%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LDA007-2 : TPTP v8.1.2. Bugfixed v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n004.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 : Thu Aug 31 09:03:03 EDT 2023

% Result   : Unsatisfiable 0.19s 0.59s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   34 (  18 unt;  16 typ;   0 def)
%            Number of atoms       :   18 (  17 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;  12 con; 0-2 aty)
%            Number of variables   :    8 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    f: ( $i * $i ) > $i ).

tff(decl_23,type,
    a: ( $i * $i ) > $i ).

tff(decl_24,type,
    critical_point: $i > $i ).

tff(decl_25,type,
    less: ( $i * $i ) > $o ).

tff(decl_26,type,
    tt: $i ).

tff(decl_27,type,
    t: $i ).

tff(decl_28,type,
    st: $i ).

tff(decl_29,type,
    s: $i ).

tff(decl_30,type,
    ts: $i ).

tff(decl_31,type,
    tt_ts: $i ).

tff(decl_32,type,
    k: $i ).

tff(decl_33,type,
    sk: $i ).

tff(decl_34,type,
    tk: $i ).

tff(decl_35,type,
    stk: $i ).

tff(decl_36,type,
    tsk: $i ).

tff(decl_37,type,
    ttk: $i ).

cnf(a1,axiom,
    f(X1,f(X2,X3)) = f(f(X1,X2),f(X1,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).

cnf(clause_1,axiom,
    tt = f(t,t),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).

cnf(clause_7,axiom,
    tk = f(t,k),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).

cnf(clause_3,axiom,
    ts = f(t,s),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).

cnf(clause_4,axiom,
    tt_ts = f(tt,ts),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).

cnf(clause_9,axiom,
    tsk = f(ts,k),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).

cnf(prove_equation,negated_conjecture,
    f(t,tsk) != f(tt_ts,tk),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).

cnf(c_0_7,axiom,
    f(X1,f(X2,X3)) = f(f(X1,X2),f(X1,X3)),
    a1 ).

cnf(c_0_8,axiom,
    tt = f(t,t),
    clause_1 ).

cnf(c_0_9,axiom,
    tk = f(t,k),
    clause_7 ).

cnf(c_0_10,plain,
    f(tt,f(t,X1)) = f(t,f(t,X1)),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,axiom,
    ts = f(t,s),
    clause_3 ).

cnf(c_0_12,axiom,
    tt_ts = f(tt,ts),
    clause_4 ).

cnf(c_0_13,plain,
    f(f(t,X1),tk) = f(t,f(X1,k)),
    inference(spm,[status(thm)],[c_0_7,c_0_9]) ).

cnf(c_0_14,plain,
    f(t,ts) = tt_ts,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).

cnf(c_0_15,axiom,
    tsk = f(ts,k),
    clause_9 ).

cnf(c_0_16,negated_conjecture,
    f(t,tsk) != f(tt_ts,tk),
    prove_equation ).

cnf(c_0_17,plain,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LDA007-2 : TPTP v8.1.2. Bugfixed v2.6.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n004.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   : Sun Aug 27 01:19:22 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.59  % Version  : CSE_E---1.5
% 0.19/0.59  % Problem  : theBenchmark.p
% 0.19/0.59  % Proof found
% 0.19/0.59  % SZS status Theorem for theBenchmark.p
% 0.19/0.59  % SZS output start Proof
% See solution above
% 0.19/0.59  % Total time : 0.008000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.011000 s
%------------------------------------------------------------------------------