%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL489+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 01:12:54 PM UTC 2026
% Result : Theorem 13.62s 3.26s
% Output : CNFRefutation 13.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 26
% Syntax : Number of formulae : 115 ( 59 unt; 0 def)
% Number of atoms : 208 ( 33 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 161 ( 68 ~; 66 |; 12 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 17 con; 0-2 aty)
% Number of variables : 170 ( 2 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X1,X2] : implies(X1,X2) = or(not(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
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(op_and,axiom,
( op_and
=> ! [X1,X2] : and(X1,X2) = not(or(not(X1),not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_and) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(principia_op_and,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).
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(r1,axiom,
( r1
<=> ! [X4] : is_a_theorem(implies(or(X4,X4),X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r1) ).
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X1,X2] :
( ( is_a_theorem(implies(X1,X2))
& is_a_theorem(X1) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(hilbert_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(principia_r1,axiom,
r1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r1) ).
fof(principia_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
fof(r5,axiom,
( r5
<=> ! [X4,X5,X6] : is_a_theorem(implies(implies(X5,X6),implies(or(X4,X5),or(X4,X6)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r5) ).
fof(principia_r5,axiom,
r5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r5) ).
fof(r3,axiom,
( r3
<=> ! [X4,X5] : is_a_theorem(implies(or(X4,X5),or(X5,X4))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r3) ).
fof(r2,axiom,
( r2
<=> ! [X4,X5] : is_a_theorem(implies(X5,or(X4,X5))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r2) ).
fof(r4,axiom,
( r4
<=> ! [X4,X5,X6] : is_a_theorem(implies(or(X4,or(X5,X6)),or(X5,or(X4,X6)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r4) ).
fof(principia_r3,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
fof(principia_r2,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
fof(principia_r4,axiom,
r4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r4) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
fof(principia_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_equiv) ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',use_substitution_of_equivalents) ).
fof(hilbert_and_3,conjecture,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(and_3,axiom,
( and_3
<=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,and(X1,X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_3) ).
fof(c_0_26,plain,
! [X123,X124] :
( implies(X123,X124) = or(not(X123),X124)
| ~ op_implies_or ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_or])])])]) ).
fof(c_0_27,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])])])]) ).
fof(c_0_28,plain,
! [X119,X120] :
( and(X119,X120) = not(or(not(X119),not(X120)))
| ~ op_and ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_and])])])]) ).
cnf(c_0_29,plain,
( ~ op_implies_or
| implies(X1,X2) = or(not(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
op_implies_or,
inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).
cnf(c_0_31,plain,
( ~ op_implies_and
| implies(X1,X2) = not(and(X1,not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_0_33,plain,
( ~ op_and
| and(X1,X2) = not(or(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
or(not(X1),X2) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_35,plain,
op_and,
inference(split_conjunct,[status(thm)],[principia_op_and]) ).
fof(c_0_36,plain,
! [X117,X118] :
( or(X117,X118) = not(and(not(X117),not(X118)))
| ~ op_or ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])]) ).
cnf(c_0_37,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
cnf(c_0_38,plain,
and(X1,X2) = not(implies(X1,not(X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
fof(c_0_39,plain,
! [X95] :
( ( r1
| ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0)) )
& ( is_a_theorem(implies(or(X95,X95),X95))
| ~ r1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r1])])])])]) ).
fof(c_0_40,plain,
! [X7,X8] :
( ( modus_ponens
| ~ is_a_theorem(esk2_0) )
& ( modus_ponens
| is_a_theorem(implies(esk1_0,esk2_0)) )
& ( modus_ponens
| is_a_theorem(esk1_0) )
& ( is_a_theorem(X8)
| ~ is_a_theorem(implies(X7,X8))
| ~ is_a_theorem(X7)
| ~ modus_ponens ) ),
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])])])])])]) ).
cnf(c_0_41,plain,
( ~ op_or
| or(X1,X2) = not(and(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,plain,
not(not(implies(X1,not(not(X2))))) = implies(X1,X2),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).
cnf(c_0_44,plain,
( ~ r1
| is_a_theorem(implies(or(X1,X1),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,plain,
r1,
inference(split_conjunct,[status(thm)],[principia_r1]) ).
cnf(c_0_46,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| ~ modus_ponens
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[principia_modus_ponens]) ).
cnf(c_0_48,plain,
or(X1,X2) = implies(not(X1),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_38]),c_0_42]),c_0_43])]) ).
cnf(c_0_49,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).
fof(c_0_50,plain,
! [X111,X112,X113] :
( ( r5
| ~ is_a_theorem(implies(implies(esk54_0,esk55_0),implies(or(esk53_0,esk54_0),or(esk53_0,esk55_0)))) )
& ( is_a_theorem(implies(implies(X112,X113),implies(or(X111,X112),or(X111,X113))))
| ~ r5 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r5])])])])]) ).
cnf(c_0_51,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
cnf(c_0_52,plain,
implies(implies(X1,not(not(X2))),X3) = implies(implies(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_42]),c_0_34]) ).
cnf(c_0_53,plain,
is_a_theorem(implies(implies(X1,not(X1)),not(X1))),
inference(spm,[status(thm)],[c_0_49,c_0_34]) ).
cnf(c_0_54,plain,
( ~ r5
| is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_55,plain,
r5,
inference(split_conjunct,[status(thm)],[principia_r5]) ).
cnf(c_0_56,plain,
( ~ is_a_theorem(implies(implies(X2,X3),X1))
| ~ is_a_theorem(implies(X2,not(not(X3))))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,plain,
is_a_theorem(implies(or(X1,X1),not(not(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_52]),c_0_48]) ).
cnf(c_0_58,plain,
is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
fof(c_0_59,plain,
! [X101,X102] :
( ( r3
| ~ is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0))) )
& ( is_a_theorem(implies(or(X101,X102),or(X102,X101)))
| ~ r3 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r3])])])])]) ).
cnf(c_0_60,plain,
( ~ is_a_theorem(implies(implies(or(X2,X2),X2),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_61,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X1),implies(X3,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_34]),c_0_34]) ).
fof(c_0_62,plain,
! [X97,X98] :
( ( r2
| ~ is_a_theorem(implies(esk47_0,or(esk46_0,esk47_0))) )
& ( is_a_theorem(implies(X98,or(X97,X98)))
| ~ r2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r2])])])])]) ).
fof(c_0_63,plain,
! [X105,X106,X107] :
( ( r4
| ~ is_a_theorem(implies(or(esk50_0,or(esk51_0,esk52_0)),or(esk51_0,or(esk50_0,esk52_0)))) )
& ( is_a_theorem(implies(or(X105,or(X106,X107)),or(X106,or(X105,X107))))
| ~ r4 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r4])])])])]) ).
cnf(c_0_64,plain,
( ~ r3
| is_a_theorem(implies(or(X1,X2),or(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_65,plain,
r3,
inference(split_conjunct,[status(thm)],[principia_r3]) ).
cnf(c_0_66,plain,
is_a_theorem(implies(implies(X1,or(X2,X2)),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_67,plain,
( ~ r2
| is_a_theorem(implies(X1,or(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_68,plain,
r2,
inference(split_conjunct,[status(thm)],[principia_r2]) ).
cnf(c_0_69,plain,
( ~ r4
| is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_70,plain,
r4,
inference(split_conjunct,[status(thm)],[principia_r4]) ).
fof(c_0_71,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])])])]) ).
cnf(c_0_72,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]) ).
cnf(c_0_73,plain,
( ~ is_a_theorem(implies(X1,or(X2,X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_66]) ).
cnf(c_0_74,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
cnf(c_0_75,plain,
is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]) ).
fof(c_0_76,plain,
! [X11,X12] :
( ( substitution_of_equivalents
| esk3_0 != esk4_0 )
& ( substitution_of_equivalents
| is_a_theorem(equiv(esk3_0,esk4_0)) )
& ( X11 = X12
| ~ is_a_theorem(equiv(X11,X12))
| ~ substitution_of_equivalents ) ),
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_of_equivalents])])])])])]) ).
cnf(c_0_77,plain,
( ~ op_equiv
| equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_78,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[principia_op_equiv]) ).
cnf(c_0_79,plain,
is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_72,c_0_34]) ).
cnf(c_0_80,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,plain,
implies(not(not(X1)),X2) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_48]) ).
cnf(c_0_82,plain,
is_a_theorem(implies(implies(X1,or(X2,X3)),or(X2,implies(X1,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_34]),c_0_34]) ).
cnf(c_0_83,plain,
( ~ is_a_theorem(equiv(X1,X2))
| ~ substitution_of_equivalents
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_84,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(c_0_85,plain,
equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78])]) ).
cnf(c_0_86,plain,
is_a_theorem(implies(implies(X1,not(X2)),implies(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_79,c_0_34]) ).
cnf(c_0_87,plain,
is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_72,c_0_34]) ).
cnf(c_0_88,plain,
( ~ is_a_theorem(implies(implies(X2,X2),X1))
| is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_80]),c_0_81]) ).
cnf(c_0_89,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X2,implies(X1,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_34]),c_0_34]) ).
cnf(c_0_90,plain,
( ~ is_a_theorem(and(implies(X1,X2),implies(X2,X1)))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84]),c_0_85])]) ).
cnf(c_0_91,plain,
( ~ is_a_theorem(implies(X2,not(X1)))
| is_a_theorem(implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_51,c_0_86]) ).
fof(c_0_92,negated_conjecture,
~ and_3,
inference(assume_negation,[status(cth)],[hilbert_and_3]) ).
cnf(c_0_93,plain,
( ~ is_a_theorem(not(X2))
| ~ is_a_theorem(or(X2,X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_48]) ).
cnf(c_0_94,plain,
( ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(or(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_51,c_0_87]) ).
cnf(c_0_95,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_96,plain,
( ~ is_a_theorem(not(implies(implies(X1,X2),not(implies(X2,X1)))))
| X1 = X2 ),
inference(rw,[status(thm)],[c_0_90,c_0_38]) ).
cnf(c_0_97,plain,
is_a_theorem(implies(X1,not(implies(X1,not(X1))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_49]),c_0_34]) ).
fof(c_0_98,negated_conjecture,
~ and_3,
inference(fof_simplification,[status(thm)],[c_0_92]) ).
cnf(c_0_99,plain,
( ~ is_a_theorem(not(X2))
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_100,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_95]) ).
cnf(c_0_101,plain,
( ~ is_a_theorem(not(implies(implies(X1,X2),not(implies(X2,X1)))))
| X1 = not(not(X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_81]),c_0_52]) ).
cnf(c_0_102,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(not(implies(X1,not(X1)))) ),
inference(spm,[status(thm)],[c_0_51,c_0_97]) ).
fof(c_0_103,plain,
! [X41,X42] :
( ( and_3
| ~ is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0)))) )
& ( is_a_theorem(implies(X41,implies(X42,and(X41,X42))))
| ~ and_3 ) ),
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_3])])])])]) ).
fof(c_0_104,negated_conjecture,
~ and_3,
inference(fof_nnf,[status(thm)],[c_0_98]) ).
cnf(c_0_105,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(not(X2))
| is_a_theorem(not(implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_106,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_80])]) ).
cnf(c_0_107,plain,
( ~ is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0))))
| and_3 ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_108,negated_conjecture,
~ and_3,
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_109,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| X1 = X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_105]),c_0_106]) ).
cnf(c_0_110,plain,
( ~ is_a_theorem(implies(X2,implies(X1,X3)))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_51,c_0_89]) ).
cnf(c_0_111,plain,
~ is_a_theorem(implies(esk18_0,implies(esk19_0,not(implies(esk18_0,not(esk19_0)))))),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_38]),c_0_108]) ).
cnf(c_0_112,plain,
implies(X1,not(X2)) = implies(X2,not(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_86]),c_0_86])]) ).
cnf(c_0_113,plain,
is_a_theorem(implies(X1,implies(implies(X2,not(X1)),not(X2)))),
inference(spm,[status(thm)],[c_0_110,c_0_86]) ).
cnf(c_0_114,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_112]),c_0_113])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL489+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 00:35:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 13.62/3.26 % Version: 3.5.1
% 13.62/3.26 % Preprocessing class: FSMSSLSSSSSNFFN.
% 13.62/3.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.62/3.26 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 13.62/3.26 % Starting new_bool_3 with 300s (1) cores
% 13.62/3.26 % Starting new_bool_1 with 300s (1) cores
% 13.62/3.26 % Starting sh5l with 300s (1) cores
% 13.62/3.26 % new_bool_3 with pid 583997 completed with status 9
% 13.62/3.26 % new_bool_1 with pid 583998 completed with status 9
% 13.62/3.26 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 583996 completed with status 0
% 13.62/3.26 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 13.62/3.26 % Preprocessing class: FSMSSLSSSSSNFFN.
% 13.62/3.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.62/3.26 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 13.62/3.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 13.62/3.26 % No SInE strategy applied
% 13.62/3.26 % Search class: FGUSF-FFMM21-MFFFFFNN
% 13.62/3.26 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 13.62/3.26 % Starting SubtermCWHack with 151s (1) cores
% 13.62/3.26 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 13.62/3.26 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 13.62/3.26 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 13.62/3.26 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 13.62/3.26 % U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 584018 completed with status 0
% 13.62/3.26 % Result found by U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 13.62/3.26 % Preprocessing class: FSMSSLSSSSSNFFN.
% 13.62/3.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.62/3.26 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 13.62/3.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 13.62/3.26 % No SInE strategy applied
% 13.62/3.26 % Search class: FGUSF-FFMM21-MFFFFFNN
% 13.62/3.26 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 13.62/3.26 % Starting SubtermCWHack with 151s (1) cores
% 13.62/3.26 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 13.62/3.26 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 13.62/3.26 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 13.62/3.26 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 13.62/3.26 % Preprocessing time : 0.002 s
% 13.62/3.26 % Presaturation interreduction done
% 13.62/3.26
% 13.62/3.26 % Proof found!
% 13.62/3.26 % SZS status Theorem
% 13.62/3.26 % SZS output start CNFRefutation
% See solution above
% 13.62/3.27 % Parsed axioms : 45
% 13.62/3.27 % Removed by relevancy pruning/SinE : 0
% 13.62/3.27 % Initial clauses : 74
% 13.62/3.27 % Removed in clause preprocessing : 0
% 13.62/3.27 % Initial clauses in saturation : 74
% 13.62/3.27 % Processed clauses : 10431
% 13.62/3.27 % ...of these trivial : 2911
% 13.62/3.27 % ...subsumed : 5328
% 13.62/3.27 % ...remaining for further processing : 2192
% 13.62/3.27 % Other redundant clauses eliminated : 0
% 13.62/3.27 % Clauses deleted for lack of memory : 0
% 13.62/3.27 % Backward-subsumed : 5
% 13.62/3.27 % Backward-rewritten : 719
% 13.62/3.27 % Generated clauses : 168012
% 13.62/3.27 % ...of the previous two non-redundant : 95988
% 13.62/3.27 % ...aggressively subsumed : 0
% 13.62/3.27 % Contextual simplify-reflections : 0
% 13.62/3.27 % Paramodulations : 168012
% 13.62/3.27 % Factorizations : 0
% 13.62/3.27 % NegExts : 0
% 13.62/3.27 % Equation resolutions : 0
% 13.62/3.27 % Disequality decompositions : 0
% 13.62/3.27 % Total rewrite steps : 415266
% 13.62/3.27 % ...of those cached : 395441
% 13.62/3.27 % Propositional unsat checks : 0
% 13.62/3.27 % Propositional check models : 0
% 13.62/3.27 % Propositional check unsatisfiable : 0
% 13.62/3.27 % Propositional clauses : 0
% 13.62/3.27 % Propositional clauses after purity: 0
% 13.62/3.27 % Propositional unsat core size : 0
% 13.62/3.27 % Propositional preprocessing time : 0.000
% 13.62/3.27 % Propositional encoding time : 0.000
% 13.62/3.27 % Propositional solver time : 0.000
% 13.62/3.27 % Success case prop preproc time : 0.000
% 13.62/3.27 % Success case prop encoding time : 0.000
% 13.62/3.27 % Success case prop solver time : 0.000
% 13.62/3.27 % Current number of processed clauses : 1407
% 13.62/3.27 % Positive orientable unit clauses : 1116
% 13.62/3.27 % Positive unorientable unit clauses: 21
% 13.62/3.27 % Negative unit clauses : 4
% 13.62/3.27 % Non-unit-clauses : 266
% 13.62/3.27 % Current number of unprocessed clauses: 84477
% 13.62/3.27 % ...number of literals in the above : 113049
% 13.62/3.27 % Current number of archived formulas : 0
% 13.62/3.27 % Current number of archived clauses : 785
% 13.62/3.27 % Clause-clause subsumption calls (NU) : 145440
% 13.62/3.27 % Rec. Clause-clause subsumption calls : 145156
% 13.62/3.27 % Non-unit clause-clause subsumptions : 4650
% 13.62/3.27 % Unit Clause-clause subsumption calls : 11175
% 13.62/3.27 % Rewrite failures with RHS unbound : 0
% 13.62/3.27 % BW rewrite match attempts : 125101
% 13.62/3.27 % BW rewrite match successes : 3331
% 13.62/3.27 % Condensation attempts : 0
% 13.62/3.27 % Condensation successes : 0
% 13.62/3.27 % Termbank termtop insertions : 3258429
% 13.62/3.27 % Search garbage collected termcells : 1092
% 13.62/3.27
% 13.62/3.27 % -------------------------------------------------
% 13.62/3.27 % User time : 2.586 s
% 13.62/3.27 % System time : 0.101 s
% 13.62/3.27 % Total time : 2.687 s
% 13.62/3.27 % Maximum resident set size: 3688 pages
% 13.62/3.27
% 13.62/3.27 % -------------------------------------------------
% 13.62/3.27 % User time : 12.909 s
% 13.62/3.27 % System time : 0.692 s
% 13.62/3.27 % Total time : 13.602 s
% 13.62/3.27 % Maximum resident set size: 4608 pages
% 13.62/3.27 % E exiting
%------------------------------------------------------------------------------