TSTP Solution File: SYN965+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN965+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n023.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 : Thu Jul 21 05:06:08 EDT 2022
% Result : Theorem 4.51s 1.93s
% Output : Proof 5.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN965+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n023.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jul 11 18:42:54 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.57 ____ _
% 0.18/0.57 ___ / __ \_____(_)___ ________ __________
% 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.57
% 0.18/0.57 A Theorem Prover for First-Order Logic
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58 Bug reports to peter@backeman.se
% 0.18/0.58
% 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.29/0.88 Prover 0: Preprocessing ...
% 1.39/0.93 Prover 0: Warning: ignoring some quantifiers
% 1.39/0.95 Prover 0: Constructing countermodel ...
% 1.89/1.11 Prover 0: gave up
% 1.89/1.11 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.89/1.12 Prover 1: Preprocessing ...
% 1.89/1.16 Prover 1: Warning: ignoring some quantifiers
% 1.89/1.16 Prover 1: Constructing countermodel ...
% 1.89/1.17 Prover 1: gave up
% 1.89/1.17 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.89/1.18 Prover 2: Preprocessing ...
% 2.28/1.22 Prover 2: Warning: ignoring some quantifiers
% 2.34/1.22 Prover 2: Constructing countermodel ...
% 2.36/1.24 Prover 2: gave up
% 2.36/1.24 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.36/1.24 Prover 3: Preprocessing ...
% 2.36/1.25 Prover 3: Warning: ignoring some quantifiers
% 2.36/1.25 Prover 3: Constructing countermodel ...
% 2.36/1.30 Prover 3: gave up
% 2.36/1.30 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.67/1.31 Prover 4: Preprocessing ...
% 2.67/1.34 Prover 4: Warning: ignoring some quantifiers
% 2.67/1.34 Prover 4: Constructing countermodel ...
% 2.96/1.42 Prover 4: gave up
% 2.96/1.42 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.96/1.42 Prover 5: Preprocessing ...
% 2.96/1.44 Prover 5: Warning: ignoring some quantifiers
% 2.96/1.44 Prover 5: Constructing countermodel ...
% 2.96/1.44 Prover 5: gave up
% 2.96/1.44 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.96/1.45 Prover 6: Preprocessing ...
% 2.96/1.47 Prover 6: Warning: ignoring some quantifiers
% 2.96/1.47 Prover 6: Constructing countermodel ...
% 3.28/1.48 Prover 6: gave up
% 3.28/1.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 3.28/1.48 Prover 7: Preprocessing ...
% 3.28/1.49 Prover 7: Proving ...
% 4.51/1.93 Prover 7: proved (449ms)
% 4.51/1.93
% 4.51/1.93 % SZS status Theorem for theBenchmark
% 4.51/1.93
% 4.51/1.93 Generating proof ... found it (size 30)
% 5.34/2.29
% 5.34/2.29 % SZS output start Proof for theBenchmark
% 5.34/2.29 Assumed formulas after preprocessing and simplification:
% 5.34/2.29 | (0) ! [v0] : ? [v1] : ! [v2] : ((p(v2, v1) & ! [v3] : ~ p(v3, v2)) | (p(v2, v0) & p(v0, v2) & ~ p(v2, v1)))
% 5.34/2.29 | Introducing new symbol ex_0_0_0 defined by:
% 5.34/2.29 | (1) ex_0_0_0 = arbitrary_constant
% 5.34/2.29 |
% 5.34/2.29 | Instantiating formula (0) with ex_0_0_0 yields:
% 5.34/2.29 | (2) ? [v0] : ! [v1] : ((p(v1, v0) & ! [v2] : ~ p(v2, v1)) | (p(v1, ex_0_0_0) & p(ex_0_0_0, v1) & ~ p(v1, v0)))
% 5.34/2.29 |
% 5.34/2.29 | Instantiating (2) with all_1_0_1 yields:
% 5.34/2.29 | (3) ! [v0] : ((p(v0, all_1_0_1) & ! [v1] : ~ p(v1, v0)) | (p(v0, ex_0_0_0) & p(ex_0_0_0, v0) & ~ p(v0, all_1_0_1)))
% 5.56/2.29 |
% 5.56/2.29 | Introducing new symbol ex_3_0_2 defined by:
% 5.56/2.29 | (4) ex_3_0_2 = all_1_0_1
% 5.56/2.29 |
% 5.56/2.29 | Instantiating formula (0) with ex_3_0_2 yields:
% 5.56/2.29 | (5) ? [v0] : ! [v1] : ((p(v1, v0) & ! [v2] : ~ p(v2, v1)) | (p(v1, ex_3_0_2) & p(ex_3_0_2, v1) & ~ p(v1, v0)))
% 5.56/2.29 |
% 5.56/2.29 | Instantiating (5) with all_4_0_3 yields:
% 5.56/2.29 | (6) ! [v0] : ((p(v0, all_4_0_3) & ! [v1] : ~ p(v1, v0)) | (p(v0, ex_3_0_2) & p(ex_3_0_2, v0) & ~ p(v0, all_4_0_3)))
% 5.56/2.30 |
% 5.56/2.30 | Introducing new symbol ex_6_0_4 defined by:
% 5.56/2.30 | (7) ex_6_0_4 = all_1_0_1
% 5.56/2.30 |
% 5.56/2.30 | Instantiating formula (3) with ex_6_0_4 yields:
% 5.56/2.30 | (8) (p(ex_6_0_4, all_1_0_1) & ! [v0] : ~ p(v0, ex_6_0_4)) | (p(ex_6_0_4, ex_0_0_0) & p(ex_0_0_0, ex_6_0_4) & ~ p(ex_6_0_4, all_1_0_1))
% 5.56/2.30 |
% 5.56/2.30 +-Applying beta-rule and splitting (8), into two cases.
% 5.56/2.30 |-Branch one:
% 5.56/2.30 | (9) p(ex_6_0_4, all_1_0_1) & ! [v0] : ~ p(v0, ex_6_0_4)
% 5.56/2.30 |
% 5.56/2.30 | Applying alpha-rule on (9) yields:
% 5.56/2.30 | (10) p(ex_6_0_4, all_1_0_1)
% 5.56/2.30 | (11) ! [v0] : ~ p(v0, ex_6_0_4)
% 5.56/2.30 |
% 5.56/2.30 | Instantiating formula (11) with all_1_0_1 yields:
% 5.56/2.30 | (12) ~ p(all_1_0_1, ex_6_0_4)
% 5.56/2.30 |
% 5.56/2.30 | From (7) and (10) follows:
% 5.56/2.30 | (13) p(all_1_0_1, all_1_0_1)
% 5.56/2.30 |
% 5.56/2.30 | From (7) and (12) follows:
% 5.56/2.30 | (14) ~ p(all_1_0_1, all_1_0_1)
% 5.56/2.30 |
% 5.56/2.30 | Using (13) and (14) yields:
% 5.56/2.30 | (15) $false
% 5.56/2.30 |
% 5.56/2.30 |-The branch is then unsatisfiable
% 5.56/2.30 |-Branch two:
% 5.56/2.30 | (16) p(ex_6_0_4, ex_0_0_0) & p(ex_0_0_0, ex_6_0_4) & ~ p(ex_6_0_4, all_1_0_1)
% 5.56/2.30 |
% 5.56/2.30 | Applying alpha-rule on (16) yields:
% 5.56/2.30 | (17) p(ex_6_0_4, ex_0_0_0)
% 5.56/2.30 | (18) p(ex_0_0_0, ex_6_0_4)
% 5.56/2.30 | (19) ~ p(ex_6_0_4, all_1_0_1)
% 5.56/2.30 |
% 5.56/2.30 | Introducing new symbol ex_18_0_7 defined by:
% 5.56/2.30 | (20) ex_18_0_7 = all_1_0_1
% 5.56/2.30 |
% 5.56/2.30 | Instantiating formula (6) with ex_18_0_7 yields:
% 5.56/2.30 | (21) (p(ex_18_0_7, all_4_0_3) & ! [v0] : ~ p(v0, ex_18_0_7)) | (p(ex_18_0_7, ex_3_0_2) & p(ex_3_0_2, ex_18_0_7) & ~ p(ex_18_0_7, all_4_0_3))
% 5.56/2.30 |
% 5.56/2.30 +-Applying beta-rule and splitting (21), into two cases.
% 5.56/2.30 |-Branch one:
% 5.56/2.30 | (22) p(ex_18_0_7, all_4_0_3) & ! [v0] : ~ p(v0, ex_18_0_7)
% 5.56/2.30 |
% 5.56/2.30 | Applying alpha-rule on (22) yields:
% 5.56/2.30 | (23) p(ex_18_0_7, all_4_0_3)
% 5.56/2.30 | (24) ! [v0] : ~ p(v0, ex_18_0_7)
% 5.56/2.30 |
% 5.56/2.30 | Instantiating formula (24) with ex_0_0_0 yields:
% 5.56/2.30 | (25) ~ p(ex_0_0_0, ex_18_0_7)
% 5.56/2.30 |
% 5.56/2.30 | From (1)(7) and (18) follows:
% 5.56/2.30 | (26) p(arbitrary_constant, all_1_0_1)
% 5.56/2.30 |
% 5.56/2.30 | From (1)(20) and (25) follows:
% 5.56/2.30 | (27) ~ p(arbitrary_constant, all_1_0_1)
% 5.56/2.30 |
% 5.56/2.30 | Using (26) and (27) yields:
% 5.56/2.30 | (15) $false
% 5.56/2.30 |
% 5.56/2.30 |-The branch is then unsatisfiable
% 5.56/2.30 |-Branch two:
% 5.56/2.30 | (29) p(ex_18_0_7, ex_3_0_2) & p(ex_3_0_2, ex_18_0_7) & ~ p(ex_18_0_7, all_4_0_3)
% 5.56/2.30 |
% 5.56/2.30 | Applying alpha-rule on (29) yields:
% 5.56/2.30 | (30) p(ex_18_0_7, ex_3_0_2)
% 5.56/2.30 | (31) p(ex_3_0_2, ex_18_0_7)
% 5.56/2.30 | (32) ~ p(ex_18_0_7, all_4_0_3)
% 5.56/2.30 |
% 5.56/2.30 | From (4)(20) and (31) follows:
% 5.56/2.30 | (13) p(all_1_0_1, all_1_0_1)
% 5.56/2.30 |
% 5.56/2.30 | From (7) and (19) follows:
% 5.56/2.30 | (14) ~ p(all_1_0_1, all_1_0_1)
% 5.56/2.31 |
% 5.56/2.31 | Using (13) and (14) yields:
% 5.56/2.31 | (15) $false
% 5.56/2.31 |
% 5.56/2.31 |-The branch is then unsatisfiable
% 5.56/2.31 % SZS output end Proof for theBenchmark
% 5.56/2.31
% 5.56/2.31 1712ms
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