TSTP Solution File: LCL555+1 by E---3.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : LCL555+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 10:45:22 EDT 2024
% Result : Theorem 3.21s 0.89s
% Output : CNFRefutation 3.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 24
% Syntax : Number of formulae : 114 ( 67 unt; 0 def)
% Number of atoms : 208 ( 49 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 156 ( 62 ~; 63 |; 16 &)
% ( 9 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 13 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 19 con; 0-2 aty)
% Number of variables : 177 ( 14 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',op_strict_equiv) ).
fof(substitution_strict_equiv,axiom,
( substitution_strict_equiv
<=> ! [X1,X2] :
( is_a_theorem(strict_equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',substitution_strict_equiv) ).
fof(s1_0_op_strict_equiv,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',s1_0_op_strict_equiv) ).
fof(adjunction,axiom,
( adjunction
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(X2) )
=> is_a_theorem(and(X1,X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',adjunction) ).
fof(s1_0_substitution_strict_equiv,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',s1_0_substitution_strict_equiv) ).
fof(s1_0_adjunction,axiom,
adjunction,
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',s1_0_adjunction) ).
fof(axiom_m4,axiom,
( axiom_m4
<=> ! [X1] : is_a_theorem(strict_implies(X1,and(X1,X1))) ),
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',axiom_m4) ).
fof(axiom_m2,axiom,
( axiom_m2
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',axiom_m2) ).
fof(axiom_m1,axiom,
( axiom_m1
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))) ),
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',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/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',axiom_m3) ).
fof(s1_0_axiom_m4,axiom,
axiom_m4,
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',s1_0_axiom_m4) ).
fof(s1_0_axiom_m2,axiom,
axiom_m2,
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',s1_0_axiom_m2) ).
fof(s1_0_axiom_m1,axiom,
axiom_m1,
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',s1_0_axiom_m1) ).
fof(s1_0_axiom_m3,axiom,
axiom_m3,
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',s1_0_axiom_m3) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',op_implies_and) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',hilbert_op_implies_and) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X1,X2] : strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',op_strict_implies) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',s1_0_op_strict_implies) ).
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/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',modus_ponens_strict_implies) ).
fof(hilbert_and_1,conjecture,
and_1,
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',hilbert_and_1) ).
fof(s1_0_modus_ponens_strict_implies,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',s1_0_modus_ponens_strict_implies) ).
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/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',axiom_m5) ).
fof(and_1,axiom,
( and_1
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',and_1) ).
fof(s1_0_axiom_m5,axiom,
axiom_m5,
file('/export/starexec/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p',s1_0_axiom_m5) ).
fof(c_0_24,plain,
! [X209,X210] :
( ~ op_strict_equiv
| strict_equiv(X209,X210) = and(strict_implies(X209,X210),strict_implies(X210,X209)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_equiv])])])]) ).
fof(c_0_25,plain,
! [X137,X138] :
( ( ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(X137,X138))
| X137 = X138 )
& ( is_a_theorem(strict_equiv(esk61_0,esk62_0))
| substitution_strict_equiv )
& ( esk61_0 != esk62_0
| substitution_strict_equiv ) ),
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_strict_equiv])])])])])]) ).
cnf(c_0_26,plain,
( strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1))
| ~ op_strict_equiv ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_27,plain,
op_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_equiv]) ).
fof(c_0_28,plain,
! [X133,X134] :
( ( ~ adjunction
| ~ is_a_theorem(X133)
| ~ is_a_theorem(X134)
| is_a_theorem(and(X133,X134)) )
& ( 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(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[adjunction])])])])])]) ).
cnf(c_0_29,plain,
( X1 = X2
| ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
substitution_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_substitution_strict_equiv]) ).
cnf(c_0_31,plain,
strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
cnf(c_0_32,plain,
( is_a_theorem(and(X1,X2))
| ~ adjunction
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
adjunction,
inference(split_conjunct,[status(thm)],[s1_0_adjunction]) ).
fof(c_0_34,plain,
! [X183] :
( ( ~ axiom_m4
| is_a_theorem(strict_implies(X183,and(X183,X183))) )
& ( ~ is_a_theorem(strict_implies(esk84_0,and(esk84_0,esk84_0)))
| axiom_m4 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m4])])])])]) ).
fof(c_0_35,plain,
! [X173,X174] :
( ( ~ axiom_m2
| is_a_theorem(strict_implies(and(X173,X174),X173)) )
& ( ~ is_a_theorem(strict_implies(and(esk79_0,esk80_0),esk79_0))
| axiom_m2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m2])])])])]) ).
fof(c_0_36,plain,
! [X169,X170] :
( ( ~ axiom_m1
| is_a_theorem(strict_implies(and(X169,X170),and(X170,X169))) )
& ( ~ is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0)))
| axiom_m1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m1])])])])]) ).
fof(c_0_37,plain,
! [X177,X178,X179] :
( ( ~ axiom_m3
| is_a_theorem(strict_implies(and(and(X177,X178),X179),and(X177,and(X178,X179)))) )
& ( ~ is_a_theorem(strict_implies(and(and(esk81_0,esk82_0),esk83_0),and(esk81_0,and(esk82_0,esk83_0))))
| axiom_m3 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m3])])])])]) ).
cnf(c_0_38,plain,
( X1 = X2
| ~ is_a_theorem(and(strict_implies(X1,X2),strict_implies(X2,X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_39,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_32,c_0_33])]) ).
cnf(c_0_40,plain,
( is_a_theorem(strict_implies(X1,and(X1,X1)))
| ~ axiom_m4 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
axiom_m4,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m4]) ).
cnf(c_0_42,plain,
( is_a_theorem(strict_implies(and(X1,X2),X1))
| ~ axiom_m2 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
axiom_m2,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m2]) ).
cnf(c_0_44,plain,
( is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))
| ~ axiom_m1 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,plain,
axiom_m1,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m1]) ).
cnf(c_0_46,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_37]) ).
cnf(c_0_47,plain,
axiom_m3,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m3]) ).
cnf(c_0_48,plain,
( X1 = X2
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_49,plain,
is_a_theorem(strict_implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).
cnf(c_0_50,plain,
is_a_theorem(strict_implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
cnf(c_0_51,plain,
is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).
fof(c_0_52,plain,
! [X121,X122] :
( ~ op_implies_and
| implies(X121,X122) = not(and(X121,not(X122))) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])]) ).
cnf(c_0_53,plain,
is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
cnf(c_0_54,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]) ).
cnf(c_0_55,plain,
and(X1,X2) = and(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_51]),c_0_51])]) ).
cnf(c_0_56,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_57,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_0_58,plain,
is_a_theorem(strict_implies(and(X1,X2),and(X1,and(X1,X2)))),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,plain,
is_a_theorem(strict_implies(and(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_50,c_0_55]) ).
fof(c_0_60,plain,
! [X207,X208] :
( ~ op_strict_implies
| strict_implies(X207,X208) = necessarily(implies(X207,X208)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])])]) ).
cnf(c_0_61,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).
cnf(c_0_62,plain,
( and(and(X1,X2),X3) = and(X1,and(X2,X3))
| ~ is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(and(X1,X2),X3))) ),
inference(spm,[status(thm)],[c_0_48,c_0_53]) ).
cnf(c_0_63,plain,
and(X1,and(X1,X2)) = and(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_58]),c_0_59])]) ).
cnf(c_0_64,plain,
( strict_implies(X1,X2) = necessarily(implies(X1,X2))
| ~ op_strict_implies ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_65,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_0_66,plain,
not(and(not(X1),X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_61,c_0_55]) ).
cnf(c_0_67,plain,
and(X1,and(and(X1,X2),X3)) = and(and(X1,X2),X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_59])]) ).
cnf(c_0_68,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]) ).
cnf(c_0_69,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(spm,[status(thm)],[c_0_61,c_0_66]) ).
cnf(c_0_70,plain,
and(X1,and(X2,X1)) = and(X2,X1),
inference(spm,[status(thm)],[c_0_63,c_0_55]) ).
cnf(c_0_71,plain,
not(and(and(not(X1),X2),X3)) = implies(and(and(not(X1),X2),X3),X1),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_72,plain,
strict_implies(not(X1),X2) = strict_implies(not(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_68]) ).
cnf(c_0_73,plain,
and(X1,and(and(X2,X1),X3)) = and(and(X2,X1),X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_70]),c_0_59])]) ).
cnf(c_0_74,plain,
implies(and(and(not(X1),X2),not(X3)),X1) = implies(and(not(X1),X2),X3),
inference(spm,[status(thm)],[c_0_61,c_0_71]) ).
cnf(c_0_75,plain,
( X1 = not(X2)
| ~ is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_48,c_0_72]) ).
cnf(c_0_76,plain,
not(not(X1)) = implies(not(X1),X1),
inference(spm,[status(thm)],[c_0_61,c_0_54]) ).
cnf(c_0_77,plain,
is_a_theorem(strict_implies(and(and(X1,X2),X3),X2)),
inference(spm,[status(thm)],[c_0_50,c_0_73]) ).
cnf(c_0_78,plain,
strict_implies(and(and(not(X1),X2),not(X3)),X1) = strict_implies(and(not(X1),X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_74]),c_0_68]) ).
cnf(c_0_79,plain,
not(and(X1,implies(X2,X3))) = implies(X1,and(X2,not(X3))),
inference(spm,[status(thm)],[c_0_61,c_0_61]) ).
cnf(c_0_80,plain,
( implies(not(X1),X1) = X1
| ~ is_a_theorem(strict_implies(X1,implies(not(X1),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_49]),c_0_54]),c_0_76]),c_0_54]),c_0_76]) ).
cnf(c_0_81,plain,
is_a_theorem(strict_implies(and(X1,not(X1)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_55]) ).
cnf(c_0_82,plain,
( and(X1,X2) = X1
| ~ is_a_theorem(strict_implies(X1,and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_48,c_0_50]) ).
cnf(c_0_83,plain,
( and(X1,X2) = X2
| ~ is_a_theorem(strict_implies(X2,and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_48,c_0_59]) ).
fof(c_0_84,plain,
! [X129,X130] :
( ( ~ modus_ponens_strict_implies
| ~ is_a_theorem(X129)
| ~ is_a_theorem(strict_implies(X129,X130))
| is_a_theorem(X130) )
& ( 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(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_strict_implies])])])])])]) ).
cnf(c_0_85,plain,
not(and(implies(X1,X2),X3)) = implies(X3,and(X1,not(X2))),
inference(spm,[status(thm)],[c_0_79,c_0_55]) ).
cnf(c_0_86,plain,
implies(implies(X1,X1),and(X1,not(X1))) = and(X1,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_61]) ).
cnf(c_0_87,plain,
and(and(X1,not(X1)),X2) = and(X1,not(X1)),
inference(spm,[status(thm)],[c_0_82,c_0_81]) ).
fof(c_0_88,negated_conjecture,
~ and_1,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_and_1])]) ).
cnf(c_0_89,plain,
and(X1,and(X2,not(X2))) = and(X2,not(X2)),
inference(spm,[status(thm)],[c_0_83,c_0_81]) ).
cnf(c_0_90,plain,
( is_a_theorem(X2)
| ~ modus_ponens_strict_implies
| ~ is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_91,plain,
modus_ponens_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_modus_ponens_strict_implies]) ).
cnf(c_0_92,plain,
implies(X1,implies(X2,X2)) = implies(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]),c_0_61]),c_0_61]),c_0_54]) ).
fof(c_0_93,plain,
! [X185,X186,X187] :
( ( ~ axiom_m5
| is_a_theorem(strict_implies(and(strict_implies(X185,X186),strict_implies(X186,X187)),strict_implies(X185,X187))) )
& ( ~ 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(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m5])])])])]) ).
fof(c_0_94,plain,
! [X33,X34] :
( ( ~ and_1
| is_a_theorem(implies(and(X33,X34),X33)) )
& ( ~ is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0))
| 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_95,negated_conjecture,
~ and_1,
inference(fof_nnf,[status(thm)],[c_0_88]) ).
cnf(c_0_96,plain,
and(and(X1,X2),not(X2)) = and(X2,not(X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_89]),c_0_81])]) ).
cnf(c_0_97,plain,
( X1 = and(X2,not(X2))
| ~ is_a_theorem(strict_implies(X1,and(X2,not(X2)))) ),
inference(spm,[status(thm)],[c_0_48,c_0_81]) ).
cnf(c_0_98,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91])]) ).
cnf(c_0_99,plain,
strict_implies(X1,X1) = strict_implies(X2,implies(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_92]),c_0_68]) ).
cnf(c_0_100,plain,
is_a_theorem(strict_implies(X1,X1)),
inference(spm,[status(thm)],[c_0_50,c_0_54]) ).
cnf(c_0_101,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_93]) ).
cnf(c_0_102,plain,
axiom_m5,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m5]) ).
cnf(c_0_103,plain,
( and_1
| ~ is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0)) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_104,negated_conjecture,
~ and_1,
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_105,plain,
implies(and(X1,X2),X2) = implies(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_96]),c_0_61]) ).
cnf(c_0_106,plain,
and(X1,not(X1)) = and(X2,not(X2)),
inference(spm,[status(thm)],[c_0_97,c_0_81]) ).
cnf(c_0_107,plain,
( is_a_theorem(implies(X1,X1))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100])]) ).
cnf(c_0_108,plain,
is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_102])]) ).
cnf(c_0_109,plain,
~ is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0)),
inference(sr,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_110,plain,
implies(and(X1,X2),X1) = implies(X1,X1),
inference(spm,[status(thm)],[c_0_105,c_0_55]) ).
cnf(c_0_111,plain,
implies(X1,X1) = implies(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_106]),c_0_61]) ).
cnf(c_0_112,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_113,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110]),c_0_111]),c_0_112])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LCL555+1 : TPTP v8.2.0. Released v3.3.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n028.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 : 300
% 0.13/0.34 % DateTime : Sat Jun 22 13:40:24 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.3VEcfg3YP6/E---3.1_1140.p
% 3.21/0.89 # Version: 3.2.0
% 3.21/0.89 # Preprocessing class: FSLSSLSSSSSNFFN.
% 3.21/0.89 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.21/0.89 # Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 3.21/0.89 # Starting new_bool_3 with 300s (1) cores
% 3.21/0.89 # Starting new_bool_1 with 300s (1) cores
% 3.21/0.89 # Starting sh5l with 300s (1) cores
% 3.21/0.89 # H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with pid 1238 completed with status 0
% 3.21/0.89 # Result found by H----_102_C18_F1_PI_AE_CS_SP_PS_S2S
% 3.21/0.89 # Preprocessing class: FSLSSLSSSSSNFFN.
% 3.21/0.89 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.21/0.89 # Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 3.21/0.89 # No SInE strategy applied
% 3.21/0.89 # Search class: FGUSF-FFMM21-MFFFFFNN
% 3.21/0.89 # Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.21/0.89 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 675s (1) cores
% 3.21/0.89 # Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 151s (1) cores
% 3.21/0.89 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 3.21/0.89 # Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 3.21/0.89 # Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 136s (1) cores
% 3.21/0.89 # U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 1254 completed with status 0
% 3.21/0.89 # Result found by U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 3.21/0.89 # Preprocessing class: FSLSSLSSSSSNFFN.
% 3.21/0.89 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.21/0.89 # Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 3.21/0.89 # No SInE strategy applied
% 3.21/0.89 # Search class: FGUSF-FFMM21-MFFFFFNN
% 3.21/0.89 # Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.21/0.89 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 675s (1) cores
% 3.21/0.89 # Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 151s (1) cores
% 3.21/0.89 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 3.21/0.89 # Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 3.21/0.89 # Preprocessing time : 0.003 s
% 3.21/0.89 # Presaturation interreduction done
% 3.21/0.89
% 3.21/0.89 # Proof found!
% 3.21/0.89 # SZS status Theorem
% 3.21/0.89 # SZS output start CNFRefutation
% See solution above
% 3.21/0.89 # Parsed axioms : 77
% 3.21/0.89 # Removed by relevancy pruning/SinE : 0
% 3.21/0.89 # Initial clauses : 135
% 3.21/0.89 # Removed in clause preprocessing : 0
% 3.21/0.89 # Initial clauses in saturation : 135
% 3.21/0.89 # Processed clauses : 1948
% 3.21/0.89 # ...of these trivial : 438
% 3.21/0.89 # ...subsumed : 936
% 3.21/0.89 # ...remaining for further processing : 574
% 3.21/0.89 # Other redundant clauses eliminated : 0
% 3.21/0.89 # Clauses deleted for lack of memory : 0
% 3.21/0.89 # Backward-subsumed : 3
% 3.21/0.89 # Backward-rewritten : 36
% 3.21/0.89 # Generated clauses : 31773
% 3.21/0.89 # ...of the previous two non-redundant : 29059
% 3.21/0.89 # ...aggressively subsumed : 0
% 3.21/0.89 # Contextual simplify-reflections : 0
% 3.21/0.89 # Paramodulations : 31773
% 3.21/0.89 # Factorizations : 0
% 3.21/0.89 # NegExts : 0
% 3.21/0.89 # Equation resolutions : 0
% 3.21/0.89 # Disequality decompositions : 0
% 3.21/0.89 # Total rewrite steps : 36171
% 3.21/0.89 # ...of those cached : 33689
% 3.21/0.89 # Propositional unsat checks : 0
% 3.21/0.89 # Propositional check models : 0
% 3.21/0.89 # Propositional check unsatisfiable : 0
% 3.21/0.89 # Propositional clauses : 0
% 3.21/0.89 # Propositional clauses after purity: 0
% 3.21/0.89 # Propositional unsat core size : 0
% 3.21/0.89 # Propositional preprocessing time : 0.000
% 3.21/0.89 # Propositional encoding time : 0.000
% 3.21/0.89 # Propositional solver time : 0.000
% 3.21/0.89 # Success case prop preproc time : 0.000
% 3.21/0.89 # Success case prop encoding time : 0.000
% 3.21/0.89 # Success case prop solver time : 0.000
% 3.21/0.89 # Current number of processed clauses : 418
% 3.21/0.89 # Positive orientable unit clauses : 177
% 3.21/0.89 # Positive unorientable unit clauses: 64
% 3.21/0.89 # Negative unit clauses : 1
% 3.21/0.89 # Non-unit-clauses : 176
% 3.21/0.89 # Current number of unprocessed clauses: 27242
% 3.21/0.89 # ...number of literals in the above : 36697
% 3.21/0.89 # Current number of archived formulas : 0
% 3.21/0.89 # Current number of archived clauses : 156
% 3.21/0.89 # Clause-clause subsumption calls (NU) : 13230
% 3.21/0.89 # Rec. Clause-clause subsumption calls : 9238
% 3.21/0.89 # Non-unit clause-clause subsumptions : 610
% 3.21/0.89 # Unit Clause-clause subsumption calls : 1791
% 3.21/0.89 # Rewrite failures with RHS unbound : 0
% 3.21/0.89 # BW rewrite match attempts : 2289
% 3.21/0.89 # BW rewrite match successes : 226
% 3.21/0.89 # Condensation attempts : 0
% 3.21/0.89 # Condensation successes : 0
% 3.21/0.89 # Termbank termtop insertions : 612364
% 3.21/0.89 # Search garbage collected termcells : 2060
% 3.21/0.89
% 3.21/0.89 # -------------------------------------------------
% 3.21/0.89 # User time : 0.349 s
% 3.21/0.89 # System time : 0.021 s
% 3.21/0.89 # Total time : 0.371 s
% 3.21/0.89 # Maximum resident set size: 2228 pages
% 3.21/0.89
% 3.21/0.89 # -------------------------------------------------
% 3.21/0.89 # User time : 1.740 s
% 3.21/0.89 # System time : 0.104 s
% 3.21/0.89 # Total time : 1.844 s
% 3.21/0.89 # Maximum resident set size: 1768 pages
% 3.21/0.89 % E---3.1 exiting
% 3.21/0.89 % E exiting
%------------------------------------------------------------------------------