TSTP Solution File: SET940+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET940+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 00:23:20 EDT 2022

% Result   : Theorem 1.99s 1.09s
% Output   : Proof 2.68s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET940+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.11/0.32  % Computer : n029.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Sun Jul 10 15:34:46 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.54/0.56          ____       _                          
% 0.54/0.56    ___  / __ \_____(_)___  ________  __________
% 0.54/0.56   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.56  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.54/0.56  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.54/0.56  
% 0.54/0.56  A Theorem Prover for First-Order Logic
% 0.54/0.56  (ePrincess v.1.0)
% 0.54/0.56  
% 0.54/0.56  (c) Philipp Rümmer, 2009-2015
% 0.54/0.56  (c) Peter Backeman, 2014-2015
% 0.54/0.56  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.56  Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.56  Bug reports to peter@backeman.se
% 0.54/0.56  
% 0.54/0.56  For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.56  
% 0.54/0.56  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.59/0.61  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.32/0.84  Prover 0: Preprocessing ...
% 1.60/0.99  Prover 0: Constructing countermodel ...
% 1.99/1.08  Prover 0: proved (474ms)
% 1.99/1.08  
% 1.99/1.08  No countermodel exists, formula is valid
% 1.99/1.09  % SZS status Theorem for theBenchmark
% 1.99/1.09  
% 1.99/1.09  Generating proof ... found it (size 10)
% 2.48/1.27  
% 2.48/1.27  % SZS output start Proof for theBenchmark
% 2.48/1.27  Assumed formulas after preprocessing and simplification: 
% 2.48/1.27  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v4 = v3) & union(v2) = v3 & unordered_pair(v0, v1) = v2 & set_union2(v0, v1) = v4 & empty(v6) &  ~ empty(v5) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (unordered_pair(v10, v9) = v8) |  ~ (unordered_pair(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (set_union2(v10, v9) = v8) |  ~ (set_union2(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (union(v9) = v8) |  ~ (union(v9) = v7)) &  ! [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] :  ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) |  ? [v10] : (union(v9) = v10 & set_union2(v7, v8) = v10)) &  ! [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] : ( ~ (set_union2(v7, v8) = v9) |  ? [v10] : (union(v10) = v9 & unordered_pair(v7, v8) = v10)) &  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (set_union2(v7, v7) = v8)))
% 2.68/1.31  | 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:
% 2.68/1.31  | (1)  ~ (all_0_2_2 = all_0_3_3) & union(all_0_4_4) = all_0_3_3 & unordered_pair(all_0_6_6, all_0_5_5) = all_0_4_4 & set_union2(all_0_6_6, all_0_5_5) = all_0_2_2 & empty(all_0_0_0) &  ~ empty(all_0_1_1) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (union(v2) = v1) |  ~ (union(v2) = v0)) &  ! [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) |  ? [v3] : (union(v2) = v3 & set_union2(v0, v1) = v3)) &  ! [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] : ( ~ (set_union2(v0, v1) = v2) |  ? [v3] : (union(v3) = v2 & unordered_pair(v0, v1) = v3)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1))
% 2.68/1.32  |
% 2.68/1.32  | Applying alpha-rule on (1) yields:
% 2.68/1.32  | (2)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ~ empty(v2) | empty(v0))
% 2.68/1.32  | (3)  ~ empty(all_0_1_1)
% 2.68/1.32  | (4) empty(all_0_0_0)
% 2.68/1.32  | (5)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (union(v2) = v1) |  ~ (union(v2) = v0))
% 2.68/1.32  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 2.68/1.32  | (7)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 2.68/1.32  | (8)  ~ (all_0_2_2 = all_0_3_3)
% 2.68/1.32  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ? [v3] : (union(v3) = v2 & unordered_pair(v0, v1) = v3))
% 2.68/1.32  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 2.68/1.32  | (11) union(all_0_4_4) = all_0_3_3
% 2.68/1.32  | (12) unordered_pair(all_0_6_6, all_0_5_5) = all_0_4_4
% 2.68/1.32  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0))
% 2.68/1.32  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ~ empty(v2) | empty(v0))
% 2.68/1.32  | (15)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 2.68/1.32  | (16)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 2.68/1.32  | (17) set_union2(all_0_6_6, all_0_5_5) = all_0_2_2
% 2.68/1.32  | (18)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1))
% 2.68/1.32  | (19)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) |  ? [v3] : (union(v2) = v3 & set_union2(v0, v1) = v3))
% 2.68/1.32  |
% 2.68/1.32  | Instantiating formula (19) with 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_4_4, yields:
% 2.68/1.33  | (20)  ? [v0] : (union(all_0_4_4) = v0 & set_union2(all_0_6_6, all_0_5_5) = v0)
% 2.68/1.33  |
% 2.68/1.33  | Instantiating (20) with all_11_0_8 yields:
% 2.68/1.33  | (21) union(all_0_4_4) = all_11_0_8 & set_union2(all_0_6_6, all_0_5_5) = all_11_0_8
% 2.68/1.33  |
% 2.68/1.33  | Applying alpha-rule on (21) yields:
% 2.68/1.33  | (22) union(all_0_4_4) = all_11_0_8
% 2.68/1.33  | (23) set_union2(all_0_6_6, all_0_5_5) = all_11_0_8
% 2.68/1.33  |
% 2.68/1.33  | Instantiating formula (5) with all_0_4_4, all_11_0_8, all_0_3_3 and discharging atoms union(all_0_4_4) = all_11_0_8, union(all_0_4_4) = all_0_3_3, yields:
% 2.68/1.33  | (24) all_11_0_8 = all_0_3_3
% 2.68/1.33  |
% 2.68/1.33  | Instantiating formula (13) with all_0_6_6, all_0_5_5, all_11_0_8, all_0_2_2 and discharging atoms set_union2(all_0_6_6, all_0_5_5) = all_11_0_8, set_union2(all_0_6_6, all_0_5_5) = all_0_2_2, yields:
% 2.68/1.33  | (25) all_11_0_8 = all_0_2_2
% 2.68/1.33  |
% 2.68/1.33  | Combining equations (24,25) yields a new equation:
% 2.68/1.33  | (26) all_0_2_2 = all_0_3_3
% 2.68/1.33  |
% 2.68/1.33  | Equations (26) can reduce 8 to:
% 2.68/1.33  | (27) $false
% 2.68/1.33  |
% 2.68/1.33  |-The branch is then unsatisfiable
% 2.68/1.33  % SZS output end Proof for theBenchmark
% 2.68/1.33  
% 2.68/1.33  758ms
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