TSTP Solution File: SET622+3 by iProver---3.9

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%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET622+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n003.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  : 300s
% DateTime : Fri May  3 03:01:00 EDT 2024

% Result   : Theorem 3.47s 1.19s
% Output   : CNFRefutation 3.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   21 (  20 unt;   0 def)
%            Number of atoms       :   22 (  21 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   10 (   9   ~;   0   |;   0   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   40 (   0 sgn  26   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1,X2] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_intersection) ).

fof(f2,axiom,
    ! [X0,X1,X2] : difference(X0,difference(X1,X2)) = union(difference(X0,X1),intersection(X0,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_difference_union2) ).

fof(f3,axiom,
    ! [X0,X1] : symmetric_difference(X0,X1) = difference(union(X0,X1),intersection(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_and_difference) ).

fof(f10,axiom,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).

fof(f15,conjecture,
    ! [X0,X1,X2] : difference(X0,symmetric_difference(X1,X2)) = union(difference(X0,union(X1,X2)),intersection(intersection(X0,X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th98) ).

fof(f16,negated_conjecture,
    ~ ! [X0,X1,X2] : difference(X0,symmetric_difference(X1,X2)) = union(difference(X0,union(X1,X2)),intersection(intersection(X0,X1),X2)),
    inference(negated_conjecture,[],[f15]) ).

fof(f18,plain,
    ? [X0,X1,X2] : difference(X0,symmetric_difference(X1,X2)) != union(difference(X0,union(X1,X2)),intersection(intersection(X0,X1),X2)),
    inference(ennf_transformation,[],[f16]) ).

fof(f35,plain,
    ( ? [X0,X1,X2] : difference(X0,symmetric_difference(X1,X2)) != union(difference(X0,union(X1,X2)),intersection(intersection(X0,X1),X2))
   => difference(sK2,symmetric_difference(sK3,sK4)) != union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)) ),
    introduced(choice_axiom,[]) ).

fof(f36,plain,
    difference(sK2,symmetric_difference(sK3,sK4)) != union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f18,f35]) ).

fof(f37,plain,
    ! [X2,X0,X1] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
    inference(cnf_transformation,[],[f1]) ).

fof(f38,plain,
    ! [X2,X0,X1] : difference(X0,difference(X1,X2)) = union(difference(X0,X1),intersection(X0,X2)),
    inference(cnf_transformation,[],[f2]) ).

fof(f39,plain,
    ! [X0,X1] : symmetric_difference(X0,X1) = difference(union(X0,X1),intersection(X0,X1)),
    inference(cnf_transformation,[],[f3]) ).

fof(f54,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f10]) ).

fof(f64,plain,
    difference(sK2,symmetric_difference(sK3,sK4)) != union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)),
    inference(cnf_transformation,[],[f36]) ).

fof(f67,plain,
    union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)) != difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),
    inference(definition_unfolding,[],[f64,f39]) ).

cnf(c_49,plain,
    intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
    inference(cnf_transformation,[],[f37]) ).

cnf(c_50,plain,
    union(difference(X0,X1),intersection(X0,X2)) = difference(X0,difference(X1,X2)),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_65,plain,
    intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f54]) ).

cnf(c_73,negated_conjecture,
    union(difference(sK2,union(sK3,sK4)),intersection(intersection(sK2,sK3),sK4)) != difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),
    inference(cnf_transformation,[],[f67]) ).

cnf(c_90,negated_conjecture,
    union(difference(sK2,union(sK3,sK4)),intersection(sK2,intersection(sK3,sK4))) != difference(sK2,difference(union(sK3,sK4),intersection(sK3,sK4))),
    inference(theory_normalisation,[status(thm)],[c_73,c_49,c_65]) ).

cnf(c_101,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_90,c_50]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SET622+3 : TPTP v8.1.2. Released v2.2.0.
% 0.04/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n003.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May  2 20:25:20 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.47/1.19  % SZS status Started for theBenchmark.p
% 3.47/1.19  % SZS status Theorem for theBenchmark.p
% 3.47/1.19  
% 3.47/1.19  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.47/1.19  
% 3.47/1.19  ------  iProver source info
% 3.47/1.19  
% 3.47/1.19  git: date: 2024-05-02 19:28:25 +0000
% 3.47/1.19  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.47/1.19  git: non_committed_changes: false
% 3.47/1.19  
% 3.47/1.19  ------ Parsing...
% 3.47/1.19  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.47/1.19  
% 3.47/1.19  ------ Preprocessing...
% 3.47/1.19  
% 3.47/1.19  % SZS status Theorem for theBenchmark.p
% 3.47/1.19  
% 3.47/1.19  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.47/1.19  
% 3.47/1.19  
%------------------------------------------------------------------------------