TSTP Solution File: SEU028+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU028+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.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 08:46:16 EDT 2022
% Result : Theorem 4.25s 1.61s
% Output : Proof 6.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU028+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.11 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.32 % Computer : n025.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Mon Jun 20 09:28:29 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.47/0.57 ____ _
% 0.47/0.57 ___ / __ \_____(_)___ ________ __________
% 0.47/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.47/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.47/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.47/0.57
% 0.47/0.57 A Theorem Prover for First-Order Logic
% 0.47/0.57 (ePrincess v.1.0)
% 0.47/0.57
% 0.47/0.57 (c) Philipp Rümmer, 2009-2015
% 0.47/0.57 (c) Peter Backeman, 2014-2015
% 0.47/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.47/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.47/0.57 Bug reports to peter@backeman.se
% 0.47/0.57
% 0.47/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.47/0.57
% 0.47/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.47/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.75/0.97 Prover 0: Preprocessing ...
% 2.72/1.25 Prover 0: Warning: ignoring some quantifiers
% 2.93/1.28 Prover 0: Constructing countermodel ...
% 4.25/1.61 Prover 0: proved (996ms)
% 4.25/1.61
% 4.25/1.61 No countermodel exists, formula is valid
% 4.25/1.61 % SZS status Theorem for theBenchmark
% 4.25/1.61
% 4.25/1.61 Generating proof ... Warning: ignoring some quantifiers
% 5.60/1.90 found it (size 72)
% 5.60/1.90
% 5.60/1.90 % SZS output start Proof for theBenchmark
% 5.60/1.90 Assumed formulas after preprocessing and simplification:
% 5.60/1.90 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (relation_rng(v0) = v6 & relation_dom(v0) = v3 & identity_relation(v6) = v7 & identity_relation(v3) = v4 & relation_composition(v1, v0) = v5 & relation_composition(v0, v1) = v2 & function_inverse(v0) = v1 & relation_empty_yielding(v8) & relation_empty_yielding(empty_set) & one_to_one(v9) & one_to_one(v0) & relation(v15) & relation(v14) & relation(v12) & relation(v11) & relation(v9) & relation(v8) & relation(v0) & relation(empty_set) & function(v15) & function(v12) & function(v9) & function(v0) & empty(v14) & empty(v13) & empty(v12) & empty(empty_set) & ~ empty(v11) & ~ empty(v10) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v19 | ~ (apply(v17, v19) = v20) | ~ (relation_dom(v17) = v18) | ~ (identity_relation(v16) = v17) | ~ relation(v17) | ~ function(v17) | ~ in(v19, v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (apply(v19, v16) = v20) | ~ (relation_composition(v18, v17) = v19) | ~ (function_inverse(v17) = v18) | ~ one_to_one(v17) | ~ relation(v17) | ~ function(v17) | ? [v21] : ? [v22] : ? [v23] : (apply(v18, v16) = v22 & apply(v17, v22) = v23 & relation_rng(v17) = v21 & ( ~ in(v16, v21) | (v23 = v16 & v20 = v16)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (apply(v19, v16) = v20) | ~ (relation_composition(v17, v18) = v19) | ~ (function_inverse(v17) = v18) | ~ one_to_one(v17) | ~ relation(v17) | ~ function(v17) | ? [v21] : ? [v22] : ? [v23] : (apply(v18, v22) = v23 & apply(v17, v16) = v22 & relation_dom(v17) = v21 & ( ~ in(v16, v21) | (v23 = v16 & v20 = v16)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (apply(v18, v19) = v20) | ~ (apply(v17, v16) = v19) | ~ (function_inverse(v17) = v18) | ~ one_to_one(v17) | ~ relation(v17) | ~ function(v17) | ? [v21] : ? [v22] : ? [v23] : (apply(v22, v16) = v23 & relation_dom(v17) = v21 & relation_composition(v17, v18) = v22 & ( ~ in(v16, v21) | (v23 = v16 & v20 = v16)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (apply(v18, v16) = v19) | ~ (apply(v17, v19) = v20) | ~ (function_inverse(v17) = v18) | ~ one_to_one(v17) | ~ relation(v17) | ~ function(v17) | ? [v21] : ? [v22] : ? [v23] : (apply(v22, v16) = v23 & relation_rng(v17) = v21 & relation_composition(v18, v17) = v22 & ( ~ in(v16, v21) | (v23 = v16 & v20 = v16)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (apply(v19, v18) = v17) | ~ (apply(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (relation_composition(v19, v18) = v17) | ~ (relation_composition(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ element(v17, v19) | ~ empty(v18) | ~ in(v16, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ element(v17, v19) | ~ in(v16, v17) | element(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : (v18 = v17 | ~ (relation_dom(v17) = v16) | ~ (identity_relation(v16) = v18) | ~ relation(v17) | ~ function(v17) | ? [v19] : ? [v20] : ( ~ (v20 = v19) & apply(v17, v19) = v20 & in(v19, v16))) & ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (relation_dom(v17) = v18) | ~ (identity_relation(v16) = v17) | ~ relation(v17) | ~ function(v17)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (relation_rng(v18) = v17) | ~ (relation_rng(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (relation_dom(v18) = v17) | ~ (relation_dom(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (powerset(v18) = v17) | ~ (powerset(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (identity_relation(v18) = v17) | ~ (identity_relation(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (function_inverse(v18) = v17) | ~ (function_inverse(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ subset(v16, v17) | element(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ element(v16, v18) | subset(v16, v17)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v17, v16) = v18) | ~ (function_inverse(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v19] : (relation_rng(v18) = v19 & relation_rng(v16) = v19 & relation_dom(v18) = v19)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v17, v16) = v18) | ~ relation(v17) | ~ empty(v16) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v17, v16) = v18) | ~ relation(v17) | ~ empty(v16) | empty(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v16, v17) = v18) | ~ (function_inverse(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v19] : (relation_rng(v18) = v19 & relation_dom(v18) = v19 & relation_dom(v16) = v19)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v16, v17) = v18) | ~ relation(v17) | ~ relation(v16) | ~ function(v17) | ~ function(v16) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v16, v17) = v18) | ~ relation(v17) | ~ relation(v16) | ~ function(v17) | ~ function(v16) | function(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v16, v17) = v18) | ~ relation(v17) | ~ relation(v16) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v16, v17) = v18) | ~ relation(v17) | ~ empty(v16) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v16, v17) = v18) | ~ relation(v17) | ~ empty(v16) | empty(v18)) & ! [v16] : ! [v17] : (v17 = v16 | ~ empty(v17) | ~ empty(v16)) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v18] : ? [v19] : (relation_rng(v19) = v17 & relation_dom(v19) = v17 & relation_composition(v18, v16) = v19 & function_inverse(v16) = v18)) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ relation(v16) | ~ empty(v17) | empty(v16)) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ empty(v16) | relation(v17)) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ empty(v16) | empty(v17)) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v18] : ? [v19] : (relation_rng(v19) = v17 & relation_dom(v19) = v17 & relation_composition(v16, v18) = v19 & function_inverse(v16) = v18)) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ relation(v16) | ~ empty(v17) | empty(v16)) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ empty(v16) | relation(v17)) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ empty(v16) | empty(v17)) & ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ empty(v17)) & ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | empty(v16) | ? [v18] : (element(v18, v17) & ~ empty(v18))) & ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ? [v18] : (element(v18, v17) & empty(v18))) & ! [v16] : ! [v17] : ( ~ (identity_relation(v16) = v17) | relation(v17)) & ! [v16] : ! [v17] : ( ~ (identity_relation(v16) = v17) | function(v17)) & ! [v16] : ! [v17] : ( ~ (function_inverse(v16) = v17) | ~ relation(v16) | ~ function(v16) | relation(v17)) & ! [v16] : ! [v17] : ( ~ (function_inverse(v16) = v17) | ~ relation(v16) | ~ function(v16) | function(v17)) & ! [v16] : ! [v17] : ( ~ element(v16, v17) | empty(v17) | in(v16, v17)) & ! [v16] : ! [v17] : ( ~ empty(v17) | ~ in(v16, v17)) & ! [v16] : ! [v17] : ( ~ in(v17, v16) | ~ in(v16, v17)) & ! [v16] : ! [v17] : ( ~ in(v16, v17) | element(v16, v17)) & ! [v16] : (v16 = empty_set | ~ empty(v16)) & ! [v16] : ( ~ relation(v16) | ~ function(v16) | ~ empty(v16) | one_to_one(v16)) & ! [v16] : ( ~ empty(v16) | relation(v16)) & ! [v16] : ( ~ empty(v16) | function(v16)) & ? [v16] : ? [v17] : element(v17, v16) & ? [v16] : subset(v16, v16) & ( ~ (v7 = v5) | ~ (v4 = v2)))
% 5.60/1.94 | 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, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15 yields:
% 5.60/1.94 | (1) relation_rng(all_0_15_15) = all_0_9_9 & relation_dom(all_0_15_15) = all_0_12_12 & identity_relation(all_0_9_9) = all_0_8_8 & identity_relation(all_0_12_12) = all_0_11_11 & relation_composition(all_0_14_14, all_0_15_15) = all_0_10_10 & relation_composition(all_0_15_15, all_0_14_14) = all_0_13_13 & function_inverse(all_0_15_15) = all_0_14_14 & relation_empty_yielding(all_0_7_7) & relation_empty_yielding(empty_set) & one_to_one(all_0_6_6) & one_to_one(all_0_15_15) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_3_3) & relation(all_0_4_4) & relation(all_0_6_6) & relation(all_0_7_7) & relation(all_0_15_15) & relation(empty_set) & function(all_0_0_0) & function(all_0_3_3) & function(all_0_6_6) & function(all_0_15_15) & empty(all_0_1_1) & empty(all_0_2_2) & empty(all_0_3_3) & empty(empty_set) & ~ empty(all_0_4_4) & ~ empty(all_0_5_5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (apply(v1, v3) = v4) | ~ (relation_dom(v1) = v2) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1) | ~ in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v3, v0) = v4) | ~ (relation_composition(v2, v1) = v3) | ~ (function_inverse(v1) = v2) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (apply(v2, v0) = v6 & apply(v1, v6) = v7 & relation_rng(v1) = v5 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v3, v0) = v4) | ~ (relation_composition(v1, v2) = v3) | ~ (function_inverse(v1) = v2) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (apply(v2, v6) = v7 & apply(v1, v0) = v6 & relation_dom(v1) = v5 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v3) = v4) | ~ (apply(v1, v0) = v3) | ~ (function_inverse(v1) = v2) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (apply(v6, v0) = v7 & relation_dom(v1) = v5 & relation_composition(v1, v2) = v6 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v3) | ~ (apply(v1, v3) = v4) | ~ (function_inverse(v1) = v2) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (apply(v6, v0) = v7 & relation_rng(v1) = v5 & relation_composition(v2, v1) = v6 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(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 | ~ (relation_dom(v1) = v0) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | ~ function(v1) | ? [v3] : ? [v4] : ( ~ (v4 = v3) & apply(v1, v3) = v4 & in(v3, v0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1)) & ! [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] : (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 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(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) | ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v3] : (relation_rng(v2) = v3 & relation_rng(v0) = v3 & relation_dom(v2) = v3)) & ! [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) | ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v3] : (relation_rng(v2) = v3 & relation_dom(v2) = v3 & relation_dom(v0) = v3)) & ! [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] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v3) = v1 & relation_dom(v3) = v1 & relation_composition(v2, v0) = v3 & function_inverse(v0) = 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) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v3) = v1 & relation_dom(v3) = v1 & relation_composition(v0, v2) = v3 & function_inverse(v0) = v2)) & ! [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] : ( ~ (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] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(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] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) & ( ~ (all_0_8_8 = all_0_10_10) | ~ (all_0_11_11 = all_0_13_13))
% 6.03/1.96 |
% 6.03/1.96 | Applying alpha-rule on (1) yields:
% 6.03/1.96 | (2) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1))
% 6.03/1.96 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v3) | ~ (apply(v1, v3) = v4) | ~ (function_inverse(v1) = v2) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (apply(v6, v0) = v7 & relation_rng(v1) = v5 & relation_composition(v2, v1) = v6 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0))))
% 6.03/1.96 | (4) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1))
% 6.03/1.96 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 6.03/1.96 | (6) relation_empty_yielding(all_0_7_7)
% 6.03/1.96 | (7) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0))
% 6.03/1.96 | (8) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1))
% 6.03/1.96 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 6.03/1.96 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2))
% 6.03/1.96 | (11) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1))
% 6.03/1.96 | (12) function(all_0_3_3)
% 6.03/1.96 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (apply(v1, v3) = v4) | ~ (relation_dom(v1) = v2) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1) | ~ in(v3, v0))
% 6.03/1.96 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v3, v0) = v4) | ~ (relation_composition(v2, v1) = v3) | ~ (function_inverse(v1) = v2) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (apply(v2, v0) = v6 & apply(v1, v6) = v7 & relation_rng(v1) = v5 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0))))
% 6.03/1.96 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 6.03/1.96 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 6.03/1.96 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 6.03/1.96 | (18) ~ (all_0_8_8 = all_0_10_10) | ~ (all_0_11_11 = all_0_13_13)
% 6.03/1.96 | (19) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 6.03/1.96 | (20) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 6.03/1.97 | (21) relation(empty_set)
% 6.03/1.97 | (22) relation(all_0_4_4)
% 6.03/1.97 | (23) relation(all_0_7_7)
% 6.03/1.97 | (24) function(all_0_6_6)
% 6.03/1.97 | (25) function(all_0_0_0)
% 6.03/1.97 | (26) ! [v0] : ( ~ empty(v0) | function(v0))
% 6.03/1.97 | (27) one_to_one(all_0_6_6)
% 6.03/1.97 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 6.03/1.97 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v3] : (relation_rng(v2) = v3 & relation_dom(v2) = v3 & relation_dom(v0) = v3))
% 6.03/1.97 | (30) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 6.03/1.97 | (31) function(all_0_15_15)
% 6.03/1.97 | (32) one_to_one(all_0_15_15)
% 6.03/1.97 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 6.03/1.97 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (relation_dom(v1) = v0) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | ~ function(v1) | ? [v3] : ? [v4] : ( ~ (v4 = v3) & apply(v1, v3) = v4 & in(v3, v0)))
% 6.03/1.97 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 6.03/1.97 | (36) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2)))
% 6.03/1.97 | (37) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1))
% 6.03/1.97 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v3] : (relation_rng(v2) = v3 & relation_rng(v0) = v3 & relation_dom(v2) = v3))
% 6.03/1.97 | (39) relation(all_0_0_0)
% 6.03/1.97 | (40) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 6.03/1.97 | (41) empty(all_0_1_1)
% 6.03/1.97 | (42) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1))
% 6.03/1.97 | (43) ~ empty(all_0_5_5)
% 6.03/1.97 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2))
% 6.03/1.97 | (45) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 6.03/1.97 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 6.03/1.97 | (47) relation_empty_yielding(empty_set)
% 6.03/1.97 | (48) empty(all_0_2_2)
% 6.03/1.97 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 6.03/1.97 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 6.03/1.97 | (51) relation(all_0_15_15)
% 6.03/1.97 | (52) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 6.03/1.97 | (53) ~ empty(all_0_4_4)
% 6.03/1.97 | (54) empty(empty_set)
% 6.03/1.97 | (55) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v3) = v1 & relation_dom(v3) = v1 & relation_composition(v0, v2) = v3 & function_inverse(v0) = v2))
% 6.03/1.97 | (56) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v3) = v1 & relation_dom(v3) = v1 & relation_composition(v2, v0) = v3 & function_inverse(v0) = v2))
% 6.03/1.98 | (57) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0))
% 6.03/1.98 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0))
% 6.03/1.98 | (59) relation(all_0_1_1)
% 6.03/1.98 | (60) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 6.03/1.98 | (61) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 6.03/1.98 | (62) relation(all_0_6_6)
% 6.03/1.98 | (63) empty(all_0_3_3)
% 6.03/1.98 | (64) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 6.03/1.98 | (65) relation_rng(all_0_15_15) = all_0_9_9
% 6.03/1.98 | (66) relation_composition(all_0_14_14, all_0_15_15) = all_0_10_10
% 6.03/1.98 | (67) identity_relation(all_0_12_12) = all_0_11_11
% 6.03/1.98 | (68) ! [v0] : ( ~ empty(v0) | relation(v0))
% 6.03/1.98 | (69) relation(all_0_3_3)
% 6.03/1.98 | (70) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1))
% 6.03/1.98 | (71) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 6.03/1.98 | (72) function_inverse(all_0_15_15) = all_0_14_14
% 6.03/1.98 | (73) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 6.03/1.98 | (74) identity_relation(all_0_9_9) = all_0_8_8
% 6.03/1.98 | (75) relation_composition(all_0_15_15, all_0_14_14) = all_0_13_13
% 6.03/1.98 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 6.03/1.98 | (77) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1))
% 6.03/1.98 | (78) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1))
% 6.03/1.98 | (79) relation_dom(all_0_15_15) = all_0_12_12
% 6.03/1.98 | (80) ? [v0] : ? [v1] : element(v1, v0)
% 6.03/1.98 | (81) ? [v0] : subset(v0, v0)
% 6.03/1.98 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v3) = v4) | ~ (apply(v1, v0) = v3) | ~ (function_inverse(v1) = v2) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (apply(v6, v0) = v7 & relation_dom(v1) = v5 & relation_composition(v1, v2) = v6 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0))))
% 6.03/1.98 | (83) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 6.03/1.98 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v3, v0) = v4) | ~ (relation_composition(v1, v2) = v3) | ~ (function_inverse(v1) = v2) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (apply(v2, v6) = v7 & apply(v1, v0) = v6 & relation_dom(v1) = v5 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0))))
% 6.03/1.98 |
% 6.03/1.98 | Instantiating formula (55) with all_0_12_12, all_0_15_15 and discharging atoms relation_dom(all_0_15_15) = all_0_12_12, one_to_one(all_0_15_15), relation(all_0_15_15), function(all_0_15_15), yields:
% 6.03/1.98 | (85) ? [v0] : ? [v1] : (relation_rng(v1) = all_0_12_12 & relation_dom(v1) = all_0_12_12 & relation_composition(all_0_15_15, v0) = v1 & function_inverse(all_0_15_15) = v0)
% 6.03/1.98 |
% 6.03/1.98 | Instantiating formula (38) with all_0_10_10, all_0_14_14, all_0_15_15 and discharging atoms relation_composition(all_0_14_14, all_0_15_15) = all_0_10_10, function_inverse(all_0_15_15) = all_0_14_14, one_to_one(all_0_15_15), relation(all_0_15_15), function(all_0_15_15), yields:
% 6.03/1.98 | (86) ? [v0] : (relation_rng(all_0_10_10) = v0 & relation_rng(all_0_15_15) = v0 & relation_dom(all_0_10_10) = v0)
% 6.03/1.99 |
% 6.03/1.99 | Instantiating formula (29) with all_0_13_13, all_0_14_14, all_0_15_15 and discharging atoms relation_composition(all_0_15_15, all_0_14_14) = all_0_13_13, function_inverse(all_0_15_15) = all_0_14_14, one_to_one(all_0_15_15), relation(all_0_15_15), function(all_0_15_15), yields:
% 6.03/1.99 | (87) ? [v0] : (relation_rng(all_0_13_13) = v0 & relation_dom(all_0_13_13) = v0 & relation_dom(all_0_15_15) = v0)
% 6.19/1.99 |
% 6.19/1.99 | Instantiating formula (56) with all_0_9_9, all_0_15_15 and discharging atoms relation_rng(all_0_15_15) = all_0_9_9, one_to_one(all_0_15_15), relation(all_0_15_15), function(all_0_15_15), yields:
% 6.19/1.99 | (88) ? [v0] : ? [v1] : (relation_rng(v1) = all_0_9_9 & relation_dom(v1) = all_0_9_9 & relation_composition(v0, all_0_15_15) = v1 & function_inverse(all_0_15_15) = v0)
% 6.19/1.99 |
% 6.19/1.99 | Instantiating formula (42) with all_0_14_14, all_0_15_15 and discharging atoms function_inverse(all_0_15_15) = all_0_14_14, relation(all_0_15_15), function(all_0_15_15), yields:
% 6.19/1.99 | (89) relation(all_0_14_14)
% 6.19/1.99 |
% 6.19/1.99 | Instantiating formula (70) with all_0_14_14, all_0_15_15 and discharging atoms function_inverse(all_0_15_15) = all_0_14_14, relation(all_0_15_15), function(all_0_15_15), yields:
% 6.19/1.99 | (90) function(all_0_14_14)
% 6.19/1.99 |
% 6.19/1.99 | Instantiating (85) with all_17_0_19, all_17_1_20 yields:
% 6.19/1.99 | (91) relation_rng(all_17_0_19) = all_0_12_12 & relation_dom(all_17_0_19) = all_0_12_12 & relation_composition(all_0_15_15, all_17_1_20) = all_17_0_19 & function_inverse(all_0_15_15) = all_17_1_20
% 6.19/1.99 |
% 6.19/1.99 | Applying alpha-rule on (91) yields:
% 6.19/1.99 | (92) relation_rng(all_17_0_19) = all_0_12_12
% 6.19/1.99 | (93) relation_dom(all_17_0_19) = all_0_12_12
% 6.19/1.99 | (94) relation_composition(all_0_15_15, all_17_1_20) = all_17_0_19
% 6.19/1.99 | (95) function_inverse(all_0_15_15) = all_17_1_20
% 6.19/1.99 |
% 6.19/1.99 | Instantiating (88) with all_19_0_21, all_19_1_22 yields:
% 6.19/1.99 | (96) relation_rng(all_19_0_21) = all_0_9_9 & relation_dom(all_19_0_21) = all_0_9_9 & relation_composition(all_19_1_22, all_0_15_15) = all_19_0_21 & function_inverse(all_0_15_15) = all_19_1_22
% 6.19/1.99 |
% 6.19/1.99 | Applying alpha-rule on (96) yields:
% 6.19/1.99 | (97) relation_rng(all_19_0_21) = all_0_9_9
% 6.19/1.99 | (98) relation_dom(all_19_0_21) = all_0_9_9
% 6.19/1.99 | (99) relation_composition(all_19_1_22, all_0_15_15) = all_19_0_21
% 6.19/1.99 | (100) function_inverse(all_0_15_15) = all_19_1_22
% 6.19/1.99 |
% 6.19/1.99 | Instantiating (87) with all_21_0_23 yields:
% 6.19/1.99 | (101) relation_rng(all_0_13_13) = all_21_0_23 & relation_dom(all_0_13_13) = all_21_0_23 & relation_dom(all_0_15_15) = all_21_0_23
% 6.19/1.99 |
% 6.19/1.99 | Applying alpha-rule on (101) yields:
% 6.19/1.99 | (102) relation_rng(all_0_13_13) = all_21_0_23
% 6.19/1.99 | (103) relation_dom(all_0_13_13) = all_21_0_23
% 6.19/1.99 | (104) relation_dom(all_0_15_15) = all_21_0_23
% 6.19/1.99 |
% 6.19/1.99 | Instantiating (86) with all_23_0_24 yields:
% 6.19/1.99 | (105) relation_rng(all_0_10_10) = all_23_0_24 & relation_rng(all_0_15_15) = all_23_0_24 & relation_dom(all_0_10_10) = all_23_0_24
% 6.19/1.99 |
% 6.19/1.99 | Applying alpha-rule on (105) yields:
% 6.19/1.99 | (106) relation_rng(all_0_10_10) = all_23_0_24
% 6.19/1.99 | (107) relation_rng(all_0_15_15) = all_23_0_24
% 6.19/1.99 | (108) relation_dom(all_0_10_10) = all_23_0_24
% 6.19/1.99 |
% 6.19/1.99 | Instantiating formula (17) with all_0_15_15, all_23_0_24, all_0_9_9 and discharging atoms relation_rng(all_0_15_15) = all_23_0_24, relation_rng(all_0_15_15) = all_0_9_9, yields:
% 6.19/1.99 | (109) all_23_0_24 = all_0_9_9
% 6.19/1.99 |
% 6.19/1.99 | Instantiating formula (64) with all_0_15_15, all_21_0_23, all_0_12_12 and discharging atoms relation_dom(all_0_15_15) = all_21_0_23, relation_dom(all_0_15_15) = all_0_12_12, yields:
% 6.19/1.99 | (110) all_21_0_23 = all_0_12_12
% 6.19/1.99 |
% 6.19/1.99 | Instantiating formula (57) with all_0_15_15, all_19_1_22, all_0_14_14 and discharging atoms function_inverse(all_0_15_15) = all_19_1_22, function_inverse(all_0_15_15) = all_0_14_14, yields:
% 6.19/1.99 | (111) all_19_1_22 = all_0_14_14
% 6.19/1.99 |
% 6.19/1.99 | Instantiating formula (57) with all_0_15_15, all_17_1_20, all_19_1_22 and discharging atoms function_inverse(all_0_15_15) = all_19_1_22, function_inverse(all_0_15_15) = all_17_1_20, yields:
% 6.19/1.99 | (112) all_19_1_22 = all_17_1_20
% 6.19/1.99 |
% 6.19/1.99 | Combining equations (111,112) yields a new equation:
% 6.19/1.99 | (113) all_17_1_20 = all_0_14_14
% 6.19/1.99 |
% 6.19/2.00 | Combining equations (113,112) yields a new equation:
% 6.19/2.00 | (111) all_19_1_22 = all_0_14_14
% 6.19/2.00 |
% 6.19/2.00 | From (109) and (107) follows:
% 6.19/2.00 | (65) relation_rng(all_0_15_15) = all_0_9_9
% 6.19/2.00 |
% 6.19/2.00 | From (110) and (104) follows:
% 6.19/2.00 | (79) relation_dom(all_0_15_15) = all_0_12_12
% 6.19/2.00 |
% 6.19/2.00 | From (111) and (99) follows:
% 6.19/2.00 | (117) relation_composition(all_0_14_14, all_0_15_15) = all_19_0_21
% 6.19/2.00 |
% 6.19/2.00 | From (113) and (94) follows:
% 6.19/2.00 | (118) relation_composition(all_0_15_15, all_0_14_14) = all_17_0_19
% 6.19/2.00 |
% 6.19/2.00 | From (113) and (95) follows:
% 6.19/2.00 | (72) function_inverse(all_0_15_15) = all_0_14_14
% 6.19/2.00 |
% 6.19/2.00 | Instantiating formula (58) with all_0_14_14, all_0_15_15, all_19_0_21, all_0_10_10 and discharging atoms relation_composition(all_0_14_14, all_0_15_15) = all_19_0_21, relation_composition(all_0_14_14, all_0_15_15) = all_0_10_10, yields:
% 6.19/2.00 | (120) all_19_0_21 = all_0_10_10
% 6.19/2.00 |
% 6.19/2.00 | Instantiating formula (58) with all_0_15_15, all_0_14_14, all_17_0_19, all_0_13_13 and discharging atoms relation_composition(all_0_15_15, all_0_14_14) = all_17_0_19, relation_composition(all_0_15_15, all_0_14_14) = all_0_13_13, yields:
% 6.19/2.00 | (121) all_17_0_19 = all_0_13_13
% 6.19/2.00 |
% 6.19/2.00 | From (120) and (98) follows:
% 6.19/2.00 | (122) relation_dom(all_0_10_10) = all_0_9_9
% 6.19/2.00 |
% 6.19/2.00 | From (121) and (93) follows:
% 6.19/2.00 | (123) relation_dom(all_0_13_13) = all_0_12_12
% 6.19/2.00 |
% 6.19/2.00 | From (120) and (117) follows:
% 6.19/2.00 | (66) relation_composition(all_0_14_14, all_0_15_15) = all_0_10_10
% 6.19/2.00 |
% 6.19/2.00 | From (121) and (118) follows:
% 6.19/2.00 | (75) relation_composition(all_0_15_15, all_0_14_14) = all_0_13_13
% 6.19/2.00 |
% 6.19/2.00 | Instantiating formula (10) with all_0_10_10, all_0_15_15, all_0_14_14 and discharging atoms relation_composition(all_0_14_14, all_0_15_15) = all_0_10_10, relation(all_0_14_14), relation(all_0_15_15), function(all_0_14_14), function(all_0_15_15), yields:
% 6.19/2.00 | (126) relation(all_0_10_10)
% 6.19/2.00 |
% 6.19/2.00 | Instantiating formula (44) with all_0_10_10, all_0_15_15, all_0_14_14 and discharging atoms relation_composition(all_0_14_14, all_0_15_15) = all_0_10_10, relation(all_0_14_14), relation(all_0_15_15), function(all_0_14_14), function(all_0_15_15), yields:
% 6.19/2.00 | (127) function(all_0_10_10)
% 6.19/2.00 |
% 6.19/2.00 | Instantiating formula (10) with all_0_13_13, all_0_14_14, all_0_15_15 and discharging atoms relation_composition(all_0_15_15, all_0_14_14) = all_0_13_13, relation(all_0_14_14), relation(all_0_15_15), function(all_0_14_14), function(all_0_15_15), yields:
% 6.19/2.00 | (128) relation(all_0_13_13)
% 6.19/2.00 |
% 6.19/2.00 | Instantiating formula (44) with all_0_13_13, all_0_14_14, all_0_15_15 and discharging atoms relation_composition(all_0_15_15, all_0_14_14) = all_0_13_13, relation(all_0_14_14), relation(all_0_15_15), function(all_0_14_14), function(all_0_15_15), yields:
% 6.19/2.00 | (129) function(all_0_13_13)
% 6.19/2.00 |
% 6.19/2.00 | Instantiating formula (34) with all_0_8_8, all_0_10_10, all_0_9_9 and discharging atoms relation_dom(all_0_10_10) = all_0_9_9, identity_relation(all_0_9_9) = all_0_8_8, relation(all_0_10_10), function(all_0_10_10), yields:
% 6.19/2.00 | (130) all_0_8_8 = all_0_10_10 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & apply(all_0_10_10, v0) = v1 & in(v0, all_0_9_9))
% 6.19/2.00 |
% 6.19/2.00 | Instantiating formula (34) with all_0_11_11, all_0_13_13, all_0_12_12 and discharging atoms relation_dom(all_0_13_13) = all_0_12_12, identity_relation(all_0_12_12) = all_0_11_11, relation(all_0_13_13), function(all_0_13_13), yields:
% 6.19/2.00 | (131) all_0_11_11 = all_0_13_13 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & apply(all_0_13_13, v0) = v1 & in(v0, all_0_12_12))
% 6.19/2.00 |
% 6.19/2.00 +-Applying beta-rule and splitting (18), into two cases.
% 6.19/2.00 |-Branch one:
% 6.19/2.00 | (132) ~ (all_0_8_8 = all_0_10_10)
% 6.19/2.00 |
% 6.19/2.00 +-Applying beta-rule and splitting (130), into two cases.
% 6.19/2.00 |-Branch one:
% 6.19/2.00 | (133) all_0_8_8 = all_0_10_10
% 6.19/2.00 |
% 6.19/2.00 | Equations (133) can reduce 132 to:
% 6.19/2.00 | (134) $false
% 6.19/2.00 |
% 6.19/2.00 |-The branch is then unsatisfiable
% 6.19/2.00 |-Branch two:
% 6.19/2.00 | (132) ~ (all_0_8_8 = all_0_10_10)
% 6.19/2.00 | (136) ? [v0] : ? [v1] : ( ~ (v1 = v0) & apply(all_0_10_10, v0) = v1 & in(v0, all_0_9_9))
% 6.19/2.00 |
% 6.19/2.00 | Instantiating (136) with all_50_0_25, all_50_1_26 yields:
% 6.19/2.00 | (137) ~ (all_50_0_25 = all_50_1_26) & apply(all_0_10_10, all_50_1_26) = all_50_0_25 & in(all_50_1_26, all_0_9_9)
% 6.19/2.00 |
% 6.19/2.00 | Applying alpha-rule on (137) yields:
% 6.19/2.00 | (138) ~ (all_50_0_25 = all_50_1_26)
% 6.19/2.00 | (139) apply(all_0_10_10, all_50_1_26) = all_50_0_25
% 6.19/2.00 | (140) in(all_50_1_26, all_0_9_9)
% 6.19/2.00 |
% 6.19/2.00 | Instantiating formula (14) with all_50_0_25, all_0_10_10, all_0_14_14, all_0_15_15, all_50_1_26 and discharging atoms apply(all_0_10_10, all_50_1_26) = all_50_0_25, relation_composition(all_0_14_14, all_0_15_15) = all_0_10_10, function_inverse(all_0_15_15) = all_0_14_14, one_to_one(all_0_15_15), relation(all_0_15_15), function(all_0_15_15), yields:
% 6.19/2.00 | (141) ? [v0] : ? [v1] : ? [v2] : (apply(all_0_14_14, all_50_1_26) = v1 & apply(all_0_15_15, v1) = v2 & relation_rng(all_0_15_15) = v0 & ( ~ in(all_50_1_26, v0) | (v2 = all_50_1_26 & all_50_0_25 = all_50_1_26)))
% 6.19/2.00 |
% 6.19/2.00 | Instantiating (141) with all_58_0_27, all_58_1_28, all_58_2_29 yields:
% 6.19/2.01 | (142) apply(all_0_14_14, all_50_1_26) = all_58_1_28 & apply(all_0_15_15, all_58_1_28) = all_58_0_27 & relation_rng(all_0_15_15) = all_58_2_29 & ( ~ in(all_50_1_26, all_58_2_29) | (all_58_0_27 = all_50_1_26 & all_50_0_25 = all_50_1_26))
% 6.19/2.01 |
% 6.19/2.01 | Applying alpha-rule on (142) yields:
% 6.19/2.01 | (143) apply(all_0_14_14, all_50_1_26) = all_58_1_28
% 6.19/2.01 | (144) apply(all_0_15_15, all_58_1_28) = all_58_0_27
% 6.19/2.01 | (145) relation_rng(all_0_15_15) = all_58_2_29
% 6.19/2.01 | (146) ~ in(all_50_1_26, all_58_2_29) | (all_58_0_27 = all_50_1_26 & all_50_0_25 = all_50_1_26)
% 6.19/2.01 |
% 6.19/2.01 +-Applying beta-rule and splitting (146), into two cases.
% 6.19/2.01 |-Branch one:
% 6.19/2.01 | (147) ~ in(all_50_1_26, all_58_2_29)
% 6.19/2.01 |
% 6.19/2.01 | Instantiating formula (17) with all_0_15_15, all_58_2_29, all_0_9_9 and discharging atoms relation_rng(all_0_15_15) = all_58_2_29, relation_rng(all_0_15_15) = all_0_9_9, yields:
% 6.19/2.01 | (148) all_58_2_29 = all_0_9_9
% 6.19/2.01 |
% 6.19/2.01 | From (148) and (147) follows:
% 6.19/2.01 | (149) ~ in(all_50_1_26, all_0_9_9)
% 6.19/2.01 |
% 6.19/2.01 | Using (140) and (149) yields:
% 6.19/2.01 | (150) $false
% 6.19/2.01 |
% 6.19/2.01 |-The branch is then unsatisfiable
% 6.19/2.01 |-Branch two:
% 6.19/2.01 | (151) in(all_50_1_26, all_58_2_29)
% 6.19/2.01 | (152) all_58_0_27 = all_50_1_26 & all_50_0_25 = all_50_1_26
% 6.19/2.01 |
% 6.19/2.01 | Applying alpha-rule on (152) yields:
% 6.19/2.01 | (153) all_58_0_27 = all_50_1_26
% 6.19/2.01 | (154) all_50_0_25 = all_50_1_26
% 6.19/2.01 |
% 6.19/2.01 | Equations (154) can reduce 138 to:
% 6.19/2.01 | (134) $false
% 6.19/2.01 |
% 6.19/2.01 |-The branch is then unsatisfiable
% 6.19/2.01 |-Branch two:
% 6.19/2.01 | (133) all_0_8_8 = all_0_10_10
% 6.19/2.01 | (157) ~ (all_0_11_11 = all_0_13_13)
% 6.19/2.01 |
% 6.19/2.01 +-Applying beta-rule and splitting (131), into two cases.
% 6.19/2.01 |-Branch one:
% 6.19/2.01 | (158) all_0_11_11 = all_0_13_13
% 6.19/2.01 |
% 6.19/2.01 | Equations (158) can reduce 157 to:
% 6.19/2.01 | (134) $false
% 6.19/2.01 |
% 6.19/2.01 |-The branch is then unsatisfiable
% 6.19/2.01 |-Branch two:
% 6.19/2.01 | (157) ~ (all_0_11_11 = all_0_13_13)
% 6.19/2.01 | (161) ? [v0] : ? [v1] : ( ~ (v1 = v0) & apply(all_0_13_13, v0) = v1 & in(v0, all_0_12_12))
% 6.19/2.01 |
% 6.19/2.01 | Instantiating (161) with all_50_0_30, all_50_1_31 yields:
% 6.19/2.01 | (162) ~ (all_50_0_30 = all_50_1_31) & apply(all_0_13_13, all_50_1_31) = all_50_0_30 & in(all_50_1_31, all_0_12_12)
% 6.19/2.01 |
% 6.19/2.01 | Applying alpha-rule on (162) yields:
% 6.19/2.01 | (163) ~ (all_50_0_30 = all_50_1_31)
% 6.19/2.01 | (164) apply(all_0_13_13, all_50_1_31) = all_50_0_30
% 6.19/2.01 | (165) in(all_50_1_31, all_0_12_12)
% 6.19/2.01 |
% 6.19/2.01 | Instantiating formula (84) with all_50_0_30, all_0_13_13, all_0_14_14, all_0_15_15, all_50_1_31 and discharging atoms apply(all_0_13_13, all_50_1_31) = all_50_0_30, relation_composition(all_0_15_15, all_0_14_14) = all_0_13_13, function_inverse(all_0_15_15) = all_0_14_14, one_to_one(all_0_15_15), relation(all_0_15_15), function(all_0_15_15), yields:
% 6.19/2.01 | (166) ? [v0] : ? [v1] : ? [v2] : (apply(all_0_14_14, v1) = v2 & apply(all_0_15_15, all_50_1_31) = v1 & relation_dom(all_0_15_15) = v0 & ( ~ in(all_50_1_31, v0) | (v2 = all_50_1_31 & all_50_0_30 = all_50_1_31)))
% 6.19/2.01 |
% 6.19/2.01 | Instantiating (166) with all_58_0_32, all_58_1_33, all_58_2_34 yields:
% 6.19/2.01 | (167) apply(all_0_14_14, all_58_1_33) = all_58_0_32 & apply(all_0_15_15, all_50_1_31) = all_58_1_33 & relation_dom(all_0_15_15) = all_58_2_34 & ( ~ in(all_50_1_31, all_58_2_34) | (all_58_0_32 = all_50_1_31 & all_50_0_30 = all_50_1_31))
% 6.19/2.01 |
% 6.19/2.01 | Applying alpha-rule on (167) yields:
% 6.19/2.01 | (168) apply(all_0_14_14, all_58_1_33) = all_58_0_32
% 6.19/2.01 | (169) apply(all_0_15_15, all_50_1_31) = all_58_1_33
% 6.19/2.01 | (170) relation_dom(all_0_15_15) = all_58_2_34
% 6.19/2.01 | (171) ~ in(all_50_1_31, all_58_2_34) | (all_58_0_32 = all_50_1_31 & all_50_0_30 = all_50_1_31)
% 6.19/2.01 |
% 6.19/2.01 +-Applying beta-rule and splitting (171), into two cases.
% 6.19/2.01 |-Branch one:
% 6.19/2.01 | (172) ~ in(all_50_1_31, all_58_2_34)
% 6.19/2.01 |
% 6.19/2.01 | Instantiating formula (64) with all_0_15_15, all_58_2_34, all_0_12_12 and discharging atoms relation_dom(all_0_15_15) = all_58_2_34, relation_dom(all_0_15_15) = all_0_12_12, yields:
% 6.19/2.01 | (173) all_58_2_34 = all_0_12_12
% 6.19/2.01 |
% 6.19/2.01 | From (173) and (172) follows:
% 6.19/2.01 | (174) ~ in(all_50_1_31, all_0_12_12)
% 6.19/2.01 |
% 6.19/2.01 | Using (165) and (174) yields:
% 6.19/2.01 | (150) $false
% 6.19/2.01 |
% 6.19/2.01 |-The branch is then unsatisfiable
% 6.19/2.01 |-Branch two:
% 6.19/2.01 | (176) in(all_50_1_31, all_58_2_34)
% 6.19/2.01 | (177) all_58_0_32 = all_50_1_31 & all_50_0_30 = all_50_1_31
% 6.19/2.01 |
% 6.19/2.01 | Applying alpha-rule on (177) yields:
% 6.19/2.01 | (178) all_58_0_32 = all_50_1_31
% 6.19/2.01 | (179) all_50_0_30 = all_50_1_31
% 6.19/2.01 |
% 6.19/2.01 | Equations (179) can reduce 163 to:
% 6.19/2.01 | (134) $false
% 6.19/2.01 |
% 6.19/2.01 |-The branch is then unsatisfiable
% 6.19/2.01 % SZS output end Proof for theBenchmark
% 6.19/2.01
% 6.19/2.01 1434ms
%------------------------------------------------------------------------------