TSTP Solution File: COL009-1 by SnakeForV---1.0

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : COL009-1 : 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 : n014.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 0.20s 0.54s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   15 (  11 unt;   0 def)
%            Number of atoms       :   21 (   4 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   16 (  10   ~;   5   |;   0   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 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   :   29 (  29   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f132,plain,
    $false,
    inference(unit_resulting_resolution,[],[f5,f9,f34,f8]) ).

fof(f8,plain,
    ! [X2,X3,X0,X1] :
      ( sQ0_eqProxy(apply(X0,X2),apply(X1,X3))
      | ~ sQ0_eqProxy(X0,X1)
      | ~ sQ0_eqProxy(X2,X3) ),
    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(f34,plain,
    ! [X0,X1] : ~ sQ0_eqProxy(apply(X0,apply(X1,X1)),apply(apply(apply(b,combinator),apply(l2,X1)),X0)),
    inference(unit_resulting_resolution,[],[f7,f18,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(f18,plain,
    ! [X0,X1] : ~ sQ0_eqProxy(apply(X0,X1),apply(apply(apply(b,combinator),X0),X1)),
    inference(unit_resulting_resolution,[],[f5,f12,f11]) ).

fof(f12,plain,
    ! [X1] : ~ sQ0_eqProxy(X1,apply(combinator,X1)),
    inference(forward_literal_rewriting,[],[f6,f10]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( ~ sQ0_eqProxy(X0,X1)
      | sQ0_eqProxy(X1,X0) ),
    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(f7,plain,
    ! [X0,X1] : sQ0_eqProxy(apply(apply(l2,X0),X1),apply(X1,apply(X0,X0))),
    inference(equality_proxy_replacement,[],[f2,f4]) ).

fof(f2,axiom,
    ! [X0,X1] : apply(apply(l2,X0),X1) = apply(X1,apply(X0,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_definition) ).

fof(f9,plain,
    ! [X0] : sQ0_eqProxy(X0,X0),
    inference(equality_proxy_axiom,[],[f4]) ).

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) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : COL009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35  % Computer : n014.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Mon Aug 29 16:40:33 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.51  % (12091)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 (2999ds/48Mi)
% 0.20/0.51  % (12092)dis+10_1:1024_anc=all:drc=off:flr=on:fsr=off:sac=on:urr=on:i=292:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/292Mi)
% 0.20/0.52  % (12103)dis+21_1:8_aac=none:bs=unit_only:er=filter:fd=off:nwc=5.0:s2pl=no:i=111:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/111Mi)
% 0.20/0.52  % (12095)dis+10_1:7_drc=off:fd=preordered:plsq=on:sp=reverse_frequency:to=lpo:i=212:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/212Mi)
% 0.20/0.52  % (12093)dis+2_1:1024_abs=on:alpa=false:anc=all_dependent:avsq=on:bce=on:drc=off:newcnf=on:slsq=on:slsqc=0:slsqr=1,1:sp=reverse_arity:i=353:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/353Mi)
% 0.20/0.52  % (12086)lrs+10_1:1_avsq=on:avsql=on:bsr=unit_only:drc=off:fsr=off:inw=on:nwc=10.0:rnwc=on:sgt=16:slsq=on:slsqc=0:slsql=off:slsqr=211,119:sp=reverse_frequency:spb=goal_then_units:ss=included:st=2.0:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.53  % (12080)lrs+10_1:16_awrs=converge:awrsf=40:br=off:ep=RSTC:flr=on:gsp=on:nwc=3.0:sos=on:urr=on:i=10:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/10Mi)
% 0.20/0.53  % (12087)lrs+1_3:1_ep=RSTC:sos=on:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.20/0.53  % (12096)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 (2999ds/48Mi)
% 0.20/0.53  % (12084)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 (2999ds/48Mi)
% 0.20/0.53  % (12101)dis+11_1:64_fd=off:nm=0:nwc=5.0:i=481:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/481Mi)
% 0.20/0.53  % (12099)lrs+10_1:128_bd=off:drc=off:fd=preordered:nwc=1.6:urr=on:i=103:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/103Mi)
% 0.20/0.53  % (12080)First to succeed.
% 0.20/0.53  % (12081)lrs+1004_1:734_av=off:awrs=converge:awrsf=70:br=off:ep=RSTC:erd=off:gs=on:nwc=3.0:s2a=on:s2agt=16:sp=occurrence:updr=off:urr=on:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.53  % (12088)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 (2999ds/37Mi)
% 0.20/0.53  % (12111)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 (2999ds/48Mi)
% 0.20/0.54  % (12080)Refutation found. Thanks to Tanya!
% 0.20/0.54  % SZS status Unsatisfiable for theBenchmark
% 0.20/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.54  % (12080)------------------------------
% 0.20/0.54  % (12080)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (12080)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (12080)Termination reason: Refutation
% 0.20/0.54  
% 0.20/0.54  % (12080)Memory used [KB]: 5500
% 0.20/0.54  % (12080)Time elapsed: 0.128 s
% 0.20/0.54  % (12080)Instructions burned: 7 (million)
% 0.20/0.54  % (12080)------------------------------
% 0.20/0.54  % (12080)------------------------------
% 0.20/0.54  % (12076)Success in time 0.179 s
%------------------------------------------------------------------------------