TSTP Solution File: SEU164+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU164+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.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 08:47:11 EDT 2022
% Result : Theorem 29.60s 9.89s
% Output : Proof 43.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU164+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.10 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.31 % Computer : n026.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Mon Jun 20 06:27:11 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.15/0.55 ____ _
% 0.15/0.55 ___ / __ \_____(_)___ ________ __________
% 0.15/0.55 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.15/0.55 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.15/0.55 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.15/0.55
% 0.15/0.55 A Theorem Prover for First-Order Logic
% 0.15/0.55 (ePrincess v.1.0)
% 0.15/0.55
% 0.15/0.55 (c) Philipp Rümmer, 2009-2015
% 0.15/0.55 (c) Peter Backeman, 2014-2015
% 0.15/0.55 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.15/0.55 Free software under GNU Lesser General Public License (LGPL).
% 0.15/0.55 Bug reports to peter@backeman.se
% 0.15/0.55
% 0.15/0.55 For more information, visit http://user.uu.se/~petba168/breu/
% 0.15/0.55
% 0.15/0.55 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.60 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.47/0.89 Prover 0: Preprocessing ...
% 1.80/1.07 Prover 0: Warning: ignoring some quantifiers
% 1.80/1.08 Prover 0: Constructing countermodel ...
% 2.51/1.26 Prover 0: gave up
% 2.51/1.26 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.51/1.28 Prover 1: Preprocessing ...
% 2.87/1.36 Prover 1: Warning: ignoring some quantifiers
% 2.87/1.36 Prover 1: Constructing countermodel ...
% 3.15/1.41 Prover 1: gave up
% 3.15/1.41 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.15/1.42 Prover 2: Preprocessing ...
% 3.48/1.49 Prover 2: Warning: ignoring some quantifiers
% 3.61/1.50 Prover 2: Constructing countermodel ...
% 3.74/1.55 Prover 2: gave up
% 3.74/1.56 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.74/1.57 Prover 3: Preprocessing ...
% 3.74/1.59 Prover 3: Warning: ignoring some quantifiers
% 3.74/1.59 Prover 3: Constructing countermodel ...
% 4.20/1.65 Prover 3: gave up
% 4.20/1.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 4.20/1.66 Prover 4: Preprocessing ...
% 4.52/1.73 Prover 4: Warning: ignoring some quantifiers
% 4.52/1.74 Prover 4: Constructing countermodel ...
% 9.29/2.88 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 9.29/2.90 Prover 5: Preprocessing ...
% 9.74/2.96 Prover 5: Warning: ignoring some quantifiers
% 9.74/2.96 Prover 5: Constructing countermodel ...
% 10.13/3.01 Prover 5: gave up
% 10.13/3.01 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 10.13/3.03 Prover 6: Preprocessing ...
% 10.13/3.06 Prover 6: Warning: ignoring some quantifiers
% 10.13/3.07 Prover 6: Constructing countermodel ...
% 10.13/3.10 Prover 6: gave up
% 10.13/3.10 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 10.59/3.11 Prover 7: Preprocessing ...
% 10.59/3.14 Prover 7: Proving ...
% 29.60/9.89 Prover 7: proved (6785ms)
% 29.60/9.89 Prover 4: stopped
% 29.60/9.89
% 29.60/9.89 % SZS status Theorem for theBenchmark
% 29.60/9.89
% 29.60/9.89 Generating proof ... found it (size 37)
% 43.01/15.64
% 43.01/15.64 % SZS output start Proof for theBenchmark
% 43.01/15.64 Assumed formulas after preprocessing and simplification:
% 43.01/15.64 | (0) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [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] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) & ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : (( ~ in(v3, v2) | ! [v4] : ( ~ in(v4, v0) | ~ in(v3, v4))) & (in(v3, v2) | ? [v4] : (in(v4, v0) & in(v3, v4)))))) & ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ( ! [v2] : ( ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3))) & ! [v2] : (in(v2, v1) | ! [v3] : ( ~ in(v3, v0) | ~ in(v2, v3))))) & ! [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] : ( ~ subset(v0, v1) | ! [v2] : ( ~ in(v2, v0) | in(v2, v1))) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) & ! [v0] : subset(v0, v0) & ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v0) & union(v1) = v2 & powerset(v0) = v1)
% 43.01/15.67 | Applying alpha-rule on (0) yields:
% 43.01/15.67 | (1) ! [v0] : subset(v0, v0)
% 43.01/15.67 | (2) ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ( ! [v2] : ( ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3))) & ! [v2] : (in(v2, v1) | ! [v3] : ( ~ in(v3, v0) | ~ in(v2, v3)))))
% 43.01/15.67 | (3) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ( ! [v2] : ( ~ subset(v2, v0) | in(v2, v1)) & ! [v2] : ( ~ in(v2, v1) | subset(v2, v0))))
% 43.01/15.67 | (4) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | (in(v0, v1) & ! [v2] : (v2 = v0 | ~ in(v2, v1))))
% 43.01/15.67 | (5) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1)))
% 43.01/15.67 | (6) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : (( ~ subset(v3, v0) | ~ in(v3, v2)) & (subset(v3, v0) | in(v3, v2)))))
% 43.01/15.67 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 43.01/15.67 | (8) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 43.01/15.67 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 43.01/15.67 | (10) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ in(v2, v0) | in(v2, v1)))
% 43.01/15.67 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 43.01/15.67 | (12) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0))))
% 43.01/15.67 | (13) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : (( ~ (v3 = v0) | ~ in(v0, v2)) & (v3 = v0 | in(v3, v2)))))
% 43.01/15.67 | (14) ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : (( ~ in(v3, v2) | ! [v4] : ( ~ in(v4, v0) | ~ in(v3, v4))) & (in(v3, v2) | ? [v4] : (in(v4, v0) & in(v3, v4))))))
% 43.01/15.67 | (15) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v0) & union(v1) = v2 & powerset(v0) = v1)
% 43.01/15.67 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1))
% 43.01/15.67 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1))
% 43.01/15.67 |
% 43.01/15.67 | Instantiating (15) with all_1_0_0, all_1_1_1, all_1_2_2 yields:
% 43.01/15.67 | (18) ~ (all_1_0_0 = all_1_2_2) & union(all_1_1_1) = all_1_0_0 & powerset(all_1_2_2) = all_1_1_1
% 43.01/15.67 |
% 43.01/15.67 | Applying alpha-rule on (18) yields:
% 43.01/15.67 | (19) ~ (all_1_0_0 = all_1_2_2)
% 43.01/15.67 | (20) union(all_1_1_1) = all_1_0_0
% 43.01/15.67 | (21) powerset(all_1_2_2) = all_1_1_1
% 43.01/15.68 |
% 43.01/15.68 | Instantiating formula (14) with all_1_0_0, all_1_1_1 and discharging atoms union(all_1_1_1) = all_1_0_0, yields:
% 43.01/15.68 | (22) ! [v0] : (v0 = all_1_0_0 | ? [v1] : (( ~ in(v1, v0) | ! [v2] : ( ~ in(v2, all_1_1_1) | ~ in(v1, v2))) & (in(v1, v0) | ? [v2] : (in(v2, all_1_1_1) & in(v1, v2)))))
% 43.01/15.68 |
% 43.01/15.68 | Instantiating formula (3) with all_1_1_1, all_1_2_2 and discharging atoms powerset(all_1_2_2) = all_1_1_1, yields:
% 43.01/15.68 | (23) ! [v0] : ( ~ subset(v0, all_1_2_2) | in(v0, all_1_1_1)) & ! [v0] : ( ~ in(v0, all_1_1_1) | subset(v0, all_1_2_2))
% 43.01/15.68 |
% 43.01/15.68 | Applying alpha-rule on (23) yields:
% 43.01/15.68 | (24) ! [v0] : ( ~ subset(v0, all_1_2_2) | in(v0, all_1_1_1))
% 43.01/15.68 | (25) ! [v0] : ( ~ in(v0, all_1_1_1) | subset(v0, all_1_2_2))
% 43.01/15.68 |
% 43.01/15.68 | Introducing new symbol ex_22_0_6 defined by:
% 43.01/15.68 | (26) ex_22_0_6 = all_1_2_2
% 43.01/15.68 |
% 43.01/15.68 | Instantiating formula (1) with ex_22_0_6 yields:
% 43.01/15.68 | (27) subset(ex_22_0_6, ex_22_0_6)
% 43.01/15.68 |
% 43.01/15.68 | Instantiating formula (24) with all_1_2_2 yields:
% 43.01/15.68 | (28) ~ subset(all_1_2_2, all_1_2_2) | in(all_1_2_2, all_1_1_1)
% 43.01/15.68 |
% 43.01/15.68 +-Applying beta-rule and splitting (28), into two cases.
% 43.01/15.68 |-Branch one:
% 43.01/15.68 | (29) in(all_1_2_2, all_1_1_1)
% 43.01/15.68 |
% 43.01/15.68 | Introducing new symbol ex_89_0_19 defined by:
% 43.01/15.68 | (30) ex_89_0_19 = all_1_2_2
% 43.01/15.68 |
% 43.01/15.68 | Instantiating formula (22) with ex_89_0_19 yields:
% 43.01/15.68 | (31) ex_89_0_19 = all_1_0_0 | ? [v0] : (( ~ in(v0, ex_89_0_19) | ! [v1] : ( ~ in(v1, all_1_1_1) | ~ in(v0, v1))) & (in(v0, ex_89_0_19) | ? [v1] : (in(v1, all_1_1_1) & in(v0, v1))))
% 43.01/15.68 |
% 43.01/15.68 +-Applying beta-rule and splitting (31), into two cases.
% 43.01/15.68 |-Branch one:
% 43.01/15.68 | (32) ex_89_0_19 = all_1_0_0
% 43.01/15.68 |
% 43.01/15.68 | Combining equations (30,32) yields a new equation:
% 43.01/15.68 | (33) all_1_0_0 = all_1_2_2
% 43.01/15.68 |
% 43.01/15.68 | Equations (33) can reduce 19 to:
% 43.01/15.68 | (34) $false
% 43.01/15.68 |
% 43.01/15.68 |-The branch is then unsatisfiable
% 43.01/15.68 |-Branch two:
% 43.01/15.68 | (35) ? [v0] : (( ~ in(v0, ex_89_0_19) | ! [v1] : ( ~ in(v1, all_1_1_1) | ~ in(v0, v1))) & (in(v0, ex_89_0_19) | ? [v1] : (in(v1, all_1_1_1) & in(v0, v1))))
% 43.01/15.68 |
% 43.01/15.68 | Instantiating (35) with all_92_0_21 yields:
% 43.01/15.68 | (36) ( ~ in(all_92_0_21, ex_89_0_19) | ! [v0] : ( ~ in(v0, all_1_1_1) | ~ in(all_92_0_21, v0))) & (in(all_92_0_21, ex_89_0_19) | ? [v0] : (in(v0, all_1_1_1) & in(all_92_0_21, v0)))
% 43.01/15.68 |
% 43.01/15.68 | Applying alpha-rule on (36) yields:
% 43.01/15.68 | (37) ~ in(all_92_0_21, ex_89_0_19) | ! [v0] : ( ~ in(v0, all_1_1_1) | ~ in(all_92_0_21, v0))
% 43.01/15.68 | (38) in(all_92_0_21, ex_89_0_19) | ? [v0] : (in(v0, all_1_1_1) & in(all_92_0_21, v0))
% 43.01/15.68 |
% 43.01/15.68 +-Applying beta-rule and splitting (37), into two cases.
% 43.01/15.68 |-Branch one:
% 43.01/15.68 | (39) ~ in(all_92_0_21, ex_89_0_19)
% 43.01/15.68 |
% 43.01/15.68 +-Applying beta-rule and splitting (38), into two cases.
% 43.01/15.68 |-Branch one:
% 43.01/15.68 | (40) in(all_92_0_21, ex_89_0_19)
% 43.01/15.68 |
% 43.01/15.68 | Using (40) and (39) yields:
% 43.01/15.68 | (41) $false
% 43.01/15.68 |
% 43.01/15.68 |-The branch is then unsatisfiable
% 43.01/15.68 |-Branch two:
% 43.01/15.68 | (42) ? [v0] : (in(v0, all_1_1_1) & in(all_92_0_21, v0))
% 43.01/15.68 |
% 43.01/15.68 | Instantiating (42) with all_103_0_25 yields:
% 43.01/15.68 | (43) in(all_103_0_25, all_1_1_1) & in(all_92_0_21, all_103_0_25)
% 43.01/15.68 |
% 43.01/15.68 | Applying alpha-rule on (43) yields:
% 43.01/15.68 | (44) in(all_103_0_25, all_1_1_1)
% 43.01/15.68 | (45) in(all_92_0_21, all_103_0_25)
% 43.01/15.68 |
% 43.01/15.68 | Instantiating formula (25) with all_103_0_25 and discharging atoms in(all_103_0_25, all_1_1_1), yields:
% 43.01/15.68 | (46) subset(all_103_0_25, all_1_2_2)
% 43.01/15.68 |
% 43.01/15.68 | Instantiating formula (10) with all_1_2_2, all_103_0_25 and discharging atoms subset(all_103_0_25, all_1_2_2), yields:
% 43.01/15.68 | (47) ! [v0] : ( ~ in(v0, all_103_0_25) | in(v0, all_1_2_2))
% 43.01/15.68 |
% 43.01/15.68 | Instantiating formula (47) with all_92_0_21 and discharging atoms in(all_92_0_21, all_103_0_25), yields:
% 43.01/15.68 | (48) in(all_92_0_21, all_1_2_2)
% 43.01/15.68 |
% 43.01/15.68 | From (30) and (39) follows:
% 43.01/15.68 | (49) ~ in(all_92_0_21, all_1_2_2)
% 43.01/15.68 |
% 43.01/15.68 | Using (48) and (49) yields:
% 43.01/15.69 | (41) $false
% 43.01/15.69 |
% 43.01/15.69 |-The branch is then unsatisfiable
% 43.01/15.69 |-Branch two:
% 43.01/15.69 | (40) in(all_92_0_21, ex_89_0_19)
% 43.01/15.69 | (52) ! [v0] : ( ~ in(v0, all_1_1_1) | ~ in(all_92_0_21, v0))
% 43.01/15.69 |
% 43.01/15.69 | Instantiating formula (52) with all_1_2_2 and discharging atoms in(all_1_2_2, all_1_1_1), yields:
% 43.01/15.69 | (49) ~ in(all_92_0_21, all_1_2_2)
% 43.01/15.69 |
% 43.01/15.69 | From (30) and (40) follows:
% 43.01/15.69 | (48) in(all_92_0_21, all_1_2_2)
% 43.01/15.69 |
% 43.01/15.69 | Using (48) and (49) yields:
% 43.01/15.69 | (41) $false
% 43.01/15.69 |
% 43.01/15.69 |-The branch is then unsatisfiable
% 43.01/15.69 |-Branch two:
% 43.01/15.69 | (56) ~ subset(all_1_2_2, all_1_2_2)
% 43.01/15.69 |
% 43.01/15.69 | From (26)(26) and (27) follows:
% 43.01/15.69 | (57) subset(all_1_2_2, all_1_2_2)
% 43.01/15.69 |
% 43.01/15.69 | Using (57) and (56) yields:
% 43.01/15.69 | (41) $false
% 43.01/15.69 |
% 43.01/15.69 |-The branch is then unsatisfiable
% 43.01/15.69 % SZS output end Proof for theBenchmark
% 43.01/15.69
% 43.01/15.69 15126ms
%------------------------------------------------------------------------------