%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LCL301-3 : 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 : n003.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 06:53:28 EDT 2023

% Result   : Unsatisfiable 0.19s 0.63s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   48 (  25 unt;   9 typ;   0 def)
%            Number of atoms       :   58 (   7 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   42 (  23   ~;  19   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   7   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :   65 (   3 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,
    equivalent: ( $i * $i ) > $i ).

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

tff(decl_30,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_5,axiom,
    axiom(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_5) ).

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

cnf(equivalent_defn,axiom,
    equivalent(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-2.ax',equivalent_defn) ).

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

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

cnf(c_0_10,axiom,
    ( theorem(X1)
    | ~ theorem(implies(X2,X1))
    | ~ theorem(X2) ),
    rule_2 ).

cnf(c_0_11,axiom,
    implies(X1,X2) = or(not(X1),X2),
    implies_definition ).

cnf(c_0_12,plain,
    ( theorem(X1)
    | ~ theorem(X2)
    | ~ theorem(or(not(X2),X1)) ),
    inference(rw,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_13,axiom,
    ( theorem(X1)
    | ~ axiom(X1) ),
    rule_1 ).

cnf(c_0_14,axiom,
    axiom(implies(or(X1,X2),or(X2,X1))),
    axiom_1_4 ).

cnf(c_0_15,plain,
    ( theorem(X1)
    | ~ theorem(X2)
    | ~ axiom(or(not(X2),X1)) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_16,plain,
    axiom(or(not(or(X1,X2)),or(X2,X1))),
    inference(rw,[status(thm)],[c_0_14,c_0_11]) ).

cnf(c_0_17,axiom,
    axiom(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
    axiom_1_5 ).

cnf(c_0_18,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(or(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_19,axiom,
    axiom(implies(or(X1,X1),X1)),
    axiom_1_2 ).

cnf(c_0_20,plain,
    axiom(or(not(or(X1,or(X2,X3))),or(X2,or(X1,X3)))),
    inference(rw,[status(thm)],[c_0_17,c_0_11]) ).

cnf(c_0_21,axiom,
    equivalent(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
    equivalent_defn ).

cnf(c_0_22,axiom,
    and(X1,X2) = not(or(not(X1),not(X2))),
    and_defn ).

cnf(c_0_23,plain,
    ( theorem(or(X1,X2))
    | ~ axiom(or(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_18,c_0_13]) ).

cnf(c_0_24,plain,
    axiom(or(not(or(X1,X1)),X1)),
    inference(rw,[status(thm)],[c_0_19,c_0_11]) ).

cnf(c_0_25,plain,
    ( theorem(or(X1,or(X2,X3)))
    | ~ theorem(or(X2,or(X1,X3))) ),
    inference(spm,[status(thm)],[c_0_15,c_0_20]) ).

cnf(c_0_26,negated_conjecture,
    ~ theorem(equivalent(not(implies(not(p),not(q))),and(not(p),q))),
    prove_this ).

cnf(c_0_27,plain,
    equivalent(X1,X2) = not(or(not(or(not(X1),X2)),not(or(not(X2),X1)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_11]),c_0_11]),c_0_22]) ).

cnf(c_0_28,plain,
    ( theorem(X1)
    | ~ theorem(X2)
    | ~ axiom(or(X1,not(X2))) ),
    inference(spm,[status(thm)],[c_0_12,c_0_23]) ).

cnf(c_0_29,plain,
    ( theorem(X1)
    | ~ theorem(or(X1,X1)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_24]) ).

cnf(c_0_30,plain,
    ( theorem(or(X1,or(X2,X3)))
    | ~ axiom(or(X2,or(X1,X3))) ),
    inference(spm,[status(thm)],[c_0_25,c_0_13]) ).

cnf(c_0_31,axiom,
    axiom(implies(X1,or(X2,X1))),
    axiom_1_3 ).

cnf(c_0_32,negated_conjecture,
    ~ theorem(not(or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_11]),c_0_22]),c_0_27]) ).

cnf(c_0_33,plain,
    ( theorem(not(or(not(X1),not(X1))))
    | ~ theorem(X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_24]) ).

cnf(c_0_34,plain,
    ( theorem(or(X1,X2))
    | ~ axiom(or(X1,or(or(X1,X2),X2))) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_35,plain,
    axiom(or(not(X1),or(X2,X1))),
    inference(rw,[status(thm)],[c_0_31,c_0_11]) ).

cnf(c_0_36,negated_conjecture,
    ~ theorem(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_37,plain,
    theorem(or(not(X1),X1)),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_38,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LCL301-3 : TPTP v8.1.2. Released v2.3.0.
% 0.13/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n003.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 06:28:53 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.63  % Version  : CSE_E---1.5
% 0.19/0.63  % Problem  : theBenchmark.p
% 0.19/0.63  % Proof found
% 0.19/0.63  % SZS status Theorem for theBenchmark.p
% 0.19/0.63  % SZS output start Proof
% See solution above
% 0.19/0.63  % Total time : 0.044000 s
% 0.19/0.63  % SZS output end Proof
% 0.19/0.63  % Total time : 0.047000 s
%------------------------------------------------------------------------------