TSTP Solution File: SYN409+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN409+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.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 05:02:12 EDT 2022
% Result : Theorem 1.83s 1.04s
% Output : Proof 2.35s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN409+1 : TPTP v8.1.0. Released v2.0.0.
% 0.00/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jul 12 06:27:22 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.58/0.57 ____ _
% 0.58/0.57 ___ / __ \_____(_)___ ________ __________
% 0.58/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.57
% 0.58/0.57 A Theorem Prover for First-Order Logic
% 0.58/0.57 (ePrincess v.1.0)
% 0.58/0.57
% 0.58/0.57 (c) Philipp Rümmer, 2009-2015
% 0.58/0.57 (c) Peter Backeman, 2014-2015
% 0.58/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.58 Bug reports to peter@backeman.se
% 0.58/0.58
% 0.58/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.58
% 0.58/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.63/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.15/0.81 Prover 0: Preprocessing ...
% 1.33/0.86 Prover 0: Warning: ignoring some quantifiers
% 1.33/0.87 Prover 0: Constructing countermodel ...
% 1.53/0.94 Prover 0: gave up
% 1.53/0.95 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.53/0.96 Prover 1: Preprocessing ...
% 1.53/1.00 Prover 1: Constructing countermodel ...
% 1.83/1.04 Prover 1: proved (92ms)
% 1.83/1.04
% 1.83/1.04 No countermodel exists, formula is valid
% 1.83/1.04 % SZS status Theorem for theBenchmark
% 1.83/1.04
% 1.83/1.04 Generating proof ... found it (size 15)
% 2.11/1.15
% 2.11/1.15 % SZS output start Proof for theBenchmark
% 2.11/1.16 Assumed formulas after preprocessing and simplification:
% 2.11/1.16 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (f(v6) = v5) | ~ (f(v6) = v4)) & (( ~ (v1 = 0) & f(v0) = v1 & ! [v4] : ! [v5] : (v5 = 0 | ~ (f(v4) = v5))) | (f(v1) = v3 & f(v0) = v2 & ! [v4] : ! [v5] : (v5 = 0 | ~ (f(v4) = v5)) & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 2.28/1.19 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 2.28/1.19 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) & (( ~ (all_0_2_2 = 0) & f(all_0_3_3) = all_0_2_2 & ! [v0] : ! [v1] : (v1 = 0 | ~ (f(v0) = v1))) | (f(all_0_2_2) = all_0_0_0 & f(all_0_3_3) = all_0_1_1 & ! [v0] : ! [v1] : (v1 = 0 | ~ (f(v0) = v1)) & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))))
% 2.28/1.19 |
% 2.28/1.19 | Applying alpha-rule on (1) yields:
% 2.28/1.19 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0))
% 2.28/1.19 | (3) ( ~ (all_0_2_2 = 0) & f(all_0_3_3) = all_0_2_2 & ! [v0] : ! [v1] : (v1 = 0 | ~ (f(v0) = v1))) | (f(all_0_2_2) = all_0_0_0 & f(all_0_3_3) = all_0_1_1 & ! [v0] : ! [v1] : (v1 = 0 | ~ (f(v0) = v1)) & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)))
% 2.28/1.19 |
% 2.28/1.19 +-Applying beta-rule and splitting (3), into two cases.
% 2.28/1.19 |-Branch one:
% 2.28/1.19 | (4) ~ (all_0_2_2 = 0) & f(all_0_3_3) = all_0_2_2 & ! [v0] : ! [v1] : (v1 = 0 | ~ (f(v0) = v1))
% 2.28/1.19 |
% 2.28/1.19 | Applying alpha-rule on (4) yields:
% 2.28/1.19 | (5) ~ (all_0_2_2 = 0)
% 2.28/1.19 | (6) f(all_0_3_3) = all_0_2_2
% 2.28/1.19 | (7) ! [v0] : ! [v1] : (v1 = 0 | ~ (f(v0) = v1))
% 2.28/1.20 |
% 2.28/1.20 | Instantiating formula (7) with all_0_2_2, all_0_3_3 and discharging atoms f(all_0_3_3) = all_0_2_2, yields:
% 2.28/1.20 | (8) all_0_2_2 = 0
% 2.28/1.20 |
% 2.28/1.20 | Equations (8) can reduce 5 to:
% 2.28/1.20 | (9) $false
% 2.28/1.20 |
% 2.28/1.20 |-The branch is then unsatisfiable
% 2.28/1.20 |-Branch two:
% 2.28/1.20 | (10) f(all_0_2_2) = all_0_0_0 & f(all_0_3_3) = all_0_1_1 & ! [v0] : ! [v1] : (v1 = 0 | ~ (f(v0) = v1)) & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))
% 2.28/1.20 |
% 2.28/1.20 | Applying alpha-rule on (10) yields:
% 2.28/1.20 | (11) f(all_0_2_2) = all_0_0_0
% 2.28/1.20 | (12) f(all_0_3_3) = all_0_1_1
% 2.28/1.20 | (7) ! [v0] : ! [v1] : (v1 = 0 | ~ (f(v0) = v1))
% 2.28/1.20 | (14) ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)
% 2.28/1.20 |
% 2.28/1.20 | Instantiating formula (7) with all_0_0_0, all_0_2_2 and discharging atoms f(all_0_2_2) = all_0_0_0, yields:
% 2.28/1.20 | (15) all_0_0_0 = 0
% 2.28/1.20 |
% 2.28/1.20 | Instantiating formula (7) with all_0_1_1, all_0_3_3 and discharging atoms f(all_0_3_3) = all_0_1_1, yields:
% 2.28/1.20 | (16) all_0_1_1 = 0
% 2.28/1.20 |
% 2.28/1.20 +-Applying beta-rule and splitting (14), into two cases.
% 2.28/1.20 |-Branch one:
% 2.28/1.20 | (17) ~ (all_0_0_0 = 0)
% 2.28/1.20 |
% 2.28/1.20 | Equations (15) can reduce 17 to:
% 2.28/1.20 | (9) $false
% 2.28/1.20 |
% 2.28/1.20 |-The branch is then unsatisfiable
% 2.28/1.20 |-Branch two:
% 2.28/1.20 | (15) all_0_0_0 = 0
% 2.28/1.20 | (20) ~ (all_0_1_1 = 0)
% 2.35/1.20 |
% 2.35/1.20 | Equations (16) can reduce 20 to:
% 2.35/1.20 | (9) $false
% 2.35/1.20 |
% 2.35/1.20 |-The branch is then unsatisfiable
% 2.35/1.20 % SZS output end Proof for theBenchmark
% 2.35/1.20
% 2.35/1.20 616ms
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