TSTP Solution File: SET907+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET907+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.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 00:23:03 EDT 2022
% Result : Theorem 2.11s 1.17s
% Output : Proof 2.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET907+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n028.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 21:56:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.57/0.59 ____ _
% 0.57/0.59 ___ / __ \_____(_)___ ________ __________
% 0.57/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.59
% 0.57/0.59 A Theorem Prover for First-Order Logic
% 0.57/0.59 (ePrincess v.1.0)
% 0.57/0.59
% 0.57/0.59 (c) Philipp Rümmer, 2009-2015
% 0.57/0.59 (c) Peter Backeman, 2014-2015
% 0.57/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.59 Bug reports to peter@backeman.se
% 0.57/0.59
% 0.57/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.59
% 0.57/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.34/0.91 Prover 0: Preprocessing ...
% 1.63/1.06 Prover 0: Warning: ignoring some quantifiers
% 1.63/1.07 Prover 0: Constructing countermodel ...
% 2.11/1.17 Prover 0: proved (526ms)
% 2.11/1.17
% 2.11/1.17 No countermodel exists, formula is valid
% 2.11/1.17 % SZS status Theorem for theBenchmark
% 2.11/1.17
% 2.11/1.17 Generating proof ... Warning: ignoring some quantifiers
% 2.66/1.34 found it (size 6)
% 2.66/1.34
% 2.66/1.34 % SZS output start Proof for theBenchmark
% 2.66/1.34 Assumed formulas after preprocessing and simplification:
% 2.66/1.34 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v4 = v1) & set_union2(v3, v1) = v4 & unordered_pair(v0, v2) = v3 & empty(v6) & in(v2, v1) & in(v0, v1) & ~ empty(v5) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_union2(v10, v9) = v8) | ~ (set_union2(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 = v8 | ~ (set_union2(v7, v8) = v9) | ~ subset(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | ~ empty(v9) | empty(v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | set_union2(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | ~ empty(v9) | empty(v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | set_union2(v8, v7) = v9) & ! [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] : (v8 = v7 | ~ (set_union2(v7, v7) = v8)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)) & ? [v7] : subset(v7, v7))
% 2.66/1.38 | 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:
% 2.66/1.38 | (1) ~ (all_0_2_2 = all_0_5_5) & set_union2(all_0_3_3, all_0_5_5) = all_0_2_2 & unordered_pair(all_0_6_6, all_0_4_4) = all_0_3_3 & empty(all_0_0_0) & in(all_0_4_4, all_0_5_5) & in(all_0_6_6, all_0_5_5) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(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 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [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] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ? [v0] : subset(v0, v0)
% 2.66/1.39 |
% 2.66/1.39 | Applying alpha-rule on (1) yields:
% 2.66/1.39 | (2) set_union2(all_0_3_3, all_0_5_5) = all_0_2_2
% 2.66/1.39 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2))
% 2.66/1.39 | (4) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 2.66/1.39 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 2.66/1.39 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 2.66/1.39 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 2.66/1.39 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2))
% 2.83/1.39 | (9) in(all_0_4_4, all_0_5_5)
% 2.83/1.39 | (10) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.83/1.39 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2))
% 2.83/1.39 | (12) empty(all_0_0_0)
% 2.83/1.39 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 2.83/1.39 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 2.83/1.39 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 2.83/1.39 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 2.83/1.39 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 2.83/1.39 | (18) in(all_0_6_6, all_0_5_5)
% 2.83/1.39 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1))
% 2.83/1.40 | (20) unordered_pair(all_0_6_6, all_0_4_4) = all_0_3_3
% 2.83/1.40 | (21) ~ (all_0_2_2 = all_0_5_5)
% 2.83/1.40 | (22) ~ empty(all_0_1_1)
% 2.83/1.40 | (23) ? [v0] : subset(v0, v0)
% 2.83/1.40 |
% 2.83/1.40 | Instantiating formula (8) with all_0_3_3, all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms unordered_pair(all_0_6_6, all_0_4_4) = all_0_3_3, in(all_0_4_4, all_0_5_5), in(all_0_6_6, all_0_5_5), yields:
% 2.83/1.40 | (24) subset(all_0_3_3, all_0_5_5)
% 2.83/1.40 |
% 2.83/1.40 | Instantiating formula (19) with all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms set_union2(all_0_3_3, all_0_5_5) = all_0_2_2, subset(all_0_3_3, all_0_5_5), yields:
% 2.83/1.40 | (25) all_0_2_2 = all_0_5_5
% 2.83/1.40 |
% 2.83/1.40 | Equations (25) can reduce 21 to:
% 2.83/1.40 | (26) $false
% 2.83/1.40 |
% 2.83/1.40 |-The branch is then unsatisfiable
% 2.83/1.40 % SZS output end Proof for theBenchmark
% 2.83/1.40
% 2.83/1.40 798ms
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