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E---3.5.1.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : LCL339-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 01:12:27 PM UTC 2026

% Result   : Unsatisfiable 176.86s 26.43s
% Output   : CNFRefutation 176.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   11
% Syntax   : Number of clauses     :  113 (  47 unt;   0 nHn;  47 RR)
%            Number of literals    :  202 (   7 equ;  96 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :   11 (   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   :  232 (  32 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(rule_2,axiom,
    ( ~ theorem(X2)
    | ~ theorem(implies(X2,X1))
    | theorem(X1) ),
    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,
    ( ~ axiom(X1)
    | theorem(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(implies(p,implies(q,r)),implies(p,implies(q,and(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(X2)
    | ~ theorem(implies(X2,X1))
    | theorem(X1) ),
    inference(fof_simplification,[status(thm)],[rule_2]) ).

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

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

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

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

cnf(c_0_16,plain,
    ( ~ axiom(X1)
    | theorem(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,
    ( ~ axiom(or(not(X2),X1))
    | ~ theorem(X2)
    | theorem(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(X2),X3))
    | theorem(or(not(or(X1,X2)),or(X1,X3))) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

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

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

cnf(c_0_27,plain,
    ( ~ theorem(or(X1,X3))
    | ~ theorem(or(not(X3),X2))
    | theorem(or(X1,X2)) ),
    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(X1)
    | theorem(or(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_30,plain,
    ( ~ axiom(or(not(X3),X2))
    | ~ theorem(or(X1,X3))
    | theorem(or(X1,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(not(X3))
    | ~ theorem(or(X1,X3))
    | theorem(or(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_27,c_0_29]) ).

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

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

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

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

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

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

cnf(c_0_39,plain,
    ( ~ theorem(X1)
    | theorem(not(or(not(X1),not(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,
    ( ~ axiom(or(X3,X1))
    | ~ theorem(not(X3))
    | theorem(or(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

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

cnf(c_0_44,plain,
    ( ~ theorem(X1)
    | theorem(or(not(not(X1)),X2)) ),
    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(not(not(or(X1,X1))))
    | theorem(or(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_42,c_0_31]) ).

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

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

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

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

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

cnf(c_0_53,plain,
    ( ~ theorem(X2)
    | ~ theorem(or(not(X2),X1))
    | theorem(not(not(X1))) ),
    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,
    ( ~ axiom(or(X1,or(or(X1,X2),X2)))
    | theorem(or(or(X1,X2),X3)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_56,plain,
    ( ~ theorem(or(X1,X1))
    | theorem(not(not(X1))) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_57,plain,
    theorem(or(or(not(X1),X1),X2)),
    inference(spm,[status(thm)],[c_0_55,c_0_23]) ).

cnf(c_0_58,plain,
    ( ~ theorem(not(not(or(X2,X1))))
    | theorem(or(or(X1,X2),X3)) ),
    inference(spm,[status(thm)],[c_0_42,c_0_22]) ).

cnf(c_0_59,plain,
    theorem(not(not(or(not(X1),X1)))),
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_60,plain,
    theorem(or(or(X1,not(X1)),X2)),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_61,plain,
    ( ~ theorem(or(not(not(X1)),X1))
    | theorem(not(not(not(not(X1))))) ),
    inference(spm,[status(thm)],[c_0_56,c_0_50]) ).

cnf(c_0_62,plain,
    theorem(or(X1,or(X2,not(X2)))),
    inference(spm,[status(thm)],[c_0_25,c_0_60]) ).

cnf(c_0_63,plain,
    ( ~ theorem(or(not(X2),X1))
    | theorem(or(not(or(X1,X2)),X1)) ),
    inference(spm,[status(thm)],[c_0_34,c_0_24]) ).

cnf(c_0_64,plain,
    ( ~ theorem(not(not(X1)))
    | theorem(or(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_32,c_0_46]) ).

cnf(c_0_65,plain,
    theorem(not(not(not(not(or(X1,not(X1))))))),
    inference(spm,[status(thm)],[c_0_61,c_0_62]) ).

cnf(c_0_66,plain,
    ( ~ theorem(or(X1,X2))
    | ~ theorem(or(not(X2),X1))
    | theorem(X1) ),
    inference(spm,[status(thm)],[c_0_15,c_0_63]) ).

cnf(c_0_67,plain,
    theorem(or(not(not(or(X1,not(X1)))),X2)),
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_68,plain,
    ( ~ theorem(or(X1,X3))
    | theorem(or(X1,or(X2,X3))) ),
    inference(spm,[status(thm)],[c_0_49,c_0_26]) ).

cnf(c_0_69,plain,
    ( ~ theorem(or(X1,not(or(X2,not(X2)))))
    | theorem(X1) ),
    inference(spm,[status(thm)],[c_0_66,c_0_67]) ).

cnf(c_0_70,plain,
    ( ~ theorem(or(not(X3),X2))
    | theorem(or(or(X1,X2),not(or(X1,X3)))) ),
    inference(spm,[status(thm)],[c_0_25,c_0_24]) ).

cnf(c_0_71,plain,
    ( ~ theorem(X3)
    | ~ theorem(or(not(X3),X2))
    | theorem(or(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_68]) ).

cnf(c_0_72,negated_conjecture,
    ~ theorem(equivalent(implies(p,implies(q,r)),implies(p,implies(q,and(p,r))))),
    inference(fof_simplification,[status(thm)],[prove_this]) ).

cnf(c_0_73,axiom,
    equivalent(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
    equivalent_defn ).

cnf(c_0_74,axiom,
    and(X1,X2) = not(or(not(X1),not(X2))),
    and_defn ).

cnf(c_0_75,plain,
    ( ~ axiom(or(X1,or(not(X3),X2)))
    | ~ theorem(X3)
    | theorem(or(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_52]) ).

cnf(c_0_76,plain,
    ( ~ theorem(or(not(not(X1)),X2))
    | theorem(or(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_69,c_0_70]) ).

cnf(c_0_77,plain,
    theorem(or(X1,or(not(X2),X2))),
    inference(spm,[status(thm)],[c_0_25,c_0_57]) ).

cnf(c_0_78,plain,
    ( ~ axiom(or(not(X3),X2))
    | ~ theorem(X3)
    | theorem(or(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_71,c_0_16]) ).

cnf(c_0_79,negated_conjecture,
    ~ theorem(equivalent(implies(p,implies(q,r)),implies(p,implies(q,and(p,r))))),
    c_0_72 ).

cnf(c_0_80,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_73,c_0_13]),c_0_13]),c_0_74]) ).

cnf(c_0_81,plain,
    ( ~ theorem(X2)
    | ~ theorem(or(X1,not(X2)))
    | theorem(X1) ),
    inference(spm,[status(thm)],[c_0_66,c_0_44]) ).

cnf(c_0_82,plain,
    ( ~ theorem(X2)
    | theorem(or(not(or(X1,not(X2))),X1)) ),
    inference(spm,[status(thm)],[c_0_75,c_0_22]) ).

cnf(c_0_83,plain,
    ( ~ theorem(not(not(or(not(X2),X3))))
    | theorem(or(or(not(or(X1,X2)),or(X1,X3)),X4)) ),
    inference(spm,[status(thm)],[c_0_42,c_0_21]) ).

cnf(c_0_84,plain,
    ( ~ axiom(or(not(X2),X1))
    | ~ theorem(X2)
    | theorem(not(not(X1))) ),
    inference(spm,[status(thm)],[c_0_53,c_0_16]) ).

cnf(c_0_85,plain,
    ( ~ theorem(or(not(not(X1)),X2))
    | theorem(or(X1,not(not(X2)))) ),
    inference(spm,[status(thm)],[c_0_76,c_0_50]) ).

cnf(c_0_86,plain,
    theorem(or(not(X1),or(X2,X1))),
    inference(spm,[status(thm)],[c_0_49,c_0_77]) ).

cnf(c_0_87,plain,
    ( ~ theorem(or(not(X2),X1))
    | ~ theorem(or(X1,or(X1,X2)))
    | theorem(X1) ),
    inference(spm,[status(thm)],[c_0_66,c_0_63]) ).

cnf(c_0_88,plain,
    ( ~ theorem(or(X3,X2))
    | theorem(or(X1,or(X2,X3))) ),
    inference(spm,[status(thm)],[c_0_78,c_0_22]) ).

cnf(c_0_89,negated_conjecture,
    ~ theorem(not(or(not(or(not(or(not(p),or(not(q),r))),or(not(p),or(not(q),not(or(not(p),not(r))))))),not(or(not(or(not(p),or(not(q),not(or(not(p),not(r)))))),or(not(p),or(not(q),r))))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_13]),c_0_13]),c_0_13]),c_0_13]),c_0_74]),c_0_80]) ).

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

cnf(c_0_91,plain,
    ( ~ theorem(not(not(or(not(X2),X3))))
    | theorem(or(not(or(X1,X2)),or(X1,X3))) ),
    inference(spm,[status(thm)],[c_0_43,c_0_83]) ).

cnf(c_0_92,plain,
    ( ~ theorem(or(not(X2),X3))
    | theorem(not(not(or(not(or(X1,X2)),or(X1,X3))))) ),
    inference(spm,[status(thm)],[c_0_84,c_0_21]) ).

cnf(c_0_93,plain,
    theorem(or(X1,not(not(or(X2,not(X1)))))),
    inference(spm,[status(thm)],[c_0_85,c_0_86]) ).

cnf(c_0_94,plain,
    ( ~ theorem(or(X2,X1))
    | ~ theorem(or(not(X2),X1))
    | theorem(X1) ),
    inference(spm,[status(thm)],[c_0_87,c_0_88]) ).

cnf(c_0_95,plain,
    ( ~ theorem(or(not(X2),X3))
    | theorem(or(X1,or(not(or(X1,X2)),X3))) ),
    inference(spm,[status(thm)],[c_0_49,c_0_24]) ).

cnf(c_0_96,plain,
    ( ~ theorem(or(X1,or(X3,X2)))
    | theorem(or(X1,or(X2,X3))) ),
    inference(spm,[status(thm)],[c_0_30,c_0_22]) ).

cnf(c_0_97,plain,
    theorem(or(X1,or(X2,not(X1)))),
    inference(spm,[status(thm)],[c_0_49,c_0_62]) ).

cnf(c_0_98,negated_conjecture,
    ( ~ theorem(or(not(or(not(p),or(not(q),not(or(not(p),not(r)))))),or(not(p),or(not(q),r))))
    | ~ theorem(or(not(or(not(p),or(not(q),r))),or(not(p),or(not(q),not(or(not(p),not(r))))))) ),
    inference(spm,[status(thm)],[c_0_89,c_0_90]) ).

cnf(c_0_99,plain,
    ( ~ theorem(or(not(X3),X4))
    | theorem(or(not(or(X1,or(X2,X3))),or(X1,or(X2,X4)))) ),
    inference(spm,[status(thm)],[c_0_91,c_0_92]) ).

cnf(c_0_100,plain,
    theorem(or(not(not(or(X1,not(X2)))),X2)),
    inference(spm,[status(thm)],[c_0_25,c_0_93]) ).

cnf(c_0_101,plain,
    ( ~ theorem(or(X2,or(X1,X2)))
    | theorem(or(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_94,c_0_86]) ).

cnf(c_0_102,plain,
    ( ~ theorem(or(X1,X2))
    | ~ theorem(or(not(X3),X4))
    | theorem(or(X1,or(not(or(not(X2),X3)),X4))) ),
    inference(spm,[status(thm)],[c_0_27,c_0_95]) ).

cnf(c_0_103,plain,
    theorem(or(X1,or(not(X1),X2))),
    inference(spm,[status(thm)],[c_0_96,c_0_97]) ).

cnf(c_0_104,negated_conjecture,
    ~ theorem(or(not(or(not(p),or(not(q),r))),or(not(p),or(not(q),not(or(not(p),not(r))))))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100])]) ).

cnf(c_0_105,plain,
    ( ~ theorem(or(X3,X1))
    | ~ theorem(or(not(X2),X3))
    | theorem(or(not(or(not(X1),X2)),X3)) ),
    inference(spm,[status(thm)],[c_0_101,c_0_102]) ).

cnf(c_0_106,plain,
    theorem(or(or(not(X1),X2),X1)),
    inference(spm,[status(thm)],[c_0_25,c_0_103]) ).

cnf(c_0_107,plain,
    ( ~ theorem(or(X1,or(not(X3),X4)))
    | theorem(or(X1,or(not(or(X2,X3)),or(X2,X4)))) ),
    inference(spm,[status(thm)],[c_0_30,c_0_21]) ).

cnf(c_0_108,plain,
    theorem(or(X1,or(not(or(X1,X2)),X2))),
    inference(spm,[status(thm)],[c_0_49,c_0_41]) ).

cnf(c_0_109,negated_conjecture,
    ~ theorem(or(not(or(not(q),r)),or(not(p),or(not(q),not(or(not(p),not(r))))))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106])]) ).

cnf(c_0_110,plain,
    ( ~ theorem(or(X3,or(not(X2),X4)))
    | theorem(or(not(or(X1,X2)),or(X3,or(X1,X4)))) ),
    inference(spm,[status(thm)],[c_0_49,c_0_107]) ).

cnf(c_0_111,plain,
    theorem(or(X1,or(X2,not(or(X1,X2))))),
    inference(spm,[status(thm)],[c_0_96,c_0_108]) ).

cnf(c_0_112,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_111])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04  % Problem  : LCL339-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07  % Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.45  % Computer : n004.cluster.edu
% 0.17/0.45  % Model    : x86_64 x86_64
% 0.17/0.45  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45  % Memory   : 8046.5625MB
% 0.17/0.45  % OS       : Linux 6.8.0-71-generic
% 0.17/0.45  % CPULimit : 300
% 0.17/0.45  % WCLimit  : 300
% 0.17/0.45  % DateTime : Mon Sep 21 00:22:21 UTC 2026
% 0.17/0.46  % CPUTime  : 
% 0.17/0.46  Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.53  Running first-order theorem proving
% 0.22/0.53  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
% 176.86/26.43  % Version: 3.5.1
% 176.86/26.43  % Preprocessing class: FSMSSMSSSSSNFFN.
% 176.86/26.43  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 176.86/26.43  % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 176.86/26.43  % Starting new_bool_3 with 300s (1) cores
% 176.86/26.43  % Starting new_bool_1 with 300s (1) cores
% 176.86/26.43  % Starting sh5l with 300s (1) cores
% 176.86/26.43  % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1858936 completed with status 0
% 176.86/26.43  % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 176.86/26.43  % Preprocessing class: FSMSSMSSSSSNFFN.
% 176.86/26.43  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 176.86/26.43  % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 176.86/26.43  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 176.86/26.43  % No SInE strategy applied
% 176.86/26.43  % Search class: FHUNM-FFSF21-DFFFFFNN
% 176.86/26.43  % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 176.86/26.43  % Starting SubtermCWHack with 136s (1) cores
% 176.86/26.43  % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 176.86/26.43  % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 300s (1) cores
% 176.86/26.43  % Starting new_bool_3 with 296s (1) cores
% 176.86/26.43  % Starting new_bool_1 with 291s (1) cores
% 176.86/26.43  % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1858942 completed with status 0
% 176.86/26.43  % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 176.86/26.43  % Preprocessing class: FSMSSMSSSSSNFFN.
% 176.86/26.43  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 176.86/26.43  % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 176.86/26.43  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 176.86/26.43  % No SInE strategy applied
% 176.86/26.43  % Search class: FHUNM-FFSF21-DFFFFFNN
% 176.86/26.43  % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 176.86/26.43  % Starting SubtermCWHack with 136s (1) cores
% 176.86/26.43  % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 176.86/26.43  % Preprocessing time       : 0.002 s
% 176.86/26.43  % Presaturation interreduction done
% 176.86/26.43  
% 176.86/26.43  % Proof found!
% 176.86/26.43  % SZS status Unsatisfiable
% 176.86/26.43  % SZS output start CNFRefutation
% See solution above
% 176.86/26.44  % Parsed axioms                        : 11
% 176.86/26.44  % Removed by relevancy pruning/SinE    : 0
% 176.86/26.44  % Initial clauses                      : 11
% 176.86/26.44  % Removed in clause preprocessing      : 3
% 176.86/26.44  % Initial clauses in saturation        : 8
% 176.86/26.44  % Processed clauses                    : 66069
% 176.86/26.44  % ...of these trivial                  : 311
% 176.86/26.44  % ...subsumed                          : 57925
% 176.86/26.44  % ...remaining for further processing  : 7833
% 176.86/26.44  % Other redundant clauses eliminated   : 0
% 176.86/26.44  % Clauses deleted for lack of memory   : 0
% 176.86/26.44  % Backward-subsumed                    : 2852
% 176.86/26.44  % Backward-rewritten                   : 24
% 176.86/26.44  % Generated clauses                    : 756671
% 176.86/26.44  % ...of the previous two non-redundant : 740366
% 176.86/26.44  % ...aggressively subsumed             : 0
% 176.86/26.44  % Contextual simplify-reflections      : 114
% 176.86/26.44  % Paramodulations                      : 756671
% 176.86/26.44  % Factorizations                       : 0
% 176.86/26.44  % NegExts                              : 0
% 176.86/26.44  % Equation resolutions                 : 0
% 176.86/26.44  % Disequality decompositions           : 0
% 176.86/26.44  % Total rewrite steps                  : 17374
% 176.86/26.44  % ...of those cached                   : 15808
% 176.86/26.44  % Propositional unsat checks           : 1
% 176.86/26.44  %    Propositional check models        : 0
% 176.86/26.44  %    Propositional check unsatisfiable : 0
% 176.86/26.44  %    Propositional clauses             : 0
% 176.86/26.44  %    Propositional clauses after purity: 0
% 176.86/26.44  %    Propositional unsat core size     : 0
% 176.86/26.44  %    Propositional preprocessing time  : 0.000
% 176.86/26.44  %    Propositional encoding time       : 0.957
% 176.86/26.44  %    Propositional solver time         : 0.696
% 176.86/26.44  %    Success case prop preproc time    : 0.000
% 176.86/26.44  %    Success case prop encoding time   : 0.000
% 176.86/26.44  %    Success case prop solver time     : 0.000
% 176.86/26.44  % Current number of processed clauses  : 4949
% 176.86/26.44  %    Positive orientable unit clauses  : 194
% 176.86/26.44  %    Positive unorientable unit clauses: 0
% 176.86/26.44  %    Negative unit clauses             : 135
% 176.86/26.44  %    Non-unit-clauses                  : 4620
% 176.86/26.44  % Current number of unprocessed clauses: 670760
% 176.86/26.44  % ...number of literals in the above   : 1914276
% 176.86/26.44  % Current number of archived formulas  : 0
% 176.86/26.44  % Current number of archived clauses   : 2887
% 176.86/26.44  % Clause-clause subsumption calls (NU) : 6700694
% 176.86/26.44  % Rec. Clause-clause subsumption calls : 5303672
% 176.86/26.44  % Non-unit clause-clause subsumptions  : 51569
% 176.86/26.44  % Unit Clause-clause subsumption calls : 61082
% 176.86/26.44  % Rewrite failures with RHS unbound    : 0
% 176.86/26.44  % BW rewrite match attempts            : 23966
% 176.86/26.44  % BW rewrite match successes           : 24
% 176.86/26.44  % Condensation attempts                : 0
% 176.86/26.44  % Condensation successes               : 0
% 176.86/26.44  % Termbank termtop insertions          : 19823817
% 176.86/26.44  % Search garbage collected termcells   : 11
% 176.86/26.44  
% 176.86/26.44  % -------------------------------------------------
% 176.86/26.44  % User time                : 24.231 s
% 176.86/26.44  % System time              : 0.763 s
% 176.86/26.44  % Total time               : 24.993 s
% 176.86/26.44  % Maximum resident set size: 3644 pages
% 176.86/26.44  
% 176.86/26.44  % -------------------------------------------------
% 176.86/26.44  % User time                : 121.766 s
% 176.86/26.44  % System time              : 4.346 s
% 176.86/26.44  % Total time               : 126.112 s
% 176.86/26.44  % Maximum resident set size: 4864 pages
% 176.86/26.44  % E exiting
%------------------------------------------------------------------------------