%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : COL004-3 : 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 : n022.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 15:51:37 EDT 2022

% Result   : Unsatisfiable 1.34s 0.52s
% Output   : Refutation 1.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   11 (  11 unt;   0 def)
%            Number of atoms       :   11 (  10 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    6 (   6   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   10 (  10   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f133,plain,
    $false,
    inference(trivial_inequality_removal,[],[f132]) ).

fof(f132,plain,
    apply(y,apply(apply(x,x),y)) != apply(y,apply(apply(x,x),y)),
    inference(forward_demodulation,[],[f131,f12]) ).

fof(f12,plain,
    ! [X3,X4] : apply(apply(apply(s,k),X4),X3) = X3,
    inference(superposition,[],[f1,f2]) ).

fof(f2,axiom,
    ! [X0,X1] : apply(apply(k,X0),X1) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).

fof(f1,axiom,
    ! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).

fof(f131,plain,
    apply(y,apply(apply(x,x),y)) != apply(apply(apply(apply(s,k),k),y),apply(apply(x,x),y)),
    inference(superposition,[],[f128,f1]) ).

fof(f128,plain,
    apply(y,apply(apply(x,x),y)) != apply(apply(apply(s,apply(apply(s,k),k)),apply(x,x)),y),
    inference(forward_demodulation,[],[f125,f12]) ).

fof(f125,plain,
    apply(y,apply(apply(x,x),y)) != apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x))),y),
    inference(superposition,[],[f29,f1]) ).

fof(f29,plain,
    apply(y,apply(apply(x,x),y)) != apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y),
    inference(backward_demodulation,[],[f3,f6]) ).

fof(f6,plain,
    ! [X2,X0,X1] : apply(apply(apply(s,apply(k,X0)),X2),X1) = apply(X0,apply(X2,X1)),
    inference(superposition,[],[f1,f2]) ).

fof(f3,axiom,
    apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_u_combinator) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : COL004-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 29 16:38:26 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.49  % (23351)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)
% 0.19/0.49  % (23350)lrs+10_1:128_plsq=on:plsqc=2:s2a=on:ss=axioms:st=1.5:urr=on:i=321:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/321Mi)
% 0.19/0.49  % (23343)lrs+1_3:1_ep=RSTC:sos=on:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.50  % (23339)lrs+10_1:1_amm=off:drc=off:sp=reverse_frequency:spb=goal_then_units:to=lpo:i=6:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.19/0.50  % (23349)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)
% 0.19/0.50  % (23359)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)
% 0.19/0.50  % (23348)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)
% 0.19/0.50  % (23342)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)
% 0.19/0.51  % (23351)First to succeed.
% 0.19/0.51  % (23358)lrs+10_5:1_br=off:ep=RSTC:sos=all:urr=on:i=267:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/267Mi)
% 1.34/0.52  % (23342)Also succeeded, but the first one will report.
% 1.34/0.52  % (23340)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)
% 1.34/0.52  % (23351)Refutation found. Thanks to Tanya!
% 1.34/0.52  % SZS status Unsatisfiable for theBenchmark
% 1.34/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 1.34/0.52  % (23351)------------------------------
% 1.34/0.52  % (23351)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.34/0.52  % (23351)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.34/0.52  % (23351)Termination reason: Refutation
% 1.34/0.52  
% 1.34/0.52  % (23351)Memory used [KB]: 5628
% 1.34/0.52  % (23351)Time elapsed: 0.111 s
% 1.34/0.52  % (23351)Instructions burned: 10 (million)
% 1.34/0.52  % (23351)------------------------------
% 1.34/0.52  % (23351)------------------------------
% 1.34/0.52  % (23335)Success in time 0.174 s
%------------------------------------------------------------------------------