%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU098+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 : n019.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 17:42:31 EDT 2023 % Result : Theorem 29.34s 4.72s % Output : Proof 29.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU098+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n019.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Wed Aug 23 13:17:44 EDT 2023 % 0.14/0.34 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.73/1.27 Prover 1: Preprocessing ... % 3.73/1.27 Prover 4: Preprocessing ... % 3.73/1.30 Prover 0: Preprocessing ... % 3.73/1.30 Prover 2: Preprocessing ... % 3.73/1.30 Prover 6: Preprocessing ... % 3.73/1.30 Prover 3: Preprocessing ... % 3.73/1.30 Prover 5: Preprocessing ... % 8.85/1.97 Prover 2: Proving ... % 8.85/1.99 Prover 1: Warning: ignoring some quantifiers % 9.19/2.00 Prover 5: Proving ... % 9.50/2.05 Prover 3: Warning: ignoring some quantifiers % 9.50/2.08 Prover 6: Proving ... % 9.50/2.09 Prover 1: Constructing countermodel ... % 9.50/2.09 Prover 3: Constructing countermodel ... % 9.50/2.10 Prover 4: Warning: ignoring some quantifiers % 10.20/2.14 Prover 4: Constructing countermodel ... % 10.20/2.19 Prover 0: Proving ... % 15.88/2.94 Prover 3: gave up % 15.88/2.95 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.88/3.04 Prover 7: Preprocessing ... % 18.17/3.22 Prover 7: Warning: ignoring some quantifiers % 18.29/3.26 Prover 7: Constructing countermodel ... % 29.34/4.71 Prover 7: Found proof (size 95) % 29.34/4.71 Prover 7: proved (1763ms) % 29.34/4.72 Prover 1: stopped % 29.34/4.72 Prover 5: stopped % 29.34/4.72 Prover 2: stopped % 29.34/4.72 Prover 0: stopped % 29.34/4.72 Prover 6: stopped % 29.34/4.72 Prover 4: stopped % 29.34/4.72 % 29.34/4.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 29.34/4.72 % 29.34/4.73 % SZS output start Proof for theBenchmark % 29.34/4.74 Assumptions after simplification: % 29.34/4.74 --------------------------------- % 29.34/4.74 % 29.34/4.74 (dt_k7_funct_3) % 29.34/4.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (first_projection(v0, v1) = v2) % 29.34/4.76 | ~ $i(v1) | ~ $i(v0) | relation(v2)) & ! [v0: $i] : ! [v1: $i] : ! % 29.34/4.76 [v2: $i] : ( ~ (first_projection(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 29.34/4.76 function(v2)) % 29.34/4.76 % 29.34/4.76 (dt_k9_funct_3) % 29.34/4.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (first_projection_as_func_of(v0, % 29.34/4.76 v1) = v2) | ~ $i(v1) | ~ $i(v0) | function(v2)) & ! [v0: $i] : ! % 29.34/4.76 [v1: $i] : ! [v2: $i] : ( ~ (first_projection_as_func_of(v0, v1) = v2) | ~ % 29.34/4.76 $i(v1) | ~ $i(v0) | ? [v3: $i] : (cartesian_product2(v0, v1) = v3 & $i(v3) % 29.34/4.76 & relation_of2_as_subset(v2, v3, v0))) & ! [v0: $i] : ! [v1: $i] : ! % 29.34/4.76 [v2: $i] : ( ~ (first_projection_as_func_of(v0, v1) = v2) | ~ $i(v1) | ~ % 29.34/4.76 $i(v0) | ? [v3: $i] : (cartesian_product2(v0, v1) = v3 & $i(v3) & % 29.34/4.76 quasi_total(v2, v3, v0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 29.34/4.76 (cartesian_product2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 29.34/4.76 (first_projection_as_func_of(v0, v1) = v3 & $i(v3) & % 29.34/4.76 relation_of2_as_subset(v3, v2, v0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 29.34/4.76 $i] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.34/4.76 [v3: $i] : (first_projection_as_func_of(v0, v1) = v3 & $i(v3) & % 29.34/4.76 quasi_total(v3, v2, v0))) % 29.34/4.76 % 29.34/4.77 (fc14_finset_1) % 29.34/4.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0, v1) = % 29.34/4.77 v2) | ~ $i(v1) | ~ $i(v0) | ~ finite(v1) | ~ finite(v0) | finite(v2)) % 29.34/4.77 % 29.34/4.77 (redefinition_k2_funct_2) % 29.34/4.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 29.34/4.77 (function_image(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 29.34/4.77 ~ $i(v0) | ~ relation_of2(v2, v0, v1) | ~ quasi_total(v2, v0, v1) | ~ % 29.34/4.77 function(v2) | (relation_image(v2, v3) = v4 & $i(v4))) % 29.34/4.77 % 29.34/4.77 (redefinition_k9_funct_3) % 29.34/4.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (first_projection_as_func_of(v0, % 29.34/4.77 v1) = v2) | ~ $i(v1) | ~ $i(v0) | (first_projection(v0, v1) = v2 & % 29.34/4.77 $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 29.34/4.77 (first_projection(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 29.34/4.77 (first_projection_as_func_of(v0, v1) = v2 & $i(v2))) % 29.34/4.77 % 29.34/4.77 (redefinition_m2_relset_1) % 29.34/4.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 29.34/4.77 ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(v2, v0, v1)) & ! [v0: % 29.34/4.77 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 29.34/4.77 relation_of2(v2, v0, v1) | relation_of2_as_subset(v2, v0, v1)) % 29.34/4.77 % 29.34/4.77 (t100_funct_3) % 29.34/4.77 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 29.34/4.77 relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 29.34/4.77 (relation_dom(v0) = v2 & first_projection_as_func_of(v2, v1) = v4 & % 29.34/4.77 function_image(v3, v2, v4, v0) = v2 & cartesian_product2(v2, v1) = v3 & % 29.34/4.77 $i(v4) & $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 29.34/4.77 (relation_dom(v0) = v1) | ~ $i(v0) | ~ relation(v0) | ~ function(v0) | ? % 29.34/4.77 [v2: $i] : ? [v3: $i] : ? [v4: $i] : (relation_rng(v0) = v2 & % 29.34/4.77 first_projection_as_func_of(v1, v2) = v4 & function_image(v3, v1, v4, v0) % 29.34/4.77 = v1 & cartesian_product2(v1, v2) = v3 & $i(v4) & $i(v3) & $i(v2) & % 29.34/4.77 $i(v1))) % 29.34/4.77 % 29.34/4.77 (t13_finset_1) % 29.34/4.77 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v1) | ~ % 29.34/4.77 finite(v1) | finite(v0)) % 29.34/4.77 % 29.34/4.77 (t17_finset_1) % 29.34/4.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_image(v1, v0) = v2) | % 29.34/4.77 ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ function(v1) | ~ finite(v0) | % 29.34/4.77 finite(v2)) % 29.34/4.77 % 29.34/4.77 (t19_finset_1) % 29.34/4.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0, v1) = % 29.34/4.77 v2) | ~ $i(v1) | ~ $i(v0) | ~ finite(v1) | ~ finite(v0) | finite(v2)) % 29.34/4.77 % 29.34/4.77 (t21_relat_1) % 29.34/4.77 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 29.34/4.77 relation(v0) | ? [v2: $i] : ? [v3: $i] : (relation_dom(v0) = v2 & % 29.34/4.77 cartesian_product2(v2, v1) = v3 & $i(v3) & $i(v2) & subset(v0, v3))) & ! % 29.34/4.77 [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~ % 29.34/4.77 relation(v0) | ? [v2: $i] : ? [v3: $i] : (relation_rng(v0) = v2 & % 29.34/4.77 cartesian_product2(v1, v2) = v3 & $i(v3) & $i(v2) & subset(v0, v3))) % 29.34/4.77 % 29.34/4.77 (t26_finset_1) % 29.34/4.78 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 29.34/4.78 relation(v0) | ~ function(v0) | finite(v1) | ? [v2: $i] : % 29.34/4.78 (relation_dom(v0) = v2 & $i(v2) & ~ finite(v2))) & ! [v0: $i] : ! [v1: % 29.34/4.78 $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~ relation(v0) | ~ % 29.34/4.78 function(v0) | ~ finite(v1) | ? [v2: $i] : (relation_rng(v0) = v2 & $i(v2) % 29.34/4.78 & finite(v2))) % 29.34/4.78 % 29.34/4.78 (t29_finset_1) % 29.34/4.78 ? [v0: $i] : ? [v1: $i] : (relation_dom(v0) = v1 & $i(v1) & $i(v0) & % 29.34/4.78 relation(v0) & function(v0) & ((finite(v1) & ~ finite(v0)) | (finite(v0) & % 29.34/4.78 ~ finite(v1)))) % 29.34/4.78 % 29.34/4.78 (function-axioms) % 29.34/4.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 29.34/4.78 $i] : (v1 = v0 | ~ (function_image(v5, v4, v3, v2) = v1) | ~ % 29.34/4.78 (function_image(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 29.34/4.78 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ % 29.34/4.78 (relation_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 29.34/4.78 ! [v3: $i] : (v1 = v0 | ~ (first_projection_as_func_of(v3, v2) = v1) | ~ % 29.34/4.78 (first_projection_as_func_of(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 29.34/4.78 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (first_projection(v3, v2) = v1) | ~ % 29.34/4.78 (first_projection(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 29.34/4.78 ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ % 29.34/4.78 (cartesian_product2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 29.34/4.78 : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! % 29.34/4.78 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | % 29.34/4.78 ~ (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 29.34/4.78 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 29.34/4.78 % 29.34/4.78 Further assumptions not needed in the proof: % 29.34/4.78 -------------------------------------------- % 29.34/4.78 antisymmetry_r2_hidden, cc1_arytm_3, cc1_finset_1, cc1_funct_1, cc1_ordinal1, % 29.34/4.78 cc1_relat_1, cc1_relset_1, cc2_arytm_3, cc2_finset_1, cc2_funct_1, cc2_ordinal1, % 29.34/4.78 cc3_ordinal1, cc4_arytm_3, dt_k2_funct_2, dt_m2_relset_1, existence_m1_relset_1, % 29.34/4.78 existence_m1_subset_1, existence_m2_relset_1, fc12_relat_1, fc13_finset_1, % 29.34/4.78 fc1_subset_1, fc1_xboole_0, fc2_ordinal1, fc4_relat_1, fc4_subset_1, % 29.34/4.78 fc5_ordinal1, fc5_relat_1, fc6_funct_1, fc6_relat_1, fc7_relat_1, fc8_arytm_3, % 29.34/4.78 fc8_relat_1, rc1_arytm_3, rc1_finset_1, rc1_funcop_1, rc1_funct_1, rc1_ordinal1, % 29.34/4.78 rc1_ordinal2, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_arytm_3, % 29.34/4.78 rc2_finset_1, rc2_funct_1, rc2_ordinal1, rc2_ordinal2, rc2_relat_1, % 29.34/4.78 rc2_subset_1, rc2_xboole_0, rc3_arytm_3, rc3_finset_1, rc3_funct_1, % 29.34/4.78 rc3_ordinal1, rc3_relat_1, rc4_finset_1, rc4_funct_1, rc4_ordinal1, rc5_funct_1, % 29.34/4.78 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, % 29.34/4.78 t6_boole, t7_boole, t8_boole % 29.34/4.78 % 29.34/4.78 Those formulas are unsatisfiable: % 29.34/4.78 --------------------------------- % 29.34/4.78 % 29.34/4.78 Begin of proof % 29.34/4.78 | % 29.34/4.78 | ALPHA: (dt_k7_funct_3) implies: % 29.34/4.78 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (first_projection(v0, v1) % 29.34/4.78 | = v2) | ~ $i(v1) | ~ $i(v0) | relation(v2)) % 29.34/4.78 | % 29.34/4.78 | ALPHA: (dt_k9_funct_3) implies: % 29.34/4.78 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0, % 29.34/4.78 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 29.34/4.78 | (first_projection_as_func_of(v0, v1) = v3 & $i(v3) & quasi_total(v3, % 29.34/4.78 | v2, v0))) % 29.34/4.78 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0, % 29.34/4.78 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 29.34/4.78 | (first_projection_as_func_of(v0, v1) = v3 & $i(v3) & % 29.34/4.78 | relation_of2_as_subset(v3, v2, v0))) % 29.34/4.78 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 29.34/4.78 | (first_projection_as_func_of(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 29.34/4.78 | ? [v3: $i] : (cartesian_product2(v0, v1) = v3 & $i(v3) & % 29.34/4.78 | quasi_total(v2, v3, v0))) % 29.34/4.78 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 29.34/4.78 | (first_projection_as_func_of(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 29.34/4.78 | ? [v3: $i] : (cartesian_product2(v0, v1) = v3 & $i(v3) & % 29.34/4.78 | relation_of2_as_subset(v2, v3, v0))) % 29.34/4.78 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 29.74/4.78 | (first_projection_as_func_of(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 29.74/4.78 | function(v2)) % 29.74/4.78 | % 29.74/4.78 | ALPHA: (redefinition_k9_funct_3) implies: % 29.74/4.79 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 29.74/4.79 | (first_projection_as_func_of(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 29.74/4.79 | (first_projection(v0, v1) = v2 & $i(v2))) % 29.74/4.79 | % 29.74/4.79 | ALPHA: (redefinition_m2_relset_1) implies: % 29.74/4.79 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 29.74/4.79 | $i(v0) | ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(v2, v0, % 29.74/4.79 | v1)) % 29.74/4.79 | % 29.74/4.79 | ALPHA: (t100_funct_3) implies: % 29.74/4.79 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 29.74/4.79 | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: $i] : ? % 29.74/4.79 | [v4: $i] : (relation_rng(v0) = v2 & first_projection_as_func_of(v1, % 29.74/4.79 | v2) = v4 & function_image(v3, v1, v4, v0) = v1 & % 29.74/4.79 | cartesian_product2(v1, v2) = v3 & $i(v4) & $i(v3) & $i(v2) & % 29.74/4.79 | $i(v1))) % 29.74/4.79 | % 29.74/4.79 | ALPHA: (t21_relat_1) implies: % 29.74/4.79 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 29.74/4.79 | ~ relation(v0) | ? [v2: $i] : ? [v3: $i] : (relation_rng(v0) = v2 % 29.74/4.79 | & cartesian_product2(v1, v2) = v3 & $i(v3) & $i(v2) & subset(v0, % 29.74/4.79 | v3))) % 29.74/4.79 | % 29.74/4.79 | ALPHA: (t26_finset_1) implies: % 29.74/4.79 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 29.74/4.79 | ~ relation(v0) | ~ function(v0) | ~ finite(v1) | ? [v2: $i] : % 29.74/4.79 | (relation_rng(v0) = v2 & $i(v2) & finite(v2))) % 29.74/4.79 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 29.74/4.79 | ~ relation(v0) | ~ function(v0) | finite(v1) | ? [v2: $i] : % 29.74/4.79 | (relation_dom(v0) = v2 & $i(v2) & ~ finite(v2))) % 29.74/4.79 | % 29.74/4.79 | ALPHA: (function-axioms) implies: % 29.74/4.79 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 29.74/4.79 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 29.74/4.79 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 29.74/4.79 | (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = % 29.74/4.79 | v0)) % 29.74/4.79 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 29.74/4.79 | (first_projection_as_func_of(v3, v2) = v1) | ~ % 29.74/4.79 | (first_projection_as_func_of(v3, v2) = v0)) % 29.74/4.79 | % 29.74/4.79 | DELTA: instantiating (t29_finset_1) with fresh symbols all_99_0, all_99_1 % 29.74/4.79 | gives: % 29.74/4.79 | (16) relation_dom(all_99_1) = all_99_0 & $i(all_99_0) & $i(all_99_1) & % 29.74/4.79 | relation(all_99_1) & function(all_99_1) & ((finite(all_99_0) & ~ % 29.74/4.79 | finite(all_99_1)) | (finite(all_99_1) & ~ finite(all_99_0))) % 29.74/4.79 | % 29.74/4.79 | ALPHA: (16) implies: % 29.74/4.79 | (17) function(all_99_1) % 29.74/4.79 | (18) relation(all_99_1) % 29.74/4.79 | (19) $i(all_99_1) % 29.74/4.79 | (20) relation_dom(all_99_1) = all_99_0 % 29.74/4.79 | (21) (finite(all_99_0) & ~ finite(all_99_1)) | (finite(all_99_1) & ~ % 29.74/4.79 | finite(all_99_0)) % 29.74/4.79 | % 29.74/4.79 | GROUND_INST: instantiating (9) with all_99_1, all_99_0, simplifying with (17), % 29.74/4.79 | (18), (19), (20) gives: % 29.74/4.79 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_rng(all_99_1) = v0 % 29.74/4.79 | & first_projection_as_func_of(all_99_0, v0) = v2 & % 29.74/4.79 | function_image(v1, all_99_0, v2, all_99_1) = all_99_0 & % 29.74/4.79 | cartesian_product2(all_99_0, v0) = v1 & $i(v2) & $i(v1) & $i(v0) & % 29.74/4.79 | $i(all_99_0)) % 29.74/4.79 | % 29.74/4.79 | GROUND_INST: instantiating (10) with all_99_1, all_99_0, simplifying with % 29.74/4.79 | (18), (19), (20) gives: % 29.74/4.79 | (23) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_99_1) = v0 & % 29.74/4.79 | cartesian_product2(all_99_0, v0) = v1 & $i(v1) & $i(v0) & % 29.74/4.79 | subset(all_99_1, v1)) % 29.74/4.79 | % 29.74/4.79 | DELTA: instantiating (23) with fresh symbols all_111_0, all_111_1 gives: % 29.74/4.80 | (24) relation_rng(all_99_1) = all_111_1 & cartesian_product2(all_99_0, % 29.74/4.80 | all_111_1) = all_111_0 & $i(all_111_0) & $i(all_111_1) & % 29.74/4.80 | subset(all_99_1, all_111_0) % 29.74/4.80 | % 29.74/4.80 | ALPHA: (24) implies: % 29.74/4.80 | (25) subset(all_99_1, all_111_0) % 29.74/4.80 | (26) cartesian_product2(all_99_0, all_111_1) = all_111_0 % 29.74/4.80 | (27) relation_rng(all_99_1) = all_111_1 % 29.74/4.80 | % 29.74/4.80 | DELTA: instantiating (22) with fresh symbols all_113_0, all_113_1, all_113_2 % 29.74/4.80 | gives: % 29.74/4.80 | (28) relation_rng(all_99_1) = all_113_2 & % 29.74/4.80 | first_projection_as_func_of(all_99_0, all_113_2) = all_113_0 & % 29.74/4.80 | function_image(all_113_1, all_99_0, all_113_0, all_99_1) = all_99_0 & % 29.74/4.80 | cartesian_product2(all_99_0, all_113_2) = all_113_1 & $i(all_113_0) & % 29.74/4.80 | $i(all_113_1) & $i(all_113_2) & $i(all_99_0) % 29.74/4.80 | % 29.74/4.80 | ALPHA: (28) implies: % 29.74/4.80 | (29) $i(all_99_0) % 29.74/4.80 | (30) $i(all_113_2) % 29.74/4.80 | (31) cartesian_product2(all_99_0, all_113_2) = all_113_1 % 29.74/4.80 | (32) function_image(all_113_1, all_99_0, all_113_0, all_99_1) = all_99_0 % 29.74/4.80 | (33) first_projection_as_func_of(all_99_0, all_113_2) = all_113_0 % 29.74/4.80 | (34) relation_rng(all_99_1) = all_113_2 % 29.74/4.80 | % 29.74/4.80 | GROUND_INST: instantiating (14) with all_111_0, all_113_1, all_111_1, % 29.74/4.80 | all_99_0, simplifying with (26) gives: % 29.74/4.80 | (35) all_113_1 = all_111_0 | ~ (cartesian_product2(all_99_0, all_111_1) = % 29.74/4.80 | all_113_1) % 29.74/4.80 | % 29.74/4.80 | GROUND_INST: instantiating (13) with all_111_1, all_113_2, all_99_1, % 29.74/4.80 | simplifying with (27), (34) gives: % 29.74/4.80 | (36) all_113_2 = all_111_1 % 29.74/4.80 | % 29.74/4.80 | REDUCE: (33), (36) imply: % 29.74/4.80 | (37) first_projection_as_func_of(all_99_0, all_111_1) = all_113_0 % 29.74/4.80 | % 29.74/4.80 | REDUCE: (31), (36) imply: % 29.74/4.80 | (38) cartesian_product2(all_99_0, all_111_1) = all_113_1 % 29.74/4.80 | % 29.74/4.80 | REDUCE: (30), (36) imply: % 29.74/4.80 | (39) $i(all_111_1) % 29.74/4.80 | % 29.74/4.80 | BETA: splitting (35) gives: % 29.74/4.80 | % 29.74/4.80 | Case 1: % 29.74/4.80 | | % 29.74/4.80 | | (40) ~ (cartesian_product2(all_99_0, all_111_1) = all_113_1) % 29.74/4.80 | | % 29.74/4.80 | | PRED_UNIFY: (38), (40) imply: % 29.74/4.80 | | (41) $false % 29.74/4.80 | | % 29.74/4.80 | | CLOSE: (41) is inconsistent. % 29.74/4.80 | | % 29.74/4.80 | Case 2: % 29.74/4.80 | | % 29.74/4.80 | | (42) all_113_1 = all_111_0 % 29.74/4.80 | | % 29.74/4.80 | | REDUCE: (32), (42) imply: % 29.74/4.80 | | (43) function_image(all_111_0, all_99_0, all_113_0, all_99_1) = all_99_0 % 29.74/4.80 | | % 29.74/4.80 | | GROUND_INST: instantiating (3) with all_99_0, all_111_1, all_111_0, % 29.74/4.80 | | simplifying with (26), (29), (39) gives: % 29.74/4.80 | | (44) ? [v0: $i] : (first_projection_as_func_of(all_99_0, all_111_1) = v0 % 29.74/4.80 | | & $i(v0) & relation_of2_as_subset(v0, all_111_0, all_99_0)) % 29.74/4.80 | | % 29.74/4.80 | | GROUND_INST: instantiating (2) with all_99_0, all_111_1, all_111_0, % 29.74/4.80 | | simplifying with (26), (29), (39) gives: % 29.74/4.80 | | (45) ? [v0: $i] : (first_projection_as_func_of(all_99_0, all_111_1) = v0 % 29.74/4.80 | | & $i(v0) & quasi_total(v0, all_111_0, all_99_0)) % 29.74/4.80 | | % 29.74/4.80 | | GROUND_INST: instantiating (6) with all_99_0, all_111_1, all_113_0, % 29.74/4.80 | | simplifying with (29), (37), (39) gives: % 29.74/4.80 | | (46) function(all_113_0) % 29.74/4.80 | | % 29.74/4.80 | | GROUND_INST: instantiating (5) with all_99_0, all_111_1, all_113_0, % 29.74/4.80 | | simplifying with (29), (37), (39) gives: % 29.74/4.80 | | (47) ? [v0: $i] : (cartesian_product2(all_99_0, all_111_1) = v0 & $i(v0) % 29.74/4.80 | | & relation_of2_as_subset(all_113_0, v0, all_99_0)) % 29.74/4.80 | | % 29.74/4.80 | | GROUND_INST: instantiating (4) with all_99_0, all_111_1, all_113_0, % 29.74/4.80 | | simplifying with (29), (37), (39) gives: % 29.74/4.80 | | (48) ? [v0: $i] : (cartesian_product2(all_99_0, all_111_1) = v0 & $i(v0) % 29.74/4.81 | | & quasi_total(all_113_0, v0, all_99_0)) % 29.74/4.81 | | % 29.74/4.81 | | GROUND_INST: instantiating (7) with all_99_0, all_111_1, all_113_0, % 29.74/4.81 | | simplifying with (29), (37), (39) gives: % 29.74/4.81 | | (49) first_projection(all_99_0, all_111_1) = all_113_0 & $i(all_113_0) % 29.74/4.81 | | % 29.74/4.81 | | ALPHA: (49) implies: % 29.74/4.81 | | (50) first_projection(all_99_0, all_111_1) = all_113_0 % 29.74/4.81 | | % 29.74/4.81 | | GROUND_INST: instantiating (12) with all_99_1, all_111_1, simplifying with % 29.74/4.81 | | (17), (18), (19), (27) gives: % 29.74/4.81 | | (51) finite(all_111_1) | ? [v0: $i] : (relation_dom(all_99_1) = v0 & % 29.74/4.81 | | $i(v0) & ~ finite(v0)) % 29.74/4.81 | | % 29.74/4.81 | | DELTA: instantiating (45) with fresh symbol all_129_0 gives: % 29.74/4.81 | | (52) first_projection_as_func_of(all_99_0, all_111_1) = all_129_0 & % 29.74/4.81 | | $i(all_129_0) & quasi_total(all_129_0, all_111_0, all_99_0) % 29.74/4.81 | | % 29.74/4.81 | | ALPHA: (52) implies: % 29.74/4.81 | | (53) $i(all_129_0) % 29.74/4.81 | | (54) first_projection_as_func_of(all_99_0, all_111_1) = all_129_0 % 29.74/4.81 | | % 29.74/4.81 | | DELTA: instantiating (47) with fresh symbol all_131_0 gives: % 29.74/4.81 | | (55) cartesian_product2(all_99_0, all_111_1) = all_131_0 & $i(all_131_0) % 29.74/4.81 | | & relation_of2_as_subset(all_113_0, all_131_0, all_99_0) % 29.74/4.81 | | % 29.74/4.81 | | ALPHA: (55) implies: % 29.74/4.81 | | (56) relation_of2_as_subset(all_113_0, all_131_0, all_99_0) % 29.74/4.81 | | (57) $i(all_131_0) % 29.74/4.81 | | (58) cartesian_product2(all_99_0, all_111_1) = all_131_0 % 29.74/4.81 | | % 29.74/4.81 | | DELTA: instantiating (44) with fresh symbol all_133_0 gives: % 29.74/4.81 | | (59) first_projection_as_func_of(all_99_0, all_111_1) = all_133_0 & % 29.74/4.81 | | $i(all_133_0) & relation_of2_as_subset(all_133_0, all_111_0, % 29.74/4.81 | | all_99_0) % 29.74/4.81 | | % 29.74/4.81 | | ALPHA: (59) implies: % 29.74/4.81 | | (60) first_projection_as_func_of(all_99_0, all_111_1) = all_133_0 % 29.74/4.81 | | % 29.74/4.81 | | DELTA: instantiating (48) with fresh symbol all_135_0 gives: % 29.74/4.81 | | (61) cartesian_product2(all_99_0, all_111_1) = all_135_0 & $i(all_135_0) % 29.74/4.81 | | & quasi_total(all_113_0, all_135_0, all_99_0) % 29.74/4.81 | | % 29.74/4.81 | | ALPHA: (61) implies: % 29.74/4.81 | | (62) quasi_total(all_113_0, all_135_0, all_99_0) % 29.74/4.81 | | (63) cartesian_product2(all_99_0, all_111_1) = all_135_0 % 29.74/4.81 | | % 29.74/4.81 | | GROUND_INST: instantiating (14) with all_111_0, all_135_0, all_111_1, % 29.74/4.81 | | all_99_0, simplifying with (26), (63) gives: % 29.74/4.81 | | (64) all_135_0 = all_111_0 % 29.74/4.81 | | % 29.74/4.81 | | GROUND_INST: instantiating (14) with all_131_0, all_135_0, all_111_1, % 29.74/4.81 | | all_99_0, simplifying with (58), (63) gives: % 29.74/4.81 | | (65) all_135_0 = all_131_0 % 29.74/4.81 | | % 29.74/4.81 | | GROUND_INST: instantiating (15) with all_113_0, all_133_0, all_111_1, % 29.74/4.81 | | all_99_0, simplifying with (37), (60) gives: % 29.74/4.81 | | (66) all_133_0 = all_113_0 % 29.74/4.81 | | % 29.74/4.81 | | GROUND_INST: instantiating (15) with all_129_0, all_133_0, all_111_1, % 29.74/4.81 | | all_99_0, simplifying with (54), (60) gives: % 29.74/4.81 | | (67) all_133_0 = all_129_0 % 29.74/4.81 | | % 29.74/4.81 | | COMBINE_EQS: (64), (65) imply: % 29.74/4.81 | | (68) all_131_0 = all_111_0 % 29.74/4.81 | | % 29.74/4.81 | | COMBINE_EQS: (66), (67) imply: % 29.74/4.81 | | (69) all_129_0 = all_113_0 % 29.74/4.81 | | % 29.74/4.81 | | REDUCE: (57), (68) imply: % 29.74/4.81 | | (70) $i(all_111_0) % 29.74/4.81 | | % 29.74/4.81 | | REDUCE: (53), (69) imply: % 29.74/4.81 | | (71) $i(all_113_0) % 29.74/4.81 | | % 29.74/4.81 | | REDUCE: (56), (68) imply: % 29.74/4.81 | | (72) relation_of2_as_subset(all_113_0, all_111_0, all_99_0) % 29.74/4.81 | | % 29.74/4.81 | | REDUCE: (62), (64) imply: % 29.74/4.81 | | (73) quasi_total(all_113_0, all_111_0, all_99_0) % 29.74/4.81 | | % 29.74/4.81 | | GROUND_INST: instantiating (8) with all_111_0, all_99_0, all_113_0, % 29.74/4.81 | | simplifying with (29), (70), (71), (72) gives: % 29.74/4.81 | | (74) relation_of2(all_113_0, all_111_0, all_99_0) % 29.74/4.81 | | % 29.74/4.81 | | GROUND_INST: instantiating (1) with all_99_0, all_111_1, all_113_0, % 29.74/4.81 | | simplifying with (29), (39), (50) gives: % 29.74/4.81 | | (75) relation(all_113_0) % 29.74/4.81 | | % 29.74/4.81 | | GROUND_INST: instantiating (redefinition_k2_funct_2) with all_111_0, % 29.74/4.81 | | all_99_0, all_113_0, all_99_1, all_99_0, simplifying with (19), % 29.74/4.81 | | (29), (43), (46), (70), (71), (73), (74) gives: % 29.74/4.82 | | (76) relation_image(all_113_0, all_99_1) = all_99_0 % 29.74/4.82 | | % 29.74/4.82 | | GROUND_INST: instantiating (t17_finset_1) with all_99_1, all_113_0, % 29.74/4.82 | | all_99_0, simplifying with (19), (46), (71), (75), (76) gives: % 29.74/4.82 | | (77) ~ finite(all_99_1) | finite(all_99_0) % 29.74/4.82 | | % 29.74/4.82 | | GROUND_INST: instantiating (11) with all_99_1, all_99_0, simplifying with % 29.74/4.82 | | (17), (18), (19), (20) gives: % 29.74/4.82 | | (78) ~ finite(all_99_0) | ? [v0: $i] : (relation_rng(all_99_1) = v0 & % 29.74/4.82 | | $i(v0) & finite(v0)) % 29.74/4.82 | | % 29.74/4.82 | | GROUND_INST: instantiating (t13_finset_1) with all_99_1, all_111_0, % 29.74/4.82 | | simplifying with (19), (25), (70) gives: % 29.74/4.82 | | (79) ~ finite(all_111_0) | finite(all_99_1) % 29.74/4.82 | | % 29.74/4.82 | | BETA: splitting (21) gives: % 29.74/4.82 | | % 29.74/4.82 | | Case 1: % 29.74/4.82 | | | % 29.74/4.82 | | | (80) finite(all_99_0) & ~ finite(all_99_1) % 29.74/4.82 | | | % 29.74/4.82 | | | ALPHA: (80) implies: % 29.74/4.82 | | | (81) ~ finite(all_99_1) % 29.74/4.82 | | | (82) finite(all_99_0) % 29.74/4.82 | | | % 29.74/4.82 | | | BETA: splitting (78) gives: % 29.74/4.82 | | | % 29.74/4.82 | | | Case 1: % 29.74/4.82 | | | | % 29.74/4.82 | | | | (83) ~ finite(all_99_0) % 29.74/4.82 | | | | % 29.74/4.82 | | | | PRED_UNIFY: (82), (83) imply: % 29.74/4.82 | | | | (84) $false % 29.74/4.82 | | | | % 29.74/4.82 | | | | CLOSE: (84) is inconsistent. % 29.74/4.82 | | | | % 29.74/4.82 | | | Case 2: % 29.74/4.82 | | | | % 29.74/4.82 | | | | (85) ? [v0: $i] : (relation_rng(all_99_1) = v0 & $i(v0) & % 29.74/4.82 | | | | finite(v0)) % 29.74/4.82 | | | | % 29.74/4.82 | | | | DELTA: instantiating (85) with fresh symbol all_268_0 gives: % 29.74/4.82 | | | | (86) relation_rng(all_99_1) = all_268_0 & $i(all_268_0) & % 29.74/4.82 | | | | finite(all_268_0) % 29.74/4.82 | | | | % 29.74/4.82 | | | | ALPHA: (86) implies: % 29.74/4.82 | | | | (87) finite(all_268_0) % 29.74/4.82 | | | | (88) $i(all_268_0) % 29.74/4.82 | | | | (89) relation_rng(all_99_1) = all_268_0 % 29.74/4.82 | | | | % 29.74/4.82 | | | | BETA: splitting (79) gives: % 29.74/4.82 | | | | % 29.74/4.82 | | | | Case 1: % 29.74/4.82 | | | | | % 29.74/4.82 | | | | | (90) ~ finite(all_111_0) % 29.74/4.82 | | | | | % 29.74/4.82 | | | | | BETA: splitting (51) gives: % 29.74/4.82 | | | | | % 29.74/4.82 | | | | | Case 1: % 29.74/4.82 | | | | | | % 29.74/4.82 | | | | | | % 29.74/4.82 | | | | | | GROUND_INST: instantiating (13) with all_111_1, all_268_0, all_99_1, % 29.74/4.82 | | | | | | simplifying with (27), (89) gives: % 29.74/4.82 | | | | | | (91) all_268_0 = all_111_1 % 29.74/4.82 | | | | | | % 29.74/4.82 | | | | | | REDUCE: (87), (91) imply: % 29.74/4.82 | | | | | | (92) finite(all_111_1) % 29.74/4.82 | | | | | | % 29.74/4.82 | | | | | | GROUND_INST: instantiating (t19_finset_1) with all_99_0, all_111_1, % 29.74/4.82 | | | | | | all_111_0, simplifying with (26), (29), (39), (82), % 29.74/4.82 | | | | | | (90), (92) gives: % 29.74/4.82 | | | | | | (93) $false % 29.74/4.82 | | | | | | % 29.74/4.82 | | | | | | CLOSE: (93) is inconsistent. % 29.74/4.82 | | | | | | % 29.74/4.82 | | | | | Case 2: % 29.74/4.82 | | | | | | % 29.74/4.82 | | | | | | (94) ~ finite(all_111_1) % 29.74/4.82 | | | | | | % 29.74/4.82 | | | | | | GROUND_INST: instantiating (13) with all_111_1, all_268_0, all_99_1, % 29.74/4.82 | | | | | | simplifying with (27), (89) gives: % 29.74/4.82 | | | | | | (95) all_268_0 = all_111_1 % 29.74/4.82 | | | | | | % 29.74/4.82 | | | | | | PRED_UNIFY: (87), (94) imply: % 29.74/4.82 | | | | | | (96) ~ (all_268_0 = all_111_1) % 29.74/4.82 | | | | | | % 29.74/4.82 | | | | | | REDUCE: (95), (96) imply: % 29.74/4.82 | | | | | | (97) $false % 29.74/4.82 | | | | | | % 29.74/4.82 | | | | | | CLOSE: (97) is inconsistent. % 29.74/4.82 | | | | | | % 29.74/4.82 | | | | | End of split % 29.74/4.82 | | | | | % 29.74/4.82 | | | | Case 2: % 29.74/4.82 | | | | | % 29.74/4.82 | | | | | (98) finite(all_99_1) % 29.74/4.82 | | | | | % 29.74/4.82 | | | | | PRED_UNIFY: (81), (98) imply: % 29.74/4.82 | | | | | (99) $false % 29.74/4.82 | | | | | % 29.74/4.82 | | | | | CLOSE: (99) is inconsistent. % 29.74/4.82 | | | | | % 29.74/4.82 | | | | End of split % 29.74/4.82 | | | | % 29.74/4.82 | | | End of split % 29.74/4.82 | | | % 29.74/4.82 | | Case 2: % 29.74/4.82 | | | % 29.74/4.82 | | | (100) finite(all_99_1) & ~ finite(all_99_0) % 29.74/4.82 | | | % 29.74/4.82 | | | ALPHA: (100) implies: % 29.74/4.82 | | | (101) ~ finite(all_99_0) % 29.74/4.82 | | | (102) finite(all_99_1) % 29.74/4.82 | | | % 29.74/4.82 | | | BETA: splitting (77) gives: % 29.74/4.82 | | | % 29.74/4.82 | | | Case 1: % 29.74/4.82 | | | | % 29.74/4.82 | | | | (103) ~ finite(all_99_1) % 29.74/4.82 | | | | % 29.74/4.82 | | | | PRED_UNIFY: (102), (103) imply: % 29.74/4.82 | | | | (104) $false % 29.74/4.82 | | | | % 29.74/4.82 | | | | CLOSE: (104) is inconsistent. % 29.74/4.82 | | | | % 29.74/4.82 | | | Case 2: % 29.74/4.82 | | | | % 29.74/4.82 | | | | (105) finite(all_99_0) % 29.74/4.82 | | | | % 29.74/4.82 | | | | PRED_UNIFY: (101), (105) imply: % 29.74/4.82 | | | | (106) $false % 29.74/4.82 | | | | % 29.74/4.82 | | | | CLOSE: (106) is inconsistent. % 29.74/4.82 | | | | % 29.74/4.82 | | | End of split % 29.74/4.82 | | | % 29.74/4.82 | | End of split % 29.74/4.82 | | % 29.74/4.82 | End of split % 29.74/4.82 | % 29.74/4.82 End of proof % 29.74/4.82 % SZS output end Proof for theBenchmark % 29.74/4.82 % 29.74/4.82 4204ms %------------------------------------------------------------------------------