TSTP Solution File: LCL282-3 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : LCL282-3 : TPTP v8.2.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n017.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 : Mon May 20 23:45:53 EDT 2024

% Result   : Unsatisfiable 258.77s 33.12s
% Output   : CNFRefutation 258.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :   11
% Syntax   : Number of clauses     :  129 (  48 unt;   0 nHn;  66 RR)
%            Number of literals    :  241 (   7 equ; 130 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-2 aty)
%            Number of variables   :  237 (  35 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(rule_2,axiom,
    ( theorem(X1)
    | ~ theorem(implies(X2,X1))
    | ~ theorem(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',rule_2) ).

cnf(implies_definition,axiom,
    implies(X1,X2) = or(not(X1),X2),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',implies_definition) ).

cnf(rule_1,axiom,
    ( theorem(X1)
    | ~ axiom(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',rule_1) ).

cnf(axiom_1_6,axiom,
    axiom(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_6) ).

cnf(axiom_1_4,axiom,
    axiom(implies(or(X1,X2),or(X2,X1))),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_4) ).

cnf(axiom_1_3,axiom,
    axiom(implies(X1,or(X2,X1))),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_3) ).

cnf(axiom_1_2,axiom,
    axiom(implies(or(X1,X1),X1)),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_2) ).

cnf(axiom_1_5,axiom,
    axiom(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_5) ).

cnf(prove_this,negated_conjecture,
    ~ theorem(equivalent(or(p,and(q,r)),and(or(p,q),or(p,r)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).

cnf(equivalent_defn,axiom,
    equivalent(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-2.ax',equivalent_defn) ).

cnf(and_defn,axiom,
    and(X1,X2) = not(or(not(X1),not(X2))),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-1.ax',and_defn) ).

cnf(c_0_11,plain,
    ( theorem(X1)
    | ~ theorem(implies(X2,X1))
    | ~ theorem(X2) ),
    inference(fof_simplification,[status(thm)],[rule_2]) ).

cnf(c_0_12,plain,
    ( theorem(X1)
    | ~ theorem(implies(X2,X1))
    | ~ theorem(X2) ),
    c_0_11 ).

cnf(c_0_13,axiom,
    implies(X1,X2) = or(not(X1),X2),
    implies_definition ).

cnf(c_0_14,plain,
    ( theorem(X1)
    | ~ axiom(X1) ),
    inference(fof_simplification,[status(thm)],[rule_1]) ).

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

cnf(c_0_16,plain,
    ( theorem(X1)
    | ~ axiom(X1) ),
    c_0_14 ).

cnf(c_0_17,axiom,
    axiom(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
    axiom_1_6 ).

cnf(c_0_18,axiom,
    axiom(implies(or(X1,X2),or(X2,X1))),
    axiom_1_4 ).

cnf(c_0_19,axiom,
    axiom(implies(X1,or(X2,X1))),
    axiom_1_3 ).

cnf(c_0_20,plain,
    ( theorem(X1)
    | ~ theorem(X2)
    | ~ axiom(or(not(X2),X1)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

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_17,c_0_13]),c_0_13]),c_0_13]) ).

cnf(c_0_22,plain,
    axiom(or(not(or(X1,X2)),or(X2,X1))),
    inference(rw,[status(thm)],[c_0_18,c_0_13]) ).

cnf(c_0_23,plain,
    axiom(or(not(X1),or(X2,X1))),
    inference(rw,[status(thm)],[c_0_19,c_0_13]) ).

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_20,c_0_21]) ).

cnf(c_0_25,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(or(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_20,c_0_22]) ).

cnf(c_0_26,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(X2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_23]) ).

cnf(c_0_27,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(or(not(X3),X2))
    | ~ theorem(or(X1,X3)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_24]) ).

cnf(c_0_28,axiom,
    axiom(implies(or(X1,X1),X1)),
    axiom_1_2 ).

cnf(c_0_29,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_30,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(or(X1,X3))
    | ~ axiom(or(not(X3),X2)) ),
    inference(spm,[status(thm)],[c_0_27,c_0_16]) ).

cnf(c_0_31,plain,
    axiom(or(not(or(X1,X1)),X1)),
    inference(rw,[status(thm)],[c_0_28,c_0_13]) ).

cnf(c_0_32,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(or(X1,X3))
    | ~ theorem(not(X3)) ),
    inference(spm,[status(thm)],[c_0_27,c_0_29]) ).

cnf(c_0_33,plain,
    ( theorem(or(X1,X2))
    | ~ axiom(or(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_25,c_0_16]) ).

cnf(c_0_34,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(or(X1,or(X2,X2))) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_35,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(not(X3))
    | ~ axiom(or(X1,X3)) ),
    inference(spm,[status(thm)],[c_0_32,c_0_16]) ).

cnf(c_0_36,plain,
    ( theorem(X1)
    | ~ theorem(X2)
    | ~ axiom(or(X1,not(X2))) ),
    inference(spm,[status(thm)],[c_0_15,c_0_33]) ).

cnf(c_0_37,plain,
    ( theorem(or(X1,X2))
    | ~ axiom(or(X1,or(X2,X2))) ),
    inference(spm,[status(thm)],[c_0_34,c_0_16]) ).

cnf(c_0_38,plain,
    ( theorem(or(not(X1),X2))
    | ~ theorem(not(or(X3,X1))) ),
    inference(spm,[status(thm)],[c_0_35,c_0_23]) ).

cnf(c_0_39,plain,
    ( theorem(not(or(not(X1),not(X1))))
    | ~ theorem(X1) ),
    inference(spm,[status(thm)],[c_0_36,c_0_31]) ).

cnf(c_0_40,axiom,
    axiom(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
    axiom_1_5 ).

cnf(c_0_41,plain,
    theorem(or(not(X1),X1)),
    inference(spm,[status(thm)],[c_0_37,c_0_23]) ).

cnf(c_0_42,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(not(X3))
    | ~ axiom(or(X3,X1)) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_43,plain,
    ( theorem(X1)
    | ~ theorem(or(X1,X1)) ),
    inference(spm,[status(thm)],[c_0_20,c_0_31]) ).

cnf(c_0_44,plain,
    ( theorem(or(not(not(X1)),X2))
    | ~ theorem(X1) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_45,plain,
    axiom(or(not(or(X1,or(X2,X3))),or(X2,or(X1,X3)))),
    inference(rw,[status(thm)],[c_0_40,c_0_13]) ).

cnf(c_0_46,plain,
    theorem(or(X1,not(X1))),
    inference(spm,[status(thm)],[c_0_25,c_0_41]) ).

cnf(c_0_47,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(not(not(or(X1,X1)))) ),
    inference(spm,[status(thm)],[c_0_42,c_0_31]) ).

cnf(c_0_48,plain,
    ( theorem(not(not(X1)))
    | ~ theorem(X1) ),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_49,plain,
    ( theorem(or(X1,or(X2,X3)))
    | ~ theorem(or(X2,or(X1,X3))) ),
    inference(spm,[status(thm)],[c_0_20,c_0_45]) ).

cnf(c_0_50,plain,
    ( theorem(or(X1,not(not(X2))))
    | ~ theorem(or(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_27,c_0_46]) ).

cnf(c_0_51,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(or(X1,X1)) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_52,plain,
    ( theorem(or(X1,or(X2,X3)))
    | ~ axiom(or(X2,or(X1,X3))) ),
    inference(spm,[status(thm)],[c_0_49,c_0_16]) ).

cnf(c_0_53,plain,
    ( theorem(not(not(X1)))
    | ~ theorem(or(not(X2),X1))
    | ~ theorem(X2) ),
    inference(spm,[status(thm)],[c_0_15,c_0_50]) ).

cnf(c_0_54,plain,
    theorem(or(not(or(X1,X1)),X1)),
    inference(spm,[status(thm)],[c_0_37,c_0_22]) ).

cnf(c_0_55,plain,
    ( theorem(or(or(X1,X2),X3))
    | ~ axiom(or(X1,or(or(X1,X2),X2))) ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_56,plain,
    ( theorem(or(not(or(X1,X2)),X1))
    | ~ theorem(or(not(X2),X1)) ),
    inference(spm,[status(thm)],[c_0_34,c_0_24]) ).

cnf(c_0_57,plain,
    ( theorem(not(not(X1)))
    | ~ theorem(or(X1,X1)) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_58,plain,
    theorem(or(or(not(X1),X1),X2)),
    inference(spm,[status(thm)],[c_0_55,c_0_23]) ).

cnf(c_0_59,negated_conjecture,
    ~ theorem(equivalent(or(p,and(q,r)),and(or(p,q),or(p,r)))),
    inference(fof_simplification,[status(thm)],[prove_this]) ).

cnf(c_0_60,axiom,
    equivalent(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
    equivalent_defn ).

cnf(c_0_61,axiom,
    and(X1,X2) = not(or(not(X1),not(X2))),
    and_defn ).

cnf(c_0_62,plain,
    ( theorem(X1)
    | ~ theorem(or(not(X2),X1))
    | ~ theorem(or(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_56]) ).

cnf(c_0_63,plain,
    ( theorem(or(X1,or(X2,X3)))
    | ~ theorem(or(X1,X3)) ),
    inference(spm,[status(thm)],[c_0_49,c_0_26]) ).

cnf(c_0_64,plain,
    ( theorem(or(or(X1,X2),X3))
    | ~ theorem(not(not(or(X2,X1)))) ),
    inference(spm,[status(thm)],[c_0_42,c_0_22]) ).

cnf(c_0_65,plain,
    theorem(not(not(or(not(X1),X1)))),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_66,negated_conjecture,
    ~ theorem(equivalent(or(p,and(q,r)),and(or(p,q),or(p,r)))),
    c_0_59 ).

cnf(c_0_67,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_60,c_0_13]),c_0_13]),c_0_61]) ).

cnf(c_0_68,plain,
    ( theorem(X1)
    | ~ theorem(or(X1,X2))
    | ~ theorem(not(X2)) ),
    inference(spm,[status(thm)],[c_0_62,c_0_29]) ).

cnf(c_0_69,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(or(not(X3),X2))
    | ~ theorem(X3) ),
    inference(spm,[status(thm)],[c_0_15,c_0_63]) ).

cnf(c_0_70,plain,
    theorem(or(or(X1,not(X1)),X2)),
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_71,negated_conjecture,
    ~ theorem(not(or(not(or(not(or(p,not(or(not(q),not(r))))),not(or(not(or(p,q)),not(or(p,r)))))),not(or(not(not(or(not(or(p,q)),not(or(p,r))))),or(p,not(or(not(q),not(r))))))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_61]),c_0_61]),c_0_67]) ).

cnf(c_0_72,plain,
    ( theorem(not(or(X1,X2)))
    | ~ theorem(or(not(X2),X1))
    | ~ theorem(not(X1)) ),
    inference(spm,[status(thm)],[c_0_68,c_0_56]) ).

cnf(c_0_73,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(X3)
    | ~ axiom(or(not(X3),X2)) ),
    inference(spm,[status(thm)],[c_0_69,c_0_16]) ).

cnf(c_0_74,plain,
    ( theorem(not(not(not(not(X1)))))
    | ~ theorem(or(not(not(X1)),X1)) ),
    inference(spm,[status(thm)],[c_0_57,c_0_50]) ).

cnf(c_0_75,plain,
    theorem(or(X1,or(X2,not(X2)))),
    inference(spm,[status(thm)],[c_0_25,c_0_70]) ).

cnf(c_0_76,negated_conjecture,
    ( ~ theorem(or(not(not(or(not(not(or(not(or(p,q)),not(or(p,r))))),or(p,not(or(not(q),not(r))))))),not(or(not(or(p,not(or(not(q),not(r))))),not(or(not(or(p,q)),not(or(p,r))))))))
    | ~ theorem(not(not(or(not(or(p,not(or(not(q),not(r))))),not(or(not(or(p,q)),not(or(p,r)))))))) ),
    inference(spm,[status(thm)],[c_0_71,c_0_72]) ).

cnf(c_0_77,plain,
    ( theorem(not(not(X1)))
    | ~ theorem(X2)
    | ~ axiom(or(not(X2),X1)) ),
    inference(spm,[status(thm)],[c_0_53,c_0_16]) ).

cnf(c_0_78,plain,
    ( theorem(X1)
    | ~ theorem(or(X1,or(X1,X2)))
    | ~ theorem(or(not(X2),X1)) ),
    inference(spm,[status(thm)],[c_0_62,c_0_56]) ).

cnf(c_0_79,plain,
    ( theorem(or(X1,or(X2,X3)))
    | ~ theorem(or(X3,X2)) ),
    inference(spm,[status(thm)],[c_0_73,c_0_22]) ).

cnf(c_0_80,plain,
    theorem(or(X1,or(not(X2),X2))),
    inference(spm,[status(thm)],[c_0_25,c_0_58]) ).

cnf(c_0_81,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(not(not(X1))) ),
    inference(spm,[status(thm)],[c_0_32,c_0_46]) ).

cnf(c_0_82,plain,
    theorem(not(not(not(not(or(X1,not(X1))))))),
    inference(spm,[status(thm)],[c_0_74,c_0_75]) ).

cnf(c_0_83,negated_conjecture,
    ( ~ theorem(not(not(or(not(or(p,not(or(not(q),not(r))))),not(or(not(or(p,q)),not(or(p,r))))))))
    | ~ theorem(or(not(not(or(not(or(p,q)),not(or(p,r))))),or(p,not(or(not(q),not(r)))))) ),
    inference(spm,[status(thm)],[c_0_76,c_0_44]) ).

cnf(c_0_84,plain,
    ( theorem(not(not(or(X1,X2))))
    | ~ theorem(or(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_77,c_0_22]) ).

cnf(c_0_85,plain,
    ( theorem(or(X1,or(X2,X3)))
    | ~ theorem(or(X1,or(X3,X2))) ),
    inference(spm,[status(thm)],[c_0_30,c_0_22]) ).

cnf(c_0_86,plain,
    ( theorem(or(not(not(X1)),X2))
    | ~ theorem(or(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_25,c_0_50]) ).

cnf(c_0_87,plain,
    ( theorem(X1)
    | ~ theorem(or(not(X2),X1))
    | ~ theorem(or(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_78,c_0_79]) ).

cnf(c_0_88,plain,
    theorem(or(not(X1),or(X2,X1))),
    inference(spm,[status(thm)],[c_0_49,c_0_80]) ).

cnf(c_0_89,plain,
    ( theorem(or(X1,or(not(or(X1,X2)),X3)))
    | ~ theorem(or(not(X2),X3)) ),
    inference(spm,[status(thm)],[c_0_49,c_0_24]) ).

cnf(c_0_90,plain,
    theorem(or(not(not(or(X1,not(X1)))),X2)),
    inference(spm,[status(thm)],[c_0_81,c_0_82]) ).

cnf(c_0_91,negated_conjecture,
    ( ~ theorem(or(not(not(or(not(or(p,q)),not(or(p,r))))),or(p,not(or(not(q),not(r))))))
    | ~ theorem(or(not(or(not(or(p,q)),not(or(p,r)))),not(or(p,not(or(not(q),not(r))))))) ),
    inference(spm,[status(thm)],[c_0_83,c_0_84]) ).

cnf(c_0_92,plain,
    ( theorem(or(not(not(X1)),or(X2,X3)))
    | ~ theorem(or(or(X3,X2),X1)) ),
    inference(spm,[status(thm)],[c_0_85,c_0_86]) ).

cnf(c_0_93,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(or(X2,or(X1,X2))) ),
    inference(spm,[status(thm)],[c_0_87,c_0_88]) ).

cnf(c_0_94,plain,
    ( theorem(or(X1,or(not(or(not(X2),X3)),X4)))
    | ~ theorem(or(not(X3),X4))
    | ~ theorem(or(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_27,c_0_89]) ).

cnf(c_0_95,plain,
    ( theorem(X1)
    | ~ theorem(or(X1,not(or(X2,not(X2))))) ),
    inference(spm,[status(thm)],[c_0_62,c_0_90]) ).

cnf(c_0_96,plain,
    ( theorem(or(or(X1,X2),not(or(X1,X3))))
    | ~ theorem(or(not(X3),X2)) ),
    inference(spm,[status(thm)],[c_0_25,c_0_24]) ).

cnf(c_0_97,negated_conjecture,
    ( ~ theorem(or(not(or(not(or(p,q)),not(or(p,r)))),not(or(p,not(or(not(q),not(r)))))))
    | ~ theorem(or(or(not(or(not(q),not(r))),p),or(not(or(p,q)),not(or(p,r))))) ),
    inference(spm,[status(thm)],[c_0_91,c_0_92]) ).

cnf(c_0_98,plain,
    ( theorem(or(not(or(not(X1),X2)),X3))
    | ~ theorem(or(not(X2),X3))
    | ~ theorem(or(X3,X1)) ),
    inference(spm,[status(thm)],[c_0_93,c_0_94]) ).

cnf(c_0_99,plain,
    ( theorem(X1)
    | ~ theorem(not(X2))
    | ~ axiom(or(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_68,c_0_33]) ).

cnf(c_0_100,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(or(not(not(X1)),X2)) ),
    inference(spm,[status(thm)],[c_0_95,c_0_96]) ).

cnf(c_0_101,negated_conjecture,
    ( ~ theorem(or(or(not(or(not(q),not(r))),p),or(not(or(p,q)),not(or(p,r)))))
    | ~ theorem(or(not(not(or(p,r))),not(or(p,not(or(not(q),not(r)))))))
    | ~ theorem(or(not(or(p,not(or(not(q),not(r))))),or(p,q))) ),
    inference(spm,[status(thm)],[c_0_97,c_0_98]) ).

cnf(c_0_102,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(not(not(or(X2,X1)))) ),
    inference(spm,[status(thm)],[c_0_99,c_0_22]) ).

cnf(c_0_103,plain,
    ( theorem(not(not(or(X1,or(X2,X3)))))
    | ~ theorem(or(X2,or(X1,X3))) ),
    inference(spm,[status(thm)],[c_0_77,c_0_45]) ).

cnf(c_0_104,plain,
    theorem(or(X1,not(not(not(X1))))),
    inference(spm,[status(thm)],[c_0_100,c_0_46]) ).

cnf(c_0_105,negated_conjecture,
    ( ~ theorem(or(or(not(or(not(q),not(r))),p),or(not(or(p,q)),not(or(p,r)))))
    | ~ theorem(or(not(or(p,not(or(not(q),not(r))))),or(p,q)))
    | ~ theorem(or(not(or(p,not(or(not(q),not(r))))),or(p,r))) ),
    inference(spm,[status(thm)],[c_0_101,c_0_86]) ).

cnf(c_0_106,plain,
    ( theorem(or(or(X1,X2),X3))
    | ~ theorem(or(X1,or(X3,X2))) ),
    inference(spm,[status(thm)],[c_0_102,c_0_103]) ).

cnf(c_0_107,plain,
    theorem(or(not(not(not(X1))),X1)),
    inference(spm,[status(thm)],[c_0_25,c_0_104]) ).

cnf(c_0_108,negated_conjecture,
    ( ~ theorem(or(not(or(not(q),not(r))),or(or(not(or(p,q)),not(or(p,r))),p)))
    | ~ theorem(or(not(or(p,not(or(not(q),not(r))))),or(p,q)))
    | ~ theorem(or(not(or(p,not(or(not(q),not(r))))),or(p,r))) ),
    inference(spm,[status(thm)],[c_0_105,c_0_106]) ).

cnf(c_0_109,plain,
    ( theorem(or(or(X1,X2),X3))
    | ~ theorem(or(X3,X2)) ),
    inference(spm,[status(thm)],[c_0_25,c_0_63]) ).

cnf(c_0_110,plain,
    ( theorem(or(X1,X2))
    | ~ theorem(or(X1,not(not(X2)))) ),
    inference(spm,[status(thm)],[c_0_27,c_0_107]) ).

cnf(c_0_111,negated_conjecture,
    ( ~ theorem(or(not(not(r)),or(or(not(or(p,q)),not(or(p,r))),p)))
    | ~ theorem(or(not(or(p,not(or(not(q),not(r))))),or(p,q)))
    | ~ theorem(or(not(or(p,not(or(not(q),not(r))))),or(p,r)))
    | ~ theorem(or(or(or(not(or(p,q)),not(or(p,r))),p),q)) ),
    inference(spm,[status(thm)],[c_0_108,c_0_98]) ).

cnf(c_0_112,plain,
    ( theorem(or(X1,or(or(X2,X3),X4)))
    | ~ theorem(or(or(X1,X4),X3)) ),
    inference(spm,[status(thm)],[c_0_49,c_0_109]) ).

cnf(c_0_113,plain,
    ( theorem(or(not(not(X1)),X2))
    | ~ theorem(or(not(not(X2)),X1)) ),
    inference(spm,[status(thm)],[c_0_110,c_0_86]) ).

cnf(c_0_114,negated_conjecture,
    ( ~ theorem(or(not(or(p,not(or(not(q),not(r))))),or(p,q)))
    | ~ theorem(or(not(or(p,not(or(not(q),not(r))))),or(p,r)))
    | ~ theorem(or(or(or(not(or(p,q)),not(or(p,r))),p),q))
    | ~ theorem(or(or(not(not(r)),p),not(or(p,r)))) ),
    inference(spm,[status(thm)],[c_0_111,c_0_112]) ).

cnf(c_0_115,plain,
    theorem(or(not(not(or(X1,not(X2)))),X2)),
    inference(spm,[status(thm)],[c_0_113,c_0_88]) ).

cnf(c_0_116,plain,
    theorem(or(not(X1),or(X1,X2))),
    inference(spm,[status(thm)],[c_0_85,c_0_88]) ).

cnf(c_0_117,negated_conjecture,
    ( ~ theorem(or(not(or(p,not(or(not(q),not(r))))),or(p,q)))
    | ~ theorem(or(or(or(not(or(p,q)),not(or(p,r))),p),q))
    | ~ theorem(or(or(not(not(r)),p),not(or(p,r)))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_24]),c_0_115])]) ).

cnf(c_0_118,plain,
    theorem(or(not(not(or(not(X1),X2))),X1)),
    inference(spm,[status(thm)],[c_0_113,c_0_116]) ).

cnf(c_0_119,plain,
    theorem(or(X1,or(X2,not(X1)))),
    inference(spm,[status(thm)],[c_0_49,c_0_75]) ).

cnf(c_0_120,negated_conjecture,
    ( ~ theorem(or(or(or(not(or(p,q)),not(or(p,r))),p),q))
    | ~ theorem(or(or(not(not(r)),p),not(or(p,r)))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_24]),c_0_118])]) ).

cnf(c_0_121,plain,
    theorem(or(X1,or(not(X1),X2))),
    inference(spm,[status(thm)],[c_0_85,c_0_119]) ).

cnf(c_0_122,negated_conjecture,
    ( ~ theorem(or(or(or(not(or(p,q)),not(or(p,r))),p),q))
    | ~ theorem(or(not(not(r)),or(not(or(p,r)),p))) ),
    inference(spm,[status(thm)],[c_0_120,c_0_106]) ).

cnf(c_0_123,plain,
    theorem(or(or(not(X1),X2),X1)),
    inference(spm,[status(thm)],[c_0_25,c_0_121]) ).

cnf(c_0_124,negated_conjecture,
    ( ~ theorem(or(or(or(not(or(p,q)),not(or(p,r))),p),q))
    | ~ theorem(or(or(not(or(p,r)),p),r)) ),
    inference(spm,[status(thm)],[c_0_122,c_0_86]) ).

cnf(c_0_125,plain,
    theorem(or(or(not(or(X1,X2)),X3),or(X2,X1))),
    inference(spm,[status(thm)],[c_0_85,c_0_123]) ).

cnf(c_0_126,negated_conjecture,
    ~ theorem(or(or(not(or(p,r)),p),r)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_106]),c_0_125])]) ).

cnf(c_0_127,plain,
    ( theorem(or(or(X1,X2),X3))
    | ~ axiom(or(X1,or(X3,X2))) ),
    inference(spm,[status(thm)],[c_0_25,c_0_52]) ).

cnf(c_0_128,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_22])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : LCL282-3 : TPTP v8.2.0. Released v2.3.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.12/0.34  % Computer : n017.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon May 20 02:47:23 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 258.77/33.12  # Version: 3.1.0
% 258.77/33.12  # Preprocessing class: FSMSSMSSSSSNFFN.
% 258.77/33.12  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 258.77/33.12  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 258.77/33.12  # Starting new_bool_3 with 300s (1) cores
% 258.77/33.12  # Starting new_bool_1 with 300s (1) cores
% 258.77/33.12  # Starting sh5l with 300s (1) cores
% 258.77/33.12  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 24464 completed with status 0
% 258.77/33.12  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 258.77/33.12  # Preprocessing class: FSMSSMSSSSSNFFN.
% 258.77/33.12  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 258.77/33.12  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 258.77/33.12  # No SInE strategy applied
% 258.77/33.12  # Search class: FHUNM-FFSF21-DFFFFFNN
% 258.77/33.12  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 258.77/33.12  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 355s (1) cores
% 258.77/33.12  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 258.77/33.12  # Starting new_bool_3 with 296s (1) cores
% 258.77/33.12  # Starting new_bool_1 with 291s (1) cores
% 258.77/33.12  # Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 258.77/33.12  # G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 24475 completed with status 0
% 258.77/33.12  # Result found by G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 258.77/33.12  # Preprocessing class: FSMSSMSSSSSNFFN.
% 258.77/33.12  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 258.77/33.12  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 258.77/33.12  # No SInE strategy applied
% 258.77/33.12  # Search class: FHUNM-FFSF21-DFFFFFNN
% 258.77/33.12  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 258.77/33.12  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 355s (1) cores
% 258.77/33.12  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 258.77/33.12  # Starting new_bool_3 with 296s (1) cores
% 258.77/33.12  # Starting new_bool_1 with 291s (1) cores
% 258.77/33.12  # Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 258.77/33.12  # Preprocessing time       : 0.001 s
% 258.77/33.12  # Presaturation interreduction done
% 258.77/33.12  
% 258.77/33.12  # Proof found!
% 258.77/33.12  # SZS status Unsatisfiable
% 258.77/33.12  # SZS output start CNFRefutation
% See solution above
% 258.77/33.12  # Parsed axioms                        : 11
% 258.77/33.12  # Removed by relevancy pruning/SinE    : 0
% 258.77/33.12  # Initial clauses                      : 11
% 258.77/33.12  # Removed in clause preprocessing      : 3
% 258.77/33.12  # Initial clauses in saturation        : 8
% 258.77/33.12  # Processed clauses                    : 93182
% 258.77/33.12  # ...of these trivial                  : 567
% 258.77/33.12  # ...subsumed                          : 72203
% 258.77/33.12  # ...remaining for further processing  : 20412
% 258.77/33.12  # Other redundant clauses eliminated   : 0
% 258.77/33.12  # Clauses deleted for lack of memory   : 0
% 258.77/33.12  # Backward-subsumed                    : 12513
% 258.77/33.12  # Backward-rewritten                   : 93
% 258.77/33.12  # Generated clauses                    : 1212199
% 258.77/33.12  # ...of the previous two non-redundant : 1181598
% 258.77/33.12  # ...aggressively subsumed             : 0
% 258.77/33.12  # Contextual simplify-reflections      : 335
% 258.77/33.12  # Paramodulations                      : 1212199
% 258.77/33.12  # Factorizations                       : 0
% 258.77/33.12  # NegExts                              : 0
% 258.77/33.12  # Equation resolutions                 : 0
% 258.77/33.12  # Disequality decompositions           : 0
% 258.77/33.12  # Total rewrite steps                  : 33889
% 258.77/33.12  # ...of those cached                   : 29189
% 258.77/33.12  # Propositional unsat checks           : 4
% 258.77/33.12  #    Propositional check models        : 0
% 258.77/33.12  #    Propositional check unsatisfiable : 0
% 258.77/33.12  #    Propositional clauses             : 0
% 258.77/33.12  #    Propositional clauses after purity: 0
% 258.77/33.12  #    Propositional unsat core size     : 0
% 258.77/33.12  #    Propositional preprocessing time  : 0.000
% 258.77/33.12  #    Propositional encoding time       : 3.450
% 258.77/33.12  #    Propositional solver time         : 0.965
% 258.77/33.12  #    Success case prop preproc time    : 0.000
% 258.77/33.12  #    Success case prop encoding time   : 0.000
% 258.77/33.12  #    Success case prop solver time     : 0.000
% 258.77/33.12  # Current number of processed clauses  : 7798
% 258.77/33.12  #    Positive orientable unit clauses  : 304
% 258.77/33.12  #    Positive unorientable unit clauses: 0
% 258.77/33.12  #    Negative unit clauses             : 242
% 258.77/33.12  #    Non-unit-clauses                  : 7252
% 258.77/33.12  # Current number of unprocessed clauses: 1075740
% 258.77/33.12  # ...number of literals in the above   : 2976440
% 258.77/33.12  # Current number of archived formulas  : 0
% 258.77/33.12  # Current number of archived clauses   : 12617
% 258.77/33.12  # Clause-clause subsumption calls (NU) : 47927471
% 258.77/33.12  # Rec. Clause-clause subsumption calls : 22546683
% 258.77/33.12  # Non-unit clause-clause subsumptions  : 52937
% 258.77/33.12  # Unit Clause-clause subsumption calls : 640208
% 258.77/33.12  # Rewrite failures with RHS unbound    : 0
% 258.77/33.12  # BW rewrite match attempts            : 81707
% 258.77/33.12  # BW rewrite match successes           : 37
% 258.77/33.12  # Condensation attempts                : 0
% 258.77/33.12  # Condensation successes               : 0
% 258.77/33.12  # Termbank termtop insertions          : 58858873
% 258.77/33.12  # Search garbage collected termcells   : 11
% 258.77/33.12  
% 258.77/33.12  # -------------------------------------------------
% 258.77/33.12  # User time                : 31.559 s
% 258.77/33.12  # System time              : 0.712 s
% 258.77/33.12  # Total time               : 32.271 s
% 258.77/33.12  # Maximum resident set size: 1688 pages
% 258.77/33.12  
% 258.77/33.12  # -------------------------------------------------
% 258.77/33.12  # User time                : 158.819 s
% 258.77/33.12  # System time              : 2.545 s
% 258.77/33.12  # Total time               : 161.364 s
% 258.77/33.12  # Maximum resident set size: 1708 pages
% 258.77/33.12  % E---3.1 exiting
% 258.77/33.12  % E exiting
%------------------------------------------------------------------------------