%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU251+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 : n019.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 17:43:39 EDT 2023 % Result : Theorem 9.99s 2.24s % Output : Proof 14.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU251+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.36 % Computer : n019.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Wed Aug 23 20:53:13 EDT 2023 % 0.15/0.36 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.60 Amanda Stjerna. % 0.21/0.60 Free software under BSD-3-Clause. % 0.21/0.60 % 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.60 % 0.21/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.61 Running up to 7 provers in parallel. % 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.81/1.12 Prover 4: Preprocessing ... % 2.81/1.13 Prover 1: Preprocessing ... % 3.19/1.16 Prover 0: Preprocessing ... % 3.19/1.16 Prover 5: Preprocessing ... % 3.19/1.16 Prover 6: Preprocessing ... % 3.19/1.16 Prover 3: Preprocessing ... % 3.19/1.16 Prover 2: Preprocessing ... % 6.13/1.63 Prover 1: Warning: ignoring some quantifiers % 6.64/1.67 Prover 5: Proving ... % 6.64/1.68 Prover 6: Proving ... % 6.64/1.68 Prover 4: Warning: ignoring some quantifiers % 6.64/1.69 Prover 3: Warning: ignoring some quantifiers % 6.64/1.70 Prover 1: Constructing countermodel ... % 6.64/1.70 Prover 3: Constructing countermodel ... % 6.95/1.71 Prover 2: Proving ... % 6.95/1.73 Prover 4: Constructing countermodel ... % 7.23/1.76 Prover 0: Proving ... % 9.99/2.24 Prover 0: proved (1618ms) % 9.99/2.24 % 9.99/2.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.99/2.24 % 10.91/2.25 Prover 2: stopped % 10.91/2.26 Prover 6: stopped % 10.91/2.26 Prover 3: stopped % 10.91/2.27 Prover 5: stopped % 10.91/2.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.91/2.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.91/2.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.91/2.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.91/2.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.30/2.32 Prover 13: Preprocessing ... % 11.30/2.32 Prover 8: Preprocessing ... % 11.30/2.32 Prover 11: Preprocessing ... % 11.30/2.32 Prover 10: Preprocessing ... % 11.30/2.34 Prover 7: Preprocessing ... % 11.70/2.41 Prover 13: Warning: ignoring some quantifiers % 11.70/2.43 Prover 13: Constructing countermodel ... % 11.70/2.44 Prover 10: Warning: ignoring some quantifiers % 11.70/2.44 Prover 8: Warning: ignoring some quantifiers % 11.70/2.44 Prover 7: Warning: ignoring some quantifiers % 12.42/2.45 Prover 10: Constructing countermodel ... % 12.42/2.45 Prover 8: Constructing countermodel ... % 12.42/2.47 Prover 7: Constructing countermodel ... % 13.15/2.55 Prover 11: Warning: ignoring some quantifiers % 13.15/2.58 Prover 11: Constructing countermodel ... % 14.00/2.66 Prover 10: gave up % 14.00/2.66 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 14.00/2.69 Prover 16: Preprocessing ... % 14.00/2.72 Prover 4: Found proof (size 90) % 14.00/2.72 Prover 4: proved (2100ms) % 14.00/2.72 Prover 7: stopped % 14.00/2.72 Prover 13: stopped % 14.00/2.72 Prover 11: stopped % 14.00/2.72 Prover 8: stopped % 14.00/2.73 Prover 1: stopped % 14.00/2.73 Prover 16: stopped % 14.00/2.74 % 14.00/2.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.00/2.74 % 14.00/2.75 % SZS output start Proof for theBenchmark % 14.60/2.75 Assumptions after simplification: % 14.60/2.75 --------------------------------- % 14.60/2.75 % 14.60/2.75 (cc2_funct_1) % 14.60/2.78 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2: % 14.60/2.78 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) = % 14.60/2.78 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) % 14.60/2.78 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 14.60/2.78 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0) % 14.60/2.78 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ % 14.60/2.78 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] % 14.60/2.78 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) | % 14.60/2.78 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) % 14.60/2.78 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & % 14.60/2.78 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = % 14.60/2.78 0))) % 14.60/2.78 % 14.60/2.78 (commutativity_k3_xboole_0) % 14.60/2.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2) % 14.60/2.78 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) & ! % 14.60/2.78 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | % 14.60/2.78 ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) % 14.60/2.78 % 14.60/2.78 (d1_wellord1) % 14.60/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 14.60/2.80 | v3 = v1 | ~ (fiber(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) % 14.60/2.80 = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? % 14.60/2.80 [v6: int] : ( ~ (v6 = 0) & ordered_pair(v3, v1) = v5 & in(v5, v0) = v6 & % 14.60/2.80 $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 14.60/2.80 $i] : (v3 = v1 | ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) | % 14.60/2.80 ~ (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 14.60/2.80 [v5: any] : ? [v6: any] : (in(v4, v0) = v5 & in(v3, v2) = v6 & ( ~ (v5 = 0) % 14.60/2.80 | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 14.60/2.80 [v4: $i] : ( ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) | ~ % 14.60/2.80 (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 14.60/2.80 any] : ? [v6: any] : (in(v4, v0) = v6 & in(v3, v2) = v5 & ( ~ (v5 = 0) | % 14.60/2.80 (v6 = 0 & ~ (v3 = v1))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 14.60/2.80 ! [v3: $i] : ( ~ (fiber(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) % 14.60/2.80 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 14.60/2.80 (ordered_pair(v3, v1) = v4 & in(v4, v0) = 0 & $i(v4))) & ? [v0: $i] : ! % 14.60/2.80 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (fiber(v1, v2) = v3) | ~ % 14.60/2.80 (relation(v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? % 14.60/2.80 [v5: any] : ? [v6: $i] : ? [v7: any] : (ordered_pair(v4, v2) = v6 & in(v6, % 14.60/2.80 v1) = v7 & in(v4, v0) = v5 & $i(v6) & $i(v4) & ( ~ (v7 = 0) | ~ (v5 = % 14.60/2.80 0) | v4 = v2) & (v5 = 0 | (v7 = 0 & ~ (v4 = v2))))) & ! [v0: $i] : % 14.60/2.80 ! [v1: $i] : ! [v2: $i] : ( ~ (fiber(v0, v1) = v2) | ~ (relation(v0) = 0) | % 14.60/2.80 ~ (in(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 14.60/2.80 % 14.60/2.80 (d3_tarski) % 14.60/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 14.60/2.80 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 14.60/2.80 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 14.60/2.80 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 14.60/2.80 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 14.60/2.80 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 14.60/2.80 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 14.60/2.80 $i(v0) | in(v2, v1) = 0) % 14.60/2.80 % 14.60/2.80 (d6_wellord1) % 14.60/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0, v1) = % 14.60/2.80 v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 14.60/2.80 (cartesian_product2(v1, v1) = v3 & set_intersection2(v0, v3) = v2 & $i(v3) & % 14.60/2.80 $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 14.60/2.80 (cartesian_product2(v1, v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~ % 14.60/2.80 $i(v0) | ? [v3: $i] : (relation_restriction(v0, v1) = v3 & % 14.60/2.80 set_intersection2(v0, v2) = v3 & $i(v3))) % 14.60/2.80 % 14.60/2.80 (dt_k2_wellord1) % 14.60/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0, v1) = % 14.60/2.80 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (relation(v2) % 14.60/2.80 = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 14.60/2.80 % 14.60/2.80 (t16_wellord1) % 14.60/2.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 14.60/2.81 (relation_restriction(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~ $i(v2) | ~ % 14.60/2.81 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: % 14.60/2.81 any] : (cartesian_product2(v1, v1) = v7 & relation(v2) = v5 & in(v0, v7) = % 14.60/2.81 v8 & in(v0, v2) = v6 & $i(v7) & ( ~ (v5 = 0) | (( ~ (v8 = 0) | ~ (v6 = 0) % 14.60/2.81 | v4 = 0) & ( ~ (v4 = 0) | (v8 = 0 & v6 = 0)))))) % 14.60/2.81 % 14.60/2.81 (t21_wellord1) % 14.60/2.81 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 14.60/2.81 $i] : ? [v6: int] : ( ~ (v6 = 0) & relation_restriction(v2, v0) = v3 & % 14.60/2.81 subset(v4, v5) = v6 & fiber(v3, v1) = v4 & fiber(v2, v1) = v5 & relation(v2) % 14.60/2.81 = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 14.60/2.81 % 14.60/2.81 (t2_subset) % 14.60/2.81 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~ % 14.60/2.81 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (element(v0, v1) = v3 & % 14.60/2.81 empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( % 14.60/2.81 ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 14.60/2.81 any] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) % 14.60/2.81 % 14.60/2.81 (function-axioms) % 14.60/2.81 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 14.60/2.81 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 14.60/2.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.60/2.81 (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) = % 14.60/2.81 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 14.60/2.81 ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 14.60/2.81 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 14.60/2.81 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 14.60/2.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.60/2.81 (fiber(v3, v2) = v1) | ~ (fiber(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 14.60/2.81 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ % 14.60/2.81 (ordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 14.60/2.81 [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ % 14.60/2.81 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 14.60/2.81 : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ % 14.60/2.81 (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.60/2.81 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = % 14.60/2.81 v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 14.60/2.81 (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : ! % 14.60/2.81 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 14.60/2.81 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.60/2.81 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ % 14.60/2.81 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.60/2.81 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 14.60/2.81 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.60/2.81 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~ % 14.60/2.81 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.60/2.81 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 14.60/2.81 (empty(v2) = v0)) % 14.60/2.81 % 14.60/2.81 Further assumptions not needed in the proof: % 14.60/2.81 -------------------------------------------- % 14.60/2.82 antisymmetry_r2_hidden, cc1_funct_1, commutativity_k2_tarski, d5_tarski, % 14.60/2.82 dt_k1_tarski, dt_k1_wellord1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski, % 14.60/2.82 dt_k2_zfmisc_1, dt_k3_xboole_0, dt_k4_tarski, dt_m1_subset_1, % 14.60/2.82 existence_m1_subset_1, fc1_xboole_0, fc1_zfmisc_1, idempotence_k3_xboole_0, % 14.60/2.82 rc1_funct_1, rc1_xboole_0, rc2_funct_1, rc2_xboole_0, rc3_funct_1, % 14.60/2.82 reflexivity_r1_tarski, t1_subset, t2_boole, t3_subset, t4_subset, t5_subset, % 14.60/2.82 t6_boole, t7_boole, t8_boole % 14.60/2.82 % 14.60/2.82 Those formulas are unsatisfiable: % 14.60/2.82 --------------------------------- % 14.60/2.82 % 14.60/2.82 Begin of proof % 14.60/2.82 | % 14.60/2.82 | ALPHA: (cc2_funct_1) implies: % 14.60/2.82 | (1) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 14.60/2.82 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & % 14.60/2.82 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 14.60/2.82 | (2) ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? % 14.60/2.82 | [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & % 14.60/2.82 | function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | % 14.60/2.82 | ~ (v2 = 0) | v1 = 0))) % 14.60/2.82 | % 14.60/2.82 | ALPHA: (commutativity_k3_xboole_0) implies: % 14.60/2.82 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, % 14.60/2.82 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = % 14.60/2.82 | v2 & $i(v2))) % 14.60/2.82 | % 14.60/2.82 | ALPHA: (d1_wellord1) implies: % 14.60/2.82 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (fiber(v0, % 14.60/2.82 | v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ~ % 14.60/2.82 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 14.60/2.82 | (ordered_pair(v3, v1) = v4 & in(v4, v0) = 0 & $i(v4))) % 14.60/2.82 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 14.60/2.82 | ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) | ~ % 14.60/2.82 | (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 14.60/2.82 | ? [v5: any] : ? [v6: any] : (in(v4, v0) = v6 & in(v3, v2) = v5 & ( ~ % 14.60/2.82 | (v5 = 0) | (v6 = 0 & ~ (v3 = v1))))) % 14.60/2.82 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 14.60/2.82 | (v3 = v1 | ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) | % 14.60/2.82 | ~ (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 14.60/2.82 | | ? [v5: any] : ? [v6: any] : (in(v4, v0) = v5 & in(v3, v2) = v6 & % 14.60/2.82 | ( ~ (v5 = 0) | v6 = 0))) % 14.60/2.82 | % 14.60/2.82 | ALPHA: (d3_tarski) implies: % 14.60/2.83 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 14.60/2.83 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 14.60/2.83 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 14.60/2.83 | % 14.60/2.83 | ALPHA: (d6_wellord1) implies: % 14.60/2.83 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0, % 14.60/2.83 | v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 14.60/2.83 | [v3: $i] : (cartesian_product2(v1, v1) = v3 & set_intersection2(v0, % 14.60/2.83 | v3) = v2 & $i(v3) & $i(v2))) % 14.60/2.83 | % 14.60/2.83 | ALPHA: (t2_subset) implies: % 14.60/2.83 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = % 14.60/2.83 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 14.60/2.83 | (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) % 14.60/2.83 | % 14.60/2.83 | ALPHA: (function-axioms) implies: % 14.60/2.83 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 14.60/2.83 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 14.60/2.83 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 14.60/2.83 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 14.60/2.83 | v0)) % 14.60/2.83 | % 14.60/2.83 | DELTA: instantiating (t21_wellord1) with fresh symbols all_38_0, all_38_1, % 14.60/2.83 | all_38_2, all_38_3, all_38_4, all_38_5, all_38_6 gives: % 14.60/2.83 | (12) ~ (all_38_0 = 0) & relation_restriction(all_38_4, all_38_6) = % 14.60/2.83 | all_38_3 & subset(all_38_2, all_38_1) = all_38_0 & fiber(all_38_3, % 14.60/2.83 | all_38_5) = all_38_2 & fiber(all_38_4, all_38_5) = all_38_1 & % 14.60/2.83 | relation(all_38_4) = 0 & $i(all_38_1) & $i(all_38_2) & $i(all_38_3) & % 14.60/2.83 | $i(all_38_4) & $i(all_38_5) & $i(all_38_6) % 14.60/2.83 | % 14.60/2.83 | ALPHA: (12) implies: % 14.60/2.83 | (13) ~ (all_38_0 = 0) % 14.60/2.83 | (14) $i(all_38_6) % 14.60/2.83 | (15) $i(all_38_5) % 14.60/2.83 | (16) $i(all_38_4) % 14.60/2.83 | (17) $i(all_38_2) % 14.60/2.83 | (18) $i(all_38_1) % 14.60/2.83 | (19) relation(all_38_4) = 0 % 14.60/2.83 | (20) fiber(all_38_4, all_38_5) = all_38_1 % 14.60/2.83 | (21) fiber(all_38_3, all_38_5) = all_38_2 % 14.60/2.83 | (22) subset(all_38_2, all_38_1) = all_38_0 % 14.60/2.83 | (23) relation_restriction(all_38_4, all_38_6) = all_38_3 % 14.60/2.83 | % 14.60/2.83 | GROUND_INST: instantiating (1) with all_38_4, simplifying with (16), (19) % 14.60/2.83 | gives: % 14.60/2.83 | (24) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_38_4) = % 14.60/2.83 | v2 & function(all_38_4) = v1 & empty(all_38_4) = v0 & ( ~ (v1 = 0) | % 14.60/2.84 | ~ (v0 = 0) | v2 = 0)) % 14.60/2.84 | % 14.60/2.84 | GROUND_INST: instantiating (7) with all_38_2, all_38_1, all_38_0, simplifying % 14.60/2.84 | with (17), (18), (22) gives: % 14.60/2.84 | (25) all_38_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 14.60/2.84 | all_38_1) = v1 & in(v0, all_38_2) = 0 & $i(v0)) % 14.60/2.84 | % 14.60/2.84 | GROUND_INST: instantiating (8) with all_38_4, all_38_6, all_38_3, simplifying % 14.60/2.84 | with (14), (16), (19), (23) gives: % 14.60/2.84 | (26) ? [v0: $i] : (cartesian_product2(all_38_6, all_38_6) = v0 & % 14.60/2.84 | set_intersection2(all_38_4, v0) = all_38_3 & $i(v0) & $i(all_38_3)) % 14.60/2.84 | % 14.60/2.84 | GROUND_INST: instantiating (dt_k2_wellord1) with all_38_4, all_38_6, all_38_3, % 14.60/2.84 | simplifying with (14), (16), (23) gives: % 14.60/2.84 | (27) ? [v0: any] : ? [v1: any] : (relation(all_38_3) = v1 & % 14.60/2.84 | relation(all_38_4) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 14.60/2.84 | % 14.60/2.84 | DELTA: instantiating (27) with fresh symbols all_50_0, all_50_1 gives: % 14.60/2.84 | (28) relation(all_38_3) = all_50_0 & relation(all_38_4) = all_50_1 & ( ~ % 14.60/2.84 | (all_50_1 = 0) | all_50_0 = 0) % 14.60/2.84 | % 14.60/2.84 | ALPHA: (28) implies: % 14.60/2.84 | (29) relation(all_38_4) = all_50_1 % 14.60/2.84 | (30) relation(all_38_3) = all_50_0 % 14.60/2.84 | (31) ~ (all_50_1 = 0) | all_50_0 = 0 % 14.60/2.84 | % 14.60/2.84 | DELTA: instantiating (26) with fresh symbol all_52_0 gives: % 14.60/2.84 | (32) cartesian_product2(all_38_6, all_38_6) = all_52_0 & % 14.60/2.84 | set_intersection2(all_38_4, all_52_0) = all_38_3 & $i(all_52_0) & % 14.60/2.84 | $i(all_38_3) % 14.60/2.84 | % 14.60/2.84 | ALPHA: (32) implies: % 14.60/2.84 | (33) $i(all_38_3) % 14.60/2.84 | (34) $i(all_52_0) % 14.60/2.84 | (35) set_intersection2(all_38_4, all_52_0) = all_38_3 % 14.60/2.84 | % 14.60/2.84 | DELTA: instantiating (24) with fresh symbols all_54_0, all_54_1, all_54_2 % 14.60/2.84 | gives: % 14.60/2.84 | (36) one_to_one(all_38_4) = all_54_0 & function(all_38_4) = all_54_1 & % 14.60/2.84 | empty(all_38_4) = all_54_2 & ( ~ (all_54_1 = 0) | ~ (all_54_2 = 0) | % 14.60/2.84 | all_54_0 = 0) % 14.60/2.84 | % 14.60/2.84 | ALPHA: (36) implies: % 14.60/2.84 | (37) one_to_one(all_38_4) = all_54_0 % 14.60/2.84 | % 14.60/2.84 | BETA: splitting (25) gives: % 14.60/2.84 | % 14.60/2.84 | Case 1: % 14.60/2.84 | | % 14.60/2.84 | | (38) all_38_0 = 0 % 14.60/2.84 | | % 14.60/2.84 | | REDUCE: (13), (38) imply: % 14.60/2.84 | | (39) $false % 14.60/2.84 | | % 14.60/2.84 | | CLOSE: (39) is inconsistent. % 14.60/2.84 | | % 14.60/2.84 | Case 2: % 14.60/2.84 | | % 14.60/2.84 | | (40) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_38_1) = v1 & % 14.60/2.84 | | in(v0, all_38_2) = 0 & $i(v0)) % 14.60/2.84 | | % 14.60/2.84 | | DELTA: instantiating (40) with fresh symbols all_78_0, all_78_1 gives: % 14.60/2.85 | | (41) ~ (all_78_0 = 0) & in(all_78_1, all_38_1) = all_78_0 & in(all_78_1, % 14.60/2.85 | | all_38_2) = 0 & $i(all_78_1) % 14.60/2.85 | | % 14.60/2.85 | | ALPHA: (41) implies: % 14.60/2.85 | | (42) ~ (all_78_0 = 0) % 14.60/2.85 | | (43) $i(all_78_1) % 14.60/2.85 | | (44) in(all_78_1, all_38_2) = 0 % 14.60/2.85 | | (45) in(all_78_1, all_38_1) = all_78_0 % 14.60/2.85 | | % 14.60/2.85 | | GROUND_INST: instantiating (10) with 0, all_50_1, all_38_4, simplifying with % 14.60/2.85 | | (19), (29) gives: % 14.60/2.85 | | (46) all_50_1 = 0 % 14.60/2.85 | | % 14.60/2.85 | | BETA: splitting (31) gives: % 14.60/2.85 | | % 14.60/2.85 | | Case 1: % 14.60/2.85 | | | % 14.60/2.85 | | | (47) ~ (all_50_1 = 0) % 14.60/2.85 | | | % 14.60/2.85 | | | REDUCE: (46), (47) imply: % 14.60/2.85 | | | (48) $false % 14.60/2.85 | | | % 14.60/2.85 | | | CLOSE: (48) is inconsistent. % 14.60/2.85 | | | % 14.60/2.85 | | Case 2: % 14.60/2.85 | | | % 14.60/2.85 | | | (49) all_50_0 = 0 % 14.60/2.85 | | | % 14.60/2.85 | | | REDUCE: (30), (49) imply: % 14.60/2.85 | | | (50) relation(all_38_3) = 0 % 14.60/2.85 | | | % 14.60/2.85 | | | GROUND_INST: instantiating (9) with all_78_1, all_38_1, all_78_0, % 14.60/2.85 | | | simplifying with (18), (43), (45) gives: % 14.60/2.85 | | | (51) all_78_0 = 0 | ? [v0: any] : ? [v1: any] : (element(all_78_1, % 14.60/2.85 | | | all_38_1) = v0 & empty(all_38_1) = v1 & ( ~ (v0 = 0) | v1 = % 14.60/2.85 | | | 0)) % 14.60/2.85 | | | % 14.60/2.85 | | | GROUND_INST: instantiating (4) with all_38_3, all_38_5, all_38_2, % 14.60/2.85 | | | all_78_1, simplifying with (15), (17), (21), (33), (43), % 14.60/2.85 | | | (44), (50) gives: % 14.60/2.85 | | | (52) ? [v0: $i] : (ordered_pair(all_78_1, all_38_5) = v0 & in(v0, % 14.60/2.85 | | | all_38_3) = 0 & $i(v0)) % 14.60/2.85 | | | % 14.60/2.85 | | | GROUND_INST: instantiating (2) with all_38_4, all_54_0, simplifying with % 14.60/2.85 | | | (16), (37) gives: % 14.60/2.85 | | | (53) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_38_4) = % 14.60/2.85 | | | v0 & function(all_38_4) = v2 & empty(all_38_4) = v1 & ( ~ (v2 = % 14.60/2.85 | | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | all_54_0 = 0)) % 14.60/2.85 | | | % 14.60/2.85 | | | GROUND_INST: instantiating (3) with all_52_0, all_38_4, all_38_3, % 14.60/2.85 | | | simplifying with (16), (34), (35) gives: % 14.60/2.85 | | | (54) set_intersection2(all_52_0, all_38_4) = all_38_3 & $i(all_38_3) % 14.60/2.85 | | | % 14.60/2.85 | | | DELTA: instantiating (52) with fresh symbol all_113_0 gives: % 14.60/2.85 | | | (55) ordered_pair(all_78_1, all_38_5) = all_113_0 & in(all_113_0, % 14.60/2.85 | | | all_38_3) = 0 & $i(all_113_0) % 14.60/2.85 | | | % 14.60/2.85 | | | ALPHA: (55) implies: % 14.60/2.85 | | | (56) $i(all_113_0) % 14.60/2.85 | | | (57) in(all_113_0, all_38_3) = 0 % 14.60/2.85 | | | (58) ordered_pair(all_78_1, all_38_5) = all_113_0 % 14.60/2.85 | | | % 14.60/2.85 | | | DELTA: instantiating (53) with fresh symbols all_125_0, all_125_1, % 14.60/2.85 | | | all_125_2 gives: % 14.60/2.85 | | | (59) relation(all_38_4) = all_125_2 & function(all_38_4) = all_125_0 & % 14.60/2.85 | | | empty(all_38_4) = all_125_1 & ( ~ (all_125_0 = 0) | ~ (all_125_1 % 14.60/2.85 | | | = 0) | ~ (all_125_2 = 0) | all_54_0 = 0) % 14.60/2.85 | | | % 14.60/2.85 | | | ALPHA: (59) implies: % 14.60/2.85 | | | (60) relation(all_38_4) = all_125_2 % 14.60/2.85 | | | % 14.60/2.85 | | | BETA: splitting (51) gives: % 14.60/2.85 | | | % 14.60/2.85 | | | Case 1: % 14.60/2.85 | | | | % 14.60/2.85 | | | | (61) all_78_0 = 0 % 14.60/2.85 | | | | % 14.60/2.85 | | | | REDUCE: (42), (61) imply: % 14.60/2.85 | | | | (62) $false % 14.60/2.85 | | | | % 14.60/2.85 | | | | CLOSE: (62) is inconsistent. % 14.60/2.85 | | | | % 14.60/2.85 | | | Case 2: % 14.60/2.85 | | | | % 14.60/2.85 | | | | % 14.60/2.85 | | | | GROUND_INST: instantiating (10) with 0, all_125_2, all_38_4, simplifying % 14.60/2.85 | | | | with (19), (60) gives: % 14.60/2.85 | | | | (63) all_125_2 = 0 % 14.60/2.85 | | | | % 14.60/2.86 | | | | GROUND_INST: instantiating (t16_wellord1) with all_113_0, all_38_6, % 14.60/2.86 | | | | all_38_4, all_38_3, 0, simplifying with (14), (16), (23), % 14.60/2.86 | | | | (56), (57) gives: % 14.60/2.86 | | | | (64) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 14.60/2.86 | | | | (cartesian_product2(all_38_6, all_38_6) = v2 & % 14.60/2.86 | | | | relation(all_38_4) = v0 & in(all_113_0, v2) = v3 & % 14.60/2.86 | | | | in(all_113_0, all_38_4) = v1 & $i(v2) & ( ~ (v0 = 0) | (v3 = 0 % 14.60/2.86 | | | | & v1 = 0))) % 14.60/2.86 | | | | % 14.60/2.86 | | | | GROUND_INST: instantiating (5) with all_38_3, all_38_5, all_38_2, % 14.60/2.86 | | | | all_78_1, all_113_0, simplifying with (15), (17), (21), % 14.60/2.86 | | | | (33), (43), (50), (58) gives: % 14.60/2.86 | | | | (65) ? [v0: any] : ? [v1: any] : (in(all_113_0, all_38_3) = v1 & % 14.60/2.86 | | | | in(all_78_1, all_38_2) = v0 & ( ~ (v0 = 0) | (v1 = 0 & ~ % 14.60/2.86 | | | | (all_78_1 = all_38_5)))) % 14.60/2.86 | | | | % 14.60/2.86 | | | | GROUND_INST: instantiating (6) with all_38_4, all_38_5, all_38_1, % 14.60/2.86 | | | | all_78_1, all_113_0, simplifying with (15), (16), (18), % 14.60/2.86 | | | | (19), (20), (43), (58) gives: % 14.60/2.86 | | | | (66) all_78_1 = all_38_5 | ? [v0: any] : ? [v1: any] : % 14.60/2.86 | | | | (in(all_113_0, all_38_4) = v0 & in(all_78_1, all_38_1) = v1 & ( % 14.60/2.86 | | | | ~ (v0 = 0) | v1 = 0)) % 14.60/2.86 | | | | % 14.60/2.86 | | | | GROUND_INST: instantiating (5) with all_38_4, all_38_5, all_38_1, % 14.60/2.86 | | | | all_78_1, all_113_0, simplifying with (15), (16), (18), % 14.60/2.86 | | | | (19), (20), (43), (58) gives: % 14.60/2.86 | | | | (67) ? [v0: any] : ? [v1: any] : (in(all_113_0, all_38_4) = v1 & % 14.60/2.86 | | | | in(all_78_1, all_38_1) = v0 & ( ~ (v0 = 0) | (v1 = 0 & ~ % 14.60/2.86 | | | | (all_78_1 = all_38_5)))) % 14.60/2.86 | | | | % 14.60/2.86 | | | | DELTA: instantiating (65) with fresh symbols all_166_0, all_166_1 gives: % 14.60/2.86 | | | | (68) in(all_113_0, all_38_3) = all_166_0 & in(all_78_1, all_38_2) = % 14.60/2.86 | | | | all_166_1 & ( ~ (all_166_1 = 0) | (all_166_0 = 0 & ~ (all_78_1 % 14.60/2.86 | | | | = all_38_5))) % 14.60/2.86 | | | | % 14.60/2.86 | | | | ALPHA: (68) implies: % 14.60/2.86 | | | | (69) in(all_78_1, all_38_2) = all_166_1 % 14.60/2.86 | | | | (70) ~ (all_166_1 = 0) | (all_166_0 = 0 & ~ (all_78_1 = all_38_5)) % 14.60/2.86 | | | | % 14.60/2.86 | | | | DELTA: instantiating (67) with fresh symbols all_168_0, all_168_1 gives: % 14.60/2.86 | | | | (71) in(all_113_0, all_38_4) = all_168_0 & in(all_78_1, all_38_1) = % 14.60/2.86 | | | | all_168_1 & ( ~ (all_168_1 = 0) | (all_168_0 = 0 & ~ (all_78_1 % 14.60/2.86 | | | | = all_38_5))) % 14.60/2.86 | | | | % 14.60/2.86 | | | | ALPHA: (71) implies: % 14.60/2.86 | | | | (72) in(all_78_1, all_38_1) = all_168_1 % 14.60/2.86 | | | | (73) in(all_113_0, all_38_4) = all_168_0 % 14.60/2.86 | | | | % 14.60/2.86 | | | | DELTA: instantiating (64) with fresh symbols all_174_0, all_174_1, % 14.60/2.86 | | | | all_174_2, all_174_3 gives: % 14.60/2.86 | | | | (74) cartesian_product2(all_38_6, all_38_6) = all_174_1 & % 14.60/2.86 | | | | relation(all_38_4) = all_174_3 & in(all_113_0, all_174_1) = % 14.60/2.86 | | | | all_174_0 & in(all_113_0, all_38_4) = all_174_2 & $i(all_174_1) % 14.60/2.86 | | | | & ( ~ (all_174_3 = 0) | (all_174_0 = 0 & all_174_2 = 0)) % 14.60/2.86 | | | | % 14.60/2.86 | | | | ALPHA: (74) implies: % 14.60/2.86 | | | | (75) in(all_113_0, all_38_4) = all_174_2 % 14.60/2.86 | | | | (76) relation(all_38_4) = all_174_3 % 14.60/2.87 | | | | (77) ~ (all_174_3 = 0) | (all_174_0 = 0 & all_174_2 = 0) % 14.60/2.87 | | | | % 14.60/2.87 | | | | GROUND_INST: instantiating (11) with 0, all_166_1, all_38_2, all_78_1, % 14.60/2.87 | | | | simplifying with (44), (69) gives: % 14.60/2.87 | | | | (78) all_166_1 = 0 % 14.60/2.87 | | | | % 14.60/2.87 | | | | GROUND_INST: instantiating (11) with all_78_0, all_168_1, all_38_1, % 14.60/2.87 | | | | all_78_1, simplifying with (45), (72) gives: % 14.60/2.87 | | | | (79) all_168_1 = all_78_0 % 14.60/2.87 | | | | % 14.60/2.87 | | | | GROUND_INST: instantiating (11) with all_168_0, all_174_2, all_38_4, % 14.60/2.87 | | | | all_113_0, simplifying with (73), (75) gives: % 14.60/2.87 | | | | (80) all_174_2 = all_168_0 % 14.60/2.87 | | | | % 14.60/2.87 | | | | GROUND_INST: instantiating (10) with 0, all_174_3, all_38_4, simplifying % 14.60/2.87 | | | | with (19), (76) gives: % 14.60/2.87 | | | | (81) all_174_3 = 0 % 14.60/2.87 | | | | % 14.60/2.87 | | | | BETA: splitting (70) gives: % 14.60/2.87 | | | | % 14.60/2.87 | | | | Case 1: % 14.60/2.87 | | | | | % 14.60/2.87 | | | | | (82) ~ (all_166_1 = 0) % 14.60/2.87 | | | | | % 14.60/2.87 | | | | | REDUCE: (78), (82) imply: % 14.60/2.87 | | | | | (83) $false % 14.60/2.87 | | | | | % 14.60/2.87 | | | | | CLOSE: (83) is inconsistent. % 14.60/2.87 | | | | | % 14.60/2.87 | | | | Case 2: % 14.60/2.87 | | | | | % 14.60/2.87 | | | | | (84) all_166_0 = 0 & ~ (all_78_1 = all_38_5) % 14.60/2.87 | | | | | % 14.60/2.87 | | | | | ALPHA: (84) implies: % 14.60/2.87 | | | | | (85) ~ (all_78_1 = all_38_5) % 14.60/2.87 | | | | | % 14.60/2.87 | | | | | BETA: splitting (66) gives: % 14.60/2.87 | | | | | % 14.60/2.87 | | | | | Case 1: % 14.60/2.87 | | | | | | % 14.60/2.87 | | | | | | (86) all_78_1 = all_38_5 % 14.60/2.87 | | | | | | % 14.60/2.87 | | | | | | REDUCE: (85), (86) imply: % 14.60/2.87 | | | | | | (87) $false % 14.60/2.87 | | | | | | % 14.60/2.87 | | | | | | CLOSE: (87) is inconsistent. % 14.60/2.87 | | | | | | % 14.60/2.87 | | | | | Case 2: % 14.60/2.87 | | | | | | % 14.60/2.87 | | | | | | (88) ? [v0: any] : ? [v1: any] : (in(all_113_0, all_38_4) = v0 % 14.60/2.87 | | | | | | & in(all_78_1, all_38_1) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 14.60/2.87 | | | | | | % 14.60/2.87 | | | | | | DELTA: instantiating (88) with fresh symbols all_223_0, all_223_1 % 14.60/2.87 | | | | | | gives: % 14.60/2.87 | | | | | | (89) in(all_113_0, all_38_4) = all_223_1 & in(all_78_1, all_38_1) % 14.60/2.87 | | | | | | = all_223_0 & ( ~ (all_223_1 = 0) | all_223_0 = 0) % 14.60/2.87 | | | | | | % 14.60/2.87 | | | | | | ALPHA: (89) implies: % 14.60/2.87 | | | | | | (90) in(all_78_1, all_38_1) = all_223_0 % 14.60/2.87 | | | | | | (91) in(all_113_0, all_38_4) = all_223_1 % 14.60/2.87 | | | | | | (92) ~ (all_223_1 = 0) | all_223_0 = 0 % 14.60/2.87 | | | | | | % 14.60/2.87 | | | | | | BETA: splitting (77) gives: % 14.60/2.87 | | | | | | % 14.60/2.87 | | | | | | Case 1: % 14.60/2.87 | | | | | | | % 14.60/2.87 | | | | | | | (93) ~ (all_174_3 = 0) % 14.60/2.87 | | | | | | | % 14.60/2.87 | | | | | | | REDUCE: (81), (93) imply: % 14.60/2.87 | | | | | | | (94) $false % 14.60/2.87 | | | | | | | % 14.60/2.87 | | | | | | | CLOSE: (94) is inconsistent. % 14.60/2.87 | | | | | | | % 14.60/2.87 | | | | | | Case 2: % 14.60/2.87 | | | | | | | % 14.60/2.87 | | | | | | | (95) all_174_0 = 0 & all_174_2 = 0 % 14.60/2.87 | | | | | | | % 14.60/2.87 | | | | | | | ALPHA: (95) implies: % 14.60/2.87 | | | | | | | (96) all_174_2 = 0 % 14.60/2.87 | | | | | | | % 14.60/2.87 | | | | | | | COMBINE_EQS: (80), (96) imply: % 14.60/2.87 | | | | | | | (97) all_168_0 = 0 % 14.60/2.87 | | | | | | | % 14.60/2.87 | | | | | | | SIMP: (97) implies: % 14.60/2.87 | | | | | | | (98) all_168_0 = 0 % 14.60/2.87 | | | | | | | % 14.60/2.87 | | | | | | | REDUCE: (73), (98) imply: % 14.60/2.87 | | | | | | | (99) in(all_113_0, all_38_4) = 0 % 14.60/2.87 | | | | | | | % 14.60/2.87 | | | | | | | GROUND_INST: instantiating (11) with all_78_0, all_223_0, % 14.60/2.87 | | | | | | | all_38_1, all_78_1, simplifying with (45), (90) % 14.60/2.87 | | | | | | | gives: % 14.60/2.87 | | | | | | | (100) all_223_0 = all_78_0 % 14.60/2.87 | | | | | | | % 14.60/2.87 | | | | | | | GROUND_INST: instantiating (11) with 0, all_223_1, all_38_4, % 14.60/2.87 | | | | | | | all_113_0, simplifying with (91), (99) gives: % 14.60/2.87 | | | | | | | (101) all_223_1 = 0 % 14.60/2.87 | | | | | | | % 14.60/2.87 | | | | | | | BETA: splitting (92) gives: % 14.60/2.87 | | | | | | | % 14.60/2.87 | | | | | | | Case 1: % 14.60/2.87 | | | | | | | | % 14.60/2.87 | | | | | | | | (102) ~ (all_223_1 = 0) % 14.60/2.87 | | | | | | | | % 14.60/2.87 | | | | | | | | REDUCE: (101), (102) imply: % 14.60/2.87 | | | | | | | | (103) $false % 14.60/2.87 | | | | | | | | % 14.60/2.87 | | | | | | | | CLOSE: (103) is inconsistent. % 14.60/2.87 | | | | | | | | % 14.60/2.87 | | | | | | | Case 2: % 14.60/2.87 | | | | | | | | % 14.60/2.87 | | | | | | | | (104) all_223_0 = 0 % 14.60/2.87 | | | | | | | | % 14.60/2.87 | | | | | | | | COMBINE_EQS: (100), (104) imply: % 14.60/2.87 | | | | | | | | (105) all_78_0 = 0 % 14.60/2.87 | | | | | | | | % 14.60/2.87 | | | | | | | | REDUCE: (42), (105) imply: % 14.60/2.87 | | | | | | | | (106) $false % 14.60/2.87 | | | | | | | | % 14.60/2.87 | | | | | | | | CLOSE: (106) is inconsistent. % 14.60/2.87 | | | | | | | | % 14.60/2.87 | | | | | | | End of split % 14.60/2.87 | | | | | | | % 14.60/2.87 | | | | | | End of split % 14.60/2.87 | | | | | | % 14.60/2.87 | | | | | End of split % 14.60/2.87 | | | | | % 14.60/2.87 | | | | End of split % 14.60/2.87 | | | | % 14.60/2.87 | | | End of split % 14.60/2.87 | | | % 14.60/2.87 | | End of split % 14.60/2.87 | | % 14.60/2.87 | End of split % 14.60/2.87 | % 14.60/2.87 End of proof % 14.60/2.87 % SZS output end Proof for theBenchmark % 14.60/2.87 % 14.60/2.87 2272ms %------------------------------------------------------------------------------