%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : LCL556+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n020.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 : Mon Sep 7 11:45:00 AM UTC 2026
% Result : Theorem 15.06s 4.61s
% Output : CNFRefutation 15.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 28
% Syntax : Number of formulae : 155 ( 84 unt; 0 def)
% Number of atoms : 282 ( 61 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 221 ( 94 ~; 94 |; 16 &)
% ( 9 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 17 ( 15 usr; 15 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 19 con; 0-2 aty)
% Number of variables : 245 ( 21 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(adjunction,axiom,
( adjunction
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(X2) )
=> is_a_theorem(and(X1,X2)) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL007+1.ax',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/sandbox2/benchmark/Axioms/LCL007+0.ax',substitution_strict_equiv) ).
fof(s1_0_adjunction,axiom,
adjunction,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_adjunction) ).
fof(s1_0_op_strict_equiv,axiom,
op_strict_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_strict_equiv) ).
fof(s1_0_substitution_strict_equiv,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_substitution_strict_equiv) ).
fof(axiom_m1,axiom,
( axiom_m1
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m1) ).
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(s1_0_axiom_m1,axiom,
axiom_m1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m1) ).
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/sandbox2/benchmark/Axioms/LCL007+0.ax',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/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m5) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X1,X2] : strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
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/theBenchmark.p',hilbert_op_implies_and) ).
fof(axiom_m4,axiom,
( axiom_m4
<=> ! [X1] : is_a_theorem(strict_implies(X1,and(X1,X1))) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m2) ).
fof(s1_0_modus_ponens_strict_implies,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_modus_ponens_strict_implies) ).
fof(s1_0_axiom_m5,axiom,
axiom_m5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m5) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_strict_implies) ).
fof(s1_0_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_or) ).
fof(s1_0_axiom_m4,axiom,
axiom_m4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m4) ).
fof(s1_0_axiom_m2,axiom,
axiom_m2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m2) ).
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/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m3) ).
fof(s1_0_axiom_m3,axiom,
axiom_m3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m3) ).
fof(hilbert_and_2,conjecture,
and_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(op_possibly,axiom,
( op_possibly
=> ! [X1] : possibly(X1) = not(necessarily(not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_possibly) ).
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(s1_0_op_possibly,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_possibly) ).
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(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[adjunction])])])])]) ).
fof(c_0_29,plain,
! [X209,X210] :
( ~ op_strict_equiv
| strict_equiv(X209,X210) = and(strict_implies(X209,X210),strict_implies(X210,X209)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_equiv])])]) ).
fof(c_0_30,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(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_strict_equiv])])])])]) ).
cnf(c_0_31,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_32,plain,
adjunction,
inference(split_conjunct,[status(thm)],[s1_0_adjunction]) ).
cnf(c_0_33,plain,
( strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1))
| ~ op_strict_equiv ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,plain,
op_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_equiv]) ).
cnf(c_0_35,plain,
( X1 = X2
| ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
substitution_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_substitution_strict_equiv]) ).
cnf(c_0_37,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_31,c_0_32])]) ).
cnf(c_0_38,plain,
and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
fof(c_0_39,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(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m1])])])]) ).
fof(c_0_40,plain,
! [X121,X122] :
( ~ op_implies_and
| implies(X121,X122) = not(and(X121,not(X122))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])]) ).
cnf(c_0_41,plain,
( X1 = X2
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
cnf(c_0_42,plain,
( is_a_theorem(strict_equiv(X1,X2))
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
( is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))
| ~ axiom_m1 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,plain,
axiom_m1,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m1]) ).
fof(c_0_45,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(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens_strict_implies])])])])]) ).
fof(c_0_46,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(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m5])])])]) ).
fof(c_0_47,plain,
! [X207,X208] :
( ~ op_strict_implies
| strict_implies(X207,X208) = necessarily(implies(X207,X208)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])]) ).
fof(c_0_48,plain,
! [X117,X118] :
( ~ op_or
| or(X117,X118) = not(and(not(X117),not(X118))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])]) ).
cnf(c_0_49,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_0_51,plain,
( X1 = X2
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_52,plain,
is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
fof(c_0_53,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(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m4])])])]) ).
fof(c_0_54,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(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m2])])])]) ).
cnf(c_0_55,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_45]) ).
cnf(c_0_56,plain,
modus_ponens_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_modus_ponens_strict_implies]) ).
cnf(c_0_57,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_46]) ).
cnf(c_0_58,plain,
axiom_m5,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m5]) ).
cnf(c_0_59,plain,
( strict_implies(X1,X2) = necessarily(implies(X1,X2))
| ~ op_strict_implies ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_60,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_0_61,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_62,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
cnf(c_0_63,plain,
op_or,
inference(split_conjunct,[status(thm)],[s1_0_op_or]) ).
cnf(c_0_64,plain,
and(X1,X2) = and(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_52])]) ).
cnf(c_0_65,plain,
( is_a_theorem(strict_implies(X1,and(X1,X1)))
| ~ axiom_m4 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_66,plain,
axiom_m4,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m4]) ).
cnf(c_0_67,plain,
( is_a_theorem(strict_implies(and(X1,X2),X1))
| ~ axiom_m2 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_68,plain,
axiom_m2,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m2]) ).
cnf(c_0_69,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_55,c_0_56])]) ).
cnf(c_0_70,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_57,c_0_58])]) ).
cnf(c_0_71,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60])]) ).
cnf(c_0_72,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62]),c_0_63])]) ).
cnf(c_0_73,plain,
not(and(not(X1),X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_62,c_0_64]) ).
cnf(c_0_74,plain,
is_a_theorem(strict_implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])]) ).
cnf(c_0_75,plain,
is_a_theorem(strict_implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
cnf(c_0_76,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(and(strict_implies(X1,X3),strict_implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_77,plain,
necessarily(or(X1,X2)) = strict_implies(not(X1),X2),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_78,plain,
or(X1,X2) = or(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_73]),c_0_72]),c_0_72]) ).
cnf(c_0_79,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_74]),c_0_75])]) ).
cnf(c_0_80,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X3,X2))
| ~ is_a_theorem(strict_implies(X1,X3)) ),
inference(spm,[status(thm)],[c_0_76,c_0_37]) ).
cnf(c_0_81,plain,
is_a_theorem(strict_implies(and(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_75,c_0_64]) ).
cnf(c_0_82,plain,
strict_implies(not(X1),X2) = strict_implies(not(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_77]) ).
cnf(c_0_83,plain,
not(not(X1)) = or(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_79]),c_0_72]) ).
cnf(c_0_84,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,and(X3,X2))) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_85,plain,
is_a_theorem(strict_implies(X1,X1)),
inference(rw,[status(thm)],[c_0_74,c_0_79]) ).
cnf(c_0_86,plain,
strict_implies(not(X1),not(X2)) = strict_implies(or(X2,X2),X1),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_87,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(not(and(X3,X2)),X1)) ),
inference(spm,[status(thm)],[c_0_84,c_0_82]) ).
cnf(c_0_88,plain,
is_a_theorem(strict_implies(or(X1,X1),X1)),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_89,plain,
is_a_theorem(strict_implies(not(X1),not(and(X2,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_85]),c_0_82]) ).
fof(c_0_90,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(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m3])])])]) ).
cnf(c_0_91,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,or(X2,X2))) ),
inference(spm,[status(thm)],[c_0_80,c_0_88]) ).
cnf(c_0_92,plain,
is_a_theorem(strict_implies(not(X1),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_89,c_0_73]) ).
cnf(c_0_93,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_90]) ).
cnf(c_0_94,plain,
axiom_m3,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m3]) ).
cnf(c_0_95,plain,
is_a_theorem(strict_implies(not(X1),not(or(X1,X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_88]),c_0_83]),c_0_82]) ).
cnf(c_0_96,plain,
is_a_theorem(strict_implies(not(not(X1)),or(X1,X2))),
inference(spm,[status(thm)],[c_0_92,c_0_72]) ).
cnf(c_0_97,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_93,c_0_94])]) ).
cnf(c_0_98,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_51,c_0_82]) ).
cnf(c_0_99,plain,
not(or(X1,X1)) = not(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_95]),c_0_82]),c_0_96])]) ).
cnf(c_0_100,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_51,c_0_97]) ).
cnf(c_0_101,plain,
( not(not(X1)) = X1
| ~ is_a_theorem(strict_implies(X1,not(not(X1)))) ),
inference(spm,[status(thm)],[c_0_98,c_0_85]) ).
cnf(c_0_102,plain,
implies(X1,or(X2,X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_99]),c_0_62]) ).
cnf(c_0_103,plain,
and(X1,and(X1,X2)) = and(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_79]),c_0_81])]) ).
cnf(c_0_104,plain,
( or(X1,X1) = X1
| ~ is_a_theorem(strict_implies(X1,or(X1,X1))) ),
inference(spm,[status(thm)],[c_0_101,c_0_83]) ).
cnf(c_0_105,plain,
strict_implies(X1,or(X2,X2)) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_102]),c_0_71]) ).
cnf(c_0_106,plain,
not(and(X1,implies(X2,X3))) = implies(X1,and(X2,not(X3))),
inference(spm,[status(thm)],[c_0_62,c_0_62]) ).
cnf(c_0_107,plain,
and(X1,and(X2,X1)) = and(X2,X1),
inference(spm,[status(thm)],[c_0_103,c_0_64]) ).
cnf(c_0_108,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_72,c_0_62]) ).
cnf(c_0_109,plain,
or(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_105]),c_0_85])]) ).
cnf(c_0_110,plain,
implies(implies(X1,X2),and(X1,not(X2))) = not(implies(X1,X2)),
inference(spm,[status(thm)],[c_0_106,c_0_79]) ).
cnf(c_0_111,plain,
is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X2,X3))),
inference(spm,[status(thm)],[c_0_84,c_0_97]) ).
cnf(c_0_112,plain,
implies(and(X1,not(X2)),X2) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_107]),c_0_62]) ).
cnf(c_0_113,plain,
and(X1,not(X2)) = not(implies(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_110]) ).
cnf(c_0_114,plain,
not(and(X1,or(X2,X2))) = implies(X1,not(X2)),
inference(spm,[status(thm)],[c_0_62,c_0_83]) ).
cnf(c_0_115,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(and(and(X3,X1),X2)) ),
inference(spm,[status(thm)],[c_0_69,c_0_111]) ).
cnf(c_0_116,plain,
implies(or(X1,X1),X2) = or(not(X1),X2),
inference(spm,[status(thm)],[c_0_72,c_0_83]) ).
cnf(c_0_117,plain,
or(X1,implies(X2,X1)) = implies(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_113]),c_0_72]),c_0_78]) ).
cnf(c_0_118,plain,
or(X1,not(X2)) = implies(or(X2,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_114]),c_0_72]) ).
cnf(c_0_119,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(and(X3,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_115,c_0_37]) ).
cnf(c_0_120,plain,
or(not(X1),X2) = implies(X1,X2),
inference(rw,[status(thm)],[c_0_116,c_0_109]) ).
cnf(c_0_121,plain,
or(X1,or(X2,X1)) = or(X2,X1),
inference(spm,[status(thm)],[c_0_117,c_0_72]) ).
cnf(c_0_122,plain,
or(X1,not(X2)) = implies(X2,X1),
inference(rw,[status(thm)],[c_0_118,c_0_109]) ).
cnf(c_0_123,plain,
( is_a_theorem(and(strict_implies(X1,X2),X3))
| ~ is_a_theorem(strict_equiv(X2,X1))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_119,c_0_38]) ).
cnf(c_0_124,plain,
strict_equiv(X1,X1) = strict_implies(X1,X1),
inference(spm,[status(thm)],[c_0_38,c_0_79]) ).
cnf(c_0_125,plain,
implies(X1,implies(X1,X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_122]),c_0_122]) ).
cnf(c_0_126,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(and(strict_implies(not(X3),X1),strict_implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_76,c_0_82]) ).
cnf(c_0_127,plain,
( is_a_theorem(and(strict_implies(X1,X1),X2))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_85])]) ).
cnf(c_0_128,plain,
( is_a_theorem(strict_implies(X1,implies(X2,X3)))
| ~ is_a_theorem(strict_implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_80,c_0_92]) ).
cnf(c_0_129,plain,
strict_implies(not(X1),X1) = necessarily(X1),
inference(spm,[status(thm)],[c_0_77,c_0_109]) ).
cnf(c_0_130,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[c_0_83,c_0_109]) ).
cnf(c_0_131,plain,
strict_implies(X1,implies(X1,X2)) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_125]),c_0_71]) ).
cnf(c_0_132,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_69,c_0_82]) ).
cnf(c_0_133,plain,
( is_a_theorem(strict_implies(not(not(X1)),X2))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_134,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(necessarily(not(X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_130]),c_0_131]) ).
cnf(c_0_135,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_136,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(necessarily(X1)) ),
inference(spm,[status(thm)],[c_0_134,c_0_130]) ).
fof(c_0_137,negated_conjecture,
~ and_2,
inference(assume_negation,[status(cth)],[hilbert_and_2]) ).
cnf(c_0_138,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(X2))
| ~ is_a_theorem(necessarily(X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_130]) ).
fof(c_0_139,plain,
! [X205] :
( ~ op_possibly
| possibly(X205) = not(necessarily(not(X205))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_possibly])])]) ).
fof(c_0_140,plain,
! [X37,X38] :
( ( ~ and_2
| is_a_theorem(implies(and(X37,X38),X38)) )
& ( ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0))
| and_2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_2])])])]) ).
fof(c_0_141,negated_conjecture,
~ and_2,
inference(fof_simplification,[status(thm)],[c_0_137]) ).
cnf(c_0_142,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_138,c_0_130]) ).
cnf(c_0_143,plain,
( possibly(X1) = not(necessarily(not(X1)))
| ~ op_possibly ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_144,plain,
op_possibly,
inference(split_conjunct,[status(thm)],[s1_0_op_possibly]) ).
cnf(c_0_145,plain,
( and_2
| ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0)) ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_146,negated_conjecture,
~ and_2,
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_147,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_142,c_0_71]) ).
cnf(c_0_148,plain,
not(necessarily(not(X1))) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_144])]) ).
cnf(c_0_149,plain,
~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0)),
inference(sr,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_150,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_147,c_0_75]) ).
cnf(c_0_151,plain,
is_a_theorem(strict_implies(possibly(X1),implies(necessarily(not(X1)),X2))),
inference(spm,[status(thm)],[c_0_92,c_0_148]) ).
cnf(c_0_152,plain,
~ is_a_theorem(implies(and(esk17_0,esk16_0),esk17_0)),
inference(rw,[status(thm)],[c_0_149,c_0_64]) ).
cnf(c_0_153,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_154,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_152,c_0_153])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL556+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : enigmatic-eprover.py %s %d 1
% 0.07/0.34 % Computer : n020.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 5 16:53:44 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.44 # ENIGMATIC: Selected SinE mode:
% 0.12/0.45 # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.45 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.12/0.45 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.12/0.45 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 15.06/4.61 # ENIGMATIC: Solved by autoschedule:
% 15.06/4.61 # No SInE strategy applied
% 15.06/4.61 # Trying AutoSched0 for 150 seconds
% 15.06/4.61 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 15.06/4.61 # and selection function SelectComplexExceptUniqMaxHorn.
% 15.06/4.61 #
% 15.06/4.61 # Preprocessing time : 0.031 s
% 15.06/4.61 # Presaturation interreduction done
% 15.06/4.61
% 15.06/4.61 # Proof found!
% 15.06/4.61 # SZS status Theorem
% 15.06/4.61 # SZS output start CNFRefutation
% See solution above
% 15.06/4.61 # Training examples: 0 positive, 0 negative
% 15.06/4.61
% 15.06/4.61 # -------------------------------------------------
% 15.06/4.61 # User time : 0.596 s
% 15.06/4.61 # System time : 0.038 s
% 15.06/4.61 # Total time : 0.634 s
% 15.06/4.61 # Maximum resident set size: 3584 pages
% 15.06/4.61
%------------------------------------------------------------------------------