all_31_6, all_31_1, simplifying % 13.64/2.59 | with (18), (19), (31), (38) gives: % 13.64/2.59 | (49) ? [v0: $i] : (relation_restriction(all_22_0, all_31_6) = v0 & % 13.64/2.59 | set_intersection2(all_22_0, all_31_1) = v0 & $i(v0)) % 13.64/2.59 | % 13.64/2.59 | COMBINE_EQS: (42), (43) imply: % 13.64/2.59 | (50) all_18_0 = empty_set % 13.64/2.59 | % 13.64/2.59 | SIMP: (50) implies: % 13.64/2.59 | (51) all_18_0 = empty_set % 13.64/2.59 | % 13.64/2.59 | DELTA: instantiating (49) with fresh symbol all_39_0 gives: % 13.64/2.59 | (52) relation_restriction(all_22_0, all_31_6) = all_39_0 & % 13.64/2.59 | set_intersection2(all_22_0, all_31_1) = all_39_0 & $i(all_39_0) % 13.64/2.59 | % 13.64/2.59 | ALPHA: (52) implies: % 13.64/2.59 | (53) $i(all_39_0) % 13.64/2.59 | (54) set_intersection2(all_22_0, all_31_1) = all_39_0 % 13.64/2.59 | % 13.64/2.59 | DELTA: instantiating (48) with fresh symbol all_41_0 gives: % 13.64/2.59 | (55) relation_restriction(all_25_0, all_31_6) = all_41_0 & % 13.64/2.60 | set_intersection2(all_25_0, all_31_1) = all_41_0 & $i(all_41_0) % 13.64/2.60 | % 13.64/2.60 | ALPHA: (55) implies: % 13.64/2.60 | (56) $i(all_41_0) % 13.64/2.60 | (57) set_intersection2(all_25_0, all_31_1) = all_41_0 % 13.64/2.60 | % 13.64/2.60 | DELTA: instantiating (47) with fresh symbol all_43_0 gives: % 13.64/2.60 | (58) relation_restriction(all_27_0, all_31_6) = all_43_0 & % 13.64/2.60 | set_intersection2(all_27_0, all_31_1) = all_43_0 & $i(all_43_0) % 13.64/2.60 | % 13.64/2.60 | ALPHA: (58) implies: % 13.64/2.60 | (59) $i(all_43_0) % 13.64/2.60 | (60) set_intersection2(all_27_0, all_31_1) = all_43_0 % 13.64/2.60 | (61) relation_restriction(all_27_0, all_31_6) = all_43_0 % 13.64/2.60 | % 13.64/2.60 | DELTA: instantiating (46) with fresh symbol all_45_0 gives: % 13.64/2.60 | (62) relation_restriction(all_31_5, all_31_6) = all_45_0 & % 13.64/2.60 | set_intersection2(all_31_5, all_31_1) = all_45_0 & $i(all_45_0) % 13.64/2.60 | % 13.64/2.60 | ALPHA: (62) implies: % 13.64/2.60 | (63) $i(all_45_0) % 13.64/2.60 | (64) set_intersection2(all_31_5, all_31_1) = all_45_0 % 13.64/2.60 | (65) relation_restriction(all_31_5, all_31_6) = all_45_0 % 13.64/2.60 | % 13.64/2.60 | DELTA: instantiating (40) with fresh symbols all_47_0, all_47_1, all_47_2 % 13.64/2.60 | gives: % 13.64/2.60 | (66) empty(all_27_0) = all_47_1 & relation(all_27_0) = all_47_2 & % 13.64/2.60 | function(all_27_0) = all_47_0 % 13.64/2.60 | % 13.64/2.60 | ALPHA: (66) implies: % 13.64/2.60 | (67) relation(all_27_0) = all_47_2 % 13.64/2.60 | % 13.64/2.60 | DELTA: instantiating (44) with fresh symbol all_49_0 gives: % 13.64/2.60 | (68) cartesian_product2(all_31_6, all_31_6) = all_49_0 & % 13.64/2.60 | set_intersection2(all_31_5, all_49_0) = all_31_4 & $i(all_49_0) & % 13.64/2.60 | $i(all_31_4) % 13.64/2.60 | % 13.64/2.60 | ALPHA: (68) implies: % 13.64/2.60 | (69) $i(all_49_0) % 13.64/2.60 | (70) cartesian_product2(all_31_6, all_31_6) = all_49_0 % 13.64/2.60 | % 13.64/2.60 | DELTA: instantiating (45) with fresh symbols all_51_0, all_51_1 gives: % 13.64/2.60 | (71) relation(all_31_4) = all_51_0 & relation(all_31_5) = all_51_1 & ( ~ % 13.64/2.60 | (all_51_1 = 0) | all_51_0 = 0) % 13.64/2.60 | % 13.64/2.60 | ALPHA: (71) implies: % 13.64/2.60 | (72) relation(all_31_5) = all_51_1 % 13.64/2.60 | (73) relation(all_31_4) = all_51_0 % 13.64/2.60 | (74) ~ (all_51_1 = 0) | all_51_0 = 0 % 13.64/2.60 | % 13.64/2.60 | DELTA: instantiating (41) with fresh symbols all_59_0, all_59_1, all_59_2 % 13.64/2.60 | gives: % 13.64/2.60 | (75) empty(all_27_0) = all_59_1 & relation(all_27_0) = all_59_2 & % 13.64/2.60 | one_to_one(all_27_0) = all_59_0 & ( ~ (all_59_1 = 0) | ~ (all_59_2 = % 13.64/2.60 | 0) | all_59_0 = 0) % 13.64/2.60 | % 13.64/2.60 | ALPHA: (75) implies: % 13.64/2.60 | (76) relation(all_27_0) = all_59_2 % 13.64/2.60 | % 13.64/2.60 | REDUCE: (43), (57) imply: % 13.64/2.60 | (77) set_intersection2(empty_set, all_31_1) = all_41_0 % 13.64/2.60 | % 13.64/2.60 | REDUCE: (15), (51) imply: % 13.64/2.60 | (78) $i(empty_set) % 13.64/2.60 | % 13.64/2.60 | GROUND_INST: instantiating (10) with 0, all_59_2, all_27_0, simplifying with % 13.64/2.60 | (28), (76) gives: % 13.64/2.60 | (79) all_59_2 = 0 % 13.64/2.60 | % 13.64/2.60 | GROUND_INST: instantiating (10) with all_47_2, all_59_2, all_27_0, simplifying % 13.64/2.60 | with (67), (76) gives: % 13.64/2.60 | (80) all_59_2 = all_47_2 % 13.64/2.60 | % 13.64/2.60 | GROUND_INST: instantiating (10) with 0, all_51_1, all_31_5, simplifying with % 13.64/2.60 | (33), (72) gives: % 13.64/2.60 | (81) all_51_1 = 0 % 13.64/2.60 | % 13.64/2.60 | GROUND_INST: instantiating (12) with all_31_4, all_45_0, all_31_6, all_31_5, % 13.64/2.60 | simplifying with (37), (65) gives: % 13.64/2.60 | (82) all_45_0 = all_31_4 % 13.64/2.60 | % 13.64/2.60 | GROUND_INST: instantiating (13) with all_31_1, all_49_0, all_31_6, all_31_6, % 13.64/2.60 | simplifying with (38), (70) gives: % 13.64/2.60 | (83) all_49_0 = all_31_1 % 13.64/2.60 | % 13.64/2.60 | COMBINE_EQS: (79), (80) imply: % 13.64/2.60 | (84) all_47_2 = 0 % 13.64/2.60 | % 13.64/2.60 | SIMP: (84) implies: % 13.64/2.60 | (85) all_47_2 = 0 % 13.64/2.60 | % 13.64/2.60 | REDUCE: (64), (82) imply: % 13.64/2.60 | (86) set_intersection2(all_31_5, all_31_1) = all_31_4 % 13.64/2.60 | % 13.64/2.60 | REDUCE: (69), (83) imply: % 13.64/2.60 | (87) $i(all_31_1) % 13.64/2.60 | % 13.64/2.60 | REDUCE: (63), (82) imply: % 13.64/2.60 | (88) $i(all_31_4) % 13.64/2.60 | % 13.64/2.60 | BETA: splitting (74) gives: % 13.64/2.60 | % 13.64/2.60 | Case 1: % 13.64/2.60 | | % 13.64/2.60 | | (89) ~ (all_51_1 = 0) % 13.64/2.60 | | % 13.64/2.60 | | REDUCE: (81), (89) imply: % 13.64/2.61 | | (90) $false % 13.64/2.61 | | % 13.64/2.61 | | CLOSE: (90) is inconsistent. % 13.64/2.61 | | % 13.64/2.61 | Case 2: % 13.64/2.61 | | % 13.64/2.61 | | (91) all_51_0 = 0 % 13.64/2.61 | | % 13.64/2.61 | | REDUCE: (73), (91) imply: % 13.64/2.61 | | (92) relation(all_31_4) = 0 % 13.64/2.61 | | % 13.64/2.61 | | GROUND_INST: instantiating (6) with all_31_4, all_31_6, all_31_1, % 13.64/2.61 | | simplifying with (31), (38), (88), (92) gives: % 13.64/2.61 | | (93) ? [v0: $i] : (relation_restriction(all_31_4, all_31_6) = v0 & % 13.64/2.61 | | set_intersection2(all_31_4, all_31_1) = v0 & $i(v0)) % 13.64/2.61 | | % 13.64/2.61 | | GROUND_INST: instantiating (8) with empty_set, all_31_1, all_41_0, all_31_7, % 13.64/2.61 | | all_31_0, simplifying with (30), (36), (56), (77), (78), (87) % 13.64/2.61 | | gives: % 13.64/2.61 | | (94) ? [v0: any] : ? [v1: any] : (in(all_31_7, all_41_0) = v0 & % 13.64/2.61 | | in(all_31_7, empty_set) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_31_0 = % 13.64/2.61 | | 0))) % 13.64/2.61 | | % 13.64/2.61 | | GROUND_INST: instantiating (4) with all_31_1, empty_set, all_41_0, % 13.64/2.61 | | simplifying with (77), (78), (87) gives: % 13.64/2.61 | | (95) set_intersection2(all_31_1, empty_set) = all_41_0 & $i(all_41_0) % 13.64/2.61 | | % 13.64/2.61 | | ALPHA: (95) implies: % 13.64/2.61 | | (96) set_intersection2(all_31_1, empty_set) = all_41_0 % 13.64/2.61 | | % 13.64/2.61 | | GROUND_INST: instantiating (8) with all_22_0, all_31_1, all_39_0, all_31_7, % 13.64/2.61 | | all_31_0, simplifying with (18), (30), (36), (53), (54), (87) % 13.64/2.61 | | gives: % 13.64/2.61 | | (97) ? [v0: any] : ? [v1: any] : (in(all_31_7, all_39_0) = v0 & % 13.64/2.61 | | in(all_31_7, all_22_0) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_31_0 = % 13.64/2.61 | | 0))) % 13.64/2.61 | | % 13.64/2.61 | | GROUND_INST: instantiating (4) with all_31_1, all_22_0, all_39_0, % 13.64/2.61 | | simplifying with (18), (54), (87) gives: % 13.64/2.61 | | (98) set_intersection2(all_31_1, all_22_0) = all_39_0 & $i(all_39_0) % 13.64/2.61 | | % 13.64/2.61 | | ALPHA: (98) implies: % 13.64/2.61 | | (99) set_intersection2(all_31_1, all_22_0) = all_39_0 % 13.64/2.61 | | % 13.64/2.61 | | GROUND_INST: instantiating (8) with all_27_0, all_31_1, all_43_0, all_31_7, % 13.64/2.61 | | all_31_0, simplifying with (25), (30), (36), (59), (60), (87) % 13.64/2.61 | | gives: % 13.64/2.61 | | (100) ? [v0: any] : ? [v1: any] : (in(all_31_7, all_43_0) = v0 & % 13.64/2.61 | | in(all_31_7, all_27_0) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_31_0 = % 13.64/2.61 | | 0))) % 13.64/2.61 | | % 13.64/2.61 | | GROUND_INST: instantiating (4) with all_31_1, all_27_0, all_43_0, % 13.64/2.61 | | simplifying with (25), (60), (87) gives: % 13.64/2.61 | | (101) set_intersection2(all_31_1, all_27_0) = all_43_0 & $i(all_43_0) % 13.64/2.61 | | % 13.64/2.61 | | ALPHA: (101) implies: % 13.64/2.61 | | (102) set_intersection2(all_31_1, all_27_0) = all_43_0 % 13.64/2.61 | | % 13.64/2.61 | | GROUND_INST: instantiating (8) with all_31_5, all_31_1, all_31_4, all_31_7, % 13.64/2.61 | | all_31_0, simplifying with (30), (32), (36), (86), (87), (88) % 13.64/2.61 | | gives: % 13.64/2.62 | | (103) ? [v0: any] : ? [v1: any] : (in(all_31_7, all_31_4) = v0 & % 13.64/2.62 | | in(all_31_7, all_31_5) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_31_0 = % 13.64/2.62 | | 0))) % 13.64/2.62 | | % 13.64/2.62 | | GROUND_INST: instantiating (9) with all_31_5, all_31_1, all_31_4, all_31_7, % 13.64/2.62 | | all_31_3, simplifying with (30), (32), (35), (86), (87), (88) % 13.64/2.62 | | gives: % 13.64/2.62 | | (104) all_31_3 = 0 | ? [v0: any] : ? [v1: any] : (in(all_31_7, % 13.64/2.62 | | all_31_1) = v1 & in(all_31_7, all_31_5) = v0 & ( ~ (v1 = 0) | % 13.64/2.62 | | ~ (v0 = 0))) % 13.64/2.62 | | % 13.64/2.62 | | GROUND_INST: instantiating (7) with all_31_5, all_31_1, all_31_4, all_31_7, % 13.64/2.62 | | all_31_2, simplifying with (30), (32), (34), (86), (87), (88) % 13.64/2.62 | | gives: % 13.64/2.62 | | (105) ? [v0: any] : ? [v1: any] : (in(all_31_7, all_31_1) = v1 & % 13.64/2.62 | | in(all_31_7, all_31_4) = v0 & ( ~ (v0 = 0) | (v1 = 0 & all_31_2 = % 13.64/2.62 | | 0))) % 13.64/2.62 | | % 13.64/2.62 | | GROUND_INST: instantiating (4) with all_31_1, all_31_5, all_31_4, % 13.64/2.62 | | simplifying with (32), (86), (87) gives: % 13.64/2.62 | | (106) set_intersection2(all_31_1, all_31_5) = all_31_4 & $i(all_31_4) % 13.64/2.62 | | % 13.64/2.62 | | ALPHA: (106) implies: % 13.64/2.62 | | (107) set_intersection2(all_31_1, all_31_5) = all_31_4 % 13.64/2.62 | | % 13.64/2.62 | | GROUND_INST: instantiating (dt_k2_wellord1) with all_27_0, all_31_6, % 13.64/2.62 | | all_43_0, simplifying with (25), (31), (61) gives: % 13.64/2.62 | | (108) ? [v0: any] : ? [v1: any] : (relation(all_43_0) = v1 & % 13.64/2.62 | | relation(all_27_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 13.64/2.62 | | % 13.64/2.62 | | DELTA: instantiating (93) with fresh symbol all_103_0 gives: % 13.64/2.62 | | (109) relation_restriction(all_31_4, all_31_6) = all_103_0 & % 13.64/2.62 | | set_intersection2(all_31_4, all_31_1) = all_103_0 & $i(all_103_0) % 13.64/2.62 | | % 13.64/2.62 | | ALPHA: (109) implies: % 13.64/2.62 | | (110) $i(all_103_0) % 13.64/2.62 | | (111) set_intersection2(all_31_4, all_31_1) = all_103_0 % 13.64/2.62 | | % 13.64/2.62 | | DELTA: instantiating (108) with fresh symbols all_105_0, all_105_1 gives: % 13.64/2.62 | | (112) relation(all_43_0) = all_105_0 & relation(all_27_0) = all_105_1 & ( % 13.64/2.62 | | ~ (all_105_1 = 0) | all_105_0 = 0) % 13.64/2.62 | | % 13.64/2.62 | | ALPHA: (112) implies: % 13.64/2.62 | | (113) relation(all_27_0) = all_105_1 % 13.64/2.62 | | (114) ~ (all_105_1 = 0) | all_105_0 = 0 % 13.64/2.62 | | % 13.64/2.62 | | DELTA: instantiating (105) with fresh symbols all_111_0, all_111_1 gives: % 13.64/2.62 | | (115) in(all_31_7, all_31_1) = all_111_0 & in(all_31_7, all_31_4) = % 13.64/2.62 | | all_111_1 & ( ~ (all_111_1 = 0) | (all_111_0 = 0 & all_31_2 = 0)) % 13.64/2.62 | | % 13.64/2.62 | | ALPHA: (115) implies: % 13.64/2.62 | | (116) in(all_31_7, all_31_4) = all_111_1 % 13.64/2.62 | | (117) in(all_31_7, all_31_1) = all_111_0 % 13.64/2.62 | | % 13.64/2.62 | | DELTA: instantiating (103) with fresh symbols all_113_0, all_113_1 gives: % 13.64/2.62 | | (118) in(all_31_7, all_31_4) = all_113_1 & in(all_31_7, all_31_5) = % 13.64/2.62 | | all_113_0 & ( ~ (all_113_1 = 0) | (all_113_0 = 0 & all_31_0 = 0)) % 13.64/2.62 | | % 13.64/2.62 | | ALPHA: (118) implies: % 13.64/2.62 | | (119) in(all_31_7, all_31_5) = all_113_0 % 13.64/2.62 | | (120) in(all_31_7, all_31_4) = all_113_1 % 13.64/2.62 | | % 13.64/2.62 | | DELTA: instantiating (94) with fresh symbols all_115_0, all_115_1 gives: % 13.64/2.62 | | (121) in(all_31_7, all_41_0) = all_115_1 & in(all_31_7, empty_set) = % 13.64/2.62 | | all_115_0 & ( ~ (all_115_1 = 0) | (all_115_0 = 0 & all_31_0 = 0)) % 13.64/2.62 | | % 13.64/2.62 | | ALPHA: (121) implies: % 13.64/2.62 | | (122) in(all_31_7, empty_set) = all_115_0 % 13.64/2.62 | | % 13.64/2.62 | | DELTA: instantiating (97) with fresh symbols all_117_0, all_117_1 gives: % 13.64/2.62 | | (123) in(all_31_7, all_39_0) = all_117_1 & in(all_31_7, all_22_0) = % 13.64/2.62 | | all_117_0 & ( ~ (all_117_1 = 0) | (all_117_0 = 0 & all_31_0 = 0)) % 13.64/2.62 | | % 13.64/2.62 | | ALPHA: (123) implies: % 14.08/2.62 | | (124) in(all_31_7, all_22_0) = all_117_0 % 14.08/2.62 | | % 14.08/2.62 | | DELTA: instantiating (100) with fresh symbols all_119_0, all_119_1 gives: % 14.08/2.62 | | (125) in(all_31_7, all_43_0) = all_119_1 & in(all_31_7, all_27_0) = % 14.08/2.62 | | all_119_0 & ( ~ (all_119_1 = 0) | (all_119_0 = 0 & all_31_0 = 0)) % 14.08/2.62 | | % 14.08/2.62 | | ALPHA: (125) implies: % 14.08/2.62 | | (126) in(all_31_7, all_27_0) = all_119_0 % 14.08/2.62 | | % 14.08/2.62 | | GROUND_INST: instantiating (10) with 0, all_105_1, all_27_0, simplifying % 14.08/2.62 | | with (28), (113) gives: % 14.08/2.62 | | (127) all_105_1 = 0 % 14.08/2.62 | | % 14.08/2.62 | | GROUND_INST: instantiating (11) with all_31_2, all_113_0, all_31_5, % 14.08/2.62 | | all_31_7, simplifying with (34), (119) gives: % 14.08/2.62 | | (128) all_113_0 = all_31_2 % 14.08/2.62 | | % 14.08/2.62 | | GROUND_INST: instantiating (11) with all_31_3, all_113_1, all_31_4, % 14.08/2.62 | | all_31_7, simplifying with (35), (120) gives: % 14.08/2.62 | | (129) all_113_1 = all_31_3 % 14.08/2.62 | | % 14.08/2.62 | | GROUND_INST: instantiating (11) with all_111_1, all_113_1, all_31_4, % 14.08/2.62 | | all_31_7, simplifying with (116), (120) gives: % 14.08/2.62 | | (130) all_113_1 = all_111_1 % 14.08/2.62 | | % 14.08/2.62 | | GROUND_INST: instantiating (11) with all_31_0, all_111_0, all_31_1, % 14.08/2.62 | | all_31_7, simplifying with (36), (117) gives: % 14.08/2.62 | | (131) all_111_0 = all_31_0 % 14.08/2.62 | | % 14.08/2.62 | | COMBINE_EQS: (129), (130) imply: % 14.08/2.62 | | (132) all_111_1 = all_31_3 % 14.08/2.62 | | % 14.08/2.62 | | BETA: splitting (114) gives: % 14.08/2.62 | | % 14.08/2.62 | | Case 1: % 14.08/2.62 | | | % 14.08/2.62 | | | (133) ~ (all_105_1 = 0) % 14.08/2.62 | | | % 14.08/2.62 | | | REDUCE: (127), (133) imply: % 14.08/2.62 | | | (134) $false % 14.08/2.62 | | | % 14.08/2.62 | | | CLOSE: (134) is inconsistent. % 14.08/2.62 | | | % 14.08/2.62 | | Case 2: % 14.08/2.62 | | | % 14.08/2.62 | | | % 14.08/2.62 | | | GROUND_INST: instantiating (7) with all_31_4, all_31_1, all_103_0, % 14.08/2.62 | | | all_31_7, all_31_3, simplifying with (30), (35), (87), (88), % 14.08/2.62 | | | (110), (111) gives: % 14.08/2.62 | | | (135) ? [v0: any] : ? [v1: any] : (in(all_31_7, all_103_0) = v0 & % 14.08/2.62 | | | in(all_31_7, all_31_1) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_31_3 % 14.08/2.62 | | | = 0))) % 14.08/2.63 | | | % 14.08/2.63 | | | GROUND_INST: instantiating (8) with all_31_1, empty_set, all_41_0, % 14.08/2.63 | | | all_31_7, all_115_0, simplifying with (30), (56), (78), (87), % 14.08/2.63 | | | (96), (122) gives: % 14.08/2.63 | | | (136) ? [v0: any] : ? [v1: any] : (in(all_31_7, all_41_0) = v0 & % 14.08/2.63 | | | in(all_31_7, all_31_1) = v1 & ( ~ (v0 = 0) | (v1 = 0 & % 14.08/2.63 | | | all_115_0 = 0))) % 14.08/2.63 | | | % 14.08/2.63 | | | GROUND_INST: instantiating (8) with all_31_1, all_22_0, all_39_0, % 14.08/2.63 | | | all_31_7, all_117_0, simplifying with (18), (30), (53), (87), % 14.08/2.63 | | | (99), (124) gives: % 14.08/2.63 | | | (137) ? [v0: any] : ? [v1: any] : (in(all_31_7, all_39_0) = v0 & % 14.08/2.63 | | | in(all_31_7, all_31_1) = v1 & ( ~ (v0 = 0) | (v1 = 0 & % 14.08/2.63 | | | all_117_0 = 0))) % 14.08/2.63 | | | % 14.08/2.63 | | | GROUND_INST: instantiating (8) with all_31_1, all_27_0, all_43_0, % 14.08/2.63 | | | all_31_7, all_119_0, simplifying with (25), (30), (59), (87), % 14.08/2.63 | | | (102), (126) gives: % 14.08/2.63 | | | (138) ? [v0: any] : ? [v1: any] : (in(all_31_7, all_43_0) = v0 & % 14.08/2.63 | | | in(all_31_7, all_31_1) = v1 & ( ~ (v0 = 0) | (v1 = 0 & % 14.08/2.63 | | | all_119_0 = 0))) % 14.08/2.63 | | | % 14.08/2.63 | | | DELTA: instantiating (138) with fresh symbols all_159_0, all_159_1 gives: % 14.08/2.63 | | | (139) in(all_31_7, all_43_0) = all_159_1 & in(all_31_7, all_31_1) = % 14.08/2.63 | | | all_159_0 & ( ~ (all_159_1 = 0) | (all_159_0 = 0 & all_119_0 = % 14.08/2.63 | | | 0)) % 14.08/2.63 | | | % 14.08/2.63 | | | ALPHA: (139) implies: % 14.08/2.63 | | | (140) in(all_31_7, all_31_1) = all_159_0 % 14.08/2.63 | | | % 14.08/2.63 | | | DELTA: instantiating (135) with fresh symbols all_161_0, all_161_1 gives: % 14.08/2.63 | | | (141) in(all_31_7, all_103_0) = all_161_1 & in(all_31_7, all_31_1) = % 14.08/2.63 | | | all_161_0 & ( ~ (all_161_1 = 0) | (all_161_0 = 0 & all_31_3 = 0)) % 14.08/2.63 | | | % 14.08/2.63 | | | ALPHA: (141) implies: % 14.08/2.63 | | | (142) in(all_31_7, all_31_1) = all_161_0 % 14.08/2.63 | | | % 14.08/2.63 | | | DELTA: instantiating (137) with fresh symbols all_165_0, all_165_1 gives: % 14.08/2.63 | | | (143) in(all_31_7, all_39_0) = all_165_1 & in(all_31_7, all_31_1) = % 14.08/2.63 | | | all_165_0 & ( ~ (all_165_1 = 0) | (all_165_0 = 0 & all_117_0 = % 14.08/2.63 | | | 0)) % 14.08/2.63 | | | % 14.08/2.63 | | | ALPHA: (143) implies: % 14.08/2.63 | | | (144) in(all_31_7, all_31_1) = all_165_0 % 14.08/2.63 | | | % 14.08/2.63 | | | DELTA: instantiating (136) with fresh symbols all_167_0, all_167_1 gives: % 14.08/2.63 | | | (145) in(all_31_7, all_41_0) = all_167_1 & in(all_31_7, all_31_1) = % 14.08/2.63 | | | all_167_0 & ( ~ (all_167_1 = 0) | (all_167_0 = 0 & all_115_0 = % 14.08/2.63 | | | 0)) % 14.08/2.63 | | | % 14.08/2.63 | | | ALPHA: (145) implies: % 14.08/2.63 | | | (146) in(all_31_7, all_31_1) = all_167_0 % 14.08/2.63 | | | % 14.08/2.63 | | | DELTA: instantiating (105) with fresh symbols all_169_0, all_169_1 gives: % 14.08/2.63 | | | (147) in(all_31_7, all_31_1) = all_169_0 & in(all_31_7, all_31_4) = % 14.08/2.63 | | | all_169_1 & ( ~ (all_169_1 = 0) | (all_169_0 = 0 & all_31_2 = 0)) % 14.08/2.63 | | | % 14.08/2.63 | | | ALPHA: (147) implies: % 14.08/2.63 | | | (148) in(all_31_7, all_31_4) = all_169_1 % 14.08/2.63 | | | (149) in(all_31_7, all_31_1) = all_169_0 % 14.08/2.63 | | | (150) ~ (all_169_1 = 0) | (all_169_0 = 0 & all_31_2 = 0) % 14.08/2.63 | | | % 14.08/2.63 | | | DELTA: instantiating (103) with fresh symbols all_173_0, all_173_1 gives: % 14.08/2.63 | | | (151) in(all_31_7, all_31_4) = all_173_1 & in(all_31_7, all_31_5) = % 14.08/2.63 | | | all_173_0 & ( ~ (all_173_1 = 0) | (all_173_0 = 0 & all_31_0 = 0)) % 14.08/2.63 | | | % 14.08/2.63 | | | ALPHA: (151) implies: % 14.08/2.63 | | | (152) in(all_31_7, all_31_5) = all_173_0 % 14.08/2.63 | | | (153) in(all_31_7, all_31_4) = all_173_1 % 14.08/2.63 | | | % 14.08/2.63 | | | GROUND_INST: instantiating (11) with all_31_2, all_173_0, all_31_5, % 14.08/2.63 | | | all_31_7, simplifying with (34), (152) gives: % 14.08/2.63 | | | (154) all_173_0 = all_31_2 % 14.08/2.63 | | | % 14.08/2.63 | | | GROUND_INST: instantiating (11) with all_31_3, all_173_1, all_31_4, % 14.08/2.63 | | | all_31_7, simplifying with (35), (153) gives: % 14.08/2.63 | | | (155) all_173_1 = all_31_3 % 14.08/2.63 | | | % 14.08/2.63 | | | GROUND_INST: instantiating (11) with all_169_1, all_173_1, all_31_4, % 14.08/2.63 | | | all_31_7, simplifying with (148), (153) gives: % 14.08/2.63 | | | (156) all_173_1 = all_169_1 % 14.08/2.63 | | | % 14.08/2.63 | | | GROUND_INST: instantiating (11) with all_165_0, all_167_0, all_31_1, % 14.08/2.63 | | | all_31_7, simplifying with (144), (146) gives: % 14.08/2.63 | | | (157) all_167_0 = all_165_0 % 14.08/2.63 | | | % 14.08/2.63 | | | GROUND_INST: instantiating (11) with all_159_0, all_167_0, all_31_1, % 14.08/2.63 | | | all_31_7, simplifying with (140), (146) gives: % 14.08/2.63 | | | (158) all_167_0 = all_159_0 % 14.08/2.63 | | | % 14.08/2.63 | | | GROUND_INST: instantiating (11) with all_31_0, all_169_0, all_31_1, % 14.08/2.63 | | | all_31_7, simplifying with (36), (149) gives: % 14.08/2.63 | | | (159) all_169_0 = all_31_0 % 14.08/2.63 | | | % 14.08/2.63 | | | GROUND_INST: instantiating (11) with all_167_0, all_169_0, all_31_1, % 14.08/2.63 | | | all_31_7, simplifying with (146), (149) gives: % 14.08/2.63 | | | (160) all_169_0 = all_167_0 % 14.08/2.63 | | | % 14.08/2.63 | | | GROUND_INST: instantiating (11) with all_161_0, all_169_0, all_31_1, % 14.08/2.63 | | | all_31_7, simplifying with (142), (149) gives: % 14.08/2.63 | | | (161) all_169_0 = all_161_0 % 14.08/2.63 | | | % 14.08/2.63 | | | COMBINE_EQS: (155), (156) imply: % 14.08/2.63 | | | (162) all_169_1 = all_31_3 % 14.08/2.63 | | | % 14.08/2.63 | | | COMBINE_EQS: (159), (161) imply: % 14.08/2.63 | | | (163) all_161_0 = all_31_0 % 14.08/2.63 | | | % 14.08/2.63 | | | COMBINE_EQS: (160), (161) imply: % 14.08/2.63 | | | (164) all_167_0 = all_161_0 % 14.08/2.63 | | | % 14.08/2.63 | | | SIMP: (164) implies: % 14.08/2.63 | | | (165) all_167_0 = all_161_0 % 14.08/2.63 | | | % 14.08/2.63 | | | COMBINE_EQS: (157), (158) imply: % 14.08/2.63 | | | (166) all_165_0 = all_159_0 % 14.08/2.63 | | | % 14.08/2.63 | | | COMBINE_EQS: (157), (165) imply: % 14.08/2.63 | | | (167) all_165_0 = all_161_0 % 14.08/2.63 | | | % 14.08/2.63 | | | COMBINE_EQS: (166), (167) imply: % 14.08/2.63 | | | (168) all_161_0 = all_159_0 % 14.08/2.63 | | | % 14.08/2.63 | | | SIMP: (168) implies: % 14.08/2.63 | | | (169) all_161_0 = all_159_0 % 14.08/2.63 | | | % 14.08/2.63 | | | COMBINE_EQS: (163), (169) imply: % 14.08/2.63 | | | (170) all_159_0 = all_31_0 % 14.08/2.63 | | | % 14.08/2.63 | | | SIMP: (170) implies: % 14.08/2.63 | | | (171) all_159_0 = all_31_0 % 14.08/2.63 | | | % 14.08/2.63 | | | BETA: splitting (39) gives: % 14.08/2.63 | | | % 14.08/2.63 | | | Case 1: % 14.08/2.63 | | | | % 14.08/2.63 | | | | (172) all_31_0 = 0 & all_31_2 = 0 & ~ (all_31_3 = 0) % 14.08/2.63 | | | | % 14.08/2.63 | | | | ALPHA: (172) implies: % 14.08/2.63 | | | | (173) all_31_2 = 0 % 14.08/2.63 | | | | (174) all_31_0 = 0 % 14.08/2.63 | | | | (175) ~ (all_31_3 = 0) % 14.08/2.63 | | | | % 14.08/2.63 | | | | REDUCE: (36), (174) imply: % 14.08/2.64 | | | | (176) in(all_31_7, all_31_1) = 0 % 14.08/2.64 | | | | % 14.08/2.64 | | | | REDUCE: (34), (173) imply: % 14.08/2.64 | | | | (177) in(all_31_7, all_31_5) = 0 % 14.08/2.64 | | | | % 14.08/2.64 | | | | BETA: splitting (104) gives: % 14.08/2.64 | | | | % 14.08/2.64 | | | | Case 1: % 14.08/2.64 | | | | | % 14.08/2.64 | | | | | (178) all_31_3 = 0 % 14.08/2.64 | | | | | % 14.08/2.64 | | | | | REDUCE: (175), (178) imply: % 14.08/2.64 | | | | | (179) $false % 14.08/2.64 | | | | | % 14.08/2.64 | | | | | CLOSE: (179) is inconsistent. % 14.08/2.64 | | | | | % 14.08/2.64 | | | | Case 2: % 14.08/2.64 | | | | | % 14.08/2.64 | | | | | (180) ? [v0: any] : ? [v1: any] : (in(all_31_7, all_31_1) = v1 & % 14.08/2.64 | | | | | in(all_31_7, all_31_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 14.08/2.64 | | | | | % 14.08/2.64 | | | | | DELTA: instantiating (180) with fresh symbols all_226_0, all_226_1 % 14.08/2.64 | | | | | gives: % 14.08/2.64 | | | | | (181) in(all_31_7, all_31_1) = all_226_0 & in(all_31_7, all_31_5) = % 14.08/2.64 | | | | | all_226_1 & ( ~ (all_226_0 = 0) | ~ (all_226_1 = 0)) % 14.08/2.64 | | | | | % 14.08/2.64 | | | | | ALPHA: (181) implies: % 14.08/2.64 | | | | | (182) in(all_31_7, all_31_5) = all_226_1 % 14.08/2.64 | | | | | (183) in(all_31_7, all_31_1) = all_226_0 % 14.08/2.64 | | | | | (184) ~ (all_226_0 = 0) | ~ (all_226_1 = 0) % 14.08/2.64 | | | | | % 14.08/2.64 | | | | | GROUND_INST: instantiating (11) with 0, all_226_1, all_31_5, all_31_7, % 14.08/2.64 | | | | | simplifying with (177), (182) gives: % 14.08/2.64 | | | | | (185) all_226_1 = 0 % 14.08/2.64 | | | | | % 14.08/2.64 | | | | | GROUND_INST: instantiating (11) with 0, all_226_0, all_31_1, all_31_7, % 14.08/2.64 | | | | | simplifying with (176), (183) gives: % 14.08/2.64 | | | | | (186) all_226_0 = 0 % 14.08/2.64 | | | | | % 14.08/2.64 | | | | | BETA: splitting (184) gives: % 14.08/2.64 | | | | | % 14.08/2.64 | | | | | Case 1: % 14.08/2.64 | | | | | | % 14.08/2.64 | | | | | | (187) ~ (all_226_0 = 0) % 14.08/2.64 | | | | | | % 14.08/2.64 | | | | | | REDUCE: (186), (187) imply: % 14.08/2.64 | | | | | | (188) $false % 14.08/2.64 | | | | | | % 14.08/2.64 | | | | | | CLOSE: (188) is inconsistent. % 14.08/2.64 | | | | | | % 14.08/2.64 | | | | | Case 2: % 14.08/2.64 | | | | | | % 14.08/2.64 | | | | | | (189) ~ (all_226_1 = 0) % 14.08/2.64 | | | | | | % 14.08/2.64 | | | | | | REDUCE: (185), (189) imply: % 14.08/2.64 | | | | | | (190) $false % 14.08/2.64 | | | | | | % 14.08/2.64 | | | | | | CLOSE: (190) is inconsistent. % 14.08/2.64 | | | | | | % 14.08/2.64 | | | | | End of split % 14.08/2.64 | | | | | % 14.08/2.64 | | | | End of split % 14.08/2.64 | | | | % 14.08/2.64 | | | Case 2: % 14.08/2.64 | | | | % 14.08/2.64 | | | | (191) all_31_3 = 0 & ( ~ (all_31_0 = 0) | ~ (all_31_2 = 0)) % 14.08/2.64 | | | | % 14.08/2.64 | | | | ALPHA: (191) implies: % 14.08/2.64 | | | | (192) all_31_3 = 0 % 14.08/2.64 | | | | (193) ~ (all_31_0 = 0) | ~ (all_31_2 = 0) % 14.08/2.64 | | | | % 14.08/2.64 | | | | COMBINE_EQS: (162), (192) imply: % 14.08/2.64 | | | | (194) all_169_1 = 0 % 14.08/2.64 | | | | % 14.08/2.64 | | | | BETA: splitting (150) gives: % 14.08/2.64 | | | | % 14.08/2.64 | | | | Case 1: % 14.08/2.64 | | | | | % 14.08/2.64 | | | | | (195) ~ (all_169_1 = 0) % 14.08/2.64 | | | | | % 14.08/2.64 | | | | | REDUCE: (194), (195) imply: % 14.08/2.64 | | | | | (196) $false % 14.08/2.64 | | | | | % 14.08/2.64 | | | | | CLOSE: (196) is inconsistent. % 14.08/2.64 | | | | | % 14.08/2.64 | | | | Case 2: % 14.08/2.64 | | | | | % 14.08/2.64 | | | | | (197) all_169_0 = 0 & all_31_2 = 0 % 14.08/2.64 | | | | | % 14.08/2.64 | | | | | ALPHA: (197) implies: % 14.08/2.64 | | | | | (198) all_31_2 = 0 % 14.08/2.64 | | | | | (199) all_169_0 = 0 % 14.08/2.64 | | | | | % 14.08/2.64 | | | | | COMBINE_EQS: (159), (199) imply: % 14.08/2.64 | | | | | (200) all_31_0 = 0 % 14.08/2.64 | | | | | % 14.08/2.64 | | | | | BETA: splitting (193) gives: % 14.08/2.64 | | | | | % 14.08/2.64 | | | | | Case 1: % 14.08/2.64 | | | | | | % 14.08/2.64 | | | | | | (201) ~ (all_31_0 = 0) % 14.08/2.64 | | | | | | % 14.08/2.64 | | | | | | REDUCE: (200), (201) imply: % 14.08/2.64 | | | | | | (202) $false % 14.08/2.64 | | | | | | % 14.08/2.64 | | | | | | CLOSE: (202) is inconsistent. % 14.08/2.64 | | | | | | % 14.08/2.64 | | | | | Case 2: % 14.08/2.64 | | | | | | % 14.08/2.64 | | | | | | (203) ~ (all_31_2 = 0) % 14.08/2.64 | | | | | | % 14.08/2.64 | | | | | | REDUCE: (198), (203) imply: % 14.08/2.64 | | | | | | (204) $false % 14.08/2.64 | | | | | | % 14.08/2.64 | | | | | | CLOSE: (204) is inconsistent. % 14.08/2.64 | | | | | | % 14.08/2.64 | | | | | End of split % 14.08/2.64 | | | | | % 14.08/2.64 | | | | End of split % 14.08/2.64 | | | | % 14.08/2.64 | | | End of split % 14.08/2.64 | | | % 14.08/2.64 | | End of split % 14.08/2.64 | | % 14.08/2.64 | End of split % 14.08/2.64 | % 14.08/2.64 End of proof % 14.08/2.64 % SZS output end Proof for theBenchmark % 14.08/2.64 % 14.08/2.64 2036ms %------------------------------------------------------------------------------