TSTP Solution File: SYN722+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN722+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n015.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 05:04:41 EDT 2022
% Result : Theorem 2.18s 1.21s
% Output : Proof 3.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN722+1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n015.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 14:33:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.59/0.58 ____ _
% 0.59/0.58 ___ / __ \_____(_)___ ________ __________
% 0.59/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.58
% 0.59/0.58 A Theorem Prover for First-Order Logic
% 0.59/0.58 (ePrincess v.1.0)
% 0.59/0.58
% 0.59/0.58 (c) Philipp Rümmer, 2009-2015
% 0.59/0.58 (c) Peter Backeman, 2014-2015
% 0.59/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.58 Bug reports to peter@backeman.se
% 0.59/0.58
% 0.59/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.58
% 0.59/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.77/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.30/0.88 Prover 0: Preprocessing ...
% 1.42/0.94 Prover 0: Warning: ignoring some quantifiers
% 1.45/0.95 Prover 0: Constructing countermodel ...
% 1.59/1.05 Prover 0: gave up
% 1.59/1.05 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.59/1.07 Prover 1: Preprocessing ...
% 1.86/1.12 Prover 1: Constructing countermodel ...
% 2.18/1.21 Prover 1: proved (156ms)
% 2.18/1.21
% 2.18/1.21 No countermodel exists, formula is valid
% 2.18/1.21 % SZS status Theorem for theBenchmark
% 2.18/1.21
% 2.18/1.21 Generating proof ... found it (size 43)
% 2.65/1.42
% 2.65/1.42 % SZS output start Proof for theBenchmark
% 2.65/1.42 Assumed formulas after preprocessing and simplification:
% 2.65/1.42 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (q(d) = v1 & q(c) = v0 & p(b) = v3 & p(a) = v2 & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (q(v6) = v5) | ~ (q(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (r(v6) = v5) | ~ (r(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (p(v6) = v5) | ~ (p(v6) = v4)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (q(v4) = v5)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (r(v4) = v5) | p(v4) = 0) & ! [v4] : ! [v5] : ( ~ (p(v4) = v5) | ? [v6] : ? [v7] : ? [v8] : (q(v7) = v8 & q(v4) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v5 = 0))) & ( ~ (v3 = 0) | ~ (v2 = 0)))
% 2.65/1.45 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 2.65/1.45 | (1) q(d) = all_0_2_2 & q(c) = all_0_3_3 & p(b) = all_0_0_0 & p(a) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (r(v2) = v1) | ~ (r(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (q(v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (r(v0) = v1) | p(v0) = 0) & ! [v0] : ! [v1] : ( ~ (p(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (q(v3) = v4 & q(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | v1 = 0))) & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))
% 2.65/1.46 |
% 2.65/1.46 | Applying alpha-rule on (1) yields:
% 2.65/1.46 | (2) q(c) = all_0_3_3
% 2.65/1.46 | (3) p(a) = all_0_1_1
% 2.65/1.46 | (4) ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)
% 2.65/1.46 | (5) p(b) = all_0_0_0
% 2.65/1.46 | (6) q(d) = all_0_2_2
% 2.65/1.46 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0))
% 3.04/1.46 | (8) ! [v0] : ! [v1] : ( ~ (p(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (q(v3) = v4 & q(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | v1 = 0)))
% 3.04/1.46 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (r(v2) = v1) | ~ (r(v2) = v0))
% 3.04/1.46 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (r(v0) = v1) | p(v0) = 0)
% 3.04/1.46 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0))
% 3.04/1.46 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (q(v0) = v1))
% 3.04/1.46 |
% 3.04/1.46 | Instantiating formula (12) with all_0_2_2, d and discharging atoms q(d) = all_0_2_2, yields:
% 3.04/1.47 | (13) all_0_2_2 = 0
% 3.04/1.47 |
% 3.04/1.47 | Instantiating formula (12) with all_0_3_3, c and discharging atoms q(c) = all_0_3_3, yields:
% 3.04/1.47 | (14) all_0_3_3 = 0
% 3.04/1.47 |
% 3.04/1.47 | Instantiating formula (8) with all_0_0_0, b and discharging atoms p(b) = all_0_0_0, yields:
% 3.04/1.47 | (15) ? [v0] : ? [v1] : ? [v2] : (q(v1) = v2 & q(b) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0) | ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | all_0_0_0 = 0))
% 3.04/1.47 |
% 3.04/1.47 | Instantiating formula (8) with all_0_1_1, a and discharging atoms p(a) = all_0_1_1, yields:
% 3.04/1.47 | (16) ? [v0] : ? [v1] : ? [v2] : (q(v1) = v2 & q(a) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0) | ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | all_0_1_1 = 0))
% 3.04/1.47 |
% 3.04/1.47 | Instantiating (16) with all_12_0_4, all_12_1_5, all_12_2_6 yields:
% 3.04/1.47 | (17) q(all_12_1_5) = all_12_0_4 & q(a) = all_12_2_6 & ( ~ (all_12_0_4 = 0) | ~ (all_12_2_6 = 0) | ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | all_0_1_1 = 0)
% 3.04/1.47 |
% 3.04/1.47 | Applying alpha-rule on (17) yields:
% 3.04/1.47 | (18) q(all_12_1_5) = all_12_0_4
% 3.04/1.47 | (19) q(a) = all_12_2_6
% 3.04/1.47 | (20) ~ (all_12_0_4 = 0) | ~ (all_12_2_6 = 0) | ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | all_0_1_1 = 0
% 3.04/1.47 |
% 3.04/1.47 | Instantiating (15) with all_14_0_7, all_14_1_8, all_14_2_9 yields:
% 3.04/1.47 | (21) q(all_14_1_8) = all_14_0_7 & q(b) = all_14_2_9 & ( ~ (all_14_0_7 = 0) | ~ (all_14_2_9 = 0) | ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | all_0_0_0 = 0)
% 3.04/1.47 |
% 3.04/1.47 | Applying alpha-rule on (21) yields:
% 3.04/1.47 | (22) q(all_14_1_8) = all_14_0_7
% 3.04/1.47 | (23) q(b) = all_14_2_9
% 3.04/1.47 | (24) ~ (all_14_0_7 = 0) | ~ (all_14_2_9 = 0) | ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | all_0_0_0 = 0
% 3.04/1.47 |
% 3.04/1.47 | Instantiating formula (12) with all_14_0_7, all_14_1_8 and discharging atoms q(all_14_1_8) = all_14_0_7, yields:
% 3.04/1.47 | (25) all_14_0_7 = 0
% 3.04/1.47 |
% 3.04/1.47 | Instantiating formula (12) with all_12_0_4, all_12_1_5 and discharging atoms q(all_12_1_5) = all_12_0_4, yields:
% 3.04/1.47 | (26) all_12_0_4 = 0
% 3.04/1.47 |
% 3.04/1.47 | Instantiating formula (12) with all_14_2_9, b and discharging atoms q(b) = all_14_2_9, yields:
% 3.04/1.47 | (27) all_14_2_9 = 0
% 3.04/1.47 |
% 3.04/1.47 | Instantiating formula (12) with all_12_2_6, a and discharging atoms q(a) = all_12_2_6, yields:
% 3.04/1.47 | (28) all_12_2_6 = 0
% 3.04/1.47 |
% 3.04/1.47 +-Applying beta-rule and splitting (24), into two cases.
% 3.04/1.47 |-Branch one:
% 3.04/1.47 | (29) ~ (all_14_0_7 = 0)
% 3.04/1.47 |
% 3.04/1.47 | Equations (25) can reduce 29 to:
% 3.04/1.47 | (30) $false
% 3.04/1.47 |
% 3.04/1.47 |-The branch is then unsatisfiable
% 3.04/1.47 |-Branch two:
% 3.04/1.47 | (25) all_14_0_7 = 0
% 3.04/1.47 | (32) ~ (all_14_2_9 = 0) | ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | all_0_0_0 = 0
% 3.04/1.47 |
% 3.04/1.47 +-Applying beta-rule and splitting (32), into two cases.
% 3.04/1.47 |-Branch one:
% 3.04/1.47 | (33) ~ (all_14_2_9 = 0)
% 3.04/1.47 |
% 3.04/1.47 | Equations (27) can reduce 33 to:
% 3.04/1.47 | (30) $false
% 3.04/1.47 |
% 3.04/1.47 |-The branch is then unsatisfiable
% 3.04/1.47 |-Branch two:
% 3.04/1.47 | (27) all_14_2_9 = 0
% 3.04/1.47 | (36) ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | all_0_0_0 = 0
% 3.04/1.48 |
% 3.04/1.48 +-Applying beta-rule and splitting (36), into two cases.
% 3.04/1.48 |-Branch one:
% 3.04/1.48 | (37) ~ (all_0_2_2 = 0)
% 3.04/1.48 |
% 3.04/1.48 | Equations (13) can reduce 37 to:
% 3.04/1.48 | (30) $false
% 3.04/1.48 |
% 3.04/1.48 |-The branch is then unsatisfiable
% 3.04/1.48 |-Branch two:
% 3.04/1.48 | (13) all_0_2_2 = 0
% 3.04/1.48 | (40) ~ (all_0_3_3 = 0) | all_0_0_0 = 0
% 3.04/1.48 |
% 3.04/1.48 +-Applying beta-rule and splitting (40), into two cases.
% 3.04/1.48 |-Branch one:
% 3.04/1.48 | (41) ~ (all_0_3_3 = 0)
% 3.04/1.48 |
% 3.04/1.48 | Equations (14) can reduce 41 to:
% 3.04/1.48 | (30) $false
% 3.04/1.48 |
% 3.04/1.48 |-The branch is then unsatisfiable
% 3.04/1.48 |-Branch two:
% 3.04/1.48 | (14) all_0_3_3 = 0
% 3.04/1.48 | (44) all_0_0_0 = 0
% 3.04/1.48 |
% 3.04/1.48 +-Applying beta-rule and splitting (4), into two cases.
% 3.04/1.48 |-Branch one:
% 3.04/1.48 | (45) ~ (all_0_0_0 = 0)
% 3.04/1.48 |
% 3.04/1.48 | Equations (44) can reduce 45 to:
% 3.04/1.48 | (30) $false
% 3.04/1.48 |
% 3.04/1.48 |-The branch is then unsatisfiable
% 3.04/1.48 |-Branch two:
% 3.04/1.48 | (44) all_0_0_0 = 0
% 3.04/1.48 | (48) ~ (all_0_1_1 = 0)
% 3.04/1.48 |
% 3.04/1.48 +-Applying beta-rule and splitting (20), into two cases.
% 3.04/1.48 |-Branch one:
% 3.04/1.48 | (49) ~ (all_12_0_4 = 0)
% 3.04/1.48 |
% 3.04/1.48 | Equations (26) can reduce 49 to:
% 3.04/1.48 | (30) $false
% 3.04/1.48 |
% 3.04/1.48 |-The branch is then unsatisfiable
% 3.04/1.48 |-Branch two:
% 3.04/1.48 | (26) all_12_0_4 = 0
% 3.04/1.48 | (52) ~ (all_12_2_6 = 0) | ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | all_0_1_1 = 0
% 3.04/1.48 |
% 3.04/1.48 +-Applying beta-rule and splitting (52), into two cases.
% 3.04/1.48 |-Branch one:
% 3.04/1.48 | (53) ~ (all_12_2_6 = 0)
% 3.04/1.48 |
% 3.04/1.48 | Equations (28) can reduce 53 to:
% 3.04/1.48 | (30) $false
% 3.04/1.48 |
% 3.04/1.48 |-The branch is then unsatisfiable
% 3.04/1.48 |-Branch two:
% 3.04/1.48 | (28) all_12_2_6 = 0
% 3.04/1.48 | (56) ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | all_0_1_1 = 0
% 3.04/1.48 |
% 3.04/1.48 +-Applying beta-rule and splitting (56), into two cases.
% 3.04/1.48 |-Branch one:
% 3.04/1.48 | (37) ~ (all_0_2_2 = 0)
% 3.04/1.48 |
% 3.04/1.48 | Equations (13) can reduce 37 to:
% 3.04/1.48 | (30) $false
% 3.04/1.48 |
% 3.04/1.48 |-The branch is then unsatisfiable
% 3.04/1.48 |-Branch two:
% 3.04/1.48 | (13) all_0_2_2 = 0
% 3.04/1.48 | (60) ~ (all_0_3_3 = 0) | all_0_1_1 = 0
% 3.04/1.48 |
% 3.04/1.48 +-Applying beta-rule and splitting (60), into two cases.
% 3.04/1.48 |-Branch one:
% 3.04/1.48 | (41) ~ (all_0_3_3 = 0)
% 3.04/1.48 |
% 3.04/1.48 | Equations (14) can reduce 41 to:
% 3.04/1.48 | (30) $false
% 3.04/1.48 |
% 3.04/1.48 |-The branch is then unsatisfiable
% 3.04/1.48 |-Branch two:
% 3.04/1.48 | (14) all_0_3_3 = 0
% 3.04/1.48 | (64) all_0_1_1 = 0
% 3.04/1.48 |
% 3.04/1.48 | Equations (64) can reduce 48 to:
% 3.04/1.48 | (30) $false
% 3.04/1.48 |
% 3.04/1.48 |-The branch is then unsatisfiable
% 3.04/1.48 % SZS output end Proof for theBenchmark
% 3.04/1.48
% 3.04/1.48 889ms
%------------------------------------------------------------------------------