TSTP Solution File: SYN374+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN374+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 : Thu Jul 21 05:01:54 EDT 2022
% Result : Theorem 2.28s 1.43s
% Output : Proof 3.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15 % Problem : SYN374+1 : TPTP v8.1.0. Released v2.0.0.
% 0.14/0.16 % Command : ePrincess-casc -timeout=%d %s
% 0.15/0.37 % Computer : n027.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Mon Jul 11 16:41:19 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.64/0.65 ____ _
% 0.64/0.65 ___ / __ \_____(_)___ ________ __________
% 0.64/0.65 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.64/0.65 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.64/0.65 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.64/0.65
% 0.64/0.65 A Theorem Prover for First-Order Logic
% 0.64/0.65 (ePrincess v.1.0)
% 0.64/0.65
% 0.64/0.65 (c) Philipp Rümmer, 2009-2015
% 0.64/0.65 (c) Peter Backeman, 2014-2015
% 0.64/0.65 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.64/0.65 Free software under GNU Lesser General Public License (LGPL).
% 0.64/0.65 Bug reports to peter@backeman.se
% 0.64/0.65
% 0.64/0.65 For more information, visit http://user.uu.se/~petba168/breu/
% 0.64/0.65
% 0.64/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.72 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.31/0.97 Prover 0: Preprocessing ...
% 1.42/1.05 Prover 0: Warning: ignoring some quantifiers
% 1.49/1.07 Prover 0: Constructing countermodel ...
% 1.76/1.22 Prover 0: gave up
% 1.76/1.22 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.76/1.24 Prover 1: Preprocessing ...
% 2.18/1.31 Prover 1: Constructing countermodel ...
% 2.28/1.43 Prover 1: proved (209ms)
% 2.28/1.43
% 2.28/1.43 No countermodel exists, formula is valid
% 2.28/1.43 % SZS status Theorem for theBenchmark
% 2.28/1.43
% 2.28/1.43 Generating proof ... found it (size 43)
% 2.98/1.65
% 2.98/1.65 % SZS output start Proof for theBenchmark
% 2.98/1.66 Assumed formulas after preprocessing and simplification:
% 2.98/1.66 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (big_p(v8) = v7) | ~ (big_p(v8) = v6)) & ((big_p(v4) = v5 & ! [v6] : ! [v7] : ( ~ (v5 = 0) | v7 = 0 | ~ (big_p(v6) = v7)) & ! [v6] : (v5 = 0 | ~ (big_p(v6) = 0)) & ((v3 = 0 & ~ (v1 = 0) & big_p(v2) = 0 & big_p(v0) = v1) | ( ! [v6] : ! [v7] : (v7 = 0 | ~ (big_p(v6) = v7)) & ! [v6] : ~ (big_p(v6) = 0)))) | ( ! [v6] : ! [v7] : ( ~ (big_p(v6) = v7) | ? [v8] : ? [v9] : (big_p(v8) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0)) & (v9 = 0 | v7 = 0))) & ((v1 = 0 & big_p(v0) = 0 & ! [v6] : ! [v7] : (v7 = 0 | ~ (big_p(v6) = v7))) | ( ~ (v1 = 0) & big_p(v0) = v1 & ! [v6] : ~ (big_p(v6) = 0))))))
% 3.09/1.70 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 3.09/1.70 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) & ((big_p(all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | v1 = 0 | ~ (big_p(v0) = v1)) & ! [v0] : (all_0_0_0 = 0 | ~ (big_p(v0) = 0)) & ((all_0_2_2 = 0 & ~ (all_0_4_4 = 0) & big_p(all_0_3_3) = 0 & big_p(all_0_5_5) = all_0_4_4) | ( ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1)) & ! [v0] : ~ (big_p(v0) = 0)))) | ( ! [v0] : ! [v1] : ( ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_p(v2) = v3 & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & ((all_0_4_4 = 0 & big_p(all_0_5_5) = 0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1))) | ( ~ (all_0_4_4 = 0) & big_p(all_0_5_5) = all_0_4_4 & ! [v0] : ~ (big_p(v0) = 0)))))
% 3.09/1.71 |
% 3.09/1.71 | Applying alpha-rule on (1) yields:
% 3.09/1.71 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0))
% 3.09/1.71 | (3) (big_p(all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | v1 = 0 | ~ (big_p(v0) = v1)) & ! [v0] : (all_0_0_0 = 0 | ~ (big_p(v0) = 0)) & ((all_0_2_2 = 0 & ~ (all_0_4_4 = 0) & big_p(all_0_3_3) = 0 & big_p(all_0_5_5) = all_0_4_4) | ( ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1)) & ! [v0] : ~ (big_p(v0) = 0)))) | ( ! [v0] : ! [v1] : ( ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_p(v2) = v3 & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & ((all_0_4_4 = 0 & big_p(all_0_5_5) = 0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1))) | ( ~ (all_0_4_4 = 0) & big_p(all_0_5_5) = all_0_4_4 & ! [v0] : ~ (big_p(v0) = 0))))
% 3.09/1.71 |
% 3.09/1.71 +-Applying beta-rule and splitting (3), into two cases.
% 3.09/1.71 |-Branch one:
% 3.09/1.71 | (4) big_p(all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | v1 = 0 | ~ (big_p(v0) = v1)) & ! [v0] : (all_0_0_0 = 0 | ~ (big_p(v0) = 0)) & ((all_0_2_2 = 0 & ~ (all_0_4_4 = 0) & big_p(all_0_3_3) = 0 & big_p(all_0_5_5) = all_0_4_4) | ( ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1)) & ! [v0] : ~ (big_p(v0) = 0)))
% 3.09/1.72 |
% 3.09/1.72 | Applying alpha-rule on (4) yields:
% 3.09/1.72 | (5) big_p(all_0_1_1) = all_0_0_0
% 3.09/1.72 | (6) ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | v1 = 0 | ~ (big_p(v0) = v1))
% 3.09/1.72 | (7) ! [v0] : (all_0_0_0 = 0 | ~ (big_p(v0) = 0))
% 3.09/1.72 | (8) (all_0_2_2 = 0 & ~ (all_0_4_4 = 0) & big_p(all_0_3_3) = 0 & big_p(all_0_5_5) = all_0_4_4) | ( ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1)) & ! [v0] : ~ (big_p(v0) = 0))
% 3.09/1.72 |
% 3.09/1.72 +-Applying beta-rule and splitting (8), into two cases.
% 3.09/1.72 |-Branch one:
% 3.09/1.72 | (9) all_0_2_2 = 0 & ~ (all_0_4_4 = 0) & big_p(all_0_3_3) = 0 & big_p(all_0_5_5) = all_0_4_4
% 3.09/1.72 |
% 3.09/1.72 | Applying alpha-rule on (9) yields:
% 3.09/1.72 | (10) all_0_2_2 = 0
% 3.09/1.72 | (11) ~ (all_0_4_4 = 0)
% 3.09/1.72 | (12) big_p(all_0_3_3) = 0
% 3.09/1.72 | (13) big_p(all_0_5_5) = all_0_4_4
% 3.09/1.72 |
% 3.09/1.72 | Instantiating formula (2) with all_0_3_3, 0, all_0_0_0 and discharging atoms big_p(all_0_3_3) = 0, yields:
% 3.09/1.72 | (14) all_0_0_0 = 0 | ~ (big_p(all_0_3_3) = all_0_0_0)
% 3.09/1.72 |
% 3.09/1.72 | Instantiating formula (7) with all_0_3_3 and discharging atoms big_p(all_0_3_3) = 0, yields:
% 3.09/1.72 | (15) all_0_0_0 = 0
% 3.09/1.72 |
% 3.09/1.72 +-Applying beta-rule and splitting (14), into two cases.
% 3.09/1.72 |-Branch one:
% 3.09/1.72 | (16) ~ (big_p(all_0_3_3) = all_0_0_0)
% 3.09/1.72 |
% 3.09/1.73 | From (15) and (16) follows:
% 3.09/1.73 | (17) ~ (big_p(all_0_3_3) = 0)
% 3.09/1.73 |
% 3.09/1.73 | Using (12) and (17) yields:
% 3.09/1.73 | (18) $false
% 3.09/1.73 |
% 3.09/1.73 |-The branch is then unsatisfiable
% 3.09/1.73 |-Branch two:
% 3.09/1.73 | (19) big_p(all_0_3_3) = all_0_0_0
% 3.09/1.73 | (15) all_0_0_0 = 0
% 3.09/1.73 |
% 3.09/1.73 | Instantiating formula (6) with all_0_4_4, all_0_5_5 and discharging atoms big_p(all_0_5_5) = all_0_4_4, yields:
% 3.09/1.73 | (21) ~ (all_0_0_0 = 0) | all_0_4_4 = 0
% 3.09/1.73 |
% 3.09/1.73 +-Applying beta-rule and splitting (21), into two cases.
% 3.09/1.73 |-Branch one:
% 3.09/1.73 | (22) ~ (all_0_0_0 = 0)
% 3.09/1.73 |
% 3.09/1.73 | Equations (15) can reduce 22 to:
% 3.09/1.73 | (23) $false
% 3.09/1.73 |
% 3.09/1.73 |-The branch is then unsatisfiable
% 3.09/1.73 |-Branch two:
% 3.09/1.73 | (15) all_0_0_0 = 0
% 3.09/1.73 | (25) all_0_4_4 = 0
% 3.09/1.73 |
% 3.09/1.73 | Equations (25) can reduce 11 to:
% 3.09/1.73 | (23) $false
% 3.09/1.73 |
% 3.09/1.73 |-The branch is then unsatisfiable
% 3.09/1.73 |-Branch two:
% 3.09/1.73 | (27) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1)) & ! [v0] : ~ (big_p(v0) = 0)
% 3.09/1.73 |
% 3.09/1.73 | Applying alpha-rule on (27) yields:
% 3.09/1.73 | (28) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1))
% 3.09/1.73 | (29) ! [v0] : ~ (big_p(v0) = 0)
% 3.09/1.73 |
% 3.09/1.73 | Instantiating formula (29) with all_0_1_1 yields:
% 3.09/1.73 | (30) ~ (big_p(all_0_1_1) = 0)
% 3.09/1.73 |
% 3.09/1.73 | Instantiating formula (28) with all_0_0_0, all_0_1_1 and discharging atoms big_p(all_0_1_1) = all_0_0_0, yields:
% 3.09/1.73 | (15) all_0_0_0 = 0
% 3.09/1.73 |
% 3.09/1.73 | From (15) and (5) follows:
% 3.09/1.73 | (32) big_p(all_0_1_1) = 0
% 3.09/1.73 |
% 3.09/1.73 | Using (32) and (30) yields:
% 3.09/1.73 | (18) $false
% 3.09/1.73 |
% 3.09/1.73 |-The branch is then unsatisfiable
% 3.09/1.73 |-Branch two:
% 3.09/1.73 | (34) ! [v0] : ! [v1] : ( ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_p(v2) = v3 & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & ((all_0_4_4 = 0 & big_p(all_0_5_5) = 0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1))) | ( ~ (all_0_4_4 = 0) & big_p(all_0_5_5) = all_0_4_4 & ! [v0] : ~ (big_p(v0) = 0)))
% 3.09/1.74 |
% 3.09/1.74 | Applying alpha-rule on (34) yields:
% 3.09/1.74 | (35) ! [v0] : ! [v1] : ( ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_p(v2) = v3 & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0)))
% 3.09/1.74 | (36) (all_0_4_4 = 0 & big_p(all_0_5_5) = 0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1))) | ( ~ (all_0_4_4 = 0) & big_p(all_0_5_5) = all_0_4_4 & ! [v0] : ~ (big_p(v0) = 0))
% 3.09/1.74 |
% 3.09/1.74 +-Applying beta-rule and splitting (36), into two cases.
% 3.09/1.74 |-Branch one:
% 3.09/1.74 | (37) all_0_4_4 = 0 & big_p(all_0_5_5) = 0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1))
% 3.09/1.74 |
% 3.09/1.74 | Applying alpha-rule on (37) yields:
% 3.09/1.74 | (25) all_0_4_4 = 0
% 3.09/1.74 | (39) big_p(all_0_5_5) = 0
% 3.09/1.74 | (28) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1))
% 3.09/1.74 |
% 3.09/1.74 | Instantiating formula (35) with 0, all_0_5_5 and discharging atoms big_p(all_0_5_5) = 0, yields:
% 3.09/1.74 | (41) ? [v0] : ? [v1] : ( ~ (v1 = 0) & big_p(v0) = v1)
% 3.09/1.74 |
% 3.09/1.74 | Instantiating (41) with all_16_0_6, all_16_1_7 yields:
% 3.09/1.74 | (42) ~ (all_16_0_6 = 0) & big_p(all_16_1_7) = all_16_0_6
% 3.09/1.74 |
% 3.09/1.74 | Applying alpha-rule on (42) yields:
% 3.09/1.74 | (43) ~ (all_16_0_6 = 0)
% 3.09/1.74 | (44) big_p(all_16_1_7) = all_16_0_6
% 3.09/1.74 |
% 3.09/1.74 | Instantiating formula (28) with all_16_0_6, all_16_1_7 and discharging atoms big_p(all_16_1_7) = all_16_0_6, yields:
% 3.09/1.74 | (45) all_16_0_6 = 0
% 3.09/1.74 |
% 3.09/1.74 | Equations (45) can reduce 43 to:
% 3.09/1.74 | (23) $false
% 3.09/1.74 |
% 3.09/1.74 |-The branch is then unsatisfiable
% 3.09/1.74 |-Branch two:
% 3.09/1.74 | (47) ~ (all_0_4_4 = 0) & big_p(all_0_5_5) = all_0_4_4 & ! [v0] : ~ (big_p(v0) = 0)
% 3.09/1.74 |
% 3.09/1.74 | Applying alpha-rule on (47) yields:
% 3.09/1.74 | (11) ~ (all_0_4_4 = 0)
% 3.09/1.74 | (13) big_p(all_0_5_5) = all_0_4_4
% 3.09/1.74 | (29) ! [v0] : ~ (big_p(v0) = 0)
% 3.09/1.74 |
% 3.09/1.74 | Instantiating formula (35) with all_0_4_4, all_0_5_5 and discharging atoms big_p(all_0_5_5) = all_0_4_4, yields:
% 3.09/1.74 | (51) ? [v0] : ? [v1] : (big_p(v0) = v1 & ( ~ (v1 = 0) | ~ (all_0_4_4 = 0)) & (v1 = 0 | all_0_4_4 = 0))
% 3.09/1.74 |
% 3.09/1.74 | Instantiating (51) with all_16_0_8, all_16_1_9 yields:
% 3.09/1.74 | (52) big_p(all_16_1_9) = all_16_0_8 & ( ~ (all_16_0_8 = 0) | ~ (all_0_4_4 = 0)) & (all_16_0_8 = 0 | all_0_4_4 = 0)
% 3.09/1.74 |
% 3.09/1.74 | Applying alpha-rule on (52) yields:
% 3.09/1.74 | (53) big_p(all_16_1_9) = all_16_0_8
% 3.09/1.74 | (54) ~ (all_16_0_8 = 0) | ~ (all_0_4_4 = 0)
% 3.09/1.74 | (55) all_16_0_8 = 0 | all_0_4_4 = 0
% 3.09/1.74 |
% 3.09/1.75 +-Applying beta-rule and splitting (55), into two cases.
% 3.09/1.75 |-Branch one:
% 3.09/1.75 | (56) all_16_0_8 = 0
% 3.09/1.75 |
% 3.09/1.75 | From (56) and (53) follows:
% 3.09/1.75 | (57) big_p(all_16_1_9) = 0
% 3.09/1.75 |
% 3.09/1.75 | Instantiating formula (29) with all_16_1_9 and discharging atoms big_p(all_16_1_9) = 0, yields:
% 3.09/1.75 | (18) $false
% 3.09/1.75 |
% 3.09/1.75 |-The branch is then unsatisfiable
% 3.09/1.75 |-Branch two:
% 3.09/1.75 | (59) ~ (all_16_0_8 = 0)
% 3.09/1.75 | (25) all_0_4_4 = 0
% 3.09/1.75 |
% 3.09/1.75 | Equations (25) can reduce 11 to:
% 3.09/1.75 | (23) $false
% 3.09/1.75 |
% 3.09/1.75 |-The branch is then unsatisfiable
% 3.09/1.75 % SZS output end Proof for theBenchmark
% 3.09/1.75
% 3.09/1.75 1083ms
%------------------------------------------------------------------------------