%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : COL057-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n016.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 30 18:22:19 EDT 2023

% Result   : Unsatisfiable 0.20s 0.89s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   24 (  18 unt;   6 typ;   0 def)
%            Number of atoms       :   18 (  17 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   34 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    s: $i ).

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

tff(decl_24,type,
    b: $i ).

tff(decl_25,type,
    c: $i ).

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

tff(decl_27,type,
    f: $i > $i ).

cnf(prove_strong_fixed_point,negated_conjecture,
    apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).

cnf(c_definition,axiom,
    apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_definition) ).

cnf(s_definition,axiom,
    apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).

cnf(i_definition,axiom,
    apply(i,X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_definition) ).

cnf(b_definition,axiom,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).

cnf(c_0_5,negated_conjecture,
    apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
    prove_strong_fixed_point ).

cnf(c_0_6,axiom,
    apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2),
    c_definition ).

cnf(c_0_7,axiom,
    apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
    s_definition ).

cnf(c_0_8,axiom,
    apply(i,X1) = X1,
    i_definition ).

cnf(c_0_9,negated_conjecture,
    apply(f(apply(apply(c,X1),X2)),apply(apply(X1,f(apply(apply(c,X1),X2))),X2)) != apply(apply(X1,f(apply(apply(c,X1),X2))),X2),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_10,plain,
    apply(apply(apply(s,i),X1),X2) = apply(X2,apply(X1,X2)),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,plain,
    apply(apply(apply(s,X1),i),X2) = apply(apply(X1,X2),X2),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    apply(apply(apply(s,i),apply(X1,X2)),f(apply(apply(c,apply(c,X1)),X2))) != apply(apply(X1,X2),f(apply(apply(c,apply(c,X1)),X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_6]),c_0_10]) ).

cnf(c_0_13,plain,
    apply(apply(apply(s,i),i),X1) = apply(X1,X1),
    inference(spm,[status(thm)],[c_0_11,c_0_8]) ).

cnf(c_0_14,axiom,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    b_definition ).

cnf(c_0_15,negated_conjecture,
    apply(apply(apply(s,i),apply(apply(apply(s,i),i),X1)),f(apply(apply(c,apply(c,X1)),X1))) != apply(apply(apply(apply(s,i),i),X1),f(apply(apply(c,apply(c,X1)),X1))),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_16,plain,
    apply(apply(apply(s,i),i),apply(apply(b,X1),X2)) = apply(X1,apply(X2,apply(apply(b,X1),X2))),
    inference(spm,[status(thm)],[c_0_14,c_0_13]) ).

cnf(c_0_17,negated_conjecture,
    $false,
    inference(spm,[status(thm)],[c_0_15,c_0_16]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : COL057-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n016.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 05:04:27 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.89  % Version  : CSE_E---1.5
% 0.20/0.89  % Problem  : theBenchmark.p
% 0.20/0.89  % Proof found
% 0.20/0.89  % SZS status Theorem for theBenchmark.p
% 0.20/0.89  % SZS output start Proof
% See solution above
% 0.20/0.89  % Total time : 0.316000 s
% 0.20/0.89  % SZS output end Proof
% 0.20/0.89  % Total time : 0.318000 s
%------------------------------------------------------------------------------