TSTP Solution File: SET890+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET890+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.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 00:22:57 EDT 2022
% Result : Theorem 10.93s 3.27s
% Output : Proof 15.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET890+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.32 % Computer : n025.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Mon Jul 11 09:40:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.56 ____ _
% 0.18/0.56 ___ / __ \_____(_)___ ________ __________
% 0.18/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.56
% 0.18/0.56 A Theorem Prover for First-Order Logic
% 0.18/0.57 (ePrincess v.1.0)
% 0.18/0.57
% 0.18/0.57 (c) Philipp Rümmer, 2009-2015
% 0.18/0.57 (c) Peter Backeman, 2014-2015
% 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.57 Bug reports to peter@backeman.se
% 0.18/0.57
% 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.57
% 0.18/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.65/0.61 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.42/0.89 Prover 0: Preprocessing ...
% 1.68/1.05 Prover 0: Warning: ignoring some quantifiers
% 1.68/1.07 Prover 0: Constructing countermodel ...
% 2.47/1.30 Prover 0: gave up
% 2.47/1.30 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.76/1.32 Prover 1: Preprocessing ...
% 2.98/1.40 Prover 1: Warning: ignoring some quantifiers
% 2.98/1.40 Prover 1: Constructing countermodel ...
% 2.98/1.45 Prover 1: gave up
% 2.98/1.45 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.24/1.47 Prover 2: Preprocessing ...
% 3.57/1.54 Prover 2: Warning: ignoring some quantifiers
% 3.57/1.55 Prover 2: Constructing countermodel ...
% 3.57/1.60 Prover 2: gave up
% 3.57/1.60 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.57/1.61 Prover 3: Preprocessing ...
% 3.95/1.63 Prover 3: Warning: ignoring some quantifiers
% 3.95/1.64 Prover 3: Constructing countermodel ...
% 4.29/1.71 Prover 3: gave up
% 4.29/1.71 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 4.29/1.72 Prover 4: Preprocessing ...
% 4.70/1.79 Prover 4: Warning: ignoring some quantifiers
% 4.78/1.80 Prover 4: Constructing countermodel ...
% 6.41/2.19 Prover 4: gave up
% 6.41/2.19 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.41/2.20 Prover 5: Preprocessing ...
% 6.61/2.23 Prover 5: Warning: ignoring some quantifiers
% 6.61/2.23 Prover 5: Constructing countermodel ...
% 6.61/2.26 Prover 5: gave up
% 6.61/2.26 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 6.61/2.27 Prover 6: Preprocessing ...
% 6.61/2.30 Prover 6: Warning: ignoring some quantifiers
% 6.61/2.31 Prover 6: Constructing countermodel ...
% 7.07/2.34 Prover 6: gave up
% 7.07/2.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 7.07/2.34 Prover 7: Preprocessing ...
% 7.07/2.36 Prover 7: Proving ...
% 10.93/3.27 Prover 7: proved (929ms)
% 10.93/3.27
% 10.93/3.27 % SZS status Theorem for theBenchmark
% 10.93/3.27
% 10.93/3.27 Generating proof ... found it (size 38)
% 15.29/4.26
% 15.29/4.26 % SZS output start Proof for theBenchmark
% 15.29/4.26 Assumed formulas after preprocessing and simplification:
% 15.29/4.26 | (0) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [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] : ( ~ (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 & singleton(v0) = v1) & ? [v0] : ~ empty(v0) & ? [v0] : empty(v0)
% 15.65/4.29 | Applying alpha-rule on (0) yields:
% 15.65/4.29 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 15.65/4.29 | (2) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ in(v2, v0) | in(v2, v1)))
% 15.65/4.29 | (3) ! [v0] : subset(v0, v0)
% 15.65/4.29 | (4) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1)))
% 15.65/4.29 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 15.65/4.29 | (6) ! [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)))))
% 15.65/4.29 | (7) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v0) & union(v1) = v2 & singleton(v0) = v1)
% 15.65/4.29 | (8) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 15.65/4.29 | (9) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | (in(v0, v1) & ! [v2] : (v2 = v0 | ~ in(v2, v1))))
% 15.65/4.29 | (10) ? [v0] : empty(v0)
% 15.65/4.29 | (11) ! [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))))))
% 15.65/4.29 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2))
% 15.65/4.29 | (13) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : (( ~ (v3 = v0) | ~ in(v0, v2)) & (v3 = v0 | in(v3, v2)))))
% 15.65/4.29 | (14) ? [v0] : ~ empty(v0)
% 15.65/4.29 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 15.65/4.29 |
% 15.65/4.29 | Instantiating (7) with all_3_0_1, all_3_1_2, all_3_2_3 yields:
% 15.65/4.29 | (16) ~ (all_3_0_1 = all_3_2_3) & union(all_3_1_2) = all_3_0_1 & singleton(all_3_2_3) = all_3_1_2
% 15.65/4.29 |
% 15.65/4.29 | Applying alpha-rule on (16) yields:
% 15.65/4.29 | (17) ~ (all_3_0_1 = all_3_2_3)
% 15.65/4.29 | (18) union(all_3_1_2) = all_3_0_1
% 15.65/4.29 | (19) singleton(all_3_2_3) = all_3_1_2
% 15.65/4.29 |
% 15.65/4.29 | Instantiating formula (6) with all_3_0_1, all_3_1_2 and discharging atoms union(all_3_1_2) = all_3_0_1, yields:
% 15.65/4.30 | (20) ! [v0] : ( ~ in(v0, all_3_0_1) | ? [v1] : (in(v1, all_3_1_2) & in(v0, v1))) & ! [v0] : (in(v0, all_3_0_1) | ! [v1] : ( ~ in(v1, all_3_1_2) | ~ in(v0, v1)))
% 15.65/4.30 |
% 15.65/4.30 | Applying alpha-rule on (20) yields:
% 15.65/4.30 | (21) ! [v0] : ( ~ in(v0, all_3_0_1) | ? [v1] : (in(v1, all_3_1_2) & in(v0, v1)))
% 15.65/4.30 | (22) ! [v0] : (in(v0, all_3_0_1) | ! [v1] : ( ~ in(v1, all_3_1_2) | ~ in(v0, v1)))
% 15.65/4.30 |
% 15.65/4.30 | Instantiating formula (9) with all_3_1_2, all_3_2_3 and discharging atoms singleton(all_3_2_3) = all_3_1_2, yields:
% 15.65/4.30 | (23) in(all_3_2_3, all_3_1_2) & ! [v0] : (v0 = all_3_2_3 | ~ in(v0, all_3_1_2))
% 15.65/4.30 |
% 15.65/4.30 | Applying alpha-rule on (23) yields:
% 15.65/4.30 | (24) in(all_3_2_3, all_3_1_2)
% 15.65/4.30 | (25) ! [v0] : (v0 = all_3_2_3 | ~ in(v0, all_3_1_2))
% 15.65/4.30 |
% 15.65/4.30 | Instantiating formula (12) with all_3_0_1, all_3_1_2, all_3_2_3 and discharging atoms union(all_3_1_2) = all_3_0_1, in(all_3_2_3, all_3_1_2), yields:
% 15.65/4.30 | (26) subset(all_3_2_3, all_3_0_1)
% 15.65/4.30 |
% 15.65/4.30 | Instantiating formula (2) with all_3_0_1, all_3_2_3 and discharging atoms subset(all_3_2_3, all_3_0_1), yields:
% 15.65/4.30 | (27) ! [v0] : ( ~ in(v0, all_3_2_3) | in(v0, all_3_0_1))
% 15.65/4.30 |
% 15.65/4.30 | Introducing new symbol ex_41_1_7 defined by:
% 15.65/4.30 | (28) ex_41_1_7 = all_3_0_1
% 15.65/4.30 |
% 15.65/4.30 | Introducing new symbol ex_41_0_6 defined by:
% 15.65/4.30 | (29) ex_41_0_6 = all_3_2_3
% 15.65/4.30 |
% 15.65/4.30 | Instantiating formula (4) with ex_41_0_6, ex_41_1_7 yields:
% 15.65/4.30 | (30) subset(ex_41_1_7, ex_41_0_6) | ? [v0] : (in(v0, ex_41_1_7) & ~ in(v0, ex_41_0_6))
% 15.65/4.30 |
% 15.65/4.30 +-Applying beta-rule and splitting (30), into two cases.
% 15.65/4.30 |-Branch one:
% 15.65/4.30 | (31) subset(ex_41_1_7, ex_41_0_6)
% 15.65/4.30 |
% 15.65/4.30 | Instantiating formula (5) with all_3_0_1, all_3_2_3 and discharging atoms subset(all_3_2_3, all_3_0_1), yields:
% 15.65/4.30 | (32) all_3_0_1 = all_3_2_3 | ~ subset(all_3_0_1, all_3_2_3)
% 15.65/4.30 |
% 15.65/4.30 +-Applying beta-rule and splitting (32), into two cases.
% 15.65/4.30 |-Branch one:
% 15.65/4.30 | (33) ~ subset(all_3_0_1, all_3_2_3)
% 15.65/4.30 |
% 15.65/4.30 | From (28)(29) and (31) follows:
% 15.65/4.30 | (34) subset(all_3_0_1, all_3_2_3)
% 15.65/4.30 |
% 15.65/4.30 | Using (34) and (33) yields:
% 15.65/4.30 | (35) $false
% 15.65/4.30 |
% 15.65/4.30 |-The branch is then unsatisfiable
% 15.65/4.30 |-Branch two:
% 15.65/4.30 | (36) all_3_0_1 = all_3_2_3
% 15.65/4.30 |
% 15.65/4.30 | Equations (36) can reduce 17 to:
% 15.65/4.30 | (37) $false
% 15.65/4.30 |
% 15.65/4.30 |-The branch is then unsatisfiable
% 15.65/4.30 |-Branch two:
% 15.65/4.30 | (38) ? [v0] : (in(v0, ex_41_1_7) & ~ in(v0, ex_41_0_6))
% 15.65/4.30 |
% 15.65/4.30 | Instantiating (38) with all_43_0_8 yields:
% 15.65/4.30 | (39) in(all_43_0_8, ex_41_1_7) & ~ in(all_43_0_8, ex_41_0_6)
% 15.65/4.30 |
% 15.65/4.30 | Applying alpha-rule on (39) yields:
% 15.65/4.30 | (40) in(all_43_0_8, ex_41_1_7)
% 15.65/4.30 | (41) ~ in(all_43_0_8, ex_41_0_6)
% 15.65/4.30 |
% 15.65/4.30 | Instantiating formula (21) with all_43_0_8 yields:
% 15.65/4.30 | (42) ~ in(all_43_0_8, all_3_0_1) | ? [v0] : (in(v0, all_3_1_2) & in(all_43_0_8, v0))
% 15.65/4.30 |
% 15.65/4.30 | Instantiating formula (27) with all_43_0_8 yields:
% 15.65/4.30 | (43) ~ in(all_43_0_8, all_3_2_3) | in(all_43_0_8, all_3_0_1)
% 15.65/4.30 |
% 15.65/4.30 +-Applying beta-rule and splitting (43), into two cases.
% 15.65/4.30 |-Branch one:
% 15.65/4.30 | (44) ~ in(all_43_0_8, all_3_2_3)
% 15.65/4.30 |
% 15.65/4.30 +-Applying beta-rule and splitting (42), into two cases.
% 15.65/4.30 |-Branch one:
% 15.65/4.30 | (45) ~ in(all_43_0_8, all_3_0_1)
% 15.65/4.30 |
% 15.65/4.30 | From (28) and (40) follows:
% 15.65/4.30 | (46) in(all_43_0_8, all_3_0_1)
% 15.65/4.30 |
% 15.65/4.30 | Using (46) and (45) yields:
% 15.65/4.30 | (35) $false
% 15.65/4.30 |
% 15.65/4.30 |-The branch is then unsatisfiable
% 15.65/4.30 |-Branch two:
% 15.65/4.30 | (48) ? [v0] : (in(v0, all_3_1_2) & in(all_43_0_8, v0))
% 15.65/4.30 |
% 15.65/4.30 | Instantiating (48) with all_69_0_17 yields:
% 15.65/4.30 | (49) in(all_69_0_17, all_3_1_2) & in(all_43_0_8, all_69_0_17)
% 15.65/4.30 |
% 15.65/4.30 | Applying alpha-rule on (49) yields:
% 15.65/4.30 | (50) in(all_69_0_17, all_3_1_2)
% 15.65/4.30 | (51) in(all_43_0_8, all_69_0_17)
% 15.65/4.30 |
% 15.65/4.30 | Instantiating formula (25) with all_69_0_17 and discharging atoms in(all_69_0_17, all_3_1_2), yields:
% 15.65/4.30 | (52) all_69_0_17 = all_3_2_3
% 15.65/4.30 |
% 15.65/4.30 | From (52) and (51) follows:
% 15.65/4.30 | (53) in(all_43_0_8, all_3_2_3)
% 15.65/4.30 |
% 15.65/4.30 | Using (53) and (44) yields:
% 15.65/4.30 | (35) $false
% 15.65/4.30 |
% 15.65/4.30 |-The branch is then unsatisfiable
% 15.65/4.30 |-Branch two:
% 15.65/4.30 | (53) in(all_43_0_8, all_3_2_3)
% 15.65/4.30 | (46) in(all_43_0_8, all_3_0_1)
% 15.65/4.30 |
% 15.65/4.30 | From (29) and (41) follows:
% 15.65/4.30 | (44) ~ in(all_43_0_8, all_3_2_3)
% 15.65/4.30 |
% 15.65/4.30 | Using (53) and (44) yields:
% 15.65/4.30 | (35) $false
% 15.65/4.30 |
% 15.65/4.30 |-The branch is then unsatisfiable
% 15.65/4.30 % SZS output end Proof for theBenchmark
% 15.65/4.30
% 15.65/4.30 3729ms
%------------------------------------------------------------------------------