%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL508+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 : n007.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 04:40:31 PM UTC 2026
% Result : Theorem 56.74s 32.94s
% Output : CNFRefutation 56.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 22
% Syntax : Number of formulae : 274 ( 107 unt; 0 def)
% Number of atoms : 519 ( 41 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 461 ( 216 ~; 216 |; 14 &)
% ( 10 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 19 con; 0-2 aty)
% Number of variables : 511 ( 79 sgn 50 !; 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(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(r3,axiom,
( r3
<=> ! [X4,X5] : is_a_theorem(implies(or(X4,X5),or(X5,X4))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r3) ).
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(and_3,axiom,
( and_3
<=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,and(X1,X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_3) ).
fof(hilbert_and_3,conjecture,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(c_0_22,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_23,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_24,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[rosser_op_implies_and]) ).
fof(c_0_26,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_27,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_28,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_30,plain,
op_or,
inference(split_conjunct,[status(thm)],[rosser_op_or]) ).
cnf(c_0_31,plain,
( is_a_theorem(X2)
| ~ modus_ponens
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[rosser_modus_ponens]) ).
cnf(c_0_33,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_27]) ).
cnf(c_0_34,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_35,plain,
kn3,
inference(split_conjunct,[status(thm)],[rosser_kn3]) ).
cnf(c_0_36,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_31,c_0_32])]) ).
cnf(c_0_37,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_33,c_0_34]),c_0_35])]) ).
cnf(c_0_38,plain,
( is_a_theorem(or(and(X1,X2),not(and(X2,X3))))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,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_38,c_0_29]),c_0_34]) ).
cnf(c_0_40,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_34,c_0_29]) ).
fof(c_0_41,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_42,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_43,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_39,c_0_34]),c_0_40]) ).
cnf(c_0_44,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ kn2 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_45,plain,
kn2,
inference(split_conjunct,[status(thm)],[rosser_kn2]) ).
cnf(c_0_46,plain,
( is_a_theorem(implies(X1,and(X1,X1)))
| ~ kn1 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_47,plain,
kn1,
inference(split_conjunct,[status(thm)],[rosser_kn1]) ).
cnf(c_0_48,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_36,c_0_43]) ).
cnf(c_0_49,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).
cnf(c_0_50,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
cnf(c_0_51,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,and(X1,X3))) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,plain,
is_a_theorem(or(X1,and(not(X1),not(X1)))),
inference(spm,[status(thm)],[c_0_50,c_0_34]) ).
cnf(c_0_53,plain,
is_a_theorem(or(not(X1),X1)),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
fof(c_0_54,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_55,plain,
is_a_theorem(or(X1,not(and(X1,X2)))),
inference(spm,[status(thm)],[c_0_51,c_0_53]) ).
cnf(c_0_56,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_57,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[rosser_op_equiv]) ).
cnf(c_0_58,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X2,X1))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_59,plain,
is_a_theorem(or(X1,implies(X1,X2))),
inference(spm,[status(thm)],[c_0_55,c_0_29]) ).
cnf(c_0_60,plain,
( is_a_theorem(or(and(X1,X1),X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_48,c_0_50]) ).
cnf(c_0_61,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).
cnf(c_0_62,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_63,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(and(X2,X2)))
| ~ is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_58,c_0_60]) ).
cnf(c_0_64,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_58,c_0_55]) ).
cnf(c_0_65,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_48,c_0_34]) ).
cnf(c_0_66,plain,
( is_a_theorem(or(X1,and(X2,X2)))
| ~ is_a_theorem(or(and(X1,X3),X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_60]) ).
cnf(c_0_67,plain,
is_a_theorem(implies(implies(X1,X1),equiv(X1,X1))),
inference(spm,[status(thm)],[c_0_50,c_0_61]) ).
cnf(c_0_68,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X3))
| ~ is_a_theorem(not(X3)) ),
inference(spm,[status(thm)],[c_0_48,c_0_62]) ).
cnf(c_0_69,plain,
is_a_theorem(or(implies(X1,X2),and(X1,not(X2)))),
inference(spm,[status(thm)],[c_0_53,c_0_29]) ).
cnf(c_0_70,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(and(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_65,c_0_55]) ).
cnf(c_0_72,plain,
( is_a_theorem(or(X1,and(X2,X2)))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_66,c_0_60]) ).
cnf(c_0_73,plain,
( is_a_theorem(or(equiv(X1,X1),X2))
| ~ is_a_theorem(or(X2,implies(X1,X1))) ),
inference(spm,[status(thm)],[c_0_48,c_0_67]) ).
cnf(c_0_74,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_68,c_0_69]),c_0_29]) ).
cnf(c_0_75,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_70,c_0_52]),c_0_29]),c_0_34]) ).
cnf(c_0_76,plain,
( is_a_theorem(or(implies(X1,X2),X3))
| ~ is_a_theorem(or(X2,X3)) ),
inference(spm,[status(thm)],[c_0_71,c_0_39]) ).
cnf(c_0_77,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(and(X2,X2)))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_70,c_0_72]) ).
cnf(c_0_78,plain,
( is_a_theorem(or(equiv(X1,X1),X2))
| ~ is_a_theorem(implies(X1,X1)) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_79,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(not(X2),X1))
| ~ is_a_theorem(or(X2,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_29]),c_0_34]) ).
cnf(c_0_81,plain,
( is_a_theorem(or(X1,equiv(X2,X2)))
| ~ is_a_theorem(implies(X2,X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_78]) ).
cnf(c_0_82,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_79,c_0_59]) ).
cnf(c_0_83,plain,
( is_a_theorem(not(and(not(X1),X2)))
| ~ is_a_theorem(or(X1,X1)) ),
inference(spm,[status(thm)],[c_0_80,c_0_55]) ).
cnf(c_0_84,plain,
is_a_theorem(or(X1,equiv(X2,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82])]) ).
cnf(c_0_85,plain,
is_a_theorem(not(and(not(equiv(X1,X1)),X2))),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_86,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,not(equiv(X2,X2)))) ),
inference(spm,[status(thm)],[c_0_63,c_0_85]) ).
cnf(c_0_87,plain,
is_a_theorem(or(not(and(and(X1,X2),X3)),X1)),
inference(spm,[status(thm)],[c_0_71,c_0_55]) ).
cnf(c_0_88,plain,
( is_a_theorem(or(or(X1,X2),X3))
| ~ is_a_theorem(or(X3,implies(X4,X1)))
| ~ is_a_theorem(or(X2,X4)) ),
inference(spm,[status(thm)],[c_0_48,c_0_43]) ).
fof(c_0_89,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_90,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_91,plain,
is_a_theorem(not(and(and(not(equiv(X1,X1)),X2),X3))),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_92,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_38,c_0_61]) ).
cnf(c_0_93,plain,
( is_a_theorem(or(or(X1,X2),X3))
| ~ is_a_theorem(or(X2,X3)) ),
inference(spm,[status(thm)],[c_0_88,c_0_59]) ).
cnf(c_0_94,plain,
( is_a_theorem(implies(implies(not(X1),X1),X1))
| ~ cn3 ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_95,plain,
not(and(X1,implies(X2,X3))) = implies(X1,and(X2,not(X3))),
inference(spm,[status(thm)],[c_0_29,c_0_29]) ).
cnf(c_0_96,plain,
( is_a_theorem(implies(X1,or(X1,X2)))
| ~ or_1 ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_97,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,and(not(equiv(X2,X2)),X3))) ),
inference(spm,[status(thm)],[c_0_63,c_0_91]) ).
cnf(c_0_98,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_66,c_0_92]) ).
cnf(c_0_99,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,or(X1,X2))) ),
inference(spm,[status(thm)],[c_0_75,c_0_93]) ).
cnf(c_0_100,plain,
is_a_theorem(or(not(X1),or(X1,X2))),
inference(spm,[status(thm)],[c_0_59,c_0_34]) ).
cnf(c_0_101,plain,
( is_a_theorem(implies(or(X1,X1),X1))
| ~ cn3 ),
inference(rw,[status(thm)],[c_0_94,c_0_34]) ).
cnf(c_0_102,plain,
implies(implies(X1,and(X2,not(X3))),X4) = or(and(X1,implies(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_34,c_0_95]) ).
cnf(c_0_103,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0)) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_104,plain,
( is_a_theorem(or(X1,X2))
| ~ or_1
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_96]) ).
cnf(c_0_105,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,X2),X1)) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_106,plain,
is_a_theorem(implies(implies(X1,X2),not(and(and(X1,not(X2)),X3)))),
inference(spm,[status(thm)],[c_0_55,c_0_40]) ).
cnf(c_0_107,plain,
is_a_theorem(or(X1,not(X1))),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_108,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_101,c_0_40]),c_0_102]) ).
cnf(c_0_109,plain,
( cn3
| ~ is_a_theorem(implies(or(esk44_0,esk44_0),esk44_0)) ),
inference(rw,[status(thm)],[c_0_103,c_0_34]) ).
cnf(c_0_110,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_60,c_0_40]),c_0_34]) ).
cnf(c_0_111,plain,
( is_a_theorem(not(and(not(X1),X2)))
| ~ or_1
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_83,c_0_104]) ).
cnf(c_0_112,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(implies(implies(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_71,c_0_40]) ).
cnf(c_0_113,plain,
is_a_theorem(not(and(and(X1,not(X1)),X2))),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_114,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_65,c_0_107]) ).
cnf(c_0_115,plain,
is_a_theorem(or(and(X1,X2),not(and(X2,X1)))),
inference(spm,[status(thm)],[c_0_105,c_0_37]) ).
cnf(c_0_116,plain,
( is_a_theorem(or(X1,and(implies(X1,X2),implies(X1,X2))))
| ~ cn3 ),
inference(spm,[status(thm)],[c_0_51,c_0_108]) ).
cnf(c_0_117,plain,
( cn3
| ~ is_a_theorem(or(esk44_0,not(esk44_0))) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_118,plain,
( is_a_theorem(X1)
| ~ or_1
| ~ is_a_theorem(or(X1,not(X2)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_111]) ).
cnf(c_0_119,plain,
is_a_theorem(or(or(and(X1,X2),not(and(X2,X3))),X3)),
inference(spm,[status(thm)],[c_0_112,c_0_37]) ).
cnf(c_0_120,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,and(X2,not(X2)))) ),
inference(spm,[status(thm)],[c_0_63,c_0_113]) ).
cnf(c_0_121,plain,
is_a_theorem(or(not(and(X1,X2)),and(X2,X1))),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_122,plain,
( is_a_theorem(or(implies(X1,X2),X1))
| ~ cn3 ),
inference(spm,[status(thm)],[c_0_51,c_0_116]) ).
cnf(c_0_123,plain,
( is_a_theorem(or(X1,X2))
| ~ cn3
| ~ is_a_theorem(or(X2,or(X1,X1))) ),
inference(spm,[status(thm)],[c_0_48,c_0_101]) ).
cnf(c_0_124,plain,
cn3,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_107])]) ).
cnf(c_0_125,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_118,c_0_119]),c_0_29]) ).
cnf(c_0_126,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_58,c_0_39]) ).
cnf(c_0_127,plain,
is_a_theorem(not(and(not(X1),X1))),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_128,plain,
( is_a_theorem(or(or(X1,X2),not(X1)))
| ~ cn3 ),
inference(spm,[status(thm)],[c_0_122,c_0_34]) ).
cnf(c_0_129,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_68,c_0_72]) ).
cnf(c_0_130,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),not(and(not(X3),X1))))),
inference(spm,[status(thm)],[c_0_37,c_0_40]) ).
cnf(c_0_131,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_63,c_0_29]),c_0_34]) ).
cnf(c_0_132,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_123,c_0_124])]) ).
cnf(c_0_133,plain,
( is_a_theorem(or(implies(X1,X2),X3))
| ~ or_1
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_125]) ).
cnf(c_0_134,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_135,plain,
is_a_theorem(or(or(X1,X2),not(X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_124])]) ).
fof(c_0_136,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])])])]) ).
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_129,c_0_113]),c_0_40]) ).
cnf(c_0_138,plain,
is_a_theorem(implies(implies(X1,X2),not(and(not(X2),X1)))),
inference(spm,[status(thm)],[c_0_105,c_0_130]) ).
cnf(c_0_139,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(and(X1,X2),and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_131,c_0_55]) ).
cnf(c_0_140,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_37,c_0_29]),c_0_34]) ).
cnf(c_0_141,plain,
( is_a_theorem(or(X1,implies(X2,X3)))
| ~ or_1
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_142,plain,
( or_1
| ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0))) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_143,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_144,plain,
( is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))
| ~ implies_2 ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
fof(c_0_145,plain,
! [X166,X167] :
( ( ~ r3
| is_a_theorem(implies(or(X166,X167),or(X167,X166))) )
& ( ~ is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0)))
| r3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r3])])])]) ).
cnf(c_0_146,plain,
( is_a_theorem(or(X1,not(not(X2))))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_65,c_0_53]) ).
cnf(c_0_147,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(or(X1,X1)) ),
inference(spm,[status(thm)],[c_0_131,c_0_53]) ).
cnf(c_0_148,plain,
is_a_theorem(or(X1,not(and(not(X2),X2)))),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_149,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,and(X1,X1))) ),
inference(spm,[status(thm)],[c_0_139,c_0_72]) ).
cnf(c_0_150,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_48,c_0_140]) ).
cnf(c_0_151,plain,
( is_a_theorem(or(X1,or(X2,X3)))
| ~ or_1
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_141,c_0_34]) ).
cnf(c_0_152,plain,
or_1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_142,c_0_143])]) ).
cnf(c_0_153,plain,
( is_a_theorem(implies(X1,X2))
| ~ implies_2
| ~ is_a_theorem(implies(X1,implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_36,c_0_144]) ).
cnf(c_0_154,plain,
( r3
| ~ is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0))) ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_155,plain,
( is_a_theorem(implies(or(X1,X2),or(X2,X3)))
| ~ is_a_theorem(or(X3,not(X1))) ),
inference(spm,[status(thm)],[c_0_43,c_0_34]) ).
cnf(c_0_156,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(not(not(X2))))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_70,c_0_146]) ).
cnf(c_0_157,plain,
is_a_theorem(not(not(not(and(not(X1),X1))))),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_158,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_149,c_0_150]) ).
cnf(c_0_159,plain,
( is_a_theorem(or(X1,or(X2,X3)))
| ~ is_a_theorem(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_152])]) ).
cnf(c_0_160,plain,
( is_a_theorem(X1)
| ~ or_1
| ~ is_a_theorem(or(not(X2),X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_111]) ).
cnf(c_0_161,plain,
( is_a_theorem(or(not(and(X1,X2)),X3))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_71,c_0_38]) ).
cnf(c_0_162,plain,
( is_a_theorem(and(X1,X1))
| ~ is_a_theorem(or(X1,and(X1,X1))) ),
inference(spm,[status(thm)],[c_0_75,c_0_72]) ).
cnf(c_0_163,plain,
( is_a_theorem(implies(implies(X1,X1),not(and(not(X1),X1))))
| ~ implies_2 ),
inference(spm,[status(thm)],[c_0_153,c_0_130]) ).
cnf(c_0_164,plain,
( r3
| ~ is_a_theorem(or(esk48_0,not(esk48_0))) ),
inference(spm,[status(thm)],[c_0_154,c_0_155]) ).
cnf(c_0_165,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(and(not(X2),X2),X1)) ),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_166,plain,
( is_a_theorem(or(and(X1,X2),implies(X2,X3)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_167,plain,
( is_a_theorem(X1)
| ~ or_1
| ~ is_a_theorem(and(X2,X3))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_168,plain,
( is_a_theorem(and(implies(X1,X2),implies(X1,X2)))
| ~ or_1
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_162,c_0_133]) ).
cnf(c_0_169,plain,
( is_a_theorem(not(and(not(X1),X1)))
| ~ implies_2
| ~ is_a_theorem(implies(X1,X1)) ),
inference(spm,[status(thm)],[c_0_36,c_0_163]) ).
cnf(c_0_170,plain,
( is_a_theorem(implies(or(X1,X2),or(X2,X1)))
| ~ r3 ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_171,plain,
r3,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_164,c_0_107])]) ).
fof(c_0_172,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_173,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(or(not(X2),X2),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_40]),c_0_34]) ).
cnf(c_0_174,plain,
( is_a_theorem(implies(X1,and(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_79,c_0_166]) ).
cnf(c_0_175,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(and(X2,X3))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_167,c_0_152])]) ).
cnf(c_0_176,plain,
( is_a_theorem(and(implies(X1,X2),implies(X1,X2)))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_168,c_0_152])]) ).
cnf(c_0_177,plain,
( is_a_theorem(not(and(not(X1),X1)))
| ~ implies_2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_169,c_0_82])]) ).
cnf(c_0_178,plain,
( is_a_theorem(or(X1,not(X2)))
| ~ is_a_theorem(implies(or(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_112,c_0_34]) ).
cnf(c_0_179,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_171])]) ).
cnf(c_0_180,plain,
is_a_theorem(or(not(and(X1,X2)),X2)),
inference(spm,[status(thm)],[c_0_71,c_0_115]) ).
cnf(c_0_181,plain,
implies(X1,and(not(X2),not(X3))) = not(and(X1,or(X2,X3))),
inference(spm,[status(thm)],[c_0_95,c_0_34]) ).
cnf(c_0_182,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
cnf(c_0_183,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(c_0_184,plain,
( is_a_theorem(and(X1,or(not(X2),X2)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_185,plain,
and(implies(X1,not(X2)),or(X2,X1)) = equiv(X1,not(X2)),
inference(spm,[status(thm)],[c_0_61,c_0_34]) ).
cnf(c_0_186,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_134,c_0_53]) ).
cnf(c_0_187,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,X3),X1))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_175,c_0_176]) ).
cnf(c_0_188,plain,
is_a_theorem(implies(equiv(X1,X2),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_49,c_0_61]) ).
cnf(c_0_189,plain,
( is_a_theorem(or(X1,not(or(X1,X1))))
| ~ cn3 ),
inference(spm,[status(thm)],[c_0_123,c_0_53]) ).
cnf(c_0_190,plain,
is_a_theorem(or(and(X1,X2),implies(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_173,c_0_140]) ).
cnf(c_0_191,plain,
( is_a_theorem(implies(X1,X2))
| ~ implies_2
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_126,c_0_177]) ).
cnf(c_0_192,plain,
is_a_theorem(or(or(X1,X2),not(X2))),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_193,plain,
is_a_theorem(or(X1,not(and(X2,or(X1,X1))))),
inference(spm,[status(thm)],[c_0_132,c_0_180]) ).
cnf(c_0_194,plain,
not(and(not(X1),or(X2,X3))) = or(X1,and(not(X2),not(X3))),
inference(spm,[status(thm)],[c_0_34,c_0_181]) ).
cnf(c_0_195,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_182,c_0_183])]) ).
cnf(c_0_196,plain,
is_a_theorem(equiv(X1,not(not(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_186])]) ).
cnf(c_0_197,plain,
( is_a_theorem(and(X1,implies(X2,X3)))
| ~ is_a_theorem(X3)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_187,c_0_174]) ).
cnf(c_0_198,plain,
( is_a_theorem(or(implies(X1,X2),X3))
| ~ is_a_theorem(or(X3,equiv(X1,X2))) ),
inference(spm,[status(thm)],[c_0_48,c_0_188]) ).
cnf(c_0_199,plain,
and(or(X1,X2),implies(X2,not(X1))) = equiv(not(X1),X2),
inference(spm,[status(thm)],[c_0_61,c_0_34]) ).
cnf(c_0_200,plain,
is_a_theorem(or(X1,not(or(X1,X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_189,c_0_124])]) ).
cnf(c_0_201,plain,
is_a_theorem(or(implies(X1,not(X2)),and(X2,X1))),
inference(spm,[status(thm)],[c_0_114,c_0_190]) ).
cnf(c_0_202,plain,
( is_a_theorem(implies(X1,or(X2,X1)))
| ~ implies_2 ),
inference(spm,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_203,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_48,c_0_110]) ).
cnf(c_0_204,plain,
is_a_theorem(or(X1,or(X2,and(not(X1),not(X1))))),
inference(spm,[status(thm)],[c_0_193,c_0_194]) ).
cnf(c_0_205,plain,
not(not(X1)) = X1,
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_206,plain,
( is_a_theorem(equiv(X1,X2))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_197,c_0_61]) ).
cnf(c_0_207,plain,
is_a_theorem(or(implies(X1,X1),X2)),
inference(spm,[status(thm)],[c_0_198,c_0_84]) ).
cnf(c_0_208,plain,
implies(or(X1,X2),and(X2,not(not(X1)))) = not(equiv(not(X1),X2)),
inference(spm,[status(thm)],[c_0_95,c_0_199]) ).
cnf(c_0_209,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(or(X2,X2),X1)) ),
inference(spm,[status(thm)],[c_0_65,c_0_200]) ).
cnf(c_0_210,plain,
is_a_theorem(or(or(X1,not(X2)),and(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_201,c_0_34]) ).
cnf(c_0_211,plain,
( is_a_theorem(or(X1,X2))
| ~ implies_2
| ~ is_a_theorem(or(X1,or(X1,X2))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_34]),c_0_34]) ).
cnf(c_0_212,plain,
( is_a_theorem(or(or(X1,X2),X3))
| ~ or_1
| ~ is_a_theorem(or(X3,X1)) ),
inference(spm,[status(thm)],[c_0_48,c_0_96]) ).
cnf(c_0_213,plain,
( is_a_theorem(or(X1,or(X2,not(X1))))
| ~ implies_2 ),
inference(spm,[status(thm)],[c_0_202,c_0_34]) ).
cnf(c_0_214,plain,
( is_a_theorem(implies(X1,or(X1,X2)))
| ~ implies_2 ),
inference(spm,[status(thm)],[c_0_191,c_0_135]) ).
cnf(c_0_215,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X1,or(X2,X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_204]),c_0_29]),c_0_34]) ).
cnf(c_0_216,plain,
or(not(X1),X2) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_205]) ).
cnf(c_0_217,plain,
( is_a_theorem(and(X1,X2))
| ~ or_1
| ~ is_a_theorem(and(X2,X1)) ),
inference(spm,[status(thm)],[c_0_118,c_0_115]) ).
cnf(c_0_218,plain,
( X1 = X2
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_195,c_0_206]) ).
cnf(c_0_219,plain,
is_a_theorem(implies(X1,implies(X2,X2))),
inference(spm,[status(thm)],[c_0_79,c_0_207]) ).
cnf(c_0_220,plain,
( is_a_theorem(not(equiv(not(X1),X1)))
| ~ is_a_theorem(implies(implies(X1,not(X1)),not(X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_208]),c_0_40]) ).
cnf(c_0_221,plain,
is_a_theorem(implies(implies(X1,not(X1)),not(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_210]),c_0_40]) ).
cnf(c_0_222,plain,
( is_a_theorem(or(or(X1,X2),X3))
| ~ or_1
| ~ implies_2
| ~ is_a_theorem(or(or(or(X1,X2),X3),X1)) ),
inference(spm,[status(thm)],[c_0_211,c_0_212]) ).
cnf(c_0_223,plain,
( is_a_theorem(or(or(X1,not(and(X2,X3))),X2))
| ~ implies_2 ),
inference(spm,[status(thm)],[c_0_71,c_0_213]) ).
cnf(c_0_224,plain,
( or_1
| ~ implies_2 ),
inference(spm,[status(thm)],[c_0_142,c_0_214]) ).
cnf(c_0_225,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_215,c_0_216]),c_0_216]) ).
cnf(c_0_226,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(and(X2,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_217,c_0_152])]) ).
cnf(c_0_227,plain,
( is_a_theorem(and(X1,implies(X2,X2)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_105,c_0_174]) ).
cnf(c_0_228,plain,
( X1 = implies(X2,X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_218,c_0_219]) ).
cnf(c_0_229,plain,
is_a_theorem(not(equiv(not(X1),X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_220,c_0_221])]) ).
cnf(c_0_230,plain,
( is_a_theorem(or(or(X1,X2),not(and(X1,X3))))
| ~ implies_2 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_223]),c_0_224]) ).
cnf(c_0_231,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_136]) ).
cnf(c_0_232,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_225,c_0_43]) ).
cnf(c_0_233,plain,
is_a_theorem(or(implies(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_124])]) ).
cnf(c_0_234,plain,
is_a_theorem(or(X1,not(and(X2,X1)))),
inference(spm,[status(thm)],[c_0_114,c_0_180]) ).
cnf(c_0_235,plain,
not(and(X1,X2)) = implies(X1,not(X2)),
inference(spm,[status(thm)],[c_0_29,c_0_205]) ).
cnf(c_0_236,plain,
( is_a_theorem(and(implies(X1,X1),X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_226,c_0_227]) ).
cnf(c_0_237,plain,
not(equiv(not(X1),X1)) = implies(X2,X2),
inference(spm,[status(thm)],[c_0_228,c_0_229]) ).
cnf(c_0_238,plain,
implies(implies(X1,X2),and(X2,not(X1))) = not(equiv(X1,X2)),
inference(spm,[status(thm)],[c_0_95,c_0_61]) ).
cnf(c_0_239,plain,
( is_a_theorem(implies(and(X1,X2),or(X1,X3)))
| ~ implies_2 ),
inference(spm,[status(thm)],[c_0_191,c_0_230]) ).
cnf(c_0_240,plain,
implies_2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_232]),c_0_233])]) ).
cnf(c_0_241,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_124])]) ).
cnf(c_0_242,plain,
is_a_theorem(implies(and(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_134,c_0_234]) ).
cnf(c_0_243,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(spm,[status(thm)],[c_0_205,c_0_235]) ).
cnf(c_0_244,plain,
( is_a_theorem(and(not(equiv(not(X1),X1)),X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_236,c_0_237]) ).
cnf(c_0_245,plain,
and(not(equiv(X1,X2)),implies(and(X2,not(X1)),implies(X1,X2))) = equiv(implies(X1,X2),and(X2,not(X1))),
inference(spm,[status(thm)],[c_0_61,c_0_238]) ).
cnf(c_0_246,plain,
is_a_theorem(implies(and(X1,X2),or(X1,X3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_239,c_0_240])]) ).
cnf(c_0_247,plain,
implies(or(X1,X1),X1) = implies(X2,X2),
inference(spm,[status(thm)],[c_0_228,c_0_241]) ).
cnf(c_0_248,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,and(X3,X1))) ),
inference(spm,[status(thm)],[c_0_48,c_0_242]) ).
cnf(c_0_249,plain,
( is_a_theorem(or(X1,and(X2,not(X3))))
| ~ is_a_theorem(implies(implies(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_114,c_0_40]) ).
cnf(c_0_250,plain,
not(implies(X1,X2)) = and(X1,not(X2)),
inference(spm,[status(thm)],[c_0_243,c_0_205]) ).
cnf(c_0_251,plain,
is_a_theorem(equiv(or(X1,X1),and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_245]),c_0_34]),c_0_205]),c_0_205]),c_0_34]),c_0_246])]) ).
cnf(c_0_252,plain,
( is_a_theorem(and(implies(or(X1,X1),X1),X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_236,c_0_247]) ).
cnf(c_0_253,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X3,X1),X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_249]),c_0_216]) ).
cnf(c_0_254,plain,
and(not(X1),not(X2)) = not(or(X1,X2)),
inference(spm,[status(thm)],[c_0_250,c_0_34]) ).
cnf(c_0_255,plain,
and(X1,X1) = or(X1,X1),
inference(spm,[status(thm)],[c_0_195,c_0_251]) ).
cnf(c_0_256,plain,
is_a_theorem(equiv(or(X1,X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_61]),c_0_143])]) ).
cnf(c_0_257,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(or(X3,X1),X2)) ),
inference(spm,[status(thm)],[c_0_253,c_0_34]) ).
cnf(c_0_258,plain,
not(or(X1,X1)) = implies(X1,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_255]),c_0_216]) ).
cnf(c_0_259,plain,
or(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_195,c_0_256]) ).
cnf(c_0_260,plain,
is_a_theorem(implies(X1,or(and(X1,X2),implies(X2,X3)))),
inference(spm,[status(thm)],[c_0_257,c_0_140]) ).
cnf(c_0_261,plain,
implies(X1,not(X1)) = not(X1),
inference(rw,[status(thm)],[c_0_258,c_0_259]) ).
cnf(c_0_262,plain,
( is_a_theorem(or(or(X1,X2),X3))
| ~ r3
| ~ is_a_theorem(or(X3,or(X2,X1))) ),
inference(spm,[status(thm)],[c_0_48,c_0_170]) ).
cnf(c_0_263,plain,
is_a_theorem(implies(X1,or(and(X1,X2),not(X2)))),
inference(spm,[status(thm)],[c_0_260,c_0_261]) ).
fof(c_0_264,plain,
! [X106,X107] :
( ( ~ and_3
| is_a_theorem(implies(X106,implies(X107,and(X106,X107)))) )
& ( ~ is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0))))
| and_3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_3])])])]) ).
fof(c_0_265,negated_conjecture,
~ and_3,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_and_3])]) ).
cnf(c_0_266,plain,
( is_a_theorem(or(or(X1,X2),X3))
| ~ is_a_theorem(or(X3,or(X2,X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_262,c_0_171])]) ).
cnf(c_0_267,plain,
is_a_theorem(or(X1,or(and(not(X1),X2),not(X2)))),
inference(spm,[status(thm)],[c_0_263,c_0_34]) ).
cnf(c_0_268,plain,
( and_3
| ~ is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_264]) ).
cnf(c_0_269,negated_conjecture,
~ and_3,
inference(split_conjunct,[status(thm)],[c_0_265]) ).
cnf(c_0_270,plain,
is_a_theorem(or(implies(X1,and(not(X2),X1)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_266,c_0_267]),c_0_216]) ).
cnf(c_0_271,plain,
~ is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0)))),
inference(sr,[status(thm)],[c_0_268,c_0_269]) ).
cnf(c_0_272,plain,
is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_270]),c_0_205]) ).
cnf(c_0_273,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_271,c_0_272])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LCL508+1 : TPTP v9.2.1. Bugfixed v9.2.0.
% 0.12/0.13 % 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
% 0.16/0.34 % Computer : n007.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 22:39:09 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.21/0.35 % start to proof: theBenchmark
% 56.74/32.94 % Version : CSE_E---1.7
% 56.74/32.94 % Problem : theBenchmark.p
% 56.74/32.94 % SZS status Theorem for theBenchmark.p
% 56.74/32.94 % SZS output start CNFRefutation
% See solution above
% 56.97/33.15 % Total time : 25.414s
%------------------------------------------------------------------------------