%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU353+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n028.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 17:44:15 EDT 2023 % Result : Theorem 13.26s 2.69s % Output : Proof 19.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU353+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n028.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 : Thu Aug 24 01:17:19 EDT 2023 % 0.13/0.33 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.02/1.20 Prover 4: Preprocessing ... % 3.02/1.20 Prover 1: Preprocessing ... % 3.46/1.24 Prover 5: Preprocessing ... % 3.46/1.24 Prover 0: Preprocessing ... % 3.46/1.24 Prover 3: Preprocessing ... % 3.46/1.24 Prover 6: Preprocessing ... % 3.46/1.25 Prover 2: Preprocessing ... % 8.13/1.89 Prover 1: Warning: ignoring some quantifiers % 8.13/1.93 Prover 2: Proving ... % 8.13/1.94 Prover 5: Proving ... % 8.13/1.94 Prover 3: Warning: ignoring some quantifiers % 8.64/1.97 Prover 3: Constructing countermodel ... % 8.64/2.00 Prover 1: Constructing countermodel ... % 8.64/2.02 Prover 6: Proving ... % 8.64/2.02 Prover 4: Warning: ignoring some quantifiers % 8.64/2.10 Prover 4: Constructing countermodel ... % 10.31/2.21 Prover 0: Proving ... % 13.26/2.68 Prover 2: proved (2061ms) % 13.26/2.68 % 13.26/2.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.26/2.69 % 13.26/2.69 Prover 3: stopped % 13.94/2.70 Prover 0: stopped % 13.94/2.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.94/2.70 Prover 6: stopped % 13.94/2.71 Prover 5: proved (2066ms) % 13.94/2.71 % 13.94/2.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.94/2.71 % 13.94/2.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.94/2.73 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.94/2.73 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.94/2.73 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.65/2.80 Prover 8: Preprocessing ... % 14.65/2.81 Prover 7: Preprocessing ... % 14.65/2.86 Prover 11: Preprocessing ... % 14.65/2.88 Prover 13: Preprocessing ... % 14.65/2.88 Prover 10: Preprocessing ... % 16.26/3.02 Prover 7: Warning: ignoring some quantifiers % 16.26/3.04 Prover 10: Warning: ignoring some quantifiers % 16.26/3.05 Prover 7: Constructing countermodel ... % 16.26/3.08 Prover 10: Constructing countermodel ... % 16.26/3.11 Prover 13: Warning: ignoring some quantifiers % 17.02/3.11 Prover 8: Warning: ignoring some quantifiers % 17.02/3.14 Prover 8: Constructing countermodel ... % 17.02/3.17 Prover 13: Constructing countermodel ... % 18.58/3.41 Prover 11: Warning: ignoring some quantifiers % 18.58/3.46 Prover 11: Constructing countermodel ... % 18.58/3.48 Prover 7: Found proof (size 51) % 18.58/3.49 Prover 7: proved (796ms) % 18.58/3.49 Prover 10: stopped % 18.58/3.49 Prover 4: stopped % 18.58/3.49 Prover 13: stopped % 18.58/3.49 Prover 1: stopped % 18.58/3.49 Prover 8: stopped % 18.58/3.50 Prover 11: stopped % 18.58/3.50 % 18.58/3.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 18.58/3.50 % 18.58/3.51 % SZS output start Proof for theBenchmark % 18.58/3.52 Assumptions after simplification: % 18.58/3.52 --------------------------------- % 18.58/3.52 % 18.58/3.52 (d11_grcat_1) % 19.82/3.55 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ % 19.82/3.55 one_sorted_str(v0) | ? [v2: $i] : (identity_on_carrier(v0) = v2 & % 19.82/3.55 identity_as_relation_of(v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : % 19.82/3.55 ( ~ (identity_on_carrier(v0) = v1) | ~ $i(v0) | ~ one_sorted_str(v0) | ? % 19.82/3.55 [v2: $i] : (the_carrier(v0) = v2 & identity_as_relation_of(v2) = v1 & $i(v2) % 19.82/3.55 & $i(v1))) % 19.82/3.55 % 19.82/3.55 (dt_k7_grcat_1) % 19.82/3.55 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ % 19.82/3.55 one_sorted_str(v0) | ? [v2: $i] : (identity_on_carrier(v0) = v2 & $i(v2) & % 19.82/3.55 relation_of2_as_subset(v2, v1, v1) & quasi_total(v2, v1, v1) & % 19.82/3.55 function(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (identity_on_carrier(v0) % 19.82/3.55 = v1) | ~ $i(v0) | ~ one_sorted_str(v0) | function(v1)) & ! [v0: $i] : % 19.82/3.55 ! [v1: $i] : ( ~ (identity_on_carrier(v0) = v1) | ~ $i(v0) | ~ % 19.82/3.55 one_sorted_str(v0) | ? [v2: $i] : (the_carrier(v0) = v2 & $i(v2) & % 19.82/3.55 relation_of2_as_subset(v1, v2, v2) & quasi_total(v1, v2, v2))) % 19.82/3.55 % 19.82/3.55 (fc1_struct_0) % 19.82/3.55 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ % 19.82/3.55 one_sorted_str(v0) | ~ empty(v1) | empty_carrier(v0)) % 19.82/3.55 % 19.82/3.55 (redefinition_k6_partfun1) % 19.82/3.55 ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ $i(v0) | % 19.82/3.55 (identity_as_relation_of(v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( % 19.82/3.55 ~ (identity_as_relation_of(v0) = v1) | ~ $i(v0) | (identity_relation(v0) = % 19.82/3.56 v1 & $i(v1))) % 19.82/3.56 % 19.82/3.56 (redefinition_k8_funct_2) % 19.82/3.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 19.82/3.56 (apply_as_element(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 19.82/3.56 | ~ $i(v0) | ~ element(v3, v0) | ~ quasi_total(v2, v0, v1) | ~ % 19.82/3.56 function(v2) | ~ relation_of2(v2, v0, v1) | empty(v0) | (apply(v2, v3) = v4 % 19.82/3.56 & $i(v4))) % 19.82/3.56 % 19.82/3.56 (redefinition_m2_relset_1) % 19.82/3.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 19.82/3.56 ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(v2, v0, v1)) & ! [v0: % 19.82/3.56 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 19.82/3.56 relation_of2(v2, v0, v1) | relation_of2_as_subset(v2, v0, v1)) % 19.82/3.56 % 19.82/3.56 (t2_subset) % 19.82/3.56 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ element(v0, v1) | % 19.82/3.56 empty(v1) | in(v0, v1)) % 19.82/3.56 % 19.82/3.56 (t35_funct_1) % 19.82/3.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ % 19.82/3.56 (apply(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ $i(v1) | ~ % 19.82/3.56 $i(v0) | ~ in(v1, v0)) % 19.82/3.56 % 19.82/3.56 (t91_tmap_1) % 19.82/3.56 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4 % 19.82/3.56 = v3) & apply_as_element(v1, v1, v2, v3) = v4 & the_carrier(v0) = v1 & % 19.82/3.56 identity_on_carrier(v0) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 19.82/3.56 one_sorted_str(v0) & element(v3, v1) & ~ empty_carrier(v0)) % 19.82/3.56 % 19.82/3.56 (function-axioms) % 19.82/3.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 19.82/3.56 $i] : (v1 = v0 | ~ (apply_as_element(v5, v4, v3, v2) = v1) | ~ % 19.82/3.56 (apply_as_element(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.82/3.56 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, % 19.82/3.56 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 19.82/3.56 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) % 19.82/3.56 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.82/3.56 (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0: % 19.82/3.56 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ % 19.82/3.56 (the_carrier(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 19.82/3.56 | ~ (identity_on_carrier(v2) = v1) | ~ (identity_on_carrier(v2) = v0)) & % 19.82/3.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.82/3.56 (identity_as_relation_of(v2) = v1) | ~ (identity_as_relation_of(v2) = v0)) % 19.82/3.57 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) % 19.82/3.57 | ~ (powerset(v2) = v0)) % 19.82/3.57 % 19.82/3.57 Further assumptions not needed in the proof: % 19.82/3.57 -------------------------------------------- % 19.82/3.57 antisymmetry_r2_hidden, cc1_funct_2, cc1_partfun1, cc1_relset_1, cc2_funct_2, % 19.82/3.57 cc3_funct_2, cc4_funct_2, cc5_funct_2, cc6_funct_2, dt_k1_funct_1, % 19.82/3.57 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_k6_partfun1, dt_k6_relat_1, % 19.82/3.57 dt_k8_funct_2, dt_l1_struct_0, dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1, % 19.82/3.57 dt_u1_struct_0, existence_l1_struct_0, existence_m1_relset_1, % 19.82/3.57 existence_m1_subset_1, existence_m2_relset_1, fc1_subset_1, fc1_xboole_0, % 19.82/3.57 fc2_partfun1, fc4_subset_1, rc1_funct_2, rc1_partfun1, rc1_subset_1, % 19.82/3.57 rc1_xboole_0, rc2_funct_2, rc2_partfun1, rc2_subset_1, rc2_xboole_0, % 19.82/3.57 rc3_partfun1, rc3_struct_0, rc5_struct_0, reflexivity_r1_tarski, t1_subset, % 19.82/3.57 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole % 19.82/3.57 % 19.82/3.57 Those formulas are unsatisfiable: % 19.82/3.57 --------------------------------- % 19.82/3.57 % 19.82/3.57 Begin of proof % 19.82/3.57 | % 19.82/3.57 | ALPHA: (d11_grcat_1) implies: % 19.82/3.57 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_on_carrier(v0) = v1) | ~ % 19.82/3.57 | $i(v0) | ~ one_sorted_str(v0) | ? [v2: $i] : (the_carrier(v0) = v2 % 19.82/3.57 | & identity_as_relation_of(v2) = v1 & $i(v2) & $i(v1))) % 19.82/3.57 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ % 19.82/3.57 | one_sorted_str(v0) | ? [v2: $i] : (identity_on_carrier(v0) = v2 & % 19.82/3.57 | identity_as_relation_of(v1) = v2 & $i(v2))) % 19.82/3.57 | % 19.82/3.57 | ALPHA: (dt_k7_grcat_1) implies: % 19.82/3.57 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_on_carrier(v0) = v1) | ~ % 19.82/3.57 | $i(v0) | ~ one_sorted_str(v0) | ? [v2: $i] : (the_carrier(v0) = v2 % 19.82/3.57 | & $i(v2) & relation_of2_as_subset(v1, v2, v2) & quasi_total(v1, v2, % 19.82/3.57 | v2))) % 19.82/3.57 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ % 19.82/3.57 | one_sorted_str(v0) | ? [v2: $i] : (identity_on_carrier(v0) = v2 & % 19.82/3.57 | $i(v2) & relation_of2_as_subset(v2, v1, v1) & quasi_total(v2, v1, % 19.82/3.57 | v1) & function(v2))) % 19.82/3.57 | % 19.82/3.57 | ALPHA: (redefinition_k6_partfun1) implies: % 19.82/3.57 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_as_relation_of(v0) = v1) | ~ % 19.82/3.57 | $i(v0) | (identity_relation(v0) = v1 & $i(v1))) % 19.82/3.57 | % 19.82/3.57 | ALPHA: (redefinition_m2_relset_1) implies: % 19.82/3.57 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 19.82/3.57 | $i(v0) | ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(v2, v0, % 19.82/3.57 | v1)) % 19.82/3.57 | % 19.82/3.57 | ALPHA: (function-axioms) implies: % 19.82/3.57 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.82/3.57 | (identity_on_carrier(v2) = v1) | ~ (identity_on_carrier(v2) = v0)) % 19.82/3.57 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.82/3.57 | (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 19.82/3.57 | % 19.82/3.57 | DELTA: instantiating (t91_tmap_1) with fresh symbols all_56_0, all_56_1, % 19.82/3.57 | all_56_2, all_56_3, all_56_4 gives: % 19.82/3.58 | (9) ~ (all_56_0 = all_56_1) & apply_as_element(all_56_3, all_56_3, % 19.82/3.58 | all_56_2, all_56_1) = all_56_0 & the_carrier(all_56_4) = all_56_3 & % 19.82/3.58 | identity_on_carrier(all_56_4) = all_56_2 & $i(all_56_0) & $i(all_56_1) % 19.82/3.58 | & $i(all_56_2) & $i(all_56_3) & $i(all_56_4) & one_sorted_str(all_56_4) % 19.82/3.58 | & element(all_56_1, all_56_3) & ~ empty_carrier(all_56_4) % 19.82/3.58 | % 19.82/3.58 | ALPHA: (9) implies: % 19.82/3.58 | (10) ~ (all_56_0 = all_56_1) % 19.82/3.58 | (11) ~ empty_carrier(all_56_4) % 19.82/3.58 | (12) element(all_56_1, all_56_3) % 19.82/3.58 | (13) one_sorted_str(all_56_4) % 19.82/3.58 | (14) $i(all_56_4) % 19.82/3.58 | (15) $i(all_56_3) % 19.82/3.58 | (16) $i(all_56_1) % 19.82/3.58 | (17) identity_on_carrier(all_56_4) = all_56_2 % 19.82/3.58 | (18) the_carrier(all_56_4) = all_56_3 % 19.82/3.58 | (19) apply_as_element(all_56_3, all_56_3, all_56_2, all_56_1) = all_56_0 % 19.82/3.58 | % 19.82/3.58 | GROUND_INST: instantiating (t2_subset) with all_56_1, all_56_3, simplifying % 19.82/3.58 | with (12), (15), (16) gives: % 19.82/3.58 | (20) empty(all_56_3) | in(all_56_1, all_56_3) % 19.82/3.58 | % 19.82/3.58 | GROUND_INST: instantiating (1) with all_56_4, all_56_2, simplifying with (13), % 19.82/3.58 | (14), (17) gives: % 19.82/3.58 | (21) ? [v0: $i] : (the_carrier(all_56_4) = v0 & % 19.82/3.58 | identity_as_relation_of(v0) = all_56_2 & $i(v0) & $i(all_56_2)) % 19.82/3.58 | % 19.82/3.58 | GROUND_INST: instantiating (3) with all_56_4, all_56_2, simplifying with (13), % 19.82/3.58 | (14), (17) gives: % 19.82/3.58 | (22) ? [v0: $i] : (the_carrier(all_56_4) = v0 & $i(v0) & % 19.82/3.58 | relation_of2_as_subset(all_56_2, v0, v0) & quasi_total(all_56_2, v0, % 19.82/3.58 | v0)) % 19.82/3.58 | % 19.82/3.58 | GROUND_INST: instantiating (2) with all_56_4, all_56_3, simplifying with (13), % 19.82/3.58 | (14), (18) gives: % 19.82/3.58 | (23) ? [v0: $i] : (identity_on_carrier(all_56_4) = v0 & % 19.82/3.58 | identity_as_relation_of(all_56_3) = v0 & $i(v0)) % 19.82/3.58 | % 19.82/3.58 | GROUND_INST: instantiating (4) with all_56_4, all_56_3, simplifying with (13), % 19.82/3.58 | (14), (18) gives: % 19.82/3.58 | (24) ? [v0: $i] : (identity_on_carrier(all_56_4) = v0 & $i(v0) & % 19.82/3.58 | relation_of2_as_subset(v0, all_56_3, all_56_3) & quasi_total(v0, % 19.82/3.58 | all_56_3, all_56_3) & function(v0)) % 19.82/3.58 | % 19.82/3.58 | DELTA: instantiating (23) with fresh symbol all_68_0 gives: % 19.82/3.58 | (25) identity_on_carrier(all_56_4) = all_68_0 & % 19.82/3.58 | identity_as_relation_of(all_56_3) = all_68_0 & $i(all_68_0) % 19.82/3.58 | % 19.82/3.58 | ALPHA: (25) implies: % 19.82/3.58 | (26) $i(all_68_0) % 19.82/3.58 | (27) identity_as_relation_of(all_56_3) = all_68_0 % 19.82/3.58 | (28) identity_on_carrier(all_56_4) = all_68_0 % 19.82/3.58 | % 19.82/3.58 | DELTA: instantiating (22) with fresh symbol all_70_0 gives: % 19.82/3.58 | (29) the_carrier(all_56_4) = all_70_0 & $i(all_70_0) & % 19.82/3.58 | relation_of2_as_subset(all_56_2, all_70_0, all_70_0) & % 19.82/3.58 | quasi_total(all_56_2, all_70_0, all_70_0) % 19.82/3.58 | % 19.82/3.58 | ALPHA: (29) implies: % 19.82/3.58 | (30) quasi_total(all_56_2, all_70_0, all_70_0) % 19.82/3.58 | (31) relation_of2_as_subset(all_56_2, all_70_0, all_70_0) % 19.82/3.58 | (32) $i(all_70_0) % 19.82/3.58 | (33) the_carrier(all_56_4) = all_70_0 % 19.82/3.58 | % 19.82/3.58 | DELTA: instantiating (21) with fresh symbol all_72_0 gives: % 19.82/3.58 | (34) the_carrier(all_56_4) = all_72_0 & identity_as_relation_of(all_72_0) = % 19.82/3.58 | all_56_2 & $i(all_72_0) & $i(all_56_2) % 19.82/3.58 | % 19.82/3.58 | ALPHA: (34) implies: % 19.82/3.58 | (35) the_carrier(all_56_4) = all_72_0 % 19.82/3.58 | % 19.82/3.58 | DELTA: instantiating (24) with fresh symbol all_74_0 gives: % 19.82/3.59 | (36) identity_on_carrier(all_56_4) = all_74_0 & $i(all_74_0) & % 19.82/3.59 | relation_of2_as_subset(all_74_0, all_56_3, all_56_3) & % 19.82/3.59 | quasi_total(all_74_0, all_56_3, all_56_3) & function(all_74_0) % 19.82/3.59 | % 19.82/3.59 | ALPHA: (36) implies: % 19.82/3.59 | (37) function(all_74_0) % 19.82/3.59 | (38) identity_on_carrier(all_56_4) = all_74_0 % 19.82/3.59 | % 19.82/3.59 | GROUND_INST: instantiating (7) with all_56_2, all_74_0, all_56_4, simplifying % 19.82/3.59 | with (17), (38) gives: % 19.82/3.59 | (39) all_74_0 = all_56_2 % 19.82/3.59 | % 19.82/3.59 | GROUND_INST: instantiating (7) with all_68_0, all_74_0, all_56_4, simplifying % 19.82/3.59 | with (28), (38) gives: % 19.82/3.59 | (40) all_74_0 = all_68_0 % 19.82/3.59 | % 19.82/3.59 | GROUND_INST: instantiating (8) with all_56_3, all_72_0, all_56_4, simplifying % 19.82/3.59 | with (18), (35) gives: % 19.82/3.59 | (41) all_72_0 = all_56_3 % 19.82/3.59 | % 19.82/3.59 | GROUND_INST: instantiating (8) with all_70_0, all_72_0, all_56_4, simplifying % 19.82/3.59 | with (33), (35) gives: % 19.82/3.59 | (42) all_72_0 = all_70_0 % 19.82/3.59 | % 19.82/3.59 | COMBINE_EQS: (39), (40) imply: % 19.82/3.59 | (43) all_68_0 = all_56_2 % 19.82/3.59 | % 19.82/3.59 | COMBINE_EQS: (41), (42) imply: % 19.82/3.59 | (44) all_70_0 = all_56_3 % 19.82/3.59 | % 19.82/3.59 | REDUCE: (27), (43) imply: % 19.82/3.59 | (45) identity_as_relation_of(all_56_3) = all_56_2 % 19.82/3.59 | % 19.82/3.59 | REDUCE: (26), (43) imply: % 19.82/3.59 | (46) $i(all_56_2) % 19.82/3.59 | % 19.82/3.59 | REDUCE: (31), (44) imply: % 19.82/3.59 | (47) relation_of2_as_subset(all_56_2, all_56_3, all_56_3) % 19.82/3.59 | % 19.82/3.59 | REDUCE: (30), (44) imply: % 19.82/3.59 | (48) quasi_total(all_56_2, all_56_3, all_56_3) % 19.82/3.59 | % 19.82/3.59 | REDUCE: (37), (39) imply: % 19.82/3.59 | (49) function(all_56_2) % 19.82/3.59 | % 19.82/3.59 | GROUND_INST: instantiating (6) with all_56_3, all_56_3, all_56_2, simplifying % 19.82/3.59 | with (15), (46), (47) gives: % 19.82/3.59 | (50) relation_of2(all_56_2, all_56_3, all_56_3) % 19.82/3.59 | % 19.82/3.59 | GROUND_INST: instantiating (5) with all_56_3, all_56_2, simplifying with (15), % 19.82/3.59 | (45) gives: % 19.82/3.59 | (51) identity_relation(all_56_3) = all_56_2 & $i(all_56_2) % 19.82/3.59 | % 19.82/3.59 | ALPHA: (51) implies: % 19.82/3.59 | (52) identity_relation(all_56_3) = all_56_2 % 19.82/3.59 | % 19.82/3.59 | GROUND_INST: instantiating (redefinition_k8_funct_2) with all_56_3, all_56_3, % 19.82/3.59 | all_56_2, all_56_1, all_56_0, simplifying with (12), (15), (16), % 19.82/3.59 | (19), (46), (48), (49), (50) gives: % 19.82/3.59 | (53) empty(all_56_3) | (apply(all_56_2, all_56_1) = all_56_0 & % 19.82/3.59 | $i(all_56_0)) % 19.82/3.59 | % 19.82/3.59 | GROUND_INST: instantiating (fc1_struct_0) with all_56_4, all_56_3, simplifying % 19.82/3.59 | with (11), (13), (14), (18) gives: % 19.82/3.59 | (54) ~ empty(all_56_3) % 19.82/3.59 | % 19.82/3.59 | BETA: splitting (53) gives: % 19.82/3.59 | % 19.82/3.59 | Case 1: % 19.82/3.59 | | % 19.82/3.59 | | (55) empty(all_56_3) % 19.82/3.59 | | % 19.82/3.59 | | PRED_UNIFY: (54), (55) imply: % 19.82/3.59 | | (56) $false % 19.82/3.59 | | % 19.82/3.59 | | CLOSE: (56) is inconsistent. % 19.82/3.59 | | % 19.82/3.59 | Case 2: % 19.82/3.59 | | % 19.82/3.59 | | (57) apply(all_56_2, all_56_1) = all_56_0 & $i(all_56_0) % 19.82/3.59 | | % 19.82/3.59 | | ALPHA: (57) implies: % 19.82/3.59 | | (58) apply(all_56_2, all_56_1) = all_56_0 % 19.82/3.59 | | % 19.82/3.59 | | BETA: splitting (20) gives: % 19.82/3.59 | | % 19.82/3.59 | | Case 1: % 19.82/3.59 | | | % 19.82/3.59 | | | (59) empty(all_56_3) % 19.82/3.59 | | | % 19.82/3.59 | | | PRED_UNIFY: (54), (59) imply: % 19.82/3.59 | | | (60) $false % 19.82/3.59 | | | % 19.82/3.59 | | | CLOSE: (60) is inconsistent. % 19.82/3.59 | | | % 19.82/3.59 | | Case 2: % 19.82/3.59 | | | % 19.82/3.60 | | | (61) in(all_56_1, all_56_3) % 19.82/3.60 | | | % 19.82/3.60 | | | GROUND_INST: instantiating (t35_funct_1) with all_56_3, all_56_1, % 19.82/3.60 | | | all_56_2, all_56_0, simplifying with (15), (16), (52), (58), % 19.82/3.60 | | | (61) gives: % 19.82/3.60 | | | (62) all_56_0 = all_56_1 % 19.82/3.60 | | | % 19.82/3.60 | | | REDUCE: (10), (62) imply: % 19.82/3.60 | | | (63) $false % 19.82/3.60 | | | % 19.82/3.60 | | | CLOSE: (63) is inconsistent. % 19.82/3.60 | | | % 19.82/3.60 | | End of split % 19.82/3.60 | | % 19.82/3.60 | End of split % 19.82/3.60 | % 19.82/3.60 End of proof % 19.82/3.60 % SZS output end Proof for theBenchmark % 19.82/3.60 % 19.82/3.60 2995ms %------------------------------------------------------------------------------