TSTP Solution File: SYN052+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN052+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 04:59:25 EDT 2022
% Result : Theorem 2.36s 1.30s
% Output : Proof 2.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SYN052+1 : TPTP v8.1.0. Released v2.0.0.
% 0.13/0.15 % Command : ePrincess-casc -timeout=%d %s
% 0.15/0.36 % Computer : n027.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
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Mon Jul 11 15:47:04 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.68/0.68 ____ _
% 0.68/0.68 ___ / __ \_____(_)___ ________ __________
% 0.68/0.68 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.68/0.68 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.68/0.68 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.68/0.68
% 0.68/0.68 A Theorem Prover for First-Order Logic
% 0.68/0.68 (ePrincess v.1.0)
% 0.68/0.68
% 0.68/0.68 (c) Philipp Rümmer, 2009-2015
% 0.68/0.68 (c) Peter Backeman, 2014-2015
% 0.68/0.68 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.68/0.68 Free software under GNU Lesser General Public License (LGPL).
% 0.68/0.68 Bug reports to peter@backeman.se
% 0.68/0.68
% 0.68/0.68 For more information, visit http://user.uu.se/~petba168/breu/
% 0.68/0.68
% 0.68/0.68 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.84/0.73 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.37/0.94 Prover 0: Preprocessing ...
% 1.43/0.99 Prover 0: Warning: ignoring some quantifiers
% 1.43/1.00 Prover 0: Constructing countermodel ...
% 1.69/1.09 Prover 0: gave up
% 1.69/1.09 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.69/1.10 Prover 1: Preprocessing ...
% 1.69/1.14 Prover 1: Constructing countermodel ...
% 2.02/1.17 Prover 1: gave up
% 2.02/1.17 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.02/1.18 Prover 2: Preprocessing ...
% 2.17/1.20 Prover 2: Warning: ignoring some quantifiers
% 2.17/1.20 Prover 2: Constructing countermodel ...
% 2.17/1.22 Prover 2: gave up
% 2.17/1.23 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.17/1.23 Prover 3: Preprocessing ...
% 2.32/1.24 Prover 3: Warning: ignoring some quantifiers
% 2.32/1.24 Prover 3: Constructing countermodel ...
% 2.36/1.25 Prover 3: gave up
% 2.36/1.25 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.36/1.26 Prover 4: Preprocessing ...
% 2.36/1.28 Prover 4: Warning: ignoring some quantifiers
% 2.36/1.28 Prover 4: Constructing countermodel ...
% 2.36/1.30 Prover 4: proved (49ms)
% 2.36/1.30
% 2.36/1.30 No countermodel exists, formula is valid
% 2.36/1.30 % SZS status Theorem for theBenchmark
% 2.36/1.30
% 2.36/1.30 Generating proof ... Warning: ignoring some quantifiers
% 2.72/1.42 found it (size 24)
% 2.72/1.42
% 2.72/1.42 % SZS output start Proof for theBenchmark
% 2.72/1.43 Assumed formulas after preprocessing and simplification:
% 2.72/1.43 | (0) ? [v0] : ? [v1] : ( ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (big_f(v4) = v3) | ~ (big_f(v4) = v2)) & ! [v2] : ! [v3] : (v3 = 0 | ~ (big_f(v2) = v3) | ~ p) & ! [v2] : ( ~ (big_f(v2) = 0) | p) & ( ~ p | ? [v2] : big_f(v2) = 0) & (p | ? [v2] : ? [v3] : ( ~ (v3 = 0) & big_f(v2) = v3)) & (( ~ (v1 = 0) & big_f(v0) = v1 & p) | ( ~ p & ! [v2] : ! [v3] : (v3 = 0 | ~ (big_f(v2) = v3)))))
% 2.91/1.46 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 2.91/1.46 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1) | ~ p) & ! [v0] : ( ~ (big_f(v0) = 0) | p) & ( ~ p | ? [v0] : big_f(v0) = 0) & (p | ? [v0] : ? [v1] : ( ~ (v1 = 0) & big_f(v0) = v1)) & (( ~ (all_0_0_0 = 0) & big_f(all_0_1_1) = all_0_0_0 & p) | ( ~ p & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1))))
% 2.91/1.47 |
% 2.91/1.47 | Applying alpha-rule on (1) yields:
% 2.91/1.47 | (2) p | ? [v0] : ? [v1] : ( ~ (v1 = 0) & big_f(v0) = v1)
% 2.91/1.47 | (3) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1) | ~ p)
% 2.91/1.47 | (4) ! [v0] : ( ~ (big_f(v0) = 0) | p)
% 2.91/1.47 | (5) ~ p | ? [v0] : big_f(v0) = 0
% 2.91/1.47 | (6) ( ~ (all_0_0_0 = 0) & big_f(all_0_1_1) = all_0_0_0 & p) | ( ~ p & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1)))
% 2.91/1.47 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0))
% 2.91/1.47 |
% 2.91/1.47 +-Applying beta-rule and splitting (2), into two cases.
% 2.91/1.47 |-Branch one:
% 2.91/1.47 | (8) p
% 2.91/1.47 |
% 2.91/1.47 +-Applying beta-rule and splitting (6), into two cases.
% 2.91/1.47 |-Branch one:
% 2.91/1.47 | (9) ~ (all_0_0_0 = 0) & big_f(all_0_1_1) = all_0_0_0 & p
% 2.91/1.47 |
% 2.91/1.47 | Applying alpha-rule on (9) yields:
% 2.91/1.47 | (10) ~ (all_0_0_0 = 0)
% 2.91/1.47 | (11) big_f(all_0_1_1) = all_0_0_0
% 2.91/1.47 | (8) p
% 2.91/1.47 |
% 2.91/1.47 +-Applying beta-rule and splitting (5), into two cases.
% 2.91/1.47 |-Branch one:
% 2.91/1.47 | (13) ~ p
% 2.91/1.47 |
% 2.91/1.47 | Using (8) and (13) yields:
% 2.91/1.47 | (14) $false
% 2.91/1.47 |
% 2.91/1.47 |-The branch is then unsatisfiable
% 2.91/1.47 |-Branch two:
% 2.91/1.47 | (8) p
% 2.91/1.47 | (16) ? [v0] : big_f(v0) = 0
% 2.91/1.47 |
% 2.91/1.47 | Instantiating formula (3) with all_0_0_0, all_0_1_1 and discharging atoms big_f(all_0_1_1) = all_0_0_0, p, yields:
% 2.91/1.47 | (17) all_0_0_0 = 0
% 2.91/1.47 |
% 2.91/1.47 | Equations (17) can reduce 10 to:
% 2.91/1.47 | (18) $false
% 2.91/1.47 |
% 2.91/1.47 |-The branch is then unsatisfiable
% 2.91/1.47 |-Branch two:
% 2.91/1.47 | (19) ~ p & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1))
% 2.91/1.47 |
% 2.91/1.47 | Applying alpha-rule on (19) yields:
% 2.91/1.48 | (13) ~ p
% 2.91/1.48 | (21) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1))
% 2.91/1.48 |
% 2.91/1.48 | Using (8) and (13) yields:
% 2.91/1.48 | (14) $false
% 2.91/1.48 |
% 2.91/1.48 |-The branch is then unsatisfiable
% 2.91/1.48 |-Branch two:
% 2.91/1.48 | (13) ~ p
% 2.91/1.48 | (24) ? [v0] : ? [v1] : ( ~ (v1 = 0) & big_f(v0) = v1)
% 2.91/1.48 |
% 2.91/1.48 | Instantiating (24) with all_6_0_3, all_6_1_4 yields:
% 2.91/1.48 | (25) ~ (all_6_0_3 = 0) & big_f(all_6_1_4) = all_6_0_3
% 2.91/1.48 |
% 2.91/1.48 | Applying alpha-rule on (25) yields:
% 2.91/1.48 | (26) ~ (all_6_0_3 = 0)
% 2.91/1.48 | (27) big_f(all_6_1_4) = all_6_0_3
% 2.91/1.48 |
% 2.91/1.48 +-Applying beta-rule and splitting (6), into two cases.
% 2.91/1.48 |-Branch one:
% 2.91/1.48 | (9) ~ (all_0_0_0 = 0) & big_f(all_0_1_1) = all_0_0_0 & p
% 2.91/1.48 |
% 2.91/1.48 | Applying alpha-rule on (9) yields:
% 2.91/1.48 | (10) ~ (all_0_0_0 = 0)
% 2.91/1.48 | (11) big_f(all_0_1_1) = all_0_0_0
% 2.91/1.48 | (8) p
% 2.91/1.48 |
% 2.91/1.48 | Using (8) and (13) yields:
% 2.91/1.48 | (14) $false
% 2.91/1.48 |
% 2.91/1.48 |-The branch is then unsatisfiable
% 2.91/1.48 |-Branch two:
% 2.91/1.48 | (19) ~ p & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1))
% 2.91/1.48 |
% 2.91/1.48 | Applying alpha-rule on (19) yields:
% 2.91/1.48 | (13) ~ p
% 2.91/1.48 | (21) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1))
% 2.91/1.48 |
% 2.91/1.48 | Instantiating formula (21) with all_6_0_3, all_6_1_4 and discharging atoms big_f(all_6_1_4) = all_6_0_3, yields:
% 2.91/1.48 | (36) all_6_0_3 = 0
% 2.91/1.48 |
% 2.91/1.48 | Equations (36) can reduce 26 to:
% 2.91/1.48 | (18) $false
% 2.91/1.48 |
% 2.91/1.48 |-The branch is then unsatisfiable
% 2.91/1.48 % SZS output end Proof for theBenchmark
% 2.91/1.48
% 2.91/1.48 786ms
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