%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU215+2 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n024.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 17:43:19 EDT 2023 % Result : Theorem 141.46s 19.35s % Output : Proof 142.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU215+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n024.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Wed Aug 23 17:40:39 EDT 2023 % 0.13/0.34 % CPUTime : % 0.18/0.61 ________ _____ % 0.18/0.61 ___ __ \_________(_)________________________________ % 0.18/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.61 % 0.18/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.61 (2023-06-19) % 0.18/0.61 % 0.18/0.61 (c) Philipp Rümmer, 2009-2023 % 0.18/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.61 Amanda Stjerna. % 0.18/0.61 Free software under BSD-3-Clause. % 0.18/0.61 % 0.18/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.61 % 0.18/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.18/0.62 Running up to 7 provers in parallel. % 0.18/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.90/1.53 Prover 1: Preprocessing ... % 5.90/1.54 Prover 4: Preprocessing ... % 5.90/1.56 Prover 6: Preprocessing ... % 5.90/1.56 Prover 3: Preprocessing ... % 5.90/1.56 Prover 0: Preprocessing ... % 5.90/1.58 Prover 5: Preprocessing ... % 5.90/1.58 Prover 2: Preprocessing ... % 18.70/3.29 Prover 1: Warning: ignoring some quantifiers % 19.37/3.36 Prover 6: Proving ... % 19.98/3.39 Prover 3: Warning: ignoring some quantifiers % 19.98/3.42 Prover 5: Proving ... % 19.98/3.42 Prover 3: Constructing countermodel ... % 19.98/3.43 Prover 1: Constructing countermodel ... % 20.90/3.60 Prover 2: Proving ... % 21.65/3.63 Prover 4: Warning: ignoring some quantifiers % 22.96/3.80 Prover 4: Constructing countermodel ... % 22.96/3.88 Prover 0: Proving ... % 73.26/10.35 Prover 2: stopped % 73.26/10.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 75.09/10.55 Prover 7: Preprocessing ... % 79.57/11.15 Prover 7: Warning: ignoring some quantifiers % 79.57/11.20 Prover 7: Constructing countermodel ... % 100.08/13.97 Prover 5: stopped % 100.08/13.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 101.96/14.11 Prover 8: Preprocessing ... % 104.72/14.59 Prover 8: Warning: ignoring some quantifiers % 105.47/14.63 Prover 8: Constructing countermodel ... % 116.74/16.00 Prover 1: stopped % 116.74/16.01 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 117.65/16.20 Prover 9: Preprocessing ... % 124.38/16.98 Prover 9: Warning: ignoring some quantifiers % 124.38/17.00 Prover 9: Constructing countermodel ... % 130.88/17.89 Prover 6: stopped % 131.46/17.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 131.96/18.06 Prover 10: Preprocessing ... % 134.28/18.30 Prover 10: Warning: ignoring some quantifiers % 134.28/18.32 Prover 10: Constructing countermodel ... % 139.79/19.11 Prover 10: Found proof (size 93) % 139.79/19.11 Prover 10: proved (1195ms) % 139.79/19.11 Prover 0: stopped % 139.79/19.11 Prover 3: stopped % 139.79/19.11 Prover 9: stopped % 139.79/19.11 Prover 8: stopped % 139.79/19.11 Prover 7: stopped % 141.46/19.34 Prover 4: stopped % 141.46/19.34 % 141.46/19.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 141.46/19.35 % 141.46/19.36 % SZS output start Proof for theBenchmark % 141.74/19.38 Assumptions after simplification: % 141.74/19.38 --------------------------------- % 141.74/19.38 % 141.74/19.38 (d1_relat_1) % 141.74/19.41 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ % 141.74/19.41 in(v1, v0) | ? [v2: $i] : ? [v3: $i] : (ordered_pair(v2, v3) = v1 & $i(v3) % 141.74/19.41 & $i(v2))) & ? [v0: $i] : ( ~ $i(v0) | relation(v0) | ? [v1: $i] : % 141.74/19.41 ($i(v1) & in(v1, v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v3) % 141.74/19.41 = v1) | ~ $i(v3) | ~ $i(v2)))) % 141.74/19.41 % 141.74/19.41 (d3_relat_1) % 141.74/19.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 141.74/19.42 (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 141.74/19.42 | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | % 141.74/19.42 in(v4, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 141.74/19.42 relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2: $i] : ? [v3: $i] % 141.74/19.42 : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & % 141.74/19.42 in(v4, v0) & ~ in(v4, v1))) % 141.74/19.42 % 141.74/19.42 (d4_funct_1) % 141.74/19.42 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 141.74/19.42 [v4: $i] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ % 141.74/19.42 $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ relation(v0) | ~ function(v0) | ~ % 141.74/19.42 in(v2, v1) | ? [v5: $i] : (( ~ in(v4, v0) | (v5 = v3 & apply(v0, v2) = v3)) % 141.74/19.42 & (in(v4, v0) | ( ~ (v5 = v3) & apply(v0, v2) = v5 & $i(v5))))) & ! [v0: % 141.74/19.42 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~ % 141.74/19.42 (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ $i(v3) | ~ $i(v2) | % 141.74/19.42 ~ $i(v0) | ~ relation(v0) | ~ function(v0) | in(v2, v1)) & ! [v0: $i] : % 141.74/19.42 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~ % 141.74/19.42 (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ $i(v2) | ~ $i(v0) | % 141.74/19.42 ~ relation(v0) | ~ function(v0) | in(v2, v1)) % 141.74/19.42 % 141.74/19.42 (d4_relat_1) % 141.74/19.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 141.74/19.43 (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 141.74/19.43 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v4, v0) | in(v2, % 141.74/19.43 v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0) = % 141.74/19.43 v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1) % 141.74/19.43 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & % 141.74/19.43 in(v4, v0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 141.74/19.43 (relation_dom(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3: % 141.74/19.43 $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ in(v3, v0) | ! % 141.74/19.43 [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v3, v6) = v7) | ~ $i(v6) | % 141.74/19.43 ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & $i(v5) & % 141.74/19.43 in(v5, v1))))) % 141.74/19.43 % 141.74/19.43 (dt_k5_relat_1) % 141.74/19.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) = % 141.74/19.43 v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ relation(v0) | % 141.74/19.43 relation(v2)) % 141.74/19.43 % 141.74/19.43 (fc1_funct_1) % 141.74/19.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) = % 141.74/19.43 v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ relation(v0) | ~ % 141.74/19.43 function(v1) | ~ function(v0) | relation(v2)) & ! [v0: $i] : ! [v1: $i] : % 141.74/19.43 ! [v2: $i] : ( ~ (relation_composition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 141.74/19.43 | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | % 141.74/19.43 function(v2)) % 141.74/19.43 % 141.74/19.43 (t21_funct_1) % 141.74/19.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 141.74/19.44 (relation_dom(v1) = v2) | ~ (apply(v3, v0) = v4) | ~ $i(v3) | ~ $i(v1) | % 141.74/19.44 ~ $i(v0) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ % 141.74/19.44 function(v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (( ~ in(v4, v2) | % 141.74/19.44 (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & $i(v6) & % 141.74/19.44 $i(v5) & in(v0, v6)) | (relation_dom(v3) = v7 & $i(v7) & ~ in(v0, % 141.74/19.44 v7))) & ((relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 % 141.74/19.44 & $i(v6) & $i(v5) & ~ in(v0, v6)) | (relation_dom(v3) = v7 & $i(v7) & % 141.74/19.44 in(v4, v2) & in(v0, v7))))) % 141.74/19.44 % 141.74/19.44 (t22_funct_1) % 141.74/19.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 141.74/19.44 (apply(v2, v0) = v3) | ~ (apply(v1, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 141.74/19.44 $i(v0) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ % 141.74/19.44 function(v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 141.74/19.44 (relation_composition(v2, v1) = v5 & $i(v5) & ((v7 = v4 & apply(v5, v0) = v4 % 141.74/19.44 & $i(v4)) | (relation_dom(v5) = v6 & $i(v6) & ~ in(v0, v6))))) % 141.74/19.44 % 141.74/19.44 (t23_funct_1) % 141.74/19.44 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 141.74/19.44 $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v6) & relation_composition(v1, % 141.74/19.44 v4) = v5 & relation_dom(v1) = v2 & apply(v5, v0) = v6 & apply(v4, v3) = v7 % 141.74/19.44 & apply(v1, v0) = v3 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 141.74/19.44 $i(v1) & $i(v0) & relation(v4) & relation(v1) & function(v4) & function(v1) % 141.74/19.44 & in(v0, v2)) % 141.74/19.44 % 141.74/19.44 (t25_relat_1) % 141.74/19.44 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 141.74/19.44 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] : % 141.74/19.44 ! [v4: $i] : ( ~ (relation_rng(v3) = v4) | ~ $i(v3) | ~ subset(v0, v3) % 141.74/19.44 | ~ relation(v3) | subset(v1, v4)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 141.74/19.44 (relation_rng(v3) = v4) | ~ $i(v3) | ~ subset(v0, v3) | ~ % 141.74/19.44 relation(v3) | ? [v5: $i] : (relation_dom(v3) = v5 & $i(v5) & % 141.74/19.44 subset(v2, v5))))) % 141.74/19.44 % 141.74/19.44 (t33_zfmisc_1) % 141.74/19.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 % 141.74/19.45 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4) | ~ % 141.74/19.45 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! % 141.74/19.45 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (ordered_pair(v2, v3) = % 141.74/19.45 v4) | ~ (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 141.74/19.45 ~ $i(v0)) % 141.74/19.45 % 141.74/19.45 (t44_relat_1) % 141.74/19.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 141.74/19.45 (relation_composition(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ $i(v2) % 141.74/19.45 | ~ $i(v0) | ~ relation(v2) | ~ relation(v0) | ? [v4: $i] : % 141.74/19.45 (relation_dom(v3) = v4 & $i(v4) & subset(v4, v1))) % 141.74/19.45 % 141.74/19.45 (t45_relat_1) % 141.74/19.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) = % 141.74/19.45 v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ relation(v0) | ? [v3: % 141.74/19.45 $i] : ? [v4: $i] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & % 141.74/19.45 $i(v4) & $i(v3) & subset(v3, v4))) % 141.74/19.45 % 141.74/19.45 (t46_relat_1) % 141.74/19.45 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 141.74/19.45 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] : % 141.74/19.45 ! [v4: $i] : ( ~ (relation_composition(v0, v3) = v4) | ~ $i(v3) | ~ % 141.74/19.45 relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = v2 & relation_dom(v4) % 141.74/19.45 = v2) | (relation_dom(v3) = v5 & $i(v5) & ~ subset(v1, v5)))))) % 141.74/19.45 % 141.74/19.45 (t8_funct_1) % 141.74/19.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 141.74/19.45 (apply(v2, v0) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ $i(v2) | ~ % 141.74/19.45 $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ function(v2) | ? [v5: $i] : (( ~ % 141.74/19.46 (v4 = v1) | in(v3, v2) | (relation_dom(v2) = v5 & $i(v5) & ~ in(v0, % 141.74/19.46 v5))) & ( ~ in(v3, v2) | (v4 = v1 & relation_dom(v2) = v5 & $i(v5) & % 141.74/19.46 in(v0, v5))))) % 141.74/19.46 % 141.74/19.46 (function-axioms) % 142.15/19.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 142.15/19.47 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, % 142.15/19.47 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 142.15/19.47 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = % 142.15/19.47 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 142.15/19.47 ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & ! % 142.15/19.47 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 142.15/19.47 (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = % 142.15/19.47 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 142.15/19.47 ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = % 142.15/19.47 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 142.15/19.47 ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & % 142.15/19.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 142.15/19.47 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 142.15/19.47 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) % 142.15/19.47 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 142.15/19.47 : ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ % 142.15/19.47 (cartesian_product2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 142.15/19.47 : ! [v3: $i] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ % 142.15/19.47 (relation_inverse_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 142.15/19.47 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ % 142.15/19.47 (relation_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 142.15/19.47 ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ % 142.15/19.47 (relation_rng_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 142.15/19.47 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) % 142.15/19.47 | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 142.15/19.47 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ % 142.15/19.47 (ordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 142.15/19.47 [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ % 142.15/19.47 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 142.15/19.47 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, % 142.15/19.47 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 142.15/19.47 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 142.15/19.47 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 142.15/19.47 (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0: $i] % 142.15/19.47 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ % 142.15/19.47 (relation_field(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 142.15/19.47 v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i] % 142.15/19.47 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = % 142.15/19.47 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 142.15/19.47 (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! % 142.15/19.47 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ % 142.15/19.47 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 142.15/19.47 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : ! % 142.15/19.47 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 142.15/19.47 (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 142.15/19.47 ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 142.15/19.47 : ! [v2: $i] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ % 142.15/19.47 (identity_relation(v2) = v0)) % 142.15/19.47 % 142.15/19.47 Further assumptions not needed in the proof: % 142.15/19.47 -------------------------------------------- % 142.15/19.47 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_funct_1, cc1_relat_1, % 142.15/19.47 commutativity_k2_tarski, commutativity_k2_xboole_0, commutativity_k3_xboole_0, % 142.15/19.47 d10_relat_1, d10_xboole_0, d11_relat_1, d12_relat_1, d13_relat_1, d14_relat_1, % 142.15/19.47 d1_setfam_1, d1_tarski, d1_xboole_0, d1_zfmisc_1, d2_relat_1, d2_subset_1, % 142.15/19.47 d2_tarski, d2_xboole_0, d2_zfmisc_1, d3_tarski, d3_xboole_0, d4_subset_1, % 142.15/19.47 d4_tarski, d4_xboole_0, d5_relat_1, d5_subset_1, d5_tarski, d6_relat_1, % 142.15/19.47 d7_relat_1, d7_xboole_0, d8_relat_1, d8_setfam_1, d8_xboole_0, dt_k10_relat_1, % 142.15/19.47 dt_k1_funct_1, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, dt_k1_xboole_0, % 142.15/19.47 dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, dt_k2_xboole_0, % 142.15/19.47 dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0, % 142.15/19.47 dt_k4_relat_1, dt_k4_tarski, dt_k4_xboole_0, dt_k5_setfam_1, dt_k6_relat_1, % 142.15/19.47 dt_k6_setfam_1, dt_k6_subset_1, dt_k7_relat_1, dt_k7_setfam_1, dt_k8_relat_1, % 142.15/19.47 dt_k9_relat_1, dt_m1_subset_1, existence_m1_subset_1, fc10_relat_1, % 142.15/19.47 fc12_relat_1, fc1_relat_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, % 142.15/19.47 fc2_relat_1, fc2_subset_1, fc2_xboole_0, fc3_subset_1, fc3_xboole_0, % 142.15/19.47 fc4_relat_1, fc4_subset_1, fc5_relat_1, fc6_relat_1, fc7_relat_1, fc8_relat_1, % 142.15/19.47 fc9_relat_1, idempotence_k2_xboole_0, idempotence_k3_xboole_0, % 142.15/19.47 involutiveness_k3_subset_1, involutiveness_k4_relat_1, % 142.15/19.47 involutiveness_k7_setfam_1, irreflexivity_r2_xboole_0, l1_zfmisc_1, % 142.15/19.47 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, % 142.15/19.47 l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, % 142.15/19.47 rc1_funct_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_relat_1, rc2_subset_1, % 142.15/19.47 rc2_xboole_0, rc3_relat_1, redefinition_k5_setfam_1, redefinition_k6_setfam_1, % 142.15/19.47 redefinition_k6_subset_1, reflexivity_r1_tarski, symmetry_r1_xboole_0, % 142.15/19.47 t106_zfmisc_1, t10_zfmisc_1, t115_relat_1, t116_relat_1, t117_relat_1, % 142.15/19.47 t118_relat_1, t118_zfmisc_1, t119_relat_1, t119_zfmisc_1, t12_xboole_1, % 142.15/19.47 t136_zfmisc_1, t140_relat_1, t143_relat_1, t144_relat_1, t145_relat_1, % 142.15/19.47 t146_relat_1, t160_relat_1, t166_relat_1, t167_relat_1, t174_relat_1, % 142.15/19.47 t178_relat_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_subset, t1_xboole_1, % 142.15/19.47 t1_zfmisc_1, t20_relat_1, t21_relat_1, t26_xboole_1, t28_xboole_1, t2_boole, % 142.15/19.47 t2_subset, t2_tarski, t2_xboole_1, t30_relat_1, t33_xboole_1, t36_xboole_1, % 142.15/19.47 t37_relat_1, t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1, % 142.15/19.47 t39_zfmisc_1, t3_boole, t3_subset, t3_xboole_0, t3_xboole_1, t40_xboole_1, % 142.15/19.47 t43_subset_1, t45_xboole_1, t46_setfam_1, t46_zfmisc_1, t47_relat_1, % 142.15/19.47 t47_setfam_1, t48_setfam_1, t48_xboole_1, t4_boole, t4_subset, t4_xboole_0, % 142.15/19.47 t50_subset_1, t54_subset_1, t56_relat_1, t5_subset, t60_relat_1, t60_xboole_1, % 142.15/19.47 t63_xboole_1, t64_relat_1, t65_relat_1, t65_zfmisc_1, t69_enumset1, t6_boole, % 142.15/19.47 t6_zfmisc_1, t71_relat_1, t74_relat_1, t7_boole, t7_xboole_1, t83_xboole_1, % 142.15/19.47 t86_relat_1, t88_relat_1, t8_boole, t8_xboole_1, t8_zfmisc_1, t90_relat_1, % 142.15/19.47 t92_zfmisc_1, t94_relat_1, t99_relat_1, t99_zfmisc_1, t9_tarski, t9_zfmisc_1 % 142.15/19.47 % 142.15/19.47 Those formulas are unsatisfiable: % 142.15/19.47 --------------------------------- % 142.15/19.47 % 142.15/19.47 Begin of proof % 142.15/19.47 | % 142.15/19.47 | ALPHA: (d1_relat_1) implies: % 142.15/19.47 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | % 142.15/19.47 | ~ in(v1, v0) | ? [v2: $i] : ? [v3: $i] : (ordered_pair(v2, v3) = v1 % 142.15/19.47 | & $i(v3) & $i(v2))) % 142.15/19.47 | % 142.15/19.47 | ALPHA: (d3_relat_1) implies: % 142.15/19.47 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | % 142.15/19.47 | ~ relation(v0) | subset(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: % 142.15/19.47 | $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & % 142.15/19.47 | in(v4, v0) & ~ in(v4, v1))) % 142.15/19.47 | % 142.15/19.47 | ALPHA: (d4_funct_1) implies: % 142.15/19.47 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = empty_set % 142.15/19.47 | | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ $i(v2) | % 142.15/19.47 | ~ $i(v0) | ~ relation(v0) | ~ function(v0) | in(v2, v1)) % 142.15/19.47 | % 142.15/19.47 | ALPHA: (d4_relat_1) implies: % 142.15/19.48 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0) = v1) | % 142.15/19.48 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1) | % 142.15/19.48 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & % 142.15/19.48 | $i(v3) & in(v4, v0))) % 142.15/19.48 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 142.15/19.48 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ % 142.15/19.48 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ % 142.15/19.48 | in(v4, v0) | in(v2, v1)) % 142.15/19.48 | % 142.15/19.48 | ALPHA: (fc1_funct_1) implies: % 142.15/19.48 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, % 142.15/19.48 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ % 142.15/19.48 | relation(v0) | ~ function(v1) | ~ function(v0) | function(v2)) % 142.15/19.48 | % 142.15/19.48 | ALPHA: (t33_zfmisc_1) implies: % 142.15/19.48 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 142.15/19.48 | (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = % 142.15/19.48 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 142.15/19.48 | % 142.15/19.48 | ALPHA: (function-axioms) implies: % 142.15/19.48 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 142.15/19.48 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 142.15/19.48 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 142.15/19.48 | (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 142.15/19.48 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 142.15/19.48 | (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, % 142.15/19.48 | v2) = v0)) % 142.15/19.48 | % 142.15/19.48 | DELTA: instantiating (t23_funct_1) with fresh symbols all_237_0, all_237_1, % 142.15/19.48 | all_237_2, all_237_3, all_237_4, all_237_5, all_237_6, all_237_7 gives: % 142.15/19.48 | (11) ~ (all_237_0 = all_237_1) & relation_composition(all_237_6, % 142.15/19.48 | all_237_3) = all_237_2 & relation_dom(all_237_6) = all_237_5 & % 142.15/19.48 | apply(all_237_2, all_237_7) = all_237_1 & apply(all_237_3, all_237_4) % 142.15/19.48 | = all_237_0 & apply(all_237_6, all_237_7) = all_237_4 & $i(all_237_0) % 142.15/19.48 | & $i(all_237_1) & $i(all_237_2) & $i(all_237_3) & $i(all_237_4) & % 142.15/19.48 | $i(all_237_5) & $i(all_237_6) & $i(all_237_7) & relation(all_237_3) & % 142.15/19.48 | relation(all_237_6) & function(all_237_3) & function(all_237_6) & % 142.15/19.48 | in(all_237_7, all_237_5) % 142.15/19.48 | % 142.15/19.48 | ALPHA: (11) implies: % 142.15/19.48 | (12) ~ (all_237_0 = all_237_1) % 142.15/19.48 | (13) in(all_237_7, all_237_5) % 142.15/19.48 | (14) function(all_237_6) % 142.15/19.48 | (15) function(all_237_3) % 142.15/19.48 | (16) relation(all_237_6) % 142.15/19.48 | (17) relation(all_237_3) % 142.15/19.48 | (18) $i(all_237_7) % 142.15/19.48 | (19) $i(all_237_6) % 142.15/19.48 | (20) $i(all_237_5) % 142.15/19.48 | (21) $i(all_237_3) % 142.15/19.48 | (22) apply(all_237_6, all_237_7) = all_237_4 % 142.15/19.48 | (23) apply(all_237_3, all_237_4) = all_237_0 % 142.15/19.48 | (24) apply(all_237_2, all_237_7) = all_237_1 % 142.15/19.48 | (25) relation_dom(all_237_6) = all_237_5 % 142.15/19.48 | (26) relation_composition(all_237_6, all_237_3) = all_237_2 % 142.15/19.48 | % 142.26/19.49 | GROUND_INST: instantiating (t22_funct_1) with all_237_7, all_237_3, all_237_6, % 142.26/19.49 | all_237_4, all_237_0, simplifying with (14), (15), (16), (17), % 142.26/19.49 | (18), (19), (21), (22), (23) gives: % 142.26/19.49 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : % 142.26/19.49 | (relation_composition(all_237_6, all_237_3) = v0 & $i(v0) & ((v2 = % 142.26/19.49 | all_237_0 & apply(v0, all_237_7) = all_237_0 & $i(all_237_0)) | % 142.26/19.49 | (relation_dom(v0) = v1 & $i(v1) & ~ in(all_237_7, v1)))) % 142.26/19.49 | % 142.26/19.49 | GROUND_INST: instantiating (4) with all_237_6, all_237_5, all_237_7, % 142.26/19.49 | simplifying with (13), (16), (18), (19), (20), (25) gives: % 142.26/19.49 | (28) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_237_7, v0) = v1 & $i(v1) % 142.26/19.49 | & $i(v0) & in(v1, all_237_6)) % 142.26/19.49 | % 142.26/19.49 | GROUND_INST: instantiating (6) with all_237_6, all_237_3, all_237_2, % 142.26/19.49 | simplifying with (14), (15), (16), (17), (19), (21), (26) gives: % 142.26/19.49 | (29) function(all_237_2) % 142.26/19.49 | % 142.26/19.49 | GROUND_INST: instantiating (dt_k5_relat_1) with all_237_6, all_237_3, % 142.26/19.49 | all_237_2, simplifying with (16), (17), (19), (21), (26) gives: % 142.26/19.49 | (30) relation(all_237_2) % 142.26/19.49 | % 142.26/19.49 | GROUND_INST: instantiating (t45_relat_1) with all_237_6, all_237_3, all_237_2, % 142.26/19.49 | simplifying with (16), (17), (19), (21), (26) gives: % 142.26/19.49 | (31) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_237_2) = v0 & % 142.26/19.49 | relation_rng(all_237_3) = v1 & $i(v1) & $i(v0) & subset(v0, v1)) % 142.26/19.49 | % 142.26/19.49 | GROUND_INST: instantiating (t44_relat_1) with all_237_6, all_237_5, all_237_3, % 142.26/19.49 | all_237_2, simplifying with (16), (17), (19), (21), (25), (26) % 142.26/19.49 | gives: % 142.26/19.49 | (32) ? [v0: $i] : (relation_dom(all_237_2) = v0 & $i(v0) & subset(v0, % 142.26/19.49 | all_237_5)) % 142.26/19.49 | % 142.26/19.49 | DELTA: instantiating (32) with fresh symbol all_256_0 gives: % 142.26/19.49 | (33) relation_dom(all_237_2) = all_256_0 & $i(all_256_0) & % 142.26/19.49 | subset(all_256_0, all_237_5) % 142.26/19.49 | % 142.26/19.49 | ALPHA: (33) implies: % 142.26/19.49 | (34) relation_dom(all_237_2) = all_256_0 % 142.26/19.49 | % 142.26/19.49 | DELTA: instantiating (28) with fresh symbols all_258_0, all_258_1 gives: % 142.26/19.49 | (35) ordered_pair(all_237_7, all_258_1) = all_258_0 & $i(all_258_0) & % 142.26/19.49 | $i(all_258_1) & in(all_258_0, all_237_6) % 142.26/19.49 | % 142.26/19.49 | ALPHA: (35) implies: % 142.26/19.49 | (36) in(all_258_0, all_237_6) % 142.26/19.49 | (37) $i(all_258_1) % 142.26/19.49 | (38) $i(all_258_0) % 142.26/19.49 | (39) ordered_pair(all_237_7, all_258_1) = all_258_0 % 142.26/19.49 | % 142.26/19.49 | DELTA: instantiating (31) with fresh symbols all_260_0, all_260_1 gives: % 142.26/19.49 | (40) relation_rng(all_237_2) = all_260_1 & relation_rng(all_237_3) = % 142.26/19.49 | all_260_0 & $i(all_260_0) & $i(all_260_1) & subset(all_260_1, % 142.26/19.49 | all_260_0) % 142.26/19.49 | % 142.26/19.49 | ALPHA: (40) implies: % 142.26/19.49 | (41) relation_rng(all_237_3) = all_260_0 % 142.26/19.49 | (42) relation_rng(all_237_2) = all_260_1 % 142.26/19.49 | % 142.26/19.49 | DELTA: instantiating (27) with fresh symbols all_262_0, all_262_1, all_262_2 % 142.26/19.49 | gives: % 142.26/19.49 | (43) relation_composition(all_237_6, all_237_3) = all_262_2 & $i(all_262_2) % 142.26/19.49 | & ((all_262_0 = all_237_0 & apply(all_262_2, all_237_7) = all_237_0 & % 142.26/19.49 | $i(all_237_0)) | (relation_dom(all_262_2) = all_262_1 & % 142.26/19.49 | $i(all_262_1) & ~ in(all_237_7, all_262_1))) % 142.26/19.49 | % 142.26/19.49 | ALPHA: (43) implies: % 142.26/19.49 | (44) $i(all_262_2) % 142.26/19.49 | (45) relation_composition(all_237_6, all_237_3) = all_262_2 % 142.26/19.49 | (46) (all_262_0 = all_237_0 & apply(all_262_2, all_237_7) = all_237_0 & % 142.26/19.49 | $i(all_237_0)) | (relation_dom(all_262_2) = all_262_1 & % 142.26/19.49 | $i(all_262_1) & ~ in(all_237_7, all_262_1)) % 142.26/19.49 | % 142.26/19.50 | GROUND_INST: instantiating (10) with all_237_2, all_262_2, all_237_3, % 142.26/19.50 | all_237_6, simplifying with (26), (45) gives: % 142.26/19.50 | (47) all_262_2 = all_237_2 % 142.26/19.50 | % 142.26/19.50 | REDUCE: (44), (47) imply: % 142.26/19.50 | (48) $i(all_237_2) % 142.26/19.50 | % 142.26/19.50 | BETA: splitting (46) gives: % 142.26/19.50 | % 142.26/19.50 | Case 1: % 142.26/19.50 | | % 142.26/19.50 | | (49) all_262_0 = all_237_0 & apply(all_262_2, all_237_7) = all_237_0 & % 142.26/19.50 | | $i(all_237_0) % 142.26/19.50 | | % 142.26/19.50 | | ALPHA: (49) implies: % 142.26/19.50 | | (50) apply(all_262_2, all_237_7) = all_237_0 % 142.26/19.50 | | % 142.26/19.50 | | REDUCE: (47), (50) imply: % 142.26/19.50 | | (51) apply(all_237_2, all_237_7) = all_237_0 % 142.26/19.50 | | % 142.26/19.50 | | GROUND_INST: instantiating (9) with all_237_1, all_237_0, all_237_7, % 142.26/19.50 | | all_237_2, simplifying with (24), (51) gives: % 142.26/19.50 | | (52) all_237_0 = all_237_1 % 142.26/19.50 | | % 142.26/19.50 | | REDUCE: (12), (52) imply: % 142.26/19.50 | | (53) $false % 142.26/19.50 | | % 142.26/19.50 | | CLOSE: (53) is inconsistent. % 142.26/19.50 | | % 142.26/19.50 | Case 2: % 142.26/19.50 | | % 142.26/19.50 | | (54) relation_dom(all_262_2) = all_262_1 & $i(all_262_1) & ~ % 142.26/19.50 | | in(all_237_7, all_262_1) % 142.26/19.50 | | % 142.26/19.50 | | ALPHA: (54) implies: % 142.26/19.50 | | (55) ~ in(all_237_7, all_262_1) % 142.26/19.50 | | (56) relation_dom(all_262_2) = all_262_1 % 142.26/19.50 | | % 142.26/19.50 | | REDUCE: (47), (56) imply: % 142.26/19.50 | | (57) relation_dom(all_237_2) = all_262_1 % 142.26/19.50 | | % 142.26/19.50 | | GROUND_INST: instantiating (8) with all_256_0, all_262_1, all_237_2, % 142.26/19.50 | | simplifying with (34), (57) gives: % 142.26/19.50 | | (58) all_262_1 = all_256_0 % 142.26/19.50 | | % 142.26/19.50 | | REDUCE: (55), (58) imply: % 142.26/19.50 | | (59) ~ in(all_237_7, all_256_0) % 142.26/19.50 | | % 142.26/19.50 | | GROUND_INST: instantiating (1) with all_237_6, all_258_0, simplifying with % 142.26/19.50 | | (16), (19), (36), (38) gives: % 142.26/19.50 | | (60) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_258_0 & % 142.26/19.50 | | $i(v1) & $i(v0)) % 142.26/19.50 | | % 142.26/19.50 | | GROUND_INST: instantiating (2) with all_237_2, all_237_2, simplifying with % 142.26/19.50 | | (30), (48) gives: % 142.26/19.50 | | (61) subset(all_237_2, all_237_2) % 142.26/19.50 | | % 142.26/19.50 | | GROUND_INST: instantiating (t8_funct_1) with all_237_7, all_258_1, % 142.26/19.50 | | all_237_6, all_258_0, all_237_4, simplifying with (14), (16), % 142.26/19.50 | | (18), (19), (22), (37), (39) gives: % 142.26/19.50 | | (62) ? [v0: $i] : (( ~ (all_258_1 = all_237_4) | in(all_258_0, % 142.26/19.50 | | all_237_6) | (relation_dom(all_237_6) = v0 & $i(v0) & ~ % 142.26/19.50 | | in(all_237_7, v0))) & ( ~ in(all_258_0, all_237_6) | % 142.26/19.50 | | (all_258_1 = all_237_4 & relation_dom(all_237_6) = v0 & $i(v0) & % 142.26/19.50 | | in(all_237_7, v0)))) % 142.26/19.50 | | % 142.26/19.50 | | GROUND_INST: instantiating (3) with all_237_2, all_256_0, all_237_7, % 142.26/19.50 | | all_237_1, simplifying with (18), (24), (29), (30), (34), (48), % 142.26/19.50 | | (59) gives: % 142.26/19.50 | | (63) all_237_1 = empty_set % 142.26/19.50 | | % 142.26/19.50 | | GROUND_INST: instantiating (t46_relat_1) with all_237_3, all_260_0, % 142.26/19.50 | | simplifying with (17), (21), (41) gives: % 142.26/19.51 | | (64) ? [v0: $i] : (relation_dom(all_237_3) = v0 & $i(v0) & ! [v1: $i] : % 142.26/19.51 | | ! [v2: $i] : ( ~ (relation_composition(all_237_3, v1) = v2) | ~ % 142.26/19.51 | | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : ((v4 = v0 % 142.26/19.51 | | & relation_dom(v2) = v0) | (relation_dom(v1) = v3 & $i(v3) & % 142.26/19.51 | | ~ subset(all_260_0, v3))))) % 142.26/19.51 | | % 142.26/19.51 | | GROUND_INST: instantiating (t25_relat_1) with all_237_2, all_260_1, % 142.26/19.51 | | simplifying with (30), (42), (48) gives: % 142.26/19.51 | | (65) ? [v0: $i] : (relation_dom(all_237_2) = v0 & $i(v0) & ! [v1: $i] : % 142.26/19.51 | | ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~ % 142.26/19.51 | | subset(all_237_2, v1) | ~ relation(v1) | subset(all_260_1, v2)) % 142.26/19.51 | | & ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ % 142.26/19.51 | | $i(v1) | ~ subset(all_237_2, v1) | ~ relation(v1) | ? [v3: % 142.26/19.51 | | $i] : (relation_dom(v1) = v3 & $i(v3) & subset(v0, v3)))) % 142.26/19.51 | | % 142.26/19.51 | | DELTA: instantiating (60) with fresh symbols all_293_0, all_293_1 gives: % 142.26/19.51 | | (66) ordered_pair(all_293_1, all_293_0) = all_258_0 & $i(all_293_0) & % 142.26/19.51 | | $i(all_293_1) % 142.26/19.51 | | % 142.26/19.51 | | ALPHA: (66) implies: % 142.26/19.51 | | (67) $i(all_293_1) % 142.26/19.51 | | (68) $i(all_293_0) % 142.26/19.51 | | (69) ordered_pair(all_293_1, all_293_0) = all_258_0 % 142.26/19.51 | | % 142.26/19.51 | | DELTA: instantiating (62) with fresh symbol all_301_0 gives: % 142.26/19.51 | | (70) ( ~ (all_258_1 = all_237_4) | in(all_258_0, all_237_6) | % 142.26/19.51 | | (relation_dom(all_237_6) = all_301_0 & $i(all_301_0) & ~ % 142.26/19.51 | | in(all_237_7, all_301_0))) & ( ~ in(all_258_0, all_237_6) | % 142.26/19.51 | | (all_258_1 = all_237_4 & relation_dom(all_237_6) = all_301_0 & % 142.26/19.51 | | $i(all_301_0) & in(all_237_7, all_301_0))) % 142.26/19.51 | | % 142.26/19.51 | | ALPHA: (70) implies: % 142.26/19.51 | | (71) ~ in(all_258_0, all_237_6) | (all_258_1 = all_237_4 & % 142.26/19.51 | | relation_dom(all_237_6) = all_301_0 & $i(all_301_0) & % 142.26/19.51 | | in(all_237_7, all_301_0)) % 142.26/19.51 | | % 142.26/19.51 | | DELTA: instantiating (64) with fresh symbol all_302_0 gives: % 142.26/19.51 | | (72) relation_dom(all_237_3) = all_302_0 & $i(all_302_0) & ! [v0: $i] : % 142.26/19.51 | | ! [v1: $i] : ( ~ (relation_composition(all_237_3, v0) = v1) | ~ % 142.26/19.51 | | $i(v0) | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = % 142.26/19.51 | | all_302_0 & relation_dom(v1) = all_302_0) | (relation_dom(v0) % 142.26/19.51 | | = v2 & $i(v2) & ~ subset(all_260_0, v2)))) % 142.26/19.51 | | % 142.26/19.51 | | ALPHA: (72) implies: % 142.26/19.51 | | (73) relation_dom(all_237_3) = all_302_0 % 142.26/19.51 | | % 142.26/19.51 | | DELTA: instantiating (65) with fresh symbol all_316_0 gives: % 142.26/19.51 | | (74) relation_dom(all_237_2) = all_316_0 & $i(all_316_0) & ! [v0: $i] : % 142.26/19.51 | | ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 142.26/19.51 | | subset(all_237_2, v0) | ~ relation(v0) | subset(all_260_1, v1)) & % 142.26/19.51 | | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) % 142.26/19.51 | | | ~ subset(all_237_2, v0) | ~ relation(v0) | ? [v2: $i] : % 142.26/19.51 | | (relation_dom(v0) = v2 & $i(v2) & subset(all_316_0, v2))) % 142.26/19.51 | | % 142.26/19.51 | | ALPHA: (74) implies: % 142.26/19.51 | | (75) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) % 142.26/19.51 | | | ~ subset(all_237_2, v0) | ~ relation(v0) | ? [v2: $i] : % 142.26/19.51 | | (relation_dom(v0) = v2 & $i(v2) & subset(all_316_0, v2))) % 142.26/19.51 | | % 142.26/19.51 | | REDUCE: (12), (63) imply: % 142.26/19.51 | | (76) ~ (all_237_0 = empty_set) % 142.26/19.51 | | % 142.26/19.51 | | BETA: splitting (71) gives: % 142.26/19.51 | | % 142.26/19.51 | | Case 1: % 142.26/19.51 | | | % 142.26/19.51 | | | (77) ~ in(all_258_0, all_237_6) % 142.26/19.51 | | | % 142.26/19.51 | | | PRED_UNIFY: (36), (77) imply: % 142.26/19.51 | | | (78) $false % 142.26/19.51 | | | % 142.26/19.51 | | | CLOSE: (78) is inconsistent. % 142.26/19.51 | | | % 142.26/19.51 | | Case 2: % 142.26/19.51 | | | % 142.26/19.51 | | | (79) all_258_1 = all_237_4 & relation_dom(all_237_6) = all_301_0 & % 142.26/19.51 | | | $i(all_301_0) & in(all_237_7, all_301_0) % 142.26/19.51 | | | % 142.26/19.51 | | | ALPHA: (79) implies: % 142.26/19.51 | | | (80) all_258_1 = all_237_4 % 142.26/19.51 | | | % 142.26/19.51 | | | REDUCE: (39), (80) imply: % 142.26/19.51 | | | (81) ordered_pair(all_237_7, all_237_4) = all_258_0 % 142.26/19.51 | | | % 142.26/19.51 | | | REDUCE: (37), (80) imply: % 142.26/19.51 | | | (82) $i(all_237_4) % 142.26/19.51 | | | % 142.26/19.52 | | | GROUND_INST: instantiating (75) with all_237_2, all_260_1, simplifying % 142.26/19.52 | | | with (30), (42), (48), (61) gives: % 142.26/19.52 | | | (83) ? [v0: $i] : (relation_dom(all_237_2) = v0 & $i(v0) & % 142.26/19.52 | | | subset(all_316_0, v0)) % 142.26/19.52 | | | % 142.26/19.52 | | | GROUND_INST: instantiating (7) with all_237_7, all_237_4, all_293_1, % 142.26/19.52 | | | all_293_0, all_258_0, simplifying with (18), (67), (68), % 142.26/19.52 | | | (69), (81), (82) gives: % 142.26/19.52 | | | (84) all_293_1 = all_237_7 % 142.26/19.52 | | | % 142.26/19.52 | | | GROUND_INST: instantiating (5) with all_237_6, all_237_5, all_293_1, % 142.26/19.52 | | | all_293_0, all_258_0, simplifying with (16), (19), (20), % 142.26/19.52 | | | (25), (36), (67), (68), (69) gives: % 142.26/19.52 | | | (85) in(all_293_1, all_237_5) % 142.26/19.52 | | | % 142.26/19.52 | | | GROUND_INST: instantiating (3) with all_237_3, all_302_0, all_237_4, % 142.26/19.52 | | | all_237_0, simplifying with (15), (17), (21), (23), (73), % 142.26/19.52 | | | (82) gives: % 142.26/19.52 | | | (86) all_237_0 = empty_set | in(all_237_4, all_302_0) % 142.26/19.52 | | | % 142.26/19.52 | | | GROUND_INST: instantiating (t21_funct_1) with all_237_7, all_237_3, % 142.26/19.52 | | | all_302_0, all_237_6, all_237_4, simplifying with (14), (15), % 142.26/19.52 | | | (16), (17), (18), (19), (21), (22), (73) gives: % 142.44/19.52 | | | (87) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (( ~ in(all_237_4, % 142.44/19.52 | | | all_302_0) | (relation_composition(all_237_6, all_237_3) = % 142.44/19.52 | | | v0 & relation_dom(v0) = v1 & $i(v1) & $i(v0) & in(all_237_7, % 142.44/19.52 | | | v1)) | (relation_dom(all_237_6) = v2 & $i(v2) & ~ % 142.44/19.52 | | | in(all_237_7, v2))) & ((relation_composition(all_237_6, % 142.44/19.52 | | | all_237_3) = v0 & relation_dom(v0) = v1 & $i(v1) & $i(v0) % 142.44/19.52 | | | & ~ in(all_237_7, v1)) | (relation_dom(all_237_6) = v2 & % 142.44/19.52 | | | $i(v2) & in(all_237_4, all_302_0) & in(all_237_7, v2)))) % 142.44/19.52 | | | % 142.44/19.52 | | | DELTA: instantiating (83) with fresh symbol all_386_0 gives: % 142.44/19.52 | | | (88) relation_dom(all_237_2) = all_386_0 & $i(all_386_0) & % 142.44/19.52 | | | subset(all_316_0, all_386_0) % 142.44/19.52 | | | % 142.44/19.52 | | | ALPHA: (88) implies: % 142.44/19.52 | | | (89) relation_dom(all_237_2) = all_386_0 % 142.44/19.52 | | | % 142.44/19.52 | | | DELTA: instantiating (87) with fresh symbols all_410_0, all_410_1, % 142.44/19.52 | | | all_410_2 gives: % 142.44/19.52 | | | (90) ( ~ in(all_237_4, all_302_0) | (relation_composition(all_237_6, % 142.44/19.52 | | | all_237_3) = all_410_2 & relation_dom(all_410_2) = all_410_1 % 142.44/19.52 | | | & $i(all_410_1) & $i(all_410_2) & in(all_237_7, all_410_1)) | % 142.44/19.52 | | | (relation_dom(all_237_6) = all_410_0 & $i(all_410_0) & ~ % 142.44/19.52 | | | in(all_237_7, all_410_0))) & ((relation_composition(all_237_6, % 142.44/19.52 | | | all_237_3) = all_410_2 & relation_dom(all_410_2) = all_410_1 % 142.44/19.52 | | | & $i(all_410_1) & $i(all_410_2) & ~ in(all_237_7, all_410_1)) % 142.44/19.52 | | | | (relation_dom(all_237_6) = all_410_0 & $i(all_410_0) & % 142.44/19.52 | | | in(all_237_4, all_302_0) & in(all_237_7, all_410_0))) % 142.44/19.52 | | | % 142.44/19.52 | | | ALPHA: (90) implies: % 142.44/19.52 | | | (91) ~ in(all_237_4, all_302_0) | (relation_composition(all_237_6, % 142.44/19.52 | | | all_237_3) = all_410_2 & relation_dom(all_410_2) = all_410_1 & % 142.44/19.52 | | | $i(all_410_1) & $i(all_410_2) & in(all_237_7, all_410_1)) | % 142.44/19.52 | | | (relation_dom(all_237_6) = all_410_0 & $i(all_410_0) & ~ % 142.44/19.52 | | | in(all_237_7, all_410_0)) % 142.44/19.52 | | | % 142.44/19.52 | | | BETA: splitting (86) gives: % 142.44/19.52 | | | % 142.44/19.52 | | | Case 1: % 142.44/19.52 | | | | % 142.44/19.52 | | | | (92) in(all_237_4, all_302_0) % 142.44/19.52 | | | | % 142.44/19.52 | | | | BETA: splitting (91) gives: % 142.44/19.52 | | | | % 142.44/19.52 | | | | Case 1: % 142.44/19.52 | | | | | % 142.44/19.52 | | | | | (93) ~ in(all_237_4, all_302_0) % 142.44/19.53 | | | | | % 142.44/19.53 | | | | | PRED_UNIFY: (92), (93) imply: % 142.44/19.53 | | | | | (94) $false % 142.44/19.53 | | | | | % 142.44/19.53 | | | | | CLOSE: (94) is inconsistent. % 142.44/19.53 | | | | | % 142.44/19.53 | | | | Case 2: % 142.44/19.53 | | | | | % 142.44/19.53 | | | | | (95) (relation_composition(all_237_6, all_237_3) = all_410_2 & % 142.44/19.53 | | | | | relation_dom(all_410_2) = all_410_1 & $i(all_410_1) & % 142.44/19.53 | | | | | $i(all_410_2) & in(all_237_7, all_410_1)) | % 142.44/19.53 | | | | | (relation_dom(all_237_6) = all_410_0 & $i(all_410_0) & ~ % 142.44/19.53 | | | | | in(all_237_7, all_410_0)) % 142.44/19.53 | | | | | % 142.44/19.53 | | | | | BETA: splitting (95) gives: % 142.44/19.53 | | | | | % 142.44/19.53 | | | | | Case 1: % 142.44/19.53 | | | | | | % 142.44/19.53 | | | | | | (96) relation_composition(all_237_6, all_237_3) = all_410_2 & % 142.44/19.53 | | | | | | relation_dom(all_410_2) = all_410_1 & $i(all_410_1) & % 142.44/19.53 | | | | | | $i(all_410_2) & in(all_237_7, all_410_1) % 142.44/19.53 | | | | | | % 142.44/19.53 | | | | | | ALPHA: (96) implies: % 142.44/19.53 | | | | | | (97) in(all_237_7, all_410_1) % 142.44/19.53 | | | | | | (98) relation_dom(all_410_2) = all_410_1 % 142.44/19.53 | | | | | | (99) relation_composition(all_237_6, all_237_3) = all_410_2 % 142.44/19.53 | | | | | | % 142.44/19.53 | | | | | | GROUND_INST: instantiating (8) with all_256_0, all_386_0, all_237_2, % 142.44/19.53 | | | | | | simplifying with (34), (89) gives: % 142.44/19.53 | | | | | | (100) all_386_0 = all_256_0 % 142.44/19.53 | | | | | | % 142.44/19.53 | | | | | | GROUND_INST: instantiating (10) with all_237_2, all_410_2, % 142.44/19.53 | | | | | | all_237_3, all_237_6, simplifying with (26), (99) % 142.44/19.53 | | | | | | gives: % 142.44/19.53 | | | | | | (101) all_410_2 = all_237_2 % 142.44/19.53 | | | | | | % 142.44/19.53 | | | | | | REDUCE: (98), (101) imply: % 142.44/19.53 | | | | | | (102) relation_dom(all_237_2) = all_410_1 % 142.44/19.53 | | | | | | % 142.44/19.53 | | | | | | GROUND_INST: instantiating (8) with all_256_0, all_410_1, all_237_2, % 142.44/19.53 | | | | | | simplifying with (34), (102) gives: % 142.44/19.53 | | | | | | (103) all_410_1 = all_256_0 % 142.44/19.53 | | | | | | % 142.44/19.53 | | | | | | REDUCE: (97), (103) imply: % 142.44/19.53 | | | | | | (104) in(all_237_7, all_256_0) % 142.44/19.53 | | | | | | % 142.44/19.53 | | | | | | PRED_UNIFY: (59), (104) imply: % 142.44/19.53 | | | | | | (105) $false % 142.44/19.53 | | | | | | % 142.44/19.53 | | | | | | CLOSE: (105) is inconsistent. % 142.44/19.53 | | | | | | % 142.44/19.53 | | | | | Case 2: % 142.44/19.53 | | | | | | % 142.44/19.53 | | | | | | (106) relation_dom(all_237_6) = all_410_0 & $i(all_410_0) & ~ % 142.44/19.53 | | | | | | in(all_237_7, all_410_0) % 142.44/19.53 | | | | | | % 142.44/19.53 | | | | | | ALPHA: (106) implies: % 142.44/19.53 | | | | | | (107) ~ in(all_237_7, all_410_0) % 142.44/19.53 | | | | | | (108) relation_dom(all_237_6) = all_410_0 % 142.44/19.53 | | | | | | % 142.44/19.53 | | | | | | GROUND_INST: instantiating (8) with all_237_5, all_410_0, all_237_6, % 142.44/19.53 | | | | | | simplifying with (25), (108) gives: % 142.50/19.53 | | | | | | (109) all_410_0 = all_237_5 % 142.50/19.53 | | | | | | % 142.50/19.53 | | | | | | REDUCE: (107), (109) imply: % 142.50/19.53 | | | | | | (110) ~ in(all_237_7, all_237_5) % 142.50/19.53 | | | | | | % 142.50/19.53 | | | | | | PRED_UNIFY: (13), (110) imply: % 142.50/19.53 | | | | | | (111) $false % 142.50/19.53 | | | | | | % 142.50/19.53 | | | | | | CLOSE: (111) is inconsistent. % 142.50/19.53 | | | | | | % 142.50/19.53 | | | | | End of split % 142.50/19.53 | | | | | % 142.50/19.53 | | | | End of split % 142.50/19.53 | | | | % 142.50/19.53 | | | Case 2: % 142.50/19.53 | | | | % 142.50/19.53 | | | | (112) all_237_0 = empty_set % 142.50/19.53 | | | | % 142.50/19.53 | | | | REDUCE: (76), (112) imply: % 142.50/19.53 | | | | (113) $false % 142.50/19.53 | | | | % 142.50/19.53 | | | | CLOSE: (113) is inconsistent. % 142.50/19.53 | | | | % 142.50/19.53 | | | End of split % 142.50/19.53 | | | % 142.50/19.53 | | End of split % 142.50/19.53 | | % 142.50/19.53 | End of split % 142.50/19.53 | % 142.50/19.53 End of proof % 142.50/19.53 % SZS output end Proof for theBenchmark % 142.50/19.53 % 142.50/19.53 18922ms %------------------------------------------------------------------------------