TSTP Solution File: SET909+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET909+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 00:23:05 EDT 2022
% Result : Theorem 2.16s 1.24s
% Output : Proof 3.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET909+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n029.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 : Sun Jul 10 16:46:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.59/0.58 ____ _
% 0.59/0.58 ___ / __ \_____(_)___ ________ __________
% 0.59/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.58
% 0.59/0.58 A Theorem Prover for First-Order Logic
% 0.59/0.58 (ePrincess v.1.0)
% 0.59/0.58
% 0.59/0.58 (c) Philipp Rümmer, 2009-2015
% 0.59/0.58 (c) Peter Backeman, 2014-2015
% 0.59/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.58 Bug reports to peter@backeman.se
% 0.59/0.58
% 0.59/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.58
% 0.59/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.63/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.30/0.90 Prover 0: Preprocessing ...
% 1.89/1.10 Prover 0: Warning: ignoring some quantifiers
% 1.89/1.12 Prover 0: Constructing countermodel ...
% 2.16/1.24 Prover 0: proved (608ms)
% 2.16/1.24
% 2.16/1.24 No countermodel exists, formula is valid
% 2.16/1.24 % SZS status Theorem for theBenchmark
% 2.16/1.24
% 2.16/1.24 Generating proof ... Warning: ignoring some quantifiers
% 2.96/1.46 found it (size 7)
% 2.96/1.46
% 2.96/1.46 % SZS output start Proof for theBenchmark
% 2.96/1.46 Assumed formulas after preprocessing and simplification:
% 2.96/1.46 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (set_union2(v3, v2) = empty_set & unordered_pair(v0, v1) = v3 & empty(v5) & empty(empty_set) & ~ empty(v4) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | v9 = v6 | ~ (unordered_pair(v6, v7) = v8) | ~ in(v9, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (set_union2(v9, v8) = v7) | ~ (set_union2(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (unordered_pair(v9, v8) = v7) | ~ (unordered_pair(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v6, v7) = v8) | ~ in(v9, v8) | in(v9, v7) | in(v9, v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v6, v7) = v8) | ~ in(v9, v7) | in(v9, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v6, v7) = v8) | ~ in(v9, v6) | in(v9, v8)) & ? [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v6 | ~ (set_union2(v7, v8) = v9) | ? [v10] : (( ~ in(v10, v6) | ( ~ in(v10, v8) & ~ in(v10, v7))) & (in(v10, v8) | in(v10, v7) | in(v10, v6)))) & ? [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v6 | ~ (unordered_pair(v7, v8) = v9) | ? [v10] : ((v10 = v8 | v10 = v7 | in(v10, v6)) & ( ~ in(v10, v6) | ( ~ (v10 = v8) & ~ (v10 = v7))))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v7, v6) = v8) | ~ empty(v8) | empty(v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v7, v6) = v8) | set_union2(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v6, v7) = v8) | ~ empty(v8) | empty(v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v6, v7) = v8) | set_union2(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (unordered_pair(v7, v6) = v8) | unordered_pair(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (unordered_pair(v6, v7) = v8) | unordered_pair(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (unordered_pair(v6, v7) = v8) | in(v7, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (unordered_pair(v6, v7) = v8) | in(v6, v8)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (set_union2(v6, v6) = v7)) & ! [v6] : ! [v7] : ( ~ in(v7, v6) | ~ in(v6, v7)) & ! [v6] : ~ in(v6, empty_set) & ? [v6] : (v6 = empty_set | ? [v7] : in(v7, v6)))
% 3.25/1.50 | 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 yields:
% 3.25/1.50 | (1) set_union2(all_0_2_2, all_0_3_3) = empty_set & unordered_pair(all_0_5_5, all_0_4_4) = all_0_2_2 & empty(all_0_0_0) & empty(empty_set) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) & ! [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] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = 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] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ~ in(v0, empty_set) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0))
% 3.25/1.51 |
% 3.25/1.51 | Applying alpha-rule on (1) yields:
% 3.25/1.51 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 3.25/1.51 | (3) unordered_pair(all_0_5_5, all_0_4_4) = all_0_2_2
% 3.25/1.51 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2))
% 3.25/1.51 | (5) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1)))))
% 3.25/1.51 | (6) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0))
% 3.25/1.51 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2))
% 3.25/1.51 | (8) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 3.25/1.51 | (9) set_union2(all_0_2_2, all_0_3_3) = empty_set
% 3.25/1.51 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 3.25/1.51 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 3.25/1.51 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 3.25/1.51 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2))
% 3.25/1.51 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 3.25/1.51 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 3.25/1.51 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 3.25/1.51 | (17) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0))))
% 3.25/1.52 | (18) ~ empty(all_0_1_1)
% 3.25/1.52 | (19) empty(all_0_0_0)
% 3.25/1.52 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0))
% 3.25/1.52 | (21) empty(empty_set)
% 3.25/1.52 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 3.25/1.52 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2))
% 3.25/1.52 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 3.25/1.52 | (25) ! [v0] : ~ in(v0, empty_set)
% 3.25/1.52 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2))
% 3.25/1.52 |
% 3.25/1.52 | Instantiating formula (15) with empty_set, all_0_2_2, all_0_3_3 and discharging atoms set_union2(all_0_2_2, all_0_3_3) = empty_set, yields:
% 3.25/1.52 | (27) set_union2(all_0_3_3, all_0_2_2) = empty_set
% 3.25/1.52 |
% 3.25/1.52 | Instantiating formula (7) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms unordered_pair(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 3.25/1.52 | (28) in(all_0_5_5, all_0_2_2)
% 3.25/1.52 |
% 3.25/1.52 | Instantiating formula (4) with all_0_5_5, empty_set, all_0_2_2, all_0_3_3 and discharging atoms set_union2(all_0_3_3, all_0_2_2) = empty_set, in(all_0_5_5, all_0_2_2), yields:
% 3.25/1.52 | (29) in(all_0_5_5, empty_set)
% 3.25/1.52 |
% 3.25/1.52 | Instantiating formula (25) with all_0_5_5 and discharging atoms in(all_0_5_5, empty_set), yields:
% 3.25/1.52 | (30) $false
% 3.25/1.52 |
% 3.25/1.52 |-The branch is then unsatisfiable
% 3.25/1.52 % SZS output end Proof for theBenchmark
% 3.25/1.52
% 3.25/1.52 930ms
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