TSTP Solution File: SET012+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET012+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 00:15:58 EDT 2022
% Result : Theorem 3.64s 1.64s
% Output : Proof 5.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET012+4 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.14 % 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 : Sat Jul 9 19:00:06 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.65/0.63 ____ _
% 0.65/0.63 ___ / __ \_____(_)___ ________ __________
% 0.65/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.65/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.65/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.65/0.63
% 0.65/0.63 A Theorem Prover for First-Order Logic
% 0.65/0.64 (ePrincess v.1.0)
% 0.65/0.64
% 0.65/0.64 (c) Philipp Rümmer, 2009-2015
% 0.65/0.64 (c) Peter Backeman, 2014-2015
% 0.65/0.64 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.65/0.64 Free software under GNU Lesser General Public License (LGPL).
% 0.65/0.64 Bug reports to peter@backeman.se
% 0.65/0.64
% 0.65/0.64 For more information, visit http://user.uu.se/~petba168/breu/
% 0.65/0.64
% 0.65/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.61/0.97 Prover 0: Preprocessing ...
% 2.15/1.18 Prover 0: Warning: ignoring some quantifiers
% 2.15/1.21 Prover 0: Constructing countermodel ...
% 2.82/1.40 Prover 0: gave up
% 2.82/1.40 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.82/1.42 Prover 1: Preprocessing ...
% 3.52/1.54 Prover 1: Constructing countermodel ...
% 3.64/1.63 Prover 1: proved (236ms)
% 3.64/1.64
% 3.64/1.64 No countermodel exists, formula is valid
% 3.64/1.64 % SZS status Theorem for theBenchmark
% 4.03/1.64
% 4.03/1.64 Generating proof ... found it (size 67)
% 5.20/1.96
% 5.20/1.96 % SZS output start Proof for theBenchmark
% 5.20/1.96 Assumed formulas after preprocessing and simplification:
% 5.20/1.96 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & difference(v1, v2) = v3 & difference(v1, v0) = v2 & equal_set(v3, v0) = v4 & subset(v0, v1) = 0 & ! [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] : ? [v11] : (member(v5, v7) = v10 & member(v5, v6) = v11 & ( ~ (v10 = 0) | v11 = 0))) & ! [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] : ? [v11] : (member(v5, v7) = v11 & member(v5, v6) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [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] : (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] : ( ~ (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] : ? [v10] : (member(v5, v7) = v10 & member(v5, v6) = v9 & (v10 = 0 | v9 = 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] : ? [v9] : (subset(v6, v5) = v9 & subset(v5, v6) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [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(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] : ~ (member(v5, empty_set) = 0))
% 5.41/2.01 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 5.41/2.01 | (1) ~ (all_0_0_0 = 0) & difference(all_0_3_3, all_0_2_2) = all_0_1_1 & difference(all_0_3_3, all_0_4_4) = all_0_2_2 & equal_set(all_0_1_1, all_0_4_4) = all_0_0_0 & subset(all_0_4_4, all_0_3_3) = 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] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [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] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [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] : (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] : ( ~ (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] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 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] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [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(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] : ~ (member(v0, empty_set) = 0)
% 5.41/2.02 |
% 5.41/2.02 | Applying alpha-rule on (1) yields:
% 5.41/2.02 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 5.41/2.02 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 5.41/2.02 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 5.41/2.02 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 5.41/2.02 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 5.41/2.02 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 5.41/2.02 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 5.41/2.02 | (9) difference(all_0_3_3, all_0_4_4) = all_0_2_2
% 5.41/2.02 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 5.41/2.02 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 5.41/2.02 | (12) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 5.41/2.03 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 5.41/2.03 | (14) ! [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))
% 5.41/2.03 | (15) ~ (all_0_0_0 = 0)
% 5.41/2.03 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 5.41/2.03 | (17) ! [v0] : ~ (member(v0, empty_set) = 0)
% 5.41/2.03 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 5.41/2.03 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 5.41/2.03 | (20) equal_set(all_0_1_1, all_0_4_4) = all_0_0_0
% 5.41/2.03 | (21) ! [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))
% 5.41/2.03 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 5.41/2.03 | (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))
% 5.41/2.03 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 5.41/2.03 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 5.41/2.03 | (26) difference(all_0_3_3, all_0_2_2) = all_0_1_1
% 5.41/2.03 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 5.41/2.03 | (28) ! [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))
% 5.41/2.03 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 5.41/2.03 | (30) subset(all_0_4_4, all_0_3_3) = 0
% 5.41/2.03 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 5.41/2.03 | (32) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 5.41/2.03 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 5.41/2.04 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 5.41/2.04 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 5.41/2.04 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 5.41/2.04 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 5.41/2.04 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 5.41/2.04 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 5.41/2.04 |
% 5.41/2.04 | Instantiating formula (32) with all_0_0_0, all_0_4_4, all_0_1_1 and discharging atoms equal_set(all_0_1_1, all_0_4_4) = all_0_0_0, yields:
% 5.41/2.04 | (40) all_0_0_0 = 0 | ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_4_4) = v0 & subset(all_0_4_4, all_0_1_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 5.41/2.04 |
% 5.41/2.04 +-Applying beta-rule and splitting (40), into two cases.
% 5.41/2.04 |-Branch one:
% 5.41/2.04 | (41) all_0_0_0 = 0
% 5.41/2.04 |
% 5.41/2.04 | Equations (41) can reduce 15 to:
% 5.41/2.04 | (42) $false
% 5.41/2.04 |
% 5.41/2.04 |-The branch is then unsatisfiable
% 5.41/2.04 |-Branch two:
% 5.41/2.04 | (15) ~ (all_0_0_0 = 0)
% 5.41/2.04 | (44) ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_4_4) = v0 & subset(all_0_4_4, all_0_1_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 5.41/2.04 |
% 5.41/2.04 | Instantiating (44) with all_14_0_5, all_14_1_6 yields:
% 5.41/2.04 | (45) subset(all_0_1_1, all_0_4_4) = all_14_1_6 & subset(all_0_4_4, all_0_1_1) = all_14_0_5 & ( ~ (all_14_0_5 = 0) | ~ (all_14_1_6 = 0))
% 5.41/2.04 |
% 5.41/2.04 | Applying alpha-rule on (45) yields:
% 5.41/2.04 | (46) subset(all_0_1_1, all_0_4_4) = all_14_1_6
% 5.41/2.04 | (47) subset(all_0_4_4, all_0_1_1) = all_14_0_5
% 5.41/2.04 | (48) ~ (all_14_0_5 = 0) | ~ (all_14_1_6 = 0)
% 5.41/2.04 |
% 5.41/2.04 | Instantiating formula (4) with all_0_4_4, all_0_3_3, all_14_0_5, 0 and discharging atoms subset(all_0_4_4, all_0_3_3) = 0, yields:
% 5.41/2.04 | (49) all_14_0_5 = 0 | ~ (subset(all_0_4_4, all_0_3_3) = all_14_0_5)
% 5.41/2.04 |
% 5.41/2.04 | Instantiating formula (22) with all_14_1_6, all_0_4_4, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_4_4) = all_14_1_6, yields:
% 5.41/2.04 | (50) all_14_1_6 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_4_4) = v1)
% 5.41/2.04 |
% 5.41/2.04 | Instantiating formula (22) with all_14_0_5, all_0_1_1, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_1_1) = all_14_0_5, yields:
% 5.41/2.04 | (51) all_14_0_5 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0)
% 5.41/2.04 |
% 5.41/2.04 +-Applying beta-rule and splitting (49), into two cases.
% 5.41/2.04 |-Branch one:
% 5.41/2.04 | (52) ~ (subset(all_0_4_4, all_0_3_3) = all_14_0_5)
% 5.41/2.04 |
% 5.41/2.04 | Using (30) and (52) yields:
% 5.41/2.04 | (53) ~ (all_14_0_5 = 0)
% 5.41/2.04 |
% 5.41/2.04 +-Applying beta-rule and splitting (51), into two cases.
% 5.41/2.04 |-Branch one:
% 5.41/2.04 | (54) all_14_0_5 = 0
% 5.41/2.04 |
% 5.41/2.04 | Equations (54) can reduce 53 to:
% 5.41/2.04 | (42) $false
% 5.41/2.04 |
% 5.41/2.04 |-The branch is then unsatisfiable
% 5.41/2.04 |-Branch two:
% 5.41/2.04 | (53) ~ (all_14_0_5 = 0)
% 5.41/2.04 | (57) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0)
% 5.41/2.05 |
% 5.41/2.05 | Instantiating (57) with all_35_0_7, all_35_1_8 yields:
% 5.41/2.05 | (58) ~ (all_35_0_7 = 0) & member(all_35_1_8, all_0_1_1) = all_35_0_7 & member(all_35_1_8, all_0_4_4) = 0
% 5.41/2.05 |
% 5.41/2.05 | Applying alpha-rule on (58) yields:
% 5.41/2.05 | (59) ~ (all_35_0_7 = 0)
% 5.41/2.05 | (60) member(all_35_1_8, all_0_1_1) = all_35_0_7
% 5.41/2.05 | (61) member(all_35_1_8, all_0_4_4) = 0
% 5.41/2.05 |
% 5.41/2.05 | Instantiating formula (13) with all_35_0_7, all_0_1_1, all_0_3_3, all_0_2_2, all_35_1_8 and discharging atoms difference(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_35_1_8, all_0_1_1) = all_35_0_7, yields:
% 5.41/2.05 | (62) all_35_0_7 = 0 | ? [v0] : ? [v1] : (member(all_35_1_8, all_0_2_2) = v1 & member(all_35_1_8, all_0_3_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 5.41/2.05 |
% 5.41/2.05 | Instantiating formula (18) with all_35_1_8, all_0_3_3, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_3_3) = 0, member(all_35_1_8, all_0_4_4) = 0, yields:
% 5.41/2.05 | (63) member(all_35_1_8, all_0_3_3) = 0
% 5.41/2.05 |
% 5.41/2.05 +-Applying beta-rule and splitting (62), into two cases.
% 5.41/2.05 |-Branch one:
% 5.41/2.05 | (64) all_35_0_7 = 0
% 5.41/2.05 |
% 5.41/2.05 | Equations (64) can reduce 59 to:
% 5.41/2.05 | (42) $false
% 5.41/2.05 |
% 5.41/2.05 |-The branch is then unsatisfiable
% 5.41/2.05 |-Branch two:
% 5.41/2.05 | (59) ~ (all_35_0_7 = 0)
% 5.41/2.05 | (67) ? [v0] : ? [v1] : (member(all_35_1_8, all_0_2_2) = v1 & member(all_35_1_8, all_0_3_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 5.41/2.05 |
% 5.41/2.05 | Instantiating (67) with all_55_0_9, all_55_1_10 yields:
% 5.41/2.05 | (68) member(all_35_1_8, all_0_2_2) = all_55_0_9 & member(all_35_1_8, all_0_3_3) = all_55_1_10 & ( ~ (all_55_1_10 = 0) | all_55_0_9 = 0)
% 5.41/2.05 |
% 5.41/2.05 | Applying alpha-rule on (68) yields:
% 5.41/2.05 | (69) member(all_35_1_8, all_0_2_2) = all_55_0_9
% 5.41/2.05 | (70) member(all_35_1_8, all_0_3_3) = all_55_1_10
% 5.41/2.05 | (71) ~ (all_55_1_10 = 0) | all_55_0_9 = 0
% 5.41/2.05 |
% 5.41/2.05 | Instantiating formula (27) with all_35_1_8, all_0_3_3, 0, all_55_1_10 and discharging atoms member(all_35_1_8, all_0_3_3) = all_55_1_10, member(all_35_1_8, all_0_3_3) = 0, yields:
% 5.41/2.05 | (72) all_55_1_10 = 0
% 5.41/2.05 |
% 5.41/2.05 +-Applying beta-rule and splitting (71), into two cases.
% 5.41/2.05 |-Branch one:
% 5.41/2.05 | (73) ~ (all_55_1_10 = 0)
% 5.41/2.05 |
% 5.41/2.05 | Equations (72) can reduce 73 to:
% 5.41/2.05 | (42) $false
% 5.41/2.05 |
% 5.41/2.05 |-The branch is then unsatisfiable
% 5.41/2.05 |-Branch two:
% 5.41/2.05 | (72) all_55_1_10 = 0
% 5.41/2.05 | (76) all_55_0_9 = 0
% 5.41/2.05 |
% 5.41/2.05 | From (76) and (69) follows:
% 5.41/2.05 | (77) member(all_35_1_8, all_0_2_2) = 0
% 5.41/2.05 |
% 5.41/2.05 | Instantiating formula (8) with all_0_2_2, all_0_3_3, all_0_4_4, all_35_1_8 and discharging atoms difference(all_0_3_3, all_0_4_4) = all_0_2_2, member(all_35_1_8, all_0_2_2) = 0, yields:
% 5.41/2.05 | (78) ? [v0] : ( ~ (v0 = 0) & member(all_35_1_8, all_0_3_3) = 0 & member(all_35_1_8, all_0_4_4) = v0)
% 5.41/2.05 |
% 5.41/2.05 | Instantiating (78) with all_78_0_11 yields:
% 5.41/2.05 | (79) ~ (all_78_0_11 = 0) & member(all_35_1_8, all_0_3_3) = 0 & member(all_35_1_8, all_0_4_4) = all_78_0_11
% 5.41/2.05 |
% 5.41/2.05 | Applying alpha-rule on (79) yields:
% 5.41/2.05 | (80) ~ (all_78_0_11 = 0)
% 5.41/2.05 | (63) member(all_35_1_8, all_0_3_3) = 0
% 5.41/2.05 | (82) member(all_35_1_8, all_0_4_4) = all_78_0_11
% 5.41/2.05 |
% 5.41/2.05 | Instantiating formula (27) with all_35_1_8, all_0_4_4, all_78_0_11, 0 and discharging atoms member(all_35_1_8, all_0_4_4) = all_78_0_11, member(all_35_1_8, all_0_4_4) = 0, yields:
% 5.41/2.05 | (83) all_78_0_11 = 0
% 5.41/2.05 |
% 5.41/2.05 | Equations (83) can reduce 80 to:
% 5.41/2.05 | (42) $false
% 5.41/2.05 |
% 5.41/2.05 |-The branch is then unsatisfiable
% 5.41/2.05 |-Branch two:
% 5.41/2.05 | (85) subset(all_0_4_4, all_0_3_3) = all_14_0_5
% 5.41/2.05 | (54) all_14_0_5 = 0
% 5.41/2.05 |
% 5.41/2.05 +-Applying beta-rule and splitting (48), into two cases.
% 5.41/2.05 |-Branch one:
% 5.41/2.05 | (53) ~ (all_14_0_5 = 0)
% 5.41/2.05 |
% 5.41/2.05 | Equations (54) can reduce 53 to:
% 5.41/2.05 | (42) $false
% 5.41/2.05 |
% 5.41/2.05 |-The branch is then unsatisfiable
% 5.41/2.05 |-Branch two:
% 5.41/2.06 | (54) all_14_0_5 = 0
% 5.41/2.06 | (90) ~ (all_14_1_6 = 0)
% 5.41/2.06 |
% 5.41/2.06 +-Applying beta-rule and splitting (50), into two cases.
% 5.41/2.06 |-Branch one:
% 5.41/2.06 | (91) all_14_1_6 = 0
% 5.41/2.06 |
% 5.41/2.06 | Equations (91) can reduce 90 to:
% 5.41/2.06 | (42) $false
% 5.41/2.06 |
% 5.41/2.06 |-The branch is then unsatisfiable
% 5.41/2.06 |-Branch two:
% 5.41/2.06 | (90) ~ (all_14_1_6 = 0)
% 5.41/2.06 | (94) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_4_4) = v1)
% 5.41/2.06 |
% 5.41/2.06 | Instantiating (94) with all_35_0_12, all_35_1_13 yields:
% 5.41/2.06 | (95) ~ (all_35_0_12 = 0) & member(all_35_1_13, all_0_1_1) = 0 & member(all_35_1_13, all_0_4_4) = all_35_0_12
% 5.41/2.06 |
% 5.41/2.06 | Applying alpha-rule on (95) yields:
% 5.41/2.06 | (96) ~ (all_35_0_12 = 0)
% 5.41/2.06 | (97) member(all_35_1_13, all_0_1_1) = 0
% 5.41/2.06 | (98) member(all_35_1_13, all_0_4_4) = all_35_0_12
% 5.41/2.06 |
% 5.41/2.06 | Instantiating formula (27) with all_35_1_13, all_0_4_4, all_35_0_12, 0 and discharging atoms member(all_35_1_13, all_0_4_4) = all_35_0_12, yields:
% 5.41/2.06 | (99) all_35_0_12 = 0 | ~ (member(all_35_1_13, all_0_4_4) = 0)
% 5.41/2.06 |
% 5.41/2.06 | Instantiating formula (8) with all_0_1_1, all_0_3_3, all_0_2_2, all_35_1_13 and discharging atoms difference(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_35_1_13, all_0_1_1) = 0, yields:
% 5.41/2.06 | (100) ? [v0] : ( ~ (v0 = 0) & member(all_35_1_13, all_0_2_2) = v0 & member(all_35_1_13, all_0_3_3) = 0)
% 5.41/2.06 |
% 5.41/2.06 | Instantiating (100) with all_50_0_14 yields:
% 5.41/2.06 | (101) ~ (all_50_0_14 = 0) & member(all_35_1_13, all_0_2_2) = all_50_0_14 & member(all_35_1_13, all_0_3_3) = 0
% 5.41/2.06 |
% 5.41/2.06 | Applying alpha-rule on (101) yields:
% 5.41/2.06 | (102) ~ (all_50_0_14 = 0)
% 5.41/2.06 | (103) member(all_35_1_13, all_0_2_2) = all_50_0_14
% 5.41/2.06 | (104) member(all_35_1_13, all_0_3_3) = 0
% 5.41/2.06 |
% 5.41/2.06 | Instantiating formula (13) with all_50_0_14, all_0_2_2, all_0_3_3, all_0_4_4, all_35_1_13 and discharging atoms difference(all_0_3_3, all_0_4_4) = all_0_2_2, member(all_35_1_13, all_0_2_2) = all_50_0_14, yields:
% 5.41/2.06 | (105) all_50_0_14 = 0 | ? [v0] : ? [v1] : (member(all_35_1_13, all_0_3_3) = v0 & member(all_35_1_13, all_0_4_4) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 5.41/2.06 |
% 5.41/2.06 +-Applying beta-rule and splitting (99), into two cases.
% 5.41/2.06 |-Branch one:
% 5.41/2.06 | (106) ~ (member(all_35_1_13, all_0_4_4) = 0)
% 5.41/2.06 |
% 5.41/2.06 +-Applying beta-rule and splitting (105), into two cases.
% 5.41/2.06 |-Branch one:
% 5.41/2.06 | (107) all_50_0_14 = 0
% 5.41/2.06 |
% 5.41/2.06 | Equations (107) can reduce 102 to:
% 5.41/2.06 | (42) $false
% 5.41/2.06 |
% 5.41/2.06 |-The branch is then unsatisfiable
% 5.41/2.06 |-Branch two:
% 5.41/2.06 | (102) ~ (all_50_0_14 = 0)
% 5.41/2.06 | (110) ? [v0] : ? [v1] : (member(all_35_1_13, all_0_3_3) = v0 & member(all_35_1_13, all_0_4_4) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 5.41/2.06 |
% 5.73/2.06 | Instantiating (110) with all_71_0_15, all_71_1_16 yields:
% 5.73/2.06 | (111) member(all_35_1_13, all_0_3_3) = all_71_1_16 & member(all_35_1_13, all_0_4_4) = all_71_0_15 & ( ~ (all_71_1_16 = 0) | all_71_0_15 = 0)
% 5.73/2.06 |
% 5.73/2.06 | Applying alpha-rule on (111) yields:
% 5.73/2.06 | (112) member(all_35_1_13, all_0_3_3) = all_71_1_16
% 5.73/2.06 | (113) member(all_35_1_13, all_0_4_4) = all_71_0_15
% 5.73/2.06 | (114) ~ (all_71_1_16 = 0) | all_71_0_15 = 0
% 5.73/2.06 |
% 5.73/2.06 | Instantiating formula (27) with all_35_1_13, all_0_3_3, all_71_1_16, 0 and discharging atoms member(all_35_1_13, all_0_3_3) = all_71_1_16, member(all_35_1_13, all_0_3_3) = 0, yields:
% 5.73/2.06 | (115) all_71_1_16 = 0
% 5.73/2.06 |
% 5.73/2.06 | Instantiating formula (27) with all_35_1_13, all_0_4_4, all_71_0_15, all_35_0_12 and discharging atoms member(all_35_1_13, all_0_4_4) = all_71_0_15, member(all_35_1_13, all_0_4_4) = all_35_0_12, yields:
% 5.73/2.06 | (116) all_71_0_15 = all_35_0_12
% 5.73/2.06 |
% 5.73/2.06 | Using (113) and (106) yields:
% 5.73/2.06 | (117) ~ (all_71_0_15 = 0)
% 5.73/2.06 |
% 5.73/2.06 | Equations (116) can reduce 117 to:
% 5.73/2.06 | (96) ~ (all_35_0_12 = 0)
% 5.73/2.06 |
% 5.73/2.06 +-Applying beta-rule and splitting (114), into two cases.
% 5.73/2.06 |-Branch one:
% 5.73/2.06 | (119) ~ (all_71_1_16 = 0)
% 5.73/2.06 |
% 5.73/2.07 | Equations (115) can reduce 119 to:
% 5.73/2.07 | (42) $false
% 5.73/2.07 |
% 5.73/2.07 |-The branch is then unsatisfiable
% 5.73/2.07 |-Branch two:
% 5.73/2.07 | (115) all_71_1_16 = 0
% 5.73/2.07 | (122) all_71_0_15 = 0
% 5.73/2.07 |
% 5.73/2.07 | Combining equations (122,116) yields a new equation:
% 5.73/2.07 | (123) all_35_0_12 = 0
% 5.73/2.07 |
% 5.73/2.07 | Equations (123) can reduce 96 to:
% 5.73/2.07 | (42) $false
% 5.73/2.07 |
% 5.73/2.07 |-The branch is then unsatisfiable
% 5.73/2.07 |-Branch two:
% 5.73/2.07 | (125) member(all_35_1_13, all_0_4_4) = 0
% 5.73/2.07 | (123) all_35_0_12 = 0
% 5.73/2.07 |
% 5.73/2.07 | Equations (123) can reduce 96 to:
% 5.73/2.07 | (42) $false
% 5.73/2.07 |
% 5.73/2.07 |-The branch is then unsatisfiable
% 5.73/2.07 % SZS output end Proof for theBenchmark
% 5.73/2.07
% 5.73/2.07 1418ms
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