TSTP Solution File: SYN967+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN967+1 : TPTP v8.1.0. Released v3.1.0.
% 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 05:06:09 EDT 2022
% Result : Theorem 2.33s 1.28s
% Output : Proof 3.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SYN967+1 : TPTP v8.1.0. Released v3.1.0.
% 0.09/0.12 % 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 : Tue Jul 12 09:17:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.57 ____ _
% 0.19/0.57 ___ / __ \_____(_)___ ________ __________
% 0.19/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.57
% 0.19/0.57 A Theorem Prover for First-Order Logic
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58 Bug reports to peter@backeman.se
% 0.19/0.58
% 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.28/0.90 Prover 0: Preprocessing ...
% 1.34/0.95 Prover 0: Warning: ignoring some quantifiers
% 1.34/0.96 Prover 0: Constructing countermodel ...
% 1.51/1.06 Prover 0: gave up
% 1.51/1.06 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.76/1.08 Prover 1: Preprocessing ...
% 1.76/1.13 Prover 1: Constructing countermodel ...
% 1.76/1.17 Prover 1: gave up
% 1.76/1.17 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.76/1.18 Prover 2: Preprocessing ...
% 2.27/1.22 Prover 2: Warning: ignoring some quantifiers
% 2.27/1.22 Prover 2: Constructing countermodel ...
% 2.33/1.28 Prover 2: proved (112ms)
% 2.33/1.28
% 2.33/1.28 No countermodel exists, formula is valid
% 2.33/1.28 % SZS status Theorem for theBenchmark
% 2.33/1.28
% 2.33/1.28 Generating proof ... Warning: ignoring some quantifiers
% 3.01/1.50 found it (size 50)
% 3.01/1.50
% 3.01/1.50 % SZS output start Proof for theBenchmark
% 3.01/1.50 Assumed formulas after preprocessing and simplification:
% 3.01/1.50 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (p(v1) = v3 & p(v0) = v2 & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (p(v6) = v5) | ~ (p(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (q(v6) = v5) | ~ (q(v6) = v4)) & ! [v4] : ! [v5] : ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (p(v4) = v5)) & ! [v4] : ! [v5] : ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (q(v4) = v5)) & ! [v4] : ! [v5] : ( ~ (v3 = 0) | v5 = 0 | ~ (p(v4) = v5)) & ! [v4] : ! [v5] : ( ~ (v3 = 0) | ~ (q(v4) = v5) | p(v4) = 0) & ! [v4] : ! [v5] : ( ~ (v2 = 0) | v5 = 0 | ~ (q(v4) = v5)) & ! [v4] : ! [v5] : ( ~ (v2 = 0) | ~ (p(v4) = v5) | q(v4) = 0) & ! [v4] : ! [v5] : (v5 = 0 | ~ (p(v4) = v5) | q(v4) = 0) & ! [v4] : ! [v5] : (v5 = 0 | ~ (p(v4) = v5) | ? [v6] : ( ~ (v6 = 0) & q(v4) = v6)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (q(v4) = v5) | p(v4) = 0) & ! [v4] : ( ~ (q(v4) = 0) | p(v4) = 0) & ? [v4] : ? [v5] : p(v4) = v5 & ? [v4] : ? [v5] : q(v4) = v5)
% 3.16/1.53 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 3.16/1.53 | (1) p(all_0_2_2) = all_0_0_0 & p(all_0_3_3) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0)) & ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0) | ~ (p(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0) | ~ (q(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | v1 = 0 | ~ (p(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | ~ (q(v0) = v1) | p(v0) = 0) & ! [v0] : ! [v1] : ( ~ (all_0_1_1 = 0) | v1 = 0 | ~ (q(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (all_0_1_1 = 0) | ~ (p(v0) = v1) | q(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (p(v0) = v1) | q(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (p(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & q(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (q(v0) = v1) | p(v0) = 0) & ! [v0] : ( ~ (q(v0) = 0) | p(v0) = 0) & ? [v0] : ? [v1] : p(v0) = v1 & ? [v0] : ? [v1] : q(v0) = v1
% 3.16/1.53 |
% 3.16/1.53 | Applying alpha-rule on (1) yields:
% 3.16/1.53 | (2) ! [v0] : ! [v1] : ( ~ (all_0_1_1 = 0) | ~ (p(v0) = v1) | q(v0) = 0)
% 3.16/1.53 | (3) ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | ~ (q(v0) = v1) | p(v0) = 0)
% 3.16/1.53 | (4) ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0) | ~ (p(v0) = v1))
% 3.16/1.54 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (p(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & q(v0) = v2))
% 3.24/1.54 | (6) ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0) | ~ (q(v0) = v1))
% 3.24/1.54 | (7) ! [v0] : ( ~ (q(v0) = 0) | p(v0) = 0)
% 3.24/1.54 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0))
% 3.24/1.54 | (9) ? [v0] : ? [v1] : q(v0) = v1
% 3.24/1.54 | (10) ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | v1 = 0 | ~ (p(v0) = v1))
% 3.24/1.54 | (11) ! [v0] : ! [v1] : ( ~ (all_0_1_1 = 0) | v1 = 0 | ~ (q(v0) = v1))
% 3.24/1.54 | (12) p(all_0_2_2) = all_0_0_0
% 3.24/1.54 | (13) p(all_0_3_3) = all_0_1_1
% 3.24/1.54 | (14) ? [v0] : ? [v1] : p(v0) = v1
% 3.24/1.54 | (15) ! [v0] : ! [v1] : (v1 = 0 | ~ (q(v0) = v1) | p(v0) = 0)
% 3.24/1.54 | (16) ! [v0] : ! [v1] : (v1 = 0 | ~ (p(v0) = v1) | q(v0) = 0)
% 3.24/1.54 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0))
% 3.24/1.54 |
% 3.24/1.54 | Instantiating (9) with all_3_0_4, all_3_1_5 yields:
% 3.24/1.54 | (18) q(all_3_1_5) = all_3_0_4
% 3.24/1.54 |
% 3.24/1.54 | Instantiating formula (4) with 0, all_0_3_3 yields:
% 3.24/1.54 | (19) ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0) | ~ (p(all_0_3_3) = 0)
% 3.24/1.54 |
% 3.24/1.54 | Instantiating formula (11) with all_3_0_4, all_3_1_5 and discharging atoms q(all_3_1_5) = all_3_0_4, yields:
% 3.24/1.54 | (20) ~ (all_0_1_1 = 0) | all_3_0_4 = 0
% 3.24/1.54 |
% 3.24/1.54 | Instantiating formula (2) with all_0_0_0, all_0_2_2 and discharging atoms p(all_0_2_2) = all_0_0_0, yields:
% 3.24/1.54 | (21) ~ (all_0_1_1 = 0) | q(all_0_2_2) = 0
% 3.24/1.54 |
% 3.24/1.54 | Instantiating formula (5) with all_0_0_0, all_0_2_2 and discharging atoms p(all_0_2_2) = all_0_0_0, yields:
% 3.24/1.54 | (22) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & q(all_0_2_2) = v0)
% 3.24/1.54 |
% 3.24/1.54 | Instantiating formula (2) with 0, all_0_3_3 yields:
% 3.24/1.54 | (23) ~ (all_0_1_1 = 0) | ~ (p(all_0_3_3) = 0) | q(all_0_3_3) = 0
% 3.24/1.54 |
% 3.24/1.54 | Instantiating formula (16) with all_0_1_1, all_0_3_3 and discharging atoms p(all_0_3_3) = all_0_1_1, yields:
% 3.24/1.54 | (24) all_0_1_1 = 0 | q(all_0_3_3) = 0
% 3.24/1.54 |
% 3.24/1.54 | Instantiating formula (5) with all_0_1_1, all_0_3_3 and discharging atoms p(all_0_3_3) = all_0_1_1, yields:
% 3.24/1.54 | (25) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & q(all_0_3_3) = v0)
% 3.24/1.54 |
% 3.24/1.54 +-Applying beta-rule and splitting (24), into two cases.
% 3.24/1.54 |-Branch one:
% 3.24/1.54 | (26) q(all_0_3_3) = 0
% 3.24/1.54 |
% 3.24/1.54 +-Applying beta-rule and splitting (25), into two cases.
% 3.24/1.54 |-Branch one:
% 3.24/1.54 | (27) all_0_1_1 = 0
% 3.24/1.54 |
% 3.24/1.54 | From (27) and (13) follows:
% 3.24/1.54 | (28) p(all_0_3_3) = 0
% 3.24/1.54 |
% 3.24/1.54 +-Applying beta-rule and splitting (19), into two cases.
% 3.24/1.54 |-Branch one:
% 3.24/1.54 | (29) ~ (p(all_0_3_3) = 0)
% 3.24/1.54 |
% 3.24/1.54 | Using (28) and (29) yields:
% 3.24/1.55 | (30) $false
% 3.24/1.55 |
% 3.24/1.55 |-The branch is then unsatisfiable
% 3.24/1.55 |-Branch two:
% 3.24/1.55 | (28) p(all_0_3_3) = 0
% 3.24/1.55 | (32) ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)
% 3.24/1.55 |
% 3.24/1.55 +-Applying beta-rule and splitting (32), into two cases.
% 3.24/1.55 |-Branch one:
% 3.24/1.55 | (33) ~ (all_0_0_0 = 0)
% 3.24/1.55 |
% 3.24/1.55 +-Applying beta-rule and splitting (21), into two cases.
% 3.24/1.55 |-Branch one:
% 3.24/1.55 | (34) q(all_0_2_2) = 0
% 3.24/1.55 |
% 3.24/1.55 +-Applying beta-rule and splitting (22), into two cases.
% 3.24/1.55 |-Branch one:
% 3.24/1.55 | (35) all_0_0_0 = 0
% 3.24/1.55 |
% 3.24/1.55 | Equations (35) can reduce 33 to:
% 3.24/1.55 | (36) $false
% 3.24/1.55 |
% 3.24/1.55 |-The branch is then unsatisfiable
% 3.24/1.55 |-Branch two:
% 3.24/1.55 | (33) ~ (all_0_0_0 = 0)
% 3.24/1.55 | (38) ? [v0] : ( ~ (v0 = 0) & q(all_0_2_2) = v0)
% 3.24/1.55 |
% 3.24/1.55 | Instantiating (38) with all_45_0_8 yields:
% 3.24/1.55 | (39) ~ (all_45_0_8 = 0) & q(all_0_2_2) = all_45_0_8
% 3.24/1.55 |
% 3.24/1.55 | Applying alpha-rule on (39) yields:
% 3.24/1.55 | (40) ~ (all_45_0_8 = 0)
% 3.24/1.55 | (41) q(all_0_2_2) = all_45_0_8
% 3.24/1.55 |
% 3.24/1.55 | Instantiating formula (8) with all_0_2_2, 0, all_45_0_8 and discharging atoms q(all_0_2_2) = all_45_0_8, q(all_0_2_2) = 0, yields:
% 3.24/1.55 | (42) all_45_0_8 = 0
% 3.24/1.55 |
% 3.24/1.55 | Equations (42) can reduce 40 to:
% 3.24/1.55 | (36) $false
% 3.24/1.55 |
% 3.24/1.55 |-The branch is then unsatisfiable
% 3.24/1.55 |-Branch two:
% 3.24/1.55 | (44) ~ (q(all_0_2_2) = 0)
% 3.24/1.55 | (45) ~ (all_0_1_1 = 0)
% 3.24/1.55 |
% 3.24/1.55 | Equations (27) can reduce 45 to:
% 3.24/1.55 | (36) $false
% 3.24/1.55 |
% 3.24/1.55 |-The branch is then unsatisfiable
% 3.24/1.55 |-Branch two:
% 3.24/1.55 | (35) all_0_0_0 = 0
% 3.24/1.55 | (45) ~ (all_0_1_1 = 0)
% 3.24/1.55 |
% 3.24/1.55 | Equations (27) can reduce 45 to:
% 3.24/1.55 | (36) $false
% 3.24/1.55 |
% 3.24/1.55 |-The branch is then unsatisfiable
% 3.24/1.55 |-Branch two:
% 3.24/1.55 | (45) ~ (all_0_1_1 = 0)
% 3.24/1.55 | (51) ? [v0] : ( ~ (v0 = 0) & q(all_0_3_3) = v0)
% 3.24/1.55 |
% 3.24/1.55 | Instantiating (51) with all_25_0_9 yields:
% 3.24/1.55 | (52) ~ (all_25_0_9 = 0) & q(all_0_3_3) = all_25_0_9
% 3.24/1.55 |
% 3.24/1.55 | Applying alpha-rule on (52) yields:
% 3.24/1.55 | (53) ~ (all_25_0_9 = 0)
% 3.24/1.55 | (54) q(all_0_3_3) = all_25_0_9
% 3.24/1.55 |
% 3.24/1.55 | Instantiating formula (8) with all_0_3_3, 0, all_25_0_9 and discharging atoms q(all_0_3_3) = all_25_0_9, q(all_0_3_3) = 0, yields:
% 3.24/1.55 | (55) all_25_0_9 = 0
% 3.24/1.55 |
% 3.24/1.55 | Equations (55) can reduce 53 to:
% 3.24/1.55 | (36) $false
% 3.24/1.55 |
% 3.24/1.55 |-The branch is then unsatisfiable
% 3.24/1.55 |-Branch two:
% 3.24/1.55 | (57) ~ (q(all_0_3_3) = 0)
% 3.24/1.55 | (27) all_0_1_1 = 0
% 3.24/1.55 |
% 3.24/1.55 | From (27) and (13) follows:
% 3.24/1.55 | (28) p(all_0_3_3) = 0
% 3.24/1.55 |
% 3.24/1.55 +-Applying beta-rule and splitting (20), into two cases.
% 3.24/1.55 |-Branch one:
% 3.24/1.55 | (45) ~ (all_0_1_1 = 0)
% 3.24/1.55 |
% 3.24/1.55 | Equations (27) can reduce 45 to:
% 3.24/1.55 | (36) $false
% 3.24/1.55 |
% 3.24/1.55 |-The branch is then unsatisfiable
% 3.24/1.55 |-Branch two:
% 3.24/1.55 | (27) all_0_1_1 = 0
% 3.24/1.55 | (63) all_3_0_4 = 0
% 3.24/1.55 |
% 3.24/1.55 +-Applying beta-rule and splitting (19), into two cases.
% 3.24/1.55 |-Branch one:
% 3.24/1.55 | (29) ~ (p(all_0_3_3) = 0)
% 3.24/1.55 |
% 3.24/1.55 | Using (28) and (29) yields:
% 3.24/1.55 | (30) $false
% 3.24/1.55 |
% 3.24/1.55 |-The branch is then unsatisfiable
% 3.24/1.55 |-Branch two:
% 3.24/1.55 | (28) p(all_0_3_3) = 0
% 3.24/1.55 | (32) ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)
% 3.24/1.55 |
% 3.24/1.55 +-Applying beta-rule and splitting (23), into two cases.
% 3.24/1.55 |-Branch one:
% 3.24/1.55 | (29) ~ (p(all_0_3_3) = 0)
% 3.24/1.55 |
% 3.24/1.55 | Using (28) and (29) yields:
% 3.24/1.55 | (30) $false
% 3.24/1.55 |
% 3.24/1.55 |-The branch is then unsatisfiable
% 3.24/1.55 |-Branch two:
% 3.24/1.55 | (28) p(all_0_3_3) = 0
% 3.24/1.55 | (71) ~ (all_0_1_1 = 0) | q(all_0_3_3) = 0
% 3.24/1.55 |
% 3.24/1.55 +-Applying beta-rule and splitting (71), into two cases.
% 3.24/1.55 |-Branch one:
% 3.24/1.55 | (26) q(all_0_3_3) = 0
% 3.24/1.55 |
% 3.24/1.55 | Using (26) and (57) yields:
% 3.24/1.55 | (30) $false
% 3.24/1.55 |
% 3.24/1.55 |-The branch is then unsatisfiable
% 3.24/1.55 |-Branch two:
% 3.24/1.55 | (57) ~ (q(all_0_3_3) = 0)
% 3.24/1.56 | (45) ~ (all_0_1_1 = 0)
% 3.24/1.56 |
% 3.24/1.56 | Equations (27) can reduce 45 to:
% 3.24/1.56 | (36) $false
% 3.24/1.56 |
% 3.24/1.56 |-The branch is then unsatisfiable
% 3.24/1.56 % SZS output end Proof for theBenchmark
% 3.24/1.56
% 3.24/1.56 969ms
%------------------------------------------------------------------------------