TSTP Solution File: SET929+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET929+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n015.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 00:23:16 EDT 2022
% Result : Theorem 1.74s 1.08s
% Output : Proof 2.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET929+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n015.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 Jul 9 21:57:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.54/0.57 ____ _
% 0.54/0.57 ___ / __ \_____(_)___ ________ __________
% 0.54/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.57
% 0.54/0.57 A Theorem Prover for First-Order Logic
% 0.54/0.57 (ePrincess v.1.0)
% 0.54/0.57
% 0.54/0.57 (c) Philipp Rümmer, 2009-2015
% 0.54/0.57 (c) Peter Backeman, 2014-2015
% 0.54/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.57 Bug reports to peter@backeman.se
% 0.54/0.57
% 0.54/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.57
% 0.54/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.60/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.10/0.84 Prover 0: Preprocessing ...
% 1.50/0.95 Prover 0: Warning: ignoring some quantifiers
% 1.55/0.97 Prover 0: Constructing countermodel ...
% 1.74/1.08 Prover 0: proved (461ms)
% 1.74/1.08
% 1.74/1.08 No countermodel exists, formula is valid
% 1.74/1.08 % SZS status Theorem for theBenchmark
% 1.74/1.08
% 1.74/1.08 Generating proof ... Warning: ignoring some quantifiers
% 2.49/1.27 found it (size 18)
% 2.49/1.27
% 2.49/1.27 % SZS output start Proof for theBenchmark
% 2.49/1.27 Assumed formulas after preprocessing and simplification:
% 2.49/1.27 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (set_difference(v3, v2) = v4 & unordered_pair(v0, v1) = v3 & empty(v6) & empty(empty_set) & ~ empty(v5) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_difference(v10, v9) = v8) | ~ (set_difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v7, v8) = v10) | ~ subset(v10, v9) | in(v8, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v7, v8) = v10) | ~ subset(v10, v9) | in(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v7, v8) = v10) | ~ in(v8, v9) | ~ in(v7, v9) | subset(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_difference(v7, v8) = v9) | ~ subset(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v8, v7) = v9) | unordered_pair(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | unordered_pair(v8, v7) = v9) & ! [v7] : ! [v8] : ( ~ (set_difference(v7, v8) = empty_set) | subset(v7, v8)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)) & ? [v7] : subset(v7, v7) & ((v4 = empty_set & ( ~ in(v1, v2) | ~ in(v0, v2))) | ( ~ (v4 = empty_set) & in(v1, v2) & in(v0, v2))))
% 2.72/1.31 | 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:
% 2.72/1.31 | (1) set_difference(all_0_3_3, all_0_4_4) = all_0_2_2 & unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3 & empty(all_0_0_0) & empty(empty_set) & ~ 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] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ? [v0] : subset(v0, v0) & ((all_0_2_2 = empty_set & ( ~ in(all_0_5_5, all_0_4_4) | ~ in(all_0_6_6, all_0_4_4))) | ( ~ (all_0_2_2 = empty_set) & in(all_0_5_5, all_0_4_4) & in(all_0_6_6, all_0_4_4)))
% 2.72/1.31 |
% 2.72/1.31 | Applying alpha-rule on (1) yields:
% 2.72/1.31 | (2) (all_0_2_2 = empty_set & ( ~ in(all_0_5_5, all_0_4_4) | ~ in(all_0_6_6, all_0_4_4))) | ( ~ (all_0_2_2 = empty_set) & in(all_0_5_5, all_0_4_4) & in(all_0_6_6, all_0_4_4))
% 2.72/1.32 | (3) empty(empty_set)
% 2.72/1.32 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1))
% 2.72/1.32 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2))
% 2.72/1.32 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2))
% 2.72/1.32 | (7) ? [v0] : subset(v0, v0)
% 2.72/1.32 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 2.72/1.32 | (9) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1))
% 2.72/1.32 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 2.72/1.32 | (11) empty(all_0_0_0)
% 2.72/1.32 | (12) set_difference(all_0_3_3, all_0_4_4) = all_0_2_2
% 2.72/1.32 | (13) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.72/1.32 | (14) ~ empty(all_0_1_1)
% 2.72/1.32 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2))
% 2.72/1.32 | (16) unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3
% 2.72/1.32 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 2.72/1.32 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 2.72/1.32 |
% 2.72/1.32 +-Applying beta-rule and splitting (2), into two cases.
% 2.72/1.32 |-Branch one:
% 2.72/1.32 | (19) all_0_2_2 = empty_set & ( ~ in(all_0_5_5, all_0_4_4) | ~ in(all_0_6_6, all_0_4_4))
% 2.72/1.32 |
% 2.72/1.32 | Applying alpha-rule on (19) yields:
% 2.72/1.32 | (20) all_0_2_2 = empty_set
% 2.72/1.32 | (21) ~ in(all_0_5_5, all_0_4_4) | ~ in(all_0_6_6, all_0_4_4)
% 2.72/1.32 |
% 2.72/1.32 | From (20) and (12) follows:
% 2.72/1.32 | (22) set_difference(all_0_3_3, all_0_4_4) = empty_set
% 2.72/1.32 |
% 2.72/1.32 | Instantiating formula (9) with all_0_4_4, all_0_3_3 and discharging atoms set_difference(all_0_3_3, all_0_4_4) = empty_set, yields:
% 2.72/1.32 | (23) subset(all_0_3_3, all_0_4_4)
% 2.72/1.32 |
% 2.72/1.32 | Instantiating formula (5) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3, subset(all_0_3_3, all_0_4_4), yields:
% 2.72/1.33 | (24) in(all_0_5_5, all_0_4_4)
% 2.72/1.33 |
% 2.72/1.33 | Instantiating formula (15) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3, subset(all_0_3_3, all_0_4_4), yields:
% 2.72/1.33 | (25) in(all_0_6_6, all_0_4_4)
% 2.72/1.33 |
% 2.72/1.33 +-Applying beta-rule and splitting (21), into two cases.
% 2.72/1.33 |-Branch one:
% 2.72/1.33 | (26) ~ in(all_0_5_5, all_0_4_4)
% 2.72/1.33 |
% 2.72/1.33 | Using (24) and (26) yields:
% 2.72/1.33 | (27) $false
% 2.72/1.33 |
% 2.72/1.33 |-The branch is then unsatisfiable
% 2.72/1.33 |-Branch two:
% 2.72/1.33 | (24) in(all_0_5_5, all_0_4_4)
% 2.72/1.33 | (29) ~ in(all_0_6_6, all_0_4_4)
% 2.72/1.33 |
% 2.72/1.33 | Using (25) and (29) yields:
% 2.72/1.33 | (27) $false
% 2.72/1.33 |
% 2.72/1.33 |-The branch is then unsatisfiable
% 2.72/1.33 |-Branch two:
% 2.72/1.33 | (31) ~ (all_0_2_2 = empty_set) & in(all_0_5_5, all_0_4_4) & in(all_0_6_6, all_0_4_4)
% 2.72/1.33 |
% 2.72/1.33 | Applying alpha-rule on (31) yields:
% 2.72/1.33 | (32) ~ (all_0_2_2 = empty_set)
% 2.72/1.33 | (24) in(all_0_5_5, all_0_4_4)
% 2.72/1.33 | (25) in(all_0_6_6, all_0_4_4)
% 2.72/1.33 |
% 2.72/1.33 | Instantiating formula (6) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3, in(all_0_5_5, all_0_4_4), in(all_0_6_6, all_0_4_4), yields:
% 2.72/1.33 | (23) subset(all_0_3_3, all_0_4_4)
% 2.72/1.33 |
% 2.72/1.33 | Instantiating formula (4) with all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms set_difference(all_0_3_3, all_0_4_4) = all_0_2_2, subset(all_0_3_3, all_0_4_4), yields:
% 2.72/1.33 | (20) all_0_2_2 = empty_set
% 2.72/1.33 |
% 2.72/1.33 | Equations (20) can reduce 32 to:
% 2.72/1.33 | (37) $false
% 2.72/1.33 |
% 2.72/1.33 |-The branch is then unsatisfiable
% 2.72/1.33 % SZS output end Proof for theBenchmark
% 2.72/1.33
% 2.72/1.33 754ms
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