TSTP Solution File: SET952+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET952+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n021.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 00:23:24 EDT 2022
% Result : Theorem 26.27s 6.92s
% Output : Proof 32.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET952+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 20:19:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.49/0.58 ____ _
% 0.49/0.58 ___ / __ \_____(_)___ ________ __________
% 0.49/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.58
% 0.49/0.58 A Theorem Prover for First-Order Logic
% 0.49/0.59 (ePrincess v.1.0)
% 0.49/0.59
% 0.49/0.59 (c) Philipp Rümmer, 2009-2015
% 0.49/0.59 (c) Peter Backeman, 2014-2015
% 0.49/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.59 Bug reports to peter@backeman.se
% 0.49/0.59
% 0.49/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.59
% 0.49/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.32/0.92 Prover 0: Preprocessing ...
% 2.16/1.20 Prover 0: Warning: ignoring some quantifiers
% 2.16/1.22 Prover 0: Constructing countermodel ...
% 21.26/5.84 Prover 0: gave up
% 21.26/5.85 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 21.62/5.87 Prover 1: Preprocessing ...
% 22.02/5.96 Prover 1: Warning: ignoring some quantifiers
% 22.02/5.96 Prover 1: Constructing countermodel ...
% 24.34/6.49 Prover 1: gave up
% 24.34/6.49 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 24.44/6.51 Prover 2: Preprocessing ...
% 24.57/6.59 Prover 2: Warning: ignoring some quantifiers
% 24.57/6.59 Prover 2: Constructing countermodel ...
% 26.27/6.92 Prover 2: proved (432ms)
% 26.27/6.92
% 26.27/6.92 No countermodel exists, formula is valid
% 26.27/6.92 % SZS status Theorem for theBenchmark
% 26.27/6.92
% 26.27/6.92 Generating proof ... Warning: ignoring some quantifiers
% 32.37/8.38 found it (size 118)
% 32.37/8.38
% 32.37/8.38 % SZS output start Proof for theBenchmark
% 32.37/8.38 Assumed formulas after preprocessing and simplification:
% 32.37/8.38 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v8 = 0) & ~ (v6 = 0) & empty(v9) = 0 & empty(v7) = v8 & cartesian_product2(v0, v1) = v2 & powerset(v4) = v5 & powerset(v3) = v4 & subset(v2, v5) = v6 & set_union2(v0, v1) = v3 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = 0 | ~ (cartesian_product2(v10, v11) = v12) | ~ (ordered_pair(v15, v16) = v13) | ~ (in(v13, v12) = v14) | ? [v17] : (( ~ (v17 = 0) & in(v16, v11) = v17) | ( ~ (v17 = 0) & in(v15, v10) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v13, v12) = v14) | ~ (unordered_pair(v10, v11) = v13) | ? [v15] : (( ~ (v15 = 0) & in(v11, v12) = v15) | ( ~ (v15 = 0) & in(v10, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (set_union2(v10, v11) = v12) | ~ (in(v13, v12) = v14) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & ~ (v15 = 0) & in(v13, v11) = v16 & in(v13, v10) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (set_union2(v10, v11) = v12) | ~ (in(v13, v11) = v14) | ? [v15] : ((v15 = 0 & in(v13, v10) = 0) | ( ~ (v15 = 0) & in(v13, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (set_union2(v10, v11) = v12) | ~ (in(v13, v10) = v14) | ? [v15] : ((v15 = 0 & in(v13, v11) = 0) | ( ~ (v15 = 0) & in(v13, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v10, v11) = v12) | ~ (in(v13, v11) = v14) | ? [v15] : ((v15 = 0 & in(v13, v12) = 0) | ( ~ (v15 = 0) & ~ (v14 = 0) & in(v13, v10) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v10, v11) = v12) | ~ (in(v13, v10) = v14) | ? [v15] : ((v15 = 0 & in(v13, v12) = 0) | ( ~ (v15 = 0) & ~ (v14 = 0) & in(v13, v11) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | v13 = v10 | ~ (unordered_pair(v10, v11) = v12) | ~ (in(v13, v12) = 0)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (singleton(v10) = v12) | ~ (subset(v12, v11) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (powerset(v10) = v11) | ~ (subset(v12, v10) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v12, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (powerset(v10) = v11) | ~ (in(v12, v11) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v12, v10) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v11, v12) = 0) | ~ (subset(v10, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v10, v12) = v13) | ~ (subset(v10, v11) = 0) | ? [v14] : ( ~ (v14 = 0) & subset(v11, v12) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v10, v11) = 0) | ~ (in(v12, v11) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v12, v10) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (unordered_pair(v10, v11) = v12) | ~ (in(v11, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (unordered_pair(v10, v11) = v12) | ~ (in(v10, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (cartesian_product2(v13, v12) = v11) | ~ (cartesian_product2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (ordered_pair(v13, v12) = v11) | ~ (ordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (subset(v13, v12) = v11) | ~ (subset(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_union2(v13, v12) = v11) | ~ (set_union2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (unordered_pair(v13, v12) = v11) | ~ (unordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (in(v13, v12) = v11) | ~ (in(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v10, v11) = v12) | ~ (in(v13, v12) = 0) | ? [v14] : ? [v15] : (ordered_pair(v14, v15) = v13 & in(v15, v11) = 0 & in(v14, v10) = 0)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (subset(v13, v12) = 0) | ~ (unordered_pair(v10, v11) = v13) | (in(v11, v12) = 0 & in(v10, v12) = 0)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v10, v11) = v12) | ~ (in(v13, v12) = 0) | ? [v14] : ((v14 = 0 & in(v13, v11) = 0) | (v14 = 0 & in(v13, v10) = 0))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (cartesian_product2(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (( ! [v21] : ! [v22] : ( ~ (ordered_pair(v21, v22) = v14) | ? [v23] : (( ~ (v23 = 0) & in(v22, v12) = v23) | ( ~ (v23 = 0) & in(v21, v11) = v23))) | ( ~ (v15 = 0) & in(v14, v10) = v15)) & ((v20 = v14 & v19 = 0 & v18 = 0 & ordered_pair(v16, v17) = v14 & in(v17, v12) = 0 & in(v16, v11) = 0) | (v15 = 0 & in(v14, v10) = 0)))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (set_union2(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (((v17 = 0 & in(v14, v12) = 0) | (v16 = 0 & in(v14, v11) = 0) | (v15 = 0 & in(v14, v10) = 0)) & (( ~ (v17 = 0) & ~ (v16 = 0) & in(v14, v12) = v17 & in(v14, v11) = v16) | ( ~ (v15 = 0) & in(v14, v10) = v15)))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (unordered_pair(v11, v12) = v13) | ? [v14] : ? [v15] : ((v14 = v12 | v14 = v11 | (v15 = 0 & in(v14, v10) = 0)) & (( ~ (v15 = 0) & in(v14, v10) = v15) | ( ~ (v14 = v12) & ~ (v14 = v11))))) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v10, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & in(v13, v11) = v14 & in(v13, v10) = 0)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (in(v10, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & singleton(v10) = v13 & subset(v13, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (empty(v12) = v11) | ~ (empty(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v12) = v11) | ~ (singleton(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (powerset(v12) = v11) | ~ (powerset(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (singleton(v10) = v12) | ~ (subset(v12, v11) = 0) | in(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ? [v13] : ? [v14] : (singleton(v10) = v14 & unordered_pair(v13, v14) = v12 & unordered_pair(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v10) = v11) | ~ (subset(v12, v10) = 0) | in(v12, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v10) = v11) | ~ (in(v12, v11) = 0) | subset(v12, v10) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (subset(v11, v12) = 0) | ~ (subset(v10, v11) = 0) | subset(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (subset(v10, v11) = 0) | ~ (in(v12, v10) = 0) | in(v12, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v11, v10) = v12) | set_union2(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v11, v10) = v12) | ? [v13] : ((v13 = 0 & empty(v10) = 0) | ( ~ (v13 = 0) & empty(v12) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | subset(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | set_union2(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | ? [v13] : ((v13 = 0 & empty(v10) = 0) | ( ~ (v13 = 0) & empty(v12) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v11, v10) = v12) | unordered_pair(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | unordered_pair(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | ? [v13] : ? [v14] : (singleton(v10) = v14 & ordered_pair(v10, v11) = v13 & unordered_pair(v12, v14) = v13)) & ? [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (powerset(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (((v15 = 0 & subset(v13, v11) = 0) | (v14 = 0 & in(v13, v10) = 0)) & (( ~ (v15 = 0) & subset(v13, v11) = v15) | ( ~ (v14 = 0) & in(v13, v10) = v14)))) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_union2(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v10, v10) = v11)) & ! [v10] : ! [v11] : ( ~ (in(v11, v10) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v10) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : (singleton(v10) = v12 & subset(v12, v11) = 0)) & ? [v10] : ? [v11] : ? [v12] : cartesian_product2(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : ordered_pair(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : subset(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : set_union2(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : unordered_pair(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : in(v11, v10) = v12 & ? [v10] : ? [v11] : empty(v10) = v11 & ? [v10] : ? [v11] : singleton(v10) = v11 & ? [v10] : ? [v11] : powerset(v10) = v11)
% 32.71/8.44 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields:
% 32.71/8.44 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & cartesian_product2(all_0_9_9, all_0_8_8) = all_0_7_7 & powerset(all_0_5_5) = all_0_4_4 & powerset(all_0_6_6) = all_0_5_5 & subset(all_0_7_7, all_0_4_4) = all_0_3_3 & set_union2(all_0_9_9, all_0_8_8) = all_0_6_6 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ? [v7] : (( ~ (v7 = 0) & in(v6, v1) = v7) | ( ~ (v7 = 0) & in(v5, v0) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ? [v5] : (( ~ (v5 = 0) & in(v1, v2) = v5) | ( ~ (v5 = 0) & in(v0, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ((v4 = 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (( ! [v11] : ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) | ? [v13] : (( ~ (v13 = 0) & in(v12, v2) = v13) | ( ~ (v13 = 0) & in(v11, v1) = v13))) | ( ~ (v5 = 0) & in(v4, v0) = v5)) & ((v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | (v6 = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & ~ (v6 = 0) & in(v4, v2) = v7 & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : ((v4 = v2 | v4 = v1 | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v5 = 0) & in(v4, v0) = v5) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & singleton(v0) = v3 & subset(v3, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | subset(v2, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3)) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & subset(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v5 = 0) & subset(v3, v1) = v5) | ( ~ (v4 = 0) & in(v3, v0) = v4)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : (singleton(v0) = v2 & subset(v2, v1) = 0)) & ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : empty(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : powerset(v0) = v1
% 32.71/8.45 |
% 32.71/8.45 | Applying alpha-rule on (1) yields:
% 32.71/8.45 | (2) ~ (all_0_1_1 = 0)
% 32.71/8.45 | (3) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 32.71/8.45 | (4) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 32.71/8.45 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 32.71/8.45 | (6) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 32.71/8.45 | (7) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 32.71/8.45 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ? [v7] : (( ~ (v7 = 0) & in(v6, v1) = v7) | ( ~ (v7 = 0) & in(v5, v0) = v7)))
% 32.71/8.45 | (9) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : ((v4 = v2 | v4 = v1 | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v5 = 0) & in(v4, v0) = v5) | ( ~ (v4 = v2) & ~ (v4 = v1)))))
% 32.71/8.45 | (10) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 32.71/8.45 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 32.71/8.45 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 32.71/8.45 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 32.71/8.45 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3))
% 32.71/8.45 | (15) ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2
% 32.71/8.45 | (16) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2
% 32.71/8.45 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 32.71/8.45 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 32.71/8.45 | (19) ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2
% 32.71/8.45 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 32.71/8.45 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0)
% 32.71/8.45 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3))
% 32.71/8.45 | (23) powerset(all_0_6_6) = all_0_5_5
% 32.71/8.45 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v2, v0) = v4))
% 32.71/8.45 | (25) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 32.71/8.45 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & singleton(v0) = v3 & subset(v3, v1) = v4))
% 32.71/8.45 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ? [v5] : (( ~ (v5 = 0) & in(v1, v2) = v5) | ( ~ (v5 = 0) & in(v0, v2) = v5)))
% 32.71/8.45 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 32.71/8.46 | (29) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (( ! [v11] : ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) | ? [v13] : (( ~ (v13 = 0) & in(v12, v2) = v13) | ( ~ (v13 = 0) & in(v11, v1) = v13))) | ( ~ (v5 = 0) & in(v4, v0) = v5)) & ((v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0) | (v5 = 0 & in(v4, v0) = 0))))
% 32.71/8.46 | (30) ? [v0] : ? [v1] : singleton(v0) = v1
% 32.71/8.46 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 32.71/8.46 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4))
% 32.71/8.46 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 32.71/8.46 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v0) = v5)))
% 32.71/8.46 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v1) = v5)))
% 32.71/8.46 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0)
% 32.71/8.46 | (37) subset(all_0_7_7, all_0_4_4) = all_0_3_3
% 32.71/8.46 | (38) empty(all_0_2_2) = all_0_1_1
% 32.71/8.46 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 32.71/8.46 | (40) set_union2(all_0_9_9, all_0_8_8) = all_0_6_6
% 32.71/8.46 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3))
% 32.71/8.46 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | subset(v2, v0) = 0)
% 32.71/8.46 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0)
% 32.71/8.46 | (44) empty(all_0_0_0) = 0
% 32.71/8.46 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 32.71/8.46 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5))
% 32.71/8.46 | (47) cartesian_product2(all_0_9_9, all_0_8_8) = all_0_7_7
% 32.71/8.46 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 32.71/8.46 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 32.71/8.46 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 32.71/8.46 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0)
% 32.71/8.46 | (52) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 32.71/8.46 | (53) ~ (all_0_3_3 = 0)
% 32.71/8.46 | (54) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & subset(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v5 = 0) & subset(v3, v1) = v5) | ( ~ (v4 = 0) & in(v3, v0) = v4))))
% 32.71/8.46 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 32.71/8.46 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 32.71/8.46 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0))
% 32.71/8.46 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 32.71/8.46 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 32.71/8.46 | (60) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : (singleton(v0) = v2 & subset(v2, v1) = 0))
% 32.71/8.46 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 32.71/8.46 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0))
% 32.71/8.46 | (63) ? [v0] : ? [v1] : powerset(v0) = v1
% 32.71/8.46 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 32.71/8.46 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 32.71/8.46 | (66) ? [v0] : ? [v1] : empty(v0) = v1
% 32.71/8.46 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0))
% 32.71/8.46 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 32.71/8.47 | (69) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | (v6 = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & ~ (v6 = 0) & in(v4, v2) = v7 & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5))))
% 32.71/8.47 | (70) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 32.71/8.47 | (71) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 32.71/8.47 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ((v4 = 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0)))
% 32.71/8.47 | (73) powerset(all_0_5_5) = all_0_4_4
% 32.71/8.47 |
% 32.71/8.47 | Instantiating formula (52) with all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_4_4) = all_0_3_3, yields:
% 32.71/8.47 | (74) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_7_7) = 0)
% 32.71/8.47 |
% 32.71/8.47 | Instantiating formula (18) with all_0_6_6, all_0_9_9, all_0_8_8 and discharging atoms set_union2(all_0_9_9, all_0_8_8) = all_0_6_6, yields:
% 32.71/8.47 | (75) set_union2(all_0_8_8, all_0_9_9) = all_0_6_6
% 32.71/8.47 |
% 32.71/8.47 | Instantiating formula (21) with all_0_6_6, all_0_8_8, all_0_9_9 and discharging atoms set_union2(all_0_9_9, all_0_8_8) = all_0_6_6, yields:
% 32.71/8.47 | (76) subset(all_0_9_9, all_0_6_6) = 0
% 32.71/8.47 |
% 32.71/8.47 +-Applying beta-rule and splitting (74), into two cases.
% 32.71/8.47 |-Branch one:
% 32.71/8.47 | (77) all_0_3_3 = 0
% 32.71/8.47 |
% 32.71/8.47 | Equations (77) can reduce 53 to:
% 32.71/8.47 | (78) $false
% 32.71/8.47 |
% 32.71/8.47 |-The branch is then unsatisfiable
% 32.71/8.47 |-Branch two:
% 32.71/8.47 | (53) ~ (all_0_3_3 = 0)
% 32.71/8.47 | (80) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_7_7) = 0)
% 32.71/8.47 |
% 32.71/8.47 | Instantiating (80) with all_41_0_40, all_41_1_41 yields:
% 32.71/8.47 | (81) ~ (all_41_0_40 = 0) & in(all_41_1_41, all_0_4_4) = all_41_0_40 & in(all_41_1_41, all_0_7_7) = 0
% 32.71/8.47 |
% 32.71/8.47 | Applying alpha-rule on (81) yields:
% 32.71/8.47 | (82) ~ (all_41_0_40 = 0)
% 32.71/8.47 | (83) in(all_41_1_41, all_0_4_4) = all_41_0_40
% 32.71/8.47 | (84) in(all_41_1_41, all_0_7_7) = 0
% 32.71/8.47 |
% 32.71/8.47 | Instantiating formula (43) with all_0_9_9, all_0_5_5, all_0_6_6 and discharging atoms powerset(all_0_6_6) = all_0_5_5, subset(all_0_9_9, all_0_6_6) = 0, yields:
% 32.71/8.47 | (85) in(all_0_9_9, all_0_5_5) = 0
% 32.71/8.47 |
% 32.71/8.47 | Instantiating formula (21) with all_0_6_6, all_0_9_9, all_0_8_8 and discharging atoms set_union2(all_0_8_8, all_0_9_9) = all_0_6_6, yields:
% 32.71/8.47 | (86) subset(all_0_8_8, all_0_6_6) = 0
% 32.71/8.47 |
% 32.71/8.47 | Instantiating formula (24) with all_41_0_40, all_41_1_41, all_0_4_4, all_0_5_5 and discharging atoms powerset(all_0_5_5) = all_0_4_4, in(all_41_1_41, all_0_4_4) = all_41_0_40, yields:
% 32.71/8.47 | (87) all_41_0_40 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_41_1_41, all_0_5_5) = v0)
% 32.71/8.47 |
% 32.71/8.47 | Instantiating formula (67) with all_41_1_41, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms cartesian_product2(all_0_9_9, all_0_8_8) = all_0_7_7, in(all_41_1_41, all_0_7_7) = 0, yields:
% 32.71/8.47 | (88) ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_41_1_41 & in(v1, all_0_8_8) = 0 & in(v0, all_0_9_9) = 0)
% 32.71/8.47 |
% 32.71/8.47 | Instantiating (88) with all_51_0_43, all_51_1_44 yields:
% 32.71/8.47 | (89) ordered_pair(all_51_1_44, all_51_0_43) = all_41_1_41 & in(all_51_0_43, all_0_8_8) = 0 & in(all_51_1_44, all_0_9_9) = 0
% 32.71/8.47 |
% 32.71/8.47 | Applying alpha-rule on (89) yields:
% 32.71/8.47 | (90) ordered_pair(all_51_1_44, all_51_0_43) = all_41_1_41
% 32.71/8.47 | (91) in(all_51_0_43, all_0_8_8) = 0
% 32.71/8.47 | (92) in(all_51_1_44, all_0_9_9) = 0
% 32.71/8.47 |
% 32.71/8.47 +-Applying beta-rule and splitting (87), into two cases.
% 32.71/8.47 |-Branch one:
% 32.71/8.47 | (93) all_41_0_40 = 0
% 32.71/8.47 |
% 32.71/8.47 | Equations (93) can reduce 82 to:
% 32.71/8.47 | (78) $false
% 32.71/8.47 |
% 32.71/8.47 |-The branch is then unsatisfiable
% 32.71/8.47 |-Branch two:
% 32.71/8.47 | (82) ~ (all_41_0_40 = 0)
% 32.71/8.47 | (96) ? [v0] : ( ~ (v0 = 0) & subset(all_41_1_41, all_0_5_5) = v0)
% 32.71/8.47 |
% 32.71/8.47 | Instantiating (96) with all_61_0_48 yields:
% 32.71/8.47 | (97) ~ (all_61_0_48 = 0) & subset(all_41_1_41, all_0_5_5) = all_61_0_48
% 32.71/8.47 |
% 32.71/8.47 | Applying alpha-rule on (97) yields:
% 32.71/8.47 | (98) ~ (all_61_0_48 = 0)
% 32.71/8.47 | (99) subset(all_41_1_41, all_0_5_5) = all_61_0_48
% 32.71/8.47 |
% 32.93/8.47 | Instantiating formula (49) with all_41_1_41, all_51_0_43, all_51_1_44 and discharging atoms ordered_pair(all_51_1_44, all_51_0_43) = all_41_1_41, yields:
% 32.93/8.47 | (100) ? [v0] : ? [v1] : (singleton(all_51_1_44) = v1 & unordered_pair(v0, v1) = all_41_1_41 & unordered_pair(all_51_1_44, all_51_0_43) = v0)
% 32.93/8.47 |
% 32.93/8.47 | Instantiating formula (52) with all_61_0_48, all_0_5_5, all_41_1_41 and discharging atoms subset(all_41_1_41, all_0_5_5) = all_61_0_48, yields:
% 32.93/8.47 | (101) all_61_0_48 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_41_1_41) = 0 & in(v0, all_0_5_5) = v1)
% 32.93/8.47 |
% 32.93/8.47 | Instantiating formula (43) with all_0_8_8, all_0_5_5, all_0_6_6 and discharging atoms powerset(all_0_6_6) = all_0_5_5, subset(all_0_8_8, all_0_6_6) = 0, yields:
% 32.93/8.47 | (102) in(all_0_8_8, all_0_5_5) = 0
% 32.93/8.47 |
% 32.93/8.47 | Instantiating formula (59) with all_51_0_43, all_0_6_6, all_0_8_8 and discharging atoms subset(all_0_8_8, all_0_6_6) = 0, in(all_51_0_43, all_0_8_8) = 0, yields:
% 32.93/8.47 | (103) in(all_51_0_43, all_0_6_6) = 0
% 32.93/8.47 |
% 32.93/8.47 | Instantiating formula (60) with all_0_8_8, all_51_0_43 and discharging atoms in(all_51_0_43, all_0_8_8) = 0, yields:
% 32.93/8.47 | (104) ? [v0] : (singleton(all_51_0_43) = v0 & subset(v0, all_0_8_8) = 0)
% 32.93/8.47 |
% 32.93/8.47 | Instantiating formula (59) with all_51_1_44, all_0_6_6, all_0_9_9 and discharging atoms subset(all_0_9_9, all_0_6_6) = 0, in(all_51_1_44, all_0_9_9) = 0, yields:
% 32.93/8.47 | (105) in(all_51_1_44, all_0_6_6) = 0
% 32.93/8.47 |
% 32.93/8.47 | Instantiating formula (60) with all_0_9_9, all_51_1_44 and discharging atoms in(all_51_1_44, all_0_9_9) = 0, yields:
% 32.93/8.47 | (106) ? [v0] : (singleton(all_51_1_44) = v0 & subset(v0, all_0_9_9) = 0)
% 32.93/8.47 |
% 32.93/8.47 | Instantiating formula (60) with all_0_5_5, all_0_9_9 and discharging atoms in(all_0_9_9, all_0_5_5) = 0, yields:
% 32.93/8.48 | (107) ? [v0] : (singleton(all_0_9_9) = v0 & subset(v0, all_0_5_5) = 0)
% 32.93/8.48 |
% 32.93/8.48 | Instantiating (100) with all_80_0_52, all_80_1_53 yields:
% 32.93/8.48 | (108) singleton(all_51_1_44) = all_80_0_52 & unordered_pair(all_80_1_53, all_80_0_52) = all_41_1_41 & unordered_pair(all_51_1_44, all_51_0_43) = all_80_1_53
% 32.93/8.48 |
% 32.93/8.48 | Applying alpha-rule on (108) yields:
% 32.93/8.48 | (109) singleton(all_51_1_44) = all_80_0_52
% 32.93/8.48 | (110) unordered_pair(all_80_1_53, all_80_0_52) = all_41_1_41
% 32.93/8.48 | (111) unordered_pair(all_51_1_44, all_51_0_43) = all_80_1_53
% 32.93/8.48 |
% 32.93/8.48 | Instantiating (107) with all_82_0_54 yields:
% 32.93/8.48 | (112) singleton(all_0_9_9) = all_82_0_54 & subset(all_82_0_54, all_0_5_5) = 0
% 32.93/8.48 |
% 32.93/8.48 | Applying alpha-rule on (112) yields:
% 32.93/8.48 | (113) singleton(all_0_9_9) = all_82_0_54
% 32.93/8.48 | (114) subset(all_82_0_54, all_0_5_5) = 0
% 32.93/8.48 |
% 32.93/8.48 | Instantiating (106) with all_88_0_57 yields:
% 32.93/8.48 | (115) singleton(all_51_1_44) = all_88_0_57 & subset(all_88_0_57, all_0_9_9) = 0
% 32.93/8.48 |
% 32.93/8.48 | Applying alpha-rule on (115) yields:
% 32.93/8.48 | (116) singleton(all_51_1_44) = all_88_0_57
% 32.93/8.48 | (117) subset(all_88_0_57, all_0_9_9) = 0
% 32.93/8.48 |
% 32.93/8.48 | Instantiating (104) with all_90_0_58 yields:
% 32.93/8.48 | (118) singleton(all_51_0_43) = all_90_0_58 & subset(all_90_0_58, all_0_8_8) = 0
% 32.93/8.48 |
% 32.93/8.48 | Applying alpha-rule on (118) yields:
% 32.93/8.48 | (119) singleton(all_51_0_43) = all_90_0_58
% 32.93/8.48 | (120) subset(all_90_0_58, all_0_8_8) = 0
% 32.93/8.48 |
% 32.93/8.48 +-Applying beta-rule and splitting (101), into two cases.
% 32.93/8.48 |-Branch one:
% 32.93/8.48 | (121) all_61_0_48 = 0
% 32.93/8.48 |
% 32.93/8.48 | Equations (121) can reduce 98 to:
% 32.93/8.48 | (78) $false
% 32.93/8.48 |
% 32.93/8.48 |-The branch is then unsatisfiable
% 32.93/8.48 |-Branch two:
% 32.93/8.48 | (98) ~ (all_61_0_48 = 0)
% 32.93/8.48 | (124) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_41_1_41) = 0 & in(v0, all_0_5_5) = v1)
% 32.93/8.48 |
% 32.93/8.48 | Instantiating (124) with all_103_0_62, all_103_1_63 yields:
% 32.93/8.48 | (125) ~ (all_103_0_62 = 0) & in(all_103_1_63, all_41_1_41) = 0 & in(all_103_1_63, all_0_5_5) = all_103_0_62
% 32.93/8.48 |
% 32.93/8.48 | Applying alpha-rule on (125) yields:
% 32.93/8.48 | (126) ~ (all_103_0_62 = 0)
% 32.93/8.48 | (127) in(all_103_1_63, all_41_1_41) = 0
% 32.93/8.48 | (128) in(all_103_1_63, all_0_5_5) = all_103_0_62
% 32.93/8.48 |
% 32.93/8.48 | Instantiating formula (20) with all_51_1_44, all_80_0_52, all_88_0_57 and discharging atoms singleton(all_51_1_44) = all_88_0_57, singleton(all_51_1_44) = all_80_0_52, yields:
% 32.93/8.48 | (129) all_88_0_57 = all_80_0_52
% 32.93/8.48 |
% 32.93/8.48 | From (129) and (116) follows:
% 32.93/8.48 | (109) singleton(all_51_1_44) = all_80_0_52
% 32.93/8.48 |
% 32.93/8.48 | Instantiating formula (12) with all_41_1_41, all_80_1_53, all_80_0_52 and discharging atoms unordered_pair(all_80_1_53, all_80_0_52) = all_41_1_41, yields:
% 32.93/8.48 | (131) unordered_pair(all_80_0_52, all_80_1_53) = all_41_1_41
% 32.93/8.48 |
% 32.93/8.48 | Instantiating formula (24) with all_103_0_62, all_103_1_63, all_0_5_5, all_0_6_6 and discharging atoms powerset(all_0_6_6) = all_0_5_5, in(all_103_1_63, all_0_5_5) = all_103_0_62, yields:
% 32.93/8.48 | (132) all_103_0_62 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_103_1_63, all_0_6_6) = v0)
% 32.93/8.48 |
% 32.93/8.48 | Instantiating formula (58) with all_103_0_62, all_103_1_63, all_0_5_5, all_82_0_54 and discharging atoms subset(all_82_0_54, all_0_5_5) = 0, in(all_103_1_63, all_0_5_5) = all_103_0_62, yields:
% 32.93/8.48 | (133) all_103_0_62 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_103_1_63, all_82_0_54) = v0)
% 32.93/8.48 |
% 32.93/8.48 | Instantiating formula (26) with all_103_0_62, all_0_5_5, all_103_1_63 and discharging atoms in(all_103_1_63, all_0_5_5) = all_103_0_62, yields:
% 32.93/8.48 | (134) all_103_0_62 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & singleton(all_103_1_63) = v0 & subset(v0, all_0_5_5) = v1)
% 32.93/8.48 |
% 32.93/8.48 | Instantiating formula (60) with all_0_6_6, all_51_0_43 and discharging atoms in(all_51_0_43, all_0_6_6) = 0, yields:
% 32.93/8.48 | (135) ? [v0] : (singleton(all_51_0_43) = v0 & subset(v0, all_0_6_6) = 0)
% 32.93/8.48 |
% 32.93/8.48 | Instantiating formula (60) with all_0_6_6, all_51_1_44 and discharging atoms in(all_51_1_44, all_0_6_6) = 0, yields:
% 32.93/8.48 | (136) ? [v0] : (singleton(all_51_1_44) = v0 & subset(v0, all_0_6_6) = 0)
% 32.93/8.48 |
% 32.93/8.48 | Instantiating formula (60) with all_0_5_5, all_0_8_8 and discharging atoms in(all_0_8_8, all_0_5_5) = 0, yields:
% 32.93/8.48 | (137) ? [v0] : (singleton(all_0_8_8) = v0 & subset(v0, all_0_5_5) = 0)
% 32.93/8.48 |
% 32.93/8.48 | Instantiating (135) with all_122_0_67 yields:
% 32.93/8.48 | (138) singleton(all_51_0_43) = all_122_0_67 & subset(all_122_0_67, all_0_6_6) = 0
% 32.93/8.48 |
% 32.93/8.48 | Applying alpha-rule on (138) yields:
% 32.93/8.48 | (139) singleton(all_51_0_43) = all_122_0_67
% 32.93/8.48 | (140) subset(all_122_0_67, all_0_6_6) = 0
% 32.93/8.48 |
% 32.93/8.48 | Instantiating (137) with all_130_0_72 yields:
% 32.93/8.48 | (141) singleton(all_0_8_8) = all_130_0_72 & subset(all_130_0_72, all_0_5_5) = 0
% 32.93/8.48 |
% 32.93/8.48 | Applying alpha-rule on (141) yields:
% 32.93/8.48 | (142) singleton(all_0_8_8) = all_130_0_72
% 32.93/8.48 | (143) subset(all_130_0_72, all_0_5_5) = 0
% 32.93/8.48 |
% 32.93/8.48 | Instantiating (136) with all_141_0_78 yields:
% 32.93/8.48 | (144) singleton(all_51_1_44) = all_141_0_78 & subset(all_141_0_78, all_0_6_6) = 0
% 32.93/8.48 |
% 32.93/8.48 | Applying alpha-rule on (144) yields:
% 32.93/8.48 | (145) singleton(all_51_1_44) = all_141_0_78
% 32.93/8.48 | (146) subset(all_141_0_78, all_0_6_6) = 0
% 32.93/8.48 |
% 32.93/8.48 +-Applying beta-rule and splitting (133), into two cases.
% 32.93/8.48 |-Branch one:
% 32.93/8.48 | (147) all_103_0_62 = 0
% 32.93/8.48 |
% 32.93/8.48 | Equations (147) can reduce 126 to:
% 32.93/8.48 | (78) $false
% 32.93/8.48 |
% 32.93/8.48 |-The branch is then unsatisfiable
% 32.93/8.48 |-Branch two:
% 32.93/8.48 | (126) ~ (all_103_0_62 = 0)
% 32.93/8.48 | (150) ? [v0] : ( ~ (v0 = 0) & in(all_103_1_63, all_82_0_54) = v0)
% 32.93/8.48 |
% 32.93/8.48 +-Applying beta-rule and splitting (134), into two cases.
% 32.93/8.48 |-Branch one:
% 32.93/8.48 | (147) all_103_0_62 = 0
% 32.93/8.48 |
% 32.93/8.48 | Equations (147) can reduce 126 to:
% 32.93/8.48 | (78) $false
% 32.93/8.48 |
% 32.93/8.48 |-The branch is then unsatisfiable
% 32.93/8.48 |-Branch two:
% 32.93/8.48 | (126) ~ (all_103_0_62 = 0)
% 32.93/8.48 | (154) ? [v0] : ? [v1] : ( ~ (v1 = 0) & singleton(all_103_1_63) = v0 & subset(v0, all_0_5_5) = v1)
% 32.93/8.48 |
% 32.93/8.48 +-Applying beta-rule and splitting (132), into two cases.
% 32.93/8.48 |-Branch one:
% 32.93/8.48 | (147) all_103_0_62 = 0
% 32.93/8.48 |
% 32.93/8.48 | Equations (147) can reduce 126 to:
% 32.93/8.48 | (78) $false
% 32.93/8.48 |
% 32.93/8.48 |-The branch is then unsatisfiable
% 32.93/8.48 |-Branch two:
% 32.93/8.48 | (126) ~ (all_103_0_62 = 0)
% 32.93/8.48 | (158) ? [v0] : ( ~ (v0 = 0) & subset(all_103_1_63, all_0_6_6) = v0)
% 32.93/8.48 |
% 32.93/8.48 | Instantiating (158) with all_205_0_97 yields:
% 32.93/8.48 | (159) ~ (all_205_0_97 = 0) & subset(all_103_1_63, all_0_6_6) = all_205_0_97
% 32.93/8.48 |
% 32.93/8.48 | Applying alpha-rule on (159) yields:
% 32.93/8.49 | (160) ~ (all_205_0_97 = 0)
% 32.93/8.49 | (161) subset(all_103_1_63, all_0_6_6) = all_205_0_97
% 32.93/8.49 |
% 32.93/8.49 | Instantiating formula (20) with all_51_0_43, all_122_0_67, all_90_0_58 and discharging atoms singleton(all_51_0_43) = all_122_0_67, singleton(all_51_0_43) = all_90_0_58, yields:
% 32.93/8.49 | (162) all_122_0_67 = all_90_0_58
% 32.93/8.49 |
% 32.93/8.49 | Instantiating formula (20) with all_51_1_44, all_141_0_78, all_80_0_52 and discharging atoms singleton(all_51_1_44) = all_141_0_78, singleton(all_51_1_44) = all_80_0_52, yields:
% 32.93/8.49 | (163) all_141_0_78 = all_80_0_52
% 32.93/8.49 |
% 32.93/8.49 | Instantiating formula (62) with all_103_1_63, all_41_1_41, all_80_1_53, all_80_0_52 and discharging atoms unordered_pair(all_80_0_52, all_80_1_53) = all_41_1_41, in(all_103_1_63, all_41_1_41) = 0, yields:
% 32.93/8.49 | (164) all_103_1_63 = all_80_0_52 | all_103_1_63 = all_80_1_53
% 32.93/8.49 |
% 32.93/8.49 | From (163) and (146) follows:
% 32.93/8.49 | (165) subset(all_80_0_52, all_0_6_6) = 0
% 32.93/8.49 |
% 32.93/8.49 | From (162) and (140) follows:
% 32.93/8.49 | (166) subset(all_90_0_58, all_0_6_6) = 0
% 32.93/8.49 |
% 32.93/8.49 | Instantiating formula (58) with all_103_0_62, all_103_1_63, all_0_5_5, all_130_0_72 and discharging atoms subset(all_130_0_72, all_0_5_5) = 0, in(all_103_1_63, all_0_5_5) = all_103_0_62, yields:
% 32.93/8.49 | (167) all_103_0_62 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_103_1_63, all_130_0_72) = v0)
% 32.93/8.49 |
% 32.93/8.49 | Instantiating formula (61) with all_205_0_97, all_0_6_6, all_0_8_8, all_103_1_63 and discharging atoms subset(all_103_1_63, all_0_6_6) = all_205_0_97, subset(all_0_8_8, all_0_6_6) = 0, yields:
% 32.93/8.49 | (168) all_205_0_97 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_103_1_63, all_0_8_8) = v0)
% 32.93/8.49 |
% 32.93/8.49 | Instantiating formula (61) with all_205_0_97, all_0_6_6, all_0_9_9, all_103_1_63 and discharging atoms subset(all_103_1_63, all_0_6_6) = all_205_0_97, subset(all_0_9_9, all_0_6_6) = 0, yields:
% 32.93/8.49 | (169) all_205_0_97 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_103_1_63, all_0_9_9) = v0)
% 32.93/8.49 |
% 32.93/8.49 | Instantiating formula (52) with all_205_0_97, all_0_6_6, all_103_1_63 and discharging atoms subset(all_103_1_63, all_0_6_6) = all_205_0_97, yields:
% 32.93/8.49 | (170) all_205_0_97 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_103_1_63) = 0 & in(v0, all_0_6_6) = v1)
% 32.93/8.49 |
% 32.93/8.49 | Instantiating formula (61) with all_205_0_97, all_0_6_6, all_90_0_58, all_103_1_63 and discharging atoms subset(all_103_1_63, all_0_6_6) = all_205_0_97, subset(all_90_0_58, all_0_6_6) = 0, yields:
% 32.93/8.49 | (171) all_205_0_97 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_103_1_63, all_90_0_58) = v0)
% 32.93/8.49 |
% 32.93/8.49 | Instantiating formula (61) with all_205_0_97, all_0_6_6, all_80_0_52, all_103_1_63 and discharging atoms subset(all_103_1_63, all_0_6_6) = all_205_0_97, subset(all_80_0_52, all_0_6_6) = 0, yields:
% 32.93/8.49 | (172) all_205_0_97 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_103_1_63, all_80_0_52) = v0)
% 32.93/8.49 |
% 32.93/8.49 | Instantiating formula (43) with all_80_0_52, all_0_5_5, all_0_6_6 and discharging atoms powerset(all_0_6_6) = all_0_5_5, subset(all_80_0_52, all_0_6_6) = 0, yields:
% 32.93/8.49 | (173) in(all_80_0_52, all_0_5_5) = 0
% 32.93/8.49 |
% 32.93/8.49 +-Applying beta-rule and splitting (167), into two cases.
% 32.93/8.49 |-Branch one:
% 32.93/8.49 | (147) all_103_0_62 = 0
% 32.93/8.49 |
% 32.93/8.49 | Equations (147) can reduce 126 to:
% 32.93/8.49 | (78) $false
% 32.93/8.49 |
% 32.93/8.49 |-The branch is then unsatisfiable
% 32.93/8.49 |-Branch two:
% 32.93/8.49 | (126) ~ (all_103_0_62 = 0)
% 32.93/8.49 | (177) ? [v0] : ( ~ (v0 = 0) & in(all_103_1_63, all_130_0_72) = v0)
% 32.93/8.49 |
% 32.93/8.49 +-Applying beta-rule and splitting (172), into two cases.
% 32.93/8.49 |-Branch one:
% 32.93/8.49 | (178) all_205_0_97 = 0
% 32.93/8.49 |
% 32.93/8.49 | Equations (178) can reduce 160 to:
% 32.93/8.49 | (78) $false
% 32.93/8.49 |
% 32.93/8.49 |-The branch is then unsatisfiable
% 32.93/8.49 |-Branch two:
% 32.93/8.49 | (160) ~ (all_205_0_97 = 0)
% 32.93/8.49 | (181) ? [v0] : ( ~ (v0 = 0) & subset(all_103_1_63, all_80_0_52) = v0)
% 32.93/8.49 |
% 32.93/8.49 +-Applying beta-rule and splitting (170), into two cases.
% 32.93/8.49 |-Branch one:
% 32.93/8.49 | (178) all_205_0_97 = 0
% 32.93/8.49 |
% 32.93/8.49 | Equations (178) can reduce 160 to:
% 32.93/8.49 | (78) $false
% 32.93/8.49 |
% 32.93/8.49 |-The branch is then unsatisfiable
% 32.93/8.49 |-Branch two:
% 32.93/8.49 | (160) ~ (all_205_0_97 = 0)
% 32.93/8.49 | (185) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_103_1_63) = 0 & in(v0, all_0_6_6) = v1)
% 32.93/8.49 |
% 32.93/8.49 +-Applying beta-rule and splitting (168), into two cases.
% 32.93/8.49 |-Branch one:
% 32.93/8.49 | (178) all_205_0_97 = 0
% 32.93/8.49 |
% 32.93/8.49 | Equations (178) can reduce 160 to:
% 32.93/8.49 | (78) $false
% 32.93/8.49 |
% 32.93/8.49 |-The branch is then unsatisfiable
% 32.93/8.49 |-Branch two:
% 32.93/8.49 | (160) ~ (all_205_0_97 = 0)
% 32.93/8.49 | (189) ? [v0] : ( ~ (v0 = 0) & subset(all_103_1_63, all_0_8_8) = v0)
% 32.93/8.49 |
% 32.93/8.49 +-Applying beta-rule and splitting (169), into two cases.
% 32.93/8.49 |-Branch one:
% 32.93/8.49 | (178) all_205_0_97 = 0
% 32.93/8.49 |
% 32.93/8.49 | Equations (178) can reduce 160 to:
% 32.93/8.49 | (78) $false
% 32.93/8.49 |
% 32.93/8.49 |-The branch is then unsatisfiable
% 32.93/8.49 |-Branch two:
% 32.93/8.49 | (160) ~ (all_205_0_97 = 0)
% 32.93/8.49 | (193) ? [v0] : ( ~ (v0 = 0) & subset(all_103_1_63, all_0_9_9) = v0)
% 32.93/8.49 |
% 32.93/8.49 +-Applying beta-rule and splitting (171), into two cases.
% 32.93/8.49 |-Branch one:
% 32.93/8.49 | (178) all_205_0_97 = 0
% 32.93/8.49 |
% 32.93/8.49 | Equations (178) can reduce 160 to:
% 32.93/8.49 | (78) $false
% 32.93/8.49 |
% 32.93/8.49 |-The branch is then unsatisfiable
% 32.93/8.49 |-Branch two:
% 32.93/8.49 | (160) ~ (all_205_0_97 = 0)
% 32.93/8.49 | (197) ? [v0] : ( ~ (v0 = 0) & subset(all_103_1_63, all_90_0_58) = v0)
% 32.93/8.49 |
% 32.93/8.49 +-Applying beta-rule and splitting (164), into two cases.
% 32.93/8.49 |-Branch one:
% 32.93/8.49 | (198) all_103_1_63 = all_80_0_52
% 32.93/8.49 |
% 32.93/8.49 | From (198) and (128) follows:
% 32.93/8.49 | (199) in(all_80_0_52, all_0_5_5) = all_103_0_62
% 32.93/8.49 |
% 32.93/8.49 | Instantiating formula (13) with all_80_0_52, all_0_5_5, all_103_0_62, 0 and discharging atoms in(all_80_0_52, all_0_5_5) = all_103_0_62, in(all_80_0_52, all_0_5_5) = 0, yields:
% 32.93/8.49 | (147) all_103_0_62 = 0
% 32.93/8.49 |
% 32.93/8.49 | Equations (147) can reduce 126 to:
% 32.93/8.49 | (78) $false
% 32.93/8.49 |
% 32.93/8.49 |-The branch is then unsatisfiable
% 32.93/8.49 |-Branch two:
% 32.93/8.49 | (202) ~ (all_103_1_63 = all_80_0_52)
% 32.93/8.49 | (203) all_103_1_63 = all_80_1_53
% 32.93/8.49 |
% 32.93/8.49 | From (203) and (161) follows:
% 32.93/8.49 | (204) subset(all_80_1_53, all_0_6_6) = all_205_0_97
% 32.93/8.49 |
% 32.93/8.49 | Instantiating formula (27) with all_205_0_97, all_80_1_53, all_0_6_6, all_51_0_43, all_51_1_44 and discharging atoms subset(all_80_1_53, all_0_6_6) = all_205_0_97, unordered_pair(all_51_1_44, all_51_0_43) = all_80_1_53, yields:
% 32.93/8.49 | (205) all_205_0_97 = 0 | ? [v0] : (( ~ (v0 = 0) & in(all_51_0_43, all_0_6_6) = v0) | ( ~ (v0 = 0) & in(all_51_1_44, all_0_6_6) = v0))
% 32.93/8.49 |
% 32.93/8.49 +-Applying beta-rule and splitting (205), into two cases.
% 32.93/8.49 |-Branch one:
% 32.93/8.49 | (178) all_205_0_97 = 0
% 32.93/8.49 |
% 32.93/8.49 | Equations (178) can reduce 160 to:
% 32.93/8.49 | (78) $false
% 32.93/8.49 |
% 32.93/8.49 |-The branch is then unsatisfiable
% 32.93/8.49 |-Branch two:
% 32.93/8.49 | (160) ~ (all_205_0_97 = 0)
% 32.93/8.49 | (209) ? [v0] : (( ~ (v0 = 0) & in(all_51_0_43, all_0_6_6) = v0) | ( ~ (v0 = 0) & in(all_51_1_44, all_0_6_6) = v0))
% 32.93/8.50 |
% 32.93/8.50 | Instantiating (209) with all_600_0_569 yields:
% 32.93/8.50 | (210) ( ~ (all_600_0_569 = 0) & in(all_51_0_43, all_0_6_6) = all_600_0_569) | ( ~ (all_600_0_569 = 0) & in(all_51_1_44, all_0_6_6) = all_600_0_569)
% 32.93/8.50 |
% 32.93/8.50 +-Applying beta-rule and splitting (210), into two cases.
% 32.93/8.50 |-Branch one:
% 32.93/8.50 | (211) ~ (all_600_0_569 = 0) & in(all_51_0_43, all_0_6_6) = all_600_0_569
% 32.93/8.50 |
% 32.93/8.50 | Applying alpha-rule on (211) yields:
% 32.93/8.50 | (212) ~ (all_600_0_569 = 0)
% 32.93/8.50 | (213) in(all_51_0_43, all_0_6_6) = all_600_0_569
% 32.93/8.50 |
% 32.93/8.50 | Instantiating formula (13) with all_51_0_43, all_0_6_6, all_600_0_569, 0 and discharging atoms in(all_51_0_43, all_0_6_6) = all_600_0_569, in(all_51_0_43, all_0_6_6) = 0, yields:
% 32.93/8.50 | (214) all_600_0_569 = 0
% 32.93/8.50 |
% 32.93/8.50 | Equations (214) can reduce 212 to:
% 32.93/8.50 | (78) $false
% 32.93/8.50 |
% 32.93/8.50 |-The branch is then unsatisfiable
% 32.93/8.50 |-Branch two:
% 32.93/8.50 | (216) ~ (all_600_0_569 = 0) & in(all_51_1_44, all_0_6_6) = all_600_0_569
% 32.93/8.50 |
% 32.93/8.50 | Applying alpha-rule on (216) yields:
% 32.93/8.50 | (212) ~ (all_600_0_569 = 0)
% 32.93/8.50 | (218) in(all_51_1_44, all_0_6_6) = all_600_0_569
% 32.93/8.50 |
% 32.93/8.50 | Instantiating formula (13) with all_51_1_44, all_0_6_6, all_600_0_569, 0 and discharging atoms in(all_51_1_44, all_0_6_6) = all_600_0_569, in(all_51_1_44, all_0_6_6) = 0, yields:
% 32.93/8.50 | (214) all_600_0_569 = 0
% 32.93/8.50 |
% 32.93/8.50 | Equations (214) can reduce 212 to:
% 32.93/8.50 | (78) $false
% 32.93/8.50 |
% 32.93/8.50 |-The branch is then unsatisfiable
% 32.93/8.50 % SZS output end Proof for theBenchmark
% 32.93/8.50
% 32.93/8.50 7902ms
%------------------------------------------------------------------------------