TSTP Solution File: ITP209_3 by Vampire-SAT---4.8

View Problem - Process Solution 
%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP209_3 : TPTP v8.2.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -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 : Mon May 20 22:57:07 EDT 2024

% Result   : Theorem 0.24s 0.40s
% Output   : Refutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   33 (  13 unt;  20 typ;   0 def)
%            Number of atoms       :   13 (  12 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   15 (  13   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   4 con; 0-2 aty)
%            Number of variables   :   16 (  16   !;   0   ?;  16   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    fun_a_fun_a_a: $tType ).

tff(type_def_6,type,
    fun_a_a: $tType ).

tff(type_def_7,type,
    a: $tType ).

tff(func_def_0,type,
    aa_a_fun_a_a: ( fun_a_fun_a_a * a ) > fun_a_a ).

tff(func_def_1,type,
    aa_a_a: ( fun_a_a * a ) > a ).

tff(func_def_2,type,
    a2: a ).

tff(func_def_3,type,
    b: a ).

tff(func_def_4,type,
    c: a ).

tff(func_def_5,type,
    f: fun_a_fun_a_a ).

tff(func_def_6,type,
    sK0: fun_a_fun_a_a > a ).

tff(func_def_7,type,
    sK1: fun_a_fun_a_a > a ).

tff(func_def_8,type,
    sK2: fun_a_fun_a_a > a ).

tff(func_def_9,type,
    sK3: fun_a_fun_a_a > a ).

tff(func_def_10,type,
    sK4: fun_a_fun_a_a > a ).

tff(func_def_11,type,
    sK5: fun_a_fun_a_a > a ).

tff(func_def_12,type,
    sK6: fun_a_fun_a_a > a ).

tff(func_def_13,type,
    sK7: fun_a_fun_a_a > a ).

tff(func_def_14,type,
    sK8: fun_a_fun_a_a > a ).

tff(func_def_15,type,
    sK9: fun_a_fun_a_a > a ).

tff(pred_def_1,type,
    syntax_ac_operator_a: fun_a_fun_a_a > $o ).

tff(f54,plain,
    $false,
    inference(subsumption_resolution,[],[f53,f44]) ).

tff(f44,plain,
    ! [X2: a,X0: a,X1: a] : ( aa_a_a(aa_a_fun_a_a(f,X0),aa_a_a(aa_a_fun_a_a(f,X1),X2)) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,X0),X1)),X2) ),
    inference(cnf_transformation,[],[f4]) ).

tff(f4,axiom,
    ! [X0: a,X1: a,X2: a] : ( aa_a_a(aa_a_fun_a_a(f,X0),aa_a_a(aa_a_fun_a_a(f,X1),X2)) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,X0),X1)),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_right__assoc) ).

tff(f53,plain,
    aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) != aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,b),c)),
    inference(forward_demodulation,[],[f51,f43]) ).

tff(f43,plain,
    ! [X2: a,X0: a,X1: a] : ( aa_a_a(aa_a_fun_a_a(f,X0),aa_a_a(aa_a_fun_a_a(f,X1),X2)) = aa_a_a(aa_a_fun_a_a(f,X1),aa_a_a(aa_a_fun_a_a(f,X0),X2)) ),
    inference(cnf_transformation,[],[f3]) ).

tff(f3,axiom,
    ! [X0: a,X1: a,X2: a] : ( aa_a_a(aa_a_fun_a_a(f,X0),aa_a_a(aa_a_fun_a_a(f,X1),X2)) = aa_a_a(aa_a_fun_a_a(f,X1),aa_a_a(aa_a_fun_a_a(f,X0),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_left__commute) ).

tff(f51,plain,
    aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) != aa_a_a(aa_a_fun_a_a(f,b),aa_a_a(aa_a_fun_a_a(f,a2),c)),
    inference(superposition,[],[f36,f42]) ).

tff(f42,plain,
    ! [X0: a,X1: a] : ( aa_a_a(aa_a_fun_a_a(f,X0),X1) = aa_a_a(aa_a_fun_a_a(f,X1),X0) ),
    inference(cnf_transformation,[],[f2]) ).

tff(f2,axiom,
    ! [X0: a,X1: a] : ( aa_a_a(aa_a_fun_a_a(f,X0),X1) = aa_a_a(aa_a_fun_a_a(f,X1),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_commute) ).

tff(f36,plain,
    aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) != aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
    inference(cnf_transformation,[],[f13]) ).

tff(f13,plain,
    aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) != aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
    inference(flattening,[],[f12]) ).

tff(f12,negated_conjecture,
    ( ~ aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b) ),
    inference(negated_conjecture,[],[f11]) ).

tff(f11,conjecture,
    aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : ITP209_3 : TPTP v8.2.0. Released v8.0.0.
% 0.07/0.16  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.37  % Computer : n007.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Sat May 18 18:35:23 EDT 2024
% 0.16/0.38  % CPUTime    : 
% 0.16/0.38  % (5471)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.39  % (5474)WARNING: value z3 for option sas not known
% 0.24/0.40  % (5475)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.24/0.40  % (5478)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.24/0.40  % (5473)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.24/0.40  % (5472)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.24/0.40  % (5476)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.24/0.40  % (5474)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.24/0.40  % (5477)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.24/0.40  % (5478)First to succeed.
% 0.24/0.40  % (5478)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-5471"
% 0.24/0.40  % (5478)Refutation found. Thanks to Tanya!
% 0.24/0.40  % SZS status Theorem for theBenchmark
% 0.24/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.40  % (5478)------------------------------
% 0.24/0.40  % (5478)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.24/0.40  % (5478)Termination reason: Refutation
% 0.24/0.40  
% 0.24/0.40  % (5478)Memory used [KB]: 828
% 0.24/0.40  % (5478)Time elapsed: 0.004 s
% 0.24/0.40  % (5478)Instructions burned: 4 (million)
% 0.24/0.40  % (5471)Success in time 0.021 s
%------------------------------------------------------------------------------