%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL507+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 01:12:56 PM UTC 2026
% Result : Theorem 6.49s 1.74s
% Output : CNFRefutation 6.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 19
% Syntax : Number of formulae : 130 ( 55 unt; 0 def)
% Number of atoms : 240 ( 23 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 199 ( 89 ~; 87 |; 11 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 14 con; 0-2 aty)
% Number of variables : 208 ( 27 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_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(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_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(rosser_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_op_implies_and) ).
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(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_kn2,axiom,
kn2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).
fof(rosser_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_op_or) ).
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(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+5.ax',use_substitution_of_equivalents) ).
fof(rosser_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_op_equiv) ).
fof(hilbert_and_2,conjecture,
and_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(and_2,axiom,
( and_2
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_2) ).
fof(c_0_19,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_20,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_21,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| ~ modus_ponens
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[rosser_modus_ponens]) ).
cnf(c_0_23,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_20]) ).
cnf(c_0_24,plain,
kn3,
inference(split_conjunct,[status(thm)],[rosser_kn3]) ).
fof(c_0_25,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_26,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_21,c_0_22])]) ).
cnf(c_0_27,plain,
is_a_theorem(implies(implies(X1,X2),implies(not(and(X2,X3)),not(and(X3,X1))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
cnf(c_0_28,plain,
( ~ kn1
| is_a_theorem(implies(X1,and(X1,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,plain,
kn1,
inference(split_conjunct,[status(thm)],[rosser_kn1]) ).
cnf(c_0_30,plain,
( ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(implies(not(and(X1,X2)),not(and(X2,X3)))) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
fof(c_0_32,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_33,plain,
is_a_theorem(implies(not(and(and(X1,X1),X2)),not(and(X2,X1)))),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
( ~ op_implies_and
| implies(X1,X2) = not(and(X1,not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_35,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[rosser_op_implies_and]) ).
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])])])])]) ).
fof(c_0_37,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_38,plain,
( ~ is_a_theorem(not(and(and(X2,X2),X1)))
| is_a_theorem(not(and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_26,c_0_33]) ).
cnf(c_0_39,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).
cnf(c_0_40,plain,
( ~ kn2
| is_a_theorem(implies(and(X1,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,plain,
kn2,
inference(split_conjunct,[status(thm)],[rosser_kn2]) ).
cnf(c_0_42,plain,
( ~ op_or
| or(X1,X2) = not(and(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
op_or,
inference(split_conjunct,[status(thm)],[rosser_op_or]) ).
cnf(c_0_44,plain,
( ~ is_a_theorem(implies(and(X2,X2),X1))
| is_a_theorem(not(and(not(X1),X2))) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).
cnf(c_0_46,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_39]),c_0_43])]) ).
cnf(c_0_47,plain,
is_a_theorem(not(and(not(X1),X1))),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,plain,
( ~ is_a_theorem(or(X3,X1))
| is_a_theorem(implies(not(and(X1,X2)),implies(X2,X3))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_46]),c_0_39]) ).
cnf(c_0_49,plain,
is_a_theorem(or(not(X1),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_39]),c_0_46]) ).
cnf(c_0_50,plain,
( ~ is_a_theorem(not(X2))
| ~ is_a_theorem(or(X2,X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_46]) ).
cnf(c_0_51,plain,
is_a_theorem(or(and(X1,X2),implies(X2,not(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_46]) ).
cnf(c_0_52,plain,
( ~ is_a_theorem(not(and(X2,X1)))
| is_a_theorem(implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_53,plain,
( ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(implies(not(X1),not(X2))) ),
inference(spm,[status(thm)],[c_0_52,c_0_39]) ).
cnf(c_0_54,plain,
is_a_theorem(implies(not(X1),not(and(X1,X2)))),
inference(spm,[status(thm)],[c_0_53,c_0_45]) ).
cnf(c_0_55,plain,
is_a_theorem(implies(not(X1),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_54,c_0_39]) ).
cnf(c_0_56,plain,
is_a_theorem(or(and(X1,X1),not(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_31]),c_0_46]) ).
cnf(c_0_57,plain,
is_a_theorem(or(and(implies(X1,X2),X3),implies(X3,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_55]),c_0_39]),c_0_46]) ).
cnf(c_0_58,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_46,c_0_39]) ).
cnf(c_0_59,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),not(and(not(X3),X1))))),
inference(spm,[status(thm)],[c_0_27,c_0_39]) ).
cnf(c_0_60,plain,
( ~ is_a_theorem(not(and(X1,X1)))
| is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_56]) ).
cnf(c_0_61,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),or(X3,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_46]),c_0_58]) ).
cnf(c_0_62,plain,
( ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(implies(implies(X1,X2),not(and(not(X2),X3)))) ),
inference(spm,[status(thm)],[c_0_26,c_0_59]) ).
cnf(c_0_63,plain,
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_49]) ).
cnf(c_0_64,plain,
( ~ is_a_theorem(or(X1,X1))
| is_a_theorem(not(not(X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_39]),c_0_46]) ).
cnf(c_0_65,plain,
( ~ is_a_theorem(implies(implies(X2,X3),X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_26,c_0_61]) ).
cnf(c_0_66,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(not(X3),X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_55]),c_0_39]) ).
cnf(c_0_67,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_52,c_0_47]) ).
fof(c_0_68,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_69,plain,
( ~ is_a_theorem(or(X1,X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_70,plain,
is_a_theorem(or(implies(not(X1),X2),implies(X2,X3))),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_71,plain,
( ~ is_a_theorem(not(X1))
| is_a_theorem(not(and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_26,c_0_54]) ).
cnf(c_0_72,plain,
( ~ is_a_theorem(not(X1))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_26,c_0_55]) ).
cnf(c_0_73,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_26,c_0_67]) ).
cnf(c_0_74,plain,
( ~ is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0)))
| r3 ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_75,plain,
is_a_theorem(implies(not(X1),not(X1))),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_76,plain,
( ~ is_a_theorem(not(and(X2,X2)))
| is_a_theorem(not(and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_38,c_0_71]) ).
cnf(c_0_77,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_78,plain,
( ~ r3
| is_a_theorem(implies(or(X1,X2),or(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_79,plain,
( ~ is_a_theorem(implies(implies(not(esk48_0),esk49_0),or(esk49_0,esk48_0)))
| r3 ),
inference(rw,[status(thm)],[c_0_74,c_0_46]) ).
cnf(c_0_80,plain,
is_a_theorem(or(and(not(X1),X2),implies(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_75]),c_0_39]),c_0_46]) ).
cnf(c_0_81,plain,
( ~ is_a_theorem(or(X2,X2))
| is_a_theorem(implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_39]),c_0_39]),c_0_46]) ).
cnf(c_0_82,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_77,c_0_46]) ).
cnf(c_0_83,plain,
( ~ is_a_theorem(implies(implies(not(esk48_0),esk49_0),or(esk49_0,esk48_0)))
| is_a_theorem(implies(or(X1,X2),or(X2,X1))) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_84,plain,
is_a_theorem(implies(implies(not(X1),X2),or(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_46]),c_0_58]) ).
cnf(c_0_85,plain,
( ~ is_a_theorem(implies(not(X3),X1))
| is_a_theorem(implies(not(and(X1,X2)),implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_48,c_0_46]) ).
cnf(c_0_86,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_87,plain,
is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_46]),c_0_58]) ).
cnf(c_0_88,plain,
( ~ is_a_theorem(and(X1,not(X2)))
| is_a_theorem(implies(implies(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_77,c_0_39]) ).
cnf(c_0_89,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(and(X1,X1)) ),
inference(spm,[status(thm)],[c_0_26,c_0_31]) ).
cnf(c_0_90,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84])]) ).
cnf(c_0_91,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(not(and(X1,X2)),implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_92,plain,
( ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(or(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_26,c_0_87]) ).
cnf(c_0_93,plain,
( ~ is_a_theorem(not(X1))
| is_a_theorem(implies(or(X1,X1),X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_46]) ).
fof(c_0_94,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_95,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_96,plain,
( ~ is_a_theorem(or(X2,X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_26,c_0_90]) ).
cnf(c_0_97,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(or(and(X1,X2),implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_91,c_0_46]) ).
cnf(c_0_98,plain,
( ~ is_a_theorem(not(X2))
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_92]) ).
cnf(c_0_99,plain,
( ~ is_a_theorem(implies(X1,not(X1)))
| is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_69,c_0_92]) ).
cnf(c_0_100,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(or(not(X1),not(X1)),X2)) ),
inference(spm,[status(thm)],[c_0_93,c_0_73]) ).
cnf(c_0_101,plain,
( ~ is_a_theorem(equiv(X1,X2))
| ~ substitution_of_equivalents
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_102,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(c_0_103,plain,
( ~ op_equiv
| equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_104,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[rosser_op_equiv]) ).
cnf(c_0_105,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(or(implies(X1,X2),and(X3,X1))) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_106,plain,
( ~ is_a_theorem(not(or(X2,not(X1))))
| is_a_theorem(not(implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_98,c_0_87]) ).
cnf(c_0_107,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(not(or(not(X1),not(X1)))) ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_108,plain,
( ~ is_a_theorem(equiv(X1,X2))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_102])]) ).
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_103,c_0_104])]) ).
cnf(c_0_110,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(not(implies(X2,X3)))
| is_a_theorem(and(X1,X2)) ),
inference(spm,[status(thm)],[c_0_50,c_0_105]) ).
cnf(c_0_111,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(not(implies(X1,not(X1)))) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_112,plain,
( ~ is_a_theorem(and(implies(X1,X2),implies(X2,X1)))
| X1 = X2 ),
inference(rw,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_113,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| is_a_theorem(and(X1,X2)) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
fof(c_0_114,negated_conjecture,
~ and_2,
inference(assume_negation,[status(cth)],[hilbert_and_2]) ).
cnf(c_0_115,plain,
( ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
fof(c_0_116,negated_conjecture,
~ and_2,
inference(fof_simplification,[status(thm)],[c_0_114]) ).
cnf(c_0_117,plain,
is_a_theorem(implies(implies(and(X1,X1),X2),not(and(not(X2),X1)))),
inference(spm,[status(thm)],[c_0_33,c_0_39]) ).
cnf(c_0_118,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_67]),c_0_46]),c_0_49])]) ).
fof(c_0_119,plain,
! [X37,X38] :
( ( and_2
| ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0)) )
& ( is_a_theorem(implies(and(X37,X38),X38))
| ~ and_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)],[and_2])])])])]) ).
fof(c_0_120,negated_conjecture,
~ and_2,
inference(fof_nnf,[status(thm)],[c_0_116]) ).
cnf(c_0_121,plain,
is_a_theorem(or(not(and(not(X1),X2)),and(X2,X2))),
inference(spm,[status(thm)],[c_0_65,c_0_117]) ).
cnf(c_0_122,plain,
or(not(X1),X2) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_46,c_0_118]) ).
cnf(c_0_123,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_31]),c_0_45])]) ).
cnf(c_0_124,plain,
( ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0))
| and_2 ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_125,negated_conjecture,
~ and_2,
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_126,plain,
is_a_theorem(implies(and(not(X1),X2),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_122]),c_0_123]) ).
cnf(c_0_127,plain,
~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0)),
inference(sr,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_128,plain,
is_a_theorem(implies(and(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_126,c_0_118]) ).
cnf(c_0_129,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_128])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL507+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % 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 00:35:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 6.49/1.74 % Version: 3.5.1
% 6.49/1.74 % Preprocessing class: FSMSSLSSSSSNFFN.
% 6.49/1.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.49/1.74 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 6.49/1.74 % Starting new_bool_3 with 300s (1) cores
% 6.49/1.74 % Starting new_bool_1 with 300s (1) cores
% 6.49/1.74 % Starting sh5l with 300s (1) cores
% 6.49/1.74 % new_bool_3 with pid 584832 completed with status 9
% 6.49/1.74 % new_bool_1 with pid 584833 completed with status 9
% 6.49/1.74 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 584831 completed with status 0
% 6.49/1.74 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 6.49/1.74 % Preprocessing class: FSMSSLSSSSSNFFN.
% 6.49/1.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.49/1.74 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 6.49/1.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.49/1.74 % No SInE strategy applied
% 6.49/1.74 % Search class: FGUSF-FFMM21-MFFFFFNN
% 6.49/1.74 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 6.49/1.74 % Starting SubtermCWHack with 151s (1) cores
% 6.49/1.74 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 6.49/1.74 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 6.49/1.74 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 6.49/1.74 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 6.49/1.74 % G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with pid 584844 completed with status 0
% 6.49/1.74 % Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI
% 6.49/1.74 % Preprocessing class: FSMSSLSSSSSNFFN.
% 6.49/1.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.49/1.74 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 6.49/1.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.49/1.74 % No SInE strategy applied
% 6.49/1.74 % Search class: FGUSF-FFMM21-MFFFFFNN
% 6.49/1.74 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 6.49/1.74 % Starting SubtermCWHack with 151s (1) cores
% 6.49/1.74 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 6.49/1.74 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 6.49/1.74 % Preprocessing time : 0.002 s
% 6.49/1.74 % Presaturation interreduction done
% 6.49/1.74
% 6.49/1.74 % Proof found!
% 6.49/1.74 % SZS status Theorem
% 6.49/1.74 % SZS output start CNFRefutation
% See solution above
% 6.49/1.74 % Parsed axioms : 43
% 6.49/1.74 % Removed by relevancy pruning/SinE : 0
% 6.49/1.74 % Initial clauses : 72
% 6.49/1.74 % Removed in clause preprocessing : 0
% 6.49/1.74 % Initial clauses in saturation : 72
% 6.49/1.74 % Processed clauses : 5440
% 6.49/1.74 % ...of these trivial : 196
% 6.49/1.74 % ...subsumed : 4017
% 6.49/1.74 % ...remaining for further processing : 1227
% 6.49/1.74 % Other redundant clauses eliminated : 0
% 6.49/1.74 % Clauses deleted for lack of memory : 0
% 6.49/1.74 % Backward-subsumed : 15
% 6.49/1.74 % Backward-rewritten : 262
% 6.49/1.74 % Generated clauses : 86807
% 6.49/1.74 % ...of the previous two non-redundant : 82357
% 6.49/1.74 % ...aggressively subsumed : 0
% 6.49/1.74 % Contextual simplify-reflections : 0
% 6.49/1.74 % Paramodulations : 86807
% 6.49/1.74 % Factorizations : 0
% 6.49/1.74 % NegExts : 0
% 6.49/1.74 % Equation resolutions : 0
% 6.49/1.74 % Disequality decompositions : 0
% 6.49/1.74 % Total rewrite steps : 17895
% 6.49/1.74 % ...of those cached : 14169
% 6.49/1.74 % Propositional unsat checks : 0
% 6.49/1.74 % Propositional check models : 0
% 6.49/1.74 % Propositional check unsatisfiable : 0
% 6.49/1.74 % Propositional clauses : 0
% 6.49/1.74 % Propositional clauses after purity: 0
% 6.49/1.74 % Propositional unsat core size : 0
% 6.49/1.74 % Propositional preprocessing time : 0.000
% 6.49/1.74 % Propositional encoding time : 0.000
% 6.49/1.74 % Propositional solver time : 0.000
% 6.49/1.74 % Success case prop preproc time : 0.000
% 6.49/1.74 % Success case prop encoding time : 0.000
% 6.49/1.74 % Success case prop solver time : 0.000
% 6.49/1.74 % Current number of processed clauses : 892
% 6.49/1.74 % Positive orientable unit clauses : 379
% 6.49/1.74 % Positive unorientable unit clauses: 28
% 6.49/1.74 % Negative unit clauses : 4
% 6.49/1.74 % Non-unit-clauses : 481
% 6.49/1.74 % Current number of unprocessed clauses: 74430
% 6.49/1.74 % ...number of literals in the above : 115695
% 6.49/1.74 % Current number of archived formulas : 0
% 6.49/1.74 % Current number of archived clauses : 335
% 6.49/1.74 % Clause-clause subsumption calls (NU) : 95868
% 6.49/1.74 % Rec. Clause-clause subsumption calls : 95768
% 6.49/1.74 % Non-unit clause-clause subsumptions : 4008
% 6.49/1.74 % Unit Clause-clause subsumption calls : 6687
% 6.49/1.74 % Rewrite failures with RHS unbound : 22
% 6.49/1.74 % BW rewrite match attempts : 11787
% 6.49/1.74 % BW rewrite match successes : 579
% 6.49/1.74 % Condensation attempts : 0
% 6.49/1.74 % Condensation successes : 0
% 6.49/1.74 % Termbank termtop insertions : 1218531
% 6.49/1.74 % Search garbage collected termcells : 1092
% 6.49/1.74
% 6.49/1.74 % -------------------------------------------------
% 6.49/1.74 % User time : 1.211 s
% 6.49/1.74 % System time : 0.068 s
% 6.49/1.74 % Total time : 1.279 s
% 6.49/1.74 % Maximum resident set size: 3688 pages
% 6.49/1.74
% 6.49/1.74 % -------------------------------------------------
% 6.49/1.74 % User time : 6.116 s
% 6.49/1.74 % System time : 0.365 s
% 6.49/1.74 % Total time : 6.482 s
% 6.49/1.74 % Maximum resident set size: 4864 pages
% 6.49/1.74 % E exiting
%------------------------------------------------------------------------------