TSTP Solution File: SYN966+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN966+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.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 2.19s 1.24s
% Output : Proof 2.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN966+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 19:46:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.61/0.61 ____ _
% 0.61/0.61 ___ / __ \_____(_)___ ________ __________
% 0.61/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.61/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.61/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.61/0.61
% 0.61/0.61 A Theorem Prover for First-Order Logic
% 0.61/0.61 (ePrincess v.1.0)
% 0.61/0.61
% 0.61/0.61 (c) Philipp Rümmer, 2009-2015
% 0.61/0.61 (c) Peter Backeman, 2014-2015
% 0.61/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.61/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.61/0.61 Bug reports to peter@backeman.se
% 0.61/0.61
% 0.61/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.61/0.61
% 0.61/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.64/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.29/0.93 Prover 0: Preprocessing ...
% 1.29/0.99 Prover 0: Warning: ignoring some quantifiers
% 1.29/1.00 Prover 0: Constructing countermodel ...
% 1.71/1.11 Prover 0: gave up
% 1.71/1.11 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.71/1.12 Prover 1: Preprocessing ...
% 1.71/1.18 Prover 1: Constructing countermodel ...
% 2.19/1.24 Prover 1: proved (131ms)
% 2.19/1.24
% 2.19/1.24 No countermodel exists, formula is valid
% 2.19/1.24 % SZS status Theorem for theBenchmark
% 2.19/1.24
% 2.19/1.24 Generating proof ... found it (size 44)
% 2.63/1.43
% 2.63/1.43 % SZS output start Proof for theBenchmark
% 2.63/1.43 Assumed formulas after preprocessing and simplification:
% 2.63/1.43 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & eq(v1, v0) = v2 & eq(v0, v1) = 0 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (eq(v3, v4) = 0) | ~ (a_member_of(v5, v3) = v6) | ? [v7] : ( ~ (v7 = 0) & a_member_of(v5, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (eq(v6, v5) = v4) | ~ (eq(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (a_member_of(v6, v5) = v4) | ~ (a_member_of(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (eq(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : (a_member_of(v6, v4) = v8 & a_member_of(v6, v3) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)) & (v8 = 0 | v7 = 0))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (eq(v3, v4) = 0) | ~ (a_member_of(v5, v3) = 0) | a_member_of(v5, v4) = 0))
% 2.63/1.46 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 2.63/1.46 | (1) ~ (all_0_0_0 = 0) & eq(all_0_1_1, all_0_2_2) = all_0_0_0 & eq(all_0_2_2, all_0_1_1) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (eq(v0, v1) = 0) | ~ (a_member_of(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & a_member_of(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (eq(v3, v2) = v1) | ~ (eq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a_member_of(v3, v2) = v1) | ~ (a_member_of(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (eq(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (a_member_of(v3, v1) = v5 & a_member_of(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (eq(v0, v1) = 0) | ~ (a_member_of(v2, v0) = 0) | a_member_of(v2, v1) = 0)
% 2.63/1.47 |
% 2.63/1.47 | Applying alpha-rule on (1) yields:
% 2.63/1.47 | (2) ~ (all_0_0_0 = 0)
% 2.63/1.47 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (eq(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (a_member_of(v3, v1) = v5 & a_member_of(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))
% 2.63/1.47 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (eq(v0, v1) = 0) | ~ (a_member_of(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & a_member_of(v2, v1) = v4))
% 2.63/1.47 | (5) eq(all_0_2_2, all_0_1_1) = 0
% 2.63/1.47 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a_member_of(v3, v2) = v1) | ~ (a_member_of(v3, v2) = v0))
% 2.63/1.47 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (eq(v3, v2) = v1) | ~ (eq(v3, v2) = v0))
% 2.63/1.47 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (eq(v0, v1) = 0) | ~ (a_member_of(v2, v0) = 0) | a_member_of(v2, v1) = 0)
% 2.63/1.47 | (9) eq(all_0_1_1, all_0_2_2) = all_0_0_0
% 2.93/1.47 |
% 2.93/1.47 | Instantiating formula (3) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms eq(all_0_1_1, all_0_2_2) = all_0_0_0, yields:
% 2.93/1.47 | (10) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (a_member_of(v0, all_0_1_1) = v1 & a_member_of(v0, all_0_2_2) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 2.93/1.47 |
% 2.93/1.47 +-Applying beta-rule and splitting (10), into two cases.
% 2.93/1.47 |-Branch one:
% 2.93/1.47 | (11) all_0_0_0 = 0
% 2.93/1.47 |
% 2.93/1.47 | Equations (11) can reduce 2 to:
% 2.93/1.47 | (12) $false
% 2.93/1.47 |
% 2.93/1.47 |-The branch is then unsatisfiable
% 2.93/1.47 |-Branch two:
% 2.93/1.47 | (2) ~ (all_0_0_0 = 0)
% 2.93/1.47 | (14) ? [v0] : ? [v1] : ? [v2] : (a_member_of(v0, all_0_1_1) = v1 & a_member_of(v0, all_0_2_2) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 2.93/1.48 |
% 2.93/1.48 | Instantiating (14) with all_10_0_3, all_10_1_4, all_10_2_5 yields:
% 2.93/1.48 | (15) a_member_of(all_10_2_5, all_0_1_1) = all_10_1_4 & a_member_of(all_10_2_5, all_0_2_2) = all_10_0_3 & ( ~ (all_10_0_3 = 0) | ~ (all_10_1_4 = 0)) & (all_10_0_3 = 0 | all_10_1_4 = 0)
% 2.93/1.48 |
% 2.93/1.48 | Applying alpha-rule on (15) yields:
% 2.93/1.48 | (16) a_member_of(all_10_2_5, all_0_1_1) = all_10_1_4
% 2.93/1.48 | (17) a_member_of(all_10_2_5, all_0_2_2) = all_10_0_3
% 2.93/1.48 | (18) ~ (all_10_0_3 = 0) | ~ (all_10_1_4 = 0)
% 2.93/1.48 | (19) all_10_0_3 = 0 | all_10_1_4 = 0
% 2.93/1.48 |
% 2.93/1.48 | Instantiating formula (6) with all_10_2_5, all_0_2_2, all_10_0_3, all_10_1_4 and discharging atoms a_member_of(all_10_2_5, all_0_2_2) = all_10_0_3, yields:
% 2.93/1.48 | (20) all_10_0_3 = all_10_1_4 | ~ (a_member_of(all_10_2_5, all_0_2_2) = all_10_1_4)
% 2.93/1.48 |
% 2.93/1.48 | Instantiating formula (4) with all_10_0_3, all_10_2_5, all_0_1_1, all_0_2_2 and discharging atoms eq(all_0_2_2, all_0_1_1) = 0, a_member_of(all_10_2_5, all_0_2_2) = all_10_0_3, yields:
% 2.93/1.48 | (21) all_10_0_3 = 0 | ? [v0] : ( ~ (v0 = 0) & a_member_of(all_10_2_5, all_0_1_1) = v0)
% 2.93/1.48 |
% 2.93/1.48 +-Applying beta-rule and splitting (20), into two cases.
% 2.93/1.48 |-Branch one:
% 2.93/1.48 | (22) ~ (a_member_of(all_10_2_5, all_0_2_2) = all_10_1_4)
% 2.93/1.48 |
% 2.93/1.48 | Using (17) and (22) yields:
% 2.93/1.48 | (23) ~ (all_10_0_3 = all_10_1_4)
% 2.93/1.48 |
% 2.93/1.48 +-Applying beta-rule and splitting (18), into two cases.
% 2.93/1.48 |-Branch one:
% 2.93/1.48 | (24) ~ (all_10_0_3 = 0)
% 2.93/1.48 |
% 2.93/1.48 +-Applying beta-rule and splitting (19), into two cases.
% 2.93/1.48 |-Branch one:
% 2.93/1.48 | (25) all_10_0_3 = 0
% 2.93/1.48 |
% 2.93/1.48 | Equations (25) can reduce 24 to:
% 2.93/1.48 | (12) $false
% 2.93/1.48 |
% 2.93/1.48 |-The branch is then unsatisfiable
% 2.93/1.48 |-Branch two:
% 2.93/1.48 | (24) ~ (all_10_0_3 = 0)
% 2.93/1.48 | (28) all_10_1_4 = 0
% 2.93/1.48 |
% 2.93/1.48 | Equations (28) can reduce 23 to:
% 2.93/1.48 | (24) ~ (all_10_0_3 = 0)
% 2.93/1.48 |
% 2.93/1.48 | From (28) and (16) follows:
% 2.93/1.48 | (30) a_member_of(all_10_2_5, all_0_1_1) = 0
% 2.93/1.48 |
% 2.93/1.48 +-Applying beta-rule and splitting (21), into two cases.
% 2.93/1.48 |-Branch one:
% 2.93/1.48 | (25) all_10_0_3 = 0
% 2.93/1.48 |
% 2.93/1.48 | Equations (25) can reduce 24 to:
% 2.93/1.48 | (12) $false
% 2.93/1.48 |
% 2.93/1.48 |-The branch is then unsatisfiable
% 2.93/1.48 |-Branch two:
% 2.93/1.48 | (24) ~ (all_10_0_3 = 0)
% 2.93/1.48 | (34) ? [v0] : ( ~ (v0 = 0) & a_member_of(all_10_2_5, all_0_1_1) = v0)
% 2.93/1.48 |
% 2.93/1.48 | Instantiating (34) with all_38_0_6 yields:
% 2.93/1.48 | (35) ~ (all_38_0_6 = 0) & a_member_of(all_10_2_5, all_0_1_1) = all_38_0_6
% 2.93/1.48 |
% 2.93/1.48 | Applying alpha-rule on (35) yields:
% 2.93/1.48 | (36) ~ (all_38_0_6 = 0)
% 2.93/1.48 | (37) a_member_of(all_10_2_5, all_0_1_1) = all_38_0_6
% 2.93/1.48 |
% 2.93/1.48 | Instantiating formula (6) with all_10_2_5, all_0_1_1, 0, all_38_0_6 and discharging atoms a_member_of(all_10_2_5, all_0_1_1) = all_38_0_6, a_member_of(all_10_2_5, all_0_1_1) = 0, yields:
% 2.93/1.48 | (38) all_38_0_6 = 0
% 2.93/1.48 |
% 2.93/1.48 | Equations (38) can reduce 36 to:
% 2.93/1.48 | (12) $false
% 2.93/1.48 |
% 2.93/1.48 |-The branch is then unsatisfiable
% 2.93/1.48 |-Branch two:
% 2.93/1.48 | (25) all_10_0_3 = 0
% 2.93/1.48 | (41) ~ (all_10_1_4 = 0)
% 2.93/1.48 |
% 2.93/1.48 | Equations (25) can reduce 23 to:
% 2.93/1.48 | (42) ~ (all_10_1_4 = 0)
% 2.93/1.48 |
% 2.93/1.48 | Simplifying 42 yields:
% 2.93/1.48 | (41) ~ (all_10_1_4 = 0)
% 2.93/1.48 |
% 2.93/1.48 | From (25) and (17) follows:
% 2.93/1.48 | (44) a_member_of(all_10_2_5, all_0_2_2) = 0
% 2.93/1.48 |
% 2.93/1.48 | Instantiating formula (8) with all_10_2_5, all_0_1_1, all_0_2_2 and discharging atoms eq(all_0_2_2, all_0_1_1) = 0, a_member_of(all_10_2_5, all_0_2_2) = 0, yields:
% 2.93/1.49 | (30) a_member_of(all_10_2_5, all_0_1_1) = 0
% 2.93/1.49 |
% 2.93/1.49 | Instantiating formula (6) with all_10_2_5, all_0_1_1, 0, all_10_1_4 and discharging atoms a_member_of(all_10_2_5, all_0_1_1) = all_10_1_4, a_member_of(all_10_2_5, all_0_1_1) = 0, yields:
% 2.93/1.49 | (28) all_10_1_4 = 0
% 2.93/1.49 |
% 2.93/1.49 | Equations (28) can reduce 41 to:
% 2.93/1.49 | (12) $false
% 2.93/1.49 |
% 2.93/1.49 |-The branch is then unsatisfiable
% 2.93/1.49 |-Branch two:
% 2.93/1.49 | (48) a_member_of(all_10_2_5, all_0_2_2) = all_10_1_4
% 2.93/1.49 | (49) all_10_0_3 = all_10_1_4
% 2.93/1.49 |
% 2.93/1.49 +-Applying beta-rule and splitting (18), into two cases.
% 2.93/1.49 |-Branch one:
% 2.93/1.49 | (24) ~ (all_10_0_3 = 0)
% 2.93/1.49 |
% 2.93/1.49 | Equations (49) can reduce 24 to:
% 2.93/1.49 | (41) ~ (all_10_1_4 = 0)
% 2.93/1.49 |
% 2.93/1.49 +-Applying beta-rule and splitting (19), into two cases.
% 2.93/1.49 |-Branch one:
% 2.93/1.49 | (25) all_10_0_3 = 0
% 2.93/1.49 |
% 2.93/1.49 | Combining equations (25,49) yields a new equation:
% 2.93/1.49 | (28) all_10_1_4 = 0
% 2.93/1.49 |
% 2.93/1.49 | Equations (28) can reduce 41 to:
% 2.93/1.49 | (12) $false
% 2.93/1.49 |
% 2.93/1.49 |-The branch is then unsatisfiable
% 2.93/1.49 |-Branch two:
% 2.93/1.49 | (24) ~ (all_10_0_3 = 0)
% 2.93/1.49 | (28) all_10_1_4 = 0
% 2.93/1.49 |
% 2.93/1.49 | Equations (28) can reduce 41 to:
% 2.93/1.49 | (12) $false
% 2.93/1.49 |
% 2.93/1.49 |-The branch is then unsatisfiable
% 2.93/1.49 |-Branch two:
% 2.93/1.49 | (25) all_10_0_3 = 0
% 2.93/1.49 | (41) ~ (all_10_1_4 = 0)
% 2.93/1.49 |
% 2.93/1.49 | Combining equations (25,49) yields a new equation:
% 2.93/1.49 | (28) all_10_1_4 = 0
% 2.93/1.49 |
% 2.93/1.49 | Equations (28) can reduce 41 to:
% 2.93/1.49 | (12) $false
% 2.93/1.49 |
% 2.93/1.49 |-The branch is then unsatisfiable
% 2.93/1.49 % SZS output end Proof for theBenchmark
% 2.93/1.49
% 2.93/1.49 863ms
%------------------------------------------------------------------------------