TSTP Solution File: SET879+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET879+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.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 : Tue Jul 19 00:22:53 EDT 2022
% Result : Theorem 1.92s 1.11s
% Output : Proof 2.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET879+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n026.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 : Sun Jul 10 17:40:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.57 ____ _
% 0.18/0.57 ___ / __ \_____(_)___ ________ __________
% 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.57
% 0.18/0.57 A Theorem Prover for First-Order Logic
% 0.18/0.57 (ePrincess v.1.0)
% 0.18/0.57
% 0.18/0.57 (c) Philipp Rümmer, 2009-2015
% 0.18/0.57 (c) Peter Backeman, 2014-2015
% 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.57 Bug reports to peter@backeman.se
% 0.18/0.57
% 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.57
% 0.18/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.73/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.18/0.85 Prover 0: Preprocessing ...
% 1.54/0.98 Prover 0: Warning: ignoring some quantifiers
% 1.54/1.00 Prover 0: Constructing countermodel ...
% 1.92/1.11 Prover 0: proved (491ms)
% 1.92/1.11
% 1.92/1.11 No countermodel exists, formula is valid
% 1.92/1.11 % SZS status Theorem for theBenchmark
% 1.92/1.11
% 1.92/1.11 Generating proof ... Warning: ignoring some quantifiers
% 2.38/1.30 found it (size 17)
% 2.38/1.30
% 2.38/1.30 % SZS output start Proof for theBenchmark
% 2.38/1.30 Assumed formulas after preprocessing and simplification:
% 2.38/1.30 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (set_difference(v2, v3) = v4 & singleton(v1) = v3 & singleton(v0) = v2 & empty(v6) & ~ empty(v5) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (set_difference(v9, v8) = v10) | ~ (singleton(v7) = v9) | in(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_difference(v10, v9) = v8) | ~ (set_difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (singleton(v7) = v8) | ~ in(v9, v8)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_difference(v9, v8) = v9) | ~ (singleton(v7) = v9) | ~ in(v7, v8)) & ? [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (singleton(v8) = v9) | ? [v10] : (( ~ (v10 = v8) | ~ in(v8, v7)) & (v10 = v8 | in(v10, v7)))) & ! [v7] : ! [v8] : ( ~ (singleton(v7) = v8) | in(v7, v8)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)) & ((v4 = v2 & v1 = v0) | ( ~ (v4 = v2) & ~ (v1 = v0))))
% 2.38/1.33 | 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, all_0_6_6 yields:
% 2.38/1.33 | (1) set_difference(all_0_4_4, all_0_3_3) = all_0_2_2 & singleton(all_0_5_5) = all_0_3_3 & singleton(all_0_6_6) = all_0_4_4 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (set_difference(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v2, v1) = v2) | ~ (singleton(v0) = v2) | ~ in(v0, v1)) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ((all_0_2_2 = all_0_4_4 & all_0_5_5 = all_0_6_6) | ( ~ (all_0_2_2 = all_0_4_4) & ~ (all_0_5_5 = all_0_6_6)))
% 2.62/1.33 |
% 2.62/1.33 | Applying alpha-rule on (1) yields:
% 2.62/1.33 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 2.62/1.34 | (3) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 2.62/1.34 | (4) singleton(all_0_5_5) = all_0_3_3
% 2.62/1.34 | (5) set_difference(all_0_4_4, all_0_3_3) = all_0_2_2
% 2.62/1.34 | (6) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.62/1.34 | (7) empty(all_0_0_0)
% 2.62/1.34 | (8) ~ empty(all_0_1_1)
% 2.62/1.34 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 2.62/1.34 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1))
% 2.62/1.34 | (11) (all_0_2_2 = all_0_4_4 & all_0_5_5 = all_0_6_6) | ( ~ (all_0_2_2 = all_0_4_4) & ~ (all_0_5_5 = all_0_6_6))
% 2.62/1.34 | (12) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 2.62/1.34 | (13) singleton(all_0_6_6) = all_0_4_4
% 2.62/1.34 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (set_difference(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1))
% 2.62/1.34 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v2, v1) = v2) | ~ (singleton(v0) = v2) | ~ in(v0, v1))
% 2.62/1.34 |
% 2.62/1.34 | Instantiating formula (3) with all_0_3_3, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_3_3, yields:
% 2.62/1.34 | (16) in(all_0_5_5, all_0_3_3)
% 2.62/1.34 |
% 2.62/1.34 | Instantiating formula (14) with all_0_2_2, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms set_difference(all_0_4_4, all_0_3_3) = all_0_2_2, singleton(all_0_6_6) = all_0_4_4, yields:
% 2.62/1.34 | (17) all_0_2_2 = all_0_4_4 | in(all_0_6_6, all_0_3_3)
% 2.62/1.34 |
% 2.62/1.34 +-Applying beta-rule and splitting (11), into two cases.
% 2.62/1.34 |-Branch one:
% 2.62/1.34 | (18) all_0_2_2 = all_0_4_4 & all_0_5_5 = all_0_6_6
% 2.62/1.34 |
% 2.62/1.34 | Applying alpha-rule on (18) yields:
% 2.62/1.34 | (19) all_0_2_2 = all_0_4_4
% 2.62/1.34 | (20) all_0_5_5 = all_0_6_6
% 2.62/1.34 |
% 2.62/1.34 | From (19) and (5) follows:
% 2.62/1.34 | (21) set_difference(all_0_4_4, all_0_3_3) = all_0_4_4
% 2.62/1.34 |
% 2.62/1.34 | From (20) and (16) follows:
% 2.62/1.34 | (22) in(all_0_6_6, all_0_3_3)
% 2.62/1.34 |
% 2.62/1.34 | Instantiating formula (15) with all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms set_difference(all_0_4_4, all_0_3_3) = all_0_4_4, singleton(all_0_6_6) = all_0_4_4, in(all_0_6_6, all_0_3_3), yields:
% 2.62/1.35 | (23) $false
% 2.62/1.35 |
% 2.62/1.35 |-The branch is then unsatisfiable
% 2.62/1.35 |-Branch two:
% 2.62/1.35 | (24) ~ (all_0_2_2 = all_0_4_4) & ~ (all_0_5_5 = all_0_6_6)
% 2.62/1.35 |
% 2.62/1.35 | Applying alpha-rule on (24) yields:
% 2.62/1.35 | (25) ~ (all_0_2_2 = all_0_4_4)
% 2.62/1.35 | (26) ~ (all_0_5_5 = all_0_6_6)
% 2.62/1.35 |
% 2.62/1.35 +-Applying beta-rule and splitting (17), into two cases.
% 2.62/1.35 |-Branch one:
% 2.62/1.35 | (22) in(all_0_6_6, all_0_3_3)
% 2.62/1.35 |
% 2.62/1.35 | Instantiating formula (10) with all_0_6_6, all_0_3_3, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_3_3, in(all_0_6_6, all_0_3_3), yields:
% 2.62/1.35 | (20) all_0_5_5 = all_0_6_6
% 2.62/1.35 |
% 2.62/1.35 | Equations (20) can reduce 26 to:
% 2.62/1.35 | (29) $false
% 2.62/1.35 |
% 2.62/1.35 |-The branch is then unsatisfiable
% 2.62/1.35 |-Branch two:
% 2.62/1.35 | (30) ~ in(all_0_6_6, all_0_3_3)
% 2.62/1.35 | (19) all_0_2_2 = all_0_4_4
% 2.62/1.35 |
% 2.62/1.35 | Equations (19) can reduce 25 to:
% 2.62/1.35 | (29) $false
% 2.62/1.35 |
% 2.62/1.35 |-The branch is then unsatisfiable
% 2.62/1.35 % SZS output end Proof for theBenchmark
% 2.62/1.35
% 2.62/1.35 765ms
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