%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : COL010-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n007.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 15:51:40 EDT 2022

% Result   : Unsatisfiable 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   11 (   8 unt;   0 def)
%            Number of atoms       :   15 (   4 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   10 (   6   ~;   3   |;   0   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   22 (  22   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f23,plain,
    $false,
    inference(unit_resulting_resolution,[],[f7,f5,f17,f11]) ).

fof(f11,plain,
    ! [X2,X0,X1] :
      ( ~ sQ0_eqProxy(X1,X2)
      | ~ sQ0_eqProxy(X0,X1)
      | sQ0_eqProxy(X0,X2) ),
    inference(equality_proxy_axiom,[],[f4]) ).

fof(f4,plain,
    ! [X0,X1] :
      ( sQ0_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ0_eqProxy])]) ).

fof(f17,plain,
    ! [X0] : ~ sQ0_eqProxy(X0,apply(combinator,X0)),
    inference(unit_resulting_resolution,[],[f6,f10]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( sQ0_eqProxy(X1,X0)
      | ~ sQ0_eqProxy(X0,X1) ),
    inference(equality_proxy_axiom,[],[f4]) ).

fof(f6,plain,
    ! [X1] : ~ sQ0_eqProxy(apply(combinator,X1),X1),
    inference(equality_proxy_replacement,[],[f3,f4]) ).

fof(f3,axiom,
    ! [X1] : apply(combinator,X1) != X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).

fof(f5,plain,
    ! [X2,X0,X1] : sQ0_eqProxy(apply(apply(apply(b,X0),X1),X2),apply(X0,apply(X1,X2))),
    inference(equality_proxy_replacement,[],[f1,f4]) ).

fof(f1,axiom,
    ! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).

fof(f7,plain,
    ! [X2,X0,X1] : sQ0_eqProxy(apply(apply(apply(s2,X0),X1),X2),apply(apply(X0,X2),apply(X1,X1))),
    inference(equality_proxy_replacement,[],[f2,f4]) ).

fof(f2,axiom,
    ! [X2,X0,X1] : apply(apply(apply(s2,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_definition) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : COL010-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33  % Computer : n007.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    : 300
% 0.12/0.34  % DateTime   : Mon Aug 29 16:24:45 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.49  % (27939)lrs+10_5:1_br=off:ep=RSTC:sos=all:urr=on:i=267:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/267Mi)
% 0.19/0.49  % (27925)dis+31_8:1_br=off:fd=off:gs=on:lcm=reverse:nm=16:nwc=5.0:sp=reverse_arity:urr=on:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/37Mi)
% 0.19/0.50  % (27924)lrs+1_3:1_ep=RSTC:sos=on:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/33Mi)
% 0.19/0.50  % (27935)lrs+1011_1:1_asg=cautious:bsr=on:cond=on:drc=off:etr=on:fd=preordered:gs=on:plsq=on:plsqr=388,511:slsq=on:slsqc=1:slsqr=21,31:urr=on:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/439Mi)
% 0.19/0.50  % (27939)First to succeed.
% 0.19/0.51  % (27942)lrs+10_1:2_bd=preordered:drc=off:fd=preordered:fde=unused:sp=const_min:to=lpo:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/177Mi)
% 0.19/0.51  % (27933)lrs+10_1:1_drc=off:fd=preordered:plsq=on:sp=occurrence:to=lpo:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/48Mi)
% 0.19/0.51  % (27939)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Unsatisfiable for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (27939)------------------------------
% 0.19/0.51  % (27939)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (27939)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (27939)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (27939)Memory used [KB]: 5373
% 0.19/0.51  % (27939)Time elapsed: 0.117 s
% 0.19/0.51  % (27939)Instructions burned: 2 (million)
% 0.19/0.51  % (27939)------------------------------
% 0.19/0.51  % (27939)------------------------------
% 0.19/0.51  % (27916)Success in time 0.167 s
%------------------------------------------------------------------------------