TSTP Solution File: SEU147+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU147+3 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n014.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 08:46:58 EDT 2022
% Result : Theorem 10.78s 3.37s
% Output : Proof 15.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU147+3 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 22:18:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.58 ____ _
% 0.18/0.58 ___ / __ \_____(_)___ ________ __________
% 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic
% 0.59/0.58 (ePrincess v.1.0)
% 0.59/0.58
% 0.59/0.58 (c) Philipp Rümmer, 2009-2015
% 0.59/0.58 (c) Peter Backeman, 2014-2015
% 0.59/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.58 Bug reports to peter@backeman.se
% 0.59/0.58
% 0.59/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.58
% 0.59/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.30/0.89 Prover 0: Preprocessing ...
% 1.67/1.04 Prover 0: Warning: ignoring some quantifiers
% 1.67/1.05 Prover 0: Constructing countermodel ...
% 2.23/1.23 Prover 0: gave up
% 2.23/1.23 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.23/1.25 Prover 1: Preprocessing ...
% 2.55/1.30 Prover 1: Warning: ignoring some quantifiers
% 2.55/1.31 Prover 1: Constructing countermodel ...
% 2.55/1.37 Prover 1: gave up
% 2.55/1.37 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.91/1.38 Prover 2: Preprocessing ...
% 3.11/1.44 Prover 2: Warning: ignoring some quantifiers
% 3.11/1.45 Prover 2: Constructing countermodel ...
% 3.11/1.51 Prover 2: gave up
% 3.11/1.51 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.47/1.52 Prover 3: Preprocessing ...
% 3.47/1.54 Prover 3: Warning: ignoring some quantifiers
% 3.47/1.54 Prover 3: Constructing countermodel ...
% 3.76/1.59 Prover 3: gave up
% 3.76/1.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 3.76/1.60 Prover 4: Preprocessing ...
% 3.76/1.66 Prover 4: Warning: ignoring some quantifiers
% 3.76/1.66 Prover 4: Constructing countermodel ...
% 4.46/1.81 Prover 4: gave up
% 4.46/1.81 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.86/1.82 Prover 5: Preprocessing ...
% 4.86/1.84 Prover 5: Warning: ignoring some quantifiers
% 4.86/1.85 Prover 5: Constructing countermodel ...
% 4.86/1.88 Prover 5: gave up
% 4.86/1.88 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.86/1.89 Prover 6: Preprocessing ...
% 5.25/1.92 Prover 6: Warning: ignoring some quantifiers
% 5.25/1.92 Prover 6: Constructing countermodel ...
% 5.25/1.95 Prover 6: gave up
% 5.25/1.95 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 5.25/1.96 Prover 7: Preprocessing ...
% 5.25/1.98 Prover 7: Proving ...
% 10.78/3.37 Prover 7: proved (1413ms)
% 10.78/3.37
% 10.78/3.37 % SZS status Theorem for theBenchmark
% 10.78/3.37
% 10.78/3.37 Generating proof ... found it (size 59)
% 15.68/4.83
% 15.68/4.83 % SZS output start Proof for theBenchmark
% 15.68/4.83 Assumed formulas after preprocessing and simplification:
% 15.68/4.83 | (0) ? [v0] : ( ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (powerset(v3) = v2) | ~ (powerset(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v3) = v2) | ~ (singleton(v3) = v1)) & ? [v1] : ? [v2] : ( ~ (v2 = v1) & powerset(v0) = v1 & singleton(v0) = v2 & empty(v0) & ! [v3] : ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ~ in(v5, v3)) & (in(v5, v4) | in(v5, v3)))) & ! [v3] : ! [v4] : ( ~ (powerset(v3) = v4) | ! [v5] : (v5 = v4 | ? [v6] : (( ~ subset(v6, v3) | ~ in(v6, v5)) & (subset(v6, v3) | in(v6, v5))))) & ! [v3] : ! [v4] : ( ~ (powerset(v3) = v4) | ( ! [v5] : ( ~ subset(v5, v3) | in(v5, v4)) & ! [v5] : ( ~ in(v5, v4) | subset(v5, v3)))) & ! [v3] : ! [v4] : ( ~ (singleton(v3) = v4) | ! [v5] : (v5 = v4 | ? [v6] : (( ~ (v6 = v3) | ~ in(v3, v5)) & (v6 = v3 | in(v6, v5))))) & ! [v3] : ! [v4] : ( ~ (singleton(v3) = v4) | (in(v3, v4) & ! [v5] : (v5 = v3 | ~ in(v5, v4)))) & ! [v3] : ! [v4] : ( ~ in(v4, v3) | ~ in(v3, v4)) & ! [v3] : (v3 = v0 | ~ subset(v3, v0)) & ! [v3] : subset(v3, v3) & ? [v3] : ~ empty(v3) & ? [v3] : empty(v3)))
% 15.68/4.85 | Instantiating (0) with all_0_0_0 yields:
% 15.68/4.85 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ? [v0] : ? [v1] : ( ~ (v1 = v0) & powerset(all_0_0_0) = v0 & singleton(all_0_0_0) = v1 & empty(all_0_0_0) & ! [v2] : ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v2)) & (in(v4, v3) | in(v4, v2)))) & ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : (( ~ subset(v5, v2) | ~ in(v5, v4)) & (subset(v5, v2) | in(v5, v4))))) & ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ( ! [v4] : ( ~ subset(v4, v2) | in(v4, v3)) & ! [v4] : ( ~ in(v4, v3) | subset(v4, v2)))) & ! [v2] : ! [v3] : ( ~ (singleton(v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : (( ~ (v5 = v2) | ~ in(v2, v4)) & (v5 = v2 | in(v5, v4))))) & ! [v2] : ! [v3] : ( ~ (singleton(v2) = v3) | (in(v2, v3) & ! [v4] : (v4 = v2 | ~ in(v4, v3)))) & ! [v2] : ! [v3] : ( ~ in(v3, v2) | ~ in(v2, v3)) & ! [v2] : (v2 = all_0_0_0 | ~ subset(v2, all_0_0_0)) & ! [v2] : subset(v2, v2) & ? [v2] : ~ empty(v2) & ? [v2] : empty(v2))
% 15.68/4.86 |
% 15.68/4.86 | Applying alpha-rule on (1) yields:
% 15.68/4.86 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 15.68/4.86 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 15.68/4.86 | (4) ? [v0] : ? [v1] : ( ~ (v1 = v0) & powerset(all_0_0_0) = v0 & singleton(all_0_0_0) = v1 & empty(all_0_0_0) & ! [v2] : ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v2)) & (in(v4, v3) | in(v4, v2)))) & ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : (( ~ subset(v5, v2) | ~ in(v5, v4)) & (subset(v5, v2) | in(v5, v4))))) & ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ( ! [v4] : ( ~ subset(v4, v2) | in(v4, v3)) & ! [v4] : ( ~ in(v4, v3) | subset(v4, v2)))) & ! [v2] : ! [v3] : ( ~ (singleton(v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : (( ~ (v5 = v2) | ~ in(v2, v4)) & (v5 = v2 | in(v5, v4))))) & ! [v2] : ! [v3] : ( ~ (singleton(v2) = v3) | (in(v2, v3) & ! [v4] : (v4 = v2 | ~ in(v4, v3)))) & ! [v2] : ! [v3] : ( ~ in(v3, v2) | ~ in(v2, v3)) & ! [v2] : (v2 = all_0_0_0 | ~ subset(v2, all_0_0_0)) & ! [v2] : subset(v2, v2) & ? [v2] : ~ empty(v2) & ? [v2] : empty(v2))
% 15.68/4.86 |
% 15.68/4.86 | Instantiating (4) with all_2_0_1, all_2_1_2 yields:
% 15.68/4.86 | (5) ~ (all_2_0_1 = all_2_1_2) & powerset(all_0_0_0) = all_2_1_2 & singleton(all_0_0_0) = all_2_0_1 & empty(all_0_0_0) & ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : (( ~ subset(v3, v0) | ~ in(v3, v2)) & (subset(v3, v0) | in(v3, v2))))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ( ! [v2] : ( ~ subset(v2, v0) | in(v2, v1)) & ! [v2] : ( ~ in(v2, v1) | subset(v2, v0)))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : (( ~ (v3 = v0) | ~ in(v0, v2)) & (v3 = v0 | in(v3, v2))))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | (in(v0, v1) & ! [v2] : (v2 = v0 | ~ in(v2, v1)))) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : (v0 = all_0_0_0 | ~ subset(v0, all_0_0_0)) & ! [v0] : subset(v0, v0) & ? [v0] : ~ empty(v0) & ? [v0] : empty(v0)
% 15.68/4.87 |
% 15.68/4.87 | Applying alpha-rule on (5) yields:
% 15.68/4.87 | (6) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : (( ~ (v3 = v0) | ~ in(v0, v2)) & (v3 = v0 | in(v3, v2)))))
% 15.68/4.87 | (7) ! [v0] : (v0 = all_0_0_0 | ~ subset(v0, all_0_0_0))
% 15.68/4.87 | (8) ? [v0] : empty(v0)
% 15.68/4.87 | (9) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ( ! [v2] : ( ~ subset(v2, v0) | in(v2, v1)) & ! [v2] : ( ~ in(v2, v1) | subset(v2, v0))))
% 15.68/4.87 | (10) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 15.68/4.87 | (11) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | (in(v0, v1) & ! [v2] : (v2 = v0 | ~ in(v2, v1))))
% 15.68/4.87 | (12) empty(all_0_0_0)
% 15.68/4.87 | (13) powerset(all_0_0_0) = all_2_1_2
% 15.68/4.87 | (14) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : (( ~ subset(v3, v0) | ~ in(v3, v2)) & (subset(v3, v0) | in(v3, v2)))))
% 15.68/4.87 | (15) ? [v0] : ~ empty(v0)
% 15.68/4.87 | (16) singleton(all_0_0_0) = all_2_0_1
% 15.68/4.87 | (17) ! [v0] : subset(v0, v0)
% 15.68/4.87 | (18) ~ (all_2_0_1 = all_2_1_2)
% 15.68/4.87 | (19) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0))))
% 15.68/4.87 |
% 15.68/4.87 | Instantiating formula (9) with all_2_1_2, all_0_0_0 and discharging atoms powerset(all_0_0_0) = all_2_1_2, yields:
% 15.68/4.87 | (20) ! [v0] : ( ~ subset(v0, all_0_0_0) | in(v0, all_2_1_2)) & ! [v0] : ( ~ in(v0, all_2_1_2) | subset(v0, all_0_0_0))
% 15.68/4.87 |
% 15.68/4.87 | Applying alpha-rule on (20) yields:
% 15.68/4.87 | (21) ! [v0] : ( ~ subset(v0, all_0_0_0) | in(v0, all_2_1_2))
% 15.68/4.87 | (22) ! [v0] : ( ~ in(v0, all_2_1_2) | subset(v0, all_0_0_0))
% 15.68/4.87 |
% 15.68/4.87 | Instantiating formula (11) with all_2_0_1, all_0_0_0 and discharging atoms singleton(all_0_0_0) = all_2_0_1, yields:
% 15.68/4.87 | (23) in(all_0_0_0, all_2_0_1) & ! [v0] : (v0 = all_0_0_0 | ~ in(v0, all_2_0_1))
% 15.68/4.87 |
% 15.68/4.87 | Applying alpha-rule on (23) yields:
% 15.68/4.87 | (24) in(all_0_0_0, all_2_0_1)
% 15.68/4.87 | (25) ! [v0] : (v0 = all_0_0_0 | ~ in(v0, all_2_0_1))
% 15.68/4.87 |
% 15.68/4.87 | Introducing new symbol ex_23_1_6 defined by:
% 15.68/4.87 | (26) ex_23_1_6 = all_2_1_2
% 15.68/4.87 |
% 15.68/4.87 | Introducing new symbol ex_23_0_5 defined by:
% 15.68/4.87 | (27) ex_23_0_5 = all_2_0_1
% 15.68/4.87 |
% 15.68/4.87 | Instantiating formula (19) with ex_23_0_5, ex_23_1_6 yields:
% 15.68/4.87 | (28) ex_23_0_5 = ex_23_1_6 | ? [v0] : (( ~ in(v0, ex_23_0_5) | ~ in(v0, ex_23_1_6)) & (in(v0, ex_23_0_5) | in(v0, ex_23_1_6)))
% 15.68/4.87 |
% 15.68/4.87 +-Applying beta-rule and splitting (28), into two cases.
% 15.68/4.87 |-Branch one:
% 15.68/4.87 | (29) ex_23_0_5 = ex_23_1_6
% 15.68/4.87 |
% 15.68/4.87 | Combining equations (27,29) yields a new equation:
% 15.68/4.87 | (30) ex_23_1_6 = all_2_0_1
% 15.68/4.87 |
% 15.68/4.87 | Combining equations (30,26) yields a new equation:
% 15.68/4.87 | (31) all_2_0_1 = all_2_1_2
% 15.68/4.87 |
% 15.68/4.87 | Simplifying 31 yields:
% 15.68/4.87 | (32) all_2_0_1 = all_2_1_2
% 15.68/4.87 |
% 15.68/4.88 | Equations (32) can reduce 18 to:
% 15.68/4.88 | (33) $false
% 15.68/4.88 |
% 15.68/4.88 |-The branch is then unsatisfiable
% 15.68/4.88 |-Branch two:
% 15.68/4.88 | (34) ? [v0] : (( ~ in(v0, ex_23_0_5) | ~ in(v0, ex_23_1_6)) & (in(v0, ex_23_0_5) | in(v0, ex_23_1_6)))
% 15.68/4.88 |
% 15.68/4.88 | Instantiating (34) with all_26_0_7 yields:
% 15.68/4.88 | (35) ( ~ in(all_26_0_7, ex_23_0_5) | ~ in(all_26_0_7, ex_23_1_6)) & (in(all_26_0_7, ex_23_0_5) | in(all_26_0_7, ex_23_1_6))
% 15.68/4.88 |
% 15.68/4.88 | Applying alpha-rule on (35) yields:
% 15.68/4.88 | (36) ~ in(all_26_0_7, ex_23_0_5) | ~ in(all_26_0_7, ex_23_1_6)
% 15.68/4.88 | (37) in(all_26_0_7, ex_23_0_5) | in(all_26_0_7, ex_23_1_6)
% 15.68/4.88 |
% 15.68/4.88 +-Applying beta-rule and splitting (36), into two cases.
% 15.68/4.88 |-Branch one:
% 15.68/4.88 | (38) ~ in(all_26_0_7, ex_23_0_5)
% 15.68/4.88 |
% 15.68/4.88 +-Applying beta-rule and splitting (37), into two cases.
% 15.68/4.88 |-Branch one:
% 15.68/4.88 | (39) in(all_26_0_7, ex_23_0_5)
% 15.68/4.88 |
% 15.68/4.88 | Using (39) and (38) yields:
% 15.68/4.88 | (40) $false
% 15.68/4.88 |
% 15.68/4.88 |-The branch is then unsatisfiable
% 15.68/4.88 |-Branch two:
% 15.68/4.88 | (41) in(all_26_0_7, ex_23_1_6)
% 15.68/4.88 |
% 15.68/4.88 | Instantiating formula (25) with all_26_0_7 yields:
% 15.68/4.88 | (42) all_26_0_7 = all_0_0_0 | ~ in(all_26_0_7, all_2_0_1)
% 15.68/4.88 |
% 15.68/4.88 | Instantiating formula (22) with all_26_0_7 yields:
% 15.68/4.88 | (43) ~ in(all_26_0_7, all_2_1_2) | subset(all_26_0_7, all_0_0_0)
% 15.68/4.88 |
% 15.68/4.88 +-Applying beta-rule and splitting (42), into two cases.
% 15.68/4.88 |-Branch one:
% 15.68/4.88 | (44) ~ in(all_26_0_7, all_2_0_1)
% 15.68/4.88 |
% 15.68/4.88 +-Applying beta-rule and splitting (43), into two cases.
% 15.68/4.88 |-Branch one:
% 15.68/4.88 | (45) ~ in(all_26_0_7, all_2_1_2)
% 15.68/4.88 |
% 15.68/4.88 | From (26) and (41) follows:
% 15.68/4.88 | (46) in(all_26_0_7, all_2_1_2)
% 15.68/4.88 |
% 15.68/4.88 | Using (46) and (45) yields:
% 15.68/4.88 | (40) $false
% 15.68/4.88 |
% 15.68/4.88 |-The branch is then unsatisfiable
% 15.68/4.88 |-Branch two:
% 15.68/4.88 | (48) subset(all_26_0_7, all_0_0_0)
% 15.68/4.88 |
% 15.68/4.88 | Instantiating formula (7) with all_26_0_7 and discharging atoms subset(all_26_0_7, all_0_0_0), yields:
% 15.68/4.88 | (49) all_26_0_7 = all_0_0_0
% 15.68/4.88 |
% 15.68/4.88 | From (49) and (44) follows:
% 15.68/4.88 | (50) ~ in(all_0_0_0, all_2_0_1)
% 15.68/4.88 |
% 15.68/4.88 | Using (24) and (50) yields:
% 15.68/4.88 | (40) $false
% 15.68/4.88 |
% 15.68/4.88 |-The branch is then unsatisfiable
% 15.68/4.88 |-Branch two:
% 15.68/4.88 | (49) all_26_0_7 = all_0_0_0
% 15.68/4.88 |
% 15.68/4.88 | From (49) and (38) follows:
% 15.68/4.88 | (53) ~ in(all_0_0_0, ex_23_0_5)
% 15.68/4.88 |
% 15.68/4.88 | From (27) and (53) follows:
% 15.68/4.88 | (50) ~ in(all_0_0_0, all_2_0_1)
% 15.68/4.88 |
% 15.68/4.88 | Using (24) and (50) yields:
% 15.68/4.88 | (40) $false
% 15.68/4.88 |
% 15.68/4.88 |-The branch is then unsatisfiable
% 15.68/4.88 |-Branch two:
% 15.68/4.88 | (39) in(all_26_0_7, ex_23_0_5)
% 15.68/4.88 | (57) ~ in(all_26_0_7, ex_23_1_6)
% 15.68/4.88 |
% 15.68/4.88 | Instantiating formula (25) with all_26_0_7 yields:
% 15.68/4.88 | (42) all_26_0_7 = all_0_0_0 | ~ in(all_26_0_7, all_2_0_1)
% 15.68/4.88 |
% 15.68/4.88 | Instantiating formula (22) with all_26_0_7 yields:
% 15.68/4.88 | (43) ~ in(all_26_0_7, all_2_1_2) | subset(all_26_0_7, all_0_0_0)
% 15.68/4.88 |
% 15.68/4.88 +-Applying beta-rule and splitting (42), into two cases.
% 15.68/4.88 |-Branch one:
% 15.68/4.88 | (44) ~ in(all_26_0_7, all_2_0_1)
% 15.68/4.88 |
% 15.68/4.88 | From (27) and (39) follows:
% 15.68/4.88 | (61) in(all_26_0_7, all_2_0_1)
% 15.68/4.88 |
% 15.68/4.88 | Using (61) and (44) yields:
% 15.68/4.88 | (40) $false
% 15.68/4.88 |
% 15.68/4.88 |-The branch is then unsatisfiable
% 15.68/4.88 |-Branch two:
% 15.68/4.88 | (49) all_26_0_7 = all_0_0_0
% 15.68/4.88 |
% 15.68/4.88 | From (49) and (57) follows:
% 15.68/4.88 | (64) ~ in(all_0_0_0, ex_23_1_6)
% 15.68/4.88 |
% 15.68/4.88 +-Applying beta-rule and splitting (43), into two cases.
% 15.68/4.88 |-Branch one:
% 15.68/4.88 | (45) ~ in(all_26_0_7, all_2_1_2)
% 15.68/4.88 |
% 15.68/4.88 | From (49) and (45) follows:
% 15.68/4.88 | (66) ~ in(all_0_0_0, all_2_1_2)
% 15.68/4.88 |
% 15.68/4.88 | Introducing new symbol ex_66_0_14 defined by:
% 15.68/4.88 | (67) ex_66_0_14 = all_26_0_7
% 15.68/4.88 |
% 15.68/4.88 | Instantiating formula (17) with ex_66_0_14 yields:
% 15.68/4.88 | (68) subset(ex_66_0_14, ex_66_0_14)
% 15.68/4.88 |
% 15.68/4.88 | Instantiating formula (21) with all_0_0_0 and discharging atoms ~ in(all_0_0_0, all_2_1_2), yields:
% 15.68/4.88 | (69) ~ subset(all_0_0_0, all_0_0_0)
% 15.68/4.88 |
% 15.68/4.88 | Combining equations (49,67) yields a new equation:
% 15.68/4.88 | (70) ex_66_0_14 = all_0_0_0
% 15.68/4.88 |
% 15.68/4.88 | From (70)(70) and (68) follows:
% 15.68/4.88 | (71) subset(all_0_0_0, all_0_0_0)
% 15.68/4.88 |
% 15.68/4.88 | Using (71) and (69) yields:
% 15.68/4.88 | (40) $false
% 15.68/4.88 |
% 15.68/4.88 |-The branch is then unsatisfiable
% 15.68/4.88 |-Branch two:
% 15.68/4.88 | (48) subset(all_26_0_7, all_0_0_0)
% 15.68/4.88 |
% 15.68/4.88 | From (49) and (48) follows:
% 15.68/4.88 | (71) subset(all_0_0_0, all_0_0_0)
% 15.68/4.88 |
% 15.68/4.88 | Instantiating formula (21) with all_0_0_0 and discharging atoms subset(all_0_0_0, all_0_0_0), yields:
% 15.68/4.88 | (75) in(all_0_0_0, all_2_1_2)
% 15.68/4.88 |
% 15.68/4.88 | From (26) and (64) follows:
% 15.68/4.88 | (66) ~ in(all_0_0_0, all_2_1_2)
% 15.68/4.88 |
% 15.68/4.88 | Using (75) and (66) yields:
% 15.68/4.88 | (40) $false
% 15.68/4.88 |
% 15.68/4.88 |-The branch is then unsatisfiable
% 15.68/4.88 % SZS output end Proof for theBenchmark
% 15.68/4.88
% 15.68/4.88 4293ms
%------------------------------------------------------------------------------