%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL562+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:13:03 PM UTC 2026
% Result : Theorem 2.96s 1.52s
% Output : CNFRefutation 2.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 26
% Syntax : Number of formulae : 120 ( 70 unt; 0 def)
% Number of atoms : 217 ( 52 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 162 ( 65 ~; 65 |; 16 &)
% ( 9 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 19 con; 0-2 aty)
% Number of variables : 183 ( 13 sgn 54 !; 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/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_op_strict_equiv,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_op_strict_equiv) ).
fof(adjunction,axiom,
( adjunction
<=> ! [X1,X2] :
( ( is_a_theorem(X2)
& is_a_theorem(X1) )
=> is_a_theorem(and(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',adjunction) ).
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_adjunction,axiom,
adjunction,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_adjunction) ).
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(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_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_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(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(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.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/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
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(hilbert_equivalence_2,conjecture,
equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
fof(modus_ponens_strict_implies,axiom,
( modus_ponens_strict_implies
<=> ! [X1,X2] :
( ( is_a_theorem(strict_implies(X1,X2))
& is_a_theorem(X1) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',modus_ponens_strict_implies) ).
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(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(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(equivalence_2,axiom,
( equivalence_2
<=> ! [X1,X2] : is_a_theorem(implies(equiv(X1,X2),implies(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',equivalence_2) ).
fof(s1_0_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_op_equiv) ).
fof(s1_0_axiom_m5,axiom,
axiom_m5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m5) ).
fof(c_0_26,plain,
! [X209,X210] :
( strict_equiv(X209,X210) = and(strict_implies(X209,X210),strict_implies(X210,X209))
| ~ op_strict_equiv ),
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_27,plain,
! [X137,X138] :
( ( substitution_strict_equiv
| esk61_0 != esk62_0 )
& ( substitution_strict_equiv
| is_a_theorem(strict_equiv(esk61_0,esk62_0)) )
& ( X137 = X138
| ~ is_a_theorem(strict_equiv(X137,X138))
| ~ 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_28,plain,
( ~ op_strict_equiv
| strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_29,plain,
op_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_equiv]) ).
fof(c_0_30,plain,
! [X133,X134] :
( ( adjunction
| ~ is_a_theorem(and(esk59_0,esk60_0)) )
& ( adjunction
| is_a_theorem(esk60_0) )
& ( adjunction
| is_a_theorem(esk59_0) )
& ( is_a_theorem(and(X133,X134))
| ~ is_a_theorem(X134)
| ~ is_a_theorem(X133)
| ~ 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_31,plain,
( ~ is_a_theorem(strict_equiv(X1,X2))
| ~ substitution_strict_equiv
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
substitution_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_substitution_strict_equiv]) ).
cnf(c_0_33,plain,
strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
cnf(c_0_34,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ adjunction
| is_a_theorem(and(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
adjunction,
inference(split_conjunct,[status(thm)],[s1_0_adjunction]) ).
fof(c_0_36,plain,
! [X183] :
( ( axiom_m4
| ~ is_a_theorem(strict_implies(esk84_0,and(esk84_0,esk84_0))) )
& ( is_a_theorem(strict_implies(X183,and(X183,X183)))
| ~ 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_37,plain,
! [X173,X174] :
( ( axiom_m2
| ~ is_a_theorem(strict_implies(and(esk79_0,esk80_0),esk79_0)) )
& ( is_a_theorem(strict_implies(and(X173,X174),X173))
| ~ 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_38,plain,
! [X169,X170] :
( ( axiom_m1
| ~ is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0))) )
& ( is_a_theorem(strict_implies(and(X169,X170),and(X170,X169)))
| ~ 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_39,plain,
! [X177,X178,X179] :
( ( axiom_m3
| ~ is_a_theorem(strict_implies(and(and(esk81_0,esk82_0),esk83_0),and(esk81_0,and(esk82_0,esk83_0)))) )
& ( is_a_theorem(strict_implies(and(and(X177,X178),X179),and(X177,and(X178,X179))))
| ~ 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_40,plain,
( ~ is_a_theorem(and(strict_implies(X1,X2),strict_implies(X2,X1)))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_41,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(X2)
| is_a_theorem(and(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).
cnf(c_0_42,plain,
( ~ axiom_m4
| is_a_theorem(strict_implies(X1,and(X1,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,plain,
axiom_m4,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m4]) ).
cnf(c_0_44,plain,
( ~ axiom_m2
| is_a_theorem(strict_implies(and(X1,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,plain,
axiom_m2,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m2]) ).
cnf(c_0_46,plain,
( ~ axiom_m1
| is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,plain,
axiom_m1,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m1]) ).
cnf(c_0_48,plain,
( ~ axiom_m3
| is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_49,plain,
axiom_m3,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m3]) ).
cnf(c_0_50,plain,
( ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X2,X1))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_51,plain,
is_a_theorem(strict_implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
cnf(c_0_52,plain,
is_a_theorem(strict_implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).
cnf(c_0_53,plain,
is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
fof(c_0_54,plain,
! [X121,X122] :
( implies(X121,X122) = not(and(X121,not(X122)))
| ~ op_implies_and ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])]) ).
cnf(c_0_55,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_48,c_0_49])]) ).
cnf(c_0_56,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).
cnf(c_0_57,plain,
and(X1,X2) = and(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_53]),c_0_53])]) ).
cnf(c_0_58,plain,
( ~ op_implies_and
| implies(X1,X2) = not(and(X1,not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_59,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_0_60,plain,
is_a_theorem(strict_implies(and(X1,X2),and(X1,and(X1,X2)))),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_61,plain,
is_a_theorem(strict_implies(and(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_52,c_0_57]) ).
fof(c_0_62,plain,
! [X207,X208] :
( strict_implies(X207,X208) = necessarily(implies(X207,X208))
| ~ op_strict_implies ),
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_63,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]) ).
cnf(c_0_64,plain,
( ~ is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(and(X1,X2),X3)))
| and(and(X1,X2),X3) = and(X1,and(X2,X3)) ),
inference(spm,[status(thm)],[c_0_50,c_0_55]) ).
cnf(c_0_65,plain,
and(X1,and(X1,X2)) = and(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_60]),c_0_61])]) ).
cnf(c_0_66,plain,
( ~ op_strict_implies
| strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_67,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_0_68,plain,
not(and(not(X1),X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_63,c_0_57]) ).
cnf(c_0_69,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_64,c_0_65]),c_0_61])]) ).
cnf(c_0_70,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67])]) ).
cnf(c_0_71,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(spm,[status(thm)],[c_0_63,c_0_68]) ).
cnf(c_0_72,plain,
and(X1,and(X2,X1)) = and(X2,X1),
inference(spm,[status(thm)],[c_0_65,c_0_57]) ).
cnf(c_0_73,plain,
not(and(and(not(X1),X2),X3)) = implies(and(and(not(X1),X2),X3),X1),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_74,plain,
strict_implies(not(X1),X2) = strict_implies(not(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_70]) ).
cnf(c_0_75,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_64,c_0_72]),c_0_61])]) ).
cnf(c_0_76,plain,
implies(and(and(not(X1),X2),not(X3)),X1) = implies(and(not(X1),X2),X3),
inference(spm,[status(thm)],[c_0_63,c_0_73]) ).
cnf(c_0_77,plain,
( ~ is_a_theorem(strict_implies(X1,not(X2)))
| ~ is_a_theorem(strict_implies(not(X1),X2))
| X1 = not(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_74]) ).
cnf(c_0_78,plain,
not(not(X1)) = implies(not(X1),X1),
inference(spm,[status(thm)],[c_0_63,c_0_56]) ).
cnf(c_0_79,plain,
is_a_theorem(strict_implies(and(and(X1,X2),X3),X2)),
inference(spm,[status(thm)],[c_0_52,c_0_75]) ).
cnf(c_0_80,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_70,c_0_76]),c_0_70]) ).
cnf(c_0_81,plain,
not(and(X1,implies(X2,X3))) = implies(X1,and(X2,not(X3))),
inference(spm,[status(thm)],[c_0_63,c_0_63]) ).
cnf(c_0_82,plain,
( ~ is_a_theorem(strict_implies(X1,implies(not(X1),X1)))
| implies(not(X1),X1) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_51]),c_0_56]),c_0_78]),c_0_56]),c_0_78]) ).
cnf(c_0_83,plain,
is_a_theorem(strict_implies(and(X1,not(X1)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_57]) ).
cnf(c_0_84,plain,
( ~ is_a_theorem(strict_implies(X1,and(X1,X2)))
| and(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_50,c_0_52]) ).
fof(c_0_85,negated_conjecture,
~ equivalence_2,
inference(assume_negation,[status(cth)],[hilbert_equivalence_2]) ).
fof(c_0_86,plain,
! [X129,X130] :
( ( modus_ponens_strict_implies
| ~ is_a_theorem(esk58_0) )
& ( modus_ponens_strict_implies
| is_a_theorem(strict_implies(esk57_0,esk58_0)) )
& ( modus_ponens_strict_implies
| is_a_theorem(esk57_0) )
& ( is_a_theorem(X130)
| ~ is_a_theorem(strict_implies(X129,X130))
| ~ is_a_theorem(X129)
| ~ 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_87,plain,
not(and(implies(X1,X2),X3)) = implies(X3,and(X1,not(X2))),
inference(spm,[status(thm)],[c_0_81,c_0_57]) ).
cnf(c_0_88,plain,
implies(implies(X1,X1),and(X1,not(X1))) = and(X1,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_63]) ).
cnf(c_0_89,plain,
and(and(X1,not(X1)),X2) = and(X1,not(X1)),
inference(spm,[status(thm)],[c_0_84,c_0_83]) ).
fof(c_0_90,plain,
! [X125,X126] :
( equiv(X125,X126) = and(implies(X125,X126),implies(X126,X125))
| ~ op_equiv ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])])]) ).
fof(c_0_91,negated_conjecture,
~ equivalence_2,
inference(fof_simplification,[status(thm)],[c_0_85]) ).
cnf(c_0_92,plain,
( ~ is_a_theorem(strict_implies(X2,and(X1,X2)))
| and(X1,X2) = X2 ),
inference(spm,[status(thm)],[c_0_50,c_0_61]) ).
cnf(c_0_93,plain,
( ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(X1)
| ~ modus_ponens_strict_implies
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_94,plain,
modus_ponens_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_modus_ponens_strict_implies]) ).
cnf(c_0_95,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_87,c_0_88]),c_0_89]),c_0_63]),c_0_63]),c_0_56]) ).
fof(c_0_96,plain,
! [X185,X186,X187] :
( ( axiom_m5
| ~ is_a_theorem(strict_implies(and(strict_implies(esk85_0,esk86_0),strict_implies(esk86_0,esk87_0)),strict_implies(esk85_0,esk87_0))) )
& ( is_a_theorem(strict_implies(and(strict_implies(X185,X186),strict_implies(X186,X187)),strict_implies(X185,X187)))
| ~ 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_97,plain,
! [X63,X64] :
( ( equivalence_2
| ~ is_a_theorem(implies(equiv(esk29_0,esk30_0),implies(esk30_0,esk29_0))) )
& ( is_a_theorem(implies(equiv(X63,X64),implies(X64,X63)))
| ~ equivalence_2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_2])])])])]) ).
cnf(c_0_98,plain,
( ~ op_equiv
| equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_99,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[s1_0_op_equiv]) ).
fof(c_0_100,negated_conjecture,
~ equivalence_2,
inference(fof_nnf,[status(thm)],[c_0_91]) ).
cnf(c_0_101,plain,
and(X1,and(X2,not(X2))) = and(X2,not(X2)),
inference(spm,[status(thm)],[c_0_92,c_0_83]) ).
cnf(c_0_102,plain,
( ~ is_a_theorem(strict_implies(X1,and(X2,not(X2))))
| X1 = and(X2,not(X2)) ),
inference(spm,[status(thm)],[c_0_50,c_0_83]) ).
cnf(c_0_103,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(strict_implies(X2,X1))
| is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94])]) ).
cnf(c_0_104,plain,
strict_implies(X1,X1) = strict_implies(X2,implies(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_95]),c_0_70]) ).
cnf(c_0_105,plain,
is_a_theorem(strict_implies(X1,X1)),
inference(spm,[status(thm)],[c_0_52,c_0_56]) ).
cnf(c_0_106,plain,
( ~ axiom_m5
| is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_107,plain,
axiom_m5,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m5]) ).
cnf(c_0_108,plain,
( ~ is_a_theorem(implies(equiv(esk29_0,esk30_0),implies(esk30_0,esk29_0)))
| equivalence_2 ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_109,plain,
equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_99])]) ).
cnf(c_0_110,negated_conjecture,
~ equivalence_2,
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_111,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_64,c_0_101]),c_0_83])]) ).
cnf(c_0_112,plain,
and(X1,not(X1)) = and(X2,not(X2)),
inference(spm,[status(thm)],[c_0_102,c_0_83]) ).
cnf(c_0_113,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_105])]) ).
cnf(c_0_114,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_106,c_0_107])]) ).
cnf(c_0_115,plain,
~ is_a_theorem(implies(and(implies(esk29_0,esk30_0),implies(esk30_0,esk29_0)),implies(esk30_0,esk29_0))),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_109]),c_0_110]) ).
cnf(c_0_116,plain,
implies(and(X1,X2),X2) = implies(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_111]),c_0_63]) ).
cnf(c_0_117,plain,
implies(X1,X1) = implies(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_112]),c_0_63]) ).
cnf(c_0_118,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_119,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_116]),c_0_117]),c_0_118])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL562+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.51 % Computer : n001.cluster.edu
% 0.20/0.51 % Model : x86_64 x86_64
% 0.20/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.51 % Memory : 8046.5625MB
% 0.20/0.51 % OS : Linux 6.8.0-71-generic
% 0.20/0.51 % CPULimit : 300
% 0.20/0.51 % WCLimit : 300
% 0.20/0.51 % DateTime : Mon Sep 21 00:44:28 UTC 2026
% 0.24/0.52 % CPUTime :
% 0.24/0.52 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.59 Running first-order theorem proving
% 0.24/0.59 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/benchmark/theBenchmark.p
% 2.96/1.52 % Version: 3.5.1
% 2.96/1.52 % Preprocessing class: FSLSSLSSSSSNFFN.
% 2.96/1.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.96/1.52 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 2.96/1.52 % Starting new_bool_3 with 300s (1) cores
% 2.96/1.52 % Starting new_bool_1 with 300s (1) cores
% 2.96/1.52 % Starting sh5l with 300s (1) cores
% 2.96/1.52 % new_bool_3 with pid 1835773 completed with status 9
% 2.96/1.52 % new_bool_1 with pid 1835774 completed with status 9
% 2.96/1.52 % sh5l with pid 1835775 completed with status 9
% 2.96/1.52 % H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with pid 1835772 completed with status 0
% 2.96/1.52 % Result found by H----_102_C18_F1_PI_AE_CS_SP_PS_S2S
% 2.96/1.52 % Preprocessing class: FSLSSLSSSSSNFFN.
% 2.96/1.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.96/1.52 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 2.96/1.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.96/1.52 % No SInE strategy applied
% 2.96/1.52 % Search class: FGUSF-FFMM21-MFFFFFNN
% 2.96/1.52 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 2.96/1.52 % Starting SubtermCWHack with 136s (1) cores
% 2.96/1.52 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 151s (1) cores
% 2.96/1.52 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 136s (1) cores
% 2.96/1.52 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 2.96/1.52 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.96/1.52 % U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 1835783 completed with status 0
% 2.96/1.52 % Result found by U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 2.96/1.52 % Preprocessing class: FSLSSLSSSSSNFFN.
% 2.96/1.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.96/1.52 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 2.96/1.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.96/1.52 % No SInE strategy applied
% 2.96/1.52 % Search class: FGUSF-FFMM21-MFFFFFNN
% 2.96/1.52 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 2.96/1.52 % Starting SubtermCWHack with 136s (1) cores
% 2.96/1.52 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 151s (1) cores
% 2.96/1.52 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 136s (1) cores
% 2.96/1.52 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 2.96/1.52 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.96/1.52 % Preprocessing time : 0.004 s
% 2.96/1.52 % Presaturation interreduction done
% 2.96/1.52
% 2.96/1.52 % Proof found!
% 2.96/1.52 % SZS status Theorem
% 2.96/1.52 % SZS output start CNFRefutation
% See solution above
% 2.96/1.52 % Parsed axioms : 77
% 2.96/1.52 % Removed by relevancy pruning/SinE : 0
% 2.96/1.52 % Initial clauses : 135
% 2.96/1.52 % Removed in clause preprocessing : 0
% 2.96/1.52 % Initial clauses in saturation : 135
% 2.96/1.52 % Processed clauses : 1851
% 2.96/1.52 % ...of these trivial : 424
% 2.96/1.52 % ...subsumed : 867
% 2.96/1.52 % ...remaining for further processing : 560
% 2.96/1.52 % Other redundant clauses eliminated : 0
% 2.96/1.52 % Clauses deleted for lack of memory : 0
% 2.96/1.52 % Backward-subsumed : 3
% 2.96/1.52 % Backward-rewritten : 27
% 2.96/1.52 % Generated clauses : 28911
% 2.96/1.52 % ...of the previous two non-redundant : 26416
% 2.96/1.52 % ...aggressively subsumed : 0
% 2.96/1.52 % Contextual simplify-reflections : 0
% 2.96/1.52 % Paramodulations : 28911
% 2.96/1.52 % Factorizations : 0
% 2.96/1.52 % NegExts : 0
% 2.96/1.52 % Equation resolutions : 0
% 2.96/1.52 % Disequality decompositions : 0
% 2.96/1.52 % Total rewrite steps : 33153
% 2.96/1.52 % ...of those cached : 30784
% 2.96/1.52 % Propositional unsat checks : 0
% 2.96/1.52 % Propositional check models : 0
% 2.96/1.52 % Propositional check unsatisfiable : 0
% 2.96/1.52 % Propositional clauses : 0
% 2.96/1.52 % Propositional clauses after purity: 0
% 2.96/1.52 % Propositional unsat core size : 0
% 2.96/1.52 % Propositional preprocessing time : 0.000
% 2.96/1.52 % Propositional encoding time : 0.000
% 2.96/1.52 % Propositional solver time : 0.000
% 2.96/1.52 % Success case prop preproc time : 0.000
% 2.96/1.52 % Success case prop encoding time : 0.000
% 2.96/1.52 % Success case prop solver time : 0.000
% 2.96/1.52 % Current number of processed clauses : 413
% 2.96/1.52 % Positive orientable unit clauses : 169
% 2.96/1.52 % Positive unorientable unit clauses: 59
% 2.96/1.52 % Negative unit clauses : 1
% 2.96/1.52 % Non-unit-clauses : 184
% 2.96/1.52 % Current number of unprocessed clauses: 24703
% 2.96/1.52 % ...number of literals in the above : 33947
% 2.96/1.52 % Current number of archived formulas : 0
% 2.96/1.52 % Current number of archived clauses : 147
% 2.96/1.52 % Clause-clause subsumption calls (NU) : 12716
% 2.96/1.52 % Rec. Clause-clause subsumption calls : 8789
% 2.96/1.52 % Non-unit clause-clause subsumptions : 579
% 2.96/1.52 % Unit Clause-clause subsumption calls : 1478
% 2.96/1.52 % Rewrite failures with RHS unbound : 0
% 2.96/1.52 % BW rewrite match attempts : 2031
% 2.96/1.52 % BW rewrite match successes : 204
% 2.96/1.52 % Condensation attempts : 0
% 2.96/1.52 % Condensation successes : 0
% 2.96/1.52 % Termbank termtop insertions : 562962
% 2.96/1.52 % Search garbage collected termcells : 2057
% 2.96/1.52
% 2.96/1.52 % -------------------------------------------------
% 2.96/1.52 % User time : 0.831 s
% 2.96/1.52 % System time : 0.042 s
% 2.96/1.52 % Total time : 0.873 s
% 2.96/1.52 % Maximum resident set size: 3988 pages
% 2.96/1.52
% 2.96/1.52 % -------------------------------------------------
% 2.96/1.52 % User time : 4.137 s
% 2.96/1.52 % System time : 0.290 s
% 2.96/1.52 % Total time : 4.427 s
% 2.96/1.52 % Maximum resident set size: 4864 pages
% 2.96/1.52 % E exiting
%------------------------------------------------------------------------------