%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL457+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:12:49 PM UTC 2026
% Result : Theorem 21.88s 16.00s
% Output : CNFRefutation 21.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 40
% Syntax : Number of formulae : 205 ( 98 unt; 0 def)
% Number of atoms : 369 ( 54 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 290 ( 126 ~; 123 |; 19 &)
% ( 15 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 23 ( 21 usr; 21 prp; 0-2 aty)
% Number of functors : 38 ( 38 usr; 33 con; 0-2 aty)
% Number of variables : 342 ( 40 sgn 86 !; 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(modus_ponens,axiom,
( modus_ponens
<=> ! [X1,X2] :
( ( is_a_theorem(implies(X1,X2))
& is_a_theorem(X1) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
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(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
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(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_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(hilbert_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_or) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X1,X2] : implies(X1,X2) = or(not(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
fof(hilbert_and_3,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
fof(hilbert_implies_2,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(implies_1,axiom,
( implies_1
<=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_1) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
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(hilbert_implies_1,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
fof(and_1,axiom,
( and_1
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_1) ).
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(hilbert_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_equiv) ).
fof(hilbert_and_1,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',use_substitution_of_equivalents) ).
fof(modus_tollens,axiom,
( modus_tollens
<=> ! [X1,X2] : is_a_theorem(implies(implies(not(X2),not(X1)),implies(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
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(op_and,axiom,
( op_and
=> ! [X1,X2] : and(X1,X2) = not(or(not(X1),not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_and) ).
fof(hilbert_modus_tollens,axiom,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).
fof(hilbert_or_1,axiom,
or_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_1) ).
fof(principia_op_and,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).
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(hilbert_and_2,axiom,
and_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_2) ).
fof(implies_3,axiom,
( implies_3
<=> ! [X1,X2,X3] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_3) ).
fof(hilbert_implies_3,axiom,
implies_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_3) ).
fof(equivalence_2,axiom,
( equivalence_2
<=> ! [X1,X2] : is_a_theorem(implies(equiv(X1,X2),implies(X2,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',equivalence_2) ).
fof(or_2,axiom,
( or_2
<=> ! [X1,X2] : is_a_theorem(implies(X2,or(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_2) ).
fof(hilbert_equivalence_2,axiom,
equivalence_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_equivalence_2) ).
fof(hilbert_or_2,axiom,
or_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_2) ).
fof(equivalence_1,axiom,
( equivalence_1
<=> ! [X1,X2] : is_a_theorem(implies(equiv(X1,X2),implies(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',equivalence_1) ).
fof(principia_r4,conjecture,
r4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r4) ).
fof(or_3,axiom,
( or_3
<=> ! [X1,X2,X3] : is_a_theorem(implies(implies(X1,X3),implies(implies(X2,X3),implies(or(X1,X2),X3)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_3) ).
fof(hilbert_equivalence_1,axiom,
equivalence_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_equivalence_1) ).
fof(hilbert_or_3,axiom,
or_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_3) ).
fof(r4,axiom,
( r4
<=> ! [X4,X5,X6] : is_a_theorem(implies(or(X4,or(X5,X6)),or(X5,or(X4,X6)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r4) ).
fof(c_0_40,plain,
! [X121,X122] :
( implies(X121,X122) = not(and(X121,not(X122)))
| ~ op_implies_and ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])]) ).
fof(c_0_41,plain,
! [X7,X8] :
( ( modus_ponens
| ~ is_a_theorem(esk2_0) )
& ( modus_ponens
| is_a_theorem(implies(esk1_0,esk2_0)) )
& ( modus_ponens
| is_a_theorem(esk1_0) )
& ( is_a_theorem(X8)
| ~ is_a_theorem(implies(X7,X8))
| ~ is_a_theorem(X7)
| ~ modus_ponens ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_42,plain,
! [X117,X118] :
( or(X117,X118) = not(and(not(X117),not(X118)))
| ~ op_or ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])]) ).
cnf(c_0_43,plain,
( ~ op_implies_and
| implies(X1,X2) = not(and(X1,not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
fof(c_0_45,plain,
! [X41,X42] :
( ( and_3
| ~ is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0)))) )
& ( is_a_theorem(implies(X41,implies(X42,and(X41,X42))))
| ~ and_3 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_3])])])])]) ).
fof(c_0_46,plain,
! [X23,X24] :
( ( implies_2
| ~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0))) )
& ( is_a_theorem(implies(implies(X23,implies(X23,X24)),implies(X23,X24)))
| ~ implies_2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])])]) ).
cnf(c_0_47,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| ~ modus_ponens
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[hilbert_modus_ponens]) ).
cnf(c_0_49,plain,
( ~ op_or
| or(X1,X2) = not(and(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
cnf(c_0_51,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).
fof(c_0_52,plain,
! [X123,X124] :
( implies(X123,X124) = or(not(X123),X124)
| ~ op_implies_or ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_or])])])]) ).
cnf(c_0_53,plain,
( ~ and_3
| is_a_theorem(implies(X1,implies(X2,and(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_54,plain,
and_3,
inference(split_conjunct,[status(thm)],[hilbert_and_3]) ).
cnf(c_0_55,plain,
( ~ implies_2
| is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_56,plain,
implies_2,
inference(split_conjunct,[status(thm)],[hilbert_implies_2]) ).
fof(c_0_57,plain,
! [X19,X20] :
( ( implies_1
| ~ is_a_theorem(implies(esk7_0,implies(esk8_0,esk7_0))) )
& ( is_a_theorem(implies(X19,implies(X20,X19)))
| ~ implies_1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_1])])])])]) ).
cnf(c_0_58,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
cnf(c_0_59,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
cnf(c_0_60,plain,
( ~ op_implies_or
| implies(X1,X2) = or(not(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_61,plain,
op_implies_or,
inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).
cnf(c_0_62,plain,
is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]) ).
fof(c_0_63,plain,
! [X125,X126] :
( equiv(X125,X126) = and(implies(X125,X126),implies(X126,X125))
| ~ op_equiv ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])])]) ).
cnf(c_0_64,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]) ).
cnf(c_0_65,plain,
( ~ implies_1
| is_a_theorem(implies(X1,implies(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_66,plain,
implies_1,
inference(split_conjunct,[status(thm)],[hilbert_implies_1]) ).
cnf(c_0_67,plain,
( ~ is_a_theorem(not(X2))
| ~ is_a_theorem(or(X2,X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_68,plain,
or(not(X1),X2) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]) ).
fof(c_0_69,plain,
! [X33,X34] :
( ( and_1
| ~ is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0)) )
& ( is_a_theorem(implies(and(X33,X34),X33))
| ~ and_1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_1])])])])]) ).
fof(c_0_70,plain,
! [X11,X12] :
( ( substitution_of_equivalents
| esk3_0 != esk4_0 )
& ( substitution_of_equivalents
| is_a_theorem(equiv(esk3_0,esk4_0)) )
& ( X11 = X12
| ~ is_a_theorem(equiv(X11,X12))
| ~ substitution_of_equivalents ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_71,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,and(X2,X1))) ),
inference(spm,[status(thm)],[c_0_58,c_0_62]) ).
cnf(c_0_72,plain,
( ~ op_equiv
| equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_73,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[hilbert_op_equiv]) ).
cnf(c_0_74,plain,
( ~ is_a_theorem(implies(X1,implies(X1,X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_58,c_0_64]) ).
cnf(c_0_75,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])]) ).
cnf(c_0_76,plain,
( ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(not(not(X2)))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_77,plain,
( ~ and_1
| is_a_theorem(implies(and(X1,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_78,plain,
and_1,
inference(split_conjunct,[status(thm)],[hilbert_and_1]) ).
cnf(c_0_79,plain,
( ~ is_a_theorem(equiv(X1,X2))
| ~ substitution_of_equivalents
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_80,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(c_0_81,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(X2)
| is_a_theorem(and(X1,X2)) ),
inference(spm,[status(thm)],[c_0_58,c_0_71]) ).
cnf(c_0_82,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73])]) ).
cnf(c_0_83,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_84,plain,
( ~ is_a_theorem(not(implies(X2,X3)))
| ~ is_a_theorem(implies(and(X2,not(X3)),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_50]) ).
cnf(c_0_85,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78])]) ).
fof(c_0_86,plain,
! [X15,X16] :
( ( modus_tollens
| ~ is_a_theorem(implies(implies(not(esk6_0),not(esk5_0)),implies(esk5_0,esk6_0))) )
& ( is_a_theorem(implies(implies(not(X16),not(X15)),implies(X15,X16)))
| ~ modus_tollens ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_tollens])])])])]) ).
cnf(c_0_87,plain,
( ~ is_a_theorem(equiv(X1,X2))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]) ).
cnf(c_0_88,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(equiv(X1,X2)) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_89,plain,
is_a_theorem(or(X1,not(X1))),
inference(spm,[status(thm)],[c_0_83,c_0_59]) ).
fof(c_0_90,plain,
! [X45,X46] :
( ( or_1
| ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0))) )
& ( is_a_theorem(implies(X45,or(X45,X46)))
| ~ or_1 ) ),
inference(fof_nnf,[status(thm)],[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(implies(X1,X2)))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
fof(c_0_92,plain,
! [X119,X120] :
( and(X119,X120) = not(or(not(X119),not(X120)))
| ~ op_and ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_and])])])]) ).
cnf(c_0_93,plain,
( ~ modus_tollens
| is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_94,plain,
modus_tollens,
inference(split_conjunct,[status(thm)],[hilbert_modus_tollens]) ).
cnf(c_0_95,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_96,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_89,c_0_68]) ).
cnf(c_0_97,plain,
( ~ or_1
| is_a_theorem(implies(X1,or(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_98,plain,
or_1,
inference(split_conjunct,[status(thm)],[hilbert_or_1]) ).
cnf(c_0_99,plain,
( ~ is_a_theorem(not(or(X1,X2)))
| is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_91,c_0_59]) ).
cnf(c_0_100,plain,
( ~ op_and
| and(X1,X2) = not(or(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_101,plain,
op_and,
inference(split_conjunct,[status(thm)],[principia_op_and]) ).
cnf(c_0_102,plain,
is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_59]),c_0_94])]) ).
cnf(c_0_103,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_59]),c_0_68]),c_0_83])]) ).
fof(c_0_104,plain,
! [X37,X38] :
( ( and_2
| ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0)) )
& ( is_a_theorem(implies(and(X37,X38),X38))
| ~ and_2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_2])])])])]) ).
cnf(c_0_105,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98])]) ).
cnf(c_0_106,plain,
( ~ is_a_theorem(not(implies(X1,X2)))
| is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_99,c_0_68]) ).
cnf(c_0_107,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_68]),c_0_101])]) ).
cnf(c_0_108,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_59]),c_0_103]) ).
cnf(c_0_109,plain,
( ~ and_2
| is_a_theorem(implies(and(X1,X2),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_110,plain,
and_2,
inference(split_conjunct,[status(thm)],[hilbert_and_2]) ).
cnf(c_0_111,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_58,c_0_105]) ).
cnf(c_0_112,plain,
( ~ is_a_theorem(and(X1,X2))
| is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_113,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(spm,[status(thm)],[c_0_74,c_0_62]) ).
cnf(c_0_114,plain,
( ~ is_a_theorem(not(and(X2,X3)))
| ~ is_a_theorem(implies(implies(X2,not(X3)),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_107]) ).
cnf(c_0_115,plain,
or(X1,X2) = or(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_108]),c_0_108])]) ).
cnf(c_0_116,plain,
not(or(X1,not(X2))) = and(not(X1),X2),
inference(spm,[status(thm)],[c_0_107,c_0_59]) ).
cnf(c_0_117,plain,
is_a_theorem(implies(and(X1,X2),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110])]) ).
fof(c_0_118,plain,
! [X27,X28,X29] :
( ( implies_3
| ~ is_a_theorem(implies(implies(esk11_0,esk12_0),implies(implies(esk12_0,esk13_0),implies(esk11_0,esk13_0)))) )
& ( is_a_theorem(implies(implies(X27,X28),implies(implies(X28,X29),implies(X27,X29))))
| ~ implies_3 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_3])])])])]) ).
cnf(c_0_119,plain,
( ~ is_a_theorem(not(X1))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_111,c_0_68]) ).
cnf(c_0_120,plain,
( ~ is_a_theorem(equiv(X1,X2))
| is_a_theorem(not(not(implies(X1,X2)))) ),
inference(spm,[status(thm)],[c_0_112,c_0_82]) ).
cnf(c_0_121,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(and(X1,X1)) ),
inference(spm,[status(thm)],[c_0_58,c_0_113]) ).
cnf(c_0_122,plain,
( ~ is_a_theorem(not(and(not(X2),X3)))
| ~ is_a_theorem(implies(or(X2,not(X3)),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_59]) ).
cnf(c_0_123,plain,
( ~ is_a_theorem(not(X2))
| ~ is_a_theorem(or(X1,X2))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_115]) ).
cnf(c_0_124,plain,
is_a_theorem(or(X1,implies(X2,and(not(X1),X2)))),
inference(spm,[status(thm)],[c_0_62,c_0_59]) ).
cnf(c_0_125,plain,
not(implies(X1,and(not(X2),X3))) = and(X1,or(X2,not(X3))),
inference(spm,[status(thm)],[c_0_107,c_0_116]) ).
cnf(c_0_126,plain,
or(X1,not(X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_68,c_0_115]) ).
cnf(c_0_127,plain,
( ~ is_a_theorem(X1)
| and(X1,X2) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_71]),c_0_117])]) ).
cnf(c_0_128,plain,
( ~ implies_3
| is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_129,plain,
implies_3,
inference(split_conjunct,[status(thm)],[hilbert_implies_3]) ).
fof(c_0_130,plain,
! [X63,X64] :
( ( equivalence_2
| ~ is_a_theorem(implies(equiv(esk29_0,esk30_0),implies(esk30_0,esk29_0))) )
& ( is_a_theorem(implies(equiv(X63,X64),implies(X64,X63)))
| ~ equivalence_2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_2])])])])]) ).
cnf(c_0_131,plain,
( ~ is_a_theorem(equiv(X1,X2))
| is_a_theorem(or(implies(X1,X2),X3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_59]) ).
cnf(c_0_132,plain,
is_a_theorem(equiv(X1,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_82]),c_0_83])]) ).
cnf(c_0_133,plain,
( ~ is_a_theorem(not(and(not(X2),X1)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_122,c_0_102]) ).
cnf(c_0_134,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_59,c_0_50]) ).
cnf(c_0_135,plain,
or(and(X1,X2),X3) = implies(implies(X1,not(X2)),X3),
inference(spm,[status(thm)],[c_0_68,c_0_107]) ).
fof(c_0_136,plain,
! [X49,X50] :
( ( or_2
| ~ is_a_theorem(implies(esk23_0,or(esk22_0,esk23_0))) )
& ( is_a_theorem(implies(X50,or(X49,X50)))
| ~ or_2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_2])])])])]) ).
cnf(c_0_137,plain,
( ~ is_a_theorem(and(X2,implies(X2,X1)))
| is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_125]),c_0_126]) ).
cnf(c_0_138,plain,
and(implies(and(X1,X2),X1),X3) = X3,
inference(spm,[status(thm)],[c_0_127,c_0_85]) ).
cnf(c_0_139,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_129])]) ).
cnf(c_0_140,plain,
( ~ equivalence_2
| is_a_theorem(implies(equiv(X1,X2),implies(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_141,plain,
equivalence_2,
inference(split_conjunct,[status(thm)],[hilbert_equivalence_2]) ).
cnf(c_0_142,plain,
( ~ is_a_theorem(or(X2,not(X1)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_58,c_0_102]) ).
cnf(c_0_143,plain,
is_a_theorem(or(implies(X1,X1),X2)),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_144,plain,
( ~ is_a_theorem(or(X2,X1))
| is_a_theorem(or(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_50]),c_0_59]),c_0_59]) ).
cnf(c_0_145,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(or(X1,and(X2,not(X1)))) ),
inference(spm,[status(thm)],[c_0_71,c_0_59]) ).
cnf(c_0_146,plain,
implies(implies(X1,not(not(X2))),X3) = implies(implies(X1,X2),X3),
inference(rw,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_147,plain,
( ~ or_2
| is_a_theorem(implies(X1,or(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_148,plain,
or_2,
inference(split_conjunct,[status(thm)],[hilbert_or_2]) ).
cnf(c_0_149,plain,
( ~ is_a_theorem(implies(implies(and(X2,X3),X2),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_150,plain,
( ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_58,c_0_139]) ).
fof(c_0_151,plain,
! [X59,X60] :
( ( equivalence_1
| ~ is_a_theorem(implies(equiv(esk27_0,esk28_0),implies(esk27_0,esk28_0))) )
& ( is_a_theorem(implies(equiv(X59,X60),implies(X59,X60)))
| ~ equivalence_1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_1])])])])]) ).
cnf(c_0_152,plain,
( ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(implies(implies(X1,X2),equiv(X2,X1))) ),
inference(spm,[status(thm)],[c_0_71,c_0_82]) ).
cnf(c_0_153,plain,
is_a_theorem(implies(equiv(X1,X2),implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_141])]) ).
cnf(c_0_154,plain,
is_a_theorem(implies(X1,implies(X2,X2))),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_155,plain,
and(implies(X1,X1),X2) = X2,
inference(spm,[status(thm)],[c_0_127,c_0_83]) ).
cnf(c_0_156,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X1,X2),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_135]),c_0_146]) ).
cnf(c_0_157,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_148])]) ).
fof(c_0_158,negated_conjecture,
~ r4,
inference(assume_negation,[status(cth)],[principia_r4]) ).
fof(c_0_159,plain,
! [X53,X54,X55] :
( ( or_3
| ~ is_a_theorem(implies(implies(esk24_0,esk26_0),implies(implies(esk25_0,esk26_0),implies(or(esk24_0,esk25_0),esk26_0)))) )
& ( is_a_theorem(implies(implies(X53,X55),implies(implies(X54,X55),implies(or(X53,X54),X55))))
| ~ or_3 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_3])])])])]) ).
cnf(c_0_160,plain,
( ~ is_a_theorem(implies(X1,and(X2,X3)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_161,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_58,c_0_75]) ).
cnf(c_0_162,plain,
( ~ equivalence_1
| is_a_theorem(implies(equiv(X1,X2),implies(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_163,plain,
equivalence_1,
inference(split_conjunct,[status(thm)],[hilbert_equivalence_1]) ).
cnf(c_0_164,plain,
( ~ is_a_theorem(implies(X1,X2))
| equiv(X1,X2) = implies(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_152]),c_0_153])]) ).
cnf(c_0_165,plain,
is_a_theorem(implies(X1,or(X2,not(X2)))),
inference(spm,[status(thm)],[c_0_154,c_0_59]) ).
cnf(c_0_166,plain,
implies(implies(X1,X1),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_155]),c_0_103]) ).
cnf(c_0_167,plain,
( ~ is_a_theorem(X1)
| implies(X1,X2) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_156]),c_0_75])]) ).
cnf(c_0_168,plain,
is_a_theorem(or(X1,or(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_157,c_0_59]) ).
fof(c_0_169,negated_conjecture,
~ r4,
inference(fof_simplification,[status(thm)],[c_0_158]) ).
cnf(c_0_170,plain,
( ~ or_3
| is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_159]) ).
cnf(c_0_171,plain,
or_3,
inference(split_conjunct,[status(thm)],[hilbert_or_3]) ).
cnf(c_0_172,plain,
( ~ is_a_theorem(or(X1,and(X2,X3)))
| is_a_theorem(or(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_59]),c_0_59]) ).
cnf(c_0_173,plain,
and(X1,not(X2)) = not(implies(X1,X2)),
inference(spm,[status(thm)],[c_0_107,c_0_103]) ).
cnf(c_0_174,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_95,c_0_161]) ).
cnf(c_0_175,plain,
is_a_theorem(implies(equiv(X1,X2),implies(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_162,c_0_163])]) ).
cnf(c_0_176,plain,
equiv(X1,implies(X2,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_126]),c_0_126]),c_0_166]) ).
cnf(c_0_177,plain,
implies(or(X1,implies(X1,X2)),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_126]) ).
fof(c_0_178,plain,
! [X105,X106,X107] :
( ( r4
| ~ is_a_theorem(implies(or(esk50_0,or(esk51_0,esk52_0)),or(esk51_0,or(esk50_0,esk52_0)))) )
& ( is_a_theorem(implies(or(X105,or(X106,X107)),or(X106,or(X105,X107))))
| ~ r4 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r4])])])])]) ).
fof(c_0_179,negated_conjecture,
~ r4,
inference(fof_nnf,[status(thm)],[c_0_169]) ).
cnf(c_0_180,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_171])]) ).
cnf(c_0_181,plain,
( ~ is_a_theorem(implies(implies(X2,X3),X1))
| is_a_theorem(or(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_126]) ).
cnf(c_0_182,plain,
and(not(X1),X2) = not(implies(X2,X1)),
inference(rw,[status(thm)],[c_0_116,c_0_126]) ).
cnf(c_0_183,plain,
( ~ is_a_theorem(equiv(X1,X2))
| equiv(X1,X2) = implies(X1,X2) ),
inference(spm,[status(thm)],[c_0_174,c_0_175]) ).
cnf(c_0_184,plain,
equiv(X1,or(X2,implies(X2,X3))) = X1,
inference(spm,[status(thm)],[c_0_176,c_0_177]) ).
cnf(c_0_185,plain,
( ~ is_a_theorem(X1)
| X1 = implies(X2,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_166]),c_0_154])]) ).
cnf(c_0_186,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_113]),c_0_85])]) ).
cnf(c_0_187,plain,
( ~ is_a_theorem(implies(or(esk50_0,or(esk51_0,esk52_0)),or(esk51_0,or(esk50_0,esk52_0))))
| r4 ),
inference(split_conjunct,[status(thm)],[c_0_178]) ).
cnf(c_0_188,negated_conjecture,
~ r4,
inference(split_conjunct,[status(thm)],[c_0_179]) ).
cnf(c_0_189,plain,
( ~ is_a_theorem(implies(X3,X2))
| is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),X2))) ),
inference(spm,[status(thm)],[c_0_58,c_0_180]) ).
cnf(c_0_190,plain,
( ~ is_a_theorem(implies(or(X1,X3),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_59]),c_0_126]) ).
cnf(c_0_191,plain,
is_a_theorem(implies(X1,or(X2,not(not(X1))))),
inference(spm,[status(thm)],[c_0_168,c_0_68]) ).
cnf(c_0_192,plain,
( ~ is_a_theorem(implies(implies(X3,X1),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_182]),c_0_126]),c_0_126]) ).
cnf(c_0_193,plain,
( ~ is_a_theorem(X1)
| implies(X1,or(X2,implies(X2,X3))) = X1 ),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_194,plain,
implies(X1,implies(X1,X2)) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_64]),c_0_75])]) ).
cnf(c_0_195,plain,
implies(X1,X1) = implies(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_113]),c_0_186]) ).
cnf(c_0_196,plain,
~ is_a_theorem(implies(or(esk50_0,or(esk51_0,esk52_0)),or(esk51_0,or(esk50_0,esk52_0)))),
inference(sr,[status(thm)],[c_0_187,c_0_188]) ).
cnf(c_0_197,plain,
( ~ is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(or(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_58,c_0_189]) ).
cnf(c_0_198,plain,
is_a_theorem(implies(X1,or(X2,or(X1,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_103]) ).
cnf(c_0_199,plain,
( ~ is_a_theorem(implies(or(X3,X1),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_192,c_0_59]) ).
cnf(c_0_200,plain,
or(X1,implies(X1,X2)) = implies(esk1_0,esk1_0),
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_193,c_0_64]),c_0_194]),c_0_195]),c_0_166]),c_0_194]),c_0_195]) ).
cnf(c_0_201,plain,
~ is_a_theorem(implies(or(esk51_0,esk52_0),or(esk51_0,or(esk50_0,esk52_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_197]),c_0_198])]) ).
cnf(c_0_202,plain,
is_a_theorem(implies(X1,or(X2,or(X3,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_191]),c_0_103]) ).
cnf(c_0_203,plain,
implies(X1,or(X1,X2)) = implies(esk1_0,esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_200]),c_0_59]) ).
cnf(c_0_204,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_197]),c_0_202]),c_0_203]),c_0_83])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL457+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/10.40 % Computer : n008.cluster.edu
% 0.11/10.40 % Model : x86_64 x86_64
% 0.11/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.40 % Memory : 8046.5625MB
% 0.11/10.40 % OS : Linux 6.8.0-71-generic
% 0.15/10.40 % CPULimit : 300
% 0.15/10.40 % WCLimit : 300
% 0.15/10.40 % DateTime : Mon Sep 21 00:34:07 UTC 2026
% 0.15/10.40 % CPUTime :
% 0.15/10.40 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/10.46 Running first-order theorem proving
% 0.15/10.46 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
% 21.88/16.00 % Version: 3.5.1
% 21.88/16.00 % Preprocessing class: FSMSSLSSSSSNFFN.
% 21.88/16.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 21.88/16.00 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 21.88/16.00 % Starting new_bool_3 with 300s (1) cores
% 21.88/16.00 % Starting new_bool_1 with 300s (1) cores
% 21.88/16.00 % Starting sh5l with 300s (1) cores
% 21.88/16.00 % new_bool_3 with pid 3971342 completed with status 9
% 21.88/16.00 % sh5l with pid 3971344 completed with status 9
% 21.88/16.00 % new_bool_1 with pid 3971343 completed with status 9
% 21.88/16.00 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 3971341 completed with status 0
% 21.88/16.00 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 21.88/16.00 % Preprocessing class: FSMSSLSSSSSNFFN.
% 21.88/16.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 21.88/16.00 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 21.88/16.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 21.88/16.00 % No SInE strategy applied
% 21.88/16.00 % Search class: FGUSF-FFMM21-MFFFFFNN
% 21.88/16.00 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 21.88/16.00 % Starting SubtermCWHack with 151s (1) cores
% 21.88/16.00 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 21.88/16.00 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 21.88/16.00 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 21.88/16.00 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 21.88/16.00 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 3971354 completed with status 0
% 21.88/16.00 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 21.88/16.00 % Preprocessing class: FSMSSLSSSSSNFFN.
% 21.88/16.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 21.88/16.00 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 21.88/16.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 21.88/16.00 % No SInE strategy applied
% 21.88/16.00 % Search class: FGUSF-FFMM21-MFFFFFNN
% 21.88/16.00 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 21.88/16.00 % Starting SubtermCWHack with 151s (1) cores
% 21.88/16.00 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 21.88/16.00 % Preprocessing time : 0.003 s
% 21.88/16.00 % Presaturation interreduction done
% 21.88/16.00
% 21.88/16.00 % Proof found!
% 21.88/16.00 % SZS status Theorem
% 21.88/16.00 % SZS output start CNFRefutation
% See solution above
% 21.88/16.00 % Parsed axioms : 53
% 21.88/16.00 % Removed by relevancy pruning/SinE : 0
% 21.88/16.00 % Initial clauses : 82
% 21.88/16.00 % Removed in clause preprocessing : 0
% 21.88/16.00 % Initial clauses in saturation : 82
% 21.88/16.00 % Processed clauses : 25473
% 21.88/16.00 % ...of these trivial : 707
% 21.88/16.00 % ...subsumed : 22380
% 21.88/16.00 % ...remaining for further processing : 2386
% 21.88/16.00 % Other redundant clauses eliminated : 0
% 21.88/16.00 % Clauses deleted for lack of memory : 0
% 21.88/16.00 % Backward-subsumed : 96
% 21.88/16.00 % Backward-rewritten : 578
% 21.88/16.00 % Generated clauses : 238806
% 21.88/16.00 % ...of the previous two non-redundant : 214100
% 21.88/16.00 % ...aggressively subsumed : 0
% 21.88/16.00 % Contextual simplify-reflections : 2
% 21.88/16.00 % Paramodulations : 238806
% 21.88/16.00 % Factorizations : 0
% 21.88/16.00 % NegExts : 0
% 21.88/16.00 % Equation resolutions : 0
% 21.88/16.00 % Disequality decompositions : 0
% 21.88/16.00 % Total rewrite steps : 256822
% 21.88/16.00 % ...of those cached : 241522
% 21.88/16.00 % Propositional unsat checks : 0
% 21.88/16.00 % Propositional check models : 0
% 21.88/16.00 % Propositional check unsatisfiable : 0
% 21.88/16.00 % Propositional clauses : 0
% 21.88/16.00 % Propositional clauses after purity: 0
% 21.88/16.00 % Propositional unsat core size : 0
% 21.88/16.00 % Propositional preprocessing time : 0.000
% 21.88/16.00 % Propositional encoding time : 0.000
% 21.88/16.00 % Propositional solver time : 0.000
% 21.88/16.00 % Success case prop preproc time : 0.000
% 21.88/16.00 % Success case prop encoding time : 0.000
% 21.88/16.00 % Success case prop solver time : 0.000
% 21.88/16.00 % Current number of processed clauses : 1653
% 21.88/16.00 % Positive orientable unit clauses : 165
% 21.88/16.00 % Positive unorientable unit clauses: 25
% 21.88/16.00 % Negative unit clauses : 8
% 21.88/16.00 % Non-unit-clauses : 1455
% 21.88/16.00 % Current number of unprocessed clauses: 181338
% 21.88/16.00 % ...number of literals in the above : 380960
% 21.88/16.00 % Current number of archived formulas : 0
% 21.88/16.00 % Current number of archived clauses : 733
% 21.88/16.00 % Clause-clause subsumption calls (NU) : 368305
% 21.88/16.00 % Rec. Clause-clause subsumption calls : 341262
% 21.88/16.00 % Non-unit clause-clause subsumptions : 18883
% 21.88/16.00 % Unit Clause-clause subsumption calls : 6263
% 21.88/16.00 % Rewrite failures with RHS unbound : 0
% 21.88/16.00 % BW rewrite match attempts : 7267
% 21.88/16.01 % BW rewrite match successes : 669
% 21.88/16.01 % Condensation attempts : 0
% 21.88/16.01 % Condensation successes : 0
% 21.88/16.01 % Termbank termtop insertions : 3400812
% 21.88/16.01 % Search garbage collected termcells : 1092
% 21.88/16.01
% 21.88/16.01 % -------------------------------------------------
% 21.88/16.01 % User time : 5.227 s
% 21.88/16.01 % System time : 0.181 s
% 21.88/16.01 % Total time : 5.408 s
% 21.88/16.01 % Maximum resident set size: 3944 pages
% 21.88/16.01
% 21.88/16.01 % -------------------------------------------------
% 21.88/16.01 % User time : 26.196 s
% 21.88/16.01 % System time : 1.169 s
% 21.88/16.01 % Total time : 27.365 s
% 21.88/16.01 % Maximum resident set size: 4608 pages
% 21.88/16.01 % E exiting
%------------------------------------------------------------------------------