%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL504+1 : TPTP v9.2.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 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 : Tue May 5 04:40:30 PM UTC 2026
% Result : Theorem 39.38s 22.94s
% Output : CNFRefutation 39.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 21
% Syntax : Number of formulae : 185 ( 69 unt; 0 def)
% Number of atoms : 357 ( 25 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 317 ( 145 ~; 145 |; 13 &)
% ( 9 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 13 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 17 con; 0-2 aty)
% Number of variables : 336 ( 56 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(rosser_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_op_implies_and) ).
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(implies(X1,X2)) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(kn3,axiom,
( kn3
<=> ! [X4,X5,X6] : is_a_theorem(implies(implies(X4,X5),implies(not(and(X5,X6)),not(and(X6,X4))))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn3) ).
fof(rosser_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_op_or) ).
fof(rosser_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_modus_ponens) ).
fof(rosser_kn3,axiom,
kn3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn3) ).
fof(kn2,axiom,
( kn2
<=> ! [X4,X5] : is_a_theorem(implies(and(X4,X5),X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn2) ).
fof(kn1,axiom,
( kn1
<=> ! [X4] : is_a_theorem(implies(X4,and(X4,X4))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(rosser_kn2,axiom,
kn2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).
fof(rosser_kn1,axiom,
kn1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn1) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(rosser_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_op_equiv) ).
fof(cn3,axiom,
( cn3
<=> ! [X4] : is_a_theorem(implies(implies(not(X4),X4),X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn3) ).
fof(or_1,axiom,
( or_1
<=> ! [X1,X2] : is_a_theorem(implies(X1,or(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_1) ).
fof(and_2,axiom,
( and_2
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_2) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X1,X2] :
( is_a_theorem(equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',use_substitution_of_equivalents) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X1,X2] : is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(hilbert_implies_2,conjecture,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(c_0_21,plain,
! [X186,X187] :
( ~ op_implies_and
| implies(X186,X187) = not(and(X186,not(X187))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])]) ).
fof(c_0_22,plain,
! [X182,X183] :
( ~ op_or
| or(X182,X183) = not(and(not(X182),not(X183))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])]) ).
cnf(c_0_23,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_24,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[rosser_op_implies_and]) ).
fof(c_0_25,plain,
! [X72,X73] :
( ( ~ modus_ponens
| ~ is_a_theorem(X72)
| ~ is_a_theorem(implies(X72,X73))
| is_a_theorem(X73) )
& ( is_a_theorem(esk1_0)
| modus_ponens )
& ( is_a_theorem(implies(esk1_0,esk2_0))
| modus_ponens )
& ( ~ is_a_theorem(esk2_0)
| modus_ponens ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens])])])])]) ).
fof(c_0_26,plain,
! [X142,X143,X144] :
( ( ~ kn3
| is_a_theorem(implies(implies(X142,X143),implies(not(and(X143,X144)),not(and(X144,X142))))) )
& ( ~ is_a_theorem(implies(implies(esk36_0,esk37_0),implies(not(and(esk37_0,esk38_0)),not(and(esk38_0,esk36_0)))))
| kn3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn3])])])]) ).
cnf(c_0_27,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
cnf(c_0_29,plain,
op_or,
inference(split_conjunct,[status(thm)],[rosser_op_or]) ).
cnf(c_0_30,plain,
( is_a_theorem(X2)
| ~ modus_ponens
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[rosser_modus_ponens]) ).
cnf(c_0_32,plain,
( is_a_theorem(implies(implies(X1,X2),implies(not(and(X2,X3)),not(and(X3,X1)))))
| ~ kn3 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_34,plain,
kn3,
inference(split_conjunct,[status(thm)],[rosser_kn3]) ).
cnf(c_0_35,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_36,plain,
is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_37,plain,
( is_a_theorem(or(and(X1,X2),not(and(X2,X3))))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,plain,
( is_a_theorem(or(and(X1,X2),implies(X2,X3)))
| ~ is_a_theorem(or(X3,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_28]),c_0_33]) ).
cnf(c_0_39,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_33,c_0_28]) ).
fof(c_0_40,plain,
! [X138,X139] :
( ( ~ kn2
| is_a_theorem(implies(and(X138,X139),X138)) )
& ( ~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0))
| kn2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn2])])])]) ).
fof(c_0_41,plain,
! [X136] :
( ( ~ kn1
| is_a_theorem(implies(X136,and(X136,X136))) )
& ( ~ is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0)))
| kn1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn1])])])]) ).
cnf(c_0_42,plain,
( is_a_theorem(implies(implies(X1,X2),or(X2,X3)))
| ~ is_a_theorem(or(X3,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_33]),c_0_39]) ).
cnf(c_0_43,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ kn2 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,plain,
kn2,
inference(split_conjunct,[status(thm)],[rosser_kn2]) ).
cnf(c_0_45,plain,
( is_a_theorem(implies(X1,and(X1,X1)))
| ~ kn1 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_46,plain,
kn1,
inference(split_conjunct,[status(thm)],[rosser_kn1]) ).
cnf(c_0_47,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(implies(X3,X1))
| ~ is_a_theorem(or(X2,X3)) ),
inference(spm,[status(thm)],[c_0_35,c_0_42]) ).
cnf(c_0_48,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
cnf(c_0_49,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
cnf(c_0_50,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,and(X1,X3))) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,plain,
is_a_theorem(or(X1,and(not(X1),not(X1)))),
inference(spm,[status(thm)],[c_0_49,c_0_33]) ).
cnf(c_0_52,plain,
is_a_theorem(or(not(X1),X1)),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_53,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X2,X1))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_35,c_0_33]) ).
cnf(c_0_54,plain,
( is_a_theorem(or(and(X1,X1),X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_47,c_0_49]) ).
cnf(c_0_55,plain,
is_a_theorem(or(X1,not(and(X1,X2)))),
inference(spm,[status(thm)],[c_0_50,c_0_52]) ).
cnf(c_0_56,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(and(X2,X2)))
| ~ is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_53,c_0_55]) ).
cnf(c_0_58,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,not(X3)))
| ~ is_a_theorem(or(X3,X1)) ),
inference(spm,[status(thm)],[c_0_47,c_0_33]) ).
cnf(c_0_59,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(and(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_58,c_0_55]) ).
fof(c_0_61,plain,
! [X190,X191] :
( ~ op_equiv
| equiv(X190,X191) = and(implies(X190,X191),implies(X191,X190)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])]) ).
cnf(c_0_62,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_51]),c_0_28]),c_0_33]) ).
cnf(c_0_63,plain,
( is_a_theorem(or(implies(X1,X2),X3))
| ~ is_a_theorem(or(X2,X3)) ),
inference(spm,[status(thm)],[c_0_60,c_0_38]) ).
cnf(c_0_64,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_65,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[rosser_op_equiv]) ).
cnf(c_0_66,plain,
is_a_theorem(or(X1,implies(X1,X2))),
inference(spm,[status(thm)],[c_0_55,c_0_28]) ).
cnf(c_0_67,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_68,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]) ).
cnf(c_0_69,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_53,c_0_66]) ).
cnf(c_0_70,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_67,c_0_66]) ).
cnf(c_0_71,plain,
is_a_theorem(implies(implies(X1,X1),equiv(X1,X1))),
inference(spm,[status(thm)],[c_0_49,c_0_68]) ).
cnf(c_0_72,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X3))
| ~ is_a_theorem(not(X3)) ),
inference(spm,[status(thm)],[c_0_47,c_0_69]) ).
cnf(c_0_73,plain,
is_a_theorem(or(implies(X1,X2),and(X1,not(X2)))),
inference(spm,[status(thm)],[c_0_52,c_0_28]) ).
cnf(c_0_74,plain,
is_a_theorem(or(X1,not(X1))),
inference(spm,[status(thm)],[c_0_70,c_0_33]) ).
cnf(c_0_75,plain,
( is_a_theorem(or(equiv(X1,X1),X2))
| ~ is_a_theorem(or(X2,implies(X1,X1))) ),
inference(spm,[status(thm)],[c_0_47,c_0_71]) ).
cnf(c_0_76,plain,
( is_a_theorem(or(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_28]) ).
cnf(c_0_77,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,not(X2)))
| ~ is_a_theorem(or(X2,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_28]),c_0_33]) ).
cnf(c_0_78,plain,
is_a_theorem(or(not(and(X1,X2)),X1)),
inference(spm,[status(thm)],[c_0_60,c_0_74]) ).
cnf(c_0_79,plain,
( is_a_theorem(or(equiv(X1,X1),X2))
| ~ is_a_theorem(implies(X1,X1)) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,plain,
( is_a_theorem(not(and(not(X1),X2)))
| ~ is_a_theorem(or(X1,X1)) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_81,plain,
is_a_theorem(or(equiv(X1,X1),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_70])]) ).
cnf(c_0_82,plain,
is_a_theorem(not(and(not(equiv(X1,X1)),X2))),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_83,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,not(equiv(X2,X2)))) ),
inference(spm,[status(thm)],[c_0_56,c_0_82]) ).
cnf(c_0_84,plain,
is_a_theorem(or(not(and(and(X1,X2),X3)),X1)),
inference(spm,[status(thm)],[c_0_60,c_0_55]) ).
fof(c_0_85,plain,
! [X158] :
( ( ~ cn3
| is_a_theorem(implies(implies(not(X158),X158),X158)) )
& ( ~ is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0))
| cn3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn3])])])]) ).
fof(c_0_86,plain,
! [X110,X111] :
( ( ~ or_1
| is_a_theorem(implies(X110,or(X110,X111))) )
& ( ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0)))
| or_1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_1])])])]) ).
cnf(c_0_87,plain,
is_a_theorem(not(and(and(not(equiv(X1,X1)),X2),X3))),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_88,plain,
( is_a_theorem(or(X1,and(X2,X2)))
| ~ is_a_theorem(or(and(X1,X3),X2)) ),
inference(spm,[status(thm)],[c_0_50,c_0_54]) ).
cnf(c_0_89,plain,
( is_a_theorem(or(and(X1,implies(X2,X3)),not(equiv(X2,X3))))
| ~ is_a_theorem(implies(implies(X3,X2),X1)) ),
inference(spm,[status(thm)],[c_0_37,c_0_68]) ).
cnf(c_0_90,plain,
( is_a_theorem(implies(implies(not(X1),X1),X1))
| ~ cn3 ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_91,plain,
not(and(X1,implies(X2,X3))) = implies(X1,and(X2,not(X3))),
inference(spm,[status(thm)],[c_0_28,c_0_28]) ).
cnf(c_0_92,plain,
( is_a_theorem(implies(X1,or(X1,X2)))
| ~ or_1 ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_93,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,and(not(equiv(X2,X2)),X3))) ),
inference(spm,[status(thm)],[c_0_56,c_0_87]) ).
cnf(c_0_94,plain,
( is_a_theorem(or(X1,and(not(equiv(X2,X3)),not(equiv(X2,X3)))))
| ~ is_a_theorem(implies(implies(X3,X2),X1)) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_95,plain,
( is_a_theorem(implies(or(X1,X1),X1))
| ~ cn3 ),
inference(rw,[status(thm)],[c_0_90,c_0_33]) ).
cnf(c_0_96,plain,
implies(implies(X1,and(X2,not(X3))),X4) = or(and(X1,implies(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_33,c_0_91]) ).
cnf(c_0_97,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0)) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_98,plain,
( is_a_theorem(or(X1,X2))
| ~ or_1
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_92]) ).
cnf(c_0_99,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,X2),X1)) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_100,plain,
is_a_theorem(implies(implies(X1,X2),not(and(and(X1,not(X2)),X3)))),
inference(spm,[status(thm)],[c_0_55,c_0_39]) ).
cnf(c_0_101,plain,
( is_a_theorem(or(and(implies(X1,X2),implies(X1,X2)),and(X1,not(X2))))
| ~ cn3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_39]),c_0_96]) ).
cnf(c_0_102,plain,
( cn3
| ~ is_a_theorem(implies(or(esk44_0,esk44_0),esk44_0)) ),
inference(rw,[status(thm)],[c_0_97,c_0_33]) ).
cnf(c_0_103,plain,
( is_a_theorem(implies(or(X1,X1),X2))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_39]),c_0_33]) ).
cnf(c_0_104,plain,
( is_a_theorem(not(and(not(X1),X2)))
| ~ or_1
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_80,c_0_98]) ).
cnf(c_0_105,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(implies(implies(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_60,c_0_39]) ).
cnf(c_0_106,plain,
is_a_theorem(not(and(and(X1,not(X1)),X2))),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_107,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_47,c_0_70]) ).
cnf(c_0_108,plain,
is_a_theorem(or(and(X1,X2),not(and(X2,X1)))),
inference(spm,[status(thm)],[c_0_99,c_0_36]) ).
cnf(c_0_109,plain,
( is_a_theorem(or(X1,and(implies(X1,X2),implies(X1,X2))))
| ~ cn3 ),
inference(spm,[status(thm)],[c_0_50,c_0_101]) ).
cnf(c_0_110,plain,
( cn3
| ~ is_a_theorem(or(esk44_0,not(esk44_0))) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_111,plain,
( is_a_theorem(X1)
| ~ or_1
| ~ is_a_theorem(or(X1,not(X2)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_104]) ).
cnf(c_0_112,plain,
is_a_theorem(or(or(and(X1,X2),not(and(X2,X3))),X3)),
inference(spm,[status(thm)],[c_0_105,c_0_36]) ).
cnf(c_0_113,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,and(X2,not(X2)))) ),
inference(spm,[status(thm)],[c_0_56,c_0_106]) ).
cnf(c_0_114,plain,
is_a_theorem(or(not(and(X1,X2)),and(X2,X1))),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_115,plain,
( is_a_theorem(or(implies(X1,X2),X1))
| ~ cn3 ),
inference(spm,[status(thm)],[c_0_50,c_0_109]) ).
cnf(c_0_116,plain,
( is_a_theorem(or(X1,X2))
| ~ cn3
| ~ is_a_theorem(or(X2,or(X1,X1))) ),
inference(spm,[status(thm)],[c_0_47,c_0_95]) ).
cnf(c_0_117,plain,
cn3,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_74])]) ).
cnf(c_0_118,plain,
( is_a_theorem(or(and(X1,X2),implies(X2,X3)))
| ~ or_1
| ~ is_a_theorem(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_28]) ).
cnf(c_0_119,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(and(X3,X1)))
| ~ is_a_theorem(or(X2,X3)) ),
inference(spm,[status(thm)],[c_0_53,c_0_38]) ).
cnf(c_0_120,plain,
is_a_theorem(not(and(not(X1),X1))),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_121,plain,
( is_a_theorem(or(or(X1,X2),not(X1)))
| ~ cn3 ),
inference(spm,[status(thm)],[c_0_115,c_0_33]) ).
cnf(c_0_122,plain,
( is_a_theorem(or(X1,and(X2,X2)))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_88,c_0_54]) ).
cnf(c_0_123,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,or(X1,X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117])]) ).
cnf(c_0_124,plain,
( is_a_theorem(or(implies(X1,X2),X3))
| ~ or_1
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_60,c_0_118]) ).
cnf(c_0_125,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_126,plain,
is_a_theorem(or(or(X1,X2),not(X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_117])]) ).
fof(c_0_127,plain,
! [X102,X103] :
( ( ~ and_2
| is_a_theorem(implies(and(X102,X103),X103)) )
& ( ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0))
| and_2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_2])])])]) ).
cnf(c_0_128,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(not(and(X3,X3)))
| ~ is_a_theorem(or(X3,X2)) ),
inference(spm,[status(thm)],[c_0_72,c_0_122]) ).
cnf(c_0_129,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),not(and(not(X3),X1))))),
inference(spm,[status(thm)],[c_0_36,c_0_39]) ).
cnf(c_0_130,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(and(X1,X2),and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_77,c_0_55]) ).
cnf(c_0_131,plain,
is_a_theorem(implies(or(X1,X2),or(and(X2,X3),implies(X3,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_28]),c_0_33]) ).
cnf(c_0_132,plain,
( is_a_theorem(or(X1,implies(X2,X3)))
| ~ or_1
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_133,plain,
( or_1
| ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0))) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_134,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_135,plain,
( is_a_theorem(implies(and(X1,X2),X2))
| ~ and_2 ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_136,plain,
( is_a_theorem(or(X1,not(not(X2))))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_58,c_0_52]) ).
cnf(c_0_137,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(implies(implies(X3,X3),X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_106]),c_0_39]) ).
cnf(c_0_138,plain,
is_a_theorem(implies(implies(X1,X2),not(and(not(X2),X1)))),
inference(spm,[status(thm)],[c_0_99,c_0_129]) ).
cnf(c_0_139,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,and(X1,X1))) ),
inference(spm,[status(thm)],[c_0_130,c_0_122]) ).
cnf(c_0_140,plain,
( is_a_theorem(or(or(and(X1,X2),implies(X2,X3)),X4))
| ~ is_a_theorem(or(X4,or(X3,X1))) ),
inference(spm,[status(thm)],[c_0_47,c_0_131]) ).
cnf(c_0_141,plain,
( is_a_theorem(or(X1,or(X2,X3)))
| ~ or_1
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_132,c_0_33]) ).
cnf(c_0_142,plain,
or_1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_134])]) ).
cnf(c_0_143,plain,
( is_a_theorem(or(X1,X2))
| ~ and_2
| ~ is_a_theorem(or(X2,and(X3,X1))) ),
inference(spm,[status(thm)],[c_0_47,c_0_135]) ).
cnf(c_0_144,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(not(X2),not(X2)))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_77,c_0_136]) ).
cnf(c_0_145,plain,
is_a_theorem(or(X1,not(and(not(X2),X2)))),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_146,plain,
( is_a_theorem(or(and(X1,X2),implies(X2,X3)))
| ~ is_a_theorem(or(and(or(and(X1,X2),implies(X2,X3)),or(and(X1,X2),implies(X2,X3))),or(X3,X1))) ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_147,plain,
( is_a_theorem(or(X1,or(X2,X3)))
| ~ is_a_theorem(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_142])]) ).
cnf(c_0_148,plain,
( is_a_theorem(or(X1,not(and(X2,X1))))
| ~ and_2 ),
inference(spm,[status(thm)],[c_0_143,c_0_52]) ).
cnf(c_0_149,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(and(not(X2),X2),X1)) ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_150,plain,
( is_a_theorem(or(and(X1,X2),implies(X2,X3)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_151,plain,
( is_a_theorem(or(not(and(X1,X2)),X2))
| ~ and_2 ),
inference(spm,[status(thm)],[c_0_107,c_0_148]) ).
cnf(c_0_152,plain,
implies(X1,and(not(X2),not(X3))) = not(and(X1,or(X2,X3))),
inference(spm,[status(thm)],[c_0_91,c_0_33]) ).
cnf(c_0_153,plain,
is_a_theorem(or(not(and(X1,X2)),X2)),
inference(spm,[status(thm)],[c_0_60,c_0_108]) ).
fof(c_0_154,plain,
! [X76,X77] :
( ( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X76,X77))
| X76 = X77 )
& ( is_a_theorem(equiv(esk3_0,esk4_0))
| substitution_of_equivalents )
& ( esk3_0 != esk4_0
| substitution_of_equivalents ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_of_equivalents])])])])]) ).
cnf(c_0_155,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(or(not(X2),X2),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_39]),c_0_33]) ).
cnf(c_0_156,plain,
( is_a_theorem(implies(X1,and(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_150]) ).
cnf(c_0_157,plain,
( is_a_theorem(or(X1,not(and(X2,or(X1,X1)))))
| ~ and_2 ),
inference(spm,[status(thm)],[c_0_123,c_0_151]) ).
cnf(c_0_158,plain,
not(and(not(X1),or(X2,X3))) = or(X1,and(not(X2),not(X3))),
inference(spm,[status(thm)],[c_0_33,c_0_152]) ).
cnf(c_0_159,plain,
is_a_theorem(or(X1,not(and(X2,X1)))),
inference(spm,[status(thm)],[c_0_107,c_0_153]) ).
cnf(c_0_160,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_154]) ).
cnf(c_0_161,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(c_0_162,plain,
( is_a_theorem(and(X1,or(not(X2),X2)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_163,plain,
and(implies(X1,not(X2)),or(X2,X1)) = equiv(X1,not(X2)),
inference(spm,[status(thm)],[c_0_68,c_0_33]) ).
cnf(c_0_164,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_125,c_0_52]) ).
cnf(c_0_165,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,or(X3,X3)))
| ~ is_a_theorem(or(X1,not(X3))) ),
inference(spm,[status(thm)],[c_0_47,c_0_103]) ).
cnf(c_0_166,plain,
( is_a_theorem(or(X1,or(X2,and(not(X1),not(X1)))))
| ~ and_2 ),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_167,plain,
( and_2
| ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0)) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_168,plain,
is_a_theorem(implies(and(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_125,c_0_159]) ).
cnf(c_0_169,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_160,c_0_161])]) ).
cnf(c_0_170,plain,
is_a_theorem(equiv(X1,not(not(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_164])]) ).
cnf(c_0_171,plain,
( is_a_theorem(or(X1,X2))
| ~ and_2
| ~ is_a_theorem(or(X1,or(X2,X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_28]),c_0_33]) ).
cnf(c_0_172,plain,
and_2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_167,c_0_168])]) ).
cnf(c_0_173,plain,
not(not(X1)) = X1,
inference(spm,[status(thm)],[c_0_169,c_0_170]) ).
fof(c_0_174,plain,
! [X88,X89] :
( ( ~ implies_2
| is_a_theorem(implies(implies(X88,implies(X88,X89)),implies(X88,X89))) )
& ( ~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0)))
| implies_2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])]) ).
fof(c_0_175,negated_conjecture,
~ implies_2,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_implies_2])]) ).
cnf(c_0_176,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X1,or(X2,X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_171,c_0_172])]) ).
cnf(c_0_177,plain,
or(not(X1),X2) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_33,c_0_173]) ).
cnf(c_0_178,plain,
( implies_2
| ~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0))) ),
inference(split_conjunct,[status(thm)],[c_0_174]) ).
cnf(c_0_179,negated_conjecture,
~ implies_2,
inference(split_conjunct,[status(thm)],[c_0_175]) ).
cnf(c_0_180,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,or(X2,X2))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_177]) ).
cnf(c_0_181,plain,
~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0))),
inference(sr,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_182,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_180,c_0_42]) ).
cnf(c_0_183,plain,
is_a_theorem(or(implies(X1,X2),X1)),
inference(spm,[status(thm)],[c_0_105,c_0_70]) ).
cnf(c_0_184,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_183])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL504+1 : TPTP v9.2.1. Bugfixed v9.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.31 % Computer : n002.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Mon May 4 22:40:16 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 39.38/22.94 % Version : CSE_E---1.7
% 39.38/22.94 % Problem : theBenchmark.p
% 39.38/22.94 % SZS status Theorem for theBenchmark.p
% 39.38/22.94 % SZS output start CNFRefutation
% See solution above
% 39.50/23.09 % Total time : 17.401s
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