TSTP Solution File: SYN399+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN399+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.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 05:02:08 EDT 2022
% Result : Theorem 2.32s 1.22s
% Output : Proof 2.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN399+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 14:08:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.53/0.57 ____ _
% 0.53/0.57 ___ / __ \_____(_)___ ________ __________
% 0.53/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.53/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.53/0.57
% 0.53/0.57 A Theorem Prover for First-Order Logic
% 0.53/0.57 (ePrincess v.1.0)
% 0.53/0.57
% 0.53/0.57 (c) Philipp Rümmer, 2009-2015
% 0.53/0.57 (c) Peter Backeman, 2014-2015
% 0.53/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.57 Bug reports to peter@backeman.se
% 0.53/0.57
% 0.53/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.57
% 0.53/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.53/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.19/0.85 Prover 0: Preprocessing ...
% 1.26/0.90 Prover 0: Warning: ignoring some quantifiers
% 1.26/0.91 Prover 0: Constructing countermodel ...
% 1.50/1.00 Prover 0: gave up
% 1.50/1.00 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.50/1.02 Prover 1: Preprocessing ...
% 1.77/1.05 Prover 1: Constructing countermodel ...
% 1.92/1.08 Prover 1: gave up
% 1.92/1.08 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.92/1.09 Prover 2: Preprocessing ...
% 1.92/1.11 Prover 2: Warning: ignoring some quantifiers
% 1.92/1.11 Prover 2: Constructing countermodel ...
% 1.92/1.14 Prover 2: gave up
% 1.92/1.14 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.15/1.14 Prover 3: Preprocessing ...
% 2.15/1.15 Prover 3: Warning: ignoring some quantifiers
% 2.15/1.15 Prover 3: Constructing countermodel ...
% 2.15/1.17 Prover 3: gave up
% 2.15/1.17 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.32/1.17 Prover 4: Preprocessing ...
% 2.32/1.20 Prover 4: Warning: ignoring some quantifiers
% 2.32/1.20 Prover 4: Constructing countermodel ...
% 2.32/1.22 Prover 4: proved (51ms)
% 2.32/1.22
% 2.32/1.22 No countermodel exists, formula is valid
% 2.32/1.22 % SZS status Theorem for theBenchmark
% 2.32/1.22
% 2.32/1.22 Generating proof ... Warning: ignoring some quantifiers
% 2.70/1.34 found it (size 24)
% 2.70/1.34
% 2.70/1.34 % SZS output start Proof for theBenchmark
% 2.70/1.35 Assumed formulas after preprocessing and simplification:
% 2.70/1.35 | (0) ? [v0] : ? [v1] : ( ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (f(v4) = v3) | ~ (f(v4) = v2)) & ! [v2] : ! [v3] : (v3 = 0 | ~ (f(v2) = v3) | ~ p) & ! [v2] : ( ~ (f(v2) = 0) | p) & ( ~ p | ? [v2] : f(v2) = 0) & (p | ? [v2] : ? [v3] : ( ~ (v3 = 0) & f(v2) = v3)) & (( ~ (v1 = 0) & f(v0) = v1 & p) | ( ~ p & ! [v2] : ! [v3] : (v3 = 0 | ~ (f(v2) = v3)))))
% 2.81/1.38 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 2.81/1.38 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (f(v0) = v1) | ~ p) & ! [v0] : ( ~ (f(v0) = 0) | p) & ( ~ p | ? [v0] : f(v0) = 0) & (p | ? [v0] : ? [v1] : ( ~ (v1 = 0) & f(v0) = v1)) & (( ~ (all_0_0_0 = 0) & f(all_0_1_1) = all_0_0_0 & p) | ( ~ p & ! [v0] : ! [v1] : (v1 = 0 | ~ (f(v0) = v1))))
% 2.81/1.39 |
% 2.81/1.39 | Applying alpha-rule on (1) yields:
% 2.81/1.39 | (2) ( ~ (all_0_0_0 = 0) & f(all_0_1_1) = all_0_0_0 & p) | ( ~ p & ! [v0] : ! [v1] : (v1 = 0 | ~ (f(v0) = v1)))
% 2.81/1.39 | (3) p | ? [v0] : ? [v1] : ( ~ (v1 = 0) & f(v0) = v1)
% 2.81/1.39 | (4) ~ p | ? [v0] : f(v0) = 0
% 2.81/1.39 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (f(v0) = v1) | ~ p)
% 2.81/1.39 | (6) ! [v0] : ( ~ (f(v0) = 0) | p)
% 2.81/1.39 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0))
% 2.81/1.39 |
% 2.81/1.39 +-Applying beta-rule and splitting (3), into two cases.
% 2.81/1.39 |-Branch one:
% 2.81/1.39 | (8) p
% 2.81/1.39 |
% 2.81/1.39 +-Applying beta-rule and splitting (2), into two cases.
% 2.81/1.39 |-Branch one:
% 2.81/1.39 | (9) ~ (all_0_0_0 = 0) & f(all_0_1_1) = all_0_0_0 & p
% 2.81/1.39 |
% 2.81/1.39 | Applying alpha-rule on (9) yields:
% 2.81/1.39 | (10) ~ (all_0_0_0 = 0)
% 2.81/1.39 | (11) f(all_0_1_1) = all_0_0_0
% 2.81/1.39 | (8) p
% 2.81/1.39 |
% 2.81/1.39 +-Applying beta-rule and splitting (4), into two cases.
% 2.81/1.39 |-Branch one:
% 2.81/1.39 | (13) ~ p
% 2.81/1.39 |
% 2.81/1.39 | Using (8) and (13) yields:
% 2.81/1.39 | (14) $false
% 2.81/1.39 |
% 2.81/1.39 |-The branch is then unsatisfiable
% 2.81/1.39 |-Branch two:
% 2.81/1.39 | (8) p
% 2.81/1.39 | (16) ? [v0] : f(v0) = 0
% 2.81/1.39 |
% 2.81/1.40 | Instantiating formula (5) with all_0_0_0, all_0_1_1 and discharging atoms f(all_0_1_1) = all_0_0_0, p, yields:
% 2.81/1.40 | (17) all_0_0_0 = 0
% 2.81/1.40 |
% 2.81/1.40 | Equations (17) can reduce 10 to:
% 2.81/1.40 | (18) $false
% 2.81/1.40 |
% 2.81/1.40 |-The branch is then unsatisfiable
% 2.81/1.40 |-Branch two:
% 2.81/1.40 | (19) ~ p & ! [v0] : ! [v1] : (v1 = 0 | ~ (f(v0) = v1))
% 2.81/1.40 |
% 2.81/1.40 | Applying alpha-rule on (19) yields:
% 2.81/1.40 | (13) ~ p
% 2.81/1.40 | (21) ! [v0] : ! [v1] : (v1 = 0 | ~ (f(v0) = v1))
% 2.81/1.40 |
% 2.81/1.40 | Using (8) and (13) yields:
% 2.81/1.40 | (14) $false
% 2.81/1.40 |
% 2.81/1.40 |-The branch is then unsatisfiable
% 2.81/1.40 |-Branch two:
% 2.81/1.40 | (13) ~ p
% 2.81/1.40 | (24) ? [v0] : ? [v1] : ( ~ (v1 = 0) & f(v0) = v1)
% 2.81/1.40 |
% 2.81/1.40 | Instantiating (24) with all_6_0_3, all_6_1_4 yields:
% 2.81/1.40 | (25) ~ (all_6_0_3 = 0) & f(all_6_1_4) = all_6_0_3
% 2.81/1.40 |
% 2.81/1.40 | Applying alpha-rule on (25) yields:
% 2.81/1.40 | (26) ~ (all_6_0_3 = 0)
% 2.81/1.40 | (27) f(all_6_1_4) = all_6_0_3
% 2.81/1.40 |
% 2.81/1.40 +-Applying beta-rule and splitting (2), into two cases.
% 2.81/1.40 |-Branch one:
% 2.81/1.40 | (9) ~ (all_0_0_0 = 0) & f(all_0_1_1) = all_0_0_0 & p
% 2.81/1.40 |
% 2.81/1.40 | Applying alpha-rule on (9) yields:
% 2.81/1.40 | (10) ~ (all_0_0_0 = 0)
% 2.81/1.40 | (11) f(all_0_1_1) = all_0_0_0
% 2.81/1.40 | (8) p
% 2.81/1.40 |
% 2.81/1.40 | Using (8) and (13) yields:
% 2.81/1.40 | (14) $false
% 2.81/1.40 |
% 2.81/1.40 |-The branch is then unsatisfiable
% 2.81/1.40 |-Branch two:
% 2.81/1.40 | (19) ~ p & ! [v0] : ! [v1] : (v1 = 0 | ~ (f(v0) = v1))
% 2.81/1.40 |
% 2.81/1.40 | Applying alpha-rule on (19) yields:
% 2.81/1.40 | (13) ~ p
% 2.81/1.40 | (21) ! [v0] : ! [v1] : (v1 = 0 | ~ (f(v0) = v1))
% 2.81/1.40 |
% 2.81/1.40 | Instantiating formula (21) with all_6_0_3, all_6_1_4 and discharging atoms f(all_6_1_4) = all_6_0_3, yields:
% 2.81/1.40 | (36) all_6_0_3 = 0
% 2.81/1.40 |
% 2.81/1.40 | Equations (36) can reduce 26 to:
% 2.81/1.40 | (18) $false
% 2.81/1.40 |
% 2.81/1.40 |-The branch is then unsatisfiable
% 2.81/1.40 % SZS output end Proof for theBenchmark
% 2.81/1.40
% 2.81/1.40 819ms
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