%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET618+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n005.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 : Wed Aug 31 18:25:07 EDT 2022

% Result   : Theorem 0.16s 0.43s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   20 (  19 unt;   0 def)
%            Number of atoms       :   21 (  20 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    9 (   8   ~;   0   |;   0   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   12 (  10   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f61,plain,
    $false,
    inference(subsumption_resolution,[],[f57,f60]) ).

fof(f60,plain,
    empty_set = sF4,
    inference(backward_demodulation,[],[f59,f41]) ).

fof(f41,plain,
    ! [X0] : union(X0,X0) = X0,
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] : union(X0,X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotency_of_union) ).

fof(f59,plain,
    union(empty_set,empty_set) = sF4,
    inference(backward_demodulation,[],[f56,f58]) ).

fof(f58,plain,
    empty_set = sF3,
    inference(backward_demodulation,[],[f55,f39]) ).

fof(f39,plain,
    ! [X0] : difference(X0,X0) = empty_set,
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : difference(X0,X0) = empty_set,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',self_difference_is_empty_set) ).

fof(f55,plain,
    difference(sK1,sK1) = sF3,
    introduced(function_definition,[]) ).

fof(f56,plain,
    union(sF3,sF3) = sF4,
    introduced(function_definition,[]) ).

fof(f57,plain,
    empty_set != sF4,
    inference(definition_folding,[],[f50,f56,f55,f55]) ).

fof(f50,plain,
    empty_set != union(difference(sK1,sK1),difference(sK1,sK1)),
    inference(definition_unfolding,[],[f37,f45]) ).

fof(f45,plain,
    ! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).

fof(f37,plain,
    empty_set != symmetric_difference(sK1,sK1),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    empty_set != symmetric_difference(sK1,sK1),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f16,f22]) ).

fof(f22,plain,
    ( ? [X0] : empty_set != symmetric_difference(X0,X0)
   => empty_set != symmetric_difference(sK1,sK1) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ? [X0] : empty_set != symmetric_difference(X0,X0),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X0] : empty_set = symmetric_difference(X0,X0),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X0] : empty_set = symmetric_difference(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th93) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SET618+3 : TPTP v8.1.0. Released v2.2.0.
% 0.00/0.11  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.10/0.31  % Computer : n005.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Tue Aug 30 14:11:33 EDT 2022
% 0.10/0.31  % CPUTime    : 
% 0.16/0.42  % (1424)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/99Mi)
% 0.16/0.42  % (1432)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/482Mi)
% 0.16/0.43  % (1432)First to succeed.
% 0.16/0.43  % (1432)Refutation found. Thanks to Tanya!
% 0.16/0.43  % SZS status Theorem for theBenchmark
% 0.16/0.43  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.43  % (1432)------------------------------
% 0.16/0.43  % (1432)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.43  % (1432)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.43  % (1432)Termination reason: Refutation
% 0.16/0.43  
% 0.16/0.43  % (1432)Memory used [KB]: 5373
% 0.16/0.43  % (1432)Time elapsed: 0.005 s
% 0.16/0.43  % (1432)Instructions burned: 2 (million)
% 0.16/0.43  % (1432)------------------------------
% 0.16/0.43  % (1432)------------------------------
% 0.16/0.43  % (1407)Success in time 0.111 s
%------------------------------------------------------------------------------