TSTP Solution File: KRS141+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KRS141+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n032.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 : Sun Jul 17 02:56:41 EDT 2022
% Result : Theorem 2.09s 1.18s
% Output : Proof 2.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : KRS141+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.10 % Command : ePrincess-casc -timeout=%d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Tue Jun 7 13:35:35 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.14/0.50 ____ _
% 0.14/0.50 ___ / __ \_____(_)___ ________ __________
% 0.14/0.50 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.14/0.50 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.14/0.50 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.14/0.50
% 0.14/0.50 A Theorem Prover for First-Order Logic
% 0.14/0.50 (ePrincess v.1.0)
% 0.14/0.50
% 0.14/0.50 (c) Philipp Rümmer, 2009-2015
% 0.14/0.50 (c) Peter Backeman, 2014-2015
% 0.14/0.50 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.14/0.50 Free software under GNU Lesser General Public License (LGPL).
% 0.14/0.50 Bug reports to peter@backeman.se
% 0.14/0.50
% 0.14/0.50 For more information, visit http://user.uu.se/~petba168/breu/
% 0.14/0.50
% 0.14/0.50 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.57/0.56 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.09/0.79 Prover 0: Preprocessing ...
% 1.24/0.86 Prover 0: Warning: ignoring some quantifiers
% 1.24/0.88 Prover 0: Constructing countermodel ...
% 1.59/0.99 Prover 0: gave up
% 1.59/0.99 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.59/1.01 Prover 1: Preprocessing ...
% 1.94/1.10 Prover 1: Constructing countermodel ...
% 2.09/1.18 Prover 1: proved (190ms)
% 2.09/1.18
% 2.09/1.18 No countermodel exists, formula is valid
% 2.09/1.18 % SZS status Theorem for theBenchmark
% 2.09/1.18
% 2.09/1.18 Generating proof ... found it (size 45)
% 2.65/1.35
% 2.65/1.35 % SZS output start Proof for theBenchmark
% 2.65/1.35 Assumed formulas after preprocessing and simplification:
% 2.65/1.35 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (cr(ii) = 0 & rp(ii, io) = 0 & cc(io) = v0 & cowlThing(io) = 0 & cowlThing(ii) = 0 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (rp(v7, v6) = v5) | ~ (rp(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (cr(v6) = v5) | ~ (cr(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (cc(v6) = v5) | ~ (cc(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (xsd_string(v6) = v5) | ~ (xsd_string(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (xsd_integer(v6) = v5) | ~ (xsd_integer(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (cowlNothing(v6) = v5) | ~ (cowlNothing(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (cowlThing(v6) = v5) | ~ (cowlThing(v6) = v4)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (xsd_string(v4) = v5) | xsd_integer(v4) = 0) & ! [v4] : ! [v5] : (v5 = 0 | ~ (cowlThing(v4) = v5)) & ! [v4] : ! [v5] : ( ~ (cr(v4) = 0) | ~ (rp(v4, v5) = 0) | cc(v5) = 0) & ! [v4] : ( ~ (xsd_string(v4) = 0) | ? [v5] : ( ~ (v5 = 0) & xsd_integer(v4) = v5)) & ! [v4] : ~ (cowlNothing(v4) = 0) & ( ~ (v0 = 0) | (xsd_string(v1) = v2 & xsd_integer(v1) = v3 & ((v3 = 0 & v2 = 0) | ( ~ (v3 = 0) & ~ (v2 = 0)))) | (cowlNothing(v1) = v3 & cowlThing(v1) = v2 & ( ~ (v2 = 0) | v3 = 0))))
% 2.81/1.39 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 2.81/1.39 | (1) cr(ii) = 0 & rp(ii, io) = 0 & cc(io) = all_0_3_3 & cowlThing(io) = 0 & cowlThing(ii) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cr(v2) = v1) | ~ (cr(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cc(v2) = v1) | ~ (cc(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (cr(v0) = 0) | ~ (rp(v0, v1) = 0) | cc(v1) = 0) & ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) & ! [v0] : ~ (cowlNothing(v0) = 0) & ( ~ (all_0_3_3 = 0) | (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)))
% 2.81/1.39 |
% 2.81/1.39 | Applying alpha-rule on (1) yields:
% 2.81/1.39 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cc(v2) = v1) | ~ (cc(v2) = v0))
% 2.81/1.40 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 2.81/1.40 | (4) ~ (all_0_3_3 = 0) | (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0))
% 2.81/1.40 | (5) cc(io) = all_0_3_3
% 2.81/1.40 | (6) cowlThing(ii) = 0
% 2.81/1.40 | (7) ! [v0] : ! [v1] : ( ~ (cr(v0) = 0) | ~ (rp(v0, v1) = 0) | cc(v1) = 0)
% 2.81/1.40 | (8) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 2.81/1.40 | (9) rp(ii, io) = 0
% 2.81/1.40 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0))
% 2.81/1.40 | (11) cr(ii) = 0
% 2.81/1.40 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0)
% 2.81/1.40 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0))
% 2.81/1.40 | (14) cowlThing(io) = 0
% 2.81/1.40 | (15) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1))
% 2.81/1.40 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0))
% 2.81/1.40 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0))
% 2.81/1.40 | (18) ! [v0] : ~ (cowlNothing(v0) = 0)
% 2.81/1.40 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cr(v2) = v1) | ~ (cr(v2) = v0))
% 2.81/1.40 |
% 2.81/1.40 | Instantiating formula (7) with io, ii and discharging atoms cr(ii) = 0, rp(ii, io) = 0, yields:
% 2.81/1.40 | (20) cc(io) = 0
% 2.81/1.40 |
% 2.81/1.40 | Instantiating formula (2) with io, 0, all_0_3_3 and discharging atoms cc(io) = all_0_3_3, cc(io) = 0, yields:
% 2.81/1.40 | (21) all_0_3_3 = 0
% 2.81/1.40 |
% 2.81/1.40 +-Applying beta-rule and splitting (4), into two cases.
% 2.81/1.40 |-Branch one:
% 2.81/1.40 | (22) ~ (all_0_3_3 = 0)
% 2.81/1.40 |
% 2.81/1.40 | Equations (21) can reduce 22 to:
% 2.81/1.40 | (23) $false
% 2.81/1.40 |
% 2.81/1.40 |-The branch is then unsatisfiable
% 2.81/1.40 |-Branch two:
% 2.81/1.40 | (21) all_0_3_3 = 0
% 2.81/1.40 | (25) (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0))
% 2.81/1.41 |
% 2.81/1.41 +-Applying beta-rule and splitting (25), into two cases.
% 2.81/1.41 |-Branch one:
% 2.81/1.41 | (26) xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))
% 2.81/1.41 |
% 2.81/1.41 | Applying alpha-rule on (26) yields:
% 2.81/1.41 | (27) xsd_string(all_0_2_2) = all_0_1_1
% 2.81/1.41 | (28) xsd_integer(all_0_2_2) = all_0_0_0
% 2.81/1.41 | (29) (all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0))
% 2.81/1.41 |
% 2.81/1.41 | Instantiating formula (8) with all_0_2_2 yields:
% 2.81/1.41 | (30) ~ (xsd_string(all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0)
% 2.81/1.41 |
% 2.81/1.41 | Instantiating formula (12) with all_0_1_1, all_0_2_2 and discharging atoms xsd_string(all_0_2_2) = all_0_1_1, yields:
% 2.81/1.41 | (31) all_0_1_1 = 0 | xsd_integer(all_0_2_2) = 0
% 2.81/1.41 |
% 2.81/1.41 +-Applying beta-rule and splitting (31), into two cases.
% 2.81/1.41 |-Branch one:
% 2.81/1.41 | (32) xsd_integer(all_0_2_2) = 0
% 2.81/1.41 |
% 2.81/1.41 | Instantiating formula (3) with all_0_2_2, 0, all_0_0_0 and discharging atoms xsd_integer(all_0_2_2) = all_0_0_0, xsd_integer(all_0_2_2) = 0, yields:
% 2.81/1.41 | (33) all_0_0_0 = 0
% 2.81/1.41 |
% 2.81/1.41 | From (33) and (28) follows:
% 2.81/1.41 | (32) xsd_integer(all_0_2_2) = 0
% 2.81/1.41 |
% 2.81/1.41 +-Applying beta-rule and splitting (30), into two cases.
% 2.81/1.41 |-Branch one:
% 2.81/1.41 | (35) ~ (xsd_string(all_0_2_2) = 0)
% 2.81/1.41 |
% 2.81/1.41 +-Applying beta-rule and splitting (29), into two cases.
% 2.81/1.41 |-Branch one:
% 2.81/1.41 | (36) all_0_0_0 = 0 & all_0_1_1 = 0
% 2.81/1.41 |
% 2.81/1.41 | Applying alpha-rule on (36) yields:
% 2.81/1.41 | (33) all_0_0_0 = 0
% 2.81/1.41 | (38) all_0_1_1 = 0
% 2.81/1.41 |
% 2.81/1.41 | From (38) and (27) follows:
% 2.81/1.41 | (39) xsd_string(all_0_2_2) = 0
% 2.81/1.41 |
% 2.81/1.41 | Using (39) and (35) yields:
% 2.81/1.41 | (40) $false
% 2.81/1.41 |
% 2.81/1.41 |-The branch is then unsatisfiable
% 2.81/1.41 |-Branch two:
% 2.81/1.41 | (41) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)
% 2.81/1.41 |
% 2.81/1.41 | Applying alpha-rule on (41) yields:
% 2.81/1.41 | (42) ~ (all_0_0_0 = 0)
% 2.81/1.41 | (43) ~ (all_0_1_1 = 0)
% 2.81/1.41 |
% 2.81/1.41 | Equations (33) can reduce 42 to:
% 2.81/1.41 | (23) $false
% 2.81/1.41 |
% 2.81/1.41 |-The branch is then unsatisfiable
% 2.81/1.41 |-Branch two:
% 2.81/1.41 | (39) xsd_string(all_0_2_2) = 0
% 2.81/1.41 | (46) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0)
% 2.81/1.41 |
% 2.81/1.41 | Instantiating (46) with all_42_0_4 yields:
% 2.81/1.41 | (47) ~ (all_42_0_4 = 0) & xsd_integer(all_0_2_2) = all_42_0_4
% 2.81/1.41 |
% 2.81/1.41 | Applying alpha-rule on (47) yields:
% 2.81/1.41 | (48) ~ (all_42_0_4 = 0)
% 2.81/1.41 | (49) xsd_integer(all_0_2_2) = all_42_0_4
% 2.81/1.41 |
% 2.81/1.41 | Instantiating formula (3) with all_0_2_2, all_42_0_4, 0 and discharging atoms xsd_integer(all_0_2_2) = all_42_0_4, xsd_integer(all_0_2_2) = 0, yields:
% 2.81/1.41 | (50) all_42_0_4 = 0
% 2.81/1.41 |
% 2.81/1.41 | Equations (50) can reduce 48 to:
% 2.81/1.41 | (23) $false
% 2.81/1.41 |
% 2.81/1.41 |-The branch is then unsatisfiable
% 2.81/1.41 |-Branch two:
% 2.81/1.41 | (52) ~ (xsd_integer(all_0_2_2) = 0)
% 2.81/1.41 | (38) all_0_1_1 = 0
% 2.81/1.41 |
% 2.81/1.41 +-Applying beta-rule and splitting (29), into two cases.
% 2.81/1.41 |-Branch one:
% 2.81/1.41 | (36) all_0_0_0 = 0 & all_0_1_1 = 0
% 2.81/1.41 |
% 2.81/1.41 | Applying alpha-rule on (36) yields:
% 2.81/1.41 | (33) all_0_0_0 = 0
% 2.81/1.41 | (38) all_0_1_1 = 0
% 2.81/1.41 |
% 2.81/1.41 | From (33) and (28) follows:
% 2.81/1.41 | (32) xsd_integer(all_0_2_2) = 0
% 2.81/1.41 |
% 2.81/1.41 | Using (32) and (52) yields:
% 2.81/1.41 | (40) $false
% 2.81/1.41 |
% 2.81/1.41 |-The branch is then unsatisfiable
% 2.81/1.41 |-Branch two:
% 2.81/1.41 | (41) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)
% 2.81/1.41 |
% 2.81/1.41 | Applying alpha-rule on (41) yields:
% 2.81/1.41 | (42) ~ (all_0_0_0 = 0)
% 2.81/1.42 | (43) ~ (all_0_1_1 = 0)
% 2.81/1.42 |
% 2.81/1.42 | Equations (38) can reduce 43 to:
% 2.81/1.42 | (23) $false
% 2.81/1.42 |
% 2.81/1.42 |-The branch is then unsatisfiable
% 2.81/1.42 |-Branch two:
% 2.81/1.42 | (63) cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)
% 2.81/1.42 |
% 2.81/1.42 | Applying alpha-rule on (63) yields:
% 2.81/1.42 | (64) cowlNothing(all_0_2_2) = all_0_0_0
% 2.81/1.42 | (65) cowlThing(all_0_2_2) = all_0_1_1
% 2.81/1.42 | (66) ~ (all_0_1_1 = 0) | all_0_0_0 = 0
% 2.81/1.42 |
% 2.81/1.42 | Instantiating formula (18) with all_0_2_2 yields:
% 2.81/1.42 | (67) ~ (cowlNothing(all_0_2_2) = 0)
% 2.81/1.42 |
% 2.81/1.42 | Instantiating formula (15) with all_0_1_1, all_0_2_2 and discharging atoms cowlThing(all_0_2_2) = all_0_1_1, yields:
% 2.81/1.42 | (38) all_0_1_1 = 0
% 2.81/1.42 |
% 2.81/1.42 +-Applying beta-rule and splitting (66), into two cases.
% 2.81/1.42 |-Branch one:
% 2.81/1.42 | (43) ~ (all_0_1_1 = 0)
% 2.81/1.42 |
% 2.81/1.42 | Equations (38) can reduce 43 to:
% 2.81/1.42 | (23) $false
% 2.81/1.42 |
% 2.81/1.42 |-The branch is then unsatisfiable
% 2.81/1.42 |-Branch two:
% 2.81/1.42 | (38) all_0_1_1 = 0
% 2.81/1.42 | (33) all_0_0_0 = 0
% 2.81/1.42 |
% 2.81/1.42 | From (33) and (64) follows:
% 2.81/1.42 | (73) cowlNothing(all_0_2_2) = 0
% 2.81/1.42 |
% 2.81/1.42 | Using (73) and (67) yields:
% 2.81/1.42 | (40) $false
% 2.81/1.42 |
% 2.81/1.42 |-The branch is then unsatisfiable
% 2.81/1.42 % SZS output end Proof for theBenchmark
% 2.81/1.42
% 2.81/1.42 907ms
%------------------------------------------------------------------------------