TSTP Solution File: SEU142+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU142+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n017.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 08:46:55 EDT 2022
% Result : Theorem 9.40s 3.15s
% Output : Proof 12.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU142+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n017.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 : Mon Jun 20 09:03:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.60 ____ _
% 0.20/0.60 ___ / __ \_____(_)___ ________ __________
% 0.20/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.20/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic
% 0.20/0.60 (ePrincess v.1.0)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2015
% 0.20/0.60 (c) Peter Backeman, 2014-2015
% 0.20/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.60 Bug reports to peter@backeman.se
% 0.20/0.60
% 0.20/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.31/0.92 Prover 0: Preprocessing ...
% 1.69/1.08 Prover 0: Warning: ignoring some quantifiers
% 1.84/1.10 Prover 0: Constructing countermodel ...
% 2.08/1.26 Prover 0: gave up
% 2.08/1.26 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.08/1.28 Prover 1: Preprocessing ...
% 2.63/1.33 Prover 1: Warning: ignoring some quantifiers
% 2.63/1.34 Prover 1: Constructing countermodel ...
% 2.75/1.39 Prover 1: gave up
% 2.75/1.39 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.75/1.40 Prover 2: Preprocessing ...
% 3.09/1.44 Prover 2: Warning: ignoring some quantifiers
% 3.09/1.45 Prover 2: Constructing countermodel ...
% 3.27/1.50 Prover 2: gave up
% 3.27/1.50 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.27/1.51 Prover 3: Preprocessing ...
% 3.27/1.53 Prover 3: Warning: ignoring some quantifiers
% 3.27/1.54 Prover 3: Constructing countermodel ...
% 3.63/1.58 Prover 3: gave up
% 3.63/1.58 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 3.63/1.59 Prover 4: Preprocessing ...
% 3.84/1.63 Prover 4: Warning: ignoring some quantifiers
% 3.84/1.64 Prover 4: Constructing countermodel ...
% 4.42/1.77 Prover 4: gave up
% 4.42/1.77 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.42/1.78 Prover 5: Preprocessing ...
% 4.65/1.80 Prover 5: Warning: ignoring some quantifiers
% 4.65/1.80 Prover 5: Constructing countermodel ...
% 4.65/1.84 Prover 5: gave up
% 4.65/1.84 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.65/1.85 Prover 6: Preprocessing ...
% 5.05/1.87 Prover 6: Warning: ignoring some quantifiers
% 5.05/1.87 Prover 6: Constructing countermodel ...
% 5.12/1.90 Prover 6: gave up
% 5.12/1.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 5.12/1.91 Prover 7: Preprocessing ...
% 5.34/1.93 Prover 7: Proving ...
% 9.40/3.15 Prover 7: proved (1250ms)
% 9.40/3.15
% 9.40/3.15 % SZS status Theorem for theBenchmark
% 9.40/3.15
% 9.40/3.15 Generating proof ... found it (size 45)
% 12.53/3.94
% 12.53/3.94 % SZS output start Proof for theBenchmark
% 12.53/3.94 Assumed formulas after preprocessing and simplification:
% 12.53/3.94 | (0) ! [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] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : ((v4 = v1 | v4 = v0 | in(v4, v3)) & ( ~ in(v4, v3) | ( ~ (v4 = v1) & ~ (v4 = v0)))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ( ! [v3] : (v3 = v1 | v3 = v0 | ~ in(v3, v2)) & ! [v3] : (in(v3, v2) | ( ~ (v3 = v1) & ~ (v3 = v0))))) & ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(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] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & singleton(v0) = v2 & unordered_pair(v0, v0) = v1)
% 12.53/3.97 | Applying alpha-rule on (0) yields:
% 12.53/3.97 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 12.53/3.97 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ( ! [v3] : (v3 = v1 | v3 = v0 | ~ in(v3, v2)) & ! [v3] : (in(v3, v2) | ( ~ (v3 = v1) & ~ (v3 = v0)))))
% 12.53/3.97 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : ((v4 = v1 | v4 = v0 | in(v4, v3)) & ( ~ in(v4, v3) | ( ~ (v4 = v1) & ~ (v4 = v0))))))
% 12.53/3.97 | (4) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0))))
% 12.53/3.97 | (5) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 12.53/3.97 | (6) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | (in(v0, v1) & ! [v2] : (v2 = v0 | ~ in(v2, v1))))
% 12.53/3.97 | (7) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : (( ~ (v3 = v0) | ~ in(v0, v2)) & (v3 = v0 | in(v3, v2)))))
% 12.53/3.97 | (8) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & singleton(v0) = v2 & unordered_pair(v0, v0) = v1)
% 12.53/3.97 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 12.53/3.97 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 12.88/3.97 |
% 12.88/3.97 | Instantiating (8) with all_1_0_0, all_1_1_1, all_1_2_2 yields:
% 12.88/3.97 | (11) ~ (all_1_0_0 = all_1_1_1) & singleton(all_1_2_2) = all_1_0_0 & unordered_pair(all_1_2_2, all_1_2_2) = all_1_1_1
% 12.88/3.97 |
% 12.88/3.97 | Applying alpha-rule on (11) yields:
% 12.88/3.97 | (12) ~ (all_1_0_0 = all_1_1_1)
% 12.88/3.97 | (13) singleton(all_1_2_2) = all_1_0_0
% 12.88/3.97 | (14) unordered_pair(all_1_2_2, all_1_2_2) = all_1_1_1
% 12.88/3.97 |
% 12.88/3.97 | Instantiating formula (6) with all_1_0_0, all_1_2_2 and discharging atoms singleton(all_1_2_2) = all_1_0_0, yields:
% 12.88/3.97 | (15) in(all_1_2_2, all_1_0_0) & ! [v0] : (v0 = all_1_2_2 | ~ in(v0, all_1_0_0))
% 12.88/3.97 |
% 12.88/3.98 | Applying alpha-rule on (15) yields:
% 12.88/3.98 | (16) in(all_1_2_2, all_1_0_0)
% 12.88/3.98 | (17) ! [v0] : (v0 = all_1_2_2 | ~ in(v0, all_1_0_0))
% 12.88/3.98 |
% 12.88/3.98 | Instantiating formula (2) with all_1_1_1, all_1_2_2, all_1_2_2 and discharging atoms unordered_pair(all_1_2_2, all_1_2_2) = all_1_1_1, yields:
% 12.88/3.98 | (18) in(all_1_2_2, all_1_1_1) & ! [v0] : (v0 = all_1_2_2 | ~ in(v0, all_1_1_1))
% 12.88/3.98 |
% 12.88/3.98 | Applying alpha-rule on (18) yields:
% 12.88/3.98 | (19) in(all_1_2_2, all_1_1_1)
% 12.88/3.98 | (20) ! [v0] : (v0 = all_1_2_2 | ~ in(v0, all_1_1_1))
% 12.88/3.98 |
% 12.88/3.98 | Introducing new symbol ex_17_1_4 defined by:
% 12.88/3.98 | (21) ex_17_1_4 = all_1_0_0
% 12.88/3.98 |
% 12.88/3.98 | Introducing new symbol ex_17_0_3 defined by:
% 12.88/3.98 | (22) ex_17_0_3 = all_1_1_1
% 12.88/3.98 |
% 12.88/3.98 | Instantiating formula (4) with ex_17_0_3, ex_17_1_4 yields:
% 12.88/3.98 | (23) ex_17_0_3 = ex_17_1_4 | ? [v0] : (( ~ in(v0, ex_17_0_3) | ~ in(v0, ex_17_1_4)) & (in(v0, ex_17_0_3) | in(v0, ex_17_1_4)))
% 12.90/3.98 |
% 12.90/3.98 +-Applying beta-rule and splitting (23), into two cases.
% 12.90/3.98 |-Branch one:
% 12.90/3.98 | (24) ex_17_0_3 = ex_17_1_4
% 12.90/3.98 |
% 12.90/3.98 | Combining equations (24,22) yields a new equation:
% 12.90/3.98 | (25) ex_17_1_4 = all_1_1_1
% 12.90/3.98 |
% 12.90/3.98 | Simplifying 25 yields:
% 12.90/3.98 | (26) ex_17_1_4 = all_1_1_1
% 12.90/3.98 |
% 12.90/3.98 | Combining equations (26,21) yields a new equation:
% 12.90/3.98 | (27) all_1_0_0 = all_1_1_1
% 12.90/3.98 |
% 12.90/3.98 | Equations (27) can reduce 12 to:
% 12.90/3.98 | (28) $false
% 12.90/3.98 |
% 12.90/3.98 |-The branch is then unsatisfiable
% 12.90/3.98 |-Branch two:
% 12.90/3.98 | (29) ? [v0] : (( ~ in(v0, ex_17_0_3) | ~ in(v0, ex_17_1_4)) & (in(v0, ex_17_0_3) | in(v0, ex_17_1_4)))
% 12.90/3.98 |
% 12.90/3.98 | Instantiating (29) with all_20_0_5 yields:
% 12.90/3.98 | (30) ( ~ in(all_20_0_5, ex_17_0_3) | ~ in(all_20_0_5, ex_17_1_4)) & (in(all_20_0_5, ex_17_0_3) | in(all_20_0_5, ex_17_1_4))
% 12.90/3.98 |
% 12.90/3.98 | Applying alpha-rule on (30) yields:
% 12.90/3.98 | (31) ~ in(all_20_0_5, ex_17_0_3) | ~ in(all_20_0_5, ex_17_1_4)
% 12.90/3.98 | (32) in(all_20_0_5, ex_17_0_3) | in(all_20_0_5, ex_17_1_4)
% 12.90/3.98 |
% 12.90/3.98 +-Applying beta-rule and splitting (32), into two cases.
% 12.90/3.98 |-Branch one:
% 12.90/3.98 | (33) in(all_20_0_5, ex_17_0_3)
% 12.90/3.98 |
% 12.90/3.98 +-Applying beta-rule and splitting (31), into two cases.
% 12.90/3.98 |-Branch one:
% 12.90/3.98 | (34) ~ in(all_20_0_5, ex_17_0_3)
% 12.90/3.98 |
% 12.90/3.98 | Using (33) and (34) yields:
% 12.90/3.98 | (35) $false
% 12.90/3.98 |
% 12.90/3.98 |-The branch is then unsatisfiable
% 12.90/3.98 |-Branch two:
% 12.90/3.98 | (36) ~ in(all_20_0_5, ex_17_1_4)
% 12.90/3.98 |
% 12.90/3.98 | Instantiating formula (20) with all_20_0_5 yields:
% 12.90/3.98 | (37) all_20_0_5 = all_1_2_2 | ~ in(all_20_0_5, all_1_1_1)
% 12.90/3.98 |
% 12.90/3.98 +-Applying beta-rule and splitting (37), into two cases.
% 12.90/3.98 |-Branch one:
% 12.90/3.98 | (38) ~ in(all_20_0_5, all_1_1_1)
% 12.90/3.98 |
% 12.90/3.98 | From (22) and (33) follows:
% 12.90/3.98 | (39) in(all_20_0_5, all_1_1_1)
% 12.90/3.98 |
% 12.90/3.98 | Using (39) and (38) yields:
% 12.90/3.98 | (35) $false
% 12.90/3.98 |
% 12.90/3.98 |-The branch is then unsatisfiable
% 12.90/3.98 |-Branch two:
% 12.90/3.98 | (41) all_20_0_5 = all_1_2_2
% 12.90/3.98 |
% 12.90/3.98 | From (41) and (36) follows:
% 12.90/3.98 | (42) ~ in(all_1_2_2, ex_17_1_4)
% 12.90/3.98 |
% 12.90/3.98 | From (21) and (42) follows:
% 12.90/3.98 | (43) ~ in(all_1_2_2, all_1_0_0)
% 12.90/3.98 |
% 12.90/3.98 | Using (16) and (43) yields:
% 12.90/3.98 | (35) $false
% 12.90/3.98 |
% 12.90/3.98 |-The branch is then unsatisfiable
% 12.90/3.98 |-Branch two:
% 12.90/3.98 | (34) ~ in(all_20_0_5, ex_17_0_3)
% 12.90/3.98 | (46) in(all_20_0_5, ex_17_1_4)
% 12.90/3.98 |
% 12.90/3.98 | Instantiating formula (17) with all_20_0_5 yields:
% 12.90/3.98 | (47) all_20_0_5 = all_1_2_2 | ~ in(all_20_0_5, all_1_0_0)
% 12.90/3.98 |
% 12.90/3.98 | Instantiating formula (20) with all_20_0_5 yields:
% 12.90/3.98 | (37) all_20_0_5 = all_1_2_2 | ~ in(all_20_0_5, all_1_1_1)
% 12.90/3.98 |
% 12.90/3.98 +-Applying beta-rule and splitting (37), into two cases.
% 12.90/3.98 |-Branch one:
% 12.90/3.98 | (38) ~ in(all_20_0_5, all_1_1_1)
% 12.90/3.98 |
% 12.90/3.98 +-Applying beta-rule and splitting (47), into two cases.
% 12.90/3.98 |-Branch one:
% 12.90/3.98 | (50) ~ in(all_20_0_5, all_1_0_0)
% 12.90/3.98 |
% 12.90/3.98 | From (21) and (46) follows:
% 12.90/3.98 | (51) in(all_20_0_5, all_1_0_0)
% 12.90/3.98 |
% 12.90/3.98 | Using (51) and (50) yields:
% 12.90/3.98 | (35) $false
% 12.90/3.98 |
% 12.90/3.98 |-The branch is then unsatisfiable
% 12.90/3.98 |-Branch two:
% 12.90/3.98 | (41) all_20_0_5 = all_1_2_2
% 12.90/3.98 |
% 12.90/3.98 | From (41) and (38) follows:
% 12.90/3.98 | (54) ~ in(all_1_2_2, all_1_1_1)
% 12.90/3.98 |
% 12.90/3.98 | Using (19) and (54) yields:
% 12.90/3.98 | (35) $false
% 12.90/3.98 |
% 12.90/3.98 |-The branch is then unsatisfiable
% 12.90/3.98 |-Branch two:
% 12.90/3.98 | (41) all_20_0_5 = all_1_2_2
% 12.90/3.98 |
% 12.90/3.98 | From (41) and (34) follows:
% 12.90/3.98 | (57) ~ in(all_1_2_2, ex_17_0_3)
% 12.90/3.98 |
% 12.90/3.98 | From (22) and (57) follows:
% 12.90/3.98 | (54) ~ in(all_1_2_2, all_1_1_1)
% 12.90/3.98 |
% 12.90/3.98 | Using (19) and (54) yields:
% 12.90/3.98 | (35) $false
% 12.90/3.98 |
% 12.90/3.98 |-The branch is then unsatisfiable
% 12.90/3.98 % SZS output end Proof for theBenchmark
% 12.90/3.99
% 12.90/3.99 3376ms
%------------------------------------------------------------------------------