TSTP Solution File: SYN317+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN317+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n006.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 05:01:18 EDT 2022
% Result : Theorem 1.98s 1.17s
% Output : Proof 2.51s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SYN317+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Tue Jul 12 04:46:50 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.56/0.61 ____ _
% 0.56/0.61 ___ / __ \_____(_)___ ________ __________
% 0.56/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.62
% 0.56/0.62 A Theorem Prover for First-Order Logic
% 0.56/0.62 (ePrincess v.1.0)
% 0.56/0.62
% 0.56/0.62 (c) Philipp Rümmer, 2009-2015
% 0.56/0.62 (c) Peter Backeman, 2014-2015
% 0.56/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.62 Bug reports to peter@backeman.se
% 0.56/0.62
% 0.56/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.62
% 0.56/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.23/0.91 Prover 0: Preprocessing ...
% 1.35/0.96 Prover 0: Warning: ignoring some quantifiers
% 1.35/0.98 Prover 0: Constructing countermodel ...
% 1.47/1.07 Prover 0: gave up
% 1.47/1.07 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.66/1.09 Prover 1: Preprocessing ...
% 1.66/1.13 Prover 1: Constructing countermodel ...
% 1.98/1.17 Prover 1: proved (102ms)
% 1.98/1.17
% 1.98/1.17 No countermodel exists, formula is valid
% 1.98/1.17 % SZS status Theorem for theBenchmark
% 1.98/1.17
% 1.98/1.17 Generating proof ... found it (size 21)
% 2.36/1.33
% 2.36/1.33 % SZS output start Proof for theBenchmark
% 2.36/1.33 Assumed formulas after preprocessing and simplification:
% 2.36/1.33 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (big_f(v6) = v5) | ~ (big_f(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (big_g(v6) = v5) | ~ (big_g(v6) = v4)) & ((big_f(v0) = v2 & big_g(v1) = v3 & ! [v4] : ! [v5] : (v5 = 0 | ~ (big_f(v4) = v5)) & ! [v4] : ~ (big_g(v4) = 0) & ( ~ (v2 = 0) | v3 = 0)) | (big_f(v0) = v1 & big_g(v0) = v2 & ! [v4] : ! [v5] : (v5 = 0 | ~ (big_f(v4) = v5)) & ! [v4] : ~ (big_g(v4) = 0) & ( ~ (v1 = 0) | v2 = 0))))
% 2.36/1.37 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 2.36/1.37 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0)) & ((big_f(all_0_3_3) = all_0_1_1 & big_g(all_0_2_2) = all_0_0_0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1)) & ! [v0] : ~ (big_g(v0) = 0) & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)) | (big_f(all_0_3_3) = all_0_2_2 & big_g(all_0_3_3) = all_0_1_1 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1)) & ! [v0] : ~ (big_g(v0) = 0) & ( ~ (all_0_2_2 = 0) | all_0_1_1 = 0)))
% 2.36/1.37 |
% 2.36/1.37 | Applying alpha-rule on (1) yields:
% 2.36/1.37 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0))
% 2.36/1.37 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0))
% 2.36/1.38 | (4) (big_f(all_0_3_3) = all_0_1_1 & big_g(all_0_2_2) = all_0_0_0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1)) & ! [v0] : ~ (big_g(v0) = 0) & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)) | (big_f(all_0_3_3) = all_0_2_2 & big_g(all_0_3_3) = all_0_1_1 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1)) & ! [v0] : ~ (big_g(v0) = 0) & ( ~ (all_0_2_2 = 0) | all_0_1_1 = 0))
% 2.36/1.38 |
% 2.36/1.38 +-Applying beta-rule and splitting (4), into two cases.
% 2.36/1.38 |-Branch one:
% 2.36/1.38 | (5) big_f(all_0_3_3) = all_0_1_1 & big_g(all_0_2_2) = all_0_0_0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1)) & ! [v0] : ~ (big_g(v0) = 0) & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)
% 2.36/1.38 |
% 2.36/1.38 | Applying alpha-rule on (5) yields:
% 2.36/1.38 | (6) ~ (all_0_1_1 = 0) | all_0_0_0 = 0
% 2.36/1.38 | (7) big_g(all_0_2_2) = all_0_0_0
% 2.36/1.38 | (8) big_f(all_0_3_3) = all_0_1_1
% 2.36/1.38 | (9) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1))
% 2.36/1.38 | (10) ! [v0] : ~ (big_g(v0) = 0)
% 2.36/1.38 |
% 2.36/1.38 | Instantiating formula (9) with all_0_1_1, all_0_3_3 and discharging atoms big_f(all_0_3_3) = all_0_1_1, yields:
% 2.36/1.38 | (11) all_0_1_1 = 0
% 2.36/1.38 |
% 2.36/1.38 | Instantiating formula (10) with all_0_2_2 yields:
% 2.36/1.38 | (12) ~ (big_g(all_0_2_2) = 0)
% 2.36/1.38 |
% 2.36/1.38 +-Applying beta-rule and splitting (6), into two cases.
% 2.36/1.38 |-Branch one:
% 2.36/1.38 | (13) ~ (all_0_1_1 = 0)
% 2.36/1.38 |
% 2.36/1.38 | Equations (11) can reduce 13 to:
% 2.36/1.38 | (14) $false
% 2.36/1.38 |
% 2.36/1.38 |-The branch is then unsatisfiable
% 2.36/1.38 |-Branch two:
% 2.36/1.38 | (11) all_0_1_1 = 0
% 2.36/1.38 | (16) all_0_0_0 = 0
% 2.36/1.38 |
% 2.36/1.38 | From (16) and (7) follows:
% 2.36/1.38 | (17) big_g(all_0_2_2) = 0
% 2.36/1.38 |
% 2.36/1.38 | Using (17) and (12) yields:
% 2.36/1.38 | (18) $false
% 2.36/1.38 |
% 2.36/1.38 |-The branch is then unsatisfiable
% 2.36/1.38 |-Branch two:
% 2.36/1.38 | (19) big_f(all_0_3_3) = all_0_2_2 & big_g(all_0_3_3) = all_0_1_1 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1)) & ! [v0] : ~ (big_g(v0) = 0) & ( ~ (all_0_2_2 = 0) | all_0_1_1 = 0)
% 2.36/1.39 |
% 2.36/1.39 | Applying alpha-rule on (19) yields:
% 2.36/1.39 | (20) big_g(all_0_3_3) = all_0_1_1
% 2.36/1.39 | (21) big_f(all_0_3_3) = all_0_2_2
% 2.36/1.39 | (22) ~ (all_0_2_2 = 0) | all_0_1_1 = 0
% 2.36/1.39 | (9) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1))
% 2.36/1.39 | (10) ! [v0] : ~ (big_g(v0) = 0)
% 2.36/1.39 |
% 2.36/1.39 | Instantiating formula (9) with all_0_2_2, all_0_3_3 and discharging atoms big_f(all_0_3_3) = all_0_2_2, yields:
% 2.36/1.39 | (25) all_0_2_2 = 0
% 2.36/1.39 |
% 2.36/1.39 | Instantiating formula (10) with all_0_3_3 yields:
% 2.36/1.39 | (26) ~ (big_g(all_0_3_3) = 0)
% 2.36/1.39 |
% 2.36/1.39 +-Applying beta-rule and splitting (22), into two cases.
% 2.36/1.39 |-Branch one:
% 2.36/1.39 | (27) ~ (all_0_2_2 = 0)
% 2.36/1.39 |
% 2.36/1.39 | Equations (25) can reduce 27 to:
% 2.36/1.39 | (14) $false
% 2.36/1.39 |
% 2.36/1.39 |-The branch is then unsatisfiable
% 2.36/1.39 |-Branch two:
% 2.51/1.39 | (25) all_0_2_2 = 0
% 2.51/1.39 | (11) all_0_1_1 = 0
% 2.51/1.39 |
% 2.51/1.39 | From (11) and (20) follows:
% 2.51/1.39 | (31) big_g(all_0_3_3) = 0
% 2.51/1.39 |
% 2.51/1.39 | Using (31) and (26) yields:
% 2.51/1.39 | (18) $false
% 2.51/1.39 |
% 2.51/1.39 |-The branch is then unsatisfiable
% 2.51/1.39 % SZS output end Proof for theBenchmark
% 2.51/1.39
% 2.51/1.39 763ms
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