%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL509+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 : n007.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 01:12:56 PM UTC 2026
% Result : Theorem 2.50s 0.91s
% Output : CNFRefutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 18
% Syntax : Number of formulae : 125 ( 50 unt; 0 def)
% Number of atoms : 243 ( 21 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 217 ( 99 ~; 97 |; 10 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-2 aty)
% Number of variables : 215 ( 38 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_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(rosser_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_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(kn3,axiom,
( kn3
<=> ! [X4,X5,X6] : is_a_theorem(implies(implies(X4,X5),implies(not(and(X5,X6)),not(and(X6,X4))))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn3) ).
fof(rosser_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_op_or) ).
fof(rosser_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_modus_ponens) ).
fof(rosser_kn3,axiom,
kn3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn3) ).
fof(kn2,axiom,
( kn2
<=> ! [X4,X5] : is_a_theorem(implies(and(X4,X5),X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn2) ).
fof(rosser_kn2,axiom,
kn2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).
fof(kn1,axiom,
( kn1
<=> ! [X4] : is_a_theorem(implies(X4,and(X4,X4))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(rosser_kn1,axiom,
kn1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn1) ).
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(rosser_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_op_equiv) ).
fof(hilbert_or_1,conjecture,
or_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_1) ).
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(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',use_substitution_of_equivalents) ).
fof(or_1,axiom,
( or_1
<=> ! [X1,X2] : is_a_theorem(implies(X1,or(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_1) ).
fof(c_0_18,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_19,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_20,plain,
( ~ op_implies_and
| implies(X1,X2) = not(and(X1,not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[rosser_op_implies_and]) ).
fof(c_0_22,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])])])])])]) ).
fof(c_0_23,plain,
! [X77,X78,X79] :
( ( kn3
| ~ is_a_theorem(implies(implies(esk36_0,esk37_0),implies(not(and(esk37_0,esk38_0)),not(and(esk38_0,esk36_0))))) )
& ( is_a_theorem(implies(implies(X77,X78),implies(not(and(X78,X79)),not(and(X79,X77)))))
| ~ kn3 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn3])])])])]) ).
cnf(c_0_24,plain,
( ~ op_or
| or(X1,X2) = not(and(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).
cnf(c_0_26,plain,
op_or,
inference(split_conjunct,[status(thm)],[rosser_op_or]) ).
cnf(c_0_27,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| ~ modus_ponens
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[rosser_modus_ponens]) ).
cnf(c_0_29,plain,
( ~ kn3
| is_a_theorem(implies(implies(X1,X2),implies(not(and(X2,X3)),not(and(X3,X1))))) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_31,plain,
kn3,
inference(split_conjunct,[status(thm)],[rosser_kn3]) ).
cnf(c_0_32,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_27,c_0_28])]) ).
cnf(c_0_33,plain,
is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_34,plain,
( ~ is_a_theorem(not(X2))
| ~ is_a_theorem(or(X2,X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_30]) ).
cnf(c_0_35,plain,
( ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(or(and(X1,X2),not(and(X2,X3)))) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_36,plain,
! [X73,X74] :
( ( kn2
| ~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0)) )
& ( is_a_theorem(implies(and(X73,X74),X73))
| ~ kn2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn2])])])])]) ).
cnf(c_0_37,plain,
( ~ is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(not(and(X3,X1)))
| is_a_theorem(not(and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
( ~ kn2
| is_a_theorem(implies(and(X1,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_39,plain,
kn2,
inference(split_conjunct,[status(thm)],[rosser_kn2]) ).
fof(c_0_40,plain,
! [X71] :
( ( kn1
| ~ is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0))) )
& ( is_a_theorem(implies(X71,and(X71,X71)))
| ~ kn1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn1])])])])]) ).
cnf(c_0_41,plain,
( ~ is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(not(and(not(X1),X2))) ),
inference(spm,[status(thm)],[c_0_37,c_0_25]) ).
cnf(c_0_42,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
cnf(c_0_43,plain,
( ~ kn1
| is_a_theorem(implies(X1,and(X1,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,plain,
kn1,
inference(split_conjunct,[status(thm)],[rosser_kn1]) ).
cnf(c_0_45,plain,
( ~ is_a_theorem(implies(X2,and(X1,X3)))
| is_a_theorem(not(and(not(X1),X2))) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
cnf(c_0_47,plain,
( ~ is_a_theorem(or(X2,and(X1,X3)))
| is_a_theorem(or(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_30]),c_0_25]),c_0_30]) ).
cnf(c_0_48,plain,
is_a_theorem(or(X1,and(not(X1),not(X1)))),
inference(spm,[status(thm)],[c_0_46,c_0_30]) ).
cnf(c_0_49,plain,
is_a_theorem(or(not(X1),X1)),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_50,plain,
is_a_theorem(or(X1,not(and(X1,X2)))),
inference(spm,[status(thm)],[c_0_47,c_0_49]) ).
cnf(c_0_51,plain,
( ~ is_a_theorem(not(X1))
| is_a_theorem(not(and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_34,c_0_50]) ).
cnf(c_0_52,plain,
is_a_theorem(not(and(not(X1),X1))),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,plain,
( ~ is_a_theorem(not(X3))
| ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(not(and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_37,c_0_51]) ).
cnf(c_0_54,plain,
( ~ is_a_theorem(implies(X2,not(X1)))
| is_a_theorem(not(and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_37,c_0_52]) ).
cnf(c_0_55,plain,
( ~ is_a_theorem(not(and(X2,X2)))
| is_a_theorem(not(and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_53,c_0_46]) ).
cnf(c_0_56,plain,
( ~ is_a_theorem(or(X2,not(X1)))
| is_a_theorem(implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_25]),c_0_30]) ).
cnf(c_0_57,plain,
( ~ is_a_theorem(not(X2))
| is_a_theorem(not(and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_55,c_0_51]) ).
cnf(c_0_58,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_56,c_0_49]) ).
cnf(c_0_59,plain,
( ~ is_a_theorem(not(not(X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_57,c_0_25]) ).
cnf(c_0_60,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_32,c_0_58]) ).
cnf(c_0_61,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_62,plain,
is_a_theorem(or(X1,implies(X1,X2))),
inference(spm,[status(thm)],[c_0_50,c_0_25]) ).
cnf(c_0_63,plain,
( ~ is_a_theorem(and(X1,X3))
| is_a_theorem(not(and(not(X1),X2))) ),
inference(spm,[status(thm)],[c_0_45,c_0_61]) ).
cnf(c_0_64,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(and(X1,X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_46]) ).
cnf(c_0_65,plain,
( ~ is_a_theorem(or(X3,X1))
| is_a_theorem(or(and(X1,X2),implies(X2,X3))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_25]),c_0_30]) ).
cnf(c_0_66,plain,
( ~ is_a_theorem(not(X1))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_34,c_0_62]) ).
cnf(c_0_67,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(not(and(not(X1),X2))) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_68,plain,
( ~ is_a_theorem(or(X2,X3))
| ~ is_a_theorem(not(and(X3,X1)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_34,c_0_65]) ).
cnf(c_0_69,plain,
( ~ is_a_theorem(implies(X2,not(X2)))
| is_a_theorem(not(and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_55,c_0_54]) ).
cnf(c_0_70,plain,
is_a_theorem(implies(and(not(X1),X1),X2)),
inference(spm,[status(thm)],[c_0_66,c_0_52]) ).
cnf(c_0_71,plain,
( ~ is_a_theorem(X3)
| ~ is_a_theorem(implies(X2,not(X3)))
| is_a_theorem(not(and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_37,c_0_67]) ).
cnf(c_0_72,plain,
( ~ is_a_theorem(or(X2,X3))
| ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(or(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_25]),c_0_30]) ).
cnf(c_0_73,plain,
is_a_theorem(not(and(X1,and(not(X2),X2)))),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,plain,
( ~ is_a_theorem(X3)
| ~ is_a_theorem(or(X2,not(X3)))
| is_a_theorem(implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_30]),c_0_25]) ).
cnf(c_0_75,plain,
( ~ is_a_theorem(or(X2,X1))
| is_a_theorem(or(and(X1,X1),X2)) ),
inference(spm,[status(thm)],[c_0_72,c_0_46]) ).
cnf(c_0_76,plain,
( ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(not(and(and(not(X1),X1),X2))) ),
inference(spm,[status(thm)],[c_0_37,c_0_73]) ).
cnf(c_0_77,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,not(not(X2)))) ),
inference(spm,[status(thm)],[c_0_74,c_0_49]) ).
cnf(c_0_78,plain,
not(and(X1,implies(X2,X3))) = implies(X1,and(X2,not(X3))),
inference(spm,[status(thm)],[c_0_25,c_0_25]) ).
cnf(c_0_79,plain,
( ~ is_a_theorem(or(X1,X2))
| ~ is_a_theorem(not(and(X2,X2)))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_75]) ).
cnf(c_0_80,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(not(and(and(not(X1),X1),X2))) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_81,plain,
is_a_theorem(or(and(X1,implies(X2,X3)),and(implies(X1,and(X2,not(X3))),implies(X1,and(X2,not(X3)))))),
inference(spm,[status(thm)],[c_0_48,c_0_78]) ).
cnf(c_0_82,plain,
( ~ is_a_theorem(not(X2))
| ~ is_a_theorem(or(X1,X2))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_51]) ).
cnf(c_0_83,plain,
is_a_theorem(not(and(and(not(X1),X1),X2))),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_84,plain,
( ~ is_a_theorem(or(X1,X1))
| is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_48]),c_0_25]),c_0_30]) ).
cnf(c_0_85,plain,
( ~ is_a_theorem(or(X2,and(not(X3),X3)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_68,c_0_83]) ).
cnf(c_0_86,plain,
is_a_theorem(or(implies(X1,X2),and(X1,not(X2)))),
inference(spm,[status(thm)],[c_0_49,c_0_25]) ).
cnf(c_0_87,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(or(X1,not(X2)))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_67]) ).
cnf(c_0_88,plain,
( ~ is_a_theorem(or(and(X1,X1),X1))
| is_a_theorem(and(X1,X1)) ),
inference(spm,[status(thm)],[c_0_84,c_0_75]) ).
cnf(c_0_89,plain,
is_a_theorem(implies(X1,or(not(X2),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_30]) ).
cnf(c_0_90,plain,
( ~ is_a_theorem(implies(X3,X1))
| ~ is_a_theorem(and(X2,X3))
| is_a_theorem(and(X1,X2)) ),
inference(spm,[status(thm)],[c_0_87,c_0_35]) ).
cnf(c_0_91,plain,
( ~ is_a_theorem(or(X1,X1))
| is_a_theorem(and(X1,X1)) ),
inference(spm,[status(thm)],[c_0_88,c_0_75]) ).
cnf(c_0_92,plain,
( ~ is_a_theorem(or(X2,X3))
| is_a_theorem(or(or(not(X1),X1),X2)) ),
inference(spm,[status(thm)],[c_0_72,c_0_89]) ).
cnf(c_0_93,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(or(X1,not(not(X2)))) ),
inference(spm,[status(thm)],[c_0_77,c_0_30]) ).
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(or(X3,X1))
| ~ is_a_theorem(or(X2,not(X3)))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_72,c_0_30]) ).
cnf(c_0_96,plain,
( ~ is_a_theorem(or(X2,X2))
| ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(and(X1,X2)) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_97,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(or(or(not(X1),X1),X2)) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_98,plain,
( ~ op_equiv
| equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_99,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[rosser_op_equiv]) ).
fof(c_0_100,negated_conjecture,
~ or_1,
inference(assume_negation,[status(cth)],[hilbert_or_1]) ).
cnf(c_0_101,plain,
( ~ is_a_theorem(or(and(X2,X3),X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_95,c_0_50]) ).
cnf(c_0_102,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
fof(c_0_103,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_104,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(or(X2,X2))
| is_a_theorem(and(X1,X2)) ),
inference(spm,[status(thm)],[c_0_96,c_0_61]) ).
cnf(c_0_105,plain,
is_a_theorem(or(or(not(X1),X1),X2)),
inference(spm,[status(thm)],[c_0_97,c_0_81]) ).
cnf(c_0_106,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_99])]) ).
fof(c_0_107,negated_conjecture,
~ or_1,
inference(fof_simplification,[status(thm)],[c_0_100]) ).
cnf(c_0_108,plain,
( ~ is_a_theorem(implies(implies(X2,X3),X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_109,plain,
( ~ is_a_theorem(equiv(X1,X2))
| ~ substitution_of_equivalents
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_110,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(c_0_111,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(and(X1,or(not(X2),X2))) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_112,plain,
and(implies(X1,not(X2)),or(X2,X1)) = equiv(X1,not(X2)),
inference(spm,[status(thm)],[c_0_106,c_0_30]) ).
fof(c_0_113,plain,
! [X45,X46] :
( ( or_1
| ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0))) )
& ( is_a_theorem(implies(X45,or(X45,X46)))
| ~ or_1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_1])])])])]) ).
fof(c_0_114,negated_conjecture,
~ or_1,
inference(fof_nnf,[status(thm)],[c_0_107]) ).
cnf(c_0_115,plain,
is_a_theorem(or(not(not(implies(X1,X2))),X1)),
inference(spm,[status(thm)],[c_0_108,c_0_58]) ).
cnf(c_0_116,plain,
( ~ is_a_theorem(equiv(X1,X2))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110])]) ).
cnf(c_0_117,plain,
is_a_theorem(equiv(X1,not(not(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_58])]) ).
cnf(c_0_118,plain,
( ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0)))
| or_1 ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_119,negated_conjecture,
~ or_1,
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_120,plain,
is_a_theorem(implies(X1,not(not(or(X1,X2))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_115]),c_0_30]) ).
cnf(c_0_121,plain,
not(not(X1)) = X1,
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_122,plain,
~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0))),
inference(sr,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_123,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_124,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL509+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 : n007.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 00:34:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.50/0.91 % Version: 3.5.1
% 2.50/0.91 % Preprocessing class: FSMSSLSSSSSNFFN.
% 2.50/0.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.50/0.91 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 2.50/0.91 % Starting new_bool_3 with 300s (1) cores
% 2.50/0.91 % Starting new_bool_1 with 300s (1) cores
% 2.50/0.91 % Starting sh5l with 300s (1) cores
% 2.50/0.91 % new_bool_1 with pid 3976732 completed with status 9
% 2.50/0.91 % new_bool_3 with pid 3976731 completed with status 9
% 2.50/0.91 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 3976730 completed with status 0
% 2.50/0.91 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 2.50/0.91 % Preprocessing class: FSMSSLSSSSSNFFN.
% 2.50/0.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.50/0.91 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 2.50/0.91 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.50/0.91 % No SInE strategy applied
% 2.50/0.91 % Search class: FGUSF-FFMM21-MFFFFFNN
% 2.50/0.91 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 2.50/0.91 % Starting SubtermCWHack with 151s (1) cores
% 2.50/0.91 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 2.50/0.91 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 2.50/0.91 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 2.50/0.91 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.50/0.91 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 3976745 completed with status 0
% 2.50/0.91 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 2.50/0.91 % Preprocessing class: FSMSSLSSSSSNFFN.
% 2.50/0.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.50/0.91 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 2.50/0.91 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.50/0.91 % No SInE strategy applied
% 2.50/0.91 % Search class: FGUSF-FFMM21-MFFFFFNN
% 2.50/0.91 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 2.50/0.91 % Starting SubtermCWHack with 151s (1) cores
% 2.50/0.91 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 2.50/0.91 % Preprocessing time : 0.002 s
% 2.50/0.91 % Presaturation interreduction done
% 2.50/0.91
% 2.50/0.91 % Proof found!
% 2.50/0.91 % SZS status Theorem
% 2.50/0.91 % SZS output start CNFRefutation
% See solution above
% 2.50/0.91 % Parsed axioms : 43
% 2.50/0.91 % Removed by relevancy pruning/SinE : 0
% 2.50/0.91 % Initial clauses : 72
% 2.50/0.91 % Removed in clause preprocessing : 0
% 2.50/0.91 % Initial clauses in saturation : 72
% 2.50/0.91 % Processed clauses : 3340
% 2.50/0.91 % ...of these trivial : 75
% 2.50/0.91 % ...subsumed : 2231
% 2.50/0.91 % ...remaining for further processing : 1034
% 2.50/0.91 % Other redundant clauses eliminated : 0
% 2.50/0.91 % Clauses deleted for lack of memory : 0
% 2.50/0.91 % Backward-subsumed : 84
% 2.50/0.91 % Backward-rewritten : 125
% 2.50/0.91 % Generated clauses : 17554
% 2.50/0.91 % ...of the previous two non-redundant : 16594
% 2.50/0.91 % ...aggressively subsumed : 0
% 2.50/0.91 % Contextual simplify-reflections : 1
% 2.50/0.91 % Paramodulations : 17554
% 2.50/0.91 % Factorizations : 0
% 2.50/0.91 % NegExts : 0
% 2.50/0.91 % Equation resolutions : 0
% 2.50/0.91 % Disequality decompositions : 0
% 2.50/0.91 % Total rewrite steps : 5888
% 2.50/0.91 % ...of those cached : 4225
% 2.50/0.91 % Propositional unsat checks : 0
% 2.50/0.91 % Propositional check models : 0
% 2.50/0.91 % Propositional check unsatisfiable : 0
% 2.50/0.91 % Propositional clauses : 0
% 2.50/0.91 % Propositional clauses after purity: 0
% 2.50/0.91 % Propositional unsat core size : 0
% 2.50/0.91 % Propositional preprocessing time : 0.000
% 2.50/0.91 % Propositional encoding time : 0.000
% 2.50/0.91 % Propositional solver time : 0.000
% 2.50/0.91 % Success case prop preproc time : 0.000
% 2.50/0.91 % Success case prop encoding time : 0.000
% 2.50/0.91 % Success case prop solver time : 0.000
% 2.50/0.91 % Current number of processed clauses : 766
% 2.50/0.91 % Positive orientable unit clauses : 131
% 2.50/0.91 % Positive unorientable unit clauses: 0
% 2.50/0.91 % Negative unit clauses : 11
% 2.50/0.91 % Non-unit-clauses : 624
% 2.50/0.91 % Current number of unprocessed clauses: 12618
% 2.50/0.91 % ...number of literals in the above : 27391
% 2.50/0.91 % Current number of archived formulas : 0
% 2.50/0.91 % Current number of archived clauses : 268
% 2.50/0.91 % Clause-clause subsumption calls (NU) : 42289
% 2.50/0.91 % Rec. Clause-clause subsumption calls : 41220
% 2.50/0.91 % Non-unit clause-clause subsumptions : 2261
% 2.50/0.91 % Unit Clause-clause subsumption calls : 2457
% 2.50/0.91 % Rewrite failures with RHS unbound : 0
% 2.50/0.91 % BW rewrite match attempts : 1072
% 2.50/0.91 % BW rewrite match successes : 75
% 2.50/0.91 % Condensation attempts : 0
% 2.50/0.91 % Condensation successes : 0
% 2.50/0.91 % Termbank termtop insertions : 249712
% 2.50/0.91 % Search garbage collected termcells : 1092
% 2.50/0.91
% 2.50/0.91 % -------------------------------------------------
% 2.50/0.91 % User time : 0.425 s
% 2.50/0.91 % System time : 0.022 s
% 2.50/0.91 % Total time : 0.447 s
% 2.50/0.91 % Maximum resident set size: 3688 pages
% 2.50/0.91
% 2.50/0.91 % -------------------------------------------------
% 2.50/0.91 % User time : 2.209 s
% 2.50/0.91 % System time : 0.142 s
% 2.50/0.91 % Total time : 2.351 s
% 2.50/0.91 % Maximum resident set size: 4864 pages
% 2.50/0.91 % E exiting
%------------------------------------------------------------------------------