TSTP Solution File: SEU012+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU012+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 08:46:11 EDT 2022
% Result : Theorem 3.76s 1.50s
% Output : Proof 7.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU012+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jun 19 19:53:39 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.50/0.57 ____ _
% 0.50/0.57 ___ / __ \_____(_)___ ________ __________
% 0.50/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.57
% 0.50/0.57 A Theorem Prover for First-Order Logic
% 0.50/0.58 (ePrincess v.1.0)
% 0.50/0.58
% 0.50/0.58 (c) Philipp Rümmer, 2009-2015
% 0.50/0.58 (c) Peter Backeman, 2014-2015
% 0.50/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.58 Bug reports to peter@backeman.se
% 0.50/0.58
% 0.50/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.58
% 0.50/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.50/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.66/0.95 Prover 0: Preprocessing ...
% 2.34/1.25 Prover 0: Warning: ignoring some quantifiers
% 2.77/1.27 Prover 0: Constructing countermodel ...
% 3.76/1.50 Prover 0: proved (872ms)
% 3.76/1.50
% 3.76/1.50 No countermodel exists, formula is valid
% 3.76/1.50 % SZS status Theorem for theBenchmark
% 3.76/1.50
% 3.76/1.50 Generating proof ... Warning: ignoring some quantifiers
% 7.17/2.23 found it (size 26)
% 7.17/2.23
% 7.17/2.23 % SZS output start Proof for theBenchmark
% 7.17/2.23 Assumed formulas after preprocessing and simplification:
% 7.17/2.23 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v3 = v2) & identity_relation(v1) = v3 & relation_composition(v0, v2) = v0 & relation_rng(v0) = v1 & relation_dom(v2) = v1 & relation_empty_yielding(v4) & relation_empty_yielding(empty_set) & relation(v9) & relation(v8) & relation(v6) & relation(v4) & relation(v2) & relation(v0) & relation(empty_set) & function(v9) & function(v2) & function(v0) & empty(v8) & empty(v7) & empty(empty_set) & ~ empty(v6) & ~ empty(v5) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (identity_relation(v10) = v11) | ~ (relation_dom(v11) = v12) | ~ (apply(v11, v13) = v14) | ~ relation(v11) | ~ function(v11) | ~ in(v13, v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (relation_composition(v13, v12) = v11) | ~ (relation_composition(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (apply(v13, v12) = v11) | ~ (apply(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ element(v11, v13) | ~ empty(v12) | ~ in(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ element(v11, v13) | ~ in(v10, v11) | element(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (identity_relation(v10) = v12) | ~ (relation_dom(v11) = v10) | ~ relation(v11) | ~ function(v11) | ? [v13] : ? [v14] : ( ~ (v14 = v13) & apply(v11, v13) = v14 & in(v13, v10))) & ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (identity_relation(v10) = v11) | ~ (relation_dom(v11) = v12) | ~ relation(v11) | ~ function(v11)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (powerset(v12) = v11) | ~ (powerset(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (identity_relation(v12) = v11) | ~ (identity_relation(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_rng(v12) = v11) | ~ (relation_rng(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_dom(v12) = v11) | ~ (relation_dom(v12) = 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_composition(v11, v10) = v12) | ~ relation(v11) | ~ empty(v10) | relation(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_composition(v11, v10) = v12) | ~ relation(v11) | ~ empty(v10) | empty(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_composition(v10, v11) = v12) | ~ relation(v11) | ~ relation(v10) | ~ function(v11) | ~ function(v10) | relation(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_composition(v10, v11) = v12) | ~ relation(v11) | ~ relation(v10) | ~ function(v11) | ~ function(v10) | function(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_composition(v10, v11) = v12) | ~ relation(v11) | ~ relation(v10) | relation(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_composition(v10, v11) = v12) | ~ relation(v11) | ~ empty(v10) | relation(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_composition(v10, v11) = v12) | ~ relation(v11) | ~ empty(v10) | empty(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (apply(v11, v10) = v12) | ~ relation(v11) | ~ function(v11) | ? [v13] : (relation_dom(v11) = v13 & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v11, v14) = v15) | ~ (apply(v15, v10) = v16) | ~ relation(v14) | ~ function(v14) | ~ in(v10, v13) | apply(v14, v12) = v16) & ! [v14] : ! [v15] : ( ~ (apply(v14, v12) = v15) | ~ relation(v14) | ~ function(v14) | ~ in(v10, v13) | ? [v16] : (relation_composition(v11, v14) = v16 & apply(v16, v10) = v15)))) & ! [v10] : ! [v11] : (v11 = v10 | ~ empty(v11) | ~ empty(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] : (element(v12, v11) & empty(v12))) & ! [v10] : ! [v11] : ( ~ (identity_relation(v10) = v11) | relation(v11)) & ! [v10] : ! [v11] : ( ~ (identity_relation(v10) = v11) | function(v11)) & ! [v10] : ! [v11] : ( ~ (relation_rng(v10) = v11) | ~ relation(v10) | ~ function(v10) | ? [v12] : (relation_dom(v10) = v12 & ! [v13] : ! [v14] : ( ~ (apply(v10, v14) = v13) | ~ in(v14, v12) | in(v13, v11)) & ! [v13] : ( ~ in(v13, v11) | ? [v14] : (apply(v10, v14) = v13 & in(v14, v12))) & ? [v13] : (v13 = v11 | ? [v14] : ? [v15] : ? [v16] : (( ~ in(v14, v13) | ! [v17] : ( ~ (apply(v10, v17) = v14) | ~ in(v17, v12))) & (in(v14, v13) | (v16 = v14 & apply(v10, v15) = v14 & in(v15, v12))))))) & ! [v10] : ! [v11] : ( ~ (relation_rng(v10) = v11) | ~ relation(v10) | ~ empty(v11) | empty(v10)) & ! [v10] : ! [v11] : ( ~ (relation_rng(v10) = v11) | ~ empty(v10) | relation(v11)) & ! [v10] : ! [v11] : ( ~ (relation_rng(v10) = v11) | ~ empty(v10) | empty(v11)) & ! [v10] : ! [v11] : ( ~ (relation_dom(v10) = v11) | ~ relation(v10) | ~ function(v10) | ? [v12] : (relation_rng(v10) = v12 & ! [v13] : ! [v14] : ( ~ (apply(v10, v14) = v13) | ~ in(v14, v11) | in(v13, v12)) & ! [v13] : ( ~ in(v13, v12) | ? [v14] : (apply(v10, v14) = v13 & in(v14, v11))) & ? [v13] : (v13 = v12 | ? [v14] : ? [v15] : ? [v16] : (( ~ in(v14, v13) | ! [v17] : ( ~ (apply(v10, v17) = v14) | ~ in(v17, v11))) & (in(v14, v13) | (v16 = v14 & apply(v10, v15) = v14 & in(v15, v11))))))) & ! [v10] : ! [v11] : ( ~ (relation_dom(v10) = v11) | ~ relation(v10) | ~ empty(v11) | empty(v10)) & ! [v10] : ! [v11] : ( ~ (relation_dom(v10) = v11) | ~ empty(v10) | relation(v11)) & ! [v10] : ! [v11] : ( ~ (relation_dom(v10) = v11) | ~ empty(v10) | empty(v11)) & ! [v10] : ! [v11] : ( ~ element(v10, v11) | empty(v11) | in(v10, v11)) & ! [v10] : ! [v11] : ( ~ empty(v11) | ~ in(v10, v11)) & ! [v10] : ! [v11] : ( ~ in(v11, v10) | ~ in(v10, v11)) & ! [v10] : ! [v11] : ( ~ in(v10, v11) | element(v10, v11)) & ! [v10] : (v10 = empty_set | ~ empty(v10)) & ! [v10] : ( ~ empty(v10) | relation(v10)) & ! [v10] : ( ~ empty(v10) | function(v10)) & ? [v10] : ? [v11] : element(v11, v10) & ? [v10] : subset(v10, v10))
% 7.29/2.27 | 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:
% 7.29/2.27 | (1) ~ (all_0_6_6 = all_0_7_7) & identity_relation(all_0_8_8) = all_0_6_6 & relation_composition(all_0_9_9, all_0_7_7) = all_0_9_9 & relation_rng(all_0_9_9) = all_0_8_8 & relation_dom(all_0_7_7) = all_0_8_8 & relation_empty_yielding(all_0_5_5) & relation_empty_yielding(empty_set) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_3_3) & relation(all_0_5_5) & relation(all_0_7_7) & relation(all_0_9_9) & relation(empty_set) & function(all_0_0_0) & function(all_0_7_7) & function(all_0_9_9) & empty(all_0_1_1) & empty(all_0_2_2) & empty(empty_set) & ~ empty(all_0_3_3) & ~ empty(all_0_4_4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (identity_relation(v0) = v1) | ~ (relation_dom(v1) = v2) | ~ (apply(v1, v3) = v4) | ~ relation(v1) | ~ function(v1) | ~ in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (identity_relation(v0) = v2) | ~ (relation_dom(v1) = v0) | ~ relation(v1) | ~ function(v1) | ? [v3] : ? [v4] : ( ~ (v4 = v3) & apply(v1, v3) = v4 & in(v3, v0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (identity_relation(v0) = v1) | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ~ function(v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = 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_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v1, v0) = v2) | ~ relation(v1) | ~ function(v1) | ? [v3] : (relation_dom(v1) = v3 & ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v1, v4) = v5) | ~ (apply(v5, v0) = v6) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | apply(v4, v2) = v6) & ! [v4] : ! [v5] : ( ~ (apply(v4, v2) = v5) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | ? [v6] : (relation_composition(v1, v4) = v6 & apply(v6, v0) = v5)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(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] : (element(v2, v1) & empty(v2))) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v2) | in(v3, v1)) & ! [v3] : ( ~ in(v3, v1) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v2))) & ? [v3] : (v3 = v1 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v2))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2))))))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v1) | in(v3, v2)) & ! [v3] : ( ~ in(v3, v2) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v1))) & ? [v3] : (v3 = v2 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v1))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v1))))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0)
% 7.29/2.29 |
% 7.29/2.29 | Applying alpha-rule on (1) yields:
% 7.29/2.29 | (2) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1))
% 7.29/2.29 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v1, v0) = v2) | ~ relation(v1) | ~ function(v1) | ? [v3] : (relation_dom(v1) = v3 & ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v1, v4) = v5) | ~ (apply(v5, v0) = v6) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | apply(v4, v2) = v6) & ! [v4] : ! [v5] : ( ~ (apply(v4, v2) = v5) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | ? [v6] : (relation_composition(v1, v4) = v6 & apply(v6, v0) = v5))))
% 7.29/2.29 | (4) relation_dom(all_0_7_7) = all_0_8_8
% 7.29/2.29 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 7.29/2.29 | (6) relation_rng(all_0_9_9) = all_0_8_8
% 7.29/2.29 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (identity_relation(v0) = v1) | ~ (relation_dom(v1) = v2) | ~ (apply(v1, v3) = v4) | ~ relation(v1) | ~ function(v1) | ~ in(v3, v0))
% 7.29/2.29 | (8) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 7.29/2.29 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0))
% 7.29/2.29 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 7.29/2.29 | (11) function(all_0_0_0)
% 7.29/2.29 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 7.29/2.29 | (13) ! [v0] : ( ~ empty(v0) | function(v0))
% 7.29/2.29 | (14) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2)))
% 7.29/2.29 | (15) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1))
% 7.29/2.29 | (16) relation_empty_yielding(empty_set)
% 7.29/2.29 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 7.29/2.29 | (18) relation(empty_set)
% 7.29/2.29 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 7.29/2.29 | (20) ! [v0] : ( ~ empty(v0) | relation(v0))
% 7.29/2.29 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (identity_relation(v0) = v2) | ~ (relation_dom(v1) = v0) | ~ relation(v1) | ~ function(v1) | ? [v3] : ? [v4] : ( ~ (v4 = v3) & apply(v1, v3) = v4 & in(v3, v0)))
% 7.29/2.29 | (22) relation_empty_yielding(all_0_5_5)
% 7.29/2.29 | (23) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 7.29/2.29 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 7.29/2.29 | (25) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v1) | in(v3, v2)) & ! [v3] : ( ~ in(v3, v2) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v1))) & ? [v3] : (v3 = v2 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v1))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v1)))))))
% 7.29/2.29 | (26) ~ empty(all_0_4_4)
% 7.29/2.29 | (27) relation(all_0_5_5)
% 7.29/2.29 | (28) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1))
% 7.29/2.29 | (29) relation(all_0_1_1)
% 7.29/2.29 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 7.29/2.29 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 7.29/2.29 | (32) ~ (all_0_6_6 = all_0_7_7)
% 7.29/2.30 | (33) ~ empty(all_0_3_3)
% 7.29/2.30 | (34) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 7.29/2.30 | (35) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 7.29/2.30 | (36) empty(all_0_2_2)
% 7.29/2.30 | (37) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1))
% 7.29/2.30 | (38) relation(all_0_0_0)
% 7.29/2.30 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 7.29/2.30 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 7.29/2.30 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 7.29/2.30 | (42) identity_relation(all_0_8_8) = all_0_6_6
% 7.29/2.30 | (43) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 7.29/2.30 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2))
% 7.29/2.30 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 7.29/2.30 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2))
% 7.29/2.30 | (47) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 7.29/2.30 | (48) empty(empty_set)
% 7.29/2.30 | (49) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 7.29/2.30 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 7.29/2.30 | (51) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1))
% 7.29/2.30 | (52) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1))
% 7.29/2.30 | (53) relation(all_0_7_7)
% 7.29/2.30 | (54) relation(all_0_3_3)
% 7.29/2.30 | (55) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 7.29/2.30 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 7.29/2.30 | (57) relation_composition(all_0_9_9, all_0_7_7) = all_0_9_9
% 7.29/2.30 | (58) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v2) | in(v3, v1)) & ! [v3] : ( ~ in(v3, v1) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v2))) & ? [v3] : (v3 = v1 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v2))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2)))))))
% 7.29/2.30 | (59) function(all_0_9_9)
% 7.29/2.30 | (60) relation(all_0_9_9)
% 7.29/2.30 | (61) empty(all_0_1_1)
% 7.29/2.30 | (62) function(all_0_7_7)
% 7.29/2.30 | (63) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 7.29/2.30 | (64) ? [v0] : subset(v0, v0)
% 7.29/2.30 | (65) ? [v0] : ? [v1] : element(v1, v0)
% 7.29/2.30 | (66) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (identity_relation(v0) = v1) | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ~ function(v1))
% 7.29/2.30 | (67) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 7.29/2.30 |
% 7.29/2.30 | Instantiating formula (21) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms identity_relation(all_0_8_8) = all_0_6_6, relation_dom(all_0_7_7) = all_0_8_8, relation(all_0_7_7), function(all_0_7_7), yields:
% 7.29/2.31 | (68) all_0_6_6 = all_0_7_7 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & apply(all_0_7_7, v0) = v1 & in(v0, all_0_8_8))
% 7.29/2.31 |
% 7.29/2.31 | Instantiating formula (58) with all_0_8_8, all_0_9_9 and discharging atoms relation_rng(all_0_9_9) = all_0_8_8, relation(all_0_9_9), function(all_0_9_9), yields:
% 7.29/2.31 | (69) ? [v0] : (relation_dom(all_0_9_9) = v0 & ! [v1] : ! [v2] : ( ~ (apply(all_0_9_9, v2) = v1) | ~ in(v2, v0) | in(v1, all_0_8_8)) & ! [v1] : ( ~ in(v1, all_0_8_8) | ? [v2] : (apply(all_0_9_9, v2) = v1 & in(v2, v0))) & ? [v1] : (v1 = all_0_8_8 | ? [v2] : ? [v3] : ? [v4] : (( ~ in(v2, v1) | ! [v5] : ( ~ (apply(all_0_9_9, v5) = v2) | ~ in(v5, v0))) & (in(v2, v1) | (v4 = v2 & apply(all_0_9_9, v3) = v2 & in(v3, v0))))))
% 7.29/2.31 |
% 7.29/2.31 | Instantiating (69) with all_17_0_13 yields:
% 7.29/2.31 | (70) relation_dom(all_0_9_9) = all_17_0_13 & ! [v0] : ! [v1] : ( ~ (apply(all_0_9_9, v1) = v0) | ~ in(v1, all_17_0_13) | in(v0, all_0_8_8)) & ! [v0] : ( ~ in(v0, all_0_8_8) | ? [v1] : (apply(all_0_9_9, v1) = v0 & in(v1, all_17_0_13))) & ? [v0] : (v0 = all_0_8_8 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_9_9, v4) = v1) | ~ in(v4, all_17_0_13))) & (in(v1, v0) | (v3 = v1 & apply(all_0_9_9, v2) = v1 & in(v2, all_17_0_13)))))
% 7.29/2.31 |
% 7.29/2.31 | Applying alpha-rule on (70) yields:
% 7.29/2.31 | (71) relation_dom(all_0_9_9) = all_17_0_13
% 7.29/2.31 | (72) ! [v0] : ! [v1] : ( ~ (apply(all_0_9_9, v1) = v0) | ~ in(v1, all_17_0_13) | in(v0, all_0_8_8))
% 7.29/2.31 | (73) ! [v0] : ( ~ in(v0, all_0_8_8) | ? [v1] : (apply(all_0_9_9, v1) = v0 & in(v1, all_17_0_13)))
% 7.29/2.31 | (74) ? [v0] : (v0 = all_0_8_8 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_9_9, v4) = v1) | ~ in(v4, all_17_0_13))) & (in(v1, v0) | (v3 = v1 & apply(all_0_9_9, v2) = v1 & in(v2, all_17_0_13)))))
% 7.29/2.31 |
% 7.29/2.31 +-Applying beta-rule and splitting (68), into two cases.
% 7.29/2.31 |-Branch one:
% 7.29/2.31 | (75) all_0_6_6 = all_0_7_7
% 7.29/2.31 |
% 7.29/2.31 | Equations (75) can reduce 32 to:
% 7.29/2.31 | (76) $false
% 7.29/2.31 |
% 7.29/2.31 |-The branch is then unsatisfiable
% 7.29/2.31 |-Branch two:
% 7.29/2.31 | (32) ~ (all_0_6_6 = all_0_7_7)
% 7.29/2.31 | (78) ? [v0] : ? [v1] : ( ~ (v1 = v0) & apply(all_0_7_7, v0) = v1 & in(v0, all_0_8_8))
% 7.29/2.31 |
% 7.29/2.31 | Instantiating (78) with all_29_0_17, all_29_1_18 yields:
% 7.29/2.31 | (79) ~ (all_29_0_17 = all_29_1_18) & apply(all_0_7_7, all_29_1_18) = all_29_0_17 & in(all_29_1_18, all_0_8_8)
% 7.29/2.31 |
% 7.29/2.31 | Applying alpha-rule on (79) yields:
% 7.29/2.31 | (80) ~ (all_29_0_17 = all_29_1_18)
% 7.29/2.31 | (81) apply(all_0_7_7, all_29_1_18) = all_29_0_17
% 7.29/2.31 | (82) in(all_29_1_18, all_0_8_8)
% 7.29/2.31 |
% 7.29/2.31 | Instantiating formula (73) with all_29_1_18 and discharging atoms in(all_29_1_18, all_0_8_8), yields:
% 7.29/2.31 | (83) ? [v0] : (apply(all_0_9_9, v0) = all_29_1_18 & in(v0, all_17_0_13))
% 7.29/2.31 |
% 7.29/2.31 | Instantiating (83) with all_40_0_20 yields:
% 7.29/2.31 | (84) apply(all_0_9_9, all_40_0_20) = all_29_1_18 & in(all_40_0_20, all_17_0_13)
% 7.29/2.31 |
% 7.29/2.31 | Applying alpha-rule on (84) yields:
% 7.29/2.31 | (85) apply(all_0_9_9, all_40_0_20) = all_29_1_18
% 7.29/2.31 | (86) in(all_40_0_20, all_17_0_13)
% 7.29/2.31 |
% 7.29/2.31 | Instantiating formula (3) with all_29_1_18, all_0_9_9, all_40_0_20 and discharging atoms apply(all_0_9_9, all_40_0_20) = all_29_1_18, relation(all_0_9_9), function(all_0_9_9), yields:
% 7.29/2.31 | (87) ? [v0] : (relation_dom(all_0_9_9) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_9_9, v1) = v2) | ~ (apply(v2, all_40_0_20) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_40_0_20, v0) | apply(v1, all_29_1_18) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_29_1_18) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_40_0_20, v0) | ? [v3] : (relation_composition(all_0_9_9, v1) = v3 & apply(v3, all_40_0_20) = v2)))
% 7.29/2.31 |
% 7.29/2.31 | Instantiating (87) with all_60_0_25 yields:
% 7.29/2.31 | (88) relation_dom(all_0_9_9) = all_60_0_25 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_9_9, v0) = v1) | ~ (apply(v1, all_40_0_20) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_40_0_20, all_60_0_25) | apply(v0, all_29_1_18) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_29_1_18) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_40_0_20, all_60_0_25) | ? [v2] : (relation_composition(all_0_9_9, v0) = v2 & apply(v2, all_40_0_20) = v1))
% 7.29/2.31 |
% 7.29/2.31 | Applying alpha-rule on (88) yields:
% 7.29/2.31 | (89) relation_dom(all_0_9_9) = all_60_0_25
% 7.29/2.31 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_9_9, v0) = v1) | ~ (apply(v1, all_40_0_20) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_40_0_20, all_60_0_25) | apply(v0, all_29_1_18) = v2)
% 7.29/2.31 | (91) ! [v0] : ! [v1] : ( ~ (apply(v0, all_29_1_18) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_40_0_20, all_60_0_25) | ? [v2] : (relation_composition(all_0_9_9, v0) = v2 & apply(v2, all_40_0_20) = v1))
% 7.29/2.31 |
% 7.29/2.31 | Instantiating formula (12) with all_0_9_9, all_60_0_25, all_17_0_13 and discharging atoms relation_dom(all_0_9_9) = all_60_0_25, relation_dom(all_0_9_9) = all_17_0_13, yields:
% 7.29/2.31 | (92) all_60_0_25 = all_17_0_13
% 7.29/2.31 |
% 7.29/2.31 | Instantiating formula (90) with all_29_1_18, all_0_9_9, all_0_7_7 and discharging atoms relation_composition(all_0_9_9, all_0_7_7) = all_0_9_9, apply(all_0_9_9, all_40_0_20) = all_29_1_18, relation(all_0_7_7), function(all_0_7_7), yields:
% 7.29/2.31 | (93) ~ in(all_40_0_20, all_60_0_25) | apply(all_0_7_7, all_29_1_18) = all_29_1_18
% 7.29/2.31 |
% 7.29/2.32 +-Applying beta-rule and splitting (93), into two cases.
% 7.29/2.32 |-Branch one:
% 7.29/2.32 | (94) ~ in(all_40_0_20, all_60_0_25)
% 7.29/2.32 |
% 7.29/2.32 | From (92) and (94) follows:
% 7.29/2.32 | (95) ~ in(all_40_0_20, all_17_0_13)
% 7.29/2.32 |
% 7.29/2.32 | Using (86) and (95) yields:
% 7.29/2.32 | (96) $false
% 7.29/2.32 |
% 7.29/2.32 |-The branch is then unsatisfiable
% 7.29/2.32 |-Branch two:
% 7.29/2.32 | (97) in(all_40_0_20, all_60_0_25)
% 7.29/2.32 | (98) apply(all_0_7_7, all_29_1_18) = all_29_1_18
% 7.29/2.32 |
% 7.29/2.32 | Instantiating formula (30) with all_0_7_7, all_29_1_18, all_29_1_18, all_29_0_17 and discharging atoms apply(all_0_7_7, all_29_1_18) = all_29_0_17, apply(all_0_7_7, all_29_1_18) = all_29_1_18, yields:
% 7.29/2.32 | (99) all_29_0_17 = all_29_1_18
% 7.29/2.32 |
% 7.29/2.32 | Equations (99) can reduce 80 to:
% 7.29/2.32 | (76) $false
% 7.29/2.32 |
% 7.29/2.32 |-The branch is then unsatisfiable
% 7.29/2.32 % SZS output end Proof for theBenchmark
% 7.29/2.32
% 7.29/2.32 1732ms
%------------------------------------------------------------------------------