TSTP Solution File: PUZ001+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : PUZ001+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 : Mon Jul 18 18:08:49 EDT 2022
% Result : Theorem 8.83s 2.89s
% Output : Proof 12.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : PUZ001+1 : TPTP v8.1.0. Released v2.0.0.
% 0.00/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n027.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 : Sat May 28 22:34:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.57/0.61 ____ _
% 0.57/0.61 ___ / __ \_____(_)___ ________ __________
% 0.57/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.61
% 0.57/0.61 A Theorem Prover for First-Order Logic
% 0.57/0.61 (ePrincess v.1.0)
% 0.57/0.61
% 0.57/0.61 (c) Philipp Rümmer, 2009-2015
% 0.57/0.61 (c) Peter Backeman, 2014-2015
% 0.57/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.61 Bug reports to peter@backeman.se
% 0.57/0.61
% 0.57/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.61
% 0.57/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.40/0.92 Prover 0: Preprocessing ...
% 1.53/0.99 Prover 0: Warning: ignoring some quantifiers
% 1.53/1.01 Prover 0: Constructing countermodel ...
% 1.87/1.16 Prover 0: gave up
% 1.87/1.16 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.14/1.18 Prover 1: Preprocessing ...
% 2.37/1.25 Prover 1: Warning: ignoring some quantifiers
% 2.37/1.26 Prover 1: Constructing countermodel ...
% 2.68/1.34 Prover 1: gave up
% 2.68/1.34 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.68/1.36 Prover 2: Preprocessing ...
% 2.98/1.41 Prover 2: Warning: ignoring some quantifiers
% 2.98/1.41 Prover 2: Constructing countermodel ...
% 3.19/1.52 Prover 2: gave up
% 3.19/1.52 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.19/1.53 Prover 3: Preprocessing ...
% 3.19/1.54 Prover 3: Warning: ignoring some quantifiers
% 3.19/1.54 Prover 3: Constructing countermodel ...
% 3.57/1.58 Prover 3: gave up
% 3.57/1.58 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 3.57/1.59 Prover 4: Preprocessing ...
% 3.85/1.63 Prover 4: Warning: ignoring some quantifiers
% 3.85/1.64 Prover 4: Constructing countermodel ...
% 4.30/1.79 Prover 4: gave up
% 4.30/1.79 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.30/1.80 Prover 5: Preprocessing ...
% 4.68/1.82 Prover 5: Warning: ignoring some quantifiers
% 4.68/1.83 Prover 5: Constructing countermodel ...
% 5.02/1.90 Prover 5: gave up
% 5.02/1.90 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.09/1.91 Prover 6: Preprocessing ...
% 5.16/1.93 Prover 6: Warning: ignoring some quantifiers
% 5.16/1.93 Prover 6: Constructing countermodel ...
% 5.16/1.99 Prover 6: gave up
% 5.16/1.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 5.16/2.00 Prover 7: Preprocessing ...
% 5.16/2.01 Prover 7: Proving ...
% 8.83/2.89 Prover 7: proved (902ms)
% 8.83/2.89
% 8.83/2.89 % SZS status Theorem for theBenchmark
% 8.83/2.89
% 8.83/2.89 Generating proof ... found it (size 52)
% 12.97/4.17
% 12.97/4.17 % SZS output start Proof for theBenchmark
% 12.97/4.17 Assumed formulas after preprocessing and simplification:
% 12.97/4.17 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & lives(v2) & lives(v1) & lives(v0) & ~ killed(v2, v2) & ! [v3] : ! [v4] : ( ~ richer(v3, v4) | ~ killed(v3, v4)) & ! [v3] : ! [v4] : ( ~ killed(v3, v4) | hates(v3, v4)) & ! [v3] : (v3 = v2 | v3 = v1 | v3 = v0 | ~ lives(v3)) & ! [v3] : (v3 = v1 | hates(v2, v3)) & ! [v3] : ( ~ hates(v2, v3) | ~ hates(v0, v3)) & ! [v3] : ( ~ hates(v2, v3) | hates(v1, v3)) & ! [v3] : (richer(v3, v2) | hates(v1, v3)) & ! [v3] : ? [v4] : ~ hates(v3, v4) & ? [v3] : (killed(v3, v2) & lives(v3)))
% 12.97/4.17 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 12.97/4.17 | (1) ~ (all_0_0_0 = all_0_1_1) & lives(all_0_0_0) & lives(all_0_1_1) & lives(all_0_2_2) & ~ killed(all_0_0_0, all_0_0_0) & ! [v0] : ! [v1] : ( ~ richer(v0, v1) | ~ killed(v0, v1)) & ! [v0] : ! [v1] : ( ~ killed(v0, v1) | hates(v0, v1)) & ! [v0] : (v0 = all_0_0_0 | v0 = all_0_1_1 | v0 = all_0_2_2 | ~ lives(v0)) & ! [v0] : (v0 = all_0_1_1 | hates(all_0_0_0, v0)) & ! [v0] : ( ~ hates(all_0_0_0, v0) | ~ hates(all_0_2_2, v0)) & ! [v0] : ( ~ hates(all_0_0_0, v0) | hates(all_0_1_1, v0)) & ! [v0] : (richer(v0, all_0_0_0) | hates(all_0_1_1, v0)) & ! [v0] : ? [v1] : ~ hates(v0, v1) & ? [v0] : (killed(v0, all_0_0_0) & lives(v0))
% 12.97/4.17 |
% 12.97/4.17 | Applying alpha-rule on (1) yields:
% 12.97/4.17 | (2) ! [v0] : ( ~ hates(all_0_0_0, v0) | ~ hates(all_0_2_2, v0))
% 12.97/4.17 | (3) ! [v0] : ? [v1] : ~ hates(v0, v1)
% 12.97/4.17 | (4) ! [v0] : (v0 = all_0_1_1 | hates(all_0_0_0, v0))
% 12.97/4.17 | (5) ! [v0] : ! [v1] : ( ~ richer(v0, v1) | ~ killed(v0, v1))
% 12.97/4.17 | (6) ! [v0] : (v0 = all_0_0_0 | v0 = all_0_1_1 | v0 = all_0_2_2 | ~ lives(v0))
% 12.97/4.17 | (7) lives(all_0_1_1)
% 12.97/4.17 | (8) ! [v0] : ! [v1] : ( ~ killed(v0, v1) | hates(v0, v1))
% 12.97/4.17 | (9) ~ (all_0_0_0 = all_0_1_1)
% 12.97/4.17 | (10) ! [v0] : (richer(v0, all_0_0_0) | hates(all_0_1_1, v0))
% 12.97/4.17 | (11) ? [v0] : (killed(v0, all_0_0_0) & lives(v0))
% 12.97/4.17 | (12) lives(all_0_0_0)
% 12.97/4.17 | (13) lives(all_0_2_2)
% 12.97/4.17 | (14) ! [v0] : ( ~ hates(all_0_0_0, v0) | hates(all_0_1_1, v0))
% 12.97/4.17 | (15) ~ killed(all_0_0_0, all_0_0_0)
% 12.97/4.17 |
% 12.97/4.17 | Instantiating (11) with all_3_0_3 yields:
% 12.97/4.17 | (16) killed(all_3_0_3, all_0_0_0) & lives(all_3_0_3)
% 12.97/4.17 |
% 12.97/4.17 | Applying alpha-rule on (16) yields:
% 12.97/4.17 | (17) killed(all_3_0_3, all_0_0_0)
% 12.97/4.17 | (18) lives(all_3_0_3)
% 12.97/4.17 |
% 12.97/4.17 | Instantiating formula (6) with all_3_0_3 and discharging atoms lives(all_3_0_3), yields:
% 12.97/4.17 | (19) all_3_0_3 = all_0_0_0 | all_3_0_3 = all_0_1_1 | all_3_0_3 = all_0_2_2
% 12.97/4.18 |
% 12.97/4.18 | Instantiating formula (8) with all_0_0_0, all_3_0_3 and discharging atoms killed(all_3_0_3, all_0_0_0), yields:
% 12.97/4.18 | (20) hates(all_3_0_3, all_0_0_0)
% 12.97/4.18 |
% 12.97/4.18 | Instantiating formula (14) with all_0_0_0 yields:
% 12.97/4.18 | (21) ~ hates(all_0_0_0, all_0_0_0) | hates(all_0_1_1, all_0_0_0)
% 12.97/4.18 |
% 12.97/4.18 +-Applying beta-rule and splitting (21), into two cases.
% 12.97/4.18 |-Branch one:
% 12.97/4.18 | (22) ~ hates(all_0_0_0, all_0_0_0)
% 12.97/4.18 |
% 12.97/4.18 | Introducing new symbol ex_38_0_4 defined by:
% 12.97/4.18 | (23) ex_38_0_4 = all_0_0_0
% 12.97/4.18 |
% 12.97/4.18 | Instantiating formula (4) with ex_38_0_4 yields:
% 12.97/4.18 | (24) ex_38_0_4 = all_0_1_1 | hates(all_0_0_0, ex_38_0_4)
% 12.97/4.18 |
% 12.97/4.18 +-Applying beta-rule and splitting (24), into two cases.
% 12.97/4.18 |-Branch one:
% 12.97/4.18 | (25) hates(all_0_0_0, ex_38_0_4)
% 12.97/4.18 |
% 12.97/4.18 | From (23) and (25) follows:
% 12.97/4.18 | (26) hates(all_0_0_0, all_0_0_0)
% 12.97/4.18 |
% 12.97/4.18 | Using (26) and (22) yields:
% 12.97/4.18 | (27) $false
% 12.97/4.18 |
% 12.97/4.18 |-The branch is then unsatisfiable
% 12.97/4.18 |-Branch two:
% 12.97/4.18 | (28) ex_38_0_4 = all_0_1_1
% 12.97/4.18 |
% 12.97/4.18 | Combining equations (23,28) yields a new equation:
% 12.97/4.18 | (29) all_0_0_0 = all_0_1_1
% 12.97/4.18 |
% 12.97/4.18 | Simplifying 29 yields:
% 12.97/4.18 | (30) all_0_0_0 = all_0_1_1
% 12.97/4.18 |
% 12.97/4.18 | Equations (30) can reduce 9 to:
% 12.97/4.18 | (31) $false
% 12.97/4.18 |
% 12.97/4.18 |-The branch is then unsatisfiable
% 12.97/4.18 |-Branch two:
% 12.97/4.18 | (26) hates(all_0_0_0, all_0_0_0)
% 12.97/4.18 | (33) hates(all_0_1_1, all_0_0_0)
% 12.97/4.18 |
% 12.97/4.18 | Instantiating formula (2) with all_0_0_0 and discharging atoms hates(all_0_0_0, all_0_0_0), yields:
% 12.97/4.18 | (34) ~ hates(all_0_2_2, all_0_0_0)
% 12.97/4.18 |
% 12.97/4.18 +-Applying beta-rule and splitting (19), into two cases.
% 12.97/4.18 |-Branch one:
% 12.97/4.18 | (35) all_3_0_3 = all_0_0_0
% 12.97/4.18 |
% 12.97/4.18 | From (35) and (17) follows:
% 12.97/4.18 | (36) killed(all_0_0_0, all_0_0_0)
% 12.97/4.18 |
% 12.97/4.18 | Using (36) and (15) yields:
% 12.97/4.18 | (27) $false
% 12.97/4.18 |
% 12.97/4.18 |-The branch is then unsatisfiable
% 12.97/4.18 |-Branch two:
% 12.97/4.18 | (38) all_3_0_3 = all_0_1_1 | all_3_0_3 = all_0_2_2
% 12.97/4.18 |
% 12.97/4.18 +-Applying beta-rule and splitting (38), into two cases.
% 12.97/4.18 |-Branch one:
% 12.97/4.18 | (39) all_3_0_3 = all_0_1_1
% 12.97/4.18 |
% 12.97/4.18 | From (39) and (17) follows:
% 12.97/4.18 | (40) killed(all_0_1_1, all_0_0_0)
% 12.97/4.18 |
% 12.97/4.18 | Introducing new symbol ex_74_0_11 defined by:
% 12.97/4.18 | (41) ex_74_0_11 = all_0_1_1
% 12.97/4.18 |
% 12.97/4.18 | Instantiating formula (10) with ex_74_0_11 yields:
% 12.97/4.18 | (42) richer(ex_74_0_11, all_0_0_0) | hates(all_0_1_1, ex_74_0_11)
% 12.97/4.18 |
% 12.97/4.18 +-Applying beta-rule and splitting (42), into two cases.
% 12.97/4.18 |-Branch one:
% 12.97/4.18 | (43) hates(all_0_1_1, ex_74_0_11)
% 12.97/4.18 |
% 12.97/4.18 | Introducing new symbol ex_83_0_12 defined by:
% 12.97/4.18 | (44) ex_83_0_12 = all_0_1_1
% 12.97/4.18 |
% 12.97/4.18 | Instantiating formula (3) with ex_83_0_12 yields:
% 12.97/4.18 | (45) ? [v0] : ~ hates(ex_83_0_12, v0)
% 12.97/4.18 |
% 12.97/4.18 | Instantiating (45) with all_84_0_13 yields:
% 12.97/4.18 | (46) ~ hates(ex_83_0_12, all_84_0_13)
% 12.97/4.18 |
% 12.97/4.18 | Introducing new symbol ex_92_0_14 defined by:
% 12.97/4.18 | (47) ex_92_0_14 = all_84_0_13
% 12.97/4.18 |
% 12.97/4.18 | Instantiating formula (4) with ex_92_0_14 yields:
% 12.97/4.18 | (48) ex_92_0_14 = all_0_1_1 | hates(all_0_0_0, ex_92_0_14)
% 12.97/4.18 |
% 12.97/4.18 +-Applying beta-rule and splitting (48), into two cases.
% 12.97/4.18 |-Branch one:
% 12.97/4.18 | (49) hates(all_0_0_0, ex_92_0_14)
% 12.97/4.18 |
% 12.97/4.18 | Instantiating formula (14) with ex_92_0_14 and discharging atoms hates(all_0_0_0, ex_92_0_14), yields:
% 12.97/4.18 | (50) hates(all_0_1_1, ex_92_0_14)
% 12.97/4.18 |
% 12.97/4.18 | From (47) and (50) follows:
% 12.97/4.18 | (51) hates(all_0_1_1, all_84_0_13)
% 12.97/4.18 |
% 12.97/4.18 | From (44) and (46) follows:
% 12.97/4.18 | (52) ~ hates(all_0_1_1, all_84_0_13)
% 12.97/4.18 |
% 12.97/4.18 | Using (51) and (52) yields:
% 12.97/4.18 | (27) $false
% 12.97/4.18 |
% 12.97/4.18 |-The branch is then unsatisfiable
% 12.97/4.18 |-Branch two:
% 12.97/4.18 | (54) ex_92_0_14 = all_0_1_1
% 12.97/4.18 |
% 12.97/4.18 | Combining equations (47,54) yields a new equation:
% 12.97/4.18 | (55) all_84_0_13 = all_0_1_1
% 12.97/4.18 |
% 12.97/4.18 | Simplifying 55 yields:
% 12.97/4.18 | (56) all_84_0_13 = all_0_1_1
% 12.97/4.18 |
% 12.97/4.18 | From (41) and (43) follows:
% 12.97/4.18 | (57) hates(all_0_1_1, all_0_1_1)
% 12.97/4.18 |
% 12.97/4.18 | From (44)(56) and (46) follows:
% 12.97/4.18 | (58) ~ hates(all_0_1_1, all_0_1_1)
% 12.97/4.18 |
% 12.97/4.18 | Using (57) and (58) yields:
% 12.97/4.18 | (27) $false
% 12.97/4.18 |
% 12.97/4.18 |-The branch is then unsatisfiable
% 12.97/4.18 |-Branch two:
% 12.97/4.18 | (60) richer(ex_74_0_11, all_0_0_0)
% 12.97/4.18 |
% 12.97/4.18 | Instantiating formula (5) with all_0_0_0, all_0_1_1 and discharging atoms killed(all_0_1_1, all_0_0_0), yields:
% 12.97/4.18 | (61) ~ richer(all_0_1_1, all_0_0_0)
% 12.97/4.18 |
% 12.97/4.18 | From (41) and (60) follows:
% 12.97/4.18 | (62) richer(all_0_1_1, all_0_0_0)
% 12.97/4.18 |
% 12.97/4.18 | Using (62) and (61) yields:
% 12.97/4.18 | (27) $false
% 12.97/4.18 |
% 12.97/4.18 |-The branch is then unsatisfiable
% 12.97/4.18 |-Branch two:
% 12.97/4.18 | (64) all_3_0_3 = all_0_2_2
% 12.97/4.18 |
% 12.97/4.18 | From (64) and (20) follows:
% 12.97/4.18 | (65) hates(all_0_2_2, all_0_0_0)
% 12.97/4.18 |
% 12.97/4.18 | Using (65) and (34) yields:
% 12.97/4.18 | (27) $false
% 12.97/4.18 |
% 12.97/4.18 |-The branch is then unsatisfiable
% 12.97/4.18 % SZS output end Proof for theBenchmark
% 12.97/4.18
% 12.97/4.18 3563ms
%------------------------------------------------------------------------------