TSTP Solution File: SET045+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET045+1 : TPTP v8.1.0. Released v2.0.0.
% 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 00:16:38 EDT 2022
% Result : Theorem 6.26s 2.41s
% Output : Proof 7.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET045+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 04:03:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.56/0.59 ____ _
% 0.56/0.59 ___ / __ \_____(_)___ ________ __________
% 0.56/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.59
% 0.56/0.59 A Theorem Prover for First-Order Logic
% 0.56/0.59 (ePrincess v.1.0)
% 0.56/0.59
% 0.56/0.59 (c) Philipp Rümmer, 2009-2015
% 0.56/0.59 (c) Peter Backeman, 2014-2015
% 0.56/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.59 Bug reports to peter@backeman.se
% 0.56/0.59
% 0.56/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.59
% 0.56/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.77/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.30/0.86 Prover 0: Preprocessing ...
% 1.38/0.91 Prover 0: Warning: ignoring some quantifiers
% 1.38/0.93 Prover 0: Constructing countermodel ...
% 1.63/1.05 Prover 0: gave up
% 1.63/1.05 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.63/1.06 Prover 1: Preprocessing ...
% 1.95/1.11 Prover 1: Warning: ignoring some quantifiers
% 1.95/1.11 Prover 1: Constructing countermodel ...
% 1.95/1.12 Prover 1: gave up
% 1.95/1.12 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.95/1.13 Prover 2: Preprocessing ...
% 1.95/1.17 Prover 2: Warning: ignoring some quantifiers
% 2.31/1.18 Prover 2: Constructing countermodel ...
% 2.31/1.20 Prover 2: gave up
% 2.31/1.20 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.31/1.20 Prover 3: Preprocessing ...
% 2.40/1.21 Prover 3: Warning: ignoring some quantifiers
% 2.40/1.21 Prover 3: Constructing countermodel ...
% 2.49/1.24 Prover 3: gave up
% 2.49/1.24 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.49/1.25 Prover 4: Preprocessing ...
% 2.49/1.29 Prover 4: Warning: ignoring some quantifiers
% 2.49/1.29 Prover 4: Constructing countermodel ...
% 3.56/1.60 Prover 4: gave up
% 3.56/1.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.56/1.61 Prover 5: Preprocessing ...
% 3.96/1.62 Prover 5: Warning: ignoring some quantifiers
% 3.96/1.63 Prover 5: Constructing countermodel ...
% 3.96/1.63 Prover 5: gave up
% 3.96/1.63 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.96/1.64 Prover 6: Preprocessing ...
% 3.96/1.65 Prover 6: Warning: ignoring some quantifiers
% 3.96/1.65 Prover 6: Constructing countermodel ...
% 3.96/1.66 Prover 6: gave up
% 3.96/1.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 3.96/1.67 Prover 7: Preprocessing ...
% 3.96/1.67 Prover 7: Proving ...
% 6.26/2.40 Prover 7: proved (743ms)
% 6.26/2.41
% 6.26/2.41 % SZS status Theorem for theBenchmark
% 6.26/2.41
% 6.26/2.41 Generating proof ... found it (size 28)
% 7.22/2.85
% 7.22/2.85 % SZS output start Proof for theBenchmark
% 7.22/2.85 Assumed formulas after preprocessing and simplification:
% 7.22/2.85 | (0) ? [v0] : ! [v1] : element(v1, v0) & ! [v0] : ? [v1] : ( ! [v2] : ( ~ element(v2, v1) | (element(v2, v0) & ~ element(v2, v2))) & ! [v2] : ( ~ element(v2, v0) | element(v2, v2) | element(v2, v1)))
% 7.22/2.85 | Applying alpha-rule on (0) yields:
% 7.22/2.85 | (1) ? [v0] : ! [v1] : element(v1, v0)
% 7.22/2.85 | (2) ! [v0] : ? [v1] : ( ! [v2] : ( ~ element(v2, v1) | (element(v2, v0) & ~ element(v2, v2))) & ! [v2] : ( ~ element(v2, v0) | element(v2, v2) | element(v2, v1)))
% 7.22/2.85 |
% 7.22/2.85 | Instantiating (1) with all_0_0_0 yields:
% 7.22/2.85 | (3) ! [v0] : element(v0, all_0_0_0)
% 7.22/2.85 |
% 7.22/2.85 | Introducing new symbol ex_10_0_2 defined by:
% 7.22/2.85 | (4) ex_10_0_2 = all_0_0_0
% 7.22/2.85 |
% 7.22/2.85 | Instantiating formula (2) with ex_10_0_2 yields:
% 7.22/2.85 | (5) ? [v0] : ( ! [v1] : ( ~ element(v1, v0) | (element(v1, ex_10_0_2) & ~ element(v1, v1))) & ! [v1] : ( ~ element(v1, ex_10_0_2) | element(v1, v1) | element(v1, v0)))
% 7.22/2.85 |
% 7.22/2.85 | Instantiating (5) with all_11_0_3 yields:
% 7.22/2.85 | (6) ! [v0] : ( ~ element(v0, all_11_0_3) | (element(v0, ex_10_0_2) & ~ element(v0, v0))) & ! [v0] : ( ~ element(v0, ex_10_0_2) | element(v0, v0) | element(v0, all_11_0_3))
% 7.22/2.85 |
% 7.22/2.85 | Applying alpha-rule on (6) yields:
% 7.22/2.85 | (7) ! [v0] : ( ~ element(v0, all_11_0_3) | (element(v0, ex_10_0_2) & ~ element(v0, v0)))
% 7.22/2.85 | (8) ! [v0] : ( ~ element(v0, ex_10_0_2) | element(v0, v0) | element(v0, all_11_0_3))
% 7.22/2.85 |
% 7.22/2.85 | Introducing new symbol ex_28_0_4 defined by:
% 7.22/2.85 | (9) ex_28_0_4 = all_11_0_3
% 7.22/2.85 |
% 7.22/2.85 | Instantiating formula (3) with ex_28_0_4 yields:
% 7.22/2.85 | (10) element(ex_28_0_4, all_0_0_0)
% 7.22/2.85 |
% 7.22/2.85 | Instantiating formula (7) with ex_28_0_4 yields:
% 7.22/2.85 | (11) ~ element(ex_28_0_4, all_11_0_3) | (element(ex_28_0_4, ex_10_0_2) & ~ element(ex_28_0_4, ex_28_0_4))
% 7.22/2.85 |
% 7.22/2.85 | Instantiating formula (8) with ex_28_0_4 yields:
% 7.22/2.85 | (12) ~ element(ex_28_0_4, ex_10_0_2) | element(ex_28_0_4, ex_28_0_4) | element(ex_28_0_4, all_11_0_3)
% 7.22/2.85 |
% 7.22/2.85 +-Applying beta-rule and splitting (12), into two cases.
% 7.22/2.85 |-Branch one:
% 7.22/2.85 | (13) ~ element(ex_28_0_4, ex_10_0_2)
% 7.22/2.85 |
% 7.22/2.85 | From (9) and (10) follows:
% 7.22/2.86 | (14) element(all_11_0_3, all_0_0_0)
% 7.22/2.86 |
% 7.22/2.86 | From (9)(4) and (13) follows:
% 7.22/2.86 | (15) ~ element(all_11_0_3, all_0_0_0)
% 7.22/2.86 |
% 7.22/2.86 | Using (14) and (15) yields:
% 7.22/2.86 | (16) $false
% 7.22/2.86 |
% 7.22/2.86 |-The branch is then unsatisfiable
% 7.22/2.86 |-Branch two:
% 7.22/2.86 | (17) element(ex_28_0_4, ex_28_0_4) | element(ex_28_0_4, all_11_0_3)
% 7.22/2.86 |
% 7.22/2.86 +-Applying beta-rule and splitting (17), into two cases.
% 7.22/2.86 |-Branch one:
% 7.22/2.86 | (18) element(ex_28_0_4, ex_28_0_4)
% 7.22/2.86 |
% 7.22/2.86 +-Applying beta-rule and splitting (11), into two cases.
% 7.22/2.86 |-Branch one:
% 7.22/2.86 | (19) ~ element(ex_28_0_4, all_11_0_3)
% 7.22/2.86 |
% 7.22/2.86 | From (9)(9) and (18) follows:
% 7.22/2.86 | (20) element(all_11_0_3, all_11_0_3)
% 7.22/2.86 |
% 7.22/2.86 | From (9) and (19) follows:
% 7.22/2.86 | (21) ~ element(all_11_0_3, all_11_0_3)
% 7.22/2.86 |
% 7.22/2.86 | Using (20) and (21) yields:
% 7.22/2.86 | (16) $false
% 7.22/2.86 |
% 7.22/2.86 |-The branch is then unsatisfiable
% 7.22/2.86 |-Branch two:
% 7.22/2.86 | (23) element(ex_28_0_4, ex_10_0_2) & ~ element(ex_28_0_4, ex_28_0_4)
% 7.22/2.86 |
% 7.22/2.86 | Applying alpha-rule on (23) yields:
% 7.22/2.86 | (24) element(ex_28_0_4, ex_10_0_2)
% 7.22/2.86 | (25) ~ element(ex_28_0_4, ex_28_0_4)
% 7.22/2.86 |
% 7.22/2.86 | Using (18) and (25) yields:
% 7.22/2.86 | (16) $false
% 7.22/2.86 |
% 7.22/2.86 |-The branch is then unsatisfiable
% 7.22/2.86 |-Branch two:
% 7.22/2.86 | (25) ~ element(ex_28_0_4, ex_28_0_4)
% 7.22/2.86 | (28) element(ex_28_0_4, all_11_0_3)
% 7.22/2.86 |
% 7.22/2.86 | From (9) and (28) follows:
% 7.22/2.86 | (20) element(all_11_0_3, all_11_0_3)
% 7.22/2.86 |
% 7.22/2.86 | From (9)(9) and (25) follows:
% 7.22/2.86 | (21) ~ element(all_11_0_3, all_11_0_3)
% 7.22/2.86 |
% 7.22/2.86 | Using (20) and (21) yields:
% 7.22/2.86 | (16) $false
% 7.22/2.86 |
% 7.22/2.86 |-The branch is then unsatisfiable
% 7.22/2.86 % SZS output end Proof for theBenchmark
% 7.22/2.86
% 7.22/2.86 2261ms
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