TSTP Solution File: SYN733+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN733+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.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 05:04:48 EDT 2022
% Result : Theorem 2.65s 1.36s
% Output : Proof 3.17s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN733+1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 19:24:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.67/0.64 ____ _
% 0.67/0.64 ___ / __ \_____(_)___ ________ __________
% 0.67/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.67/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.67/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.67/0.64
% 0.67/0.64 A Theorem Prover for First-Order Logic
% 0.67/0.65 (ePrincess v.1.0)
% 0.67/0.65
% 0.67/0.65 (c) Philipp Rümmer, 2009-2015
% 0.67/0.65 (c) Peter Backeman, 2014-2015
% 0.67/0.65 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.67/0.65 Free software under GNU Lesser General Public License (LGPL).
% 0.67/0.65 Bug reports to peter@backeman.se
% 0.67/0.65
% 0.67/0.65 For more information, visit http://user.uu.se/~petba168/breu/
% 0.67/0.65
% 0.67/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.71 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.31/0.92 Prover 0: Preprocessing ...
% 1.42/0.96 Prover 0: Warning: ignoring some quantifiers
% 1.42/0.98 Prover 0: Constructing countermodel ...
% 1.56/1.07 Prover 0: gave up
% 1.56/1.07 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.56/1.08 Prover 1: Preprocessing ...
% 1.79/1.16 Prover 1: Constructing countermodel ...
% 1.79/1.16 Prover 1: gave up
% 1.79/1.17 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.12/1.18 Prover 2: Preprocessing ...
% 2.32/1.23 Prover 2: Warning: ignoring some quantifiers
% 2.32/1.23 Prover 2: Constructing countermodel ...
% 2.32/1.25 Prover 2: gave up
% 2.32/1.25 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.32/1.26 Prover 3: Preprocessing ...
% 2.32/1.26 Prover 3: Warning: ignoring some quantifiers
% 2.32/1.27 Prover 3: Constructing countermodel ...
% 2.32/1.28 Prover 3: gave up
% 2.32/1.28 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.32/1.29 Prover 4: Preprocessing ...
% 2.32/1.32 Prover 4: Warning: ignoring some quantifiers
% 2.32/1.32 Prover 4: Constructing countermodel ...
% 2.65/1.36 Prover 4: proved (79ms)
% 2.65/1.36
% 2.65/1.36 No countermodel exists, formula is valid
% 2.65/1.36 % SZS status Theorem for theBenchmark
% 2.65/1.36
% 2.65/1.36 Generating proof ... Warning: ignoring some quantifiers
% 3.17/1.53 found it (size 25)
% 3.17/1.53
% 3.17/1.53 % SZS output start Proof for theBenchmark
% 3.17/1.53 Assumed formulas after preprocessing and simplification:
% 3.17/1.53 | (0) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0)) & ! [v0] : ! [v1] : ( ~ (p(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (v1 = 0 & q(v3) = v4 & q(v0) = v2 & (v4 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (q(v0) = v1) | ? [v2] : ? [v3] : (p(v0) = 0 & q(v2) = v3 & (v3 = 0 | v1 = 0))) & ! [v0] : ( ~ (p(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & q(v0) = v1)) & ! [v0] : ( ~ (q(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & p(v0) = v1)) & ? [v0] : ? [v1] : ? [v2] : (p(v0) = v1 & q(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0)))
% 3.17/1.56 | Applying alpha-rule on (0) yields:
% 3.17/1.56 | (1) ! [v0] : ! [v1] : ( ~ (p(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (v1 = 0 & q(v3) = v4 & q(v0) = v2 & (v4 = 0 | v2 = 0)))
% 3.17/1.56 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0))
% 3.17/1.56 | (3) ! [v0] : ! [v1] : ( ~ (q(v0) = v1) | ? [v2] : ? [v3] : (p(v0) = 0 & q(v2) = v3 & (v3 = 0 | v1 = 0)))
% 3.17/1.56 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0))
% 3.17/1.56 | (5) ! [v0] : ( ~ (q(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & p(v0) = v1))
% 3.17/1.56 | (6) ! [v0] : ( ~ (p(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & q(v0) = v1))
% 3.17/1.56 | (7) ? [v0] : ? [v1] : ? [v2] : (p(v0) = v1 & q(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0)))
% 3.17/1.56 |
% 3.17/1.56 | Instantiating (7) with all_1_0_0, all_1_1_1, all_1_2_2 yields:
% 3.17/1.56 | (8) p(all_1_2_2) = all_1_1_1 & q(all_1_2_2) = all_1_0_0 & ( ~ (all_1_0_0 = 0) | ~ (all_1_1_1 = 0))
% 3.17/1.56 |
% 3.17/1.56 | Applying alpha-rule on (8) yields:
% 3.17/1.56 | (9) p(all_1_2_2) = all_1_1_1
% 3.17/1.56 | (10) q(all_1_2_2) = all_1_0_0
% 3.17/1.56 | (11) ~ (all_1_0_0 = 0) | ~ (all_1_1_1 = 0)
% 3.17/1.56 |
% 3.17/1.56 | Instantiating formula (1) with all_1_1_1, all_1_2_2 and discharging atoms p(all_1_2_2) = all_1_1_1, yields:
% 3.17/1.56 | (12) ? [v0] : ? [v1] : ? [v2] : (all_1_1_1 = 0 & q(v1) = v2 & q(all_1_2_2) = v0 & (v2 = 0 | v0 = 0))
% 3.17/1.56 |
% 3.17/1.56 | Instantiating formula (3) with all_1_0_0, all_1_2_2 and discharging atoms q(all_1_2_2) = all_1_0_0, yields:
% 3.17/1.56 | (13) ? [v0] : ? [v1] : (p(all_1_2_2) = 0 & q(v0) = v1 & (v1 = 0 | all_1_0_0 = 0))
% 3.17/1.57 |
% 3.17/1.57 | Instantiating (13) with all_8_0_3, all_8_1_4 yields:
% 3.17/1.57 | (14) p(all_1_2_2) = 0 & q(all_8_1_4) = all_8_0_3 & (all_8_0_3 = 0 | all_1_0_0 = 0)
% 3.17/1.57 |
% 3.17/1.57 | Applying alpha-rule on (14) yields:
% 3.17/1.57 | (15) p(all_1_2_2) = 0
% 3.17/1.57 | (16) q(all_8_1_4) = all_8_0_3
% 3.17/1.57 | (17) all_8_0_3 = 0 | all_1_0_0 = 0
% 3.17/1.57 |
% 3.17/1.57 | Instantiating (12) with all_10_0_5, all_10_1_6, all_10_2_7 yields:
% 3.17/1.57 | (18) all_1_1_1 = 0 & q(all_10_1_6) = all_10_0_5 & q(all_1_2_2) = all_10_2_7 & (all_10_0_5 = 0 | all_10_2_7 = 0)
% 3.17/1.57 |
% 3.17/1.57 | Applying alpha-rule on (18) yields:
% 3.17/1.57 | (19) all_1_1_1 = 0
% 3.17/1.57 | (20) q(all_10_1_6) = all_10_0_5
% 3.17/1.57 | (21) q(all_1_2_2) = all_10_2_7
% 3.17/1.57 | (22) all_10_0_5 = 0 | all_10_2_7 = 0
% 3.17/1.57 |
% 3.17/1.57 +-Applying beta-rule and splitting (11), into two cases.
% 3.17/1.57 |-Branch one:
% 3.17/1.57 | (23) ~ (all_1_0_0 = 0)
% 3.17/1.57 |
% 3.17/1.57 +-Applying beta-rule and splitting (17), into two cases.
% 3.17/1.57 |-Branch one:
% 3.17/1.57 | (24) all_8_0_3 = 0
% 3.17/1.57 |
% 3.17/1.57 | From (24) and (16) follows:
% 3.17/1.57 | (25) q(all_8_1_4) = 0
% 3.17/1.57 |
% 3.17/1.57 | Instantiating formula (5) with all_8_1_4 and discharging atoms q(all_8_1_4) = 0, yields:
% 3.17/1.57 | (26) ? [v0] : ( ~ (v0 = 0) & p(all_8_1_4) = v0)
% 3.17/1.57 |
% 3.17/1.57 | Instantiating formula (3) with 0, all_8_1_4 and discharging atoms q(all_8_1_4) = 0, yields:
% 3.17/1.57 | (27) ? [v0] : ? [v1] : (p(all_8_1_4) = 0 & q(v0) = v1)
% 3.17/1.57 |
% 3.17/1.57 | Instantiating (27) with all_33_0_8, all_33_1_9 yields:
% 3.17/1.57 | (28) p(all_8_1_4) = 0 & q(all_33_1_9) = all_33_0_8
% 3.17/1.57 |
% 3.17/1.57 | Applying alpha-rule on (28) yields:
% 3.17/1.57 | (29) p(all_8_1_4) = 0
% 3.17/1.57 | (30) q(all_33_1_9) = all_33_0_8
% 3.17/1.57 |
% 3.17/1.57 | Instantiating (26) with all_35_0_10 yields:
% 3.17/1.57 | (31) ~ (all_35_0_10 = 0) & p(all_8_1_4) = all_35_0_10
% 3.17/1.57 |
% 3.17/1.57 | Applying alpha-rule on (31) yields:
% 3.17/1.57 | (32) ~ (all_35_0_10 = 0)
% 3.17/1.57 | (33) p(all_8_1_4) = all_35_0_10
% 3.17/1.57 |
% 3.17/1.57 | Instantiating formula (4) with all_8_1_4, 0, all_35_0_10 and discharging atoms p(all_8_1_4) = all_35_0_10, p(all_8_1_4) = 0, yields:
% 3.17/1.57 | (34) all_35_0_10 = 0
% 3.17/1.57 |
% 3.17/1.57 | Equations (34) can reduce 32 to:
% 3.17/1.57 | (35) $false
% 3.17/1.57 |
% 3.17/1.57 |-The branch is then unsatisfiable
% 3.17/1.57 |-Branch two:
% 3.17/1.57 | (36) ~ (all_8_0_3 = 0)
% 3.17/1.57 | (37) all_1_0_0 = 0
% 3.17/1.57 |
% 3.17/1.57 | Equations (37) can reduce 23 to:
% 3.17/1.57 | (35) $false
% 3.17/1.57 |
% 3.17/1.57 |-The branch is then unsatisfiable
% 3.17/1.57 |-Branch two:
% 3.17/1.57 | (37) all_1_0_0 = 0
% 3.17/1.57 | (40) ~ (all_1_1_1 = 0)
% 3.17/1.57 |
% 3.17/1.57 | Equations (19) can reduce 40 to:
% 3.17/1.57 | (35) $false
% 3.17/1.57 |
% 3.17/1.57 |-The branch is then unsatisfiable
% 3.17/1.57 % SZS output end Proof for theBenchmark
% 3.17/1.57
% 3.17/1.57 910ms
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