TSTP Solution File: SYN367+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN367+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n022.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 05:01:51 EDT 2022
% Result : Theorem 2.37s 1.28s
% Output : Proof 2.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN367+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n022.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 14:52:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.49/0.62 ____ _
% 0.49/0.62 ___ / __ \_____(_)___ ________ __________
% 0.49/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.62
% 0.49/0.62 A Theorem Prover for First-Order Logic
% 0.49/0.62 (ePrincess v.1.0)
% 0.49/0.62
% 0.49/0.62 (c) Philipp Rümmer, 2009-2015
% 0.49/0.63 (c) Peter Backeman, 2014-2015
% 0.49/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.66/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.66/0.63 Bug reports to peter@backeman.se
% 0.66/0.63
% 0.66/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.66/0.63
% 0.66/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.31/0.93 Prover 0: Preprocessing ...
% 1.31/0.98 Prover 0: Warning: ignoring some quantifiers
% 1.44/1.00 Prover 0: Constructing countermodel ...
% 1.71/1.09 Prover 0: gave up
% 1.71/1.09 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.71/1.11 Prover 1: Preprocessing ...
% 1.92/1.15 Prover 1: Constructing countermodel ...
% 2.05/1.21 Prover 1: gave up
% 2.05/1.21 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.05/1.22 Prover 2: Preprocessing ...
% 2.25/1.25 Prover 2: Warning: ignoring some quantifiers
% 2.25/1.25 Prover 2: Constructing countermodel ...
% 2.37/1.28 Prover 2: proved (67ms)
% 2.37/1.28
% 2.37/1.28 No countermodel exists, formula is valid
% 2.37/1.28 % SZS status Theorem for theBenchmark
% 2.37/1.28
% 2.37/1.28 Generating proof ... Warning: ignoring some quantifiers
% 2.68/1.42 found it (size 9)
% 2.68/1.42
% 2.68/1.42 % SZS output start Proof for theBenchmark
% 2.68/1.42 Assumed formulas after preprocessing and simplification:
% 2.68/1.42 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & ~ (v1 = 0) & big_r(v0) = v1 & big_q(v2) = v3 & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (big_r(v6) = v5) | ~ (big_r(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (big_q(v6) = v5) | ~ (big_q(v6) = v4)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (big_r(v4) = v5) | big_q(v4) = 0) & ! [v4] : ! [v5] : (v5 = 0 | ~ (big_r(v4) = v5) | p) & ! [v4] : ! [v5] : (v5 = 0 | ~ (big_q(v4) = v5) | ~ p) & ! [v4] : ! [v5] : (v5 = 0 | ~ (big_q(v4) = v5) | big_r(v4) = 0) & ! [v4] : ! [v5] : ( ~ (big_r(v4) = v5) | ~ p | big_q(v4) = 0) & ! [v4] : ! [v5] : ( ~ (big_q(v4) = v5) | big_r(v4) = 0 | p) & ? [v4] : ? [v5] : big_r(v4) = v5 & ? [v4] : ? [v5] : big_q(v4) = v5)
% 2.84/1.46 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 2.84/1.46 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_2_2 = 0) & big_r(all_0_3_3) = all_0_2_2 & big_q(all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_r(v2) = v1) | ~ (big_r(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_q(v2) = v1) | ~ (big_q(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_r(v0) = v1) | big_q(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_r(v0) = v1) | p) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ p) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_q(v0) = v1) | big_r(v0) = 0) & ! [v0] : ! [v1] : ( ~ (big_r(v0) = v1) | ~ p | big_q(v0) = 0) & ! [v0] : ! [v1] : ( ~ (big_q(v0) = v1) | big_r(v0) = 0 | p) & ? [v0] : ? [v1] : big_r(v0) = v1 & ? [v0] : ? [v1] : big_q(v0) = v1
% 2.84/1.46 |
% 2.84/1.46 | Applying alpha-rule on (1) yields:
% 2.84/1.46 | (2) ? [v0] : ? [v1] : big_r(v0) = v1
% 2.84/1.46 | (3) big_r(all_0_3_3) = all_0_2_2
% 2.93/1.46 | (4) ! [v0] : ! [v1] : ( ~ (big_r(v0) = v1) | ~ p | big_q(v0) = 0)
% 2.93/1.46 | (5) ~ (all_0_2_2 = 0)
% 2.93/1.46 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_r(v0) = v1) | p)
% 2.93/1.46 | (7) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ p)
% 2.93/1.46 | (8) ~ (all_0_0_0 = 0)
% 2.93/1.46 | (9) ? [v0] : ? [v1] : big_q(v0) = v1
% 2.93/1.46 | (10) ! [v0] : ! [v1] : ( ~ (big_q(v0) = v1) | big_r(v0) = 0 | p)
% 2.93/1.46 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_r(v2) = v1) | ~ (big_r(v2) = v0))
% 2.93/1.46 | (12) big_q(all_0_1_1) = all_0_0_0
% 2.93/1.46 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_q(v2) = v1) | ~ (big_q(v2) = v0))
% 2.93/1.46 | (14) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_q(v0) = v1) | big_r(v0) = 0)
% 2.93/1.46 | (15) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_r(v0) = v1) | big_q(v0) = 0)
% 2.93/1.46 |
% 2.93/1.47 | Instantiating formula (6) with all_0_2_2, all_0_3_3 and discharging atoms big_r(all_0_3_3) = all_0_2_2, yields:
% 2.93/1.47 | (16) all_0_2_2 = 0 | p
% 2.93/1.47 |
% 2.93/1.47 +-Applying beta-rule and splitting (16), into two cases.
% 2.93/1.47 |-Branch one:
% 2.93/1.47 | (17) p
% 2.93/1.47 |
% 2.93/1.47 | Instantiating formula (7) with all_0_0_0, all_0_1_1 and discharging atoms big_q(all_0_1_1) = all_0_0_0, p, yields:
% 2.93/1.47 | (18) all_0_0_0 = 0
% 2.93/1.47 |
% 2.93/1.47 | Equations (18) can reduce 8 to:
% 2.93/1.47 | (19) $false
% 2.93/1.47 |
% 2.93/1.47 |-The branch is then unsatisfiable
% 2.93/1.47 |-Branch two:
% 2.93/1.47 | (20) ~ p
% 2.93/1.47 | (21) all_0_2_2 = 0
% 2.93/1.47 |
% 2.93/1.47 | Equations (21) can reduce 5 to:
% 2.93/1.47 | (19) $false
% 2.93/1.47 |
% 2.93/1.47 |-The branch is then unsatisfiable
% 2.93/1.47 % SZS output end Proof for theBenchmark
% 2.93/1.47
% 2.93/1.47 830ms
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