TSTP Solution File: SET921+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET921+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 00:23:10 EDT 2022
% Result : Theorem 2.12s 1.20s
% Output : Proof 2.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET921+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.12 % 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 21:14:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.58/0.59 ____ _
% 0.58/0.59 ___ / __ \_____(_)___ ________ __________
% 0.58/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.59
% 0.58/0.59 A Theorem Prover for First-Order Logic
% 0.58/0.60 (ePrincess v.1.0)
% 0.58/0.60
% 0.58/0.60 (c) Philipp Rümmer, 2009-2015
% 0.58/0.60 (c) Peter Backeman, 2014-2015
% 0.58/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.60 Bug reports to peter@backeman.se
% 0.58/0.60
% 0.58/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.60
% 0.58/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.32/0.92 Prover 0: Preprocessing ...
% 1.61/1.06 Prover 0: Warning: ignoring some quantifiers
% 1.61/1.08 Prover 0: Constructing countermodel ...
% 2.12/1.19 Prover 0: proved (551ms)
% 2.12/1.20
% 2.12/1.20 No countermodel exists, formula is valid
% 2.12/1.20 % SZS status Theorem for theBenchmark
% 2.12/1.20
% 2.12/1.20 Generating proof ... Warning: ignoring some quantifiers
% 2.61/1.38 found it (size 17)
% 2.61/1.38
% 2.61/1.38 % SZS output start Proof for theBenchmark
% 2.61/1.38 Assumed formulas after preprocessing and simplification:
% 2.61/1.38 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (set_difference(v1, v3) = v4 & singleton(v2) = v3 & empty(v6) & ~ empty(v5) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_difference(v10, v9) = v8) | ~ (set_difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ in(v10, v9) | ~ in(v10, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ in(v10, v9) | in(v10, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ in(v10, v7) | in(v10, v9) | in(v10, v8)) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_difference(v8, v9) = v10) | ? [v11] : (( ~ in(v11, v8) | ~ in(v11, v7) | in(v11, v9)) & (in(v11, v7) | (in(v11, v8) & ~ in(v11, v9))))) & ! [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] : (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)) & (( ~ (v2 = v0) & in(v0, v1) & ~ in(v0, v4)) | (in(v0, v4) & (v2 = v0 | ~ in(v0, v1)))))
% 2.82/1.42 | 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:
% 2.82/1.42 | (1) set_difference(all_0_5_5, all_0_3_3) = all_0_2_2 & singleton(all_0_4_4) = all_0_3_3 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) & (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2))))) & ! [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] : (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_4_4 = all_0_6_6) & in(all_0_6_6, all_0_5_5) & ~ in(all_0_6_6, all_0_2_2)) | (in(all_0_6_6, all_0_2_2) & (all_0_4_4 = all_0_6_6 | ~ in(all_0_6_6, all_0_5_5))))
% 2.82/1.42 |
% 2.82/1.42 | Applying alpha-rule on (1) yields:
% 2.82/1.42 | (2) empty(all_0_0_0)
% 2.82/1.42 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1))
% 2.82/1.42 | (4) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 2.82/1.42 | (5) ( ~ (all_0_4_4 = all_0_6_6) & in(all_0_6_6, all_0_5_5) & ~ in(all_0_6_6, all_0_2_2)) | (in(all_0_6_6, all_0_2_2) & (all_0_4_4 = all_0_6_6 | ~ in(all_0_6_6, all_0_5_5)))
% 2.82/1.42 | (6) singleton(all_0_4_4) = all_0_3_3
% 2.82/1.42 | (7) ~ empty(all_0_1_1)
% 2.82/1.43 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0))
% 2.82/1.43 | (9) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) & (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2)))))
% 2.82/1.43 | (10) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.82/1.43 | (11) set_difference(all_0_5_5, all_0_3_3) = all_0_2_2
% 2.82/1.43 | (12) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 2.82/1.43 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 2.82/1.43 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1))
% 2.82/1.43 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 2.82/1.43 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1))
% 2.82/1.43 |
% 2.82/1.43 | Instantiating formula (12) with all_0_3_3, all_0_4_4 and discharging atoms singleton(all_0_4_4) = all_0_3_3, yields:
% 2.82/1.43 | (17) in(all_0_4_4, all_0_3_3)
% 2.82/1.43 |
% 2.82/1.43 +-Applying beta-rule and splitting (5), into two cases.
% 2.82/1.43 |-Branch one:
% 2.82/1.43 | (18) ~ (all_0_4_4 = all_0_6_6) & in(all_0_6_6, all_0_5_5) & ~ in(all_0_6_6, all_0_2_2)
% 2.82/1.43 |
% 2.82/1.43 | Applying alpha-rule on (18) yields:
% 2.82/1.43 | (19) ~ (all_0_4_4 = all_0_6_6)
% 2.82/1.43 | (20) in(all_0_6_6, all_0_5_5)
% 2.82/1.43 | (21) ~ in(all_0_6_6, all_0_2_2)
% 2.82/1.43 |
% 2.82/1.43 | Instantiating formula (3) with all_0_6_6, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms set_difference(all_0_5_5, all_0_3_3) = all_0_2_2, in(all_0_6_6, all_0_5_5), ~ in(all_0_6_6, all_0_2_2), yields:
% 2.82/1.43 | (22) in(all_0_6_6, all_0_3_3)
% 2.82/1.43 |
% 2.82/1.43 | Instantiating formula (16) with all_0_6_6, all_0_3_3, all_0_4_4 and discharging atoms singleton(all_0_4_4) = all_0_3_3, in(all_0_6_6, all_0_3_3), yields:
% 2.82/1.43 | (23) all_0_4_4 = all_0_6_6
% 2.82/1.43 |
% 2.82/1.43 | Equations (23) can reduce 19 to:
% 2.82/1.43 | (24) $false
% 2.82/1.43 |
% 2.82/1.43 |-The branch is then unsatisfiable
% 2.82/1.43 |-Branch two:
% 2.82/1.43 | (25) in(all_0_6_6, all_0_2_2) & (all_0_4_4 = all_0_6_6 | ~ in(all_0_6_6, all_0_5_5))
% 2.82/1.43 |
% 2.82/1.43 | Applying alpha-rule on (25) yields:
% 2.82/1.43 | (26) in(all_0_6_6, all_0_2_2)
% 2.82/1.43 | (27) all_0_4_4 = all_0_6_6 | ~ in(all_0_6_6, all_0_5_5)
% 2.82/1.43 |
% 2.82/1.43 | Instantiating formula (8) with all_0_6_6, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms set_difference(all_0_5_5, all_0_3_3) = all_0_2_2, in(all_0_6_6, all_0_2_2), yields:
% 2.82/1.43 | (20) in(all_0_6_6, all_0_5_5)
% 2.82/1.43 |
% 2.82/1.43 +-Applying beta-rule and splitting (27), into two cases.
% 2.82/1.43 |-Branch one:
% 2.82/1.43 | (29) ~ in(all_0_6_6, all_0_5_5)
% 2.82/1.43 |
% 2.82/1.44 | Using (20) and (29) yields:
% 2.82/1.44 | (30) $false
% 2.82/1.44 |
% 2.82/1.44 |-The branch is then unsatisfiable
% 2.82/1.44 |-Branch two:
% 2.82/1.44 | (20) in(all_0_6_6, all_0_5_5)
% 2.82/1.44 | (23) all_0_4_4 = all_0_6_6
% 2.82/1.44 |
% 2.82/1.44 | From (23) and (17) follows:
% 2.82/1.44 | (22) in(all_0_6_6, all_0_3_3)
% 2.82/1.44 |
% 2.82/1.44 | Instantiating formula (14) with all_0_6_6, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms set_difference(all_0_5_5, all_0_3_3) = all_0_2_2, in(all_0_6_6, all_0_2_2), in(all_0_6_6, all_0_3_3), yields:
% 2.82/1.44 | (30) $false
% 2.82/1.44 |
% 2.82/1.44 |-The branch is then unsatisfiable
% 2.82/1.44 % SZS output end Proof for theBenchmark
% 2.82/1.44
% 2.82/1.44 830ms
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