%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LCL134-1 : 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 : n010.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 06:52:27 EDT 2023

% Result   : Unsatisfiable 0.19s 0.64s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   18 (  14 unt;   4 typ;   0 def)
%            Number of atoms       :   14 (  13 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    :    4 (   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    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   18 (   2 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    not: $i > $i ).

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

cnf(wajsberg_2,axiom,
    implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).

cnf(wajsberg_1,axiom,
    implies(truth,X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).

cnf(wajsberg_3,axiom,
    implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).

cnf(prove_wajsberg_lemma,negated_conjecture,
    implies(x,truth) != truth,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_lemma) ).

cnf(c_0_4,axiom,
    implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
    wajsberg_2 ).

cnf(c_0_5,axiom,
    implies(truth,X1) = X1,
    wajsberg_1 ).

cnf(c_0_6,axiom,
    implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
    wajsberg_3 ).

cnf(c_0_7,plain,
    implies(X1,implies(implies(X1,X2),X2)) = truth,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_5]),c_0_5]) ).

cnf(c_0_8,plain,
    implies(implies(X1,truth),truth) = implies(X1,X1),
    inference(spm,[status(thm)],[c_0_6,c_0_5]) ).

cnf(c_0_9,plain,
    implies(X1,X1) = truth,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_7]),c_0_5]) ).

cnf(c_0_10,plain,
    implies(implies(X1,truth),truth) = truth,
    inference(rw,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_11,negated_conjecture,
    implies(x,truth) != truth,
    prove_wajsberg_lemma ).

cnf(c_0_12,plain,
    implies(X1,truth) = truth,
    inference(spm,[status(thm)],[c_0_7,c_0_10]) ).

cnf(c_0_13,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LCL134-1 : 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 : n010.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   : Thu Aug 24 19:22:20 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.62  start to proof: theBenchmark
% 0.19/0.64  % Version  : CSE_E---1.5
% 0.19/0.64  % Problem  : theBenchmark.p
% 0.19/0.64  % Proof found
% 0.19/0.64  % SZS status Theorem for theBenchmark.p
% 0.19/0.64  % SZS output start Proof
% See solution above
% 0.19/0.64  % Total time : 0.005000 s
% 0.19/0.64  % SZS output end Proof
% 0.19/0.64  % Total time : 0.007000 s
%------------------------------------------------------------------------------