TSTP Solution File: COM012+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : COM012+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 : Fri Jul 15 01:07:48 EDT 2022
% Result : Theorem 2.22s 1.19s
% Output : Proof 2.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COM012+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n029.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 : Thu Jun 16 19:47:42 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.54/0.58 ____ _
% 0.54/0.58 ___ / __ \_____(_)___ ________ __________
% 0.54/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.58
% 0.54/0.58 A Theorem Prover for First-Order Logic
% 0.54/0.59 (ePrincess v.1.0)
% 0.54/0.59
% 0.54/0.59 (c) Philipp Rümmer, 2009-2015
% 0.54/0.59 (c) Peter Backeman, 2014-2015
% 0.54/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.59 Bug reports to peter@backeman.se
% 0.54/0.59
% 0.54/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.59
% 0.54/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.54/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.38/0.93 Prover 0: Preprocessing ...
% 1.76/1.06 Prover 0: Constructing countermodel ...
% 2.22/1.19 Prover 0: proved (551ms)
% 2.22/1.19
% 2.22/1.19 No countermodel exists, formula is valid
% 2.22/1.19 % SZS status Theorem for theBenchmark
% 2.22/1.19
% 2.22/1.19 Generating proof ... found it (size 14)
% 2.74/1.34
% 2.74/1.34 % SZS output start Proof for theBenchmark
% 2.74/1.34 Assumed formulas after preprocessing and simplification:
% 2.74/1.34 | (0) ? [v0] : ? [v1] : ( ~ (xz = xx) & sdtmndtasgtdt0(xy, xR, xz) & sdtmndtasgtdt0(xx, xR, xy) & aRewritingSystem0(xR) & aElement0(xz) & aElement0(xy) & aElement0(xx) & ~ sdtmndtasgtdt0(xx, xR, xz) & ~ sdtmndtplgtdt0(xx, xR, xz) & ~ aReductOfIn0(xz, xx, xR) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ sdtmndtplgtdt0(v5, v3, v4) | ~ aReductOfIn0(v5, v2, v3) | ~ aRewritingSystem0(v3) | ~ aElement0(v5) | ~ aElement0(v4) | ~ aElement0(v2) | sdtmndtplgtdt0(v2, v3, v4)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ sdtmndtplgtdt0(v4, v3, v5) | ~ sdtmndtplgtdt0(v2, v3, v4) | ~ aRewritingSystem0(v3) | ~ aElement0(v5) | ~ aElement0(v4) | ~ aElement0(v2) | sdtmndtplgtdt0(v2, v3, v5)) & ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ sdtmndtasgtdt0(v2, v3, v4) | ~ aRewritingSystem0(v3) | ~ aElement0(v4) | ~ aElement0(v2) | sdtmndtplgtdt0(v2, v3, v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ sdtmndtplgtdt0(v2, v3, v4) | ~ aRewritingSystem0(v3) | ~ aElement0(v4) | ~ aElement0(v2) | sdtmndtasgtdt0(v2, v3, v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ sdtmndtplgtdt0(v2, v3, v4) | ~ aRewritingSystem0(v3) | ~ aElement0(v4) | ~ aElement0(v2) | aReductOfIn0(v4, v2, v3) | ? [v5] : (sdtmndtplgtdt0(v5, v3, v4) & aReductOfIn0(v5, v2, v3) & aElement0(v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ aReductOfIn0(v4, v2, v3) | ~ aRewritingSystem0(v3) | ~ aElement0(v4) | ~ aElement0(v2) | sdtmndtplgtdt0(v2, v3, v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ aReductOfIn0(v4, v2, v3) | ~ aRewritingSystem0(v3) | ~ aElement0(v2) | aElement0(v4)) & ! [v2] : ! [v3] : ( ~ aRewritingSystem0(v3) | ~ aElement0(v2) | sdtmndtasgtdt0(v2, v3, v2)) & ! [v2] : ( ~ sdtmndtplgtdt0(v2, xR, xz) | ~ aReductOfIn0(v2, xx, xR) | ~ aElement0(v2)) & (xz = xy | (sdtmndtplgtdt0(xy, xR, xz) & (aReductOfIn0(xz, xy, xR) | (sdtmndtplgtdt0(v0, xR, xz) & aReductOfIn0(v0, xy, xR) & aElement0(v0))))) & (xy = xx | (sdtmndtplgtdt0(xx, xR, xy) & (aReductOfIn0(xy, xx, xR) | (sdtmndtplgtdt0(v1, xR, xy) & aReductOfIn0(v1, xx, xR) & aElement0(v1))))))
% 2.86/1.35 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 2.86/1.35 | (1) ~ (xz = xx) & sdtmndtasgtdt0(xy, xR, xz) & sdtmndtasgtdt0(xx, xR, xy) & aRewritingSystem0(xR) & aElement0(xz) & aElement0(xy) & aElement0(xx) & ~ sdtmndtasgtdt0(xx, xR, xz) & ~ sdtmndtplgtdt0(xx, xR, xz) & ~ aReductOfIn0(xz, xx, xR) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ sdtmndtplgtdt0(v3, v1, v2) | ~ aReductOfIn0(v3, v0, v1) | ~ aRewritingSystem0(v1) | ~ aElement0(v3) | ~ aElement0(v2) | ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ sdtmndtplgtdt0(v2, v1, v3) | ~ sdtmndtplgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ aElement0(v3) | ~ aElement0(v2) | ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ sdtmndtasgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ aElement0(v2) | ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ sdtmndtplgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ aElement0(v2) | ~ aElement0(v0) | sdtmndtasgtdt0(v0, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ sdtmndtplgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ aElement0(v2) | ~ aElement0(v0) | aReductOfIn0(v2, v0, v1) | ? [v3] : (sdtmndtplgtdt0(v3, v1, v2) & aReductOfIn0(v3, v0, v1) & aElement0(v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ aReductOfIn0(v2, v0, v1) | ~ aRewritingSystem0(v1) | ~ aElement0(v2) | ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ aReductOfIn0(v2, v0, v1) | ~ aRewritingSystem0(v1) | ~ aElement0(v0) | aElement0(v2)) & ! [v0] : ! [v1] : ( ~ aRewritingSystem0(v1) | ~ aElement0(v0) | sdtmndtasgtdt0(v0, v1, v0)) & ! [v0] : ( ~ sdtmndtplgtdt0(v0, xR, xz) | ~ aReductOfIn0(v0, xx, xR) | ~ aElement0(v0)) & (xz = xy | (sdtmndtplgtdt0(xy, xR, xz) & (aReductOfIn0(xz, xy, xR) | (sdtmndtplgtdt0(all_0_1_1, xR, xz) & aReductOfIn0(all_0_1_1, xy, xR) & aElement0(all_0_1_1))))) & (xy = xx | (sdtmndtplgtdt0(xx, xR, xy) & (aReductOfIn0(xy, xx, xR) | (sdtmndtplgtdt0(all_0_0_0, xR, xy) & aReductOfIn0(all_0_0_0, xx, xR) & aElement0(all_0_0_0)))))
% 2.86/1.36 |
% 2.86/1.36 | Applying alpha-rule on (1) yields:
% 2.86/1.36 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ aReductOfIn0(v2, v0, v1) | ~ aRewritingSystem0(v1) | ~ aElement0(v2) | ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v2))
% 2.86/1.36 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ sdtmndtplgtdt0(v2, v1, v3) | ~ sdtmndtplgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ aElement0(v3) | ~ aElement0(v2) | ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v3))
% 2.86/1.36 | (4) aElement0(xz)
% 2.86/1.36 | (5) ~ aReductOfIn0(xz, xx, xR)
% 2.86/1.36 | (6) aElement0(xy)
% 2.86/1.36 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtmndtplgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ aElement0(v2) | ~ aElement0(v0) | aReductOfIn0(v2, v0, v1) | ? [v3] : (sdtmndtplgtdt0(v3, v1, v2) & aReductOfIn0(v3, v0, v1) & aElement0(v3)))
% 2.86/1.37 | (8) ~ sdtmndtplgtdt0(xx, xR, xz)
% 2.86/1.37 | (9) aRewritingSystem0(xR)
% 2.86/1.37 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtmndtplgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ aElement0(v2) | ~ aElement0(v0) | sdtmndtasgtdt0(v0, v1, v2))
% 2.86/1.37 | (11) xy = xx | (sdtmndtplgtdt0(xx, xR, xy) & (aReductOfIn0(xy, xx, xR) | (sdtmndtplgtdt0(all_0_0_0, xR, xy) & aReductOfIn0(all_0_0_0, xx, xR) & aElement0(all_0_0_0))))
% 2.86/1.37 | (12) ~ (xz = xx)
% 2.86/1.37 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ aReductOfIn0(v2, v0, v1) | ~ aRewritingSystem0(v1) | ~ aElement0(v0) | aElement0(v2))
% 2.86/1.37 | (14) sdtmndtasgtdt0(xx, xR, xy)
% 2.86/1.37 | (15) ! [v0] : ! [v1] : ( ~ aRewritingSystem0(v1) | ~ aElement0(v0) | sdtmndtasgtdt0(v0, v1, v0))
% 2.86/1.37 | (16) xz = xy | (sdtmndtplgtdt0(xy, xR, xz) & (aReductOfIn0(xz, xy, xR) | (sdtmndtplgtdt0(all_0_1_1, xR, xz) & aReductOfIn0(all_0_1_1, xy, xR) & aElement0(all_0_1_1))))
% 2.86/1.37 | (17) aElement0(xx)
% 2.86/1.37 | (18) ~ sdtmndtasgtdt0(xx, xR, xz)
% 2.86/1.37 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ sdtmndtasgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ aElement0(v2) | ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v2))
% 2.86/1.37 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ sdtmndtplgtdt0(v3, v1, v2) | ~ aReductOfIn0(v3, v0, v1) | ~ aRewritingSystem0(v1) | ~ aElement0(v3) | ~ aElement0(v2) | ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v2))
% 2.86/1.37 | (21) ! [v0] : ( ~ sdtmndtplgtdt0(v0, xR, xz) | ~ aReductOfIn0(v0, xx, xR) | ~ aElement0(v0))
% 2.86/1.37 | (22) sdtmndtasgtdt0(xy, xR, xz)
% 2.86/1.37 |
% 2.86/1.37 +-Applying beta-rule and splitting (11), into two cases.
% 2.86/1.37 |-Branch one:
% 2.86/1.37 | (23) xy = xx
% 2.86/1.37 |
% 2.86/1.37 | From (23) and (22) follows:
% 2.86/1.37 | (24) sdtmndtasgtdt0(xx, xR, xz)
% 2.86/1.37 |
% 2.86/1.37 | Using (24) and (18) yields:
% 2.86/1.37 | (25) $false
% 2.86/1.37 |
% 2.86/1.37 |-The branch is then unsatisfiable
% 2.86/1.37 |-Branch two:
% 2.86/1.37 | (26) ~ (xy = xx)
% 2.86/1.37 | (27) sdtmndtplgtdt0(xx, xR, xy) & (aReductOfIn0(xy, xx, xR) | (sdtmndtplgtdt0(all_0_0_0, xR, xy) & aReductOfIn0(all_0_0_0, xx, xR) & aElement0(all_0_0_0)))
% 2.86/1.37 |
% 2.86/1.37 | Applying alpha-rule on (27) yields:
% 2.86/1.37 | (28) sdtmndtplgtdt0(xx, xR, xy)
% 2.86/1.37 | (29) aReductOfIn0(xy, xx, xR) | (sdtmndtplgtdt0(all_0_0_0, xR, xy) & aReductOfIn0(all_0_0_0, xx, xR) & aElement0(all_0_0_0))
% 2.86/1.37 |
% 2.86/1.37 +-Applying beta-rule and splitting (16), into two cases.
% 2.86/1.37 |-Branch one:
% 2.86/1.37 | (30) xz = xy
% 2.86/1.37 |
% 2.86/1.37 | From (30) and (18) follows:
% 2.86/1.37 | (31) ~ sdtmndtasgtdt0(xx, xR, xy)
% 2.86/1.37 |
% 2.86/1.37 | Using (14) and (31) yields:
% 2.86/1.37 | (25) $false
% 2.86/1.37 |
% 2.86/1.37 |-The branch is then unsatisfiable
% 2.86/1.37 |-Branch two:
% 2.86/1.37 | (33) ~ (xz = xy)
% 2.86/1.37 | (34) sdtmndtplgtdt0(xy, xR, xz) & (aReductOfIn0(xz, xy, xR) | (sdtmndtplgtdt0(all_0_1_1, xR, xz) & aReductOfIn0(all_0_1_1, xy, xR) & aElement0(all_0_1_1)))
% 2.86/1.38 |
% 2.86/1.38 | Applying alpha-rule on (34) yields:
% 2.86/1.38 | (35) sdtmndtplgtdt0(xy, xR, xz)
% 2.86/1.38 | (36) aReductOfIn0(xz, xy, xR) | (sdtmndtplgtdt0(all_0_1_1, xR, xz) & aReductOfIn0(all_0_1_1, xy, xR) & aElement0(all_0_1_1))
% 2.86/1.38 |
% 2.86/1.38 | Instantiating formula (3) with xz, xy, xR, xx and discharging atoms sdtmndtplgtdt0(xy, xR, xz), sdtmndtplgtdt0(xx, xR, xy), aRewritingSystem0(xR), aElement0(xz), aElement0(xy), aElement0(xx), ~ sdtmndtplgtdt0(xx, xR, xz), yields:
% 2.86/1.38 | (25) $false
% 2.86/1.38 |
% 2.86/1.38 |-The branch is then unsatisfiable
% 2.86/1.38 % SZS output end Proof for theBenchmark
% 2.86/1.38
% 2.86/1.38 782ms
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