%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM410+1 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n015.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 11:47:36 EDT 2023 % Result : Theorem 14.16s 2.70s % Output : Proof 24.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM410+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n015.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 09:48:06 EDT 2023 % 0.13/0.34 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.63 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 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 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 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 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 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 % 2.87/1.14 Prover 1: Preprocessing ... % 2.87/1.14 Prover 4: Preprocessing ... % 2.87/1.18 Prover 5: Preprocessing ... % 2.87/1.18 Prover 3: Preprocessing ... % 2.87/1.18 Prover 0: Preprocessing ... % 2.87/1.18 Prover 6: Preprocessing ... % 2.87/1.18 Prover 2: Preprocessing ... % 6.33/1.63 Prover 1: Warning: ignoring some quantifiers % 6.33/1.66 Prover 1: Constructing countermodel ... % 6.33/1.66 Prover 2: Proving ... % 6.33/1.67 Prover 5: Proving ... % 7.00/1.74 Prover 3: Warning: ignoring some quantifiers % 7.00/1.74 Prover 4: Warning: ignoring some quantifiers % 7.00/1.75 Prover 3: Constructing countermodel ... % 7.00/1.76 Prover 6: Proving ... % 7.64/1.79 Prover 4: Constructing countermodel ... % 8.42/1.90 Prover 0: Proving ... % 10.62/2.27 Prover 3: gave up % 10.62/2.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.21/2.35 Prover 7: Preprocessing ... % 12.22/2.41 Prover 7: Warning: ignoring some quantifiers % 12.22/2.42 Prover 7: Constructing countermodel ... % 12.43/2.51 Prover 1: gave up % 12.43/2.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.10/2.56 Prover 8: Preprocessing ... % 14.16/2.70 Prover 0: proved (2075ms) % 14.16/2.70 % 14.16/2.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.16/2.70 % 14.16/2.71 Prover 6: stopped % 14.16/2.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.16/2.71 Prover 5: stopped % 14.45/2.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.45/2.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.45/2.73 Prover 2: stopped % 14.65/2.74 Prover 8: Warning: ignoring some quantifiers % 14.65/2.74 Prover 8: Constructing countermodel ... % 14.65/2.75 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 14.65/2.75 Prover 13: Preprocessing ... % 14.65/2.77 Prover 11: Preprocessing ... % 14.65/2.78 Prover 10: Preprocessing ... % 14.65/2.82 Prover 16: Preprocessing ... % 14.65/2.83 Prover 13: Warning: ignoring some quantifiers % 14.65/2.83 Prover 13: Constructing countermodel ... % 14.65/2.86 Prover 10: Warning: ignoring some quantifiers % 14.65/2.87 Prover 10: Constructing countermodel ... % 14.65/2.91 Prover 16: Warning: ignoring some quantifiers % 14.65/2.92 Prover 16: Constructing countermodel ... % 15.84/3.00 Prover 10: gave up % 16.70/3.03 Prover 11: Warning: ignoring some quantifiers % 16.70/3.03 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 16.70/3.04 Prover 11: Constructing countermodel ... % 16.70/3.05 Prover 7: gave up % 16.70/3.07 Prover 19: Preprocessing ... % 16.70/3.07 Prover 8: gave up % 17.80/3.18 Prover 19: Warning: ignoring some quantifiers % 17.80/3.19 Prover 19: Constructing countermodel ... % 18.97/3.34 Prover 13: gave up % 19.51/3.46 Prover 19: gave up % 23.57/4.07 Prover 4: Found proof (size 134) % 23.57/4.07 Prover 4: proved (3435ms) % 23.57/4.07 Prover 16: stopped % 23.57/4.07 Prover 11: stopped % 23.57/4.07 % 23.57/4.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 23.57/4.07 % 23.57/4.10 % SZS output start Proof for theBenchmark % 23.57/4.10 Assumptions after simplification: % 23.57/4.10 --------------------------------- % 23.57/4.10 % 23.57/4.10 (cc2_funct_1) % 24.09/4.13 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2: % 24.09/4.13 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) = % 24.09/4.13 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) % 24.09/4.13 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 24.09/4.13 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0) % 24.09/4.13 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ % 24.09/4.13 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] % 24.09/4.13 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) | % 24.09/4.13 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) % 24.09/4.13 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & % 24.09/4.13 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = % 24.09/4.13 0))) % 24.09/4.13 % 24.09/4.13 (d7_ordinal1) % 24.09/4.14 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 24.09/4.14 any] : ? [v3: any] : ? [v4: any] : ? [v5: any] : % 24.09/4.14 (transfinite_sequence(v0) = v4 & relation(v0) = v2 & ordinal(v1) = v5 & % 24.09/4.14 function(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | (( ~ (v5 = 0) | v4 = 0) & % 24.09/4.14 ( ~ (v4 = 0) | v5 = 0))))) & ! [v0: $i] : ! [v1: any] : ( ~ % 24.09/4.14 (transfinite_sequence(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 24.09/4.14 ? [v4: $i] : ? [v5: any] : (relation_dom(v0) = v4 & relation(v0) = v2 & % 24.09/4.14 ordinal(v4) = v5 & function(v0) = v3 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) % 24.09/4.14 | (( ~ (v5 = 0) | v1 = 0) & ( ~ (v1 = 0) | v5 = 0))))) & ! [v0: $i] : ( % 24.09/4.14 ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: $i] % 24.09/4.14 : ? [v4: any] : (relation_dom(v0) = v3 & transfinite_sequence(v0) = v2 & % 24.09/4.14 ordinal(v3) = v4 & function(v0) = v1 & $i(v3) & ( ~ (v1 = 0) | (( ~ (v4 = % 24.09/4.14 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ! [v0: $i] : ( ~ % 24.09/4.14 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: $i] : % 24.09/4.14 ? [v4: any] : (relation_dom(v0) = v3 & transfinite_sequence(v0) = v2 & % 24.09/4.14 relation(v0) = v1 & ordinal(v3) = v4 & $i(v3) & ( ~ (v1 = 0) | (( ~ (v4 = % 24.09/4.14 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) % 24.09/4.14 % 24.09/4.14 (d8_ordinal1) % 24.09/4.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (relation_rng(v1) % 24.09/4.14 = v2) | ~ (subset(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : % 24.09/4.14 ? [v5: any] : ? [v6: any] : ? [v7: any] : (transfinite_sequence_of(v1, v0) % 24.09/4.14 = v7 & transfinite_sequence(v1) = v6 & relation(v1) = v4 & function(v1) = % 24.09/4.14 v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | (( ~ (v7 = 0) | v3 = 0) & % 24.09/4.14 ( ~ (v3 = 0) | v7 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] % 24.09/4.14 : ( ~ (transfinite_sequence_of(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 24.09/4.14 any] : ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: any] : % 24.09/4.14 (relation_rng(v1) = v6 & subset(v6, v0) = v7 & transfinite_sequence(v1) = v5 % 24.09/4.14 & relation(v1) = v3 & function(v1) = v4 & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = % 24.09/4.14 0) | ~ (v3 = 0) | (( ~ (v7 = 0) | v2 = 0) & ( ~ (v2 = 0) | v7 = % 24.09/4.14 0))))) % 24.09/4.14 % 24.09/4.14 (fc5_relat_1) % 24.09/4.14 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 24.09/4.14 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3 & % 24.09/4.14 relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = % 24.09/4.14 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ % 24.09/4.14 $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & % 24.09/4.14 empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & % 24.09/4.14 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] % 24.09/4.14 : ? [v3: any] : (relation_dom(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & % 24.09/4.14 $i(v2) & ( ~ (v3 = 0) | v1 = 0))) % 24.09/4.14 % 24.09/4.14 (fc6_funct_1) % 24.09/4.15 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 24.09/4.15 any] : ? [v3: any] : ? [v4: any] : ? [v5: any] : % 24.09/4.15 (relation_non_empty(v0) = v3 & with_non_empty_elements(v1) = v5 & % 24.09/4.15 relation(v0) = v2 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ % 24.09/4.15 (v2 = 0) | v5 = 0))) & ! [v0: $i] : ( ~ (relation_non_empty(v0) = 0) | % 24.09/4.15 ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 24.09/4.15 (with_non_empty_elements(v3) = v4 & relation_rng(v0) = v3 & relation(v0) = % 24.09/4.15 v1 & function(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = 0))) & % 24.09/4.15 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] % 24.09/4.15 : ? [v3: $i] : ? [v4: any] : (relation_non_empty(v0) = v1 & % 24.09/4.15 with_non_empty_elements(v3) = v4 & relation_rng(v0) = v3 & function(v0) = % 24.09/4.15 v2 & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = 0))) & ! [v0: $i] : ( ~ % 24.09/4.15 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: $i] : % 24.09/4.15 ? [v4: any] : (relation_non_empty(v0) = v2 & with_non_empty_elements(v3) = % 24.09/4.15 v4 & relation_rng(v0) = v3 & relation(v0) = v1 & $i(v3) & ( ~ (v2 = 0) | % 24.09/4.15 ~ (v1 = 0) | v4 = 0))) % 24.09/4.15 % 24.09/4.15 (fc6_relat_1) % 24.09/4.15 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 24.09/4.15 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_rng(v0) = v3 & % 24.09/4.15 relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = % 24.09/4.15 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ % 24.09/4.15 $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & % 24.09/4.15 empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & % 24.09/4.15 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] % 24.09/4.15 : ? [v3: any] : (relation_rng(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & % 24.09/4.15 $i(v2) & ( ~ (v3 = 0) | v1 = 0))) % 24.09/4.15 % 24.09/4.15 (reflexivity_r1_tarski) % 24.09/4.15 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0)) % 24.09/4.15 % 24.09/4.15 (t46_ordinal1) % 24.09/4.15 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 24.09/4.15 relation_rng(v0) = v2 & transfinite_sequence_of(v0, v2) = v3 & % 24.09/4.15 relation_dom(v0) = v1 & relation(v0) = 0 & ordinal(v1) = 0 & function(v0) = % 24.09/4.15 0 & $i(v2) & $i(v1) & $i(v0)) % 24.09/4.15 % 24.09/4.15 (function-axioms) % 24.09/4.16 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 24.09/4.16 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 24.09/4.16 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 24.09/4.16 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 24.09/4.16 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 24.09/4.16 $i] : (v1 = v0 | ~ (transfinite_sequence_of(v3, v2) = v1) | ~ % 24.09/4.16 (transfinite_sequence_of(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 24.09/4.16 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, % 24.09/4.16 v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 24.09/4.16 $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: % 24.09/4.16 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 24.09/4.16 ~ (relation_non_empty(v2) = v1) | ~ (relation_non_empty(v2) = v0)) & ! % 24.09/4.16 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 24.09/4.16 | ~ (with_non_empty_elements(v2) = v1) | ~ (with_non_empty_elements(v2) = % 24.09/4.16 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 24.09/4.16 $i] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ % 24.09/4.16 (relation_empty_yielding(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 24.09/4.16 $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & % 24.09/4.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) % 24.09/4.16 | ~ (relation_dom(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 24.09/4.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (transfinite_sequence(v2) = % 24.09/4.16 v1) | ~ (transfinite_sequence(v2) = v0)) & ! [v0: MultipleValueBool] : % 24.09/4.16 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) % 24.09/4.16 | ~ (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 24.09/4.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 24.09/4.16 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 24.09/4.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_transitive(v2) = % 24.09/4.16 v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 24.09/4.16 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ % 24.09/4.16 (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 24.09/4.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_connected(v2) = % 24.09/4.16 v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 24.09/4.16 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~ % 24.09/4.16 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 24.09/4.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 24.09/4.16 (empty(v2) = v0)) % 24.09/4.16 % 24.09/4.16 Further assumptions not needed in the proof: % 24.09/4.16 -------------------------------------------- % 24.09/4.16 antisymmetry_r2_hidden, cc1_funct_1, cc1_ordinal1, cc1_relat_1, cc2_ordinal1, % 24.09/4.16 cc3_ordinal1, dt_m1_ordinal1, existence_m1_ordinal1, existence_m1_subset_1, % 24.09/4.16 fc12_relat_1, fc1_xboole_0, fc2_ordinal1, fc4_relat_1, fc7_relat_1, fc8_relat_1, % 24.09/4.16 rc1_funct_1, rc1_ordinal1, rc1_relat_1, rc1_xboole_0, rc2_funct_1, rc2_ordinal1, % 24.09/4.16 rc2_relat_1, rc2_xboole_0, rc3_funct_1, rc3_ordinal1, rc3_relat_1, rc4_funct_1, % 24.09/4.16 rc4_ordinal1, rc5_funct_1, t1_subset, t2_subset, t3_subset, t4_subset, % 24.09/4.16 t5_subset, t6_boole, t7_boole, t8_boole % 24.09/4.16 % 24.09/4.16 Those formulas are unsatisfiable: % 24.09/4.16 --------------------------------- % 24.09/4.16 % 24.09/4.16 Begin of proof % 24.09/4.16 | % 24.09/4.16 | ALPHA: (cc2_funct_1) implies: % 24.09/4.16 | (1) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 24.09/4.16 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & % 24.09/4.16 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 24.09/4.16 | % 24.09/4.16 | ALPHA: (d7_ordinal1) implies: % 24.09/4.16 | (2) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 24.09/4.16 | [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3 & % 24.09/4.16 | transfinite_sequence(v0) = v2 & relation(v0) = v1 & ordinal(v3) = % 24.09/4.16 | v4 & $i(v3) & ( ~ (v1 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) % 24.09/4.16 | | v4 = 0))))) % 24.09/4.16 | (3) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 24.09/4.16 | [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3 & % 24.09/4.16 | transfinite_sequence(v0) = v2 & ordinal(v3) = v4 & function(v0) = % 24.09/4.16 | v1 & $i(v3) & ( ~ (v1 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) % 24.09/4.16 | | v4 = 0))))) % 24.09/4.16 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 24.09/4.16 | ? [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5: any] : % 24.09/4.16 | (transfinite_sequence(v0) = v4 & relation(v0) = v2 & ordinal(v1) = v5 % 24.09/4.16 | & function(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | (( ~ (v5 = 0) | % 24.09/4.16 | v4 = 0) & ( ~ (v4 = 0) | v5 = 0))))) % 24.09/4.16 | % 24.09/4.16 | ALPHA: (d8_ordinal1) implies: % 24.09/4.17 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 24.09/4.17 | (transfinite_sequence_of(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 24.09/4.17 | [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: any] % 24.09/4.17 | : (relation_rng(v1) = v6 & subset(v6, v0) = v7 & % 24.09/4.17 | transfinite_sequence(v1) = v5 & relation(v1) = v3 & function(v1) = % 24.09/4.17 | v4 & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v7 = % 24.09/4.17 | 0) | v2 = 0) & ( ~ (v2 = 0) | v7 = 0))))) % 24.09/4.17 | % 24.09/4.17 | ALPHA: (fc5_relat_1) implies: % 24.09/4.17 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 24.09/4.17 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & % 24.09/4.17 | empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = % 24.09/4.17 | 0))) % 24.09/4.17 | % 24.09/4.17 | ALPHA: (fc6_funct_1) implies: % 24.09/4.17 | (7) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 24.09/4.17 | [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_non_empty(v0) = v2 % 24.09/4.17 | & with_non_empty_elements(v3) = v4 & relation_rng(v0) = v3 & % 24.09/4.17 | relation(v0) = v1 & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = 0))) % 24.09/4.17 | (8) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 24.09/4.17 | [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_non_empty(v0) = v1 % 24.09/4.17 | & with_non_empty_elements(v3) = v4 & relation_rng(v0) = v3 & % 24.09/4.17 | function(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = 0))) % 24.09/4.17 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 24.09/4.17 | ? [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5: any] : % 24.09/4.17 | (relation_non_empty(v0) = v3 & with_non_empty_elements(v1) = v5 & % 24.09/4.17 | relation(v0) = v2 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) % 24.09/4.17 | | ~ (v2 = 0) | v5 = 0))) % 24.09/4.17 | % 24.09/4.17 | ALPHA: (fc6_relat_1) implies: % 24.09/4.17 | (10) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 24.09/4.17 | [v2: $i] : ? [v3: any] : (relation_rng(v0) = v2 & empty(v2) = v3 & % 24.09/4.17 | empty(v0) = v1 & $i(v2) & ( ~ (v3 = 0) | v1 = 0))) % 24.09/4.17 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 24.09/4.17 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & % 24.09/4.17 | empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 % 24.09/4.17 | = 0))) % 24.09/4.17 | % 24.09/4.17 | ALPHA: (function-axioms) implies: % 24.09/4.17 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 24.09/4.17 | : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 24.09/4.17 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 24.09/4.17 | : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) % 24.09/4.17 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 24.09/4.17 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 24.09/4.18 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 24.09/4.18 | : (v1 = v0 | ~ (transfinite_sequence(v2) = v1) | ~ % 24.09/4.18 | (transfinite_sequence(v2) = v0)) % 24.09/4.18 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 24.09/4.18 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 24.09/4.18 | % 24.09/4.18 | DELTA: instantiating (t46_ordinal1) with fresh symbols all_58_0, all_58_1, % 24.09/4.18 | all_58_2, all_58_3 gives: % 24.09/4.18 | (17) ~ (all_58_0 = 0) & relation_rng(all_58_3) = all_58_1 & % 24.09/4.18 | transfinite_sequence_of(all_58_3, all_58_1) = all_58_0 & % 24.09/4.18 | relation_dom(all_58_3) = all_58_2 & relation(all_58_3) = 0 & % 24.09/4.18 | ordinal(all_58_2) = 0 & function(all_58_3) = 0 & $i(all_58_1) & % 24.09/4.18 | $i(all_58_2) & $i(all_58_3) % 24.09/4.18 | % 24.09/4.18 | ALPHA: (17) implies: % 24.09/4.18 | (18) ~ (all_58_0 = 0) % 24.09/4.18 | (19) $i(all_58_3) % 24.09/4.18 | (20) $i(all_58_1) % 24.09/4.18 | (21) function(all_58_3) = 0 % 24.09/4.18 | (22) ordinal(all_58_2) = 0 % 24.09/4.18 | (23) relation(all_58_3) = 0 % 24.09/4.18 | (24) relation_dom(all_58_3) = all_58_2 % 24.09/4.18 | (25) transfinite_sequence_of(all_58_3, all_58_1) = all_58_0 % 24.09/4.18 | (26) relation_rng(all_58_3) = all_58_1 % 24.09/4.18 | % 24.09/4.18 | GROUND_INST: instantiating (7) with all_58_3, simplifying with (19), (21) % 24.09/4.18 | gives: % 24.09/4.18 | (27) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 24.09/4.18 | (relation_non_empty(all_58_3) = v1 & with_non_empty_elements(v2) = v3 % 24.09/4.18 | & relation_rng(all_58_3) = v2 & relation(all_58_3) = v0 & $i(v2) & ( % 24.09/4.18 | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 24.09/4.18 | % 24.09/4.18 | GROUND_INST: instantiating (2) with all_58_3, simplifying with (19), (21) % 24.09/4.18 | gives: % 24.09/4.18 | (28) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 24.09/4.18 | (relation_dom(all_58_3) = v2 & transfinite_sequence(all_58_3) = v1 & % 24.09/4.18 | relation(all_58_3) = v0 & ordinal(v2) = v3 & $i(v2) & ( ~ (v0 = 0) | % 24.09/4.18 | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))) % 24.09/4.18 | % 24.09/4.18 | GROUND_INST: instantiating (8) with all_58_3, simplifying with (19), (23) % 24.09/4.18 | gives: % 24.09/4.18 | (29) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 24.09/4.18 | (relation_non_empty(all_58_3) = v0 & with_non_empty_elements(v2) = v3 % 24.09/4.18 | & relation_rng(all_58_3) = v2 & function(all_58_3) = v1 & $i(v2) & ( % 24.09/4.18 | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 24.09/4.18 | % 24.09/4.18 | GROUND_INST: instantiating (3) with all_58_3, simplifying with (19), (23) % 24.09/4.18 | gives: % 24.09/4.18 | (30) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 24.09/4.18 | (relation_dom(all_58_3) = v2 & transfinite_sequence(all_58_3) = v1 & % 24.09/4.18 | ordinal(v2) = v3 & function(all_58_3) = v0 & $i(v2) & ( ~ (v0 = 0) | % 24.09/4.18 | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))) % 24.09/4.18 | % 24.09/4.19 | GROUND_INST: instantiating (10) with all_58_3, simplifying with (19), (23) % 24.09/4.19 | gives: % 24.09/4.19 | (31) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_rng(all_58_3) = % 24.09/4.19 | v1 & empty(v1) = v2 & empty(all_58_3) = v0 & $i(v1) & ( ~ (v2 = 0) | % 24.09/4.19 | v0 = 0)) % 24.09/4.19 | % 24.09/4.19 | GROUND_INST: instantiating (1) with all_58_3, simplifying with (19), (23) % 24.09/4.19 | gives: % 24.09/4.19 | (32) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_58_3) = % 24.09/4.19 | v2 & function(all_58_3) = v1 & empty(all_58_3) = v0 & ( ~ (v1 = 0) | % 24.09/4.19 | ~ (v0 = 0) | v2 = 0)) % 24.09/4.19 | % 24.09/4.19 | GROUND_INST: instantiating (4) with all_58_3, all_58_2, simplifying with (19), % 24.09/4.19 | (24) gives: % 24.09/4.19 | (33) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 24.09/4.19 | (transfinite_sequence(all_58_3) = v2 & relation(all_58_3) = v0 & % 24.09/4.19 | ordinal(all_58_2) = v3 & function(all_58_3) = v1 & ( ~ (v1 = 0) | ~ % 24.09/4.19 | (v0 = 0) | (( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0)))) % 24.09/4.19 | % 24.09/4.19 | GROUND_INST: instantiating (6) with all_58_3, all_58_2, simplifying with (19), % 24.09/4.19 | (24) gives: % 24.09/4.19 | (34) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_58_3) = v1 % 24.09/4.19 | & empty(all_58_2) = v2 & empty(all_58_3) = v0 & ( ~ (v2 = 0) | ~ % 24.09/4.19 | (v1 = 0) | v0 = 0)) % 24.09/4.19 | % 24.09/4.19 | GROUND_INST: instantiating (5) with all_58_1, all_58_3, all_58_0, simplifying % 24.09/4.19 | with (19), (20), (25) gives: % 24.09/4.19 | (35) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: % 24.09/4.19 | any] : (relation_rng(all_58_3) = v3 & subset(v3, all_58_1) = v4 & % 24.09/4.19 | transfinite_sequence(all_58_3) = v2 & relation(all_58_3) = v0 & % 24.09/4.19 | function(all_58_3) = v1 & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 24.09/4.19 | (v0 = 0) | (( ~ (v4 = 0) | all_58_0 = 0) & ( ~ (all_58_0 = 0) | v4 % 24.09/4.19 | = 0)))) % 24.09/4.19 | % 24.09/4.19 | GROUND_INST: instantiating (9) with all_58_3, all_58_1, simplifying with (19), % 24.09/4.19 | (26) gives: % 24.09/4.19 | (36) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 24.09/4.19 | (relation_non_empty(all_58_3) = v1 & with_non_empty_elements(all_58_1) % 24.09/4.19 | = v3 & relation(all_58_3) = v0 & function(all_58_3) = v2 & ( ~ (v2 = % 24.09/4.19 | 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 24.09/4.19 | % 24.09/4.19 | GROUND_INST: instantiating (11) with all_58_3, all_58_1, simplifying with % 24.09/4.19 | (19), (26) gives: % 24.09/4.19 | (37) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_58_3) = v1 % 24.09/4.19 | & empty(all_58_1) = v2 & empty(all_58_3) = v0 & ( ~ (v2 = 0) | ~ % 24.09/4.19 | (v1 = 0) | v0 = 0)) % 24.09/4.19 | % 24.09/4.19 | DELTA: instantiating (32) with fresh symbols all_88_0, all_88_1, all_88_2 % 24.09/4.19 | gives: % 24.09/4.19 | (38) one_to_one(all_58_3) = all_88_0 & function(all_58_3) = all_88_1 & % 24.09/4.19 | empty(all_58_3) = all_88_2 & ( ~ (all_88_1 = 0) | ~ (all_88_2 = 0) | % 24.09/4.19 | all_88_0 = 0) % 24.09/4.19 | % 24.09/4.19 | ALPHA: (38) implies: % 24.09/4.19 | (39) function(all_58_3) = all_88_1 % 24.09/4.19 | % 24.09/4.19 | DELTA: instantiating (31) with fresh symbols all_134_0, all_134_1, all_134_2 % 24.09/4.19 | gives: % 24.09/4.19 | (40) relation_rng(all_58_3) = all_134_1 & empty(all_134_1) = all_134_0 & % 24.09/4.19 | empty(all_58_3) = all_134_2 & $i(all_134_1) & ( ~ (all_134_0 = 0) | % 24.09/4.19 | all_134_2 = 0) % 24.09/4.19 | % 24.09/4.19 | ALPHA: (40) implies: % 24.09/4.19 | (41) $i(all_134_1) % 24.09/4.19 | (42) relation_rng(all_58_3) = all_134_1 % 24.09/4.19 | % 24.09/4.19 | DELTA: instantiating (37) with fresh symbols all_142_0, all_142_1, all_142_2 % 24.09/4.19 | gives: % 24.09/4.19 | (43) relation(all_58_3) = all_142_1 & empty(all_58_1) = all_142_0 & % 24.09/4.19 | empty(all_58_3) = all_142_2 & ( ~ (all_142_0 = 0) | ~ (all_142_1 = 0) % 24.09/4.19 | | all_142_2 = 0) % 24.09/4.19 | % 24.09/4.19 | ALPHA: (43) implies: % 24.09/4.19 | (44) relation(all_58_3) = all_142_1 % 24.09/4.19 | % 24.09/4.19 | DELTA: instantiating (34) with fresh symbols all_184_0, all_184_1, all_184_2 % 24.09/4.19 | gives: % 24.09/4.20 | (45) relation(all_58_3) = all_184_1 & empty(all_58_2) = all_184_0 & % 24.09/4.20 | empty(all_58_3) = all_184_2 & ( ~ (all_184_0 = 0) | ~ (all_184_1 = 0) % 24.09/4.20 | | all_184_2 = 0) % 24.09/4.20 | % 24.09/4.20 | ALPHA: (45) implies: % 24.09/4.20 | (46) relation(all_58_3) = all_184_1 % 24.09/4.20 | % 24.09/4.20 | DELTA: instantiating (36) with fresh symbols all_220_0, all_220_1, all_220_2, % 24.09/4.20 | all_220_3 gives: % 24.09/4.20 | (47) relation_non_empty(all_58_3) = all_220_2 & % 24.09/4.20 | with_non_empty_elements(all_58_1) = all_220_0 & relation(all_58_3) = % 24.09/4.20 | all_220_3 & function(all_58_3) = all_220_1 & ( ~ (all_220_1 = 0) | ~ % 24.09/4.20 | (all_220_2 = 0) | ~ (all_220_3 = 0) | all_220_0 = 0) % 24.09/4.20 | % 24.09/4.20 | ALPHA: (47) implies: % 24.09/4.20 | (48) function(all_58_3) = all_220_1 % 24.09/4.20 | (49) relation(all_58_3) = all_220_3 % 24.09/4.20 | % 24.09/4.20 | DELTA: instantiating (27) with fresh symbols all_224_0, all_224_1, all_224_2, % 24.09/4.20 | all_224_3 gives: % 24.45/4.20 | (50) relation_non_empty(all_58_3) = all_224_2 & % 24.45/4.20 | with_non_empty_elements(all_224_1) = all_224_0 & % 24.45/4.20 | relation_rng(all_58_3) = all_224_1 & relation(all_58_3) = all_224_3 & % 24.45/4.20 | $i(all_224_1) & ( ~ (all_224_2 = 0) | ~ (all_224_3 = 0) | all_224_0 = % 24.45/4.20 | 0) % 24.45/4.20 | % 24.45/4.20 | ALPHA: (50) implies: % 24.45/4.20 | (51) relation(all_58_3) = all_224_3 % 24.45/4.20 | (52) relation_rng(all_58_3) = all_224_1 % 24.45/4.20 | % 24.45/4.20 | DELTA: instantiating (29) with fresh symbols all_226_0, all_226_1, all_226_2, % 24.45/4.20 | all_226_3 gives: % 24.45/4.20 | (53) relation_non_empty(all_58_3) = all_226_3 & % 24.45/4.20 | with_non_empty_elements(all_226_1) = all_226_0 & % 24.45/4.20 | relation_rng(all_58_3) = all_226_1 & function(all_58_3) = all_226_2 & % 24.45/4.20 | $i(all_226_1) & ( ~ (all_226_2 = 0) | ~ (all_226_3 = 0) | all_226_0 = % 24.45/4.20 | 0) % 24.45/4.20 | % 24.45/4.20 | ALPHA: (53) implies: % 24.45/4.20 | (54) function(all_58_3) = all_226_2 % 24.45/4.20 | (55) relation_rng(all_58_3) = all_226_1 % 24.45/4.20 | % 24.45/4.20 | DELTA: instantiating (30) with fresh symbols all_254_0, all_254_1, all_254_2, % 24.45/4.20 | all_254_3 gives: % 24.45/4.20 | (56) relation_dom(all_58_3) = all_254_1 & transfinite_sequence(all_58_3) = % 24.45/4.20 | all_254_2 & ordinal(all_254_1) = all_254_0 & function(all_58_3) = % 24.45/4.20 | all_254_3 & $i(all_254_1) & ( ~ (all_254_3 = 0) | (( ~ (all_254_0 = 0) % 24.45/4.20 | | all_254_2 = 0) & ( ~ (all_254_2 = 0) | all_254_0 = 0))) % 24.45/4.20 | % 24.45/4.20 | ALPHA: (56) implies: % 24.45/4.20 | (57) function(all_58_3) = all_254_3 % 24.45/4.20 | (58) transfinite_sequence(all_58_3) = all_254_2 % 24.45/4.20 | % 24.45/4.20 | DELTA: instantiating (33) with fresh symbols all_256_0, all_256_1, all_256_2, % 24.45/4.20 | all_256_3 gives: % 24.45/4.20 | (59) transfinite_sequence(all_58_3) = all_256_1 & relation(all_58_3) = % 24.45/4.20 | all_256_3 & ordinal(all_58_2) = all_256_0 & function(all_58_3) = % 24.45/4.20 | all_256_2 & ( ~ (all_256_2 = 0) | ~ (all_256_3 = 0) | (( ~ (all_256_0 % 24.45/4.20 | = 0) | all_256_1 = 0) & ( ~ (all_256_1 = 0) | all_256_0 = 0))) % 24.45/4.20 | % 24.45/4.20 | ALPHA: (59) implies: % 24.45/4.20 | (60) function(all_58_3) = all_256_2 % 24.45/4.20 | (61) ordinal(all_58_2) = all_256_0 % 24.45/4.20 | (62) relation(all_58_3) = all_256_3 % 24.45/4.20 | (63) transfinite_sequence(all_58_3) = all_256_1 % 24.45/4.20 | (64) ~ (all_256_2 = 0) | ~ (all_256_3 = 0) | (( ~ (all_256_0 = 0) | % 24.45/4.20 | all_256_1 = 0) & ( ~ (all_256_1 = 0) | all_256_0 = 0)) % 24.45/4.20 | % 24.45/4.20 | DELTA: instantiating (28) with fresh symbols all_258_0, all_258_1, all_258_2, % 24.45/4.20 | all_258_3 gives: % 24.45/4.20 | (65) relation_dom(all_58_3) = all_258_1 & transfinite_sequence(all_58_3) = % 24.45/4.20 | all_258_2 & relation(all_58_3) = all_258_3 & ordinal(all_258_1) = % 24.45/4.20 | all_258_0 & $i(all_258_1) & ( ~ (all_258_3 = 0) | (( ~ (all_258_0 = 0) % 24.45/4.20 | | all_258_2 = 0) & ( ~ (all_258_2 = 0) | all_258_0 = 0))) % 24.45/4.20 | % 24.45/4.20 | ALPHA: (65) implies: % 24.45/4.20 | (66) relation(all_58_3) = all_258_3 % 24.45/4.20 | (67) transfinite_sequence(all_58_3) = all_258_2 % 24.45/4.20 | % 24.45/4.20 | DELTA: instantiating (35) with fresh symbols all_284_0, all_284_1, all_284_2, % 24.45/4.20 | all_284_3, all_284_4 gives: % 24.45/4.20 | (68) relation_rng(all_58_3) = all_284_1 & subset(all_284_1, all_58_1) = % 24.45/4.20 | all_284_0 & transfinite_sequence(all_58_3) = all_284_2 & % 24.45/4.20 | relation(all_58_3) = all_284_4 & function(all_58_3) = all_284_3 & % 24.45/4.20 | $i(all_284_1) & ( ~ (all_284_2 = 0) | ~ (all_284_3 = 0) | ~ % 24.45/4.20 | (all_284_4 = 0) | (( ~ (all_284_0 = 0) | all_58_0 = 0) & ( ~ % 24.45/4.20 | (all_58_0 = 0) | all_284_0 = 0))) % 24.45/4.20 | % 24.45/4.20 | ALPHA: (68) implies: % 24.45/4.20 | (69) function(all_58_3) = all_284_3 % 24.45/4.20 | (70) relation(all_58_3) = all_284_4 % 24.45/4.20 | (71) transfinite_sequence(all_58_3) = all_284_2 % 24.45/4.20 | (72) subset(all_284_1, all_58_1) = all_284_0 % 24.45/4.20 | (73) relation_rng(all_58_3) = all_284_1 % 24.45/4.20 | (74) ~ (all_284_2 = 0) | ~ (all_284_3 = 0) | ~ (all_284_4 = 0) | (( ~ % 24.45/4.20 | (all_284_0 = 0) | all_58_0 = 0) & ( ~ (all_58_0 = 0) | all_284_0 = % 24.45/4.20 | 0)) % 24.45/4.20 | % 24.45/4.20 | GROUND_INST: instantiating (12) with 0, all_220_1, all_58_3, simplifying with % 24.45/4.20 | (21), (48) gives: % 24.45/4.20 | (75) all_220_1 = 0 % 24.45/4.20 | % 24.45/4.20 | GROUND_INST: instantiating (12) with all_220_1, all_226_2, all_58_3, % 24.45/4.20 | simplifying with (48), (54) gives: % 24.45/4.20 | (76) all_226_2 = all_220_1 % 24.45/4.20 | % 24.45/4.20 | GROUND_INST: instantiating (12) with all_226_2, all_254_3, all_58_3, % 24.45/4.20 | simplifying with (54), (57) gives: % 24.45/4.20 | (77) all_254_3 = all_226_2 % 24.45/4.20 | % 24.45/4.21 | GROUND_INST: instantiating (12) with all_254_3, all_256_2, all_58_3, % 24.45/4.21 | simplifying with (57), (60) gives: % 24.45/4.21 | (78) all_256_2 = all_254_3 % 24.45/4.21 | % 24.45/4.21 | GROUND_INST: instantiating (12) with all_256_2, all_284_3, all_58_3, % 24.45/4.21 | simplifying with (60), (69) gives: % 24.45/4.21 | (79) all_284_3 = all_256_2 % 24.45/4.21 | % 24.45/4.21 | GROUND_INST: instantiating (12) with all_88_1, all_284_3, all_58_3, % 24.45/4.21 | simplifying with (39), (69) gives: % 24.45/4.21 | (80) all_284_3 = all_88_1 % 24.45/4.21 | % 24.45/4.21 | GROUND_INST: instantiating (13) with 0, all_256_0, all_58_2, simplifying with % 24.45/4.21 | (22), (61) gives: % 24.45/4.21 | (81) all_256_0 = 0 % 24.45/4.21 | % 24.45/4.21 | GROUND_INST: instantiating (14) with all_224_3, all_256_3, all_58_3, % 24.45/4.21 | simplifying with (51), (62) gives: % 24.45/4.21 | (82) all_256_3 = all_224_3 % 24.45/4.21 | % 24.45/4.21 | GROUND_INST: instantiating (14) with all_142_1, all_256_3, all_58_3, % 24.45/4.21 | simplifying with (44), (62) gives: % 24.45/4.21 | (83) all_256_3 = all_142_1 % 24.45/4.21 | % 24.45/4.21 | GROUND_INST: instantiating (14) with all_256_3, all_258_3, all_58_3, % 24.45/4.21 | simplifying with (62), (66) gives: % 24.45/4.21 | (84) all_258_3 = all_256_3 % 24.45/4.21 | % 24.45/4.21 | GROUND_INST: instantiating (14) with all_220_3, all_258_3, all_58_3, % 24.45/4.21 | simplifying with (49), (66) gives: % 24.45/4.21 | (85) all_258_3 = all_220_3 % 24.45/4.21 | % 24.45/4.21 | GROUND_INST: instantiating (14) with all_184_1, all_258_3, all_58_3, % 24.45/4.21 | simplifying with (46), (66) gives: % 24.45/4.21 | (86) all_258_3 = all_184_1 % 24.45/4.21 | % 24.45/4.21 | GROUND_INST: instantiating (14) with 0, all_284_4, all_58_3, simplifying with % 24.45/4.21 | (23), (70) gives: % 24.45/4.21 | (87) all_284_4 = 0 % 24.45/4.21 | % 24.45/4.21 | GROUND_INST: instantiating (14) with all_184_1, all_284_4, all_58_3, % 24.45/4.21 | simplifying with (46), (70) gives: % 24.45/4.21 | (88) all_284_4 = all_184_1 % 24.45/4.21 | % 24.45/4.21 | GROUND_INST: instantiating (15) with all_258_2, all_284_2, all_58_3, % 24.45/4.21 | simplifying with (67), (71) gives: % 24.45/4.21 | (89) all_284_2 = all_258_2 % 24.45/4.21 | % 24.45/4.21 | GROUND_INST: instantiating (15) with all_256_1, all_284_2, all_58_3, % 24.45/4.21 | simplifying with (63), (71) gives: % 24.45/4.21 | (90) all_284_2 = all_256_1 % 24.45/4.21 | % 24.45/4.21 | GROUND_INST: instantiating (15) with all_254_2, all_284_2, all_58_3, % 24.45/4.21 | simplifying with (58), (71) gives: % 24.45/4.21 | (91) all_284_2 = all_254_2 % 24.45/4.21 | % 24.45/4.21 | GROUND_INST: instantiating (16) with all_134_1, all_224_1, all_58_3, % 24.45/4.21 | simplifying with (42), (52) gives: % 24.45/4.21 | (92) all_224_1 = all_134_1 % 24.45/4.21 | % 24.45/4.21 | GROUND_INST: instantiating (16) with all_224_1, all_226_1, all_58_3, % 24.45/4.21 | simplifying with (52), (55) gives: % 24.45/4.21 | (93) all_226_1 = all_224_1 % 24.45/4.21 | % 24.45/4.21 | GROUND_INST: instantiating (16) with all_58_1, all_284_1, all_58_3, % 24.45/4.21 | simplifying with (26), (73) gives: % 24.45/4.21 | (94) all_284_1 = all_58_1 % 24.45/4.21 | % 24.45/4.21 | GROUND_INST: instantiating (16) with all_226_1, all_284_1, all_58_3, % 24.45/4.21 | simplifying with (55), (73) gives: % 24.45/4.21 | (95) all_284_1 = all_226_1 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (94), (95) imply: % 24.45/4.21 | (96) all_226_1 = all_58_1 % 24.45/4.21 | % 24.45/4.21 | SIMP: (96) implies: % 24.45/4.21 | (97) all_226_1 = all_58_1 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (89), (91) imply: % 24.45/4.21 | (98) all_258_2 = all_254_2 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (89), (90) imply: % 24.45/4.21 | (99) all_258_2 = all_256_1 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (79), (80) imply: % 24.45/4.21 | (100) all_256_2 = all_88_1 % 24.45/4.21 | % 24.45/4.21 | SIMP: (100) implies: % 24.45/4.21 | (101) all_256_2 = all_88_1 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (87), (88) imply: % 24.45/4.21 | (102) all_184_1 = 0 % 24.45/4.21 | % 24.45/4.21 | SIMP: (102) implies: % 24.45/4.21 | (103) all_184_1 = 0 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (98), (99) imply: % 24.45/4.21 | (104) all_256_1 = all_254_2 % 24.45/4.21 | % 24.45/4.21 | SIMP: (104) implies: % 24.45/4.21 | (105) all_256_1 = all_254_2 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (85), (86) imply: % 24.45/4.21 | (106) all_220_3 = all_184_1 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (84), (85) imply: % 24.45/4.21 | (107) all_256_3 = all_220_3 % 24.45/4.21 | % 24.45/4.21 | SIMP: (107) implies: % 24.45/4.21 | (108) all_256_3 = all_220_3 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (78), (101) imply: % 24.45/4.21 | (109) all_254_3 = all_88_1 % 24.45/4.21 | % 24.45/4.21 | SIMP: (109) implies: % 24.45/4.21 | (110) all_254_3 = all_88_1 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (82), (83) imply: % 24.45/4.21 | (111) all_224_3 = all_142_1 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (82), (108) imply: % 24.45/4.21 | (112) all_224_3 = all_220_3 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (77), (110) imply: % 24.45/4.21 | (113) all_226_2 = all_88_1 % 24.45/4.21 | % 24.45/4.21 | SIMP: (113) implies: % 24.45/4.21 | (114) all_226_2 = all_88_1 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (93), (97) imply: % 24.45/4.21 | (115) all_224_1 = all_58_1 % 24.45/4.21 | % 24.45/4.21 | SIMP: (115) implies: % 24.45/4.21 | (116) all_224_1 = all_58_1 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (76), (114) imply: % 24.45/4.21 | (117) all_220_1 = all_88_1 % 24.45/4.21 | % 24.45/4.21 | SIMP: (117) implies: % 24.45/4.21 | (118) all_220_1 = all_88_1 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (92), (116) imply: % 24.45/4.21 | (119) all_134_1 = all_58_1 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (111), (112) imply: % 24.45/4.21 | (120) all_220_3 = all_142_1 % 24.45/4.21 | % 24.45/4.21 | SIMP: (120) implies: % 24.45/4.21 | (121) all_220_3 = all_142_1 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (75), (118) imply: % 24.45/4.21 | (122) all_88_1 = 0 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (106), (121) imply: % 24.45/4.21 | (123) all_184_1 = all_142_1 % 24.45/4.21 | % 24.45/4.21 | SIMP: (123) implies: % 24.45/4.21 | (124) all_184_1 = all_142_1 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (103), (124) imply: % 24.45/4.21 | (125) all_142_1 = 0 % 24.45/4.21 | % 24.45/4.21 | SIMP: (125) implies: % 24.45/4.21 | (126) all_142_1 = 0 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (111), (126) imply: % 24.45/4.21 | (127) all_224_3 = 0 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (82), (127) imply: % 24.45/4.21 | (128) all_256_3 = 0 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (101), (122) imply: % 24.45/4.21 | (129) all_256_2 = 0 % 24.45/4.21 | % 24.45/4.21 | COMBINE_EQS: (80), (122) imply: % 24.45/4.21 | (130) all_284_3 = 0 % 24.45/4.21 | % 24.45/4.21 | REDUCE: (72), (94) imply: % 24.45/4.22 | (131) subset(all_58_1, all_58_1) = all_284_0 % 24.45/4.22 | % 24.45/4.22 | BETA: splitting (64) gives: % 24.45/4.22 | % 24.45/4.22 | Case 1: % 24.45/4.22 | | % 24.45/4.22 | | (132) ~ (all_256_2 = 0) % 24.45/4.22 | | % 24.45/4.22 | | REDUCE: (129), (132) imply: % 24.45/4.22 | | (133) $false % 24.45/4.22 | | % 24.45/4.22 | | CLOSE: (133) is inconsistent. % 24.45/4.22 | | % 24.45/4.22 | Case 2: % 24.45/4.22 | | % 24.45/4.22 | | (134) ~ (all_256_3 = 0) | (( ~ (all_256_0 = 0) | all_256_1 = 0) & ( ~ % 24.45/4.22 | | (all_256_1 = 0) | all_256_0 = 0)) % 24.45/4.22 | | % 24.45/4.22 | | BETA: splitting (134) gives: % 24.45/4.22 | | % 24.45/4.22 | | Case 1: % 24.45/4.22 | | | % 24.45/4.22 | | | (135) ~ (all_256_3 = 0) % 24.45/4.22 | | | % 24.45/4.22 | | | REDUCE: (128), (135) imply: % 24.45/4.22 | | | (136) $false % 24.45/4.22 | | | % 24.45/4.22 | | | CLOSE: (136) is inconsistent. % 24.45/4.22 | | | % 24.45/4.22 | | Case 2: % 24.45/4.22 | | | % 24.45/4.22 | | | (137) ( ~ (all_256_0 = 0) | all_256_1 = 0) & ( ~ (all_256_1 = 0) | % 24.45/4.22 | | | all_256_0 = 0) % 24.45/4.22 | | | % 24.45/4.22 | | | ALPHA: (137) implies: % 24.45/4.22 | | | (138) ~ (all_256_0 = 0) | all_256_1 = 0 % 24.45/4.22 | | | % 24.45/4.22 | | | BETA: splitting (138) gives: % 24.45/4.22 | | | % 24.45/4.22 | | | Case 1: % 24.45/4.22 | | | | % 24.45/4.22 | | | | (139) ~ (all_256_0 = 0) % 24.45/4.22 | | | | % 24.45/4.22 | | | | REDUCE: (81), (139) imply: % 24.45/4.22 | | | | (140) $false % 24.45/4.22 | | | | % 24.45/4.22 | | | | CLOSE: (140) is inconsistent. % 24.45/4.22 | | | | % 24.45/4.22 | | | Case 2: % 24.45/4.22 | | | | % 24.45/4.22 | | | | (141) all_256_1 = 0 % 24.45/4.22 | | | | % 24.45/4.22 | | | | COMBINE_EQS: (105), (141) imply: % 24.45/4.22 | | | | (142) all_254_2 = 0 % 24.45/4.22 | | | | % 24.45/4.22 | | | | COMBINE_EQS: (91), (142) imply: % 24.45/4.22 | | | | (143) all_284_2 = 0 % 24.45/4.22 | | | | % 24.45/4.22 | | | | BETA: splitting (74) gives: % 24.45/4.22 | | | | % 24.45/4.22 | | | | Case 1: % 24.45/4.22 | | | | | % 24.45/4.22 | | | | | (144) ~ (all_284_2 = 0) % 24.45/4.22 | | | | | % 24.45/4.22 | | | | | REDUCE: (143), (144) imply: % 24.45/4.22 | | | | | (145) $false % 24.45/4.22 | | | | | % 24.45/4.22 | | | | | CLOSE: (145) is inconsistent. % 24.45/4.22 | | | | | % 24.45/4.22 | | | | Case 2: % 24.45/4.22 | | | | | % 24.45/4.22 | | | | | (146) ~ (all_284_3 = 0) | ~ (all_284_4 = 0) | (( ~ (all_284_0 = % 24.45/4.22 | | | | | 0) | all_58_0 = 0) & ( ~ (all_58_0 = 0) | all_284_0 = % 24.45/4.22 | | | | | 0)) % 24.45/4.22 | | | | | % 24.45/4.22 | | | | | BETA: splitting (146) gives: % 24.45/4.22 | | | | | % 24.45/4.22 | | | | | Case 1: % 24.45/4.22 | | | | | | % 24.45/4.22 | | | | | | (147) ~ (all_284_3 = 0) % 24.45/4.22 | | | | | | % 24.45/4.22 | | | | | | REDUCE: (130), (147) imply: % 24.45/4.22 | | | | | | (148) $false % 24.45/4.22 | | | | | | % 24.45/4.22 | | | | | | CLOSE: (148) is inconsistent. % 24.45/4.22 | | | | | | % 24.45/4.22 | | | | | Case 2: % 24.45/4.22 | | | | | | % 24.45/4.22 | | | | | | (149) ~ (all_284_4 = 0) | (( ~ (all_284_0 = 0) | all_58_0 = 0) & % 24.45/4.22 | | | | | | ( ~ (all_58_0 = 0) | all_284_0 = 0)) % 24.45/4.22 | | | | | | % 24.45/4.22 | | | | | | BETA: splitting (149) gives: % 24.45/4.22 | | | | | | % 24.45/4.22 | | | | | | Case 1: % 24.45/4.22 | | | | | | | % 24.45/4.22 | | | | | | | (150) ~ (all_284_4 = 0) % 24.45/4.22 | | | | | | | % 24.45/4.22 | | | | | | | REDUCE: (87), (150) imply: % 24.45/4.22 | | | | | | | (151) $false % 24.45/4.22 | | | | | | | % 24.45/4.22 | | | | | | | CLOSE: (151) is inconsistent. % 24.45/4.22 | | | | | | | % 24.45/4.22 | | | | | | Case 2: % 24.45/4.22 | | | | | | | % 24.45/4.22 | | | | | | | (152) ( ~ (all_284_0 = 0) | all_58_0 = 0) & ( ~ (all_58_0 = 0) % 24.45/4.22 | | | | | | | | all_284_0 = 0) % 24.45/4.22 | | | | | | | % 24.45/4.22 | | | | | | | ALPHA: (152) implies: % 24.45/4.22 | | | | | | | (153) ~ (all_284_0 = 0) | all_58_0 = 0 % 24.45/4.22 | | | | | | | % 24.45/4.22 | | | | | | | BETA: splitting (153) gives: % 24.45/4.22 | | | | | | | % 24.45/4.22 | | | | | | | Case 1: % 24.45/4.22 | | | | | | | | % 24.45/4.22 | | | | | | | | (154) ~ (all_284_0 = 0) % 24.45/4.22 | | | | | | | | % 24.45/4.22 | | | | | | | | GROUND_INST: instantiating (reflexivity_r1_tarski) with % 24.45/4.22 | | | | | | | | all_58_1, all_284_0, simplifying with (20), (131) % 24.45/4.22 | | | | | | | | gives: % 24.45/4.22 | | | | | | | | (155) all_284_0 = 0 % 24.45/4.22 | | | | | | | | % 24.45/4.22 | | | | | | | | REDUCE: (154), (155) imply: % 24.45/4.22 | | | | | | | | (156) $false % 24.45/4.22 | | | | | | | | % 24.45/4.22 | | | | | | | | CLOSE: (156) is inconsistent. % 24.45/4.22 | | | | | | | | % 24.45/4.22 | | | | | | | Case 2: % 24.45/4.22 | | | | | | | | % 24.45/4.22 | | | | | | | | (157) all_58_0 = 0 % 24.45/4.22 | | | | | | | | % 24.45/4.22 | | | | | | | | REDUCE: (18), (157) imply: % 24.45/4.22 | | | | | | | | (158) $false % 24.45/4.22 | | | | | | | | % 24.45/4.22 | | | | | | | | CLOSE: (158) is inconsistent. % 24.45/4.22 | | | | | | | | % 24.45/4.22 | | | | | | | End of split % 24.45/4.22 | | | | | | | % 24.45/4.22 | | | | | | End of split % 24.45/4.22 | | | | | | % 24.45/4.22 | | | | | End of split % 24.45/4.22 | | | | | % 24.45/4.22 | | | | End of split % 24.45/4.22 | | | | % 24.45/4.22 | | | End of split % 24.45/4.22 | | | % 24.45/4.22 | | End of split % 24.45/4.22 | | % 24.45/4.22 | End of split % 24.45/4.22 | % 24.45/4.22 End of proof % 24.45/4.22 % SZS output end Proof for theBenchmark % 24.45/4.22 % 24.45/4.22 3611ms %------------------------------------------------------------------------------