TSTP Solution File: SEU353+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU353+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.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 : 600s
% DateTime : Tue Jul 19 08:49:07 EDT 2022
% Result : Theorem 4.27s 1.63s
% Output : Proof 6.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SEU353+1 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 11:45:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.58 ____ _
% 0.18/0.58 ___ / __ \_____(_)___ ________ __________
% 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58 Bug reports to peter@backeman.se
% 0.18/0.58
% 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.78/0.95 Prover 0: Preprocessing ...
% 2.72/1.29 Prover 0: Warning: ignoring some quantifiers
% 3.03/1.33 Prover 0: Constructing countermodel ...
% 4.27/1.62 Prover 0: proved (992ms)
% 4.27/1.63
% 4.27/1.63 No countermodel exists, formula is valid
% 4.27/1.63 % SZS status Theorem for theBenchmark
% 4.27/1.63
% 4.27/1.63 Generating proof ... Warning: ignoring some quantifiers
% 5.92/2.05 found it (size 53)
% 5.92/2.05
% 5.92/2.05 % SZS output start Proof for theBenchmark
% 5.92/2.05 Assumed formulas after preprocessing and simplification:
% 5.92/2.05 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v4 = v3) & apply_as_element(v1, v1, v2, v3) = v4 & identity_on_carrier(v0) = v2 & the_carrier(v0) = v1 & one_sorted_str(v9) & one_sorted_str(v5) & one_sorted_str(v0) & empty(v8) & empty(v7) & empty(empty_set) & one_to_one(v8) & element(v3, v1) & relation(v8) & function(v8) & ~ empty_carrier(v5) & ~ empty_carrier(v0) & ~ empty(v6) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v11 = v10 | ~ (apply_as_element(v15, v14, v13, v12) = v11) | ~ (apply_as_element(v15, v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (apply_as_element(v10, v11, v12, v13) = v14) | ~ element(v13, v10) | ~ quasi_total(v12, v10, v11) | ~ function(v12) | ~ relation_of2(v12, v10, v11) | apply(v12, v13) = v14 | empty(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (apply_as_element(v10, v11, v12, v13) = v14) | ~ element(v13, v10) | ~ quasi_total(v12, v10, v11) | ~ function(v12) | ~ relation_of2(v12, v10, v11) | empty(v10) | element(v14, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (apply(v12, v11) = v13) | ~ (identity_relation(v10) = v12) | ~ in(v11, v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (apply(v13, v12) = v11) | ~ (apply(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (cartesian_product2(v13, v12) = v11) | ~ (cartesian_product2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v10, v11) = v13) | ~ relation_of2_as_subset(v12, v10, v11) | ? [v14] : (powerset(v13) = v14 & element(v12, v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ empty(v12) | ~ element(v11, v13) | ~ in(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ element(v11, v13) | ~ in(v10, v11) | element(v10, v12)) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v11, v12) = v13) | relation(v10) | ? [v14] : (powerset(v13) = v14 & ~ element(v10, v14))) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (identity_relation(v12) = v11) | ~ (identity_relation(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (identity_on_carrier(v12) = v11) | ~ (identity_on_carrier(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (the_carrier(v12) = v11) | ~ (the_carrier(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (identity_as_relation_of(v12) = v11) | ~ (identity_as_relation_of(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (powerset(v12) = v11) | ~ (powerset(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (cartesian_product2(v10, v11) = v12) | ~ empty(v12) | empty(v11) | empty(v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ subset(v10, v11) | element(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ element(v10, v12) | subset(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ relation_of2_as_subset(v12, v10, v11) | relation_of2(v12, v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ empty(v12) | ~ quasi_total(v12, v10, v11) | ~ function(v12) | ~ relation_of2(v12, v10, v11) | empty(v11) | empty(v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ onto(v12, v10, v11) | ~ one_to_one(v12) | ~ quasi_total(v12, v10, v11) | ~ function(v12) | ~ relation_of2(v12, v10, v11) | bijective(v12, v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ bijective(v12, v10, v11) | ~ quasi_total(v12, v10, v11) | ~ function(v12) | ~ relation_of2(v12, v10, v11) | onto(v12, v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ bijective(v12, v10, v11) | ~ quasi_total(v12, v10, v11) | ~ function(v12) | ~ relation_of2(v12, v10, v11) | one_to_one(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ quasi_total(v12, v10, v11) | ~ function(v12) | ~ relation_of2(v12, v10, v11) | empty(v11) | empty(v10) | v1_partfun1(v12, v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ quasi_total(v12, v10, v11) | ~ function(v12) | ~ relation_of2(v12, v10, v11) | empty(v11) | v1_partfun1(v12, v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ v1_partfun1(v12, v10, v11) | ~ function(v12) | ~ relation_of2(v12, v10, v11) | quasi_total(v12, v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ relation_of2(v12, v10, v11) | relation_of2_as_subset(v12, v10, v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ empty(v11) | ~ empty(v10)) & ! [v10] : ! [v11] : ( ~ (identity_relation(v10) = v11) | identity_as_relation_of(v10) = v11) & ! [v10] : ! [v11] : ( ~ (identity_relation(v10) = v11) | antisymmetric(v11)) & ! [v10] : ! [v11] : ( ~ (identity_relation(v10) = v11) | reflexive(v11)) & ! [v10] : ! [v11] : ( ~ (identity_relation(v10) = v11) | transitive(v11)) & ! [v10] : ! [v11] : ( ~ (identity_relation(v10) = v11) | symmetric(v11)) & ! [v10] : ! [v11] : ( ~ (identity_relation(v10) = v11) | relation(v11)) & ! [v10] : ! [v11] : ( ~ (identity_relation(v10) = v11) | function(v11)) & ! [v10] : ! [v11] : ( ~ (identity_on_carrier(v10) = v11) | ~ one_sorted_str(v10) | function(v11)) & ! [v10] : ! [v11] : ( ~ (identity_on_carrier(v10) = v11) | ~ one_sorted_str(v10) | ? [v12] : (the_carrier(v10) = v12 & identity_as_relation_of(v12) = v11)) & ! [v10] : ! [v11] : ( ~ (identity_on_carrier(v10) = v11) | ~ one_sorted_str(v10) | ? [v12] : (the_carrier(v10) = v12 & relation_of2_as_subset(v11, v12, v12) & quasi_total(v11, v12, v12))) & ! [v10] : ! [v11] : ( ~ (the_carrier(v10) = v11) | ~ one_sorted_str(v10) | ~ empty(v11) | empty_carrier(v10)) & ! [v10] : ! [v11] : ( ~ (the_carrier(v10) = v11) | ~ one_sorted_str(v10) | empty_carrier(v10) | ? [v12] : ? [v13] : (powerset(v11) = v12 & element(v13, v12) & ~ empty(v13))) & ! [v10] : ! [v11] : ( ~ (the_carrier(v10) = v11) | ~ one_sorted_str(v10) | ? [v12] : (identity_on_carrier(v10) = v12 & identity_as_relation_of(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (the_carrier(v10) = v11) | ~ one_sorted_str(v10) | ? [v12] : (identity_on_carrier(v10) = v12 & relation_of2_as_subset(v12, v11, v11) & quasi_total(v12, v11, v11) & function(v12))) & ! [v10] : ! [v11] : ( ~ (identity_as_relation_of(v10) = v11) | identity_relation(v10) = v11) & ! [v10] : ! [v11] : ( ~ (identity_as_relation_of(v10) = v11) | relation_of2_as_subset(v11, v10, v10)) & ! [v10] : ! [v11] : ( ~ (identity_as_relation_of(v10) = v11) | v1_partfun1(v11, v10, v10)) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ empty(v11)) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | empty(v10) | ? [v12] : (element(v12, v11) & ~ empty(v12))) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ? [v12] : (empty(v12) & element(v12, v11))) & ! [v10] : ! [v11] : ( ~ empty(v11) | ~ in(v10, v11)) & ! [v10] : ! [v11] : ( ~ element(v10, v11) | empty(v11) | in(v10, v11)) & ! [v10] : ! [v11] : ( ~ reflexive(v11) | ~ quasi_total(v11, v10, v10) | ~ v1_partfun1(v11, v10, v10) | ~ function(v11) | ~ relation_of2(v11, v10, v10) | onto(v11, v10, v10)) & ! [v10] : ! [v11] : ( ~ reflexive(v11) | ~ quasi_total(v11, v10, v10) | ~ v1_partfun1(v11, v10, v10) | ~ function(v11) | ~ relation_of2(v11, v10, v10) | one_to_one(v11)) & ! [v10] : ! [v11] : ( ~ reflexive(v11) | ~ quasi_total(v11, v10, v10) | ~ v1_partfun1(v11, v10, v10) | ~ function(v11) | ~ relation_of2(v11, v10, v10) | bijective(v11, v10, v10)) & ! [v10] : ! [v11] : ( ~ in(v11, v10) | ~ in(v10, v11)) & ! [v10] : ! [v11] : ( ~ in(v10, v11) | element(v10, v11)) & ! [v10] : (v10 = empty_set | ~ empty(v10)) & ! [v10] : ( ~ transitive(v10) | ~ symmetric(v10) | ~ relation(v10) | reflexive(v10)) & ? [v10] : ? [v11] : ? [v12] : relation_of2_as_subset(v12, v10, v11) & ? [v10] : ? [v11] : ? [v12] : relation_of2(v12, v10, v11) & ? [v10] : ? [v11] : ? [v12] : (relation(v12) & quasi_total(v12, v10, v11) & function(v12) & relation_of2(v12, v10, v11)) & ? [v10] : ? [v11] : ? [v12] : (relation(v12) & function(v12) & relation_of2(v12, v10, v11)) & ? [v10] : ? [v11] : element(v11, v10) & ? [v10] : ? [v11] : (antisymmetric(v11) & reflexive(v11) & transitive(v11) & symmetric(v11) & relation(v11) & v1_partfun1(v11, v10, v10) & relation_of2(v11, v10, v10)) & ? [v10] : ? [v11] : (onto(v11, v10, v10) & one_to_one(v11) & bijective(v11, v10, v10) & relation(v11) & quasi_total(v11, v10, v10) & function(v11) & relation_of2(v11, v10, v10)) & ? [v10] : subset(v10, v10))
% 6.34/2.10 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields:
% 6.34/2.10 | (1) ~ (all_0_5_5 = all_0_6_6) & apply_as_element(all_0_8_8, all_0_8_8, all_0_7_7, all_0_6_6) = all_0_5_5 & identity_on_carrier(all_0_9_9) = all_0_7_7 & the_carrier(all_0_9_9) = all_0_8_8 & one_sorted_str(all_0_0_0) & one_sorted_str(all_0_4_4) & one_sorted_str(all_0_9_9) & empty(all_0_1_1) & empty(all_0_2_2) & empty(empty_set) & one_to_one(all_0_1_1) & element(all_0_6_6, all_0_8_8) & relation(all_0_1_1) & function(all_0_1_1) & ~ empty_carrier(all_0_4_4) & ~ empty_carrier(all_0_9_9) & ~ empty(all_0_3_3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (apply_as_element(v5, v4, v3, v2) = v1) | ~ (apply_as_element(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply_as_element(v0, v1, v2, v3) = v4) | ~ element(v3, v0) | ~ quasi_total(v2, v0, v1) | ~ function(v2) | ~ relation_of2(v2, v0, v1) | apply(v2, v3) = v4 | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply_as_element(v0, v1, v2, v3) = v4) | ~ element(v3, v0) | ~ quasi_total(v2, v0, v1) | ~ function(v2) | ~ relation_of2(v2, v0, v1) | empty(v0) | element(v4, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (apply(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | ? [v4] : (powerset(v3) = v4 & element(v2, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v1, v2) = v3) | relation(v0) | ? [v4] : (powerset(v3) = v4 & ~ element(v0, v4))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_on_carrier(v2) = v1) | ~ (identity_on_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_as_relation_of(v2) = v1) | ~ (identity_as_relation_of(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ empty(v2) | ~ quasi_total(v2, v0, v1) | ~ function(v2) | ~ relation_of2(v2, v0, v1) | empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ onto(v2, v0, v1) | ~ one_to_one(v2) | ~ quasi_total(v2, v0, v1) | ~ function(v2) | ~ relation_of2(v2, v0, v1) | bijective(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ bijective(v2, v0, v1) | ~ quasi_total(v2, v0, v1) | ~ function(v2) | ~ relation_of2(v2, v0, v1) | onto(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ bijective(v2, v0, v1) | ~ quasi_total(v2, v0, v1) | ~ function(v2) | ~ relation_of2(v2, v0, v1) | one_to_one(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ quasi_total(v2, v0, v1) | ~ function(v2) | ~ relation_of2(v2, v0, v1) | empty(v1) | empty(v0) | v1_partfun1(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ quasi_total(v2, v0, v1) | ~ function(v2) | ~ relation_of2(v2, v0, v1) | empty(v1) | v1_partfun1(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ v1_partfun1(v2, v0, v1) | ~ function(v2) | ~ relation_of2(v2, v0, v1) | quasi_total(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ relation_of2(v2, v0, v1) | relation_of2_as_subset(v2, v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | identity_as_relation_of(v0) = v1) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | antisymmetric(v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | reflexive(v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | transitive(v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | symmetric(v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1)) & ! [v0] : ! [v1] : ( ~ (identity_on_carrier(v0) = v1) | ~ one_sorted_str(v0) | function(v1)) & ! [v0] : ! [v1] : ( ~ (identity_on_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : (the_carrier(v0) = v2 & identity_as_relation_of(v2) = v1)) & ! [v0] : ! [v1] : ( ~ (identity_on_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : (the_carrier(v0) = v2 & relation_of2_as_subset(v1, v2, v2) & quasi_total(v1, v2, v2))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ~ empty(v1) | empty_carrier(v0)) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | empty_carrier(v0) | ? [v2] : ? [v3] : (powerset(v1) = v2 & element(v3, v2) & ~ empty(v3))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : (identity_on_carrier(v0) = v2 & identity_as_relation_of(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : (identity_on_carrier(v0) = v2 & relation_of2_as_subset(v2, v1, v1) & quasi_total(v2, v1, v1) & function(v2))) & ! [v0] : ! [v1] : ( ~ (identity_as_relation_of(v0) = v1) | identity_relation(v0) = v1) & ! [v0] : ! [v1] : ( ~ (identity_as_relation_of(v0) = v1) | relation_of2_as_subset(v1, v0, v0)) & ! [v0] : ! [v1] : ( ~ (identity_as_relation_of(v0) = v1) | v1_partfun1(v1, v0, v0)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ reflexive(v1) | ~ quasi_total(v1, v0, v0) | ~ v1_partfun1(v1, v0, v0) | ~ function(v1) | ~ relation_of2(v1, v0, v0) | onto(v1, v0, v0)) & ! [v0] : ! [v1] : ( ~ reflexive(v1) | ~ quasi_total(v1, v0, v0) | ~ v1_partfun1(v1, v0, v0) | ~ function(v1) | ~ relation_of2(v1, v0, v0) | one_to_one(v1)) & ! [v0] : ! [v1] : ( ~ reflexive(v1) | ~ quasi_total(v1, v0, v0) | ~ v1_partfun1(v1, v0, v0) | ~ function(v1) | ~ relation_of2(v1, v0, v0) | bijective(v1, v0, v0)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ transitive(v0) | ~ symmetric(v0) | ~ relation(v0) | reflexive(v0)) & ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) & ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) & ? [v0] : ? [v1] : ? [v2] : (relation(v2) & quasi_total(v2, v0, v1) & function(v2) & relation_of2(v2, v0, v1)) & ? [v0] : ? [v1] : ? [v2] : (relation(v2) & function(v2) & relation_of2(v2, v0, v1)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : ? [v1] : (antisymmetric(v1) & reflexive(v1) & transitive(v1) & symmetric(v1) & relation(v1) & v1_partfun1(v1, v0, v0) & relation_of2(v1, v0, v0)) & ? [v0] : ? [v1] : (onto(v1, v0, v0) & one_to_one(v1) & bijective(v1, v0, v0) & relation(v1) & quasi_total(v1, v0, v0) & function(v1) & relation_of2(v1, v0, v0)) & ? [v0] : subset(v0, v0)
% 6.49/2.12 |
% 6.49/2.12 | Applying alpha-rule on (1) yields:
% 6.49/2.12 | (2) ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1)
% 6.49/2.12 | (3) the_carrier(all_0_9_9) = all_0_8_8
% 6.49/2.12 | (4) ? [v0] : ? [v1] : (onto(v1, v0, v0) & one_to_one(v1) & bijective(v1, v0, v0) & relation(v1) & quasi_total(v1, v0, v0) & function(v1) & relation_of2(v1, v0, v0))
% 6.49/2.12 | (5) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1))
% 6.49/2.12 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_as_relation_of(v2) = v1) | ~ (identity_as_relation_of(v2) = v0))
% 6.49/2.12 | (7) relation(all_0_1_1)
% 6.49/2.12 | (8) one_sorted_str(all_0_4_4)
% 6.49/2.12 | (9) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 6.49/2.12 | (10) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 6.49/2.12 | (11) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 6.49/2.12 | (12) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | empty_carrier(v0) | ? [v2] : ? [v3] : (powerset(v1) = v2 & element(v3, v2) & ~ empty(v3)))
% 6.49/2.12 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ v1_partfun1(v2, v0, v1) | ~ function(v2) | ~ relation_of2(v2, v0, v1) | quasi_total(v2, v0, v1))
% 6.49/2.12 | (14) ! [v0] : ! [v1] : ( ~ (identity_on_carrier(v0) = v1) | ~ one_sorted_str(v0) | function(v1))
% 6.49/2.12 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ empty(v2) | ~ quasi_total(v2, v0, v1) | ~ function(v2) | ~ relation_of2(v2, v0, v1) | empty(v1) | empty(v0))
% 6.49/2.12 | (16) ! [v0] : ! [v1] : ( ~ (identity_on_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : (the_carrier(v0) = v2 & relation_of2_as_subset(v1, v2, v2) & quasi_total(v1, v2, v2)))
% 6.49/2.12 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (apply(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ in(v1, v0))
% 6.49/2.13 | (18) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 6.49/2.13 | (19) element(all_0_6_6, all_0_8_8)
% 6.49/2.13 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ in(v0, v1))
% 6.56/2.13 | (21) ? [v0] : ? [v1] : (antisymmetric(v1) & reflexive(v1) & transitive(v1) & symmetric(v1) & relation(v1) & v1_partfun1(v1, v0, v0) & relation_of2(v1, v0, v0))
% 6.56/2.13 | (22) ? [v0] : subset(v0, v0)
% 6.56/2.13 | (23) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | reflexive(v1))
% 6.56/2.13 | (24) function(all_0_1_1)
% 6.56/2.13 | (25) one_to_one(all_0_1_1)
% 6.56/2.13 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply_as_element(v0, v1, v2, v3) = v4) | ~ element(v3, v0) | ~ quasi_total(v2, v0, v1) | ~ function(v2) | ~ relation_of2(v2, v0, v1) | empty(v0) | element(v4, v1))
% 6.56/2.13 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | ? [v4] : (powerset(v3) = v4 & element(v2, v4)))
% 6.56/2.13 | (28) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1))
% 6.56/2.13 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ quasi_total(v2, v0, v1) | ~ function(v2) | ~ relation_of2(v2, v0, v1) | empty(v1) | empty(v0) | v1_partfun1(v2, v0, v1))
% 6.56/2.13 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_of2(v2, v0, v1) | relation_of2_as_subset(v2, v0, v1))
% 6.56/2.13 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(v2, v0, v1))
% 6.56/2.13 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 6.56/2.13 | (33) ! [v0] : ! [v1] : ( ~ reflexive(v1) | ~ quasi_total(v1, v0, v0) | ~ v1_partfun1(v1, v0, v0) | ~ function(v1) | ~ relation_of2(v1, v0, v0) | onto(v1, v0, v0))
% 6.56/2.13 | (34) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 6.56/2.13 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ bijective(v2, v0, v1) | ~ quasi_total(v2, v0, v1) | ~ function(v2) | ~ relation_of2(v2, v0, v1) | onto(v2, v0, v1))
% 6.56/2.13 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ onto(v2, v0, v1) | ~ one_to_one(v2) | ~ quasi_total(v2, v0, v1) | ~ function(v2) | ~ relation_of2(v2, v0, v1) | bijective(v2, v0, v1))
% 6.56/2.13 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ quasi_total(v2, v0, v1) | ~ function(v2) | ~ relation_of2(v2, v0, v1) | empty(v1) | v1_partfun1(v2, v0, v1))
% 6.56/2.13 | (38) ! [v0] : ! [v1] : ( ~ reflexive(v1) | ~ quasi_total(v1, v0, v0) | ~ v1_partfun1(v1, v0, v0) | ~ function(v1) | ~ relation_of2(v1, v0, v0) | bijective(v1, v0, v0))
% 6.56/2.13 | (39) empty(empty_set)
% 6.56/2.13 | (40) ! [v0] : ! [v1] : ( ~ (identity_as_relation_of(v0) = v1) | v1_partfun1(v1, v0, v0))
% 6.56/2.13 | (41) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | antisymmetric(v1))
% 6.56/2.13 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 6.56/2.13 | (43) ! [v0] : ! [v1] : ( ~ reflexive(v1) | ~ quasi_total(v1, v0, v0) | ~ v1_partfun1(v1, v0, v0) | ~ function(v1) | ~ relation_of2(v1, v0, v0) | one_to_one(v1))
% 6.56/2.13 | (44) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | transitive(v1))
% 6.56/2.13 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (apply_as_element(v5, v4, v3, v2) = v1) | ~ (apply_as_element(v5, v4, v3, v2) = v0))
% 6.56/2.13 | (46) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 6.56/2.13 | (47) ~ (all_0_5_5 = all_0_6_6)
% 6.56/2.13 | (48) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : (identity_on_carrier(v0) = v2 & relation_of2_as_subset(v2, v1, v1) & quasi_total(v2, v1, v1) & function(v2)))
% 6.56/2.14 | (49) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : (identity_on_carrier(v0) = v2 & identity_as_relation_of(v1) = v2))
% 6.56/2.14 | (50) ! [v0] : ! [v1] : ( ~ (identity_on_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : (the_carrier(v0) = v2 & identity_as_relation_of(v2) = v1))
% 6.56/2.14 | (51) empty(all_0_2_2)
% 6.56/2.14 | (52) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 6.56/2.14 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_on_carrier(v2) = v1) | ~ (identity_on_carrier(v2) = v0))
% 6.56/2.14 | (54) ~ empty(all_0_3_3)
% 6.56/2.14 | (55) ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1)
% 6.56/2.14 | (56) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ~ empty(v1) | empty_carrier(v0))
% 6.56/2.14 | (57) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 6.56/2.14 | (58) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1)))
% 6.56/2.14 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply_as_element(v0, v1, v2, v3) = v4) | ~ element(v3, v0) | ~ quasi_total(v2, v0, v1) | ~ function(v2) | ~ relation_of2(v2, v0, v1) | apply(v2, v3) = v4 | empty(v0))
% 6.56/2.14 | (60) empty(all_0_1_1)
% 6.56/2.14 | (61) apply_as_element(all_0_8_8, all_0_8_8, all_0_7_7, all_0_6_6) = all_0_5_5
% 6.56/2.14 | (62) ? [v0] : ? [v1] : ? [v2] : (relation(v2) & function(v2) & relation_of2(v2, v0, v1))
% 6.56/2.14 | (63) ! [v0] : ( ~ transitive(v0) | ~ symmetric(v0) | ~ relation(v0) | reflexive(v0))
% 6.56/2.14 | (64) ! [v0] : ! [v1] : ( ~ (identity_as_relation_of(v0) = v1) | identity_relation(v0) = v1)
% 6.56/2.14 | (65) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | identity_as_relation_of(v0) = v1)
% 6.56/2.14 | (66) identity_on_carrier(all_0_9_9) = all_0_7_7
% 6.56/2.14 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ bijective(v2, v0, v1) | ~ quasi_total(v2, v0, v1) | ~ function(v2) | ~ relation_of2(v2, v0, v1) | one_to_one(v2))
% 6.56/2.14 | (68) ? [v0] : ? [v1] : ? [v2] : (relation(v2) & quasi_total(v2, v0, v1) & function(v2) & relation_of2(v2, v0, v1))
% 6.56/2.14 | (69) ~ empty_carrier(all_0_9_9)
% 6.56/2.14 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 6.56/2.14 | (71) one_sorted_str(all_0_9_9)
% 6.56/2.14 | (72) ! [v0] : ! [v1] : ( ~ (identity_as_relation_of(v0) = v1) | relation_of2_as_subset(v1, v0, v0))
% 6.56/2.14 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0))
% 6.56/2.14 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 6.56/2.14 | (75) ? [v0] : ? [v1] : element(v1, v0)
% 6.56/2.14 | (76) ~ empty_carrier(all_0_4_4)
% 6.56/2.14 | (77) one_sorted_str(all_0_0_0)
% 6.56/2.14 | (78) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 6.56/2.14 | (79) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v1, v2) = v3) | relation(v0) | ? [v4] : (powerset(v3) = v4 & ~ element(v0, v4)))
% 6.56/2.14 | (80) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 6.56/2.14 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 6.56/2.14 | (82) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 6.56/2.14 | (83) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | symmetric(v1))
% 6.56/2.14 |
% 6.56/2.15 | Instantiating formula (50) with all_0_7_7, all_0_9_9 and discharging atoms identity_on_carrier(all_0_9_9) = all_0_7_7, one_sorted_str(all_0_9_9), yields:
% 6.56/2.15 | (84) ? [v0] : (the_carrier(all_0_9_9) = v0 & identity_as_relation_of(v0) = all_0_7_7)
% 6.56/2.15 |
% 6.56/2.15 | Instantiating formula (16) with all_0_7_7, all_0_9_9 and discharging atoms identity_on_carrier(all_0_9_9) = all_0_7_7, one_sorted_str(all_0_9_9), yields:
% 6.56/2.15 | (85) ? [v0] : (the_carrier(all_0_9_9) = v0 & relation_of2_as_subset(all_0_7_7, v0, v0) & quasi_total(all_0_7_7, v0, v0))
% 6.56/2.15 |
% 6.56/2.15 | Instantiating formula (12) with all_0_8_8, all_0_9_9 and discharging atoms the_carrier(all_0_9_9) = all_0_8_8, one_sorted_str(all_0_9_9), ~ empty_carrier(all_0_9_9), yields:
% 6.56/2.15 | (86) ? [v0] : ? [v1] : (powerset(all_0_8_8) = v0 & element(v1, v0) & ~ empty(v1))
% 6.56/2.15 |
% 6.56/2.15 | Instantiating formula (49) with all_0_8_8, all_0_9_9 and discharging atoms the_carrier(all_0_9_9) = all_0_8_8, one_sorted_str(all_0_9_9), yields:
% 6.56/2.15 | (87) ? [v0] : (identity_on_carrier(all_0_9_9) = v0 & identity_as_relation_of(all_0_8_8) = v0)
% 6.56/2.15 |
% 6.56/2.15 | Instantiating formula (48) with all_0_8_8, all_0_9_9 and discharging atoms the_carrier(all_0_9_9) = all_0_8_8, one_sorted_str(all_0_9_9), yields:
% 6.56/2.15 | (88) ? [v0] : (identity_on_carrier(all_0_9_9) = v0 & relation_of2_as_subset(v0, all_0_8_8, all_0_8_8) & quasi_total(v0, all_0_8_8, all_0_8_8) & function(v0))
% 6.56/2.15 |
% 6.56/2.15 | Instantiating formula (46) with all_0_8_8, all_0_6_6 and discharging atoms element(all_0_6_6, all_0_8_8), yields:
% 6.56/2.15 | (89) empty(all_0_8_8) | in(all_0_6_6, all_0_8_8)
% 6.56/2.15 |
% 6.56/2.15 | Instantiating (88) with all_31_0_30 yields:
% 6.56/2.15 | (90) identity_on_carrier(all_0_9_9) = all_31_0_30 & relation_of2_as_subset(all_31_0_30, all_0_8_8, all_0_8_8) & quasi_total(all_31_0_30, all_0_8_8, all_0_8_8) & function(all_31_0_30)
% 6.56/2.15 |
% 6.56/2.15 | Applying alpha-rule on (90) yields:
% 6.56/2.15 | (91) identity_on_carrier(all_0_9_9) = all_31_0_30
% 6.56/2.15 | (92) relation_of2_as_subset(all_31_0_30, all_0_8_8, all_0_8_8)
% 6.56/2.15 | (93) quasi_total(all_31_0_30, all_0_8_8, all_0_8_8)
% 6.56/2.15 | (94) function(all_31_0_30)
% 6.56/2.15 |
% 6.56/2.15 | Instantiating (87) with all_33_0_31 yields:
% 6.56/2.15 | (95) identity_on_carrier(all_0_9_9) = all_33_0_31 & identity_as_relation_of(all_0_8_8) = all_33_0_31
% 6.56/2.15 |
% 6.56/2.15 | Applying alpha-rule on (95) yields:
% 6.56/2.15 | (96) identity_on_carrier(all_0_9_9) = all_33_0_31
% 6.56/2.15 | (97) identity_as_relation_of(all_0_8_8) = all_33_0_31
% 6.56/2.15 |
% 6.56/2.15 | Instantiating (85) with all_35_0_32 yields:
% 6.56/2.15 | (98) the_carrier(all_0_9_9) = all_35_0_32 & relation_of2_as_subset(all_0_7_7, all_35_0_32, all_35_0_32) & quasi_total(all_0_7_7, all_35_0_32, all_35_0_32)
% 6.56/2.15 |
% 6.56/2.15 | Applying alpha-rule on (98) yields:
% 6.56/2.15 | (99) the_carrier(all_0_9_9) = all_35_0_32
% 6.56/2.15 | (100) relation_of2_as_subset(all_0_7_7, all_35_0_32, all_35_0_32)
% 6.56/2.15 | (101) quasi_total(all_0_7_7, all_35_0_32, all_35_0_32)
% 6.56/2.15 |
% 6.56/2.15 | Instantiating (84) with all_37_0_33 yields:
% 6.56/2.15 | (102) the_carrier(all_0_9_9) = all_37_0_33 & identity_as_relation_of(all_37_0_33) = all_0_7_7
% 6.56/2.15 |
% 6.56/2.15 | Applying alpha-rule on (102) yields:
% 6.56/2.15 | (103) the_carrier(all_0_9_9) = all_37_0_33
% 6.56/2.15 | (104) identity_as_relation_of(all_37_0_33) = all_0_7_7
% 6.56/2.15 |
% 6.56/2.15 | Instantiating (86) with all_39_0_34, all_39_1_35 yields:
% 6.56/2.15 | (105) powerset(all_0_8_8) = all_39_1_35 & element(all_39_0_34, all_39_1_35) & ~ empty(all_39_0_34)
% 6.56/2.15 |
% 6.56/2.15 | Applying alpha-rule on (105) yields:
% 6.56/2.15 | (106) powerset(all_0_8_8) = all_39_1_35
% 6.56/2.15 | (107) element(all_39_0_34, all_39_1_35)
% 6.56/2.15 | (108) ~ empty(all_39_0_34)
% 6.56/2.15 |
% 6.56/2.15 | Instantiating formula (53) with all_0_9_9, all_33_0_31, all_0_7_7 and discharging atoms identity_on_carrier(all_0_9_9) = all_33_0_31, identity_on_carrier(all_0_9_9) = all_0_7_7, yields:
% 6.56/2.15 | (109) all_33_0_31 = all_0_7_7
% 6.56/2.15 |
% 6.56/2.15 | Instantiating formula (53) with all_0_9_9, all_31_0_30, all_33_0_31 and discharging atoms identity_on_carrier(all_0_9_9) = all_33_0_31, identity_on_carrier(all_0_9_9) = all_31_0_30, yields:
% 6.56/2.15 | (110) all_33_0_31 = all_31_0_30
% 6.56/2.15 |
% 6.56/2.15 | Instantiating formula (78) with all_0_9_9, all_37_0_33, all_0_8_8 and discharging atoms the_carrier(all_0_9_9) = all_37_0_33, the_carrier(all_0_9_9) = all_0_8_8, yields:
% 6.56/2.15 | (111) all_37_0_33 = all_0_8_8
% 6.56/2.15 |
% 6.56/2.15 | Instantiating formula (78) with all_0_9_9, all_35_0_32, all_37_0_33 and discharging atoms the_carrier(all_0_9_9) = all_37_0_33, the_carrier(all_0_9_9) = all_35_0_32, yields:
% 6.56/2.15 | (112) all_37_0_33 = all_35_0_32
% 6.56/2.15 |
% 6.56/2.16 | Combining equations (111,112) yields a new equation:
% 6.56/2.16 | (113) all_35_0_32 = all_0_8_8
% 6.56/2.16 |
% 6.56/2.16 | Combining equations (110,109) yields a new equation:
% 6.56/2.16 | (114) all_31_0_30 = all_0_7_7
% 6.56/2.16 |
% 6.56/2.16 | Simplifying 114 yields:
% 6.56/2.16 | (115) all_31_0_30 = all_0_7_7
% 6.56/2.16 |
% 6.56/2.16 | From (113) and (99) follows:
% 6.56/2.16 | (3) the_carrier(all_0_9_9) = all_0_8_8
% 6.56/2.16 |
% 6.56/2.16 | From (109) and (97) follows:
% 6.56/2.16 | (117) identity_as_relation_of(all_0_8_8) = all_0_7_7
% 6.56/2.16 |
% 6.56/2.16 | From (113)(113) and (100) follows:
% 6.56/2.16 | (118) relation_of2_as_subset(all_0_7_7, all_0_8_8, all_0_8_8)
% 6.56/2.16 |
% 6.56/2.16 | From (113)(113) and (101) follows:
% 6.56/2.16 | (119) quasi_total(all_0_7_7, all_0_8_8, all_0_8_8)
% 6.56/2.16 |
% 6.56/2.16 | From (115) and (94) follows:
% 6.56/2.16 | (120) function(all_0_7_7)
% 6.56/2.16 |
% 6.56/2.16 | Instantiating formula (64) with all_0_7_7, all_0_8_8 and discharging atoms identity_as_relation_of(all_0_8_8) = all_0_7_7, yields:
% 6.56/2.16 | (121) identity_relation(all_0_8_8) = all_0_7_7
% 6.56/2.16 |
% 6.56/2.16 | Instantiating formula (9) with all_39_1_35, all_0_8_8 and discharging atoms powerset(all_0_8_8) = all_39_1_35, yields:
% 6.56/2.16 | (122) empty(all_0_8_8) | ? [v0] : (element(v0, all_39_1_35) & ~ empty(v0))
% 6.56/2.16 |
% 6.56/2.16 | Instantiating formula (31) with all_0_7_7, all_0_8_8, all_0_8_8 and discharging atoms relation_of2_as_subset(all_0_7_7, all_0_8_8, all_0_8_8), yields:
% 6.56/2.16 | (123) relation_of2(all_0_7_7, all_0_8_8, all_0_8_8)
% 6.56/2.16 |
% 6.56/2.16 | Instantiating formula (59) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_8_8 and discharging atoms apply_as_element(all_0_8_8, all_0_8_8, all_0_7_7, all_0_6_6) = all_0_5_5, element(all_0_6_6, all_0_8_8), quasi_total(all_0_7_7, all_0_8_8, all_0_8_8), function(all_0_7_7), relation_of2(all_0_7_7, all_0_8_8, all_0_8_8), yields:
% 6.56/2.16 | (124) apply(all_0_7_7, all_0_6_6) = all_0_5_5 | empty(all_0_8_8)
% 6.56/2.16 |
% 6.56/2.16 | Instantiating formula (26) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_8_8 and discharging atoms apply_as_element(all_0_8_8, all_0_8_8, all_0_7_7, all_0_6_6) = all_0_5_5, element(all_0_6_6, all_0_8_8), quasi_total(all_0_7_7, all_0_8_8, all_0_8_8), function(all_0_7_7), relation_of2(all_0_7_7, all_0_8_8, all_0_8_8), yields:
% 6.56/2.16 | (125) empty(all_0_8_8) | element(all_0_5_5, all_0_8_8)
% 6.56/2.16 |
% 6.56/2.16 +-Applying beta-rule and splitting (89), into two cases.
% 6.56/2.16 |-Branch one:
% 6.56/2.16 | (126) empty(all_0_8_8)
% 6.56/2.16 |
% 6.56/2.16 | Instantiating formula (80) with all_0_8_8 and discharging atoms empty(all_0_8_8), yields:
% 6.56/2.16 | (127) all_0_8_8 = empty_set
% 6.56/2.16 |
% 6.56/2.16 | From (127) and (3) follows:
% 6.56/2.16 | (128) the_carrier(all_0_9_9) = empty_set
% 6.56/2.16 |
% 6.56/2.16 | From (127) and (126) follows:
% 6.56/2.16 | (39) empty(empty_set)
% 6.56/2.16 |
% 6.56/2.16 | Instantiating formula (56) with empty_set, all_0_9_9 and discharging atoms the_carrier(all_0_9_9) = empty_set, one_sorted_str(all_0_9_9), empty(empty_set), ~ empty_carrier(all_0_9_9), yields:
% 6.56/2.16 | (130) $false
% 6.56/2.16 |
% 6.56/2.16 |-The branch is then unsatisfiable
% 6.56/2.16 |-Branch two:
% 6.56/2.16 | (131) ~ empty(all_0_8_8)
% 6.56/2.16 | (132) in(all_0_6_6, all_0_8_8)
% 6.56/2.16 |
% 6.56/2.16 +-Applying beta-rule and splitting (125), into two cases.
% 6.56/2.16 |-Branch one:
% 6.56/2.16 | (126) empty(all_0_8_8)
% 6.56/2.16 |
% 6.56/2.16 | Using (126) and (131) yields:
% 6.56/2.16 | (130) $false
% 6.56/2.16 |
% 6.56/2.16 |-The branch is then unsatisfiable
% 6.56/2.16 |-Branch two:
% 6.56/2.16 | (131) ~ empty(all_0_8_8)
% 6.56/2.16 | (136) element(all_0_5_5, all_0_8_8)
% 6.56/2.16 |
% 6.56/2.16 +-Applying beta-rule and splitting (122), into two cases.
% 6.56/2.16 |-Branch one:
% 6.56/2.16 | (126) empty(all_0_8_8)
% 6.56/2.16 |
% 6.56/2.16 | Using (126) and (131) yields:
% 6.56/2.16 | (130) $false
% 6.56/2.16 |
% 6.56/2.16 |-The branch is then unsatisfiable
% 6.56/2.16 |-Branch two:
% 6.56/2.16 | (131) ~ empty(all_0_8_8)
% 6.56/2.16 | (140) ? [v0] : (element(v0, all_39_1_35) & ~ empty(v0))
% 6.56/2.16 |
% 6.56/2.16 +-Applying beta-rule and splitting (124), into two cases.
% 6.56/2.16 |-Branch one:
% 6.56/2.16 | (126) empty(all_0_8_8)
% 6.56/2.16 |
% 6.56/2.16 | Using (126) and (131) yields:
% 6.56/2.16 | (130) $false
% 6.56/2.16 |
% 6.56/2.16 |-The branch is then unsatisfiable
% 6.56/2.16 |-Branch two:
% 6.56/2.16 | (131) ~ empty(all_0_8_8)
% 6.56/2.16 | (144) apply(all_0_7_7, all_0_6_6) = all_0_5_5
% 6.56/2.16 |
% 6.56/2.16 | Instantiating formula (17) with all_0_5_5, all_0_7_7, all_0_6_6, all_0_8_8 and discharging atoms apply(all_0_7_7, all_0_6_6) = all_0_5_5, identity_relation(all_0_8_8) = all_0_7_7, in(all_0_6_6, all_0_8_8), yields:
% 6.56/2.16 | (145) all_0_5_5 = all_0_6_6
% 6.56/2.16 |
% 6.56/2.16 | Equations (145) can reduce 47 to:
% 6.56/2.16 | (146) $false
% 6.56/2.16 |
% 6.56/2.16 |-The branch is then unsatisfiable
% 6.56/2.16 % SZS output end Proof for theBenchmark
% 6.56/2.16
% 6.56/2.16 1570ms
%------------------------------------------------------------------------------