TSTP Solution File: LCL666+1.001 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : LCL666+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 : Sun Jul 17 09:38:04 EDT 2022
% Result : Theorem 2.14s 1.23s
% Output : Proof 2.89s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL666+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 4 22:18:06 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.50/0.59 ____ _
% 0.50/0.59 ___ / __ \_____(_)___ ________ __________
% 0.50/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.59
% 0.50/0.59 A Theorem Prover for First-Order Logic
% 0.50/0.59 (ePrincess v.1.0)
% 0.50/0.59
% 0.50/0.59 (c) Philipp Rümmer, 2009-2015
% 0.50/0.59 (c) Peter Backeman, 2014-2015
% 0.50/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.59 Bug reports to peter@backeman.se
% 0.50/0.59
% 0.50/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.59
% 0.50/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.24/0.88 Prover 0: Preprocessing ...
% 1.24/0.93 Prover 0: Warning: ignoring some quantifiers
% 1.43/0.94 Prover 0: Constructing countermodel ...
% 1.52/1.03 Prover 0: gave up
% 1.52/1.03 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.52/1.05 Prover 1: Preprocessing ...
% 1.88/1.11 Prover 1: Constructing countermodel ...
% 2.01/1.13 Prover 1: gave up
% 2.01/1.13 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.01/1.14 Prover 2: Preprocessing ...
% 2.14/1.19 Prover 2: Warning: ignoring some quantifiers
% 2.14/1.19 Prover 2: Constructing countermodel ...
% 2.14/1.23 Prover 2: proved (95ms)
% 2.14/1.23
% 2.14/1.23 No countermodel exists, formula is valid
% 2.14/1.23 % SZS status Theorem for theBenchmark
% 2.14/1.23
% 2.14/1.23 Generating proof ... Warning: ignoring some quantifiers
% 2.73/1.40 found it (size 13)
% 2.73/1.40
% 2.73/1.40 % SZS output start Proof for theBenchmark
% 2.73/1.40 Assumed formulas after preprocessing and simplification:
% 2.73/1.40 | (0) ? [v0] : (p201(v0) = 0 & p101(v0) = 0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (r1(v4, v3) = v2) | ~ (r1(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (p201(v3) = v2) | ~ (p201(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (p101(v3) = v2) | ~ (p101(v3) = v1)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (r1(v1, v1) = v2)) & ! [v1] : ( ~ (p201(v1) = 0) | ? [v2] : (( ~ (v2 = 0) & p101(v1) = v2) | ( ~ (v2 = 0) & r1(v0, v1) = v2))) & ! [v1] : ( ~ (p101(v1) = 0) | ? [v2] : (( ~ (v2 = 0) & p201(v1) = v2) | ( ~ (v2 = 0) & r1(v0, v1) = v2))) & ! [v1] : ( ~ (r1(v0, v1) = 0) | ? [v2] : (( ~ (v2 = 0) & p201(v1) = v2) | ( ~ (v2 = 0) & p101(v1) = v2))) & ? [v1] : ? [v2] : ? [v3] : r1(v2, v1) = v3 & ? [v1] : ? [v2] : p201(v1) = v2 & ? [v1] : ? [v2] : p101(v1) = v2)
% 2.89/1.43 | Instantiating (0) with all_0_0_0 yields:
% 2.89/1.43 | (1) p201(all_0_0_0) = 0 & p101(all_0_0_0) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p201(v2) = v1) | ~ (p201(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p101(v2) = v1) | ~ (p101(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (r1(v0, v0) = v1)) & ! [v0] : ( ~ (p201(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p101(v0) = v1) | ( ~ (v1 = 0) & r1(all_0_0_0, v0) = v1))) & ! [v0] : ( ~ (p101(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p201(v0) = v1) | ( ~ (v1 = 0) & r1(all_0_0_0, v0) = v1))) & ! [v0] : ( ~ (r1(all_0_0_0, v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p201(v0) = v1) | ( ~ (v1 = 0) & p101(v0) = v1))) & ? [v0] : ? [v1] : ? [v2] : r1(v1, v0) = v2 & ? [v0] : ? [v1] : p201(v0) = v1 & ? [v0] : ? [v1] : p101(v0) = v1
% 2.89/1.43 |
% 2.89/1.43 | Applying alpha-rule on (1) yields:
% 2.89/1.43 | (2) p101(all_0_0_0) = 0
% 2.89/1.44 | (3) ? [v0] : ? [v1] : p201(v0) = v1
% 2.89/1.44 | (4) ! [v0] : ( ~ (p201(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p101(v0) = v1) | ( ~ (v1 = 0) & r1(all_0_0_0, v0) = v1)))
% 2.89/1.44 | (5) ? [v0] : ? [v1] : p101(v0) = v1
% 2.89/1.44 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (r1(v0, v0) = v1))
% 2.89/1.44 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p201(v2) = v1) | ~ (p201(v2) = v0))
% 2.89/1.44 | (8) ? [v0] : ? [v1] : ? [v2] : r1(v1, v0) = v2
% 2.89/1.44 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p101(v2) = v1) | ~ (p101(v2) = v0))
% 2.89/1.44 | (10) ! [v0] : ( ~ (r1(all_0_0_0, v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p201(v0) = v1) | ( ~ (v1 = 0) & p101(v0) = v1)))
% 2.89/1.44 | (11) ! [v0] : ( ~ (p101(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p201(v0) = v1) | ( ~ (v1 = 0) & r1(all_0_0_0, v0) = v1)))
% 2.89/1.44 | (12) p201(all_0_0_0) = 0
% 2.89/1.44 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0))
% 2.89/1.44 |
% 2.89/1.44 | Instantiating formula (11) with all_0_0_0 and discharging atoms p101(all_0_0_0) = 0, yields:
% 2.89/1.44 | (14) ? [v0] : (( ~ (v0 = 0) & p201(all_0_0_0) = v0) | ( ~ (v0 = 0) & r1(all_0_0_0, all_0_0_0) = v0))
% 2.89/1.44 |
% 2.89/1.44 | Instantiating (14) with all_14_0_8 yields:
% 2.89/1.44 | (15) ( ~ (all_14_0_8 = 0) & p201(all_0_0_0) = all_14_0_8) | ( ~ (all_14_0_8 = 0) & r1(all_0_0_0, all_0_0_0) = all_14_0_8)
% 2.89/1.44 |
% 2.89/1.44 +-Applying beta-rule and splitting (15), into two cases.
% 2.89/1.44 |-Branch one:
% 2.89/1.44 | (16) ~ (all_14_0_8 = 0) & p201(all_0_0_0) = all_14_0_8
% 2.89/1.44 |
% 2.89/1.44 | Applying alpha-rule on (16) yields:
% 2.89/1.44 | (17) ~ (all_14_0_8 = 0)
% 2.89/1.44 | (18) p201(all_0_0_0) = all_14_0_8
% 2.89/1.44 |
% 2.89/1.44 | Instantiating formula (7) with all_0_0_0, all_14_0_8, 0 and discharging atoms p201(all_0_0_0) = all_14_0_8, p201(all_0_0_0) = 0, yields:
% 2.89/1.44 | (19) all_14_0_8 = 0
% 2.89/1.44 |
% 2.89/1.44 | Equations (19) can reduce 17 to:
% 2.89/1.44 | (20) $false
% 2.89/1.44 |
% 2.89/1.45 |-The branch is then unsatisfiable
% 2.89/1.45 |-Branch two:
% 2.89/1.45 | (21) ~ (all_14_0_8 = 0) & r1(all_0_0_0, all_0_0_0) = all_14_0_8
% 2.89/1.45 |
% 2.89/1.45 | Applying alpha-rule on (21) yields:
% 2.89/1.45 | (17) ~ (all_14_0_8 = 0)
% 2.89/1.45 | (23) r1(all_0_0_0, all_0_0_0) = all_14_0_8
% 2.89/1.45 |
% 2.89/1.45 | Instantiating formula (6) with all_14_0_8, all_0_0_0 and discharging atoms r1(all_0_0_0, all_0_0_0) = all_14_0_8, yields:
% 2.89/1.45 | (19) all_14_0_8 = 0
% 2.89/1.45 |
% 2.89/1.45 | Equations (19) can reduce 17 to:
% 2.89/1.45 | (20) $false
% 2.89/1.45 |
% 2.89/1.45 |-The branch is then unsatisfiable
% 2.89/1.45 % SZS output end Proof for theBenchmark
% 2.89/1.45
% 2.89/1.45 848ms
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