%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : LCL331-3 : 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 : n016.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 01:19:09 PM UTC 2026
% Result : Unsatisfiable 164.94s 29.72s
% Output : CNFRefutation 164.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 11
% Syntax : Number of clauses : 119 ( 46 unt; 0 nHn; 57 RR)
% Number of literals : 220 ( 7 equ; 110 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 : 235 ( 35 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(and(p,q),r),implies(and(p,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,plain,
( ~ axiom(or(not(X2),X1))
| ~ theorem(X2)
| theorem(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,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_20,axiom,
axiom(implies(or(X1,X2),or(X2,X1))),
axiom_1_4 ).
cnf(c_0_21,axiom,
axiom(implies(X1,or(X2,X1))),
axiom_1_3 ).
cnf(c_0_22,plain,
( ~ theorem(or(not(X2),X3))
| theorem(or(not(or(X1,X2)),or(X1,X3))) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
axiom(or(not(or(X1,X2)),or(X2,X1))),
inference(rw,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_24,plain,
axiom(or(not(X1),or(X2,X1))),
inference(rw,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_25,plain,
( ~ theorem(or(X1,X3))
| ~ theorem(or(not(X3),X2))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_26,axiom,
axiom(implies(or(X1,X1),X1)),
axiom_1_2 ).
cnf(c_0_27,plain,
( ~ theorem(or(X2,X1))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_28,plain,
( ~ theorem(X2)
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_29,plain,
( ~ axiom(or(not(X3),X2))
| ~ theorem(or(X1,X3))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_30,plain,
axiom(or(not(or(X1,X1)),X1)),
inference(rw,[status(thm)],[c_0_26,c_0_13]) ).
cnf(c_0_31,plain,
( ~ theorem(X1)
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( ~ theorem(or(X1,or(X2,X2)))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
( ~ theorem(not(X3))
| ~ theorem(or(X1,X3))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_31]) ).
cnf(c_0_34,plain,
( ~ axiom(or(X2,X1))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_16]) ).
cnf(c_0_35,plain,
( ~ axiom(or(X1,or(X2,X2)))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_32,c_0_16]) ).
cnf(c_0_36,plain,
( ~ axiom(or(X1,X3))
| ~ theorem(not(X3))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_16]) ).
cnf(c_0_37,plain,
( ~ axiom(or(X1,not(X2)))
| ~ theorem(X2)
| theorem(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_34]) ).
cnf(c_0_38,plain,
theorem(or(not(X1),X1)),
inference(spm,[status(thm)],[c_0_35,c_0_24]) ).
cnf(c_0_39,plain,
( ~ theorem(not(or(X3,X1)))
| theorem(or(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_36,c_0_24]) ).
cnf(c_0_40,plain,
( ~ theorem(X1)
| theorem(not(or(not(X1),not(X1)))) ),
inference(spm,[status(thm)],[c_0_37,c_0_30]) ).
cnf(c_0_41,axiom,
axiom(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
axiom_1_5 ).
cnf(c_0_42,plain,
theorem(or(X1,not(X1))),
inference(spm,[status(thm)],[c_0_27,c_0_38]) ).
cnf(c_0_43,plain,
( ~ axiom(or(X3,X1))
| ~ theorem(not(X3))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_44,plain,
( ~ theorem(or(X1,X1))
| theorem(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_30]) ).
cnf(c_0_45,plain,
( ~ theorem(X1)
| theorem(or(not(not(X1)),X2)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,plain,
axiom(or(not(or(X1,or(X2,X3))),or(X2,or(X1,X3)))),
inference(rw,[status(thm)],[c_0_41,c_0_13]) ).
cnf(c_0_47,plain,
( ~ theorem(or(X1,X2))
| theorem(or(X1,not(not(X2)))) ),
inference(spm,[status(thm)],[c_0_25,c_0_42]) ).
cnf(c_0_48,plain,
( ~ theorem(not(not(or(X1,X1))))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_30]) ).
cnf(c_0_49,plain,
( ~ theorem(X1)
| theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
( ~ theorem(or(X2,or(X1,X3)))
| theorem(or(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_18,c_0_46]) ).
cnf(c_0_51,plain,
( ~ theorem(X2)
| ~ theorem(or(not(X2),X1))
| theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_15,c_0_47]) ).
cnf(c_0_52,plain,
theorem(or(not(or(X1,X1)),X1)),
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
cnf(c_0_53,plain,
( ~ theorem(or(X1,X1))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,plain,
( ~ axiom(or(X2,or(X1,X3)))
| theorem(or(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_50,c_0_16]) ).
cnf(c_0_55,plain,
( ~ theorem(or(X1,X1))
| theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,plain,
( ~ axiom(or(X1,or(or(X1,X2),X2)))
| theorem(or(or(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,plain,
( ~ theorem(or(X2,X1))
| theorem(or(not(not(X1)),X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_47]) ).
cnf(c_0_58,plain,
( ~ theorem(or(not(not(X1)),X1))
| theorem(not(not(not(not(X1))))) ),
inference(spm,[status(thm)],[c_0_55,c_0_47]) ).
cnf(c_0_59,plain,
theorem(or(or(not(X1),X1),X2)),
inference(spm,[status(thm)],[c_0_56,c_0_24]) ).
cnf(c_0_60,plain,
( ~ theorem(not(X2))
| ~ theorem(or(X1,X2))
| theorem(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_57]) ).
cnf(c_0_61,plain,
( ~ theorem(or(X1,X1))
| theorem(not(not(not(not(X1))))) ),
inference(spm,[status(thm)],[c_0_58,c_0_57]) ).
cnf(c_0_62,plain,
( ~ theorem(or(X1,or(X3,X2)))
| theorem(or(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_63,plain,
theorem(or(X1,or(not(X2),X2))),
inference(spm,[status(thm)],[c_0_27,c_0_59]) ).
cnf(c_0_64,plain,
( ~ theorem(or(X1,X2))
| ~ theorem(not(not(not(X2))))
| theorem(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_47]) ).
cnf(c_0_65,plain,
( ~ theorem(or(not(not(X1)),X1))
| theorem(not(not(not(not(not(not(X1))))))) ),
inference(spm,[status(thm)],[c_0_61,c_0_57]) ).
cnf(c_0_66,plain,
theorem(or(X1,or(X2,not(X2)))),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,plain,
( ~ theorem(or(X1,X2))
| ~ theorem(not(not(not(not(not(X2))))))
| theorem(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_47]) ).
cnf(c_0_68,plain,
theorem(not(not(not(not(not(not(or(X1,not(X1))))))))),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_69,plain,
( ~ theorem(or(X1,X3))
| theorem(or(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_50,c_0_28]) ).
cnf(c_0_70,plain,
( ~ theorem(or(X1,not(or(X2,not(X2)))))
| theorem(X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,plain,
( ~ theorem(or(not(X3),X2))
| theorem(or(or(X1,X2),not(or(X1,X3)))) ),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_72,plain,
( ~ theorem(or(not(X2),X1))
| theorem(or(not(or(X1,X2)),X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_22]) ).
cnf(c_0_73,plain,
( ~ theorem(X3)
| ~ theorem(or(not(X3),X2))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_69]) ).
cnf(c_0_74,negated_conjecture,
~ theorem(equivalent(implies(and(p,q),r),implies(and(p,q),and(p,r)))),
inference(fof_simplification,[status(thm)],[prove_this]) ).
cnf(c_0_75,axiom,
equivalent(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
equivalent_defn ).
cnf(c_0_76,axiom,
and(X1,X2) = not(or(not(X1),not(X2))),
and_defn ).
cnf(c_0_77,plain,
( ~ theorem(or(X1,X3))
| ~ theorem(not(or(X2,X3)))
| theorem(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_69]) ).
cnf(c_0_78,plain,
( ~ axiom(or(X1,or(not(X3),X2)))
| ~ theorem(X3)
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_54]) ).
cnf(c_0_79,plain,
( ~ theorem(or(not(not(X1)),X2))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_80,plain,
( ~ theorem(or(X1,X2))
| ~ theorem(or(not(X2),X1))
| theorem(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_72]) ).
cnf(c_0_81,plain,
( ~ axiom(or(not(X3),X2))
| ~ theorem(X3)
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_73,c_0_16]) ).
cnf(c_0_82,negated_conjecture,
~ theorem(equivalent(implies(and(p,q),r),implies(and(p,q),and(p,r)))),
c_0_74 ).
cnf(c_0_83,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_75,c_0_13]),c_0_13]),c_0_76]) ).
cnf(c_0_84,plain,
( ~ theorem(X2)
| ~ theorem(or(X1,not(X2)))
| theorem(X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_40]) ).
cnf(c_0_85,plain,
( ~ theorem(X2)
| theorem(or(not(or(X1,not(X2))),X1)) ),
inference(spm,[status(thm)],[c_0_78,c_0_23]) ).
cnf(c_0_86,plain,
( ~ theorem(or(not(not(X1)),X2))
| theorem(or(X1,not(not(X2)))) ),
inference(spm,[status(thm)],[c_0_79,c_0_47]) ).
cnf(c_0_87,plain,
theorem(or(not(X1),or(X2,X1))),
inference(spm,[status(thm)],[c_0_50,c_0_63]) ).
cnf(c_0_88,plain,
( ~ theorem(or(not(X2),X1))
| ~ theorem(or(X1,or(X1,X2)))
| theorem(X1) ),
inference(spm,[status(thm)],[c_0_80,c_0_72]) ).
cnf(c_0_89,plain,
( ~ theorem(or(X3,X2))
| theorem(or(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_81,c_0_23]) ).
cnf(c_0_90,negated_conjecture,
~ theorem(not(or(not(or(not(or(not(not(or(not(p),not(q)))),r)),or(not(not(or(not(p),not(q)))),not(or(not(p),not(r)))))),not(or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(r))))),or(not(not(or(not(p),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_82,c_0_13]),c_0_13]),c_0_76]),c_0_76]),c_0_76]),c_0_83]) ).
cnf(c_0_91,plain,
( ~ theorem(X2)
| ~ theorem(X1)
| theorem(not(or(not(X1),not(X2)))) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_92,plain,
theorem(or(X1,not(not(or(X2,not(X1)))))),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_93,plain,
( ~ theorem(or(X2,X1))
| ~ theorem(or(not(X2),X1))
| theorem(X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_94,plain,
( ~ theorem(or(not(X2),X3))
| theorem(or(X1,or(not(or(X1,X2)),X3))) ),
inference(spm,[status(thm)],[c_0_50,c_0_22]) ).
cnf(c_0_95,plain,
theorem(or(not(X1),or(X1,X2))),
inference(spm,[status(thm)],[c_0_62,c_0_87]) ).
cnf(c_0_96,negated_conjecture,
( ~ theorem(or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(r))))),or(not(not(or(not(p),not(q)))),r)))
| ~ theorem(or(not(or(not(not(or(not(p),not(q)))),r)),or(not(not(or(not(p),not(q)))),not(or(not(p),not(r)))))) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_97,plain,
theorem(or(not(not(or(X1,not(X2)))),X2)),
inference(spm,[status(thm)],[c_0_27,c_0_92]) ).
cnf(c_0_98,plain,
( ~ theorem(or(X2,or(X1,X2)))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_93,c_0_87]) ).
cnf(c_0_99,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_25,c_0_94]) ).
cnf(c_0_100,plain,
theorem(or(X1,or(not(X1),X2))),
inference(spm,[status(thm)],[c_0_50,c_0_95]) ).
cnf(c_0_101,plain,
( ~ theorem(not(not(X1)))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_42]) ).
cnf(c_0_102,negated_conjecture,
~ theorem(or(not(or(not(not(or(not(p),not(q)))),r)),or(not(not(or(not(p),not(q)))),not(or(not(p),not(r)))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_22]),c_0_97])]) ).
cnf(c_0_103,plain,
( ~ theorem(or(X3,X1))
| ~ theorem(or(not(X2),X3))
| theorem(or(not(or(not(X1),X2)),X3)) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_104,plain,
theorem(or(or(not(X1),X2),X1)),
inference(spm,[status(thm)],[c_0_27,c_0_100]) ).
cnf(c_0_105,plain,
( ~ theorem(not(not(X2)))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_101]) ).
cnf(c_0_106,plain,
( ~ theorem(X3)
| ~ theorem(or(X1,not(X3)))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_45]) ).
cnf(c_0_107,negated_conjecture,
~ theorem(or(not(r),or(not(not(or(not(p),not(q)))),not(or(not(p),not(r)))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104])]) ).
cnf(c_0_108,plain,
( ~ theorem(or(or(X1,X3),X2))
| theorem(or(X1,or(not(not(X2)),X3))) ),
inference(spm,[status(thm)],[c_0_50,c_0_57]) ).
cnf(c_0_109,plain,
( ~ theorem(not(not(or(X1,X3))))
| theorem(or(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_50,c_0_105]) ).
cnf(c_0_110,plain,
( ~ axiom(or(not(X3),X1))
| ~ theorem(X3)
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_106,c_0_34]) ).
cnf(c_0_111,negated_conjecture,
~ theorem(or(or(not(r),not(or(not(p),not(r)))),or(not(p),not(q)))),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_112,plain,
( ~ theorem(not(not(or(X1,X2))))
| theorem(or(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_62,c_0_109]) ).
cnf(c_0_113,plain,
( ~ theorem(or(X2,X1))
| theorem(or(or(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_110,c_0_23]) ).
cnf(c_0_114,plain,
theorem(or(X1,or(not(or(X1,X2)),X2))),
inference(spm,[status(thm)],[c_0_50,c_0_38]) ).
cnf(c_0_115,negated_conjecture,
~ theorem(not(not(or(or(not(r),not(or(not(p),not(r)))),not(p))))),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_116,plain,
( ~ theorem(or(X2,X1))
| theorem(not(not(or(X1,X2)))) ),
inference(spm,[status(thm)],[c_0_55,c_0_113]) ).
cnf(c_0_117,plain,
theorem(or(X1,or(X2,not(or(X1,X2))))),
inference(spm,[status(thm)],[c_0_62,c_0_114]) ).
cnf(c_0_118,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL331-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/5.47 % Computer : n016.cluster.edu
% 0.22/5.47 % Model : x86_64 x86_64
% 0.22/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/5.47 % Memory : 8046.5625MB
% 0.22/5.47 % OS : Linux 6.8.0-71-generic
% 0.22/5.47 % CPULimit : 300
% 0.22/5.47 % WCLimit : 300
% 0.22/5.47 % DateTime : Mon Sep 21 00:26:14 UTC 2026
% 0.22/5.48 % CPUTime :
% 0.22/5.48 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/5.55 Running first-order theorem proving
% 0.25/5.55 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
% 164.94/29.72 % Version: 3.5.1
% 164.94/29.72 % Preprocessing class: FSMSSMSSSSSNFFN.
% 164.94/29.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 164.94/29.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 164.94/29.72 % Starting new_bool_3 with 300s (1) cores
% 164.94/29.72 % Starting new_bool_1 with 300s (1) cores
% 164.94/29.72 % Starting sh5l with 300s (1) cores
% 164.94/29.72 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1178091 completed with status 0
% 164.94/29.72 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 164.94/29.72 % Preprocessing class: FSMSSMSSSSSNFFN.
% 164.94/29.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 164.94/29.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 164.94/29.72 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 164.94/29.72 % No SInE strategy applied
% 164.94/29.72 % Search class: FHUNM-FFSF21-DFFFFFNN
% 164.94/29.72 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 164.94/29.72 % Starting SubtermCWHack with 136s (1) cores
% 164.94/29.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 164.94/29.72 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 300s (1) cores
% 164.94/29.72 % Starting new_bool_3 with 296s (1) cores
% 164.94/29.72 % Starting new_bool_1 with 291s (1) cores
% 164.94/29.72 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1178096 completed with status 0
% 164.94/29.72 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 164.94/29.72 % Preprocessing class: FSMSSMSSSSSNFFN.
% 164.94/29.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 164.94/29.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 164.94/29.72 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 164.94/29.72 % No SInE strategy applied
% 164.94/29.72 % Search class: FHUNM-FFSF21-DFFFFFNN
% 164.94/29.72 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 164.94/29.72 % Starting SubtermCWHack with 136s (1) cores
% 164.94/29.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 164.94/29.72 % Preprocessing time : 0.002 s
% 164.94/29.72 % Presaturation interreduction done
% 164.94/29.72
% 164.94/29.72 % Proof found!
% 164.94/29.72 % SZS status Unsatisfiable
% 164.94/29.72 % SZS output start CNFRefutation
% See solution above
% 164.94/29.72 % Parsed axioms : 11
% 164.94/29.72 % Removed by relevancy pruning/SinE : 0
% 164.94/29.72 % Initial clauses : 11
% 164.94/29.72 % Removed in clause preprocessing : 3
% 164.94/29.72 % Initial clauses in saturation : 8
% 164.94/29.72 % Processed clauses : 61702
% 164.94/29.72 % ...of these trivial : 204
% 164.94/29.72 % ...subsumed : 56263
% 164.94/29.72 % ...remaining for further processing : 5235
% 164.94/29.72 % Other redundant clauses eliminated : 0
% 164.94/29.72 % Clauses deleted for lack of memory : 0
% 164.94/29.72 % Backward-subsumed : 179
% 164.94/29.72 % Backward-rewritten : 22
% 164.94/29.72 % Generated clauses : 630229
% 164.94/29.72 % ...of the previous two non-redundant : 616603
% 164.94/29.72 % ...aggressively subsumed : 0
% 164.94/29.72 % Contextual simplify-reflections : 0
% 164.94/29.72 % Paramodulations : 630229
% 164.94/29.72 % Factorizations : 0
% 164.94/29.72 % NegExts : 0
% 164.94/29.72 % Equation resolutions : 0
% 164.94/29.72 % Disequality decompositions : 0
% 164.94/29.72 % Total rewrite steps : 13485
% 164.94/29.72 % ...of those cached : 12427
% 164.94/29.72 % Propositional unsat checks : 1
% 164.94/29.72 % Propositional check models : 0
% 164.94/29.72 % Propositional check unsatisfiable : 0
% 164.94/29.72 % Propositional clauses : 0
% 164.94/29.72 % Propositional clauses after purity: 0
% 164.94/29.72 % Propositional unsat core size : 0
% 164.94/29.72 % Propositional preprocessing time : 0.000
% 164.94/29.72 % Propositional encoding time : 2.078
% 164.94/29.72 % Propositional solver time : 1.042
% 164.94/29.72 % Success case prop preproc time : 0.000
% 164.94/29.72 % Success case prop encoding time : 0.000
% 164.94/29.72 % Success case prop solver time : 0.000
% 164.94/29.72 % Current number of processed clauses : 5026
% 164.94/29.72 % Positive orientable unit clauses : 183
% 164.94/29.72 % Positive unorientable unit clauses: 0
% 164.94/29.72 % Negative unit clauses : 259
% 164.94/29.72 % Non-unit-clauses : 4584
% 164.94/29.72 % Current number of unprocessed clauses: 553834
% 164.94/29.72 % ...number of literals in the above : 1558350
% 164.94/29.72 % Current number of archived formulas : 0
% 164.94/29.72 % Current number of archived clauses : 212
% 164.94/29.72 % Clause-clause subsumption calls (NU) : 3895965
% 164.94/29.72 % Rec. Clause-clause subsumption calls : 3655694
% 164.94/29.72 % Non-unit clause-clause subsumptions : 54444
% 164.94/29.72 % Unit Clause-clause subsumption calls : 13156
% 164.94/29.72 % Rewrite failures with RHS unbound : 0
% 164.94/29.72 % BW rewrite match attempts : 21738
% 164.94/29.72 % BW rewrite match successes : 22
% 164.94/29.72 % Condensation attempts : 0
% 164.94/29.72 % Condensation successes : 0
% 164.94/29.72 % Termbank termtop insertions : 18139961
% 164.94/29.72 % Search garbage collected termcells : 11
% 164.94/29.72
% 164.94/29.72 % -------------------------------------------------
% 164.94/29.72 % User time : 22.684 s
% 164.94/29.72 % System time : 0.680 s
% 164.94/29.72 % Total time : 23.364 s
% 164.94/29.72 % Maximum resident set size: 3388 pages
% 164.94/29.72
% 164.94/29.72 % -------------------------------------------------
% 164.94/29.72 % User time : 112.821 s
% 164.94/29.72 % System time : 3.810 s
% 164.94/29.72 % Total time : 116.631 s
% 164.94/29.72 % Maximum resident set size: 4608 pages
% 164.94/29.72 % E exiting
%------------------------------------------------------------------------------