TSTP Solution File: LCL556+1 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : LCL556+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n019.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 : 600s
% DateTime : Sun Jul 17 10:11:51 EDT 2022
% Result : Theorem 0.41s 30.60s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 31
% Syntax : Number of formulae : 196 ( 95 unt; 0 def)
% Number of atoms : 364 ( 64 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 296 ( 128 ~; 129 |; 19 &)
% ( 11 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 19 ( 17 usr; 17 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 22 con; 0-2 aty)
% Number of variables : 307 ( 28 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X1,X2] : strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
fof(adjunction,axiom,
( adjunction
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(X2) )
=> is_a_theorem(and(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',adjunction) ).
fof(op_strict_equiv,axiom,
( op_strict_equiv
=> ! [X1,X2] : strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_strict_equiv) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_op_strict_implies) ).
fof(s1_0_adjunction,axiom,
adjunction,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_adjunction) ).
fof(s1_0_op_strict_equiv,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_op_strict_equiv) ).
fof(axiom_m1,axiom,
( axiom_m1
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m1) ).
fof(axiom_m4,axiom,
( axiom_m4
<=> ! [X1] : is_a_theorem(strict_implies(X1,and(X1,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m4) ).
fof(axiom_m2,axiom,
( axiom_m2
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m2) ).
fof(substitution_strict_equiv,axiom,
( substitution_strict_equiv
<=> ! [X1,X2] :
( is_a_theorem(strict_equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',substitution_strict_equiv) ).
fof(s1_0_axiom_m1,axiom,
axiom_m1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m1) ).
fof(axiom_m3,axiom,
( axiom_m3
<=> ! [X1,X2,X3] : is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m3) ).
fof(s1_0_axiom_m4,axiom,
axiom_m4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m4) ).
fof(s1_0_axiom_m2,axiom,
axiom_m2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m2) ).
fof(s1_0_substitution_strict_equiv,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_substitution_strict_equiv) ).
fof(s1_0_axiom_m3,axiom,
axiom_m3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m3) ).
fof(modus_ponens_strict_implies,axiom,
( modus_ponens_strict_implies
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(strict_implies(X1,X2)) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',modus_ponens_strict_implies) ).
fof(s1_0_modus_ponens_strict_implies,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_modus_ponens_strict_implies) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(axiom_m5,axiom,
( axiom_m5
<=> ! [X1,X2,X3] : is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m5) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',hilbert_op_implies_and) ).
fof(s1_0_axiom_m5,axiom,
axiom_m5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m5) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X1,X2] :
( is_a_theorem(equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
fof(s1_0_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_op_equiv) ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',substitution_of_equivalents) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(r1,axiom,
( r1
<=> ! [X4] : is_a_theorem(implies(or(X4,X4),X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r1) ).
fof(s1_0_op_or,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_op_or) ).
fof(hilbert_and_2,conjecture,
and_2,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',hilbert_and_2) ).
fof(and_2,axiom,
( and_2
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_2) ).
fof(c_0_31,plain,
! [X3,X4] :
( ~ op_strict_implies
| strict_implies(X3,X4) = necessarily(implies(X3,X4)) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])])])]) ).
fof(c_0_32,plain,
! [X3,X4] :
( ( ~ adjunction
| ~ is_a_theorem(X3)
| ~ is_a_theorem(X4)
| is_a_theorem(and(X3,X4)) )
& ( is_a_theorem(esk59_0)
| adjunction )
& ( is_a_theorem(esk60_0)
| adjunction )
& ( ~ is_a_theorem(and(esk59_0,esk60_0))
| adjunction ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[adjunction])])])])])])]) ).
fof(c_0_33,plain,
! [X3,X4] :
( ~ op_strict_equiv
| strict_equiv(X3,X4) = and(strict_implies(X3,X4),strict_implies(X4,X3)) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_equiv])])])])]) ).
cnf(c_0_34,plain,
( strict_implies(X1,X2) = necessarily(implies(X1,X2))
| ~ op_strict_implies ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_0_36,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ adjunction ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
adjunction,
inference(split_conjunct,[status(thm)],[s1_0_adjunction]) ).
cnf(c_0_38,plain,
( strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1))
| ~ op_strict_equiv ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,plain,
strict_implies(X1,X2) = necessarily(implies(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).
cnf(c_0_40,plain,
op_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_equiv]) ).
fof(c_0_41,plain,
! [X3,X4] :
( ( ~ axiom_m1
| is_a_theorem(strict_implies(and(X3,X4),and(X4,X3))) )
& ( ~ is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0)))
| axiom_m1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m1])])])])])]) ).
fof(c_0_42,plain,
! [X2] :
( ( ~ axiom_m4
| is_a_theorem(strict_implies(X2,and(X2,X2))) )
& ( ~ is_a_theorem(strict_implies(esk84_0,and(esk84_0,esk84_0)))
| axiom_m4 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m4])])])])])]) ).
fof(c_0_43,plain,
! [X3,X4] :
( ( ~ axiom_m2
| is_a_theorem(strict_implies(and(X3,X4),X3)) )
& ( ~ is_a_theorem(strict_implies(and(esk79_0,esk80_0),esk79_0))
| axiom_m2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m2])])])])])]) ).
fof(c_0_44,plain,
! [X3,X4] :
( ( ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(X3,X4))
| X3 = X4 )
& ( is_a_theorem(strict_equiv(esk61_0,esk62_0))
| substitution_strict_equiv )
& ( esk61_0 != esk62_0
| substitution_strict_equiv ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_strict_equiv])])])])])])]) ).
cnf(c_0_45,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
cnf(c_0_46,plain,
and(necessarily(implies(X1,X2)),necessarily(implies(X2,X1))) = strict_equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_39]),c_0_40])]) ).
cnf(c_0_47,plain,
( is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))
| ~ axiom_m1 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,plain,
axiom_m1,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m1]) ).
fof(c_0_49,plain,
! [X4,X5,X6] :
( ( ~ axiom_m3
| is_a_theorem(strict_implies(and(and(X4,X5),X6),and(X4,and(X5,X6)))) )
& ( ~ is_a_theorem(strict_implies(and(and(esk81_0,esk82_0),esk83_0),and(esk81_0,and(esk82_0,esk83_0))))
| axiom_m3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m3])])])])])]) ).
cnf(c_0_50,plain,
( is_a_theorem(strict_implies(X1,and(X1,X1)))
| ~ axiom_m4 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,plain,
axiom_m4,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m4]) ).
cnf(c_0_52,plain,
( is_a_theorem(strict_implies(and(X1,X2),X1))
| ~ axiom_m2 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_53,plain,
axiom_m2,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m2]) ).
cnf(c_0_54,plain,
( X1 = X2
| ~ is_a_theorem(strict_equiv(X1,X2))
| ~ substitution_strict_equiv ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_55,plain,
substitution_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_substitution_strict_equiv]) ).
cnf(c_0_56,plain,
( is_a_theorem(strict_equiv(X1,X2))
| ~ is_a_theorem(necessarily(implies(X2,X1)))
| ~ is_a_theorem(necessarily(implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_57,plain,
is_a_theorem(necessarily(implies(and(X1,X2),and(X2,X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_39]),c_0_48])]) ).
cnf(c_0_58,plain,
( is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))
| ~ axiom_m3 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_59,plain,
axiom_m3,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m3]) ).
cnf(c_0_60,plain,
is_a_theorem(necessarily(implies(X1,and(X1,X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_39]),c_0_51])]) ).
cnf(c_0_61,plain,
is_a_theorem(necessarily(implies(and(X1,X2),X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_39]),c_0_53])]) ).
cnf(c_0_62,plain,
( X1 = X2
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
cnf(c_0_63,plain,
is_a_theorem(strict_equiv(and(X1,X2),and(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_57])]) ).
fof(c_0_64,plain,
! [X3,X4] :
( ( ~ modus_ponens_strict_implies
| ~ is_a_theorem(X3)
| ~ is_a_theorem(strict_implies(X3,X4))
| is_a_theorem(X4) )
& ( is_a_theorem(esk57_0)
| modus_ponens_strict_implies )
& ( is_a_theorem(strict_implies(esk57_0,esk58_0))
| modus_ponens_strict_implies )
& ( ~ is_a_theorem(esk58_0)
| modus_ponens_strict_implies ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens_strict_implies])])])])])])]) ).
cnf(c_0_65,plain,
is_a_theorem(necessarily(implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_39]),c_0_59])]) ).
cnf(c_0_66,plain,
is_a_theorem(strict_equiv(and(X1,X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_60]),c_0_61])]) ).
cnf(c_0_67,plain,
and(X1,X2) = and(X2,X1),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_68,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(X2)
| ~ modus_ponens_strict_implies ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_69,plain,
modus_ponens_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_modus_ponens_strict_implies]) ).
cnf(c_0_70,plain,
( is_a_theorem(strict_equiv(and(X1,and(X2,X3)),and(and(X1,X2),X3)))
| ~ is_a_theorem(necessarily(implies(and(X1,and(X2,X3)),and(and(X1,X2),X3)))) ),
inference(spm,[status(thm)],[c_0_56,c_0_65]) ).
cnf(c_0_71,plain,
and(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_62,c_0_66]) ).
cnf(c_0_72,plain,
is_a_theorem(necessarily(implies(and(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_61,c_0_67]) ).
cnf(c_0_73,plain,
strict_equiv(X1,X2) = strict_equiv(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_67]),c_0_46]) ).
fof(c_0_74,plain,
! [X3,X4] :
( ~ op_implies_and
| implies(X3,X4) = not(and(X3,not(X4))) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])])]) ).
cnf(c_0_75,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(necessarily(implies(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69]),c_0_39])]) ).
cnf(c_0_76,plain,
is_a_theorem(strict_equiv(and(X1,X2),and(X1,and(X1,X2)))),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]),c_0_73]) ).
fof(c_0_77,plain,
! [X4,X5,X6] :
( ( ~ axiom_m5
| is_a_theorem(strict_implies(and(strict_implies(X4,X5),strict_implies(X5,X6)),strict_implies(X4,X6))) )
& ( ~ is_a_theorem(strict_implies(and(strict_implies(esk85_0,esk86_0),strict_implies(esk86_0,esk87_0)),strict_implies(esk85_0,esk87_0)))
| axiom_m5 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m5])])])])])]) ).
cnf(c_0_78,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_79,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_0_80,plain,
( is_a_theorem(and(X1,and(X2,X3)))
| ~ is_a_theorem(and(and(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_75,c_0_65]) ).
cnf(c_0_81,plain,
and(X1,and(X1,X2)) = and(X1,X2),
inference(spm,[status(thm)],[c_0_62,c_0_76]) ).
cnf(c_0_82,plain,
( is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))
| ~ axiom_m5 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_83,plain,
axiom_m5,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m5]) ).
cnf(c_0_84,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79])]) ).
cnf(c_0_85,plain,
( is_a_theorem(and(X1,and(X2,X3)))
| ~ is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_80,c_0_45]) ).
cnf(c_0_86,plain,
and(necessarily(implies(X1,X2)),strict_equiv(X1,X2)) = strict_equiv(X1,X2),
inference(spm,[status(thm)],[c_0_81,c_0_46]) ).
cnf(c_0_87,plain,
is_a_theorem(necessarily(implies(and(necessarily(implies(X1,X2)),necessarily(implies(X2,X3))),necessarily(implies(X1,X3))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_83])]) ).
cnf(c_0_88,plain,
not(and(not(X1),X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_84,c_0_67]) ).
cnf(c_0_89,plain,
( is_a_theorem(and(necessarily(implies(X1,X2)),and(strict_equiv(X1,X2),X3)))
| ~ is_a_theorem(strict_equiv(X1,X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_90,plain,
strict_equiv(X1,X1) = necessarily(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_46,c_0_71]) ).
cnf(c_0_91,plain,
is_a_theorem(necessarily(implies(X1,X1))),
inference(rw,[status(thm)],[c_0_60,c_0_71]) ).
cnf(c_0_92,plain,
( is_a_theorem(necessarily(implies(X1,X2)))
| ~ is_a_theorem(and(necessarily(implies(X1,X3)),necessarily(implies(X3,X2)))) ),
inference(spm,[status(thm)],[c_0_75,c_0_87]) ).
cnf(c_0_93,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(spm,[status(thm)],[c_0_84,c_0_88]) ).
cnf(c_0_94,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(and(X2,X1)) ),
inference(spm,[status(thm)],[c_0_75,c_0_57]) ).
cnf(c_0_95,plain,
( is_a_theorem(and(necessarily(implies(X1,X1)),X2))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_81]),c_0_91])]) ).
cnf(c_0_96,plain,
( is_a_theorem(necessarily(implies(X1,X2)))
| ~ is_a_theorem(and(necessarily(implies(X1,not(X3))),necessarily(implies(not(X2),X3)))) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_97,plain,
( is_a_theorem(and(X1,necessarily(implies(X2,X2))))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_98,plain,
( is_a_theorem(necessarily(implies(not(X1),X2)))
| ~ is_a_theorem(and(necessarily(implies(not(X3),X1)),necessarily(implies(X3,X2)))) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_99,plain,
( is_a_theorem(necessarily(implies(X1,X2)))
| ~ is_a_theorem(necessarily(implies(X1,not(not(X2))))) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_100,plain,
( is_a_theorem(necessarily(implies(not(not(X1)),X2)))
| ~ is_a_theorem(necessarily(implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_98,c_0_95]) ).
cnf(c_0_101,plain,
is_a_theorem(necessarily(implies(and(not(not(X1)),X2),X1))),
inference(spm,[status(thm)],[c_0_99,c_0_61]) ).
cnf(c_0_102,plain,
( is_a_theorem(strict_equiv(X1,not(X2)))
| ~ is_a_theorem(necessarily(implies(not(X1),X2)))
| ~ is_a_theorem(necessarily(implies(X1,not(X2)))) ),
inference(spm,[status(thm)],[c_0_56,c_0_93]) ).
cnf(c_0_103,plain,
is_a_theorem(necessarily(implies(not(X1),implies(X2,not(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_88]),c_0_93]) ).
cnf(c_0_104,plain,
implies(not(X1),X1) = not(not(X1)),
inference(spm,[status(thm)],[c_0_84,c_0_71]) ).
cnf(c_0_105,plain,
( is_a_theorem(strict_equiv(X1,not(not(X1))))
| ~ is_a_theorem(necessarily(implies(X1,not(not(X1))))) ),
inference(spm,[status(thm)],[c_0_102,c_0_91]) ).
cnf(c_0_106,plain,
is_a_theorem(necessarily(implies(not(X1),not(not(not(X1)))))),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_107,plain,
is_a_theorem(strict_equiv(not(X1),not(not(not(X1))))),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_108,plain,
not(not(not(X1))) = not(X1),
inference(spm,[status(thm)],[c_0_62,c_0_107]) ).
cnf(c_0_109,plain,
implies(X1,not(not(X2))) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_108]),c_0_84]) ).
cnf(c_0_110,plain,
( is_a_theorem(necessarily(implies(X1,X2)))
| ~ is_a_theorem(necessarily(implies(X3,X2)))
| ~ is_a_theorem(necessarily(implies(X1,X3))) ),
inference(spm,[status(thm)],[c_0_92,c_0_45]) ).
cnf(c_0_111,plain,
is_a_theorem(strict_equiv(X1,not(not(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_109]),c_0_91])]) ).
cnf(c_0_112,plain,
( is_a_theorem(necessarily(implies(X1,X2)))
| ~ is_a_theorem(necessarily(implies(X1,and(X2,X3)))) ),
inference(spm,[status(thm)],[c_0_110,c_0_61]) ).
fof(c_0_113,plain,
! [X3,X4] :
( ~ op_equiv
| equiv(X3,X4) = and(implies(X3,X4),implies(X4,X3)) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])])])]) ).
cnf(c_0_114,plain,
not(not(X1)) = X1,
inference(spm,[status(thm)],[c_0_62,c_0_111]) ).
cnf(c_0_115,plain,
( is_a_theorem(necessarily(implies(not(X1),X2)))
| ~ is_a_theorem(necessarily(implies(not(and(X2,X3)),X1))) ),
inference(spm,[status(thm)],[c_0_112,c_0_93]) ).
fof(c_0_116,plain,
! [X3,X4] :
( ( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X3,X4))
| X3 = X4 )
& ( 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(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_of_equivalents])])])])])])]) ).
cnf(c_0_117,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_118,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[s1_0_op_equiv]) ).
cnf(c_0_119,plain,
not(and(X1,X2)) = implies(X1,not(X2)),
inference(spm,[status(thm)],[c_0_84,c_0_114]) ).
cnf(c_0_120,plain,
is_a_theorem(necessarily(implies(not(X1),not(and(X1,X2))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_91]),c_0_93]) ).
cnf(c_0_121,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2))
| ~ substitution_of_equivalents ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_122,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[substitution_of_equivalents]) ).
cnf(c_0_123,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_118])]) ).
cnf(c_0_124,plain,
and(X1,X2) = not(implies(X1,not(X2))),
inference(spm,[status(thm)],[c_0_114,c_0_119]) ).
cnf(c_0_125,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_75,c_0_120]) ).
cnf(c_0_126,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_122])]) ).
cnf(c_0_127,plain,
equiv(X1,X2) = not(implies(implies(X1,X2),not(implies(X2,X1)))),
inference(rw,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_128,plain,
( is_a_theorem(not(and(and(not(X1),X2),X3)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_125,c_0_88]) ).
cnf(c_0_129,plain,
and(X1,and(X2,X1)) = and(X2,X1),
inference(spm,[status(thm)],[c_0_81,c_0_67]) ).
cnf(c_0_130,plain,
( X1 = X2
| ~ is_a_theorem(not(implies(implies(X1,X2),not(implies(X2,X1))))) ),
inference(rw,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_131,plain,
( is_a_theorem(not(implies(X1,not(X2))))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(rw,[status(thm)],[c_0_45,c_0_124]) ).
cnf(c_0_132,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(not(X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_104]),c_0_71]),c_0_88]) ).
fof(c_0_133,plain,
! [X3,X4] :
( ~ op_or
| or(X3,X4) = not(and(not(X3),not(X4))) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])])]) ).
cnf(c_0_134,plain,
implies(and(X1,not(X2)),X2) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_129]),c_0_84]) ).
cnf(c_0_135,plain,
( X1 = X2
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_136,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X2) ),
inference(rw,[status(thm)],[c_0_132,c_0_114]) ).
fof(c_0_137,plain,
! [X5] :
( ( ~ r1
| is_a_theorem(implies(or(X5,X5),X5)) )
& ( ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))
| r1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r1])])])])])]) ).
cnf(c_0_138,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_139,plain,
op_or,
inference(split_conjunct,[status(thm)],[s1_0_op_or]) ).
cnf(c_0_140,plain,
is_a_theorem(necessarily(implies(not(not(X1)),implies(X2,X1)))),
inference(spm,[status(thm)],[c_0_120,c_0_88]) ).
cnf(c_0_141,plain,
implies(not(X1),implies(X2,X1)) = implies(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_124]),c_0_114]),c_0_93]) ).
cnf(c_0_142,plain,
implies(not(X1),not(X2)) = implies(X2,X1),
inference(rw,[status(thm)],[c_0_88,c_0_119]) ).
cnf(c_0_143,plain,
( X1 = X2
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_144,plain,
( r1
| ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0)) ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_145,plain,
or(X1,X2) = implies(not(X1),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_138,c_0_84]),c_0_139])]) ).
cnf(c_0_146,plain,
( is_a_theorem(necessarily(implies(X1,implies(X2,X3))))
| ~ is_a_theorem(necessarily(implies(X1,not(not(X3))))) ),
inference(spm,[status(thm)],[c_0_110,c_0_140]) ).
cnf(c_0_147,plain,
implies(X1,implies(X1,X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_114]) ).
cnf(c_0_148,plain,
( X1 = X2
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_143,c_0_136]) ).
cnf(c_0_149,plain,
( r1
| ~ is_a_theorem(implies(implies(not(esk45_0),esk45_0),esk45_0)) ),
inference(rw,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_150,plain,
( is_a_theorem(necessarily(implies(X1,implies(X2,X3))))
| ~ is_a_theorem(necessarily(implies(X1,X3))) ),
inference(rw,[status(thm)],[c_0_146,c_0_109]) ).
cnf(c_0_151,plain,
implies(not(X1),X1) = X1,
inference(rw,[status(thm)],[c_0_104,c_0_114]) ).
cnf(c_0_152,plain,
( implies(X1,X2) = X2
| ~ is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_153,plain,
is_a_theorem(necessarily(implies(and(and(X1,implies(X2,X3)),implies(X3,X2)),and(X1,equiv(X2,X3))))),
inference(spm,[status(thm)],[c_0_65,c_0_123]) ).
cnf(c_0_154,plain,
not(and(X1,implies(X2,X3))) = implies(X1,and(X2,not(X3))),
inference(spm,[status(thm)],[c_0_84,c_0_84]) ).
cnf(c_0_155,plain,
( is_a_theorem(implies(or(X1,X1),X1))
| ~ r1 ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_156,plain,
( r1
| ~ is_a_theorem(implies(not(not(esk45_0)),esk45_0)) ),
inference(rw,[status(thm)],[c_0_149,c_0_104]) ).
cnf(c_0_157,plain,
( is_a_theorem(necessarily(implies(X1,X2)))
| ~ is_a_theorem(necessarily(X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_141]) ).
cnf(c_0_158,plain,
is_a_theorem(necessarily(implies(strict_equiv(X1,X2),necessarily(implies(X1,X1))))),
inference(spm,[status(thm)],[c_0_87,c_0_46]) ).
cnf(c_0_159,plain,
( implies(X1,X2) = X2
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_152,c_0_136]) ).
cnf(c_0_160,plain,
is_a_theorem(necessarily(implies(and(implies(X1,X2),and(X3,implies(X2,X1))),and(X3,equiv(X2,X1))))),
inference(rw,[status(thm)],[c_0_153,c_0_67]) ).
cnf(c_0_161,plain,
implies(implies(X1,X2),and(X1,not(X2))) = not(implies(X1,X2)),
inference(spm,[status(thm)],[c_0_154,c_0_71]) ).
cnf(c_0_162,plain,
( is_a_theorem(implies(implies(not(X1),X1),X1))
| ~ r1 ),
inference(rw,[status(thm)],[c_0_155,c_0_145]) ).
cnf(c_0_163,plain,
( r1
| ~ is_a_theorem(implies(not(esk45_0),not(esk45_0))) ),
inference(rw,[status(thm)],[c_0_156,c_0_93]) ).
cnf(c_0_164,plain,
is_a_theorem(necessarily(implies(X1,implies(X2,X2)))),
inference(spm,[status(thm)],[c_0_157,c_0_91]) ).
cnf(c_0_165,plain,
is_a_theorem(necessarily(implies(strict_equiv(X1,X2),necessarily(implies(X2,X2))))),
inference(spm,[status(thm)],[c_0_158,c_0_73]) ).
cnf(c_0_166,plain,
strict_equiv(X1,X2) = not(implies(necessarily(implies(X1,X2)),not(necessarily(implies(X2,X1))))),
inference(rw,[status(thm)],[c_0_46,c_0_124]) ).
cnf(c_0_167,plain,
( implies(X1,X2) = X2
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_159,c_0_91]) ).
fof(c_0_168,negated_conjecture,
~ and_2,
inference(assume_negation,[status(cth)],[hilbert_and_2]) ).
cnf(c_0_169,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(necessarily(implies(not(X1),X2)))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_75,c_0_93]) ).
cnf(c_0_170,plain,
is_a_theorem(necessarily(implies(and(not(not(X1)),and(X2,implies(X1,not(X1)))),and(X2,equiv(X1,not(X1)))))),
inference(spm,[status(thm)],[c_0_160,c_0_104]) ).
cnf(c_0_171,plain,
implies(X1,not(X1)) = not(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_151]),c_0_71]) ).
cnf(c_0_172,plain,
not(not(implies(X1,X2))) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_108,c_0_88]) ).
cnf(c_0_173,plain,
( is_a_theorem(implies(not(not(X1)),X1))
| ~ r1 ),
inference(rw,[status(thm)],[c_0_162,c_0_104]) ).
cnf(c_0_174,plain,
( r1
| ~ is_a_theorem(implies(esk45_0,esk45_0)) ),
inference(rw,[status(thm)],[c_0_163,c_0_142]) ).
cnf(c_0_175,plain,
( is_a_theorem(implies(X1,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_75,c_0_164]) ).
cnf(c_0_176,plain,
is_a_theorem(necessarily(implies(not(necessarily(implies(X1,X1))),implies(necessarily(implies(X2,X1)),not(necessarily(implies(X1,X2))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_165,c_0_142]),c_0_166]),c_0_114]) ).
cnf(c_0_177,plain,
( implies(not(X1),X2) = X1
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_167]) ).
fof(c_0_178,plain,
! [X3,X4] :
( ( ~ and_2
| is_a_theorem(implies(and(X3,X4),X4)) )
& ( ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0))
| and_2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_2])])])])])]) ).
fof(c_0_179,negated_conjecture,
~ and_2,
inference(fof_simplification,[status(thm)],[c_0_168]) ).
cnf(c_0_180,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(necessarily(implies(not(X1),not(X2))))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_169,c_0_114]) ).
cnf(c_0_181,plain,
is_a_theorem(necessarily(implies(not(implies(X1,implies(X2,X1))),not(implies(X2,implies(X1,X1)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_114]),c_0_171]),c_0_124]),c_0_109]),c_0_124]),c_0_172]),c_0_124]),c_0_127]),c_0_171]),c_0_104]),c_0_114]),c_0_142]),c_0_114]) ).
cnf(c_0_182,plain,
( is_a_theorem(implies(not(X1),not(X1)))
| ~ r1 ),
inference(rw,[status(thm)],[c_0_173,c_0_93]) ).
cnf(c_0_183,plain,
( r1
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_174,c_0_175]) ).
cnf(c_0_184,plain,
is_a_theorem(necessarily(necessarily(implies(X1,X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_91])]) ).
cnf(c_0_185,plain,
( and_2
| ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0)) ),
inference(split_conjunct,[status(thm)],[c_0_178]) ).
cnf(c_0_186,negated_conjecture,
~ and_2,
inference(split_conjunct,[status(thm)],[c_0_179]) ).
cnf(c_0_187,plain,
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ is_a_theorem(implies(X2,implies(X1,X1))) ),
inference(spm,[status(thm)],[c_0_180,c_0_181]) ).
cnf(c_0_188,plain,
( is_a_theorem(implies(X1,X1))
| ~ r1 ),
inference(rw,[status(thm)],[c_0_182,c_0_142]) ).
cnf(c_0_189,plain,
r1,
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_190,plain,
~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0)),
inference(sr,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_191,plain,
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ is_a_theorem(implies(X1,X1)) ),
inference(spm,[status(thm)],[c_0_187,c_0_167]) ).
cnf(c_0_192,plain,
is_a_theorem(implies(X1,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_188,c_0_189])]) ).
cnf(c_0_193,plain,
~ is_a_theorem(implies(not(esk17_0),implies(esk16_0,not(esk17_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_190,c_0_124]),c_0_93]) ).
cnf(c_0_194,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_191,c_0_192])]) ).
cnf(c_0_195,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_193,c_0_194])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL556+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 2 23:16:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.36/23.41 eprover: CPU time limit exceeded, terminating
% 0.36/23.42 eprover: CPU time limit exceeded, terminating
% 0.36/23.43 eprover: CPU time limit exceeded, terminating
% 0.36/23.47 eprover: CPU time limit exceeded, terminating
% 0.41/30.60 # Running protocol protocol_eprover_2d86bd69119e7e9cc4417c0ee581499eaf828bb2 for 23 seconds:
% 0.41/30.60 # SinE strategy is GSinE(CountFormulas,,1.1,,02,500,1.0)
% 0.41/30.60 # Preprocessing time : 0.015 s
% 0.41/30.60
% 0.41/30.60 # Failure: Out of unprocessed clauses!
% 0.41/30.60 # OLD status GaveUp
% 0.41/30.60 # Parsed axioms : 77
% 0.41/30.60 # Removed by relevancy pruning/SinE : 75
% 0.41/30.60 # Initial clauses : 3
% 0.41/30.60 # Removed in clause preprocessing : 0
% 0.41/30.60 # Initial clauses in saturation : 3
% 0.41/30.60 # Processed clauses : 3
% 0.41/30.60 # ...of these trivial : 0
% 0.41/30.60 # ...subsumed : 1
% 0.41/30.60 # ...remaining for further processing : 2
% 0.41/30.60 # Other redundant clauses eliminated : 0
% 0.41/30.60 # Clauses deleted for lack of memory : 0
% 0.41/30.60 # Backward-subsumed : 0
% 0.41/30.60 # Backward-rewritten : 0
% 0.41/30.60 # Generated clauses : 0
% 0.41/30.60 # ...of the previous two non-trivial : 0
% 0.41/30.60 # Contextual simplify-reflections : 0
% 0.41/30.60 # Paramodulations : 0
% 0.41/30.60 # Factorizations : 0
% 0.41/30.60 # Equation resolutions : 0
% 0.41/30.60 # Current number of processed clauses : 2
% 0.41/30.60 # Positive orientable unit clauses : 0
% 0.41/30.60 # Positive unorientable unit clauses: 0
% 0.41/30.60 # Negative unit clauses : 2
% 0.41/30.60 # Non-unit-clauses : 0
% 0.41/30.60 # Current number of unprocessed clauses: 0
% 0.41/30.60 # ...number of literals in the above : 0
% 0.41/30.60 # Current number of archived formulas : 0
% 0.41/30.60 # Current number of archived clauses : 0
% 0.41/30.60 # Clause-clause subsumption calls (NU) : 0
% 0.41/30.60 # Rec. Clause-clause subsumption calls : 0
% 0.41/30.60 # Non-unit clause-clause subsumptions : 0
% 0.41/30.60 # Unit Clause-clause subsumption calls : 0
% 0.41/30.60 # Rewrite failures with RHS unbound : 0
% 0.41/30.60 # BW rewrite match attempts : 0
% 0.41/30.60 # BW rewrite match successes : 0
% 0.41/30.60 # Condensation attempts : 0
% 0.41/30.60 # Condensation successes : 0
% 0.41/30.60 # Termbank termtop insertions : 786
% 0.41/30.60
% 0.41/30.60 # -------------------------------------------------
% 0.41/30.60 # User time : 0.012 s
% 0.41/30.60 # System time : 0.003 s
% 0.41/30.60 # Total time : 0.015 s
% 0.41/30.60 # Maximum resident set size: 2844 pages
% 0.41/30.60 # Running protocol protocol_eprover_230b6c199cce1dcf6700db59e75a93feb83d1bd9 for 23 seconds:
% 0.41/30.60 # SinE strategy is GSinE(CountFormulas,hypos,1.1,,01,20000,1.0)
% 0.41/30.60 # Preprocessing time : 0.015 s
% 0.41/30.60
% 0.41/30.60 # Failure: Out of unprocessed clauses!
% 0.41/30.60 # OLD status GaveUp
% 0.41/30.60 # Parsed axioms : 77
% 0.41/30.60 # Removed by relevancy pruning/SinE : 75
% 0.41/30.60 # Initial clauses : 3
% 0.41/30.60 # Removed in clause preprocessing : 0
% 0.41/30.60 # Initial clauses in saturation : 3
% 0.41/30.60 # Processed clauses : 3
% 0.41/30.60 # ...of these trivial : 0
% 0.41/30.60 # ...subsumed : 1
% 0.41/30.60 # ...remaining for further processing : 2
% 0.41/30.60 # Other redundant clauses eliminated : 0
% 0.41/30.60 # Clauses deleted for lack of memory : 0
% 0.41/30.60 # Backward-subsumed : 0
% 0.41/30.60 # Backward-rewritten : 0
% 0.41/30.60 # Generated clauses : 0
% 0.41/30.60 # ...of the previous two non-trivial : 0
% 0.41/30.60 # Contextual simplify-reflections : 0
% 0.41/30.60 # Paramodulations : 0
% 0.41/30.60 # Factorizations : 0
% 0.41/30.60 # Equation resolutions : 0
% 0.41/30.60 # Current number of processed clauses : 2
% 0.41/30.60 # Positive orientable unit clauses : 0
% 0.41/30.60 # Positive unorientable unit clauses: 0
% 0.41/30.60 # Negative unit clauses : 1
% 0.41/30.60 # Non-unit-clauses : 1
% 0.41/30.60 # Current number of unprocessed clauses: 0
% 0.41/30.60 # ...number of literals in the above : 0
% 0.41/30.60 # Current number of archived formulas : 0
% 0.41/30.60 # Current number of archived clauses : 0
% 0.41/30.60 # Clause-clause subsumption calls (NU) : 0
% 0.41/30.60 # Rec. Clause-clause subsumption calls : 0
% 0.41/30.60 # Non-unit clause-clause subsumptions : 0
% 0.41/30.60 # Unit Clause-clause subsumption calls : 0
% 0.41/30.60 # Rewrite failures with RHS unbound : 0
% 0.41/30.60 # BW rewrite match attempts : 0
% 0.41/30.60 # BW rewrite match successes : 0
% 0.41/30.60 # Condensation attempts : 0
% 0.41/30.60 # Condensation successes : 0
% 0.41/30.60 # Termbank termtop insertions : 786
% 0.41/30.60
% 0.41/30.60 # -------------------------------------------------
% 0.41/30.60 # User time : 0.013 s
% 0.41/30.60 # System time : 0.002 s
% 0.41/30.60 # Total time : 0.015 s
% 0.41/30.60 # Maximum resident set size: 2848 pages
% 0.41/30.60 # Running protocol protocol_eprover_48e494e00e0717ec2eabf59b73b2d711334607de for 23 seconds:
% 0.41/30.60 # SinE strategy is GSinE(CountFormulas,hypos,1.1,,03,20000,1.0)
% 0.41/30.60 # Preprocessing time : 0.015 s
% 0.41/30.60
% 0.41/30.60 # Failure: Out of unprocessed clauses!
% 0.41/30.60 # OLD status GaveUp
% 0.41/30.60 # Parsed axioms : 77
% 0.41/30.60 # Removed by relevancy pruning/SinE : 75
% 0.41/30.60 # Initial clauses : 3
% 0.41/30.60 # Removed in clause preprocessing : 0
% 0.41/30.60 # Initial clauses in saturation : 3
% 0.41/30.60 # Processed clauses : 3
% 0.41/30.60 # ...of these trivial : 0
% 0.41/30.60 # ...subsumed : 1
% 0.41/30.60 # ...remaining for further processing : 2
% 0.41/30.60 # Other redundant clauses eliminated : 0
% 0.41/30.60 # Clauses deleted for lack of memory : 0
% 0.41/30.60 # Backward-subsumed : 0
% 0.41/30.60 # Backward-rewritten : 0
% 0.41/30.60 # Generated clauses : 0
% 0.41/30.60 # ...of the previous two non-trivial : 0
% 0.41/30.60 # Contextual simplify-reflections : 0
% 0.41/30.60 # Paramodulations : 0
% 0.41/30.60 # Factorizations : 0
% 0.41/30.60 # Equation resolutions : 0
% 0.41/30.60 # Current number of processed clauses : 2
% 0.41/30.60 # Positive orientable unit clauses : 0
% 0.41/30.60 # Positive unorientable unit clauses: 0
% 0.41/30.60 # Negative unit clauses : 2
% 0.41/30.60 # Non-unit-clauses : 0
% 0.41/30.60 # Current number of unprocessed clauses: 0
% 0.41/30.60 # ...number of literals in the above : 0
% 0.41/30.60 # Current number of archived formulas : 0
% 0.41/30.60 # Current number of archived clauses : 0
% 0.41/30.60 # Clause-clause subsumption calls (NU) : 0
% 0.41/30.60 # Rec. Clause-clause subsumption calls : 0
% 0.41/30.60 # Non-unit clause-clause subsumptions : 0
% 0.41/30.60 # Unit Clause-clause subsumption calls : 0
% 0.41/30.60 # Rewrite failures with RHS unbound : 0
% 0.41/30.60 # BW rewrite match attempts : 0
% 0.41/30.60 # BW rewrite match successes : 0
% 0.41/30.60 # Condensation attempts : 0
% 0.41/30.60 # Condensation successes : 0
% 0.41/30.60 # Termbank termtop insertions : 786
% 0.41/30.60
% 0.41/30.60 # -------------------------------------------------
% 0.41/30.60 # User time : 0.012 s
% 0.41/30.60 # System time : 0.003 s
% 0.41/30.60 # Total time : 0.015 s
% 0.41/30.60 # Maximum resident set size: 2904 pages
% 0.41/30.60 # Running protocol protocol_eprover_33aa8a325940064c53b389b41203bb48a5cb5006 for 23 seconds:
% 0.41/30.60
% 0.41/30.60 # Failure: Resource limit exceeded (time)
% 0.41/30.60 # OLD status Res
% 0.41/30.60 # Preprocessing time : 0.022 s
% 0.41/30.60 # Running protocol protocol_eprover_260890dcdd2d907655d788d68835201aeffdef4a for 23 seconds:
% 0.41/30.60 # SinE strategy is GSinE(CountFormulas,,1.5,,03,100,1.0)
% 0.41/30.60 # Preprocessing time : 0.016 s
% 0.41/30.60
% 0.41/30.60 # Failure: Out of unprocessed clauses!
% 0.41/30.60 # OLD status GaveUp
% 0.41/30.60 # Parsed axioms : 77
% 0.41/30.60 # Removed by relevancy pruning/SinE : 75
% 0.41/30.60 # Initial clauses : 3
% 0.41/30.60 # Removed in clause preprocessing : 0
% 0.41/30.60 # Initial clauses in saturation : 3
% 0.41/30.60 # Processed clauses : 3
% 0.41/30.60 # ...of these trivial : 0
% 0.41/30.60 # ...subsumed : 1
% 0.41/30.60 # ...remaining for further processing : 2
% 0.41/30.60 # Other redundant clauses eliminated : 0
% 0.41/30.60 # Clauses deleted for lack of memory : 0
% 0.41/30.60 # Backward-subsumed : 0
% 0.41/30.60 # Backward-rewritten : 0
% 0.41/30.60 # Generated clauses : 0
% 0.41/30.60 # ...of the previous two non-trivial : 0
% 0.41/30.60 # Contextual simplify-reflections : 0
% 0.41/30.60 # Paramodulations : 0
% 0.41/30.60 # Factorizations : 0
% 0.41/30.60 # Equation resolutions : 0
% 0.41/30.60 # Current number of processed clauses : 2
% 0.41/30.60 # Positive orientable unit clauses : 0
% 0.41/30.60 # Positive unorientable unit clauses: 0
% 0.41/30.60 # Negative unit clauses : 2
% 0.41/30.60 # Non-unit-clauses : 0
% 0.41/30.60 # Current number of unprocessed clauses: 0
% 0.41/30.60 # ...number of literals in the above : 0
% 0.41/30.60 # Current number of archived formulas : 0
% 0.41/30.60 # Current number of archived clauses : 0
% 0.41/30.60 # Clause-clause subsumption calls (NU) : 0
% 0.41/30.60 # Rec. Clause-clause subsumption calls : 0
% 0.41/30.60 # Non-unit clause-clause subsumptions : 0
% 0.41/30.60 # Unit Clause-clause subsumption calls : 0
% 0.41/30.60 # Rewrite failures with RHS unbound : 0
% 0.41/30.60 # BW rewrite match attempts : 0
% 0.41/30.60 # BW rewrite match successes : 0
% 0.41/30.60 # Condensation attempts : 0
% 0.41/30.60 # Condensation successes : 0
% 0.41/30.60 # Termbank termtop insertions : 786
% 0.41/30.60
% 0.41/30.60 # -------------------------------------------------
% 0.41/30.60 # User time : 0.014 s
% 0.41/30.60 # System time : 0.002 s
% 0.41/30.60 # Total time : 0.016 s
% 0.41/30.60 # Maximum resident set size: 2848 pages
% 0.41/30.60 # Running protocol protocol_eprover_9a428cb4e1feff5dec19b8494e78e7f0e8ede446 for 23 seconds:
% 0.41/30.60 # Preprocessing time : 0.024 s
% 0.41/30.60
% 0.41/30.60 # Proof found!
% 0.41/30.60 # SZS status Theorem
% 0.41/30.60 # SZS output start CNFRefutation
% See solution above
% 0.41/30.60 # Proof object total steps : 196
% 0.41/30.60 # Proof object clause steps : 147
% 0.41/30.60 # Proof object formula steps : 49
% 0.41/30.60 # Proof object conjectures : 4
% 0.41/30.60 # Proof object clause conjectures : 1
% 0.41/30.60 # Proof object formula conjectures : 3
% 0.41/30.60 # Proof object initial clauses used : 32
% 0.41/30.60 # Proof object initial formulas used : 31
% 0.41/30.60 # Proof object generating inferences : 74
% 0.41/30.60 # Proof object simplifying inferences : 112
% 0.41/30.60 # Training examples: 0 positive, 0 negative
% 0.41/30.60 # Parsed axioms : 77
% 0.41/30.60 # Removed by relevancy pruning/SinE : 0
% 0.41/30.60 # Initial clauses : 135
% 0.41/30.60 # Removed in clause preprocessing : 0
% 0.41/30.60 # Initial clauses in saturation : 135
% 0.41/30.60 # Processed clauses : 9273
% 0.41/30.60 # ...of these trivial : 834
% 0.41/30.60 # ...subsumed : 6021
% 0.41/30.60 # ...remaining for further processing : 2418
% 0.41/30.60 # Other redundant clauses eliminated : 0
% 0.41/30.60 # Clauses deleted for lack of memory : 143677
% 0.41/30.60 # Backward-subsumed : 134
% 0.41/30.60 # Backward-rewritten : 1320
% 0.41/30.60 # Generated clauses : 431041
% 0.41/30.60 # ...of the previous two non-trivial : 392476
% 0.41/30.60 # Contextual simplify-reflections : 0
% 0.41/30.60 # Paramodulations : 431041
% 0.41/30.60 # Factorizations : 0
% 0.41/30.60 # Equation resolutions : 0
% 0.41/30.60 # Current number of processed clauses : 964
% 0.41/30.60 # Positive orientable unit clauses : 234
% 0.41/30.60 # Positive unorientable unit clauses: 13
% 0.41/30.60 # Negative unit clauses : 4
% 0.41/30.60 # Non-unit-clauses : 713
% 0.41/30.60 # Current number of unprocessed clauses: 80741
% 0.41/30.60 # ...number of literals in the above : 222643
% 0.41/30.60 # Current number of archived formulas : 0
% 0.41/30.60 # Current number of archived clauses : 1454
% 0.41/30.60 # Clause-clause subsumption calls (NU) : 184735
% 0.41/30.60 # Rec. Clause-clause subsumption calls : 165733
% 0.41/30.60 # Non-unit clause-clause subsumptions : 5905
% 0.41/30.60 # Unit Clause-clause subsumption calls : 10488
% 0.41/30.60 # Rewrite failures with RHS unbound : 0
% 0.41/30.60 # BW rewrite match attempts : 109123
% 0.41/30.60 # BW rewrite match successes : 2291
% 0.41/30.60 # Condensation attempts : 0
% 0.41/30.60 # Condensation successes : 0
% 0.41/30.60 # Termbank termtop insertions : 13249601
% 0.41/30.60
% 0.41/30.60 # -------------------------------------------------
% 0.41/30.60 # User time : 6.882 s
% 0.41/30.60 # System time : 0.102 s
% 0.41/30.60 # Total time : 6.984 s
% 0.41/30.60 # Maximum resident set size: 164460 pages
% 0.41/46.44 eprover: CPU time limit exceeded, terminating
% 0.41/46.45 eprover: CPU time limit exceeded, terminating
% 0.41/46.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.46 eprover: No such file or directory
% 0.41/46.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.46 eprover: No such file or directory
% 0.41/46.46 eprover: CPU time limit exceeded, terminating
% 0.41/46.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.41/46.46 eprover: No such file or directory
% 0.41/46.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.46 eprover: No such file or directory
% 0.41/46.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.41/46.47 eprover: No such file or directory
% 0.41/46.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.47 eprover: No such file or directory
% 0.41/46.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.41/46.47 eprover: No such file or directory
% 0.41/46.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.47 eprover: No such file or directory
% 0.41/46.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.41/46.48 eprover: No such file or directory
% 0.41/46.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.48 eprover: No such file or directory
% 0.41/46.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.48 eprover: No such file or directory
% 0.41/46.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.41/46.48 eprover: No such file or directory
% 0.41/46.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.48 eprover: No such file or directory
% 0.41/46.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.41/46.48 eprover: No such file or directory
% 0.41/46.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.48 eprover: No such file or directory
% 0.41/46.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.48 eprover: No such file or directory
% 0.41/46.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.41/46.49 eprover: No such file or directory
% 0.41/46.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.49 eprover: No such file or directory
% 0.41/46.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.49 eprover: No such file or directory
% 0.41/46.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.41/46.49 eprover: No such file or directory
% 0.41/46.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.49 eprover: No such file or directory
% 0.41/46.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.50 eprover: No such file or directory
% 0.41/46.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.41/46.50 eprover: No such file or directory
% 0.41/46.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.50 eprover: No such file or directory
% 0.41/46.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.50 eprover: No such file or directory
% 0.41/46.51 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.51 eprover: No such file or directory
% 0.41/46.51 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.51 eprover: No such file or directory
%------------------------------------------------------------------------------