TSTP Solution File: SET949+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET949+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n014.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 00:23:23 EDT 2022

% Result   : Theorem 20.56s 6.05s
% Output   : Proof 21.59s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET949+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n014.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 13:20:35 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.56/0.57          ____       _                          
% 0.56/0.57    ___  / __ \_____(_)___  ________  __________
% 0.56/0.57   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.57  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.56/0.57  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.56/0.57  
% 0.56/0.57  A Theorem Prover for First-Order Logic
% 0.56/0.58  (ePrincess v.1.0)
% 0.56/0.58  
% 0.56/0.58  (c) Philipp Rümmer, 2009-2015
% 0.56/0.58  (c) Peter Backeman, 2014-2015
% 0.56/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.58  Bug reports to peter@backeman.se
% 0.56/0.58  
% 0.56/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.58  
% 0.56/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.56/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.30/0.88  Prover 0: Preprocessing ...
% 1.67/1.06  Prover 0: Warning: ignoring some quantifiers
% 1.81/1.08  Prover 0: Constructing countermodel ...
% 20.23/5.92  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 20.23/5.94  Prover 1: Preprocessing ...
% 20.56/6.02  Prover 1: Warning: ignoring some quantifiers
% 20.56/6.02  Prover 1: Constructing countermodel ...
% 20.56/6.05  Prover 1: proved (129ms)
% 20.56/6.05  Prover 0: stopped
% 20.56/6.05  
% 20.56/6.05  No countermodel exists, formula is valid
% 20.56/6.05  % SZS status Theorem for theBenchmark
% 20.56/6.05  
% 20.56/6.05  Generating proof ... Warning: ignoring some quantifiers
% 20.96/6.17  found it (size 7)
% 20.96/6.17  
% 20.96/6.17  % SZS output start Proof for theBenchmark
% 20.96/6.17  Assumed formulas after preprocessing and simplification: 
% 20.96/6.17  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v5 = 0) & empty(v6) = 0 & empty(v4) = v5 & cartesian_product2(v1, v2) = v3 & in(v0, v3) = 0 &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = 0 |  ~ (cartesian_product2(v7, v8) = v9) |  ~ (ordered_pair(v12, v13) = v10) |  ~ (in(v10, v9) = v11) |  ? [v14] :  ? [v15] : (in(v13, v8) = v15 & in(v12, v7) = v14 & ( ~ (v15 = 0) |  ~ (v14 = 0)))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (singleton(v7) = v10) |  ~ (unordered_pair(v9, v10) = v11) |  ~ (unordered_pair(v7, v8) = v9) | ordered_pair(v7, v8) = v11) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (cartesian_product2(v10, v9) = v8) |  ~ (cartesian_product2(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (ordered_pair(v10, v9) = v8) |  ~ (ordered_pair(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (unordered_pair(v10, v9) = v8) |  ~ (unordered_pair(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (in(v10, v9) = v8) |  ~ (in(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (cartesian_product2(v7, v8) = v9) |  ~ (in(v10, v9) = 0) |  ? [v11] :  ? [v12] : (ordered_pair(v11, v12) = v10 & in(v12, v8) = 0 & in(v11, v7) = 0)) &  ? [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v7 |  ~ (cartesian_product2(v8, v9) = v10) |  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] : (in(v11, v7) = v12 & ( ~ (v12 = 0) |  ! [v18] :  ! [v19] : ( ~ (ordered_pair(v18, v19) = v11) |  ? [v20] :  ? [v21] : (in(v19, v9) = v21 & in(v18, v8) = v20 & ( ~ (v21 = 0) |  ~ (v20 = 0))))) & (v12 = 0 | (v17 = v11 & v16 = 0 & v15 = 0 & ordered_pair(v13, v14) = v11 & in(v14, v9) = 0 & in(v13, v8) = 0)))) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (empty(v9) = v8) |  ~ (empty(v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (singleton(v9) = v8) |  ~ (singleton(v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) |  ? [v10] : ( ~ (v10 = 0) & empty(v9) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | unordered_pair(v8, v7) = v9) &  ! [v7] :  ! [v8] :  ~ (ordered_pair(v7, v8) = v0) &  ! [v7] :  ! [v8] : ( ~ (in(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & in(v8, v7) = v9)))
% 21.51/6.20  | 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:
% 21.51/6.20  | (1)  ~ (all_0_1_1 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & cartesian_product2(all_0_5_5, all_0_4_4) = all_0_3_3 & in(all_0_6_6, all_0_3_3) = 0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = 0 |  ~ (cartesian_product2(v0, v1) = v2) |  ~ (ordered_pair(v5, v6) = v3) |  ~ (in(v3, v2) = v4) |  ? [v7] :  ? [v8] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v0) = v3) |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cartesian_product2(v3, v2) = v1) |  ~ (cartesian_product2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) |  ~ (in(v3, v2) = 0) |  ? [v4] :  ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0)) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (cartesian_product2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : (in(v4, v0) = v5 & ( ~ (v5 = 0) |  ! [v11] :  ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) |  ? [v13] :  ? [v14] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ (v14 = 0) |  ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ~ (ordered_pair(v0, v1) = all_0_6_6) &  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 21.51/6.21  |
% 21.51/6.21  | Applying alpha-rule on (1) yields:
% 21.51/6.21  | (2) empty(all_0_2_2) = all_0_1_1
% 21.51/6.21  | (3)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
% 21.51/6.21  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0))
% 21.59/6.21  | (5)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 21.59/6.21  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 21.59/6.21  | (7)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (cartesian_product2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : (in(v4, v0) = v5 & ( ~ (v5 = 0) |  ! [v11] :  ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) |  ? [v13] :  ? [v14] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ (v14 = 0) |  ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0))))
% 21.59/6.22  | (8)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 21.59/6.22  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 21.59/6.22  | (10) cartesian_product2(all_0_5_5, all_0_4_4) = all_0_3_3
% 21.59/6.22  | (11)  ! [v0] :  ! [v1] :  ~ (ordered_pair(v0, v1) = all_0_6_6)
% 21.59/6.22  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v0) = v3) |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 21.59/6.22  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 21.59/6.22  | (14) empty(all_0_0_0) = 0
% 21.59/6.22  | (15) in(all_0_6_6, all_0_3_3) = 0
% 21.59/6.22  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cartesian_product2(v3, v2) = v1) |  ~ (cartesian_product2(v3, v2) = v0))
% 21.59/6.22  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) |  ~ (in(v3, v2) = 0) |  ? [v4] :  ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0))
% 21.59/6.22  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = 0 |  ~ (cartesian_product2(v0, v1) = v2) |  ~ (ordered_pair(v5, v6) = v3) |  ~ (in(v3, v2) = v4) |  ? [v7] :  ? [v8] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0))))
% 21.59/6.22  | (19)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 21.59/6.22  | (20)  ~ (all_0_1_1 = 0)
% 21.59/6.22  |
% 21.59/6.22  | Instantiating formula (17) with all_0_6_6, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms cartesian_product2(all_0_5_5, all_0_4_4) = all_0_3_3, in(all_0_6_6, all_0_3_3) = 0, yields:
% 21.59/6.22  | (21)  ? [v0] :  ? [v1] : (ordered_pair(v0, v1) = all_0_6_6 & in(v1, all_0_4_4) = 0 & in(v0, all_0_5_5) = 0)
% 21.59/6.22  |
% 21.59/6.22  | Instantiating (21) with all_12_0_9, all_12_1_10 yields:
% 21.59/6.22  | (22) ordered_pair(all_12_1_10, all_12_0_9) = all_0_6_6 & in(all_12_0_9, all_0_4_4) = 0 & in(all_12_1_10, all_0_5_5) = 0
% 21.59/6.22  |
% 21.59/6.22  | Applying alpha-rule on (22) yields:
% 21.59/6.22  | (23) ordered_pair(all_12_1_10, all_12_0_9) = all_0_6_6
% 21.59/6.22  | (24) in(all_12_0_9, all_0_4_4) = 0
% 21.59/6.22  | (25) in(all_12_1_10, all_0_5_5) = 0
% 21.59/6.22  |
% 21.59/6.22  | Instantiating formula (11) with all_12_0_9, all_12_1_10 and discharging atoms ordered_pair(all_12_1_10, all_12_0_9) = all_0_6_6, yields:
% 21.59/6.22  | (26) $false
% 21.59/6.22  |
% 21.59/6.22  |-The branch is then unsatisfiable
% 21.59/6.22  % SZS output end Proof for theBenchmark
% 21.59/6.22  
% 21.59/6.22  5638ms
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