TSTP Solution File: KRS169+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KRS169+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n017.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 02:56:47 EDT 2022
% Result : Theorem 2.42s 1.29s
% Output : Proof 3.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS169+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n017.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 Jun 7 12:41:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.55/0.57 ____ _
% 0.55/0.57 ___ / __ \_____(_)___ ________ __________
% 0.55/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.57
% 0.55/0.57 A Theorem Prover for First-Order Logic
% 0.55/0.57 (ePrincess v.1.0)
% 0.55/0.57
% 0.55/0.57 (c) Philipp Rümmer, 2009-2015
% 0.55/0.57 (c) Peter Backeman, 2014-2015
% 0.55/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.57 Bug reports to peter@backeman.se
% 0.55/0.57
% 0.55/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.57
% 0.55/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.55/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.27/0.88 Prover 0: Preprocessing ...
% 1.45/0.95 Prover 0: Warning: ignoring some quantifiers
% 1.45/0.97 Prover 0: Constructing countermodel ...
% 1.83/1.09 Prover 0: gave up
% 1.83/1.10 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.83/1.12 Prover 1: Preprocessing ...
% 2.25/1.22 Prover 1: Constructing countermodel ...
% 2.42/1.29 Prover 1: proved (193ms)
% 2.42/1.29
% 2.42/1.29 No countermodel exists, formula is valid
% 2.42/1.29 % SZS status Theorem for theBenchmark
% 2.42/1.29
% 2.42/1.29 Generating proof ... found it (size 45)
% 2.99/1.46
% 2.99/1.46 % SZS output start Proof for theBenchmark
% 2.99/1.46 Assumed formulas after preprocessing and simplification:
% 2.99/1.46 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (rhasLeader(iX, iY) = 0 & rhasHead(iX, iY) = v0 & cowlThing(iY) = 0 & cowlThing(iX) = 0 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (rhasLeader(v7, v6) = v5) | ~ (rhasLeader(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (rhasHead(v7, v6) = v5) | ~ (rhasHead(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (rhasLeader(v4, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & rhasHead(v4, v5) = v7)) & ! [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] : ( ~ (rhasLeader(v4, v5) = 0) | rhasHead(v4, 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))))
% 3.09/1.49 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 3.09/1.49 | (1) rhasLeader(iX, iY) = 0 & rhasHead(iX, iY) = all_0_3_3 & cowlThing(iY) = 0 & cowlThing(iX) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rhasLeader(v3, v2) = v1) | ~ (rhasLeader(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rhasHead(v3, v2) = v1) | ~ (rhasHead(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rhasLeader(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & rhasHead(v0, v1) = v3)) & ! [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] : ( ~ (rhasLeader(v0, v1) = 0) | rhasHead(v0, 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)))
% 3.09/1.50 |
% 3.09/1.50 | Applying alpha-rule on (1) yields:
% 3.09/1.50 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rhasHead(v3, v2) = v1) | ~ (rhasHead(v3, v2) = v0))
% 3.09/1.50 | (3) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 3.09/1.50 | (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))
% 3.09/1.50 | (5) cowlThing(iX) = 0
% 3.09/1.50 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0)
% 3.09/1.50 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rhasLeader(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & rhasHead(v0, v1) = v3))
% 3.09/1.50 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 3.09/1.50 | (9) ! [v0] : ! [v1] : ( ~ (rhasLeader(v0, v1) = 0) | rhasHead(v0, v1) = 0)
% 3.09/1.50 | (10) ! [v0] : ~ (cowlNothing(v0) = 0)
% 3.09/1.50 | (11) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1))
% 3.09/1.50 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0))
% 3.09/1.50 | (13) rhasLeader(iX, iY) = 0
% 3.09/1.50 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rhasLeader(v3, v2) = v1) | ~ (rhasLeader(v3, v2) = v0))
% 3.09/1.50 | (15) rhasHead(iX, iY) = all_0_3_3
% 3.09/1.50 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0))
% 3.09/1.50 | (17) cowlThing(iY) = 0
% 3.09/1.50 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0))
% 3.09/1.50 |
% 3.09/1.50 | Instantiating formula (9) with iY, iX and discharging atoms rhasLeader(iX, iY) = 0, yields:
% 3.09/1.50 | (19) rhasHead(iX, iY) = 0
% 3.09/1.51 |
% 3.09/1.51 | Instantiating formula (2) with iX, iY, 0, all_0_3_3 and discharging atoms rhasHead(iX, iY) = all_0_3_3, rhasHead(iX, iY) = 0, yields:
% 3.09/1.51 | (20) all_0_3_3 = 0
% 3.09/1.51 |
% 3.09/1.51 +-Applying beta-rule and splitting (4), into two cases.
% 3.09/1.51 |-Branch one:
% 3.09/1.51 | (21) ~ (all_0_3_3 = 0)
% 3.09/1.51 |
% 3.09/1.51 | Equations (20) can reduce 21 to:
% 3.09/1.51 | (22) $false
% 3.09/1.51 |
% 3.09/1.51 |-The branch is then unsatisfiable
% 3.09/1.51 |-Branch two:
% 3.09/1.51 | (20) all_0_3_3 = 0
% 3.09/1.51 | (24) (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))
% 3.09/1.51 |
% 3.09/1.51 +-Applying beta-rule and splitting (24), into two cases.
% 3.09/1.51 |-Branch one:
% 3.09/1.51 | (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)))
% 3.09/1.51 |
% 3.09/1.51 | Applying alpha-rule on (25) yields:
% 3.09/1.51 | (26) xsd_string(all_0_2_2) = all_0_1_1
% 3.09/1.51 | (27) xsd_integer(all_0_2_2) = all_0_0_0
% 3.09/1.51 | (28) (all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0))
% 3.09/1.51 |
% 3.09/1.51 | Instantiating formula (3) with all_0_2_2 yields:
% 3.09/1.51 | (29) ~ (xsd_string(all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0)
% 3.09/1.51 |
% 3.09/1.51 | Instantiating formula (6) with all_0_1_1, all_0_2_2 and discharging atoms xsd_string(all_0_2_2) = all_0_1_1, yields:
% 3.09/1.51 | (30) all_0_1_1 = 0 | xsd_integer(all_0_2_2) = 0
% 3.09/1.51 |
% 3.09/1.51 +-Applying beta-rule and splitting (30), into two cases.
% 3.09/1.51 |-Branch one:
% 3.09/1.51 | (31) xsd_integer(all_0_2_2) = 0
% 3.09/1.51 |
% 3.09/1.51 | Instantiating formula (8) 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:
% 3.09/1.51 | (32) all_0_0_0 = 0
% 3.09/1.51 |
% 3.09/1.51 | From (32) and (27) follows:
% 3.09/1.51 | (31) xsd_integer(all_0_2_2) = 0
% 3.09/1.51 |
% 3.09/1.51 +-Applying beta-rule and splitting (29), into two cases.
% 3.09/1.51 |-Branch one:
% 3.09/1.51 | (34) ~ (xsd_string(all_0_2_2) = 0)
% 3.09/1.51 |
% 3.09/1.51 +-Applying beta-rule and splitting (28), into two cases.
% 3.09/1.51 |-Branch one:
% 3.09/1.51 | (35) all_0_0_0 = 0 & all_0_1_1 = 0
% 3.09/1.51 |
% 3.09/1.51 | Applying alpha-rule on (35) yields:
% 3.09/1.51 | (32) all_0_0_0 = 0
% 3.09/1.51 | (37) all_0_1_1 = 0
% 3.09/1.51 |
% 3.09/1.51 | From (37) and (26) follows:
% 3.09/1.51 | (38) xsd_string(all_0_2_2) = 0
% 3.09/1.51 |
% 3.09/1.51 | Using (38) and (34) yields:
% 3.09/1.51 | (39) $false
% 3.09/1.51 |
% 3.09/1.51 |-The branch is then unsatisfiable
% 3.09/1.51 |-Branch two:
% 3.09/1.51 | (40) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)
% 3.09/1.51 |
% 3.09/1.51 | Applying alpha-rule on (40) yields:
% 3.09/1.51 | (41) ~ (all_0_0_0 = 0)
% 3.09/1.51 | (42) ~ (all_0_1_1 = 0)
% 3.09/1.51 |
% 3.09/1.51 | Equations (32) can reduce 41 to:
% 3.09/1.51 | (22) $false
% 3.09/1.51 |
% 3.09/1.51 |-The branch is then unsatisfiable
% 3.09/1.51 |-Branch two:
% 3.09/1.51 | (38) xsd_string(all_0_2_2) = 0
% 3.09/1.51 | (45) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0)
% 3.09/1.51 |
% 3.09/1.51 | Instantiating (45) with all_42_0_4 yields:
% 3.09/1.51 | (46) ~ (all_42_0_4 = 0) & xsd_integer(all_0_2_2) = all_42_0_4
% 3.09/1.51 |
% 3.09/1.51 | Applying alpha-rule on (46) yields:
% 3.09/1.51 | (47) ~ (all_42_0_4 = 0)
% 3.09/1.51 | (48) xsd_integer(all_0_2_2) = all_42_0_4
% 3.09/1.51 |
% 3.09/1.51 | Instantiating formula (8) 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:
% 3.09/1.51 | (49) all_42_0_4 = 0
% 3.09/1.51 |
% 3.09/1.51 | Equations (49) can reduce 47 to:
% 3.09/1.51 | (22) $false
% 3.09/1.51 |
% 3.09/1.51 |-The branch is then unsatisfiable
% 3.09/1.51 |-Branch two:
% 3.09/1.51 | (51) ~ (xsd_integer(all_0_2_2) = 0)
% 3.09/1.51 | (37) all_0_1_1 = 0
% 3.09/1.51 |
% 3.09/1.51 +-Applying beta-rule and splitting (28), into two cases.
% 3.09/1.51 |-Branch one:
% 3.09/1.51 | (35) all_0_0_0 = 0 & all_0_1_1 = 0
% 3.09/1.51 |
% 3.09/1.51 | Applying alpha-rule on (35) yields:
% 3.09/1.51 | (32) all_0_0_0 = 0
% 3.09/1.51 | (37) all_0_1_1 = 0
% 3.09/1.51 |
% 3.09/1.51 | From (32) and (27) follows:
% 3.09/1.51 | (31) xsd_integer(all_0_2_2) = 0
% 3.09/1.51 |
% 3.09/1.51 | Using (31) and (51) yields:
% 3.09/1.51 | (39) $false
% 3.09/1.51 |
% 3.09/1.51 |-The branch is then unsatisfiable
% 3.09/1.51 |-Branch two:
% 3.09/1.51 | (40) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)
% 3.09/1.52 |
% 3.09/1.52 | Applying alpha-rule on (40) yields:
% 3.09/1.52 | (41) ~ (all_0_0_0 = 0)
% 3.09/1.52 | (42) ~ (all_0_1_1 = 0)
% 3.09/1.52 |
% 3.09/1.52 | Equations (37) can reduce 42 to:
% 3.09/1.52 | (22) $false
% 3.09/1.52 |
% 3.09/1.52 |-The branch is then unsatisfiable
% 3.09/1.52 |-Branch two:
% 3.09/1.52 | (62) 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)
% 3.09/1.52 |
% 3.09/1.52 | Applying alpha-rule on (62) yields:
% 3.09/1.52 | (63) cowlNothing(all_0_2_2) = all_0_0_0
% 3.09/1.52 | (64) cowlThing(all_0_2_2) = all_0_1_1
% 3.09/1.52 | (65) ~ (all_0_1_1 = 0) | all_0_0_0 = 0
% 3.09/1.52 |
% 3.09/1.52 | Instantiating formula (10) with all_0_2_2 yields:
% 3.09/1.52 | (66) ~ (cowlNothing(all_0_2_2) = 0)
% 3.09/1.52 |
% 3.09/1.52 | Instantiating formula (11) with all_0_1_1, all_0_2_2 and discharging atoms cowlThing(all_0_2_2) = all_0_1_1, yields:
% 3.09/1.52 | (37) all_0_1_1 = 0
% 3.09/1.52 |
% 3.09/1.52 +-Applying beta-rule and splitting (65), into two cases.
% 3.09/1.52 |-Branch one:
% 3.09/1.52 | (42) ~ (all_0_1_1 = 0)
% 3.09/1.52 |
% 3.09/1.52 | Equations (37) can reduce 42 to:
% 3.09/1.52 | (22) $false
% 3.09/1.52 |
% 3.09/1.52 |-The branch is then unsatisfiable
% 3.09/1.52 |-Branch two:
% 3.09/1.52 | (37) all_0_1_1 = 0
% 3.09/1.52 | (32) all_0_0_0 = 0
% 3.09/1.52 |
% 3.09/1.52 | From (32) and (63) follows:
% 3.09/1.52 | (72) cowlNothing(all_0_2_2) = 0
% 3.09/1.52 |
% 3.09/1.52 | Using (72) and (66) yields:
% 3.09/1.52 | (39) $false
% 3.09/1.52 |
% 3.09/1.52 |-The branch is then unsatisfiable
% 3.09/1.52 % SZS output end Proof for theBenchmark
% 3.09/1.52
% 3.09/1.52 935ms
%------------------------------------------------------------------------------