TSTP Solution File: SEU187+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU187+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n003.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 08:47:26 EDT 2022
% Result : Theorem 22.85s 6.18s
% Output : Proof 26.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU187+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 21:48:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.66/0.63 ____ _
% 0.66/0.63 ___ / __ \_____(_)___ ________ __________
% 0.66/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.66/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.66/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.66/0.63
% 0.66/0.63 A Theorem Prover for First-Order Logic
% 0.66/0.63 (ePrincess v.1.0)
% 0.66/0.63
% 0.66/0.63 (c) Philipp Rümmer, 2009-2015
% 0.66/0.63 (c) Peter Backeman, 2014-2015
% 0.66/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.66/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.66/0.63 Bug reports to peter@backeman.se
% 0.66/0.63
% 0.66/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.66/0.63
% 0.66/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.55/1.00 Prover 0: Preprocessing ...
% 2.07/1.21 Prover 0: Warning: ignoring some quantifiers
% 2.21/1.24 Prover 0: Constructing countermodel ...
% 2.79/1.44 Prover 0: gave up
% 2.79/1.44 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.06/1.47 Prover 1: Preprocessing ...
% 3.51/1.56 Prover 1: Warning: ignoring some quantifiers
% 3.51/1.57 Prover 1: Constructing countermodel ...
% 4.15/1.73 Prover 1: gave up
% 4.15/1.73 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.15/1.75 Prover 2: Preprocessing ...
% 4.82/1.84 Prover 2: Warning: ignoring some quantifiers
% 4.82/1.85 Prover 2: Constructing countermodel ...
% 6.59/2.24 Prover 2: gave up
% 6.59/2.24 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.59/2.26 Prover 3: Preprocessing ...
% 6.59/2.28 Prover 3: Warning: ignoring some quantifiers
% 6.59/2.29 Prover 3: Constructing countermodel ...
% 6.91/2.33 Prover 3: gave up
% 6.91/2.33 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 6.91/2.34 Prover 4: Preprocessing ...
% 7.18/2.42 Prover 4: Warning: ignoring some quantifiers
% 7.18/2.42 Prover 4: Constructing countermodel ...
% 11.84/3.50 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 11.84/3.52 Prover 5: Preprocessing ...
% 12.33/3.60 Prover 5: Warning: ignoring some quantifiers
% 12.33/3.61 Prover 5: Constructing countermodel ...
% 14.15/4.02 Prover 5: gave up
% 14.15/4.02 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 14.15/4.04 Prover 6: Preprocessing ...
% 14.41/4.09 Prover 6: Warning: ignoring some quantifiers
% 14.41/4.10 Prover 6: Constructing countermodel ...
% 15.16/4.30 Prover 6: gave up
% 15.16/4.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 15.16/4.32 Prover 7: Preprocessing ...
% 15.49/4.33 Prover 7: Proving ...
% 22.85/6.18 Prover 7: proved (1878ms)
% 22.85/6.18 Prover 4: stopped
% 22.85/6.18
% 22.85/6.18 % SZS status Theorem for theBenchmark
% 22.85/6.18
% 22.85/6.18 Generating proof ... found it (size 73)
% 26.24/7.30
% 26.24/7.30 % SZS output start Proof for theBenchmark
% 26.24/7.30 Assumed formulas after preprocessing and simplification:
% 26.24/7.30 | (0) ? [v0] : ( ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (ordered_pair(v4, v3) = v2) | ~ (ordered_pair(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (unordered_pair(v4, v3) = v2) | ~ (unordered_pair(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v3) = v2) | ~ (singleton(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (relation_rng(v3) = v2) | ~ (relation_rng(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (relation_dom(v3) = v2) | ~ (relation_dom(v3) = v1)) & ? [v1] : ? [v2] : (relation(v0) & empty(v0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (singleton(v3) = v6) | ~ (unordered_pair(v5, v6) = v7) | ~ (unordered_pair(v3, v4) = v5) | ordered_pair(v3, v4) = v7) & ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v3, v4) = v5) | ~ empty(v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (unordered_pair(v3, v4) = v5) | ~ empty(v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (unordered_pair(v3, v4) = v5) | unordered_pair(v4, v3) = v5) & ! [v3] : ! [v4] : (v4 = v3 | ~ empty(v4) | ~ empty(v3)) & ! [v3] : ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ~ in(v5, v3)) & (in(v5, v4) | in(v5, v3)))) & ! [v3] : ! [v4] : ( ~ (singleton(v3) = v4) | ~ empty(v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ relation(v3) | ~ empty(v4) | empty(v3)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ relation(v3) | ( ! [v5] : (v5 = v4 | ? [v6] : (( ~ in(v6, v5) | ! [v7] : ? [v8] : (ordered_pair(v7, v6) = v8 & ~ in(v8, v3))) & (in(v6, v5) | ? [v7] : ? [v8] : (ordered_pair(v7, v6) = v8 & in(v8, v3))))) & ! [v5] : ( ~ in(v5, v4) | ? [v6] : ? [v7] : (ordered_pair(v6, v5) = v7 & in(v7, v3))) & ! [v5] : (in(v5, v4) | ! [v6] : ? [v7] : (ordered_pair(v6, v5) = v7 & ~ in(v7, v3))))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ relation(v3) | ~ empty(v4) | empty(v3)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ relation(v3) | ( ! [v5] : (v5 = v4 | ? [v6] : (( ~ in(v6, v5) | ! [v7] : ? [v8] : (ordered_pair(v6, v7) = v8 & ~ in(v8, v3))) & (in(v6, v5) | ? [v7] : ? [v8] : (ordered_pair(v6, v7) = v8 & in(v8, v3))))) & ! [v5] : ( ~ in(v5, v4) | ? [v6] : ? [v7] : (ordered_pair(v5, v6) = v7 & in(v7, v3))) & ! [v5] : (in(v5, v4) | ! [v6] : ? [v7] : (ordered_pair(v5, v6) = v7 & ~ in(v7, v3))))) & ! [v3] : ! [v4] : ( ~ element(v3, v4) | empty(v4) | in(v3, v4)) & ! [v3] : ! [v4] : ( ~ empty(v4) | ~ in(v3, v4)) & ! [v3] : ! [v4] : ( ~ in(v4, v3) | ~ in(v3, v4)) & ! [v3] : ! [v4] : ( ~ in(v3, v4) | element(v3, v4)) & ! [v3] : (v3 = v0 | ~ empty(v3)) & ! [v3] : ( ~ empty(v3) | relation(v3)) & ! [v3] : ? [v4] : element(v4, v3) & ? [v3] : ~ empty(v3) & ? [v3] : empty(v3) & ? [v3] : (relation(v3) & empty(v3)) & ? [v3] : (relation(v3) & ~ empty(v3)) & (( ~ (v2 = v0) & relation_rng(v0) = v2) | ( ~ (v1 = v0) & relation_dom(v0) = v1))))
% 26.53/7.33 | Instantiating (0) with all_0_0_0 yields:
% 26.53/7.33 | (1) ! [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] : (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_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ? [v0] : ? [v1] : (relation(all_0_0_0) & empty(all_0_0_0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (singleton(v2) = v5) | ~ (unordered_pair(v4, v5) = v6) | ~ (unordered_pair(v2, v3) = v4) | ordered_pair(v2, v3) = v6) & ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ empty(v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (unordered_pair(v2, v3) = v4) | ~ empty(v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (unordered_pair(v2, v3) = v4) | unordered_pair(v3, v2) = v4) & ! [v2] : ! [v3] : (v3 = v2 | ~ empty(v3) | ~ empty(v2)) & ! [v2] : ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v2)) & (in(v4, v3) | in(v4, v2)))) & ! [v2] : ! [v3] : ( ~ (singleton(v2) = v3) | ~ empty(v3)) & ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ~ relation(v2) | ~ empty(v3) | empty(v2)) & ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ~ relation(v2) | ( ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ! [v6] : ? [v7] : (ordered_pair(v6, v5) = v7 & ~ in(v7, v2))) & (in(v5, v4) | ? [v6] : ? [v7] : (ordered_pair(v6, v5) = v7 & in(v7, v2))))) & ! [v4] : ( ~ in(v4, v3) | ? [v5] : ? [v6] : (ordered_pair(v5, v4) = v6 & in(v6, v2))) & ! [v4] : (in(v4, v3) | ! [v5] : ? [v6] : (ordered_pair(v5, v4) = v6 & ~ in(v6, v2))))) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ~ relation(v2) | ~ empty(v3) | empty(v2)) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ~ relation(v2) | ( ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ! [v6] : ? [v7] : (ordered_pair(v5, v6) = v7 & ~ in(v7, v2))) & (in(v5, v4) | ? [v6] : ? [v7] : (ordered_pair(v5, v6) = v7 & in(v7, v2))))) & ! [v4] : ( ~ in(v4, v3) | ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & in(v6, v2))) & ! [v4] : (in(v4, v3) | ! [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ~ in(v6, v2))))) & ! [v2] : ! [v3] : ( ~ element(v2, v3) | empty(v3) | in(v2, v3)) & ! [v2] : ! [v3] : ( ~ empty(v3) | ~ in(v2, v3)) & ! [v2] : ! [v3] : ( ~ in(v3, v2) | ~ in(v2, v3)) & ! [v2] : ! [v3] : ( ~ in(v2, v3) | element(v2, v3)) & ! [v2] : (v2 = all_0_0_0 | ~ empty(v2)) & ! [v2] : ( ~ empty(v2) | relation(v2)) & ! [v2] : ? [v3] : element(v3, v2) & ? [v2] : ~ empty(v2) & ? [v2] : empty(v2) & ? [v2] : (relation(v2) & empty(v2)) & ? [v2] : (relation(v2) & ~ empty(v2)) & (( ~ (v1 = all_0_0_0) & relation_rng(all_0_0_0) = v1) | ( ~ (v0 = all_0_0_0) & relation_dom(all_0_0_0) = v0)))
% 26.53/7.33 |
% 26.53/7.33 | Applying alpha-rule on (1) yields:
% 26.53/7.33 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 26.53/7.33 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 26.53/7.33 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 26.53/7.33 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 26.53/7.33 | (6) ? [v0] : ? [v1] : (relation(all_0_0_0) & empty(all_0_0_0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (singleton(v2) = v5) | ~ (unordered_pair(v4, v5) = v6) | ~ (unordered_pair(v2, v3) = v4) | ordered_pair(v2, v3) = v6) & ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ empty(v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (unordered_pair(v2, v3) = v4) | ~ empty(v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (unordered_pair(v2, v3) = v4) | unordered_pair(v3, v2) = v4) & ! [v2] : ! [v3] : (v3 = v2 | ~ empty(v3) | ~ empty(v2)) & ! [v2] : ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v2)) & (in(v4, v3) | in(v4, v2)))) & ! [v2] : ! [v3] : ( ~ (singleton(v2) = v3) | ~ empty(v3)) & ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ~ relation(v2) | ~ empty(v3) | empty(v2)) & ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ~ relation(v2) | ( ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ! [v6] : ? [v7] : (ordered_pair(v6, v5) = v7 & ~ in(v7, v2))) & (in(v5, v4) | ? [v6] : ? [v7] : (ordered_pair(v6, v5) = v7 & in(v7, v2))))) & ! [v4] : ( ~ in(v4, v3) | ? [v5] : ? [v6] : (ordered_pair(v5, v4) = v6 & in(v6, v2))) & ! [v4] : (in(v4, v3) | ! [v5] : ? [v6] : (ordered_pair(v5, v4) = v6 & ~ in(v6, v2))))) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ~ relation(v2) | ~ empty(v3) | empty(v2)) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ~ relation(v2) | ( ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ! [v6] : ? [v7] : (ordered_pair(v5, v6) = v7 & ~ in(v7, v2))) & (in(v5, v4) | ? [v6] : ? [v7] : (ordered_pair(v5, v6) = v7 & in(v7, v2))))) & ! [v4] : ( ~ in(v4, v3) | ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & in(v6, v2))) & ! [v4] : (in(v4, v3) | ! [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ~ in(v6, v2))))) & ! [v2] : ! [v3] : ( ~ element(v2, v3) | empty(v3) | in(v2, v3)) & ! [v2] : ! [v3] : ( ~ empty(v3) | ~ in(v2, v3)) & ! [v2] : ! [v3] : ( ~ in(v3, v2) | ~ in(v2, v3)) & ! [v2] : ! [v3] : ( ~ in(v2, v3) | element(v2, v3)) & ! [v2] : (v2 = all_0_0_0 | ~ empty(v2)) & ! [v2] : ( ~ empty(v2) | relation(v2)) & ! [v2] : ? [v3] : element(v3, v2) & ? [v2] : ~ empty(v2) & ? [v2] : empty(v2) & ? [v2] : (relation(v2) & empty(v2)) & ? [v2] : (relation(v2) & ~ empty(v2)) & (( ~ (v1 = all_0_0_0) & relation_rng(all_0_0_0) = v1) | ( ~ (v0 = all_0_0_0) & relation_dom(all_0_0_0) = v0)))
% 26.53/7.34 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 26.53/7.34 |
% 26.53/7.34 | Instantiating (6) with all_2_0_1, all_2_1_2 yields:
% 26.53/7.34 | (8) relation(all_0_0_0) & empty(all_0_0_0) & ! [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] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ( ! [v2] : (v2 = v1 | ? [v3] : (( ~ in(v3, v2) | ! [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & ~ in(v5, v0))) & (in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0))))) & ! [v2] : ( ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) & ! [v2] : (in(v2, v1) | ! [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & ~ in(v4, v0))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ( ! [v2] : (v2 = v1 | ? [v3] : (( ~ in(v3, v2) | ! [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & ~ in(v5, v0))) & (in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0))))) & ! [v2] : ( ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) & ! [v2] : (in(v2, v1) | ! [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & ~ in(v4, v0))))) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = all_0_0_0 | ~ empty(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ? [v1] : element(v1, v0) & ? [v0] : ~ empty(v0) & ? [v0] : empty(v0) & ? [v0] : (relation(v0) & empty(v0)) & ? [v0] : (relation(v0) & ~ empty(v0)) & (( ~ (all_2_0_1 = all_0_0_0) & relation_rng(all_0_0_0) = all_2_0_1) | ( ~ (all_2_1_2 = all_0_0_0) & relation_dom(all_0_0_0) = all_2_1_2))
% 26.53/7.34 |
% 26.53/7.34 | Applying alpha-rule on (8) yields:
% 26.53/7.34 | (9) ? [v0] : empty(v0)
% 26.53/7.34 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2))
% 26.53/7.34 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2))
% 26.53/7.34 | (12) ? [v0] : (relation(v0) & ~ empty(v0))
% 26.53/7.34 | (13) relation(all_0_0_0)
% 26.53/7.34 | (14) ? [v0] : ~ empty(v0)
% 26.53/7.34 | (15) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1))
% 26.53/7.34 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 26.53/7.34 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 26.53/7.34 | (18) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ( ! [v2] : (v2 = v1 | ? [v3] : (( ~ in(v3, v2) | ! [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & ~ in(v5, v0))) & (in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0))))) & ! [v2] : ( ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) & ! [v2] : (in(v2, v1) | ! [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & ~ in(v4, v0)))))
% 26.53/7.34 | (19) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ( ! [v2] : (v2 = v1 | ? [v3] : (( ~ in(v3, v2) | ! [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & ~ in(v5, v0))) & (in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0))))) & ! [v2] : ( ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) & ! [v2] : (in(v2, v1) | ! [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & ~ in(v4, v0)))))
% 26.53/7.35 | (20) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0))))
% 26.53/7.35 | (21) ! [v0] : ( ~ empty(v0) | relation(v0))
% 26.53/7.35 | (22) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 26.53/7.35 | (23) ! [v0] : (v0 = all_0_0_0 | ~ empty(v0))
% 26.53/7.35 | (24) ( ~ (all_2_0_1 = all_0_0_0) & relation_rng(all_0_0_0) = all_2_0_1) | ( ~ (all_2_1_2 = all_0_0_0) & relation_dom(all_0_0_0) = all_2_1_2)
% 26.53/7.35 | (25) ! [v0] : ? [v1] : element(v1, v0)
% 26.53/7.35 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 26.53/7.35 | (27) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 26.53/7.35 | (28) empty(all_0_0_0)
% 26.53/7.35 | (29) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 26.53/7.35 | (30) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 26.53/7.35 | (31) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 26.53/7.35 | (32) ? [v0] : (relation(v0) & empty(v0))
% 26.53/7.35 | (33) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 26.53/7.35 |
% 26.53/7.35 | Instantiating (9) with all_9_0_5 yields:
% 26.53/7.35 | (34) empty(all_9_0_5)
% 26.53/7.35 |
% 26.53/7.35 | Instantiating formula (16) with all_0_0_0, all_9_0_5 and discharging atoms empty(all_9_0_5), empty(all_0_0_0), yields:
% 26.53/7.35 | (35) all_9_0_5 = all_0_0_0
% 26.53/7.35 |
% 26.53/7.35 +-Applying beta-rule and splitting (24), into two cases.
% 26.53/7.35 |-Branch one:
% 26.53/7.35 | (36) ~ (all_2_0_1 = all_0_0_0) & relation_rng(all_0_0_0) = all_2_0_1
% 26.53/7.35 |
% 26.53/7.35 | Applying alpha-rule on (36) yields:
% 26.53/7.35 | (37) ~ (all_2_0_1 = all_0_0_0)
% 26.53/7.35 | (38) relation_rng(all_0_0_0) = all_2_0_1
% 26.53/7.35 |
% 26.53/7.35 | Instantiating formula (19) with all_2_0_1, all_0_0_0 and discharging atoms relation_rng(all_0_0_0) = all_2_0_1, relation(all_0_0_0), yields:
% 26.53/7.35 | (39) ! [v0] : (v0 = all_2_0_1 | ? [v1] : (( ~ in(v1, v0) | ! [v2] : ? [v3] : (ordered_pair(v2, v1) = v3 & ~ in(v3, all_0_0_0))) & (in(v1, v0) | ? [v2] : ? [v3] : (ordered_pair(v2, v1) = v3 & in(v3, all_0_0_0))))) & ! [v0] : ( ~ in(v0, all_2_0_1) | ? [v1] : ? [v2] : (ordered_pair(v1, v0) = v2 & in(v2, all_0_0_0))) & ! [v0] : (in(v0, all_2_0_1) | ! [v1] : ? [v2] : (ordered_pair(v1, v0) = v2 & ~ in(v2, all_0_0_0)))
% 26.53/7.35 |
% 26.53/7.35 | Applying alpha-rule on (39) yields:
% 26.53/7.35 | (40) ! [v0] : (v0 = all_2_0_1 | ? [v1] : (( ~ in(v1, v0) | ! [v2] : ? [v3] : (ordered_pair(v2, v1) = v3 & ~ in(v3, all_0_0_0))) & (in(v1, v0) | ? [v2] : ? [v3] : (ordered_pair(v2, v1) = v3 & in(v3, all_0_0_0)))))
% 26.53/7.35 | (41) ! [v0] : ( ~ in(v0, all_2_0_1) | ? [v1] : ? [v2] : (ordered_pair(v1, v0) = v2 & in(v2, all_0_0_0)))
% 26.53/7.35 | (42) ! [v0] : (in(v0, all_2_0_1) | ! [v1] : ? [v2] : (ordered_pair(v1, v0) = v2 & ~ in(v2, all_0_0_0)))
% 26.53/7.35 |
% 26.53/7.35 | Introducing new symbol ex_32_1_8 defined by:
% 26.53/7.35 | (43) ex_32_1_8 = all_9_0_5
% 26.53/7.35 |
% 26.53/7.35 | Introducing new symbol ex_32_0_7 defined by:
% 26.53/7.35 | (44) ex_32_0_7 = all_2_0_1
% 26.53/7.35 |
% 26.53/7.35 | Instantiating formula (20) with ex_32_0_7, ex_32_1_8 yields:
% 26.53/7.35 | (45) ex_32_0_7 = ex_32_1_8 | ? [v0] : (( ~ in(v0, ex_32_0_7) | ~ in(v0, ex_32_1_8)) & (in(v0, ex_32_0_7) | in(v0, ex_32_1_8)))
% 26.53/7.35 |
% 26.53/7.35 +-Applying beta-rule and splitting (45), into two cases.
% 26.53/7.35 |-Branch one:
% 26.53/7.35 | (46) ex_32_0_7 = ex_32_1_8
% 26.53/7.35 |
% 26.53/7.35 | Combining equations (44,46) yields a new equation:
% 26.53/7.35 | (47) ex_32_1_8 = all_2_0_1
% 26.53/7.35 |
% 26.53/7.35 | Combining equations (47,43) yields a new equation:
% 26.53/7.35 | (48) all_9_0_5 = all_2_0_1
% 26.53/7.35 |
% 26.53/7.35 | Combining equations (48,35) yields a new equation:
% 26.53/7.35 | (49) all_2_0_1 = all_0_0_0
% 26.53/7.35 |
% 26.53/7.35 | Simplifying 49 yields:
% 26.53/7.35 | (50) all_2_0_1 = all_0_0_0
% 26.53/7.35 |
% 26.53/7.35 | Equations (50) can reduce 37 to:
% 26.53/7.35 | (51) $false
% 26.53/7.35 |
% 26.53/7.35 |-The branch is then unsatisfiable
% 26.53/7.35 |-Branch two:
% 26.53/7.35 | (52) ? [v0] : (( ~ in(v0, ex_32_0_7) | ~ in(v0, ex_32_1_8)) & (in(v0, ex_32_0_7) | in(v0, ex_32_1_8)))
% 26.53/7.35 |
% 26.53/7.35 | Instantiating (52) with all_35_0_9 yields:
% 26.53/7.35 | (53) ( ~ in(all_35_0_9, ex_32_0_7) | ~ in(all_35_0_9, ex_32_1_8)) & (in(all_35_0_9, ex_32_0_7) | in(all_35_0_9, ex_32_1_8))
% 26.53/7.36 |
% 26.53/7.36 | Applying alpha-rule on (53) yields:
% 26.53/7.36 | (54) ~ in(all_35_0_9, ex_32_0_7) | ~ in(all_35_0_9, ex_32_1_8)
% 26.53/7.36 | (55) in(all_35_0_9, ex_32_0_7) | in(all_35_0_9, ex_32_1_8)
% 26.53/7.36 |
% 26.53/7.36 +-Applying beta-rule and splitting (54), into two cases.
% 26.53/7.36 |-Branch one:
% 26.53/7.36 | (56) ~ in(all_35_0_9, ex_32_0_7)
% 26.53/7.36 |
% 26.53/7.36 +-Applying beta-rule and splitting (55), into two cases.
% 26.53/7.36 |-Branch one:
% 26.53/7.36 | (57) in(all_35_0_9, ex_32_0_7)
% 26.53/7.36 |
% 26.53/7.36 | Using (57) and (56) yields:
% 26.53/7.36 | (58) $false
% 26.53/7.36 |
% 26.53/7.36 |-The branch is then unsatisfiable
% 26.53/7.36 |-Branch two:
% 26.53/7.36 | (59) in(all_35_0_9, ex_32_1_8)
% 26.53/7.36 |
% 26.53/7.36 | Instantiating formula (30) with all_0_0_0, all_35_0_9 and discharging atoms empty(all_0_0_0), yields:
% 26.53/7.36 | (60) ~ in(all_35_0_9, all_0_0_0)
% 26.53/7.36 |
% 26.53/7.36 | Combining equations (35,43) yields a new equation:
% 26.53/7.36 | (61) ex_32_1_8 = all_0_0_0
% 26.53/7.36 |
% 26.53/7.36 | From (61) and (59) follows:
% 26.53/7.36 | (62) in(all_35_0_9, all_0_0_0)
% 26.53/7.36 |
% 26.53/7.36 | Using (62) and (60) yields:
% 26.53/7.36 | (58) $false
% 26.53/7.36 |
% 26.53/7.36 |-The branch is then unsatisfiable
% 26.53/7.36 |-Branch two:
% 26.53/7.36 | (57) in(all_35_0_9, ex_32_0_7)
% 26.53/7.36 | (65) ~ in(all_35_0_9, ex_32_1_8)
% 26.53/7.36 |
% 26.53/7.36 | Instantiating formula (41) with all_35_0_9 yields:
% 26.53/7.36 | (66) ~ in(all_35_0_9, all_2_0_1) | ? [v0] : ? [v1] : (ordered_pair(v0, all_35_0_9) = v1 & in(v1, all_0_0_0))
% 26.53/7.36 |
% 26.53/7.36 +-Applying beta-rule and splitting (66), into two cases.
% 26.53/7.36 |-Branch one:
% 26.53/7.36 | (67) ~ in(all_35_0_9, all_2_0_1)
% 26.53/7.36 |
% 26.53/7.36 | From (44) and (57) follows:
% 26.53/7.36 | (68) in(all_35_0_9, all_2_0_1)
% 26.53/7.36 |
% 26.53/7.36 | Using (68) and (67) yields:
% 26.53/7.36 | (58) $false
% 26.53/7.36 |
% 26.53/7.36 |-The branch is then unsatisfiable
% 26.53/7.36 |-Branch two:
% 26.53/7.36 | (70) ? [v0] : ? [v1] : (ordered_pair(v0, all_35_0_9) = v1 & in(v1, all_0_0_0))
% 26.53/7.36 |
% 26.53/7.36 | Instantiating (70) with all_63_0_14, all_63_1_15 yields:
% 26.53/7.36 | (71) ordered_pair(all_63_1_15, all_35_0_9) = all_63_0_14 & in(all_63_0_14, all_0_0_0)
% 26.53/7.36 |
% 26.53/7.36 | Applying alpha-rule on (71) yields:
% 26.53/7.36 | (72) ordered_pair(all_63_1_15, all_35_0_9) = all_63_0_14
% 26.53/7.36 | (73) in(all_63_0_14, all_0_0_0)
% 26.53/7.36 |
% 26.53/7.36 | Instantiating formula (30) with all_0_0_0, all_63_0_14 and discharging atoms empty(all_0_0_0), in(all_63_0_14, all_0_0_0), yields:
% 26.53/7.36 | (58) $false
% 26.53/7.36 |
% 26.53/7.36 |-The branch is then unsatisfiable
% 26.53/7.36 |-Branch two:
% 26.53/7.36 | (75) ~ (all_2_1_2 = all_0_0_0) & relation_dom(all_0_0_0) = all_2_1_2
% 26.53/7.36 |
% 26.53/7.36 | Applying alpha-rule on (75) yields:
% 26.53/7.36 | (76) ~ (all_2_1_2 = all_0_0_0)
% 26.53/7.36 | (77) relation_dom(all_0_0_0) = all_2_1_2
% 26.53/7.36 |
% 26.53/7.36 | Instantiating formula (18) with all_2_1_2, all_0_0_0 and discharging atoms relation_dom(all_0_0_0) = all_2_1_2, relation(all_0_0_0), yields:
% 26.53/7.36 | (78) ! [v0] : (v0 = all_2_1_2 | ? [v1] : (( ~ in(v1, v0) | ! [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & ~ in(v3, all_0_0_0))) & (in(v1, v0) | ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, all_0_0_0))))) & ! [v0] : ( ~ in(v0, all_2_1_2) | ? [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & in(v2, all_0_0_0))) & ! [v0] : (in(v0, all_2_1_2) | ! [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & ~ in(v2, all_0_0_0)))
% 26.53/7.36 |
% 26.53/7.36 | Applying alpha-rule on (78) yields:
% 26.53/7.36 | (79) ! [v0] : (v0 = all_2_1_2 | ? [v1] : (( ~ in(v1, v0) | ! [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & ~ in(v3, all_0_0_0))) & (in(v1, v0) | ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, all_0_0_0)))))
% 26.53/7.36 | (80) ! [v0] : ( ~ in(v0, all_2_1_2) | ? [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & in(v2, all_0_0_0)))
% 26.53/7.36 | (81) ! [v0] : (in(v0, all_2_1_2) | ! [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & ~ in(v2, all_0_0_0)))
% 26.53/7.36 |
% 26.53/7.36 | Introducing new symbol ex_32_1_17 defined by:
% 26.53/7.36 | (82) ex_32_1_17 = all_9_0_5
% 26.53/7.36 |
% 26.53/7.36 | Introducing new symbol ex_32_0_16 defined by:
% 26.53/7.36 | (83) ex_32_0_16 = all_2_1_2
% 26.53/7.36 |
% 26.53/7.36 | Instantiating formula (20) with ex_32_0_16, ex_32_1_17 yields:
% 26.53/7.36 | (84) ex_32_0_16 = ex_32_1_17 | ? [v0] : (( ~ in(v0, ex_32_0_16) | ~ in(v0, ex_32_1_17)) & (in(v0, ex_32_0_16) | in(v0, ex_32_1_17)))
% 26.53/7.36 |
% 26.53/7.36 +-Applying beta-rule and splitting (84), into two cases.
% 26.53/7.36 |-Branch one:
% 26.53/7.36 | (85) ex_32_0_16 = ex_32_1_17
% 26.53/7.36 |
% 26.53/7.36 | Combining equations (83,85) yields a new equation:
% 26.53/7.36 | (86) ex_32_1_17 = all_2_1_2
% 26.53/7.36 |
% 26.53/7.36 | Combining equations (86,82) yields a new equation:
% 26.53/7.36 | (87) all_9_0_5 = all_2_1_2
% 26.53/7.36 |
% 26.53/7.36 | Combining equations (87,35) yields a new equation:
% 26.53/7.36 | (88) all_2_1_2 = all_0_0_0
% 26.53/7.36 |
% 26.53/7.36 | Simplifying 88 yields:
% 26.53/7.36 | (89) all_2_1_2 = all_0_0_0
% 26.53/7.36 |
% 26.53/7.36 | Equations (89) can reduce 76 to:
% 26.53/7.36 | (51) $false
% 26.53/7.36 |
% 26.53/7.36 |-The branch is then unsatisfiable
% 26.53/7.36 |-Branch two:
% 26.53/7.36 | (91) ? [v0] : (( ~ in(v0, ex_32_0_16) | ~ in(v0, ex_32_1_17)) & (in(v0, ex_32_0_16) | in(v0, ex_32_1_17)))
% 26.53/7.36 |
% 26.53/7.36 | Instantiating (91) with all_35_0_18 yields:
% 26.53/7.36 | (92) ( ~ in(all_35_0_18, ex_32_0_16) | ~ in(all_35_0_18, ex_32_1_17)) & (in(all_35_0_18, ex_32_0_16) | in(all_35_0_18, ex_32_1_17))
% 26.53/7.36 |
% 26.53/7.36 | Applying alpha-rule on (92) yields:
% 26.53/7.36 | (93) ~ in(all_35_0_18, ex_32_0_16) | ~ in(all_35_0_18, ex_32_1_17)
% 26.53/7.36 | (94) in(all_35_0_18, ex_32_0_16) | in(all_35_0_18, ex_32_1_17)
% 26.53/7.36 |
% 26.53/7.36 +-Applying beta-rule and splitting (93), into two cases.
% 26.53/7.36 |-Branch one:
% 26.53/7.36 | (95) ~ in(all_35_0_18, ex_32_0_16)
% 26.53/7.36 |
% 26.53/7.36 +-Applying beta-rule and splitting (94), into two cases.
% 26.53/7.36 |-Branch one:
% 26.53/7.36 | (96) in(all_35_0_18, ex_32_0_16)
% 26.53/7.36 |
% 26.53/7.36 | Using (96) and (95) yields:
% 26.53/7.36 | (58) $false
% 26.53/7.36 |
% 26.53/7.36 |-The branch is then unsatisfiable
% 26.53/7.36 |-Branch two:
% 26.53/7.36 | (98) in(all_35_0_18, ex_32_1_17)
% 26.53/7.36 |
% 26.53/7.36 | Instantiating formula (30) with all_0_0_0, all_35_0_18 and discharging atoms empty(all_0_0_0), yields:
% 26.53/7.36 | (99) ~ in(all_35_0_18, all_0_0_0)
% 26.53/7.36 |
% 26.53/7.37 | Combining equations (35,82) yields a new equation:
% 26.53/7.37 | (100) ex_32_1_17 = all_0_0_0
% 26.53/7.37 |
% 26.53/7.37 | From (100) and (98) follows:
% 26.53/7.37 | (101) in(all_35_0_18, all_0_0_0)
% 26.53/7.37 |
% 26.53/7.37 | Using (101) and (99) yields:
% 26.53/7.37 | (58) $false
% 26.53/7.37 |
% 26.53/7.37 |-The branch is then unsatisfiable
% 26.53/7.37 |-Branch two:
% 26.53/7.37 | (96) in(all_35_0_18, ex_32_0_16)
% 26.53/7.37 | (104) ~ in(all_35_0_18, ex_32_1_17)
% 26.53/7.37 |
% 26.53/7.37 | Instantiating formula (80) with all_35_0_18 yields:
% 26.53/7.37 | (105) ~ in(all_35_0_18, all_2_1_2) | ? [v0] : ? [v1] : (ordered_pair(all_35_0_18, v0) = v1 & in(v1, all_0_0_0))
% 26.53/7.37 |
% 26.53/7.37 +-Applying beta-rule and splitting (105), into two cases.
% 26.53/7.37 |-Branch one:
% 26.53/7.37 | (106) ~ in(all_35_0_18, all_2_1_2)
% 26.53/7.37 |
% 26.53/7.37 | From (83) and (96) follows:
% 26.53/7.37 | (107) in(all_35_0_18, all_2_1_2)
% 26.53/7.37 |
% 26.53/7.37 | Using (107) and (106) yields:
% 26.53/7.37 | (58) $false
% 26.53/7.37 |
% 26.53/7.37 |-The branch is then unsatisfiable
% 26.53/7.37 |-Branch two:
% 26.53/7.37 | (109) ? [v0] : ? [v1] : (ordered_pair(all_35_0_18, v0) = v1 & in(v1, all_0_0_0))
% 26.53/7.37 |
% 26.53/7.37 | Instantiating (109) with all_63_0_23, all_63_1_24 yields:
% 26.53/7.37 | (110) ordered_pair(all_35_0_18, all_63_1_24) = all_63_0_23 & in(all_63_0_23, all_0_0_0)
% 26.53/7.37 |
% 26.53/7.37 | Applying alpha-rule on (110) yields:
% 26.53/7.37 | (111) ordered_pair(all_35_0_18, all_63_1_24) = all_63_0_23
% 26.53/7.37 | (112) in(all_63_0_23, all_0_0_0)
% 26.53/7.37 |
% 26.53/7.37 | Instantiating formula (30) with all_0_0_0, all_63_0_23 and discharging atoms empty(all_0_0_0), in(all_63_0_23, all_0_0_0), yields:
% 26.53/7.37 | (58) $false
% 26.53/7.37 |
% 26.53/7.37 |-The branch is then unsatisfiable
% 26.53/7.37 % SZS output end Proof for theBenchmark
% 26.53/7.37
% 26.53/7.37 6722ms
%------------------------------------------------------------------------------