TSTP Solution File: SEU204+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU204+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 08:47:36 EDT 2022
% Result : Theorem 4.65s 1.88s
% Output : Proof 6.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU204+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n019.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 : Sun Jun 19 02:00:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.55/0.62 ____ _
% 0.55/0.62 ___ / __ \_____(_)___ ________ __________
% 0.55/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.62
% 0.55/0.62 A Theorem Prover for First-Order Logic
% 0.55/0.63 (ePrincess v.1.0)
% 0.55/0.63
% 0.55/0.63 (c) Philipp Rümmer, 2009-2015
% 0.55/0.63 (c) Peter Backeman, 2014-2015
% 0.55/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.63 Bug reports to peter@backeman.se
% 0.55/0.63
% 0.55/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.63
% 0.55/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.69/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.56/1.01 Prover 0: Preprocessing ...
% 2.30/1.27 Prover 0: Warning: ignoring some quantifiers
% 2.30/1.30 Prover 0: Constructing countermodel ...
% 3.40/1.60 Prover 0: gave up
% 3.40/1.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.75/1.63 Prover 1: Preprocessing ...
% 4.16/1.75 Prover 1: Warning: ignoring some quantifiers
% 4.16/1.76 Prover 1: Constructing countermodel ...
% 4.65/1.87 Prover 1: proved (273ms)
% 4.65/1.88
% 4.65/1.88 No countermodel exists, formula is valid
% 4.65/1.88 % SZS status Theorem for theBenchmark
% 4.65/1.88
% 4.65/1.88 Generating proof ... Warning: ignoring some quantifiers
% 6.52/2.27 found it (size 25)
% 6.52/2.27
% 6.52/2.27 % SZS output start Proof for theBenchmark
% 6.52/2.27 Assumed formulas after preprocessing and simplification:
% 6.52/2.27 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v8 = 0) & ~ (v6 = 0) & ~ (v4 = 0) & relation_rng(v1) = v3 & subset(v2, v3) = v4 & relation_image(v1, v0) = v2 & relation(v10) = 0 & relation(v7) = 0 & relation(v1) = 0 & relation(empty_set) = 0 & empty(v10) = 0 & empty(v9) = 0 & empty(v7) = v8 & empty(v5) = v6 & empty(empty_set) = 0 & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = 0 | ~ (relation_image(v11, v12) = v13) | ~ (ordered_pair(v16, v14) = v17) | ~ (relation(v11) = 0) | ~ (in(v17, v11) = 0) | ~ (in(v14, v13) = v15) | ? [v18] : ( ~ (v18 = 0) & in(v16, v12) = v18)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = 0 | ~ (relation_rng(v11) = v12) | ~ (ordered_pair(v15, v13) = v16) | ~ (in(v16, v11) = 0) | ~ (in(v13, v12) = v14) | ? [v17] : ( ~ (v17 = 0) & relation(v11) = v17)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (powerset(v13) = v14) | ~ (element(v12, v14) = 0) | ~ (element(v11, v13) = v15) | ? [v16] : ( ~ (v16 = 0) & in(v11, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (singleton(v11) = v14) | ~ (unordered_pair(v13, v14) = v15) | ~ (unordered_pair(v11, v12) = v13) | ordered_pair(v11, v12) = v15) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (powerset(v12) = v13) | ~ (element(v11, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (element(v14, v13) = v12) | ~ (element(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (subset(v14, v13) = v12) | ~ (subset(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (relation_image(v14, v13) = v12) | ~ (relation_image(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (ordered_pair(v14, v13) = v12) | ~ (ordered_pair(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (unordered_pair(v14, v13) = v12) | ~ (unordered_pair(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (in(v14, v13) = v12) | ~ (in(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ (element(v12, v14) = 0) | ~ (in(v11, v12) = 0) | ? [v15] : ( ~ (v15 = 0) & empty(v13) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_image(v11, v12) = v13) | ~ (relation(v11) = 0) | ~ (in(v14, v13) = 0) | ? [v15] : ? [v16] : (ordered_pair(v15, v14) = v16 & in(v16, v11) = 0 & in(v15, v12) = 0)) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (relation_image(v12, v13) = v14) | ~ (relation(v12) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (in(v15, v11) = v16 & ( ~ (v16 = 0) | ! [v21] : ! [v22] : ( ~ (ordered_pair(v21, v15) = v22) | ~ (in(v22, v12) = 0) | ? [v23] : ( ~ (v23 = 0) & in(v21, v13) = v23))) & (v16 = 0 | (v20 = 0 & v19 = 0 & ordered_pair(v17, v15) = v18 & in(v18, v12) = 0 & in(v17, v13) = 0)))) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (element(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v11, v12) = v13) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & in(v14, v12) = v15 & in(v14, v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (powerset(v13) = v12) | ~ (powerset(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (singleton(v13) = v12) | ~ (singleton(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation_rng(v13) = v12) | ~ (relation_rng(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation(v13) = v12) | ~ (relation(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (empty(v13) = v12) | ~ (empty(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ (element(v11, v13) = 0) | subset(v11, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_rng(v11) = v12) | ~ (in(v13, v12) = 0) | ? [v14] : ? [v15] : ? [v16] : ((v16 = 0 & ordered_pair(v14, v13) = v15 & in(v15, v11) = 0) | ( ~ (v14 = 0) & relation(v11) = v14))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (subset(v11, v12) = 0) | ~ (in(v13, v11) = 0) | in(v13, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (ordered_pair(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v11, v12) = v13) | unordered_pair(v12, v11) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (relation_rng(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (( ~ (v14 = 0) & relation(v12) = v14) | (in(v14, v11) = v15 & ( ~ (v15 = 0) | ! [v19] : ! [v20] : ( ~ (ordered_pair(v19, v14) = v20) | ~ (in(v20, v12) = 0))) & (v15 = 0 | (v18 = 0 & ordered_pair(v16, v14) = v17 & in(v17, v12) = 0))))) & ! [v11] : ! [v12] : (v12 = v11 | ~ (empty(v12) = 0) | ~ (empty(v11) = 0)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v11, v11) = v12)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (relation(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v11) = v13)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ((v14 = 0 & ~ (v15 = 0) & element(v13, v12) = 0 & empty(v13) = v15) | (v13 = 0 & empty(v11) = 0))) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : (element(v13, v12) = 0 & empty(v13) = 0)) & ! [v11] : ! [v12] : ( ~ (element(v11, v12) = 0) | ? [v13] : ? [v14] : (empty(v12) = v13 & in(v11, v12) = v14 & (v14 = 0 | v13 = 0))) & ! [v11] : ! [v12] : ( ~ (singleton(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (relation(v12) = v15 & empty(v12) = v14 & empty(v11) = v13 & ( ~ (v13 = 0) | (v15 = 0 & v14 = 0)))) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (relation(v11) = v14 & empty(v12) = v15 & empty(v11) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | v13 = 0))) & ! [v11] : ! [v12] : ( ~ (in(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (in(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & in(v12, v11) = v13)) & ! [v11] : (v11 = empty_set | ~ (empty(v11) = 0)) & ? [v11] : ? [v12] : element(v12, v11) = 0)
% 6.52/2.31 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10 yields:
% 6.52/2.31 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_4_4 = 0) & ~ (all_0_6_6 = 0) & relation_rng(all_0_9_9) = all_0_7_7 & subset(all_0_8_8, all_0_7_7) = all_0_6_6 & relation_image(all_0_9_9, all_0_10_10) = all_0_8_8 & relation(all_0_0_0) = 0 & relation(all_0_3_3) = 0 & relation(all_0_9_9) = 0 & relation(empty_set) = 0 & empty(all_0_0_0) = 0 & empty(all_0_1_1) = 0 & empty(all_0_3_3) = all_0_2_2 & empty(all_0_5_5) = all_0_4_4 & empty(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v5, v3) = v6) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ( ~ (v7 = 0) & in(v5, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v4, v2) = v5) | ~ (in(v5, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & relation(v0) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(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 | ~ (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] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v4) = v11) | ~ (in(v11, v1) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v2) = v12))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v6, v4) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v3, v2) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v3) = v9) | ~ (in(v9, v1) = 0))) & (v4 = 0 | (v7 = 0 & ordered_pair(v5, v3) = v6 & in(v6, v1) = 0))))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ? [v0] : ? [v1] : element(v1, v0) = 0
% 6.93/2.32 |
% 6.93/2.32 | Applying alpha-rule on (1) yields:
% 6.93/2.32 | (2) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 6.93/2.32 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 6.93/2.33 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 6.93/2.33 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 6.93/2.33 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 6.93/2.33 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0))
% 6.93/2.33 | (8) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 6.93/2.33 | (9) relation(all_0_0_0) = 0
% 6.93/2.33 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 6.93/2.33 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 6.93/2.33 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 6.93/2.33 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 6.93/2.33 | (14) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v3) = v9) | ~ (in(v9, v1) = 0))) & (v4 = 0 | (v7 = 0 & ordered_pair(v5, v3) = v6 & in(v6, v1) = 0)))))
% 6.93/2.33 | (15) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 6.93/2.33 | (16) empty(all_0_5_5) = all_0_4_4
% 6.93/2.33 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 6.93/2.33 | (18) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0)))
% 6.93/2.33 | (19) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 6.93/2.33 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 6.93/2.33 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 6.93/2.33 | (22) relation_image(all_0_9_9, all_0_10_10) = all_0_8_8
% 6.93/2.33 | (23) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 6.93/2.33 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0))
% 6.93/2.33 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v3, v2) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3)))
% 6.93/2.33 | (26) empty(all_0_0_0) = 0
% 6.93/2.33 | (27) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 6.93/2.34 | (28) empty(all_0_1_1) = 0
% 6.93/2.34 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v5, v3) = v6) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ( ~ (v7 = 0) & in(v5, v1) = v7))
% 6.93/2.34 | (30) ~ (all_0_4_4 = 0)
% 6.93/2.34 | (31) relation(empty_set) = 0
% 6.93/2.34 | (32) subset(all_0_8_8, all_0_7_7) = all_0_6_6
% 6.93/2.34 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 6.93/2.34 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 6.93/2.34 | (35) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0))))
% 6.93/2.34 | (36) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 6.93/2.34 | (37) relation(all_0_3_3) = 0
% 6.93/2.34 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 6.93/2.34 | (39) relation_rng(all_0_9_9) = all_0_7_7
% 6.93/2.34 | (40) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v4) = v11) | ~ (in(v11, v1) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v2) = v12))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v6, v4) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0))))
% 6.93/2.34 | (41) empty(empty_set) = 0
% 6.93/2.34 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 6.93/2.34 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 6.93/2.34 | (44) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 6.93/2.34 | (45) ~ (all_0_2_2 = 0)
% 6.93/2.34 | (46) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 6.93/2.34 | (47) ? [v0] : ? [v1] : element(v1, v0) = 0
% 6.93/2.34 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 6.93/2.34 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v4, v2) = v5) | ~ (in(v5, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & relation(v0) = v6))
% 6.93/2.34 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 6.93/2.34 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 6.93/2.34 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 6.93/2.34 | (53) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 6.93/2.35 | (54) ~ (all_0_6_6 = 0)
% 6.93/2.35 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 6.93/2.35 | (56) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 6.93/2.35 | (57) relation(all_0_9_9) = 0
% 6.93/2.35 | (58) empty(all_0_3_3) = all_0_2_2
% 6.93/2.35 |
% 6.93/2.35 | Instantiating formula (46) with all_0_7_7, all_0_9_9 and discharging atoms relation_rng(all_0_9_9) = all_0_7_7, yields:
% 6.93/2.35 | (59) ? [v0] : ? [v1] : ? [v2] : (relation(all_0_9_9) = v1 & empty(all_0_7_7) = v2 & empty(all_0_9_9) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | v0 = 0))
% 6.93/2.35 |
% 6.93/2.35 | Instantiating formula (10) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms subset(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 6.93/2.35 | (60) all_0_6_6 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = v1 & in(v0, all_0_8_8) = 0)
% 6.93/2.35 |
% 6.93/2.35 | Instantiating (59) with all_26_0_15, all_26_1_16, all_26_2_17 yields:
% 6.93/2.35 | (61) relation(all_0_9_9) = all_26_1_16 & empty(all_0_7_7) = all_26_0_15 & empty(all_0_9_9) = all_26_2_17 & ( ~ (all_26_0_15 = 0) | ~ (all_26_1_16 = 0) | all_26_2_17 = 0)
% 6.93/2.35 |
% 6.93/2.35 | Applying alpha-rule on (61) yields:
% 6.93/2.35 | (62) relation(all_0_9_9) = all_26_1_16
% 6.93/2.35 | (63) empty(all_0_7_7) = all_26_0_15
% 6.93/2.35 | (64) empty(all_0_9_9) = all_26_2_17
% 6.93/2.35 | (65) ~ (all_26_0_15 = 0) | ~ (all_26_1_16 = 0) | all_26_2_17 = 0
% 6.93/2.35 |
% 6.93/2.35 +-Applying beta-rule and splitting (60), into two cases.
% 6.93/2.35 |-Branch one:
% 6.93/2.35 | (66) all_0_6_6 = 0
% 6.93/2.35 |
% 6.93/2.35 | Equations (66) can reduce 54 to:
% 6.93/2.35 | (67) $false
% 6.93/2.35 |
% 6.93/2.35 |-The branch is then unsatisfiable
% 6.93/2.35 |-Branch two:
% 6.93/2.35 | (54) ~ (all_0_6_6 = 0)
% 6.93/2.35 | (69) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = v1 & in(v0, all_0_8_8) = 0)
% 6.93/2.35 |
% 6.93/2.35 | Instantiating (69) with all_36_0_23, all_36_1_24 yields:
% 6.93/2.35 | (70) ~ (all_36_0_23 = 0) & in(all_36_1_24, all_0_7_7) = all_36_0_23 & in(all_36_1_24, all_0_8_8) = 0
% 6.93/2.35 |
% 6.93/2.35 | Applying alpha-rule on (70) yields:
% 6.93/2.35 | (71) ~ (all_36_0_23 = 0)
% 6.93/2.35 | (72) in(all_36_1_24, all_0_7_7) = all_36_0_23
% 6.93/2.35 | (73) in(all_36_1_24, all_0_8_8) = 0
% 6.93/2.35 |
% 6.93/2.35 | Instantiating formula (3) with all_0_9_9, all_26_1_16, 0 and discharging atoms relation(all_0_9_9) = all_26_1_16, relation(all_0_9_9) = 0, yields:
% 6.93/2.35 | (74) all_26_1_16 = 0
% 6.93/2.35 |
% 6.93/2.35 | From (74) and (62) follows:
% 6.93/2.35 | (57) relation(all_0_9_9) = 0
% 6.93/2.35 |
% 6.93/2.35 | Instantiating formula (24) with all_36_1_24, all_0_8_8, all_0_10_10, all_0_9_9 and discharging atoms relation_image(all_0_9_9, all_0_10_10) = all_0_8_8, relation(all_0_9_9) = 0, in(all_36_1_24, all_0_8_8) = 0, yields:
% 6.93/2.35 | (76) ? [v0] : ? [v1] : (ordered_pair(v0, all_36_1_24) = v1 & in(v1, all_0_9_9) = 0 & in(v0, all_0_10_10) = 0)
% 6.93/2.35 |
% 6.93/2.35 | Instantiating (76) with all_51_0_27, all_51_1_28 yields:
% 6.93/2.35 | (77) ordered_pair(all_51_1_28, all_36_1_24) = all_51_0_27 & in(all_51_0_27, all_0_9_9) = 0 & in(all_51_1_28, all_0_10_10) = 0
% 6.93/2.36 |
% 6.93/2.36 | Applying alpha-rule on (77) yields:
% 6.93/2.36 | (78) ordered_pair(all_51_1_28, all_36_1_24) = all_51_0_27
% 6.93/2.36 | (79) in(all_51_0_27, all_0_9_9) = 0
% 6.93/2.36 | (80) in(all_51_1_28, all_0_10_10) = 0
% 6.93/2.36 |
% 6.93/2.36 | Instantiating formula (49) with all_51_0_27, all_51_1_28, all_36_0_23, all_36_1_24, all_0_7_7, all_0_9_9 and discharging atoms relation_rng(all_0_9_9) = all_0_7_7, ordered_pair(all_51_1_28, all_36_1_24) = all_51_0_27, in(all_51_0_27, all_0_9_9) = 0, in(all_36_1_24, all_0_7_7) = all_36_0_23, yields:
% 6.93/2.36 | (81) all_36_0_23 = 0 | ? [v0] : ( ~ (v0 = 0) & relation(all_0_9_9) = v0)
% 6.93/2.36 |
% 6.93/2.36 +-Applying beta-rule and splitting (81), into two cases.
% 6.93/2.36 |-Branch one:
% 6.93/2.36 | (82) all_36_0_23 = 0
% 6.93/2.36 |
% 6.93/2.36 | Equations (82) can reduce 71 to:
% 6.93/2.36 | (67) $false
% 6.93/2.36 |
% 6.93/2.36 |-The branch is then unsatisfiable
% 6.93/2.36 |-Branch two:
% 6.93/2.36 | (71) ~ (all_36_0_23 = 0)
% 6.93/2.36 | (85) ? [v0] : ( ~ (v0 = 0) & relation(all_0_9_9) = v0)
% 6.93/2.36 |
% 6.93/2.36 | Instantiating (85) with all_72_0_34 yields:
% 6.93/2.36 | (86) ~ (all_72_0_34 = 0) & relation(all_0_9_9) = all_72_0_34
% 6.93/2.36 |
% 6.93/2.36 | Applying alpha-rule on (86) yields:
% 6.93/2.36 | (87) ~ (all_72_0_34 = 0)
% 6.93/2.36 | (88) relation(all_0_9_9) = all_72_0_34
% 6.93/2.36 |
% 6.93/2.36 | Instantiating formula (3) with all_0_9_9, all_72_0_34, 0 and discharging atoms relation(all_0_9_9) = all_72_0_34, relation(all_0_9_9) = 0, yields:
% 6.93/2.36 | (89) all_72_0_34 = 0
% 6.93/2.36 |
% 6.93/2.36 | Equations (89) can reduce 87 to:
% 6.93/2.36 | (67) $false
% 6.93/2.36 |
% 6.93/2.36 |-The branch is then unsatisfiable
% 6.93/2.36 % SZS output end Proof for theBenchmark
% 6.93/2.36
% 6.93/2.36 1716ms
%------------------------------------------------------------------------------