%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL550+1 : TPTP v9.2.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:40:34 PM UTC 2026
% Result : Theorem 25.45s 15.30s
% Output : CNFRefutation 25.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 30
% Syntax : Number of formulae : 149 ( 75 unt; 0 def)
% Number of atoms : 292 ( 52 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 238 ( 95 ~; 102 |; 21 &)
% ( 10 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 16 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 21 con; 0-2 aty)
% Number of variables : 225 ( 13 sgn 62 !; 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/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(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_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(s1_0_substitution_strict_equiv,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL007+0.ax',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_m1,axiom,
axiom_m1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m1) ).
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(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(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(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(s1_0_axiom_m5,axiom,
axiom_m5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m5) ).
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(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(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox/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/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(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_op_or,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_op_or) ).
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(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(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(implies(X1,X2)) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(hilbert_modus_ponens,conjecture,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(c_0_30,plain,
! [X243,X244] :
( ( ~ adjunction
| ~ is_a_theorem(X243)
| ~ is_a_theorem(X244)
| is_a_theorem(and(X243,X244)) )
& ( 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_31,plain,
! [X319,X320] :
( ~ op_strict_equiv
| strict_equiv(X319,X320) = and(strict_implies(X319,X320),strict_implies(X320,X319)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_equiv])])]) ).
fof(c_0_32,plain,
! [X247,X248] :
( ( ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(X247,X248))
| X247 = X248 )
& ( 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_33,plain,
( is_a_theorem(and(X1,X2))
| ~ adjunction
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
adjunction,
inference(split_conjunct,[status(thm)],[s1_0_adjunction]) ).
cnf(c_0_35,plain,
( strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1))
| ~ op_strict_equiv ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,plain,
op_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_equiv]) ).
cnf(c_0_37,plain,
( X1 = X2
| ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
substitution_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_substitution_strict_equiv]) ).
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_33,c_0_34])]) ).
cnf(c_0_40,plain,
and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
fof(c_0_41,plain,
! [X279,X280] :
( ( ~ axiom_m1
| is_a_theorem(strict_implies(and(X279,X280),and(X280,X279))) )
& ( ~ 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_42,plain,
! [X287,X288,X289] :
( ( ~ axiom_m3
| is_a_theorem(strict_implies(and(and(X287,X288),X289),and(X287,and(X288,X289)))) )
& ( ~ 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_43,plain,
( X1 = X2
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_44,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_39,c_0_40]) ).
cnf(c_0_45,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_46,plain,
axiom_m1,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m1]) ).
cnf(c_0_47,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_42]) ).
cnf(c_0_48,plain,
axiom_m3,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m3]) ).
cnf(c_0_49,plain,
( X1 = X2
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,plain,
is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
fof(c_0_51,plain,
! [X239,X240] :
( ( ~ modus_ponens_strict_implies
| ~ is_a_theorem(X239)
| ~ is_a_theorem(strict_implies(X239,X240))
| is_a_theorem(X240) )
& ( 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_52,plain,
! [X295,X296,X297] :
( ( ~ axiom_m5
| is_a_theorem(strict_implies(and(strict_implies(X295,X296),strict_implies(X296,X297)),strict_implies(X295,X297))) )
& ( ~ 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_53,plain,
! [X231,X232] :
( ~ op_implies_and
| implies(X231,X232) = not(and(X231,not(X232))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])]) ).
cnf(c_0_54,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_47,c_0_48])]) ).
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_49,c_0_50]),c_0_50])]) ).
cnf(c_0_56,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_51]) ).
cnf(c_0_57,plain,
modus_ponens_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_modus_ponens_strict_implies]) ).
cnf(c_0_58,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_52]) ).
cnf(c_0_59,plain,
axiom_m5,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m5]) ).
fof(c_0_60,plain,
! [X317,X318] :
( ~ op_strict_implies
| strict_implies(X317,X318) = necessarily(implies(X317,X318)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])]) ).
fof(c_0_61,plain,
! [X227,X228] :
( ~ op_or
| or(X227,X228) = not(and(not(X227),not(X228))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])]) ).
cnf(c_0_62,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_63,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
fof(c_0_64,plain,
! [X293] :
( ( ~ axiom_m4
| is_a_theorem(strict_implies(X293,and(X293,X293))) )
& ( ~ 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_65,plain,
! [X283,X284] :
( ( ~ axiom_m2
| is_a_theorem(strict_implies(and(X283,X284),X283)) )
& ( ~ 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_66,plain,
is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(X2,and(X3,X1)))),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_67,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_56,c_0_57])]) ).
cnf(c_0_68,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_58,c_0_59])]) ).
cnf(c_0_69,plain,
( strict_implies(X1,X2) = necessarily(implies(X1,X2))
| ~ op_strict_implies ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_70,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_0_71,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_72,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]) ).
cnf(c_0_73,plain,
op_or,
inference(split_conjunct,[status(thm)],[s1_0_op_or]) ).
cnf(c_0_74,plain,
( is_a_theorem(strict_implies(X1,and(X1,X1)))
| ~ axiom_m4 ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_75,plain,
axiom_m4,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m4]) ).
cnf(c_0_76,plain,
( is_a_theorem(strict_implies(and(X1,X2),X1))
| ~ axiom_m2 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_77,plain,
axiom_m2,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m2]) ).
cnf(c_0_78,plain,
is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(X2,and(X1,X3)))),
inference(spm,[status(thm)],[c_0_66,c_0_55]) ).
cnf(c_0_79,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_67,c_0_68]) ).
cnf(c_0_80,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]) ).
cnf(c_0_81,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
cnf(c_0_82,plain,
not(and(not(X1),X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_72,c_0_55]) ).
cnf(c_0_83,plain,
is_a_theorem(strict_implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
cnf(c_0_84,plain,
is_a_theorem(strict_implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]) ).
cnf(c_0_85,plain,
and(X1,and(X2,X3)) = and(X2,and(X1,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_78]),c_0_78])]) ).
cnf(c_0_86,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_79,c_0_39]) ).
cnf(c_0_87,plain,
necessarily(or(X1,X2)) = strict_implies(not(X1),X2),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_88,plain,
or(X1,X2) = or(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_82]),c_0_81]),c_0_81]) ).
cnf(c_0_89,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_83]),c_0_84])]) ).
cnf(c_0_90,plain,
( is_a_theorem(and(X1,and(X2,X3)))
| ~ is_a_theorem(and(and(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_67,c_0_54]) ).
cnf(c_0_91,plain,
and(and(X1,X2),X3) = and(X1,and(X3,X2)),
inference(spm,[status(thm)],[c_0_55,c_0_85]) ).
cnf(c_0_92,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,and(X2,X3))) ),
inference(spm,[status(thm)],[c_0_86,c_0_84]) ).
cnf(c_0_93,plain,
strict_implies(not(X1),X2) = strict_implies(not(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_87]) ).
cnf(c_0_94,plain,
not(not(X1)) = or(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_89]),c_0_81]) ).
cnf(c_0_95,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_90,c_0_39]) ).
cnf(c_0_96,plain,
and(X1,and(X2,X3)) = and(X3,and(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_55]),c_0_91]) ).
cnf(c_0_97,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(not(and(X2,X3)),X1)) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_98,plain,
is_a_theorem(strict_implies(X1,X1)),
inference(rw,[status(thm)],[c_0_83,c_0_89]) ).
cnf(c_0_99,plain,
strict_implies(not(X1),not(X2)) = strict_implies(or(X2,X2),X1),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_100,plain,
( is_a_theorem(and(X1,and(X2,X3)))
| ~ is_a_theorem(and(X3,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_101,plain,
is_a_theorem(strict_implies(strict_implies(X1,X1),strict_equiv(X1,X1))),
inference(spm,[status(thm)],[c_0_83,c_0_40]) ).
cnf(c_0_102,plain,
is_a_theorem(strict_implies(strict_equiv(X1,X2),strict_implies(X1,X1))),
inference(spm,[status(thm)],[c_0_68,c_0_40]) ).
cnf(c_0_103,plain,
is_a_theorem(strict_implies(not(X1),not(and(X1,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_93]) ).
cnf(c_0_104,plain,
is_a_theorem(strict_implies(not(not(X1)),or(X1,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_93]) ).
cnf(c_0_105,plain,
( is_a_theorem(and(X1,strict_equiv(X2,X3)))
| ~ is_a_theorem(strict_equiv(X3,X2))
| ~ is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_40]),c_0_40]) ).
cnf(c_0_106,plain,
strict_equiv(X1,X1) = strict_implies(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_101]),c_0_102])]) ).
cnf(c_0_107,plain,
is_a_theorem(strict_implies(or(X1,X1),implies(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_94]),c_0_82]) ).
cnf(c_0_108,plain,
is_a_theorem(strict_implies(not(or(X1,X1)),not(not(not(X1))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_94]),c_0_94]) ).
cnf(c_0_109,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(and(strict_implies(X1,not(X3)),strict_implies(not(X2),X3))) ),
inference(spm,[status(thm)],[c_0_79,c_0_93]) ).
cnf(c_0_110,plain,
( is_a_theorem(and(X1,strict_implies(X2,X2)))
| ~ is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_106]),c_0_98])]) ).
cnf(c_0_111,plain,
( is_a_theorem(strict_implies(X1,implies(X2,X3)))
| ~ is_a_theorem(strict_implies(X1,or(X3,X3))) ),
inference(spm,[status(thm)],[c_0_86,c_0_107]) ).
cnf(c_0_112,plain,
is_a_theorem(strict_implies(not(not(not(not(X1)))),or(X1,X1))),
inference(spm,[status(thm)],[c_0_108,c_0_93]) ).
cnf(c_0_113,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,not(not(X2)))) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_114,plain,
is_a_theorem(strict_implies(not(not(not(not(X1)))),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_115,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,or(X2,X2))) ),
inference(spm,[status(thm)],[c_0_113,c_0_94]) ).
cnf(c_0_116,plain,
is_a_theorem(strict_implies(not(not(not(not(X1)))),or(X2,X1))),
inference(spm,[status(thm)],[c_0_114,c_0_81]) ).
fof(c_0_117,plain,
! [X235,X236] :
( ~ op_equiv
| equiv(X235,X236) = and(implies(X235,X236),implies(X236,X235)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])]) ).
cnf(c_0_118,plain,
is_a_theorem(strict_implies(not(X1),not(not(not(X1))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_93]) ).
fof(c_0_119,plain,
! [X121,X122] :
( ( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X121,X122))
| X121 = X122 )
& ( is_a_theorem(equiv(esk3_0,esk4_0))
| substitution_of_equivalents )
& ( esk3_0 != esk4_0
| substitution_of_equivalents ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_of_equivalents])])])])]) ).
cnf(c_0_120,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_121,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[s1_0_op_equiv]) ).
cnf(c_0_122,plain,
not(not(not(X1))) = not(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_118]),c_0_93]),c_0_98])]) ).
cnf(c_0_123,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_124,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(c_0_125,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_121])]) ).
fof(c_0_126,plain,
! [X117,X118] :
( ( ~ modus_ponens
| ~ is_a_theorem(X117)
| ~ is_a_theorem(implies(X117,X118))
| is_a_theorem(X118) )
& ( is_a_theorem(esk1_0)
| modus_ponens )
& ( is_a_theorem(implies(esk1_0,esk2_0))
| modus_ponens )
& ( ~ is_a_theorem(esk2_0)
| modus_ponens ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens])])])])]) ).
fof(c_0_127,negated_conjecture,
~ modus_ponens,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_modus_ponens])]) ).
cnf(c_0_128,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_49,c_0_93]) ).
cnf(c_0_129,plain,
implies(X1,not(not(X2))) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_122]),c_0_72]) ).
cnf(c_0_130,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124])]) ).
cnf(c_0_131,plain,
( is_a_theorem(equiv(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_39,c_0_125]) ).
cnf(c_0_132,plain,
( is_a_theorem(implies(esk1_0,esk2_0))
| modus_ponens ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_133,negated_conjecture,
~ modus_ponens,
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_134,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_67,c_0_103]) ).
cnf(c_0_135,plain,
( not(not(X1)) = X1
| ~ is_a_theorem(strict_implies(X1,not(not(X1)))) ),
inference(spm,[status(thm)],[c_0_128,c_0_98]) ).
cnf(c_0_136,plain,
strict_implies(X1,not(not(X2))) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_129]),c_0_80]) ).
cnf(c_0_137,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_138,plain,
is_a_theorem(implies(esk1_0,esk2_0)),
inference(sr,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_139,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(not(X2))) ),
inference(spm,[status(thm)],[c_0_134,c_0_82]) ).
cnf(c_0_140,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_135,c_0_136]),c_0_98])]) ).
cnf(c_0_141,plain,
( is_a_theorem(esk1_0)
| modus_ponens ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_142,plain,
( modus_ponens
| ~ is_a_theorem(esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_143,plain,
( esk2_0 = esk1_0
| ~ is_a_theorem(implies(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_144,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X2) ),
inference(rw,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_145,plain,
is_a_theorem(esk1_0),
inference(sr,[status(thm)],[c_0_141,c_0_133]) ).
cnf(c_0_146,plain,
~ is_a_theorem(esk2_0),
inference(sr,[status(thm)],[c_0_142,c_0_133]) ).
cnf(c_0_147,plain,
esk2_0 = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_145])]) ).
cnf(c_0_148,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_146,c_0_147]),c_0_145])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL550+1 : TPTP v9.2.1. Bugfixed v9.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n018.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 22:41:02 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 25.45/15.30 % Version : CSE_E---1.7
% 25.45/15.30 % Problem : theBenchmark.p
% 25.45/15.30 % SZS status Theorem for theBenchmark.p
% 25.45/15.30 % SZS output start CNFRefutation
% See solution above
% 25.54/15.40 % Total time : 11.393s
%------------------------------------------------------------------------------