TSTP Solution File: SET693+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET693+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n006.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 00:21:27 EDT 2022
% Result : Theorem 4.98s 1.92s
% Output : Proof 7.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET693+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 11 05:51:50 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.61/0.61 ____ _
% 0.61/0.62 ___ / __ \_____(_)___ ________ __________
% 0.61/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.61/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.61/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.61/0.62
% 0.61/0.62 A Theorem Prover for First-Order Logic
% 0.61/0.62 (ePrincess v.1.0)
% 0.61/0.62
% 0.61/0.62 (c) Philipp Rümmer, 2009-2015
% 0.61/0.62 (c) Peter Backeman, 2014-2015
% 0.61/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.61/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.61/0.62 Bug reports to peter@backeman.se
% 0.61/0.62
% 0.61/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.61/0.62
% 0.61/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.63/0.98 Prover 0: Preprocessing ...
% 2.19/1.18 Prover 0: Warning: ignoring some quantifiers
% 2.26/1.20 Prover 0: Constructing countermodel ...
% 2.86/1.37 Prover 0: gave up
% 2.86/1.37 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.86/1.39 Prover 1: Preprocessing ...
% 3.45/1.50 Prover 1: Constructing countermodel ...
% 3.88/1.62 Prover 1: gave up
% 3.88/1.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.88/1.64 Prover 2: Preprocessing ...
% 4.18/1.73 Prover 2: Warning: ignoring some quantifiers
% 4.18/1.73 Prover 2: Constructing countermodel ...
% 4.98/1.92 Prover 2: proved (299ms)
% 4.98/1.92
% 4.98/1.92 No countermodel exists, formula is valid
% 4.98/1.92 % SZS status Theorem for theBenchmark
% 4.98/1.92
% 4.98/1.92 Generating proof ... Warning: ignoring some quantifiers
% 6.35/2.24 found it (size 76)
% 6.35/2.24
% 6.35/2.24 % SZS output start Proof for theBenchmark
% 6.35/2.24 Assumed formulas after preprocessing and simplification:
% 6.78/2.24 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (union(v0, v1) = v2 & equal_set(v0, v2) = v3 & subset(v1, v0) = v4 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (product(v6) = v7) | ~ (member(v5, v8) = v9) | ~ (member(v5, v7) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v8, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (difference(v7, v6) = v8) | ~ (member(v5, v8) = v9) | ? [v10] : ((v10 = 0 & member(v5, v6) = 0) | ( ~ (v10 = 0) & member(v5, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (union(v6, v7) = v8) | ~ (member(v5, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & ~ (v10 = 0) & member(v5, v7) = v11 & member(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (intersection(v6, v7) = v8) | ~ (member(v5, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & member(v5, v7) = v10) | ( ~ (v10 = 0) & member(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (sum(v6) = v7) | ~ (member(v9, v6) = 0) | ~ (member(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & member(v5, v9) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (sum(v6) = v7) | ~ (member(v5, v9) = 0) | ~ (member(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & member(v9, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (product(v6) = v7) | ~ (member(v5, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & member(v9, v6) = 0 & member(v5, v9) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unordered_pair(v6, v5) = v7) | ~ (member(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unordered_pair(v5, v6) = v7) | ~ (member(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (power_set(v6) = v7) | ~ (member(v5, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & subset(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v5, v6) = 0) | ~ (member(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v5 | v6 = v5 | ~ (unordered_pair(v6, v7) = v8) | ~ (member(v5, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unordered_pair(v8, v7) = v6) | ~ (unordered_pair(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (difference(v8, v7) = v6) | ~ (difference(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (union(v8, v7) = v6) | ~ (union(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection(v8, v7) = v6) | ~ (intersection(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (equal_set(v8, v7) = v6) | ~ (equal_set(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (subset(v8, v7) = v6) | ~ (subset(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (member(v8, v7) = v6) | ~ (member(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (product(v6) = v7) | ~ (member(v8, v6) = 0) | ~ (member(v5, v7) = 0) | member(v5, v8) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (difference(v7, v6) = v8) | ~ (member(v5, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v5, v7) = 0 & member(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v6, v7) = v8) | ~ (member(v5, v8) = 0) | ? [v9] : ((v9 = 0 & member(v5, v7) = 0) | (v9 = 0 & member(v5, v6) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection(v6, v7) = v8) | ~ (member(v5, v8) = 0) | (member(v5, v7) = 0 & member(v5, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (singleton(v5) = v6) | ~ (member(v5, v6) = v7)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (equal_set(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & subset(v6, v5) = v8) | ( ~ (v8 = 0) & subset(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & power_set(v6) = v8 & member(v5, v8) = v9)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & member(v8, v6) = v9 & member(v8, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (product(v7) = v6) | ~ (product(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (sum(v7) = v6) | ~ (sum(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v7) = v6) | ~ (singleton(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v6) = v7) | ~ (member(v5, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (power_set(v7) = v6) | ~ (power_set(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sum(v6) = v7) | ~ (member(v5, v7) = 0) | ? [v8] : (member(v8, v6) = 0 & member(v5, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (power_set(v6) = v7) | ~ (member(v5, v7) = 0) | subset(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (subset(v6, v5) = v7) | ? [v8] : ((v8 = 0 & v7 = 0 & subset(v5, v6) = 0) | ( ~ (v8 = 0) & equal_set(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (subset(v5, v6) = v7) | ? [v8] : ((v8 = 0 & v7 = 0 & subset(v6, v5) = 0) | ( ~ (v8 = 0) & equal_set(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (subset(v5, v6) = 0) | ~ (member(v7, v5) = 0) | member(v7, v6) = 0) & ! [v5] : ! [v6] : ( ~ (equal_set(v5, v6) = 0) | (subset(v6, v5) = 0 & subset(v5, v6) = 0)) & ! [v5] : ! [v6] : ( ~ (subset(v6, v5) = 0) | ? [v7] : ((v7 = 0 & equal_set(v5, v6) = 0) | ( ~ (v7 = 0) & subset(v5, v6) = v7))) & ! [v5] : ! [v6] : ( ~ (subset(v5, v6) = 0) | ? [v7] : (power_set(v6) = v7 & member(v5, v7) = 0)) & ! [v5] : ! [v6] : ( ~ (subset(v5, v6) = 0) | ? [v7] : ((v7 = 0 & equal_set(v5, v6) = 0) | ( ~ (v7 = 0) & subset(v6, v5) = v7))) & ! [v5] : ~ (member(v5, empty_set) = 0) & ? [v5] : ? [v6] : ? [v7] : unordered_pair(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : difference(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : union(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : intersection(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : equal_set(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : subset(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : member(v6, v5) = v7 & ? [v5] : ? [v6] : product(v5) = v6 & ? [v5] : ? [v6] : sum(v5) = v6 & ? [v5] : ? [v6] : singleton(v5) = v6 & ? [v5] : ? [v6] : power_set(v5) = v6 & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0))))
% 6.78/2.28 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 6.78/2.28 | (1) union(all_0_4_4, all_0_3_3) = all_0_2_2 & equal_set(all_0_4_4, all_0_2_2) = all_0_1_1 & subset(all_0_3_3, all_0_4_4) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ((v5 = 0 & member(v0, v1) = 0) | ( ~ (v5 = 0) & member(v0, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & member(v0, v2) = v5) | ( ~ (v5 = 0) & member(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v4, v1) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ((v4 = 0 & member(v0, v2) = 0) | (v4 = 0 & member(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2))) & ! [v0] : ~ (member(v0, empty_set) = 0) & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2 & ? [v0] : ? [v1] : product(v0) = v1 & ? [v0] : ? [v1] : sum(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : power_set(v0) = v1 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)))
% 6.78/2.30 |
% 6.78/2.30 | Applying alpha-rule on (1) yields:
% 6.78/2.30 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 6.78/2.30 | (3) (all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0))
% 6.78/2.30 | (4) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 6.78/2.30 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 6.78/2.30 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 6.78/2.30 | (7) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 6.78/2.30 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 6.78/2.30 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 6.78/2.30 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4))
% 6.78/2.30 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 6.78/2.30 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 6.78/2.30 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 6.78/2.30 | (14) ? [v0] : ? [v1] : singleton(v0) = v1
% 6.78/2.30 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ((v4 = 0 & member(v0, v2) = 0) | (v4 = 0 & member(v0, v1) = 0)))
% 6.78/2.30 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 6.78/2.30 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 6.78/2.30 | (18) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 6.78/2.30 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 6.78/2.30 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 6.78/2.30 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 6.78/2.30 | (22) ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2
% 6.78/2.30 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5))
% 6.78/2.30 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 6.78/2.30 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v4, v1) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5))
% 6.78/2.30 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & member(v0, v2) = v5) | ( ~ (v5 = 0) & member(v0, v1) = v5)))
% 6.78/2.30 | (27) union(all_0_4_4, all_0_3_3) = all_0_2_2
% 6.78/2.31 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 6.78/2.31 | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 6.78/2.31 | (30) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0))
% 6.78/2.31 | (31) ? [v0] : ? [v1] : sum(v0) = v1
% 6.78/2.31 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 6.78/2.31 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 6.78/2.31 | (34) ? [v0] : ? [v1] : product(v0) = v1
% 6.78/2.31 | (35) ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2
% 6.78/2.31 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 6.78/2.31 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5))
% 6.78/2.31 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0)
% 6.78/2.31 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 6.78/2.31 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 6.78/2.31 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 6.78/2.31 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 6.78/2.31 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ((v5 = 0 & member(v0, v1) = 0) | ( ~ (v5 = 0) & member(v0, v2) = v5)))
% 6.78/2.31 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 7.14/2.31 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 7.14/2.31 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5))
% 7.14/2.31 | (47) equal_set(all_0_4_4, all_0_2_2) = all_0_1_1
% 7.14/2.31 | (48) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2
% 7.14/2.31 | (49) ? [v0] : ? [v1] : power_set(v0) = v1
% 7.14/2.31 | (50) subset(all_0_3_3, all_0_4_4) = all_0_0_0
% 7.14/2.31 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 7.14/2.31 | (52) ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2)))
% 7.14/2.31 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 7.14/2.32 | (54) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2)))
% 7.14/2.32 | (55) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2
% 7.14/2.32 | (56) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2
% 7.14/2.32 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 7.14/2.32 | (58) ! [v0] : ~ (member(v0, empty_set) = 0)
% 7.14/2.32 |
% 7.14/2.32 | Instantiating formula (29) with all_0_1_1, all_0_2_2, all_0_4_4 and discharging atoms equal_set(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 7.14/2.32 | (59) all_0_1_1 = 0 | ? [v0] : (( ~ (v0 = 0) & subset(all_0_2_2, all_0_4_4) = v0) | ( ~ (v0 = 0) & subset(all_0_4_4, all_0_2_2) = v0))
% 7.14/2.32 |
% 7.14/2.32 | Instantiating formula (12) with all_0_0_0, all_0_4_4, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_4_4) = all_0_0_0, yields:
% 7.14/2.32 | (60) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = 0 & member(v0, all_0_4_4) = v1)
% 7.14/2.32 |
% 7.14/2.32 +-Applying beta-rule and splitting (3), into two cases.
% 7.14/2.32 |-Branch one:
% 7.14/2.32 | (61) all_0_0_0 = 0 & ~ (all_0_1_1 = 0)
% 7.14/2.32 |
% 7.14/2.32 | Applying alpha-rule on (61) yields:
% 7.14/2.32 | (62) all_0_0_0 = 0
% 7.14/2.32 | (63) ~ (all_0_1_1 = 0)
% 7.14/2.32 |
% 7.14/2.32 | From (62) and (50) follows:
% 7.14/2.32 | (64) subset(all_0_3_3, all_0_4_4) = 0
% 7.14/2.32 |
% 7.14/2.32 +-Applying beta-rule and splitting (59), into two cases.
% 7.14/2.32 |-Branch one:
% 7.14/2.32 | (65) all_0_1_1 = 0
% 7.14/2.32 |
% 7.14/2.32 | Equations (65) can reduce 63 to:
% 7.14/2.32 | (66) $false
% 7.14/2.32 |
% 7.14/2.32 |-The branch is then unsatisfiable
% 7.14/2.32 |-Branch two:
% 7.14/2.32 | (63) ~ (all_0_1_1 = 0)
% 7.14/2.32 | (68) ? [v0] : (( ~ (v0 = 0) & subset(all_0_2_2, all_0_4_4) = v0) | ( ~ (v0 = 0) & subset(all_0_4_4, all_0_2_2) = v0))
% 7.14/2.32 |
% 7.14/2.32 | Instantiating (68) with all_38_0_36 yields:
% 7.14/2.32 | (69) ( ~ (all_38_0_36 = 0) & subset(all_0_2_2, all_0_4_4) = all_38_0_36) | ( ~ (all_38_0_36 = 0) & subset(all_0_4_4, all_0_2_2) = all_38_0_36)
% 7.14/2.32 |
% 7.14/2.32 +-Applying beta-rule and splitting (69), into two cases.
% 7.14/2.32 |-Branch one:
% 7.14/2.32 | (70) ~ (all_38_0_36 = 0) & subset(all_0_2_2, all_0_4_4) = all_38_0_36
% 7.14/2.32 |
% 7.14/2.32 | Applying alpha-rule on (70) yields:
% 7.14/2.32 | (71) ~ (all_38_0_36 = 0)
% 7.14/2.32 | (72) subset(all_0_2_2, all_0_4_4) = all_38_0_36
% 7.14/2.32 |
% 7.14/2.32 | Instantiating formula (12) with all_38_0_36, all_0_4_4, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_4_4) = all_38_0_36, yields:
% 7.14/2.32 | (73) all_38_0_36 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = 0 & member(v0, all_0_4_4) = v1)
% 7.14/2.32 |
% 7.14/2.32 +-Applying beta-rule and splitting (73), into two cases.
% 7.14/2.32 |-Branch one:
% 7.14/2.32 | (74) all_38_0_36 = 0
% 7.14/2.32 |
% 7.14/2.32 | Equations (74) can reduce 71 to:
% 7.14/2.32 | (66) $false
% 7.14/2.32 |
% 7.14/2.32 |-The branch is then unsatisfiable
% 7.14/2.32 |-Branch two:
% 7.14/2.32 | (71) ~ (all_38_0_36 = 0)
% 7.14/2.32 | (77) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = 0 & member(v0, all_0_4_4) = v1)
% 7.14/2.32 |
% 7.14/2.32 | Instantiating (77) with all_89_0_42, all_89_1_43 yields:
% 7.14/2.32 | (78) ~ (all_89_0_42 = 0) & member(all_89_1_43, all_0_2_2) = 0 & member(all_89_1_43, all_0_4_4) = all_89_0_42
% 7.14/2.32 |
% 7.14/2.32 | Applying alpha-rule on (78) yields:
% 7.14/2.32 | (79) ~ (all_89_0_42 = 0)
% 7.14/2.32 | (80) member(all_89_1_43, all_0_2_2) = 0
% 7.14/2.32 | (81) member(all_89_1_43, all_0_4_4) = all_89_0_42
% 7.14/2.33 |
% 7.14/2.33 | Instantiating formula (15) with all_0_2_2, all_0_3_3, all_0_4_4, all_89_1_43 and discharging atoms union(all_0_4_4, all_0_3_3) = all_0_2_2, member(all_89_1_43, all_0_2_2) = 0, yields:
% 7.14/2.33 | (82) ? [v0] : ((v0 = 0 & member(all_89_1_43, all_0_3_3) = 0) | (v0 = 0 & member(all_89_1_43, all_0_4_4) = 0))
% 7.14/2.33 |
% 7.14/2.33 | Instantiating formula (2) with all_89_0_42, all_89_1_43, all_0_4_4, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_4_4) = 0, member(all_89_1_43, all_0_4_4) = all_89_0_42, yields:
% 7.14/2.33 | (83) all_89_0_42 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_89_1_43, all_0_3_3) = v0)
% 7.14/2.33 |
% 7.14/2.33 | Instantiating (82) with all_109_0_46 yields:
% 7.14/2.33 | (84) (all_109_0_46 = 0 & member(all_89_1_43, all_0_3_3) = 0) | (all_109_0_46 = 0 & member(all_89_1_43, all_0_4_4) = 0)
% 7.14/2.33 |
% 7.14/2.33 +-Applying beta-rule and splitting (83), into two cases.
% 7.14/2.33 |-Branch one:
% 7.14/2.33 | (85) all_89_0_42 = 0
% 7.14/2.33 |
% 7.14/2.33 | Equations (85) can reduce 79 to:
% 7.14/2.33 | (66) $false
% 7.14/2.33 |
% 7.14/2.33 |-The branch is then unsatisfiable
% 7.14/2.33 |-Branch two:
% 7.14/2.33 | (79) ~ (all_89_0_42 = 0)
% 7.14/2.33 | (88) ? [v0] : ( ~ (v0 = 0) & member(all_89_1_43, all_0_3_3) = v0)
% 7.14/2.33 |
% 7.14/2.33 | Instantiating (88) with all_112_0_47 yields:
% 7.14/2.33 | (89) ~ (all_112_0_47 = 0) & member(all_89_1_43, all_0_3_3) = all_112_0_47
% 7.14/2.33 |
% 7.14/2.33 | Applying alpha-rule on (89) yields:
% 7.14/2.33 | (90) ~ (all_112_0_47 = 0)
% 7.14/2.33 | (91) member(all_89_1_43, all_0_3_3) = all_112_0_47
% 7.14/2.33 |
% 7.14/2.33 +-Applying beta-rule and splitting (84), into two cases.
% 7.14/2.33 |-Branch one:
% 7.14/2.33 | (92) all_109_0_46 = 0 & member(all_89_1_43, all_0_3_3) = 0
% 7.14/2.33 |
% 7.14/2.33 | Applying alpha-rule on (92) yields:
% 7.14/2.33 | (93) all_109_0_46 = 0
% 7.14/2.33 | (94) member(all_89_1_43, all_0_3_3) = 0
% 7.14/2.33 |
% 7.14/2.33 | Instantiating formula (28) with all_89_1_43, all_0_3_3, 0, all_112_0_47 and discharging atoms member(all_89_1_43, all_0_3_3) = all_112_0_47, member(all_89_1_43, all_0_3_3) = 0, yields:
% 7.14/2.33 | (95) all_112_0_47 = 0
% 7.14/2.33 |
% 7.14/2.33 | Equations (95) can reduce 90 to:
% 7.14/2.33 | (66) $false
% 7.14/2.33 |
% 7.14/2.33 |-The branch is then unsatisfiable
% 7.14/2.33 |-Branch two:
% 7.14/2.33 | (97) all_109_0_46 = 0 & member(all_89_1_43, all_0_4_4) = 0
% 7.14/2.33 |
% 7.14/2.33 | Applying alpha-rule on (97) yields:
% 7.14/2.33 | (93) all_109_0_46 = 0
% 7.14/2.33 | (99) member(all_89_1_43, all_0_4_4) = 0
% 7.14/2.33 |
% 7.14/2.33 | Instantiating formula (28) with all_89_1_43, all_0_4_4, 0, all_89_0_42 and discharging atoms member(all_89_1_43, all_0_4_4) = all_89_0_42, member(all_89_1_43, all_0_4_4) = 0, yields:
% 7.14/2.33 | (85) all_89_0_42 = 0
% 7.14/2.33 |
% 7.14/2.33 | Equations (85) can reduce 79 to:
% 7.14/2.33 | (66) $false
% 7.14/2.33 |
% 7.14/2.33 |-The branch is then unsatisfiable
% 7.14/2.33 |-Branch two:
% 7.14/2.33 | (102) ~ (all_38_0_36 = 0) & subset(all_0_4_4, all_0_2_2) = all_38_0_36
% 7.14/2.33 |
% 7.14/2.33 | Applying alpha-rule on (102) yields:
% 7.14/2.33 | (71) ~ (all_38_0_36 = 0)
% 7.14/2.33 | (104) subset(all_0_4_4, all_0_2_2) = all_38_0_36
% 7.14/2.33 |
% 7.14/2.33 | Instantiating formula (12) with all_38_0_36, all_0_2_2, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_2_2) = all_38_0_36, yields:
% 7.14/2.33 | (105) all_38_0_36 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = v1 & member(v0, all_0_4_4) = 0)
% 7.14/2.33 |
% 7.14/2.33 +-Applying beta-rule and splitting (105), into two cases.
% 7.14/2.33 |-Branch one:
% 7.14/2.33 | (74) all_38_0_36 = 0
% 7.14/2.33 |
% 7.14/2.33 | Equations (74) can reduce 71 to:
% 7.14/2.33 | (66) $false
% 7.14/2.33 |
% 7.14/2.33 |-The branch is then unsatisfiable
% 7.14/2.33 |-Branch two:
% 7.14/2.33 | (71) ~ (all_38_0_36 = 0)
% 7.14/2.33 | (109) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = v1 & member(v0, all_0_4_4) = 0)
% 7.14/2.33 |
% 7.14/2.33 | Instantiating (109) with all_89_0_51, all_89_1_52 yields:
% 7.14/2.33 | (110) ~ (all_89_0_51 = 0) & member(all_89_1_52, all_0_2_2) = all_89_0_51 & member(all_89_1_52, all_0_4_4) = 0
% 7.14/2.33 |
% 7.14/2.33 | Applying alpha-rule on (110) yields:
% 7.14/2.33 | (111) ~ (all_89_0_51 = 0)
% 7.14/2.33 | (112) member(all_89_1_52, all_0_2_2) = all_89_0_51
% 7.14/2.34 | (113) member(all_89_1_52, all_0_4_4) = 0
% 7.14/2.34 |
% 7.14/2.34 | Instantiating formula (37) with all_89_0_51, all_0_2_2, all_0_3_3, all_0_4_4, all_89_1_52 and discharging atoms union(all_0_4_4, all_0_3_3) = all_0_2_2, member(all_89_1_52, all_0_2_2) = all_89_0_51, yields:
% 7.14/2.34 | (114) all_89_0_51 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_89_1_52, all_0_3_3) = v1 & member(all_89_1_52, all_0_4_4) = v0)
% 7.14/2.34 |
% 7.14/2.34 +-Applying beta-rule and splitting (114), into two cases.
% 7.14/2.34 |-Branch one:
% 7.14/2.34 | (115) all_89_0_51 = 0
% 7.14/2.34 |
% 7.14/2.34 | Equations (115) can reduce 111 to:
% 7.14/2.34 | (66) $false
% 7.14/2.34 |
% 7.14/2.34 |-The branch is then unsatisfiable
% 7.14/2.34 |-Branch two:
% 7.14/2.34 | (111) ~ (all_89_0_51 = 0)
% 7.14/2.34 | (118) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_89_1_52, all_0_3_3) = v1 & member(all_89_1_52, all_0_4_4) = v0)
% 7.14/2.34 |
% 7.14/2.34 | Instantiating (118) with all_110_0_55, all_110_1_56 yields:
% 7.14/2.34 | (119) ~ (all_110_0_55 = 0) & ~ (all_110_1_56 = 0) & member(all_89_1_52, all_0_3_3) = all_110_0_55 & member(all_89_1_52, all_0_4_4) = all_110_1_56
% 7.14/2.34 |
% 7.14/2.34 | Applying alpha-rule on (119) yields:
% 7.14/2.34 | (120) ~ (all_110_0_55 = 0)
% 7.14/2.34 | (121) ~ (all_110_1_56 = 0)
% 7.14/2.34 | (122) member(all_89_1_52, all_0_3_3) = all_110_0_55
% 7.14/2.34 | (123) member(all_89_1_52, all_0_4_4) = all_110_1_56
% 7.14/2.34 |
% 7.14/2.34 | Instantiating formula (28) with all_89_1_52, all_0_4_4, all_110_1_56, 0 and discharging atoms member(all_89_1_52, all_0_4_4) = all_110_1_56, member(all_89_1_52, all_0_4_4) = 0, yields:
% 7.14/2.34 | (124) all_110_1_56 = 0
% 7.14/2.34 |
% 7.14/2.34 | Equations (124) can reduce 121 to:
% 7.14/2.34 | (66) $false
% 7.14/2.34 |
% 7.14/2.34 |-The branch is then unsatisfiable
% 7.14/2.34 |-Branch two:
% 7.14/2.34 | (126) all_0_1_1 = 0 & ~ (all_0_0_0 = 0)
% 7.14/2.34 |
% 7.14/2.34 | Applying alpha-rule on (126) yields:
% 7.14/2.34 | (65) all_0_1_1 = 0
% 7.14/2.34 | (128) ~ (all_0_0_0 = 0)
% 7.14/2.34 |
% 7.14/2.34 | From (65) and (47) follows:
% 7.14/2.34 | (129) equal_set(all_0_4_4, all_0_2_2) = 0
% 7.14/2.34 |
% 7.14/2.34 +-Applying beta-rule and splitting (60), into two cases.
% 7.14/2.34 |-Branch one:
% 7.14/2.34 | (62) all_0_0_0 = 0
% 7.14/2.34 |
% 7.14/2.34 | Equations (62) can reduce 128 to:
% 7.14/2.34 | (66) $false
% 7.14/2.34 |
% 7.14/2.34 |-The branch is then unsatisfiable
% 7.14/2.34 |-Branch two:
% 7.14/2.34 | (128) ~ (all_0_0_0 = 0)
% 7.14/2.34 | (133) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = 0 & member(v0, all_0_4_4) = v1)
% 7.14/2.34 |
% 7.14/2.34 | Instantiating (133) with all_41_0_58, all_41_1_59 yields:
% 7.14/2.34 | (134) ~ (all_41_0_58 = 0) & member(all_41_1_59, all_0_3_3) = 0 & member(all_41_1_59, all_0_4_4) = all_41_0_58
% 7.14/2.34 |
% 7.14/2.34 | Applying alpha-rule on (134) yields:
% 7.14/2.34 | (135) ~ (all_41_0_58 = 0)
% 7.14/2.34 | (136) member(all_41_1_59, all_0_3_3) = 0
% 7.14/2.34 | (137) member(all_41_1_59, all_0_4_4) = all_41_0_58
% 7.14/2.34 |
% 7.14/2.34 | Instantiating formula (18) with all_0_2_2, all_0_4_4 and discharging atoms equal_set(all_0_4_4, all_0_2_2) = 0, yields:
% 7.14/2.34 | (138) subset(all_0_2_2, all_0_4_4) = 0 & subset(all_0_4_4, all_0_2_2) = 0
% 7.14/2.34 |
% 7.14/2.34 | Applying alpha-rule on (138) yields:
% 7.14/2.34 | (139) subset(all_0_2_2, all_0_4_4) = 0
% 7.14/2.34 | (140) subset(all_0_4_4, all_0_2_2) = 0
% 7.14/2.34 |
% 7.14/2.34 | Instantiating formula (2) with all_41_0_58, all_41_1_59, all_0_4_4, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_4_4) = 0, member(all_41_1_59, all_0_4_4) = all_41_0_58, yields:
% 7.14/2.34 | (141) all_41_0_58 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_41_1_59, all_0_2_2) = v0)
% 7.14/2.34 |
% 7.14/2.34 +-Applying beta-rule and splitting (141), into two cases.
% 7.14/2.34 |-Branch one:
% 7.14/2.34 | (142) all_41_0_58 = 0
% 7.14/2.34 |
% 7.14/2.34 | Equations (142) can reduce 135 to:
% 7.14/2.34 | (66) $false
% 7.14/2.34 |
% 7.14/2.34 |-The branch is then unsatisfiable
% 7.14/2.34 |-Branch two:
% 7.14/2.34 | (135) ~ (all_41_0_58 = 0)
% 7.14/2.34 | (145) ? [v0] : ( ~ (v0 = 0) & member(all_41_1_59, all_0_2_2) = v0)
% 7.14/2.34 |
% 7.14/2.34 | Instantiating (145) with all_87_0_70 yields:
% 7.14/2.34 | (146) ~ (all_87_0_70 = 0) & member(all_41_1_59, all_0_2_2) = all_87_0_70
% 7.14/2.34 |
% 7.14/2.34 | Applying alpha-rule on (146) yields:
% 7.14/2.34 | (147) ~ (all_87_0_70 = 0)
% 7.14/2.34 | (148) member(all_41_1_59, all_0_2_2) = all_87_0_70
% 7.14/2.34 |
% 7.14/2.34 | Instantiating formula (37) with all_87_0_70, all_0_2_2, all_0_3_3, all_0_4_4, all_41_1_59 and discharging atoms union(all_0_4_4, all_0_3_3) = all_0_2_2, member(all_41_1_59, all_0_2_2) = all_87_0_70, yields:
% 7.14/2.34 | (149) all_87_0_70 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_41_1_59, all_0_3_3) = v1 & member(all_41_1_59, all_0_4_4) = v0)
% 7.14/2.34 |
% 7.14/2.34 +-Applying beta-rule and splitting (149), into two cases.
% 7.14/2.34 |-Branch one:
% 7.14/2.34 | (150) all_87_0_70 = 0
% 7.14/2.34 |
% 7.14/2.34 | Equations (150) can reduce 147 to:
% 7.14/2.34 | (66) $false
% 7.14/2.34 |
% 7.14/2.34 |-The branch is then unsatisfiable
% 7.14/2.34 |-Branch two:
% 7.14/2.34 | (147) ~ (all_87_0_70 = 0)
% 7.14/2.34 | (153) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_41_1_59, all_0_3_3) = v1 & member(all_41_1_59, all_0_4_4) = v0)
% 7.14/2.34 |
% 7.14/2.34 | Instantiating (153) with all_116_0_71, all_116_1_72 yields:
% 7.14/2.34 | (154) ~ (all_116_0_71 = 0) & ~ (all_116_1_72 = 0) & member(all_41_1_59, all_0_3_3) = all_116_0_71 & member(all_41_1_59, all_0_4_4) = all_116_1_72
% 7.14/2.34 |
% 7.14/2.34 | Applying alpha-rule on (154) yields:
% 7.14/2.34 | (155) ~ (all_116_0_71 = 0)
% 7.14/2.34 | (156) ~ (all_116_1_72 = 0)
% 7.14/2.34 | (157) member(all_41_1_59, all_0_3_3) = all_116_0_71
% 7.14/2.35 | (158) member(all_41_1_59, all_0_4_4) = all_116_1_72
% 7.14/2.35 |
% 7.14/2.35 | Instantiating formula (28) with all_41_1_59, all_0_3_3, all_116_0_71, 0 and discharging atoms member(all_41_1_59, all_0_3_3) = all_116_0_71, member(all_41_1_59, all_0_3_3) = 0, yields:
% 7.14/2.35 | (159) all_116_0_71 = 0
% 7.14/2.35 |
% 7.14/2.35 | Equations (159) can reduce 155 to:
% 7.14/2.35 | (66) $false
% 7.14/2.35 |
% 7.14/2.35 |-The branch is then unsatisfiable
% 7.14/2.35 % SZS output end Proof for theBenchmark
% 7.14/2.35
% 7.14/2.35 1719ms
%------------------------------------------------------------------------------