%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : COL036-1 : 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 : n012.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 18:22:10 EDT 2023

% Result   : Unsatisfiable 19.13s 19.16s
% Output   : CNFRefutation 19.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   19 (  14 unt;   5 typ;   0 def)
%            Number of atoms       :   14 (  13 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    8 (   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    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   27 (   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,
    t: $i ).

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

cnf(t_definition,axiom,
    apply(apply(t,X1),X2) = apply(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_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(prove_fixed_point,negated_conjecture,
    apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).

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_4,axiom,
    apply(apply(t,X1),X2) = apply(X2,X1),
    t_definition ).

cnf(c_0_5,axiom,
    apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
    s_definition ).

cnf(c_0_6,plain,
    apply(apply(apply(s,t),X1),X2) = apply(apply(X1,X2),X2),
    inference(spm,[status(thm)],[c_0_4,c_0_5]) ).

cnf(c_0_7,negated_conjecture,
    apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
    prove_fixed_point ).

cnf(c_0_8,axiom,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    b_definition ).

cnf(c_0_9,plain,
    apply(apply(apply(s,apply(s,t)),X1),X2) = apply(apply(X2,apply(X1,X2)),apply(X1,X2)),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    apply(f(apply(apply(b,X1),X2)),apply(X1,apply(X2,f(apply(apply(b,X1),X2))))) != apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,plain,
    apply(X1,apply(apply(apply(s,X2),X2),apply(b,X1))) = apply(apply(apply(s,apply(s,t)),X2),apply(b,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_5]) ).

cnf(c_0_12,negated_conjecture,
    apply(apply(apply(s,apply(s,t)),X1),apply(b,f(apply(apply(b,apply(apply(s,X1),X1)),b)))) != apply(apply(apply(s,X1),X1),apply(b,f(apply(apply(b,apply(apply(s,X1),X1)),b)))),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_13,negated_conjecture,
    $false,
    inference(er,[status(thm)],[c_0_12]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : COL036-1 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n012.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 03:57:40 EDT 2023
% 0.19/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 19.13/19.16  % Version  : CSE_E---1.5
% 19.13/19.16  % Problem  : theBenchmark.p
% 19.13/19.16  % Proof found
% 19.13/19.16  % SZS status Theorem for theBenchmark.p
% 19.13/19.16  % SZS output start Proof
% See solution above
% 19.13/19.16  % Total time : 18.578000 s
% 19.13/19.16  % SZS output end Proof
% 19.13/19.16  % Total time : 18.581000 s
%------------------------------------------------------------------------------