%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : ARI081_1 : TPTP v8.1.0. Released v5.0.0.
% 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 : n020.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 15:47:23 EDT 2022

% Result   : Theorem 0.22s 0.53s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   23 (  14 unt;   4 typ;   0 def)
%            Number of atoms       :   29 (  28 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   17 (   7   ~;   0   |;   7   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number arithmetic     :   59 (   0 atm;  14 fun;  35 num;  10 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   4 usr;   7 con; 0-2 aty)
%            Number of variables   :   10 (   6   !;   4   ?;  10   :)

% Comments : 
%------------------------------------------------------------------------------
tff(func_def_6,type,
    sK0: $int ).

tff(func_def_7,type,
    sK1: $int ).

tff(func_def_8,type,
    sF2: $int ).

tff(func_def_9,type,
    sF3: $int ).

tff(f33,plain,
    $false,
    inference(trivial_inequality_removal,[],[f32]) ).

tff(f32,plain,
    13 != 13,
    inference(superposition,[],[f31,f30]) ).

tff(f30,plain,
    sK0 = 13,
    inference(superposition,[],[f24,f26]) ).

tff(f26,plain,
    sF3 = 13,
    inference(evaluation,[],[f23]) ).

tff(f23,plain,
    $sum(6,7) = sF3,
    introduced(function_definition,[]) ).

tff(f24,plain,
    sF3 = sK0,
    inference(definition_folding,[],[f19,f23]) ).

tff(f19,plain,
    $sum(6,7) = sK0,
    inference(cnf_transformation,[],[f17]) ).

tff(f17,plain,
    ? [X1: $int,X0: $int] :
      ( ( $sum(7,6) = X0 )
      & ( $sum(6,7) = X1 )
      & ( X0 != X1 ) ),
    inference(flattening,[],[f16]) ).

tff(f16,plain,
    ? [X0: $int,X1: $int] :
      ( ( X0 != X1 )
      & ( $sum(6,7) = X1 )
      & ( $sum(7,6) = X0 ) ),
    inference(ennf_transformation,[],[f15]) ).

tff(f15,plain,
    ~ ! [X0: $int,X1: $int] :
        ( ( ( $sum(6,7) = X1 )
          & ( $sum(7,6) = X0 ) )
       => ( X0 = X1 ) ),
    inference(rectify,[],[f2]) ).

tff(f2,negated_conjecture,
    ~ ! [X1: $int,X0: $int] :
        ( ( ( $sum(7,6) = X1 )
          & ( $sum(6,7) = X0 ) )
       => ( X0 = X1 ) ),
    inference(negated_conjecture,[],[f1]) ).

tff(f1,conjecture,
    ! [X1: $int,X0: $int] :
      ( ( ( $sum(7,6) = X1 )
        & ( $sum(6,7) = X0 ) )
     => ( X0 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',communative_sum_6_7) ).

tff(f31,plain,
    sK0 != 13,
    inference(superposition,[],[f18,f28]) ).

tff(f28,plain,
    sK1 = 13,
    inference(superposition,[],[f22,f25]) ).

tff(f25,plain,
    sF2 = 13,
    inference(evaluation,[],[f21]) ).

tff(f21,plain,
    $sum(7,6) = sF2,
    introduced(function_definition,[]) ).

tff(f22,plain,
    sK1 = sF2,
    inference(definition_folding,[],[f20,f21]) ).

tff(f20,plain,
    $sum(7,6) = sK1,
    inference(cnf_transformation,[],[f17]) ).

tff(f18,plain,
    sK1 != sK0,
    inference(cnf_transformation,[],[f17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem    : ARI081=1 : TPTP v8.1.0. Released v5.0.0.
% 0.14/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.36  % Computer : n020.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Mon Aug 29 15:22:45 EDT 2022
% 0.14/0.36  % CPUTime    : 
% 0.22/0.52  % (10299)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.22/0.52  % (10293)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.22/0.52  % (10300)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/100Mi)
% 0.22/0.52  % (10300)First to succeed.
% 0.22/0.52  % (10303)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/68Mi)
% 0.22/0.53  % (10300)Refutation found. Thanks to Tanya!
% 0.22/0.53  % SZS status Theorem for theBenchmark
% 0.22/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.53  % (10300)------------------------------
% 0.22/0.53  % (10300)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.53  % (10300)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.22/0.53  % (10300)Termination reason: Refutation
% 0.22/0.53  
% 0.22/0.53  % (10300)Memory used [KB]: 5373
% 0.22/0.53  % (10300)Time elapsed: 0.111 s
% 0.22/0.53  % (10300)Instructions burned: 2 (million)
% 0.22/0.53  % (10300)------------------------------
% 0.22/0.53  % (10300)------------------------------
% 0.22/0.53  % (10288)Success in time 0.154 s
%------------------------------------------------------------------------------