%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LCL236-3 : TPTP v8.1.2. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n002.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 06:53:08 EDT 2023

% Result   : Unsatisfiable 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   45 (  27 unt;   8 typ;   0 def)
%            Number of atoms       :   51 (   4 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   31 (  17   ~;  14   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   6   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   61 (   5 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    axiom: $i > $o ).

tff(decl_25,type,
    not: $i > $i ).

tff(decl_26,type,
    theorem: $i > $o ).

tff(decl_27,type,
    and: ( $i * $i ) > $i ).

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

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

cnf(rule_2,axiom,
    ( theorem(X1)
    | ~ theorem(implies(X2,X1))
    | ~ theorem(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',rule_2) ).

cnf(implies_definition,axiom,
    implies(X1,X2) = or(not(X1),X2),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',implies_definition) ).

cnf(rule_1,axiom,
    ( theorem(X1)
    | ~ axiom(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',rule_1) ).

cnf(axiom_1_4,axiom,
    axiom(implies(or(X1,X2),or(X2,X1))),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_4) ).

cnf(axiom_1_2,axiom,
    axiom(implies(or(X1,X1),X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_2) ).

cnf(axiom_1_6,axiom,
    axiom(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_6) ).

cnf(axiom_1_3,axiom,
    axiom(implies(X1,or(X2,X1))),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_3) ).

cnf(prove_this,negated_conjecture,
    ~ theorem(implies(or(not(p),not(q)),not(and(p,q)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

cnf(and_defn,axiom,
    and(X1,X2) = not(or(not(X1),not(X2))),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-1.ax',and_defn) ).

cnf(c_0_9,axiom,
    ( theorem(X1)
    | ~ theorem(implies(X2,X1))
    | ~ theorem(X2) ),
    rule_2 ).

cnf(c_0_10,axiom,
    implies(X1,X2) = or(not(X1),X2),
    implies_definition ).

cnf(c_0_11,plain,
    ( theorem(X1)
    | ~ theorem(X2)
    | ~ theorem(or(not(X2),X1)) ),
    inference(rw,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_12,axiom,
    ( theorem(X1)
    | ~ axiom(X1) ),
    rule_1 ).

cnf(c_0_13,axiom,
    axiom(implies(or(X1,X2),or(X2,X1))),
    axiom_1_4 ).

cnf(c_0_14,plain,
    ( theorem(X1)
    | ~ theorem(X2)
    | ~ axiom(or(not(X2),X1)) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_15,plain,
    axiom(or(not(or(X1,X2)),or(X2,X1))),
    inference(rw,[status(thm)],[c_0_13,c_0_10]) ).

cnf(c_0_16,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(or(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_17,axiom,
    axiom(implies(or(X1,X1),X1)),
    axiom_1_2 ).

cnf(c_0_18,axiom,
    axiom(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
    axiom_1_6 ).

cnf(c_0_19,plain,
    ( theorem(or(X1,X2))
    | ~ axiom(or(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_16,c_0_12]) ).

cnf(c_0_20,plain,
    axiom(or(not(or(X1,X1)),X1)),
    inference(rw,[status(thm)],[c_0_17,c_0_10]) ).

cnf(c_0_21,plain,
    axiom(or(not(or(not(X1),X2)),or(not(or(X3,X1)),or(X3,X2)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_10]),c_0_10]),c_0_10]) ).

cnf(c_0_22,plain,
    theorem(or(X1,not(or(X1,X1)))),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,axiom,
    axiom(implies(X1,or(X2,X1))),
    axiom_1_3 ).

cnf(c_0_24,plain,
    ( theorem(or(not(or(X1,X2)),or(X1,X3)))
    | ~ theorem(or(not(X2),X3)) ),
    inference(spm,[status(thm)],[c_0_14,c_0_21]) ).

cnf(c_0_25,plain,
    theorem(or(not(or(X1,X1)),X1)),
    inference(spm,[status(thm)],[c_0_16,c_0_22]) ).

cnf(c_0_26,plain,
    axiom(or(not(X1),or(X2,X1))),
    inference(rw,[status(thm)],[c_0_23,c_0_10]) ).

cnf(c_0_27,plain,
    theorem(or(not(or(X1,or(X2,X2))),or(X1,X2))),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_28,plain,
    theorem(or(or(X1,X2),not(X2))),
    inference(spm,[status(thm)],[c_0_19,c_0_26]) ).

cnf(c_0_29,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(or(X1,or(X2,X2))) ),
    inference(spm,[status(thm)],[c_0_11,c_0_27]) ).

cnf(c_0_30,plain,
    theorem(or(not(X1),or(X2,X1))),
    inference(spm,[status(thm)],[c_0_16,c_0_28]) ).

cnf(c_0_31,negated_conjecture,
    ~ theorem(implies(or(not(p),not(q)),not(and(p,q)))),
    prove_this ).

cnf(c_0_32,axiom,
    and(X1,X2) = not(or(not(X1),not(X2))),
    and_defn ).

cnf(c_0_33,plain,
    theorem(or(not(X1),X1)),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_34,negated_conjecture,
    ~ theorem(or(not(or(not(p),not(q))),not(not(or(not(p),not(q)))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_10]),c_0_32]) ).

cnf(c_0_35,plain,
    theorem(or(X1,not(X1))),
    inference(spm,[status(thm)],[c_0_16,c_0_33]) ).

cnf(c_0_36,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : LCL236-3 : TPTP v8.1.2. Released v2.3.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n002.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   : Fri Aug 25 02:25:17 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.006000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.009000 s
%------------------------------------------------------------------------------