%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL485+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 : n004.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 01:12:53 PM UTC 2026
% Result : Theorem 2.53s 1.01s
% Output : CNFRefutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 26
% Syntax : Number of formulae : 155 ( 73 unt; 0 def)
% Number of atoms : 277 ( 37 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 219 ( 97 ~; 95 |; 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 : 256 ( 30 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_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(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(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(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(principia_op_and,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
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(principia_r5,axiom,
r5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r5) ).
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(hilbert_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(principia_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
fof(principia_r2,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
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(principia_r3,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
fof(r1,axiom,
( r1
<=> ! [X4] : is_a_theorem(implies(or(X4,X4),X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r1) ).
fof(principia_r1,axiom,
r1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r1) ).
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_r4,axiom,
r4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r4) ).
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(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(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',use_substitution_of_equivalents) ).
fof(principia_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_equiv) ).
fof(hilbert_implies_2,conjecture,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X1,X2] : is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_2) ).
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,
! [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_28,plain,
( ~ op_implies_or
| implies(X1,X2) = or(not(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_29,plain,
op_implies_or,
inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).
fof(c_0_30,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_31,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])])])])]) ).
fof(c_0_32,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_33,plain,
( ~ op_and
| and(X1,X2) = not(or(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
or(not(X1),X2) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
cnf(c_0_35,plain,
op_and,
inference(split_conjunct,[status(thm)],[principia_op_and]) ).
cnf(c_0_36,plain,
( ~ op_implies_and
| implies(X1,X2) = not(and(X1,not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
fof(c_0_38,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_39,plain,
( ~ r5
| is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,plain,
r5,
inference(split_conjunct,[status(thm)],[principia_r5]) ).
fof(c_0_41,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])])])])]) ).
cnf(c_0_42,plain,
( ~ op_or
| or(X1,X2) = not(and(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_43,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])]) ).
cnf(c_0_44,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).
cnf(c_0_45,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
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_38]) ).
cnf(c_0_47,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[principia_modus_ponens]) ).
cnf(c_0_48,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_39,c_0_40])]) ).
cnf(c_0_49,plain,
( ~ r2
| is_a_theorem(implies(X1,or(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,plain,
r2,
inference(split_conjunct,[status(thm)],[principia_r2]) ).
cnf(c_0_51,plain,
not(not(implies(not(X1),not(not(X2))))) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_52,plain,
not(not(implies(X1,not(not(X2))))) = implies(X1,X2),
inference(rw,[status(thm)],[c_0_45,c_0_43]) ).
fof(c_0_53,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_54,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_55,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_48,c_0_34]),c_0_34]) ).
cnf(c_0_56,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
cnf(c_0_57,plain,
implies(not(X1),X2) = or(X1,X2),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,plain,
( ~ r3
| is_a_theorem(implies(or(X1,X2),or(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_59,plain,
r3,
inference(split_conjunct,[status(thm)],[principia_r3]) ).
cnf(c_0_60,plain,
( ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(implies(X1,X2),implies(X1,X3))) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_56,c_0_34]) ).
cnf(c_0_62,plain,
implies(not(not(X1)),X2) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_57]) ).
cnf(c_0_63,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]) ).
cnf(c_0_64,plain,
( ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X1,X3))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_54,c_0_60]) ).
cnf(c_0_65,plain,
is_a_theorem(implies(X1,implies(X2,not(not(X1))))),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,plain,
( ~ is_a_theorem(or(X2,X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_54,c_0_63]) ).
cnf(c_0_67,plain,
( ~ is_a_theorem(implies(implies(X3,X1),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_64,c_0_61]) ).
cnf(c_0_68,plain,
is_a_theorem(implies(implies(not(X1),X2),or(X2,X1))),
inference(spm,[status(thm)],[c_0_63,c_0_57]) ).
fof(c_0_69,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])])])])]) ).
cnf(c_0_70,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,not(not(X2)))) ),
inference(spm,[status(thm)],[c_0_54,c_0_65]) ).
cnf(c_0_71,plain,
( ~ is_a_theorem(implies(not(X2),X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_66,c_0_57]) ).
cnf(c_0_72,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,plain,
( ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(or(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_66,c_0_34]) ).
cnf(c_0_74,plain,
( ~ r1
| is_a_theorem(implies(or(X1,X1),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_75,plain,
r1,
inference(split_conjunct,[status(thm)],[principia_r1]) ).
fof(c_0_76,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_77,plain,
( ~ is_a_theorem(X3)
| ~ is_a_theorem(implies(X3,X2))
| is_a_theorem(implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_70]),c_0_62]) ).
cnf(c_0_78,plain,
is_a_theorem(or(implies(X1,X2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_34]) ).
cnf(c_0_79,plain,
( ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(implies(not(X1),not(X2))) ),
inference(spm,[status(thm)],[c_0_73,c_0_57]) ).
cnf(c_0_80,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
cnf(c_0_81,plain,
( ~ r4
| is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_82,plain,
r4,
inference(split_conjunct,[status(thm)],[principia_r4]) ).
cnf(c_0_83,plain,
( ~ is_a_theorem(or(X3,X2))
| is_a_theorem(implies(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_77,c_0_63]) ).
cnf(c_0_84,plain,
is_a_theorem(or(X1,implies(X1,X2))),
inference(spm,[status(thm)],[c_0_66,c_0_78]) ).
cnf(c_0_85,plain,
is_a_theorem(implies(not(X1),not(or(X1,X1)))),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_86,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_81,c_0_82])]) ).
cnf(c_0_87,plain,
is_a_theorem(implies(X1,or(implies(X2,X3),X2))),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_88,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_54,c_0_56]) ).
cnf(c_0_89,plain,
( ~ is_a_theorem(not(X2))
| ~ is_a_theorem(or(X2,X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_57]) ).
cnf(c_0_90,plain,
is_a_theorem(implies(or(X1,X1),not(not(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_85]),c_0_62]) ).
cnf(c_0_91,plain,
( ~ is_a_theorem(or(X2,or(X1,X3)))
| is_a_theorem(or(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_54,c_0_86]) ).
cnf(c_0_92,plain,
is_a_theorem(or(X1,or(implies(X2,X3),X2))),
inference(spm,[status(thm)],[c_0_87,c_0_57]) ).
fof(c_0_93,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])])])])])]) ).
fof(c_0_94,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_95,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_66,c_0_88]) ).
cnf(c_0_96,plain,
( ~ is_a_theorem(not(X2))
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_89,c_0_73]) ).
cnf(c_0_97,plain,
( ~ is_a_theorem(or(X1,X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_80]) ).
cnf(c_0_98,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(or(X1,X1),X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_90]),c_0_62]) ).
cnf(c_0_99,plain,
is_a_theorem(or(implies(X1,X2),or(X3,X1))),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_100,plain,
( ~ is_a_theorem(equiv(X1,X2))
| ~ substitution_of_equivalents
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_101,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(c_0_102,plain,
( ~ op_equiv
| equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_103,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[principia_op_equiv]) ).
cnf(c_0_104,plain,
( ~ is_a_theorem(not(X1))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_95,c_0_34]) ).
cnf(c_0_105,plain,
( ~ is_a_theorem(not(X1))
| is_a_theorem(not(or(X1,X1))) ),
inference(spm,[status(thm)],[c_0_96,c_0_80]) ).
cnf(c_0_106,plain,
( ~ is_a_theorem(implies(X1,not(X1)))
| is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_97,c_0_34]) ).
cnf(c_0_107,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_95,c_0_57]) ).
cnf(c_0_108,plain,
( ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(or(X2,X2))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_98]) ).
cnf(c_0_109,plain,
is_a_theorem(or(implies(X1,X2),implies(X3,X1))),
inference(spm,[status(thm)],[c_0_99,c_0_34]) ).
cnf(c_0_110,plain,
( ~ is_a_theorem(equiv(X1,X2))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101])]) ).
cnf(c_0_111,plain,
equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_103])]) ).
cnf(c_0_112,plain,
( ~ is_a_theorem(not(X1))
| is_a_theorem(implies(or(X1,X1),X2)) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_113,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_114,plain,
is_a_theorem(implies(implies(X1,not(X1)),not(X1))),
inference(spm,[status(thm)],[c_0_80,c_0_34]) ).
cnf(c_0_115,plain,
( ~ is_a_theorem(implies(implies(X2,X2),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_116,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_86,c_0_34]),c_0_34]) ).
cnf(c_0_117,plain,
( ~ is_a_theorem(not(implies(implies(X1,X2),not(implies(X2,X1)))))
| X1 = X2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_111]),c_0_43]) ).
cnf(c_0_118,plain,
implies(implies(X1,not(not(X2))),X3) = implies(implies(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_52]),c_0_34]) ).
cnf(c_0_119,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X1,not(X1)),X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_34]) ).
cnf(c_0_120,plain,
is_a_theorem(implies(not(X1),not(X1))),
inference(spm,[status(thm)],[c_0_67,c_0_114]) ).
cnf(c_0_121,plain,
is_a_theorem(or(X1,implies(or(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_122,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_117,c_0_62]),c_0_118]) ).
cnf(c_0_123,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(not(implies(X1,not(X1)))) ),
inference(spm,[status(thm)],[c_0_106,c_0_119]) ).
cnf(c_0_124,plain,
is_a_theorem(implies(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_120]),c_0_34]) ).
cnf(c_0_125,plain,
( ~ is_a_theorem(not(X1))
| is_a_theorem(implies(or(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_89,c_0_121]) ).
cnf(c_0_126,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_124])]) ).
cnf(c_0_127,plain,
( ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(or(X1,X2),or(X1,X3))) ),
inference(spm,[status(thm)],[c_0_54,c_0_48]) ).
cnf(c_0_128,plain,
( ~ is_a_theorem(implies(X1,X3))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_67,c_0_60]) ).
fof(c_0_129,negated_conjecture,
~ implies_2,
inference(assume_negation,[status(cth)],[hilbert_implies_2]) ).
cnf(c_0_130,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X1,X2),X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_34]) ).
cnf(c_0_131,plain,
( ~ is_a_theorem(implies(X2,X4))
| ~ is_a_theorem(implies(or(X1,X4),X3))
| is_a_theorem(implies(or(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_64,c_0_127]) ).
cnf(c_0_132,plain,
( ~ is_a_theorem(implies(not(X3),X2))
| is_a_theorem(or(implies(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_71,c_0_128]) ).
cnf(c_0_133,plain,
is_a_theorem(implies(X1,not(implies(X1,not(X1))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_114]),c_0_62]) ).
fof(c_0_134,negated_conjecture,
~ implies_2,
inference(fof_simplification,[status(thm)],[c_0_129]) ).
cnf(c_0_135,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(not(X2))
| is_a_theorem(not(implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_96,c_0_130]) ).
cnf(c_0_136,plain,
( ~ is_a_theorem(implies(or(X2,X1),X3))
| is_a_theorem(implies(or(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_64,c_0_63]) ).
cnf(c_0_137,plain,
( ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(implies(or(X1,X2),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_90]),c_0_126]) ).
cnf(c_0_138,plain,
is_a_theorem(or(implies(X1,not(or(X2,X2))),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_126]),c_0_57]) ).
fof(c_0_139,plain,
! [X23,X24] :
( ( implies_2
| ~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0))) )
& ( is_a_theorem(implies(implies(X23,implies(X23,X24)),implies(X23,X24)))
| ~ implies_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)],[implies_2])])])])]) ).
fof(c_0_140,negated_conjecture,
~ implies_2,
inference(fof_nnf,[status(thm)],[c_0_134]) ).
cnf(c_0_141,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_117,c_0_135]),c_0_126]) ).
cnf(c_0_142,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(or(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_143,plain,
is_a_theorem(or(or(X1,not(or(X2,X2))),X2)),
inference(spm,[status(thm)],[c_0_138,c_0_57]) ).
cnf(c_0_144,plain,
is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_63,c_0_34]) ).
cnf(c_0_145,plain,
is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_63,c_0_34]) ).
cnf(c_0_146,plain,
( ~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0)))
| implies_2 ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_147,negated_conjecture,
~ implies_2,
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_148,plain,
( ~ is_a_theorem(implies(X1,X2))
| or(X1,X2) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_56])]) ).
cnf(c_0_149,plain,
is_a_theorem(implies(not(X1),or(X2,not(or(X1,X1))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_143]),c_0_57]) ).
cnf(c_0_150,plain,
or(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_90]),c_0_126]),c_0_126]),c_0_72])]) ).
cnf(c_0_151,plain,
or(X1,not(X2)) = implies(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_144]),c_0_145])]) ).
cnf(c_0_152,plain,
~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0))),
inference(sr,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_153,plain,
implies(X1,implies(X1,X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_150]),c_0_151]),c_0_34]),c_0_150]),c_0_151]) ).
cnf(c_0_154,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_124])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL485+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 % Computer : n004.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Mon Sep 21 00:35:34 UTC 2026
% 0.08/0.33 % CPUTime :
% 0.08/0.33 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 2.53/1.01 % Version: 3.5.1
% 2.53/1.01 % Preprocessing class: FSMSSLSSSSSNFFN.
% 2.53/1.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.53/1.01 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 2.53/1.01 % Starting new_bool_3 with 300s (1) cores
% 2.53/1.01 % Starting new_bool_1 with 300s (1) cores
% 2.53/1.01 % Starting sh5l with 300s (1) cores
% 2.53/1.01 % new_bool_3 with pid 1877539 completed with status 9
% 2.53/1.01 % new_bool_1 with pid 1877540 completed with status 9
% 2.53/1.01 % sh5l with pid 1877541 completed with status 9
% 2.53/1.01 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 1877538 completed with status 0
% 2.53/1.01 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 2.53/1.01 % Preprocessing class: FSMSSLSSSSSNFFN.
% 2.53/1.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.53/1.01 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 2.53/1.01 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.53/1.01 % No SInE strategy applied
% 2.53/1.01 % Search class: FGUSF-FFMM21-MFFFFFNN
% 2.53/1.01 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 2.53/1.01 % Starting SubtermCWHack with 151s (1) cores
% 2.53/1.01 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 2.53/1.01 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 2.53/1.01 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 2.53/1.01 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.53/1.01 % G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with pid 1877553 completed with status 0
% 2.53/1.01 % Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI
% 2.53/1.01 % Preprocessing class: FSMSSLSSSSSNFFN.
% 2.53/1.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.53/1.01 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 2.53/1.01 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.53/1.01 % No SInE strategy applied
% 2.53/1.01 % Search class: FGUSF-FFMM21-MFFFFFNN
% 2.53/1.01 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 2.53/1.01 % Starting SubtermCWHack with 151s (1) cores
% 2.53/1.01 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 2.53/1.01 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 2.53/1.01 % Preprocessing time : 0.002 s
% 2.53/1.01 % Presaturation interreduction done
% 2.53/1.01
% 2.53/1.01 % Proof found!
% 2.53/1.01 % SZS status Theorem
% 2.53/1.01 % SZS output start CNFRefutation
% See solution above
% 2.53/1.02 % Parsed axioms : 45
% 2.53/1.02 % Removed by relevancy pruning/SinE : 0
% 2.53/1.02 % Initial clauses : 74
% 2.53/1.02 % Removed in clause preprocessing : 0
% 2.53/1.02 % Initial clauses in saturation : 74
% 2.53/1.02 % Processed clauses : 7903
% 2.53/1.02 % ...of these trivial : 757
% 2.53/1.02 % ...subsumed : 6062
% 2.53/1.02 % ...remaining for further processing : 1084
% 2.53/1.02 % Other redundant clauses eliminated : 0
% 2.53/1.02 % Clauses deleted for lack of memory : 0
% 2.53/1.02 % Backward-subsumed : 15
% 2.53/1.02 % Backward-rewritten : 171
% 2.53/1.02 % Generated clauses : 95421
% 2.53/1.02 % ...of the previous two non-redundant : 81293
% 2.53/1.02 % ...aggressively subsumed : 0
% 2.53/1.02 % Contextual simplify-reflections : 0
% 2.53/1.02 % Paramodulations : 95421
% 2.53/1.02 % Factorizations : 0
% 2.53/1.02 % NegExts : 0
% 2.53/1.02 % Equation resolutions : 0
% 2.53/1.02 % Disequality decompositions : 0
% 2.53/1.02 % Total rewrite steps : 28809
% 2.53/1.02 % ...of those cached : 24041
% 2.53/1.02 % Propositional unsat checks : 0
% 2.53/1.02 % Propositional check models : 0
% 2.53/1.02 % Propositional check unsatisfiable : 0
% 2.53/1.02 % Propositional clauses : 0
% 2.53/1.02 % Propositional clauses after purity: 0
% 2.53/1.02 % Propositional unsat core size : 0
% 2.53/1.02 % Propositional preprocessing time : 0.000
% 2.53/1.02 % Propositional encoding time : 0.000
% 2.53/1.02 % Propositional solver time : 0.000
% 2.53/1.02 % Success case prop preproc time : 0.000
% 2.53/1.02 % Success case prop encoding time : 0.000
% 2.53/1.02 % Success case prop solver time : 0.000
% 2.53/1.02 % Current number of processed clauses : 837
% 2.53/1.02 % Positive orientable unit clauses : 307
% 2.53/1.02 % Positive unorientable unit clauses: 6
% 2.53/1.02 % Negative unit clauses : 7
% 2.53/1.02 % Non-unit-clauses : 517
% 2.53/1.02 % Current number of unprocessed clauses: 69420
% 2.53/1.02 % ...number of literals in the above : 104298
% 2.53/1.02 % Current number of archived formulas : 0
% 2.53/1.02 % Current number of archived clauses : 247
% 2.53/1.02 % Clause-clause subsumption calls (NU) : 105468
% 2.53/1.02 % Rec. Clause-clause subsumption calls : 105384
% 2.53/1.02 % Non-unit clause-clause subsumptions : 6007
% 2.53/1.02 % Unit Clause-clause subsumption calls : 4524
% 2.53/1.02 % Rewrite failures with RHS unbound : 40
% 2.53/1.02 % BW rewrite match attempts : 12540
% 2.53/1.02 % BW rewrite match successes : 643
% 2.53/1.02 % Condensation attempts : 0
% 2.53/1.02 % Condensation successes : 0
% 2.53/1.02 % Termbank termtop insertions : 945127
% 2.53/1.02 % Search garbage collected termcells : 1092
% 2.53/1.02
% 2.53/1.02 % -------------------------------------------------
% 2.53/1.02 % User time : 0.521 s
% 2.53/1.02 % System time : 0.029 s
% 2.53/1.02 % Total time : 0.550 s
% 2.53/1.02 % Maximum resident set size: 3944 pages
% 2.53/1.02
% 2.53/1.02 % -------------------------------------------------
% 2.53/1.02 % User time : 2.766 s
% 2.53/1.02 % System time : 0.205 s
% 2.53/1.02 % Total time : 2.971 s
% 2.53/1.02 % Maximum resident set size: 4608 pages
% 2.53/1.02 % E exiting
%------------------------------------------------------------------------------