TSTP Solution File: SEU296+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU296+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n012.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 08:48:35 EDT 2022
% Result : Theorem 5.41s 1.86s
% Output : Proof 8.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU296+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.15/0.36 % Computer : n012.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jun 19 09:10:53 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.22/0.61 ____ _
% 0.22/0.61 ___ / __ \_____(_)___ ________ __________
% 0.22/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.22/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.22/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.22/0.61
% 0.22/0.61 A Theorem Prover for First-Order Logic
% 0.22/0.61 (ePrincess v.1.0)
% 0.22/0.61
% 0.22/0.61 (c) Philipp Rümmer, 2009-2015
% 0.22/0.61 (c) Peter Backeman, 2014-2015
% 0.22/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.22/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.22/0.61 Bug reports to peter@backeman.se
% 0.22/0.61
% 0.22/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.22/0.61
% 0.22/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.92/1.01 Prover 0: Preprocessing ...
% 2.86/1.33 Prover 0: Warning: ignoring some quantifiers
% 3.15/1.36 Prover 0: Constructing countermodel ...
% 5.41/1.86 Prover 0: proved (1199ms)
% 5.41/1.86
% 5.41/1.86 No countermodel exists, formula is valid
% 5.41/1.86 % SZS status Theorem for theBenchmark
% 5.41/1.86
% 5.41/1.86 Generating proof ... Warning: ignoring some quantifiers
% 8.48/2.57 found it (size 80)
% 8.48/2.57
% 8.48/2.57 % SZS output start Proof for theBenchmark
% 8.48/2.57 Assumed formulas after preprocessing and simplification:
% 8.48/2.57 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (relation_image(v1, v0) = v2 & relation_empty_yielding(v4) & relation_empty_yielding(v3) & relation_empty_yielding(empty_set) & one_to_one(v9) & one_to_one(v6) & one_to_one(empty_set) & natural(v16) & relation(v14) & relation(v12) & relation(v10) & relation(v9) & relation(v8) & relation(v6) & relation(v4) & relation(v3) & relation(v1) & relation(empty_set) & function(v14) & function(v10) & function(v9) & function(v6) & function(v3) & function(v1) & function(empty_set) & finite(v15) & finite(v0) & empty(v12) & empty(v11) & empty(v10) & empty(v9) & empty(empty_set) & epsilon_connected(v16) & epsilon_connected(v13) & epsilon_connected(v9) & epsilon_connected(v5) & epsilon_connected(empty_set) & epsilon_connected(omega) & epsilon_transitive(v16) & epsilon_transitive(v13) & epsilon_transitive(v9) & epsilon_transitive(v5) & epsilon_transitive(empty_set) & epsilon_transitive(omega) & ordinal(v16) & ordinal(v13) & ordinal(v9) & ordinal(v5) & ordinal(empty_set) & ordinal(omega) & ~ finite(v2) & ~ empty(v16) & ~ empty(v15) & ~ empty(v8) & ~ empty(v7) & ~ empty(v5) & ~ empty(omega) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_image(v18, v20) = v21) | ~ (relation_dom(v18) = v19) | ~ (set_intersection2(v19, v17) = v20) | ~ relation(v18) | relation_image(v18, v17) = v21) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (relation_image(v20, v19) = v18) | ~ (relation_image(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (relation_composition(v20, v19) = v18) | ~ (relation_composition(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (set_intersection2(v20, v19) = v18) | ~ (set_intersection2(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_image(v19, v18) = v20) | ~ (relation_rng(v17) = v18) | ~ relation(v19) | ~ relation(v17) | ? [v21] : (relation_composition(v17, v19) = v21 & relation_rng(v21) = v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_composition(v17, v19) = v20) | ~ (relation_rng(v17) = v18) | ~ relation(v19) | ~ relation(v17) | ? [v21] : (relation_image(v19, v18) = v21 & relation_rng(v20) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (powerset(v19) = v20) | ~ empty(v19) | ~ element(v18, v20) | ~ in(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (powerset(v19) = v20) | ~ element(v18, v20) | ~ in(v17, v18) | element(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_rng(v19) = v18) | ~ (relation_rng(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_dom(v19) = v18) | ~ (relation_dom(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (powerset(v19) = v18) | ~ (powerset(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_image(v18, v17) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_image(v18, v21) = v19 & relation_dom(v18) = v20 & set_intersection2(v20, v17) = v21)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v18, v17) = v19) | ~ relation(v18) | ~ empty(v17) | relation(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v18, v17) = v19) | ~ relation(v18) | ~ empty(v17) | empty(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v17, v18) = v19) | ~ relation(v18) | ~ relation(v17) | ~ function(v18) | ~ function(v17) | relation(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v17, v18) = v19) | ~ relation(v18) | ~ relation(v17) | ~ function(v18) | ~ function(v17) | function(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v17, v18) = v19) | ~ relation(v18) | ~ relation(v17) | relation(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v17, v18) = v19) | ~ relation(v18) | ~ empty(v17) | relation(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v17, v18) = v19) | ~ relation(v18) | ~ empty(v17) | empty(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v18, v17) = v19) | set_intersection2(v17, v18) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | ~ relation(v18) | ~ relation(v17) | relation(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | ~ finite(v18) | finite(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | ~ finite(v17) | finite(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | set_intersection2(v18, v17) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | subset(v19, v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ subset(v17, v18) | element(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ element(v17, v19) | subset(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v17) = v18) | ~ finite(v17) | ~ element(v19, v18) | finite(v19)) & ? [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ relation(v18) | ~ function(v18) | ~ in(v19, omega) | finite(v17) | ? [v20] : ( ~ (v20 = v17) & relation_rng(v18) = v20)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (set_intersection2(v17, v17) = v18)) & ! [v17] : ! [v18] : (v18 = v17 | ~ empty(v18) | ~ empty(v17)) & ! [v17] : ! [v18] : (v18 = empty_set | ~ (set_intersection2(v17, empty_set) = v18)) & ! [v17] : ! [v18] : ( ~ (relation_rng(v18) = v17) | ~ relation(v18) | ~ function(v18) | finite(v17) | ? [v19] : (relation_dom(v18) = v19 & ~ in(v19, omega))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ~ relation(v17) | ~ empty(v18) | empty(v17)) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ~ relation(v17) | ? [v19] : (relation_dom(v17) = v19 & ! [v20] : ! [v21] : ( ~ (relation_composition(v17, v20) = v21) | ~ relation(v20) | ? [v22] : ? [v23] : (relation_dom(v21) = v23 & relation_dom(v20) = v22 & (v23 = v19 | ~ subset(v18, v22)))) & ! [v20] : ! [v21] : ( ~ (relation_dom(v20) = v21) | ~ subset(v18, v21) | ~ relation(v20) | ? [v22] : (relation_composition(v17, v20) = v22 & relation_dom(v22) = v19)))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ~ empty(v17) | relation(v18)) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ~ empty(v17) | empty(v18)) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ~ relation(v17) | ~ empty(v18) | empty(v17)) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ~ relation(v17) | ? [v19] : (relation_rng(v17) = v19 & ! [v20] : ! [v21] : ( ~ (relation_composition(v17, v20) = v21) | ~ relation(v20) | ? [v22] : ? [v23] : (relation_dom(v21) = v23 & relation_dom(v20) = v22 & (v23 = v18 | ~ subset(v19, v22)))) & ! [v20] : ! [v21] : ( ~ (relation_dom(v20) = v21) | ~ subset(v19, v21) | ~ relation(v20) | ? [v22] : (relation_composition(v17, v20) = v22 & relation_dom(v22) = v18)))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ~ empty(v17) | relation(v18)) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ~ empty(v17) | empty(v18)) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ empty(v18)) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | empty(v17) | ? [v19] : (finite(v19) & element(v19, v18) & ~ empty(v19))) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | empty(v17) | ? [v19] : (element(v19, v18) & ~ empty(v19))) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ? [v19] : (one_to_one(v19) & natural(v19) & relation(v19) & function(v19) & finite(v19) & empty(v19) & epsilon_connected(v19) & epsilon_transitive(v19) & element(v19, v18) & ordinal(v19))) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ? [v19] : (empty(v19) & element(v19, v18))) & ! [v17] : ! [v18] : ( ~ empty(v18) | ~ in(v17, v18)) & ! [v17] : ! [v18] : ( ~ element(v18, v17) | ~ ordinal(v17) | epsilon_connected(v18)) & ! [v17] : ! [v18] : ( ~ element(v18, v17) | ~ ordinal(v17) | epsilon_transitive(v18)) & ! [v17] : ! [v18] : ( ~ element(v18, v17) | ~ ordinal(v17) | ordinal(v18)) & ! [v17] : ! [v18] : ( ~ element(v17, v18) | empty(v18) | in(v17, v18)) & ! [v17] : ! [v18] : ( ~ in(v18, v17) | ~ in(v17, v18)) & ! [v17] : ! [v18] : ( ~ in(v17, v18) | element(v17, v18)) & ! [v17] : (v17 = empty_set | ~ empty(v17)) & ! [v17] : ( ~ relation(v17) | ~ function(v17) | ~ empty(v17) | one_to_one(v17)) & ! [v17] : ( ~ finite(v17) | ? [v18] : ? [v19] : (relation_rng(v18) = v17 & relation_dom(v18) = v19 & relation(v18) & function(v18) & in(v19, omega))) & ! [v17] : ( ~ empty(v17) | ~ ordinal(v17) | natural(v17)) & ! [v17] : ( ~ empty(v17) | ~ ordinal(v17) | epsilon_connected(v17)) & ! [v17] : ( ~ empty(v17) | ~ ordinal(v17) | epsilon_transitive(v17)) & ! [v17] : ( ~ empty(v17) | relation(v17)) & ! [v17] : ( ~ empty(v17) | function(v17)) & ! [v17] : ( ~ empty(v17) | finite(v17)) & ! [v17] : ( ~ empty(v17) | epsilon_connected(v17)) & ! [v17] : ( ~ empty(v17) | epsilon_transitive(v17)) & ! [v17] : ( ~ empty(v17) | ordinal(v17)) & ! [v17] : ( ~ epsilon_connected(v17) | ~ epsilon_transitive(v17) | ordinal(v17)) & ! [v17] : ( ~ element(v17, omega) | natural(v17)) & ! [v17] : ( ~ element(v17, omega) | epsilon_connected(v17)) & ! [v17] : ( ~ element(v17, omega) | epsilon_transitive(v17)) & ! [v17] : ( ~ element(v17, omega) | ordinal(v17)) & ! [v17] : ( ~ ordinal(v17) | epsilon_connected(v17)) & ! [v17] : ( ~ ordinal(v17) | epsilon_transitive(v17)) & ? [v17] : ? [v18] : element(v18, v17) & ? [v17] : subset(v17, v17))
% 8.48/2.61 | 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, all_0_16_16 yields:
% 8.48/2.61 | (1) relation_image(all_0_15_15, all_0_16_16) = all_0_14_14 & relation_empty_yielding(all_0_12_12) & relation_empty_yielding(all_0_13_13) & relation_empty_yielding(empty_set) & one_to_one(all_0_7_7) & one_to_one(all_0_10_10) & one_to_one(empty_set) & natural(all_0_0_0) & relation(all_0_2_2) & relation(all_0_4_4) & relation(all_0_6_6) & relation(all_0_7_7) & relation(all_0_8_8) & relation(all_0_10_10) & relation(all_0_12_12) & relation(all_0_13_13) & relation(all_0_15_15) & relation(empty_set) & function(all_0_2_2) & function(all_0_6_6) & function(all_0_7_7) & function(all_0_10_10) & function(all_0_13_13) & function(all_0_15_15) & function(empty_set) & finite(all_0_1_1) & finite(all_0_16_16) & empty(all_0_4_4) & empty(all_0_5_5) & empty(all_0_6_6) & empty(all_0_7_7) & empty(empty_set) & epsilon_connected(all_0_0_0) & epsilon_connected(all_0_3_3) & epsilon_connected(all_0_7_7) & epsilon_connected(all_0_11_11) & epsilon_connected(empty_set) & epsilon_connected(omega) & epsilon_transitive(all_0_0_0) & epsilon_transitive(all_0_3_3) & epsilon_transitive(all_0_7_7) & epsilon_transitive(all_0_11_11) & epsilon_transitive(empty_set) & epsilon_transitive(omega) & ordinal(all_0_0_0) & ordinal(all_0_3_3) & ordinal(all_0_7_7) & ordinal(all_0_11_11) & ordinal(empty_set) & ordinal(omega) & ~ finite(all_0_14_14) & ~ empty(all_0_0_0) & ~ empty(all_0_1_1) & ~ empty(all_0_8_8) & ~ empty(all_0_9_9) & ~ empty(all_0_11_11) & ~ empty(omega) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_image(v1, v3) = v4) | ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | relation_image(v1, v0) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v2, v1) = v3) | ~ (relation_rng(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_composition(v0, v2) = v4 & relation_rng(v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_rng(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_image(v2, v1) = v4 & relation_rng(v3) = 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] : (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] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_image(v1, v4) = v2 & relation_dom(v1) = v3 & set_intersection2(v3, v0) = v4)) & ! [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] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ finite(v1) | finite(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ finite(v0) | finite(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(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] : ( ~ (powerset(v0) = v1) | ~ finite(v0) | ~ element(v2, v1) | finite(v2)) & ? [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(v2, omega) | finite(v0) | ? [v3] : ( ~ (v3 = v0) & relation_rng(v1) = v3)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v1) = v0) | ~ relation(v1) | ~ function(v1) | finite(v0) | ? [v2] : (relation_dom(v1) = v2 & ~ in(v2, omega))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v2 | ~ subset(v1, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v1, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v2)))) & ! [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) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v1 | ~ subset(v2, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v2, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v1)))) & ! [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] : (finite(v2) & element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (one_to_one(v2) & natural(v2) & relation(v2) & function(v2) & finite(v2) & empty(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & element(v2, v1) & ordinal(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ ordinal(v0) | epsilon_connected(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ ordinal(v0) | epsilon_transitive(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ ordinal(v0) | ordinal(v1)) & ! [v0] : ! [v1] : ( ~ element(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] : ( ~ finite(v0) | ? [v1] : ? [v2] : (relation_rng(v1) = v0 & relation_dom(v1) = v2 & relation(v1) & function(v1) & in(v2, omega))) & ! [v0] : ( ~ empty(v0) | ~ ordinal(v0) | natural(v0)) & ! [v0] : ( ~ empty(v0) | ~ ordinal(v0) | epsilon_connected(v0)) & ! [v0] : ( ~ empty(v0) | ~ ordinal(v0) | epsilon_transitive(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ! [v0] : ( ~ empty(v0) | finite(v0)) & ! [v0] : ( ~ empty(v0) | epsilon_connected(v0)) & ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0)) & ! [v0] : ( ~ empty(v0) | ordinal(v0)) & ! [v0] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0)) & ! [v0] : ( ~ element(v0, omega) | natural(v0)) & ! [v0] : ( ~ element(v0, omega) | epsilon_connected(v0)) & ! [v0] : ( ~ element(v0, omega) | epsilon_transitive(v0)) & ! [v0] : ( ~ element(v0, omega) | ordinal(v0)) & ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0)) & ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0)
% 8.48/2.63 |
% 8.48/2.63 | Applying alpha-rule on (1) yields:
% 8.48/2.63 | (2) empty(all_0_7_7)
% 8.48/2.63 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0))
% 8.48/2.63 | (4) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1))
% 8.48/2.63 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v2, v1) = v3) | ~ (relation_rng(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_composition(v0, v2) = v4 & relation_rng(v4) = v3))
% 8.48/2.63 | (6) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 8.48/2.63 | (7) epsilon_transitive(all_0_7_7)
% 8.48/2.63 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 8.48/2.63 | (9) ordinal(all_0_7_7)
% 8.48/2.63 | (10) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 8.48/2.63 | (11) epsilon_transitive(all_0_11_11)
% 8.48/2.63 | (12) relation(all_0_13_13)
% 8.48/2.63 | (13) function(all_0_2_2)
% 8.48/2.63 | (14) ~ finite(all_0_14_14)
% 8.48/2.63 | (15) ordinal(all_0_0_0)
% 8.48/2.63 | (16) one_to_one(all_0_10_10)
% 8.48/2.63 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ finite(v0) | finite(v2))
% 8.48/2.63 | (18) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 8.48/2.63 | (19) epsilon_transitive(empty_set)
% 8.48/2.63 | (20) ? [v0] : subset(v0, v0)
% 8.48/2.63 | (21) ! [v0] : ( ~ empty(v0) | relation(v0))
% 8.48/2.63 | (22) finite(all_0_16_16)
% 8.48/2.63 | (23) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 8.48/2.63 | (24) relation(all_0_2_2)
% 8.48/2.63 | (25) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ ordinal(v0) | epsilon_transitive(v1))
% 8.48/2.63 | (26) function(empty_set)
% 8.48/2.63 | (27) ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0))
% 8.48/2.63 | (28) empty(all_0_4_4)
% 8.48/2.63 | (29) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 8.48/2.63 | (30) relation(all_0_7_7)
% 8.48/2.63 | (31) ! [v0] : ( ~ empty(v0) | ~ ordinal(v0) | epsilon_connected(v0))
% 8.48/2.63 | (32) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 8.48/2.63 | (33) ! [v0] : ( ~ empty(v0) | ordinal(v0))
% 8.48/2.63 | (34) ! [v0] : ( ~ element(v0, omega) | natural(v0))
% 8.48/2.63 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 8.48/2.64 | (36) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1))
% 8.48/2.64 | (37) ordinal(empty_set)
% 8.48/2.64 | (38) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (finite(v2) & element(v2, v1) & ~ empty(v2)))
% 8.48/2.64 | (39) ! [v0] : ( ~ element(v0, omega) | ordinal(v0))
% 8.48/2.64 | (40) function(all_0_15_15)
% 8.48/2.64 | (41) finite(all_0_1_1)
% 8.48/2.64 | (42) ~ empty(all_0_9_9)
% 8.48/2.64 | (43) epsilon_connected(omega)
% 8.48/2.64 | (44) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 8.48/2.64 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 8.48/2.64 | (46) ! [v0] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0))
% 8.48/2.64 | (47) ? [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(v2, omega) | finite(v0) | ? [v3] : ( ~ (v3 = v0) & relation_rng(v1) = v3))
% 8.48/2.64 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2))
% 8.48/2.64 | (49) natural(all_0_0_0)
% 8.48/2.64 | (50) ! [v0] : ( ~ empty(v0) | epsilon_connected(v0))
% 8.48/2.64 | (51) ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0))
% 8.48/2.64 | (52) ordinal(all_0_3_3)
% 8.48/2.64 | (53) function(all_0_13_13)
% 8.48/2.64 | (54) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1)))
% 8.48/2.64 | (55) ! [v0] : ( ~ element(v0, omega) | epsilon_connected(v0))
% 8.48/2.64 | (56) empty(all_0_5_5)
% 8.48/2.64 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_image(v1, v3) = v4) | ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | relation_image(v1, v0) = v4)
% 8.48/2.64 | (58) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 8.48/2.64 | (59) relation_empty_yielding(all_0_12_12)
% 8.48/2.64 | (60) ! [v0] : ! [v1] : ( ~ (relation_rng(v1) = v0) | ~ relation(v1) | ~ function(v1) | finite(v0) | ? [v2] : (relation_dom(v1) = v2 & ~ in(v2, omega)))
% 8.48/2.64 | (61) ! [v0] : ( ~ empty(v0) | function(v0))
% 8.48/2.64 | (62) relation(all_0_6_6)
% 8.48/2.64 | (63) ordinal(all_0_11_11)
% 8.48/2.64 | (64) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ ordinal(v0) | epsilon_connected(v1))
% 8.48/2.64 | (65) ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0))
% 8.48/2.64 | (66) epsilon_connected(empty_set)
% 8.48/2.64 | (67) epsilon_connected(all_0_0_0)
% 8.48/2.64 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 8.48/2.64 | (69) ! [v0] : ( ~ empty(v0) | finite(v0))
% 8.48/2.64 | (70) relation_empty_yielding(empty_set)
% 8.48/2.64 | (71) relation(all_0_4_4)
% 8.48/2.64 | (72) function(all_0_7_7)
% 8.48/2.64 | (73) relation_image(all_0_15_15, all_0_16_16) = all_0_14_14
% 8.48/2.64 | (74) function(all_0_10_10)
% 8.48/2.64 | (75) ~ empty(omega)
% 8.48/2.64 | (76) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ ordinal(v0) | ordinal(v1))
% 8.48/2.64 | (77) epsilon_transitive(all_0_0_0)
% 8.48/2.64 | (78) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 8.48/2.64 | (79) empty(empty_set)
% 8.48/2.64 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ finite(v1) | finite(v2))
% 8.48/2.64 | (81) one_to_one(all_0_7_7)
% 8.48/2.64 | (82) ~ empty(all_0_8_8)
% 8.48/2.64 | (83) ! [v0] : ( ~ empty(v0) | ~ ordinal(v0) | natural(v0))
% 8.48/2.64 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2))
% 8.48/2.65 | (85) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 8.48/2.65 | (86) relation(all_0_8_8)
% 8.48/2.65 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 8.48/2.65 | (88) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 8.48/2.65 | (89) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 8.48/2.65 | (90) epsilon_transitive(all_0_3_3)
% 8.48/2.65 | (91) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 8.48/2.65 | (92) relation(empty_set)
% 8.48/2.65 | (93) ~ empty(all_0_0_0)
% 8.48/2.65 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ in(v0, v1))
% 8.48/2.65 | (95) function(all_0_6_6)
% 8.48/2.65 | (96) one_to_one(empty_set)
% 8.48/2.65 | (97) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v1 | ~ subset(v2, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v2, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v1))))
% 8.48/2.65 | (98) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1))
% 8.48/2.65 | (99) epsilon_connected(all_0_11_11)
% 8.48/2.65 | (100) relation(all_0_10_10)
% 8.48/2.65 | (101) ordinal(omega)
% 8.48/2.65 | (102) ! [v0] : ( ~ element(v0, omega) | epsilon_transitive(v0))
% 8.48/2.65 | (103) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (one_to_one(v2) & natural(v2) & relation(v2) & function(v2) & finite(v2) & empty(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & element(v2, v1) & ordinal(v2)))
% 8.48/2.65 | (104) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 8.48/2.65 | (105) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 8.48/2.65 | (106) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 8.48/2.65 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_rng(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_image(v2, v1) = v4 & relation_rng(v3) = v4))
% 8.48/2.65 | (108) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1))
% 8.48/2.65 | (109) ! [v0] : ( ~ empty(v0) | ~ ordinal(v0) | epsilon_transitive(v0))
% 8.48/2.65 | (110) ~ empty(all_0_1_1)
% 8.48/2.65 | (111) empty(all_0_6_6)
% 8.48/2.65 | (112) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0))
% 8.48/2.65 | (113) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ finite(v0) | ~ element(v2, v1) | finite(v2))
% 8.48/2.65 | (114) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0))
% 8.48/2.65 | (115) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 8.48/2.65 | (116) epsilon_transitive(omega)
% 8.48/2.65 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0))
% 8.48/2.65 | (118) relation_empty_yielding(all_0_13_13)
% 8.48/2.65 | (119) ! [v0] : ( ~ finite(v0) | ? [v1] : ? [v2] : (relation_rng(v1) = v0 & relation_dom(v1) = v2 & relation(v1) & function(v1) & in(v2, omega)))
% 8.48/2.65 | (120) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_image(v1, v4) = v2 & relation_dom(v1) = v3 & set_intersection2(v3, v0) = v4))
% 8.48/2.65 | (121) epsilon_connected(all_0_7_7)
% 8.48/2.65 | (122) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 8.48/2.65 | (123) relation(all_0_15_15)
% 8.48/2.65 | (124) epsilon_connected(all_0_3_3)
% 8.48/2.65 | (125) ~ empty(all_0_11_11)
% 8.48/2.65 | (126) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 8.48/2.65 | (127) relation(all_0_12_12)
% 8.48/2.65 | (128) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 8.48/2.65 | (129) ? [v0] : ? [v1] : element(v1, v0)
% 8.48/2.65 | (130) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v2 | ~ subset(v1, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v1, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v2))))
% 8.48/2.65 | (131) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 8.48/2.65 | (132) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 8.48/2.65 |
% 8.48/2.65 | Instantiating formula (120) with all_0_14_14, all_0_15_15, all_0_16_16 and discharging atoms relation_image(all_0_15_15, all_0_16_16) = all_0_14_14, relation(all_0_15_15), yields:
% 8.48/2.66 | (133) ? [v0] : ? [v1] : (relation_image(all_0_15_15, v1) = all_0_14_14 & relation_dom(all_0_15_15) = v0 & set_intersection2(v0, all_0_16_16) = v1)
% 8.48/2.66 |
% 8.48/2.66 | Instantiating formula (119) with all_0_16_16 and discharging atoms finite(all_0_16_16), yields:
% 8.48/2.66 | (134) ? [v0] : ? [v1] : (relation_rng(v0) = all_0_16_16 & relation_dom(v0) = v1 & relation(v0) & function(v0) & in(v1, omega))
% 8.48/2.66 |
% 8.48/2.66 | Instantiating (134) with all_19_0_21, all_19_1_22 yields:
% 8.48/2.66 | (135) relation_rng(all_19_1_22) = all_0_16_16 & relation_dom(all_19_1_22) = all_19_0_21 & relation(all_19_1_22) & function(all_19_1_22) & in(all_19_0_21, omega)
% 8.48/2.66 |
% 8.48/2.66 | Applying alpha-rule on (135) yields:
% 8.48/2.66 | (136) in(all_19_0_21, omega)
% 8.48/2.66 | (137) relation_dom(all_19_1_22) = all_19_0_21
% 8.48/2.66 | (138) relation_rng(all_19_1_22) = all_0_16_16
% 8.48/2.66 | (139) relation(all_19_1_22)
% 8.48/2.66 | (140) function(all_19_1_22)
% 8.48/2.66 |
% 8.48/2.66 | Instantiating (133) with all_23_0_25, all_23_1_26 yields:
% 8.48/2.66 | (141) relation_image(all_0_15_15, all_23_0_25) = all_0_14_14 & relation_dom(all_0_15_15) = all_23_1_26 & set_intersection2(all_23_1_26, all_0_16_16) = all_23_0_25
% 8.48/2.66 |
% 8.48/2.66 | Applying alpha-rule on (141) yields:
% 8.48/2.66 | (142) relation_image(all_0_15_15, all_23_0_25) = all_0_14_14
% 8.96/2.66 | (143) relation_dom(all_0_15_15) = all_23_1_26
% 8.96/2.66 | (144) set_intersection2(all_23_1_26, all_0_16_16) = all_23_0_25
% 8.96/2.66 |
% 8.96/2.66 | Instantiating formula (120) with all_0_14_14, all_0_15_15, all_23_0_25 and discharging atoms relation_image(all_0_15_15, all_23_0_25) = all_0_14_14, relation(all_0_15_15), yields:
% 8.96/2.66 | (145) ? [v0] : ? [v1] : (relation_image(all_0_15_15, v1) = all_0_14_14 & relation_dom(all_0_15_15) = v0 & set_intersection2(v0, all_23_0_25) = v1)
% 8.96/2.66 |
% 8.96/2.66 | Instantiating formula (97) with all_23_1_26, all_0_15_15 and discharging atoms relation_dom(all_0_15_15) = all_23_1_26, relation(all_0_15_15), yields:
% 8.96/2.66 | (146) ? [v0] : (relation_rng(all_0_15_15) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_15_15, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = all_23_1_26 | ~ subset(v0, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(v0, v2) | ~ relation(v1) | ? [v3] : (relation_composition(all_0_15_15, v1) = v3 & relation_dom(v3) = all_23_1_26)))
% 8.96/2.66 |
% 8.96/2.66 | Instantiating formula (80) with all_23_0_25, all_0_16_16, all_23_1_26 and discharging atoms set_intersection2(all_23_1_26, all_0_16_16) = all_23_0_25, finite(all_0_16_16), yields:
% 8.96/2.66 | (147) finite(all_23_0_25)
% 8.96/2.66 |
% 8.96/2.66 | Instantiating formula (112) with all_23_0_25, all_0_16_16, all_23_1_26 and discharging atoms set_intersection2(all_23_1_26, all_0_16_16) = all_23_0_25, yields:
% 8.96/2.66 | (148) subset(all_23_0_25, all_23_1_26)
% 8.96/2.66 |
% 8.96/2.66 | Instantiating formula (5) with all_0_14_14, all_0_15_15, all_0_16_16, all_19_1_22 and discharging atoms relation_image(all_0_15_15, all_0_16_16) = all_0_14_14, relation_rng(all_19_1_22) = all_0_16_16, relation(all_19_1_22), relation(all_0_15_15), yields:
% 8.96/2.66 | (149) ? [v0] : (relation_composition(all_19_1_22, all_0_15_15) = v0 & relation_rng(v0) = all_0_14_14)
% 8.96/2.66 |
% 8.96/2.66 | Instantiating formula (130) with all_0_16_16, all_19_1_22 and discharging atoms relation_rng(all_19_1_22) = all_0_16_16, relation(all_19_1_22), yields:
% 8.96/2.66 | (150) ? [v0] : (relation_dom(all_19_1_22) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(all_19_1_22, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = v0 | ~ subset(all_0_16_16, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_16_16, v2) | ~ relation(v1) | ? [v3] : (relation_composition(all_19_1_22, v1) = v3 & relation_dom(v3) = v0)))
% 8.96/2.66 |
% 8.96/2.66 | Instantiating formula (97) with all_19_0_21, all_19_1_22 and discharging atoms relation_dom(all_19_1_22) = all_19_0_21, relation(all_19_1_22), yields:
% 8.96/2.66 | (151) ? [v0] : (relation_rng(all_19_1_22) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(all_19_1_22, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = all_19_0_21 | ~ subset(v0, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(v0, v2) | ~ relation(v1) | ? [v3] : (relation_composition(all_19_1_22, v1) = v3 & relation_dom(v3) = all_19_0_21)))
% 8.96/2.66 |
% 8.96/2.66 | Instantiating (150) with all_33_0_29 yields:
% 8.96/2.66 | (152) relation_dom(all_19_1_22) = all_33_0_29 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_19_1_22, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_33_0_29 | ~ subset(all_0_16_16, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_16_16, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_19_1_22, v0) = v2 & relation_dom(v2) = all_33_0_29))
% 8.96/2.66 |
% 8.96/2.66 | Applying alpha-rule on (152) yields:
% 8.96/2.66 | (153) relation_dom(all_19_1_22) = all_33_0_29
% 8.96/2.66 | (154) ! [v0] : ! [v1] : ( ~ (relation_composition(all_19_1_22, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_33_0_29 | ~ subset(all_0_16_16, v2))))
% 8.96/2.66 | (155) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_16_16, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_19_1_22, v0) = v2 & relation_dom(v2) = all_33_0_29))
% 8.96/2.66 |
% 8.96/2.66 | Instantiating (146) with all_36_0_30 yields:
% 8.96/2.66 | (156) relation_rng(all_0_15_15) = all_36_0_30 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_15_15, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_23_1_26 | ~ subset(all_36_0_30, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_36_0_30, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_15_15, v0) = v2 & relation_dom(v2) = all_23_1_26))
% 8.96/2.66 |
% 8.96/2.66 | Applying alpha-rule on (156) yields:
% 8.96/2.66 | (157) relation_rng(all_0_15_15) = all_36_0_30
% 8.96/2.66 | (158) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_15_15, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_23_1_26 | ~ subset(all_36_0_30, v2))))
% 8.96/2.66 | (159) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_36_0_30, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_15_15, v0) = v2 & relation_dom(v2) = all_23_1_26))
% 8.96/2.66 |
% 8.96/2.66 | Instantiating (151) with all_39_0_31 yields:
% 8.96/2.66 | (160) relation_rng(all_19_1_22) = all_39_0_31 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_19_1_22, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_19_0_21 | ~ subset(all_39_0_31, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_39_0_31, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_19_1_22, v0) = v2 & relation_dom(v2) = all_19_0_21))
% 8.96/2.66 |
% 8.96/2.66 | Applying alpha-rule on (160) yields:
% 8.96/2.66 | (161) relation_rng(all_19_1_22) = all_39_0_31
% 8.96/2.66 | (162) ! [v0] : ! [v1] : ( ~ (relation_composition(all_19_1_22, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_19_0_21 | ~ subset(all_39_0_31, v2))))
% 8.96/2.66 | (163) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_39_0_31, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_19_1_22, v0) = v2 & relation_dom(v2) = all_19_0_21))
% 8.96/2.66 |
% 8.96/2.66 | Instantiating (149) with all_48_0_34 yields:
% 8.96/2.66 | (164) relation_composition(all_19_1_22, all_0_15_15) = all_48_0_34 & relation_rng(all_48_0_34) = all_0_14_14
% 8.96/2.66 |
% 8.96/2.66 | Applying alpha-rule on (164) yields:
% 8.96/2.66 | (165) relation_composition(all_19_1_22, all_0_15_15) = all_48_0_34
% 8.96/2.66 | (166) relation_rng(all_48_0_34) = all_0_14_14
% 8.96/2.66 |
% 8.96/2.66 | Instantiating (145) with all_50_0_35, all_50_1_36 yields:
% 8.96/2.66 | (167) relation_image(all_0_15_15, all_50_0_35) = all_0_14_14 & relation_dom(all_0_15_15) = all_50_1_36 & set_intersection2(all_50_1_36, all_23_0_25) = all_50_0_35
% 8.96/2.66 |
% 8.96/2.66 | Applying alpha-rule on (167) yields:
% 8.96/2.66 | (168) relation_image(all_0_15_15, all_50_0_35) = all_0_14_14
% 8.96/2.66 | (169) relation_dom(all_0_15_15) = all_50_1_36
% 8.96/2.66 | (170) set_intersection2(all_50_1_36, all_23_0_25) = all_50_0_35
% 8.96/2.66 |
% 8.96/2.66 | Instantiating formula (58) with all_0_15_15, all_50_1_36, all_23_1_26 and discharging atoms relation_dom(all_0_15_15) = all_50_1_36, relation_dom(all_0_15_15) = all_23_1_26, yields:
% 8.96/2.66 | (171) all_50_1_36 = all_23_1_26
% 8.96/2.66 |
% 8.96/2.66 | From (171) and (169) follows:
% 8.96/2.66 | (143) relation_dom(all_0_15_15) = all_23_1_26
% 8.96/2.66 |
% 8.96/2.66 | Instantiating formula (120) with all_0_14_14, all_0_15_15, all_50_0_35 and discharging atoms relation_image(all_0_15_15, all_50_0_35) = all_0_14_14, relation(all_0_15_15), yields:
% 8.96/2.66 | (173) ? [v0] : ? [v1] : (relation_image(all_0_15_15, v1) = all_0_14_14 & relation_dom(all_0_15_15) = v0 & set_intersection2(v0, all_50_0_35) = v1)
% 8.96/2.66 |
% 8.96/2.66 | Instantiating formula (154) with all_48_0_34, all_0_15_15 and discharging atoms relation_composition(all_19_1_22, all_0_15_15) = all_48_0_34, relation(all_0_15_15), yields:
% 8.96/2.66 | (174) ? [v0] : ? [v1] : (relation_dom(all_48_0_34) = v1 & relation_dom(all_0_15_15) = v0 & (v1 = all_33_0_29 | ~ subset(all_0_16_16, v0)))
% 8.96/2.66 |
% 8.96/2.66 | Instantiating formula (162) with all_48_0_34, all_0_15_15 and discharging atoms relation_composition(all_19_1_22, all_0_15_15) = all_48_0_34, relation(all_0_15_15), yields:
% 8.96/2.66 | (175) ? [v0] : ? [v1] : (relation_dom(all_48_0_34) = v1 & relation_dom(all_0_15_15) = v0 & (v1 = all_19_0_21 | ~ subset(all_39_0_31, v0)))
% 8.96/2.66 |
% 8.96/2.66 | Instantiating formula (130) with all_36_0_30, all_0_15_15 and discharging atoms relation_rng(all_0_15_15) = all_36_0_30, relation(all_0_15_15), yields:
% 8.96/2.66 | (176) ? [v0] : (relation_dom(all_0_15_15) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_15_15, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = v0 | ~ subset(all_36_0_30, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_36_0_30, v2) | ~ relation(v1) | ? [v3] : (relation_composition(all_0_15_15, v1) = v3 & relation_dom(v3) = v0)))
% 8.96/2.67 |
% 8.96/2.67 | Instantiating formula (119) with all_23_0_25 and discharging atoms finite(all_23_0_25), yields:
% 8.96/2.67 | (177) ? [v0] : ? [v1] : (relation_rng(v0) = all_23_0_25 & relation_dom(v0) = v1 & relation(v0) & function(v0) & in(v1, omega))
% 8.96/2.67 |
% 8.96/2.67 | Instantiating (173) with all_65_0_38, all_65_1_39 yields:
% 8.96/2.67 | (178) relation_image(all_0_15_15, all_65_0_38) = all_0_14_14 & relation_dom(all_0_15_15) = all_65_1_39 & set_intersection2(all_65_1_39, all_50_0_35) = all_65_0_38
% 8.96/2.67 |
% 8.96/2.67 | Applying alpha-rule on (178) yields:
% 8.96/2.67 | (179) relation_image(all_0_15_15, all_65_0_38) = all_0_14_14
% 8.96/2.67 | (180) relation_dom(all_0_15_15) = all_65_1_39
% 8.96/2.67 | (181) set_intersection2(all_65_1_39, all_50_0_35) = all_65_0_38
% 8.96/2.67 |
% 8.96/2.67 | Instantiating (177) with all_70_0_41, all_70_1_42 yields:
% 8.96/2.67 | (182) relation_rng(all_70_1_42) = all_23_0_25 & relation_dom(all_70_1_42) = all_70_0_41 & relation(all_70_1_42) & function(all_70_1_42) & in(all_70_0_41, omega)
% 8.96/2.67 |
% 8.96/2.67 | Applying alpha-rule on (182) yields:
% 8.96/2.67 | (183) relation(all_70_1_42)
% 8.96/2.67 | (184) relation_dom(all_70_1_42) = all_70_0_41
% 8.96/2.67 | (185) relation_rng(all_70_1_42) = all_23_0_25
% 8.96/2.67 | (186) function(all_70_1_42)
% 8.96/2.67 | (187) in(all_70_0_41, omega)
% 8.96/2.67 |
% 8.96/2.67 | Instantiating (176) with all_72_0_43 yields:
% 8.96/2.67 | (188) relation_dom(all_0_15_15) = all_72_0_43 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_15_15, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_72_0_43 | ~ subset(all_36_0_30, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_36_0_30, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_15_15, v0) = v2 & relation_dom(v2) = all_72_0_43))
% 8.96/2.67 |
% 8.96/2.67 | Applying alpha-rule on (188) yields:
% 8.96/2.67 | (189) relation_dom(all_0_15_15) = all_72_0_43
% 8.96/2.67 | (190) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_15_15, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_72_0_43 | ~ subset(all_36_0_30, v2))))
% 8.96/2.67 | (191) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_36_0_30, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_15_15, v0) = v2 & relation_dom(v2) = all_72_0_43))
% 8.96/2.67 |
% 8.96/2.67 | Instantiating (175) with all_75_0_44, all_75_1_45 yields:
% 8.96/2.67 | (192) relation_dom(all_48_0_34) = all_75_0_44 & relation_dom(all_0_15_15) = all_75_1_45 & (all_75_0_44 = all_19_0_21 | ~ subset(all_39_0_31, all_75_1_45))
% 8.96/2.67 |
% 8.96/2.67 | Applying alpha-rule on (192) yields:
% 8.96/2.67 | (193) relation_dom(all_48_0_34) = all_75_0_44
% 8.96/2.67 | (194) relation_dom(all_0_15_15) = all_75_1_45
% 8.96/2.67 | (195) all_75_0_44 = all_19_0_21 | ~ subset(all_39_0_31, all_75_1_45)
% 8.96/2.67 |
% 8.96/2.67 | Instantiating (174) with all_77_0_46, all_77_1_47 yields:
% 8.96/2.67 | (196) relation_dom(all_48_0_34) = all_77_0_46 & relation_dom(all_0_15_15) = all_77_1_47 & (all_77_0_46 = all_33_0_29 | ~ subset(all_0_16_16, all_77_1_47))
% 8.96/2.67 |
% 8.96/2.67 | Applying alpha-rule on (196) yields:
% 8.96/2.67 | (197) relation_dom(all_48_0_34) = all_77_0_46
% 8.96/2.67 | (198) relation_dom(all_0_15_15) = all_77_1_47
% 8.96/2.67 | (199) all_77_0_46 = all_33_0_29 | ~ subset(all_0_16_16, all_77_1_47)
% 8.96/2.67 |
% 8.96/2.67 | Instantiating formula (58) with all_0_15_15, all_75_1_45, all_23_1_26 and discharging atoms relation_dom(all_0_15_15) = all_75_1_45, relation_dom(all_0_15_15) = all_23_1_26, yields:
% 8.96/2.67 | (200) all_75_1_45 = all_23_1_26
% 8.96/2.67 |
% 8.96/2.67 | Instantiating formula (58) with all_0_15_15, all_75_1_45, all_77_1_47 and discharging atoms relation_dom(all_0_15_15) = all_77_1_47, relation_dom(all_0_15_15) = all_75_1_45, yields:
% 8.96/2.67 | (201) all_77_1_47 = all_75_1_45
% 8.96/2.67 |
% 8.96/2.67 | Instantiating formula (58) with all_0_15_15, all_72_0_43, all_77_1_47 and discharging atoms relation_dom(all_0_15_15) = all_77_1_47, relation_dom(all_0_15_15) = all_72_0_43, yields:
% 8.96/2.67 | (202) all_77_1_47 = all_72_0_43
% 8.96/2.67 |
% 8.96/2.67 | Instantiating formula (58) with all_0_15_15, all_65_1_39, all_77_1_47 and discharging atoms relation_dom(all_0_15_15) = all_77_1_47, relation_dom(all_0_15_15) = all_65_1_39, yields:
% 8.96/2.67 | (203) all_77_1_47 = all_65_1_39
% 8.96/2.67 |
% 8.96/2.67 | Combining equations (201,202) yields a new equation:
% 8.96/2.67 | (204) all_75_1_45 = all_72_0_43
% 8.96/2.67 |
% 8.96/2.67 | Simplifying 204 yields:
% 8.96/2.67 | (205) all_75_1_45 = all_72_0_43
% 8.96/2.67 |
% 8.96/2.67 | Combining equations (203,202) yields a new equation:
% 8.96/2.67 | (206) all_72_0_43 = all_65_1_39
% 8.96/2.67 |
% 8.96/2.67 | Combining equations (205,200) yields a new equation:
% 8.96/2.67 | (207) all_72_0_43 = all_23_1_26
% 8.96/2.67 |
% 8.96/2.67 | Simplifying 207 yields:
% 8.96/2.67 | (208) all_72_0_43 = all_23_1_26
% 8.96/2.67 |
% 8.96/2.67 | Combining equations (208,206) yields a new equation:
% 8.96/2.67 | (209) all_65_1_39 = all_23_1_26
% 8.96/2.67 |
% 8.96/2.67 | From (209) and (180) follows:
% 8.96/2.67 | (143) relation_dom(all_0_15_15) = all_23_1_26
% 8.96/2.67 |
% 8.96/2.67 | Instantiating formula (5) with all_0_14_14, all_0_15_15, all_23_0_25, all_70_1_42 and discharging atoms relation_image(all_0_15_15, all_23_0_25) = all_0_14_14, relation_rng(all_70_1_42) = all_23_0_25, relation(all_70_1_42), relation(all_0_15_15), yields:
% 8.96/2.67 | (211) ? [v0] : (relation_composition(all_70_1_42, all_0_15_15) = v0 & relation_rng(v0) = all_0_14_14)
% 8.96/2.67 |
% 8.96/2.67 | Instantiating formula (130) with all_23_0_25, all_70_1_42 and discharging atoms relation_rng(all_70_1_42) = all_23_0_25, relation(all_70_1_42), yields:
% 8.96/2.67 | (212) ? [v0] : (relation_dom(all_70_1_42) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(all_70_1_42, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = v0 | ~ subset(all_23_0_25, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_23_0_25, v2) | ~ relation(v1) | ? [v3] : (relation_composition(all_70_1_42, v1) = v3 & relation_dom(v3) = v0)))
% 8.96/2.67 |
% 8.96/2.67 | Instantiating (212) with all_102_0_54 yields:
% 8.96/2.67 | (213) relation_dom(all_70_1_42) = all_102_0_54 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_70_1_42, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_102_0_54 | ~ subset(all_23_0_25, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_23_0_25, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_70_1_42, v0) = v2 & relation_dom(v2) = all_102_0_54))
% 8.96/2.67 |
% 8.96/2.67 | Applying alpha-rule on (213) yields:
% 8.96/2.67 | (214) relation_dom(all_70_1_42) = all_102_0_54
% 8.96/2.67 | (215) ! [v0] : ! [v1] : ( ~ (relation_composition(all_70_1_42, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_102_0_54 | ~ subset(all_23_0_25, v2))))
% 8.96/2.67 | (216) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_23_0_25, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_70_1_42, v0) = v2 & relation_dom(v2) = all_102_0_54))
% 8.96/2.67 |
% 8.96/2.67 | Instantiating formula (216) with all_23_1_26, all_0_15_15 and discharging atoms relation_dom(all_0_15_15) = all_23_1_26, subset(all_23_0_25, all_23_1_26), relation(all_0_15_15), yields:
% 8.96/2.67 | (217) ? [v0] : (relation_composition(all_70_1_42, all_0_15_15) = v0 & relation_dom(v0) = all_102_0_54)
% 8.96/2.67 |
% 8.96/2.67 | Instantiating (211) with all_105_0_55 yields:
% 8.96/2.67 | (218) relation_composition(all_70_1_42, all_0_15_15) = all_105_0_55 & relation_rng(all_105_0_55) = all_0_14_14
% 8.96/2.67 |
% 8.96/2.67 | Applying alpha-rule on (218) yields:
% 8.96/2.67 | (219) relation_composition(all_70_1_42, all_0_15_15) = all_105_0_55
% 8.96/2.67 | (220) relation_rng(all_105_0_55) = all_0_14_14
% 8.96/2.67 |
% 8.96/2.67 | Instantiating (217) with all_109_0_58 yields:
% 8.96/2.67 | (221) relation_composition(all_70_1_42, all_0_15_15) = all_109_0_58 & relation_dom(all_109_0_58) = all_102_0_54
% 8.96/2.67 |
% 8.96/2.67 | Applying alpha-rule on (221) yields:
% 8.96/2.67 | (222) relation_composition(all_70_1_42, all_0_15_15) = all_109_0_58
% 8.96/2.67 | (223) relation_dom(all_109_0_58) = all_102_0_54
% 8.96/2.67 |
% 8.96/2.67 | Instantiating formula (3) with all_70_1_42, all_0_15_15, all_105_0_55, all_109_0_58 and discharging atoms relation_composition(all_70_1_42, all_0_15_15) = all_109_0_58, relation_composition(all_70_1_42, all_0_15_15) = all_105_0_55, yields:
% 8.96/2.67 | (224) all_109_0_58 = all_105_0_55
% 8.96/2.67 |
% 8.96/2.67 | Instantiating formula (58) with all_70_1_42, all_102_0_54, all_70_0_41 and discharging atoms relation_dom(all_70_1_42) = all_102_0_54, relation_dom(all_70_1_42) = all_70_0_41, yields:
% 8.96/2.67 | (225) all_102_0_54 = all_70_0_41
% 8.96/2.67 |
% 8.96/2.67 | From (224) and (222) follows:
% 8.96/2.67 | (219) relation_composition(all_70_1_42, all_0_15_15) = all_105_0_55
% 8.96/2.67 |
% 8.96/2.67 | From (224)(225) and (223) follows:
% 8.96/2.67 | (227) relation_dom(all_105_0_55) = all_70_0_41
% 8.96/2.67 |
% 8.96/2.67 | Instantiating formula (48) with all_105_0_55, all_0_15_15, all_70_1_42 and discharging atoms relation_composition(all_70_1_42, all_0_15_15) = all_105_0_55, relation(all_70_1_42), relation(all_0_15_15), function(all_70_1_42), function(all_0_15_15), yields:
% 8.96/2.67 | (228) function(all_105_0_55)
% 8.96/2.67 |
% 8.96/2.67 | Instantiating formula (126) with all_105_0_55, all_0_15_15, all_70_1_42 and discharging atoms relation_composition(all_70_1_42, all_0_15_15) = all_105_0_55, relation(all_70_1_42), relation(all_0_15_15), yields:
% 8.96/2.67 | (229) relation(all_105_0_55)
% 8.96/2.67 |
% 8.96/2.67 | Instantiating formula (130) with all_0_14_14, all_105_0_55 and discharging atoms relation_rng(all_105_0_55) = all_0_14_14, relation(all_105_0_55), yields:
% 8.96/2.67 | (230) ? [v0] : (relation_dom(all_105_0_55) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(all_105_0_55, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = v0 | ~ subset(all_0_14_14, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_14_14, v2) | ~ relation(v1) | ? [v3] : (relation_composition(all_105_0_55, v1) = v3 & relation_dom(v3) = v0)))
% 8.96/2.67 |
% 8.96/2.67 | Instantiating formula (60) with all_105_0_55, all_0_14_14 and discharging atoms relation_rng(all_105_0_55) = all_0_14_14, relation(all_105_0_55), function(all_105_0_55), ~ finite(all_0_14_14), yields:
% 8.96/2.67 | (231) ? [v0] : (relation_dom(all_105_0_55) = v0 & ~ in(v0, omega))
% 8.96/2.67 |
% 8.96/2.67 | Instantiating (231) with all_162_0_72 yields:
% 8.96/2.67 | (232) relation_dom(all_105_0_55) = all_162_0_72 & ~ in(all_162_0_72, omega)
% 8.96/2.68 |
% 8.96/2.68 | Applying alpha-rule on (232) yields:
% 8.96/2.68 | (233) relation_dom(all_105_0_55) = all_162_0_72
% 8.96/2.68 | (234) ~ in(all_162_0_72, omega)
% 8.96/2.68 |
% 8.96/2.68 | Instantiating (230) with all_167_0_74 yields:
% 8.96/2.68 | (235) relation_dom(all_105_0_55) = all_167_0_74 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_105_0_55, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_167_0_74 | ~ subset(all_0_14_14, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_14_14, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_105_0_55, v0) = v2 & relation_dom(v2) = all_167_0_74))
% 8.96/2.68 |
% 8.96/2.68 | Applying alpha-rule on (235) yields:
% 8.96/2.68 | (236) relation_dom(all_105_0_55) = all_167_0_74
% 8.96/2.68 | (237) ! [v0] : ! [v1] : ( ~ (relation_composition(all_105_0_55, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_167_0_74 | ~ subset(all_0_14_14, v2))))
% 8.96/2.68 | (238) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_14_14, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_105_0_55, v0) = v2 & relation_dom(v2) = all_167_0_74))
% 8.96/2.68 |
% 8.96/2.68 | Instantiating formula (58) with all_105_0_55, all_167_0_74, all_70_0_41 and discharging atoms relation_dom(all_105_0_55) = all_167_0_74, relation_dom(all_105_0_55) = all_70_0_41, yields:
% 8.96/2.68 | (239) all_167_0_74 = all_70_0_41
% 8.96/2.68 |
% 8.96/2.68 | Instantiating formula (58) with all_105_0_55, all_162_0_72, all_167_0_74 and discharging atoms relation_dom(all_105_0_55) = all_167_0_74, relation_dom(all_105_0_55) = all_162_0_72, yields:
% 8.96/2.68 | (240) all_167_0_74 = all_162_0_72
% 8.96/2.68 |
% 8.96/2.68 | Combining equations (239,240) yields a new equation:
% 8.96/2.68 | (241) all_162_0_72 = all_70_0_41
% 8.96/2.68 |
% 8.96/2.68 | From (241) and (234) follows:
% 8.96/2.68 | (242) ~ in(all_70_0_41, omega)
% 8.96/2.68 |
% 8.96/2.68 | Using (187) and (242) yields:
% 8.96/2.68 | (243) $false
% 8.96/2.68 |
% 8.96/2.68 |-The branch is then unsatisfiable
% 8.96/2.68 % SZS output end Proof for theBenchmark
% 8.96/2.68
% 8.96/2.68 2055ms
%------------------------------------------------------------------------------