%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL504+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 75.23s 19.53s
% Output : CNFRefutation 75.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 14
% Syntax : Number of formulae : 130 ( 72 unt; 0 def)
% Number of atoms : 215 ( 11 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 157 ( 72 ~; 69 |; 8 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 225 ( 25 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(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/sandbox/benchmark/Axioms/LCL006+0.ax',kn3) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(rosser_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_op_implies_and) ).
fof(rosser_kn3,axiom,
kn3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn3) ).
fof(rosser_op_or,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_op_or) ).
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/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(rosser_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_modus_ponens) ).
fof(kn1,axiom,
( kn1
<=> ! [X4] : is_a_theorem(implies(X4,and(X4,X4))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(rosser_kn1,axiom,
kn1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn1) ).
fof(kn2,axiom,
( kn2
<=> ! [X4,X5] : is_a_theorem(implies(and(X4,X5),X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn2) ).
fof(rosser_kn2,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).
fof(hilbert_implies_2,conjecture,
implies_2,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(c_0_14,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_15,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])])])])]) ).
fof(c_0_16,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_17,plain,
( ~ op_implies_and
| implies(X1,X2) = not(and(X1,not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[rosser_op_implies_and]) ).
cnf(c_0_19,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_15]) ).
cnf(c_0_20,plain,
kn3,
inference(split_conjunct,[status(thm)],[rosser_kn3]) ).
cnf(c_0_21,plain,
( ~ op_or
| or(X1,X2) = not(and(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_23,plain,
op_or,
inference(split_conjunct,[status(thm)],[rosser_op_or]) ).
fof(c_0_24,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_25,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_19,c_0_20])]) ).
cnf(c_0_26,plain,
or(X1,X2) = implies(not(X1),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
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_24]) ).
cnf(c_0_28,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[rosser_modus_ponens]) ).
cnf(c_0_29,plain,
is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1))))),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,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_31,plain,
is_a_theorem(implies(or(X1,X2),or(and(X2,X3),implies(X3,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_26]),c_0_22]) ).
fof(c_0_32,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_33,plain,
( ~ is_a_theorem(or(X3,X1))
| is_a_theorem(or(and(X1,X2),implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
( ~ kn1
| is_a_theorem(implies(X1,and(X1,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_35,plain,
kn1,
inference(split_conjunct,[status(thm)],[rosser_kn1]) ).
cnf(c_0_36,plain,
( ~ is_a_theorem(implies(not(X3),X1))
| is_a_theorem(or(and(X1,X2),implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_33,c_0_26]) ).
cnf(c_0_37,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).
cnf(c_0_38,plain,
is_a_theorem(or(and(and(not(X1),not(X1)),X2),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
fof(c_0_40,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_41,plain,
is_a_theorem(implies(implies(and(not(X1),not(X1)),X2),or(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_26]),c_0_39]) ).
cnf(c_0_42,plain,
( ~ kn2
| is_a_theorem(implies(and(X1,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_43,plain,
kn2,
inference(split_conjunct,[status(thm)],[rosser_kn2]) ).
cnf(c_0_44,plain,
is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),or(X3,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_26]),c_0_39]) ).
cnf(c_0_45,plain,
( ~ is_a_theorem(implies(and(not(X2),not(X2)),X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_30,c_0_41]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
cnf(c_0_47,plain,
( ~ is_a_theorem(or(X3,X1))
| is_a_theorem(implies(implies(X1,X2),or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_30,c_0_44]) ).
cnf(c_0_48,plain,
is_a_theorem(or(not(X1),X1)),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,plain,
is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_50,plain,
is_a_theorem(implies(or(X1,X2),or(X2,not(not(X1))))),
inference(spm,[status(thm)],[c_0_49,c_0_26]) ).
cnf(c_0_51,plain,
( ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(or(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_30,c_0_49]) ).
cnf(c_0_52,plain,
( ~ is_a_theorem(or(X2,X1))
| is_a_theorem(or(X1,not(not(X2)))) ),
inference(spm,[status(thm)],[c_0_30,c_0_50]) ).
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_51,c_0_26]) ).
cnf(c_0_54,plain,
is_a_theorem(implies(not(X1),not(not(not(X1))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_48]),c_0_26]) ).
cnf(c_0_55,plain,
is_a_theorem(or(and(X1,X1),not(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_37]),c_0_26]) ).
cnf(c_0_56,plain,
is_a_theorem(or(and(not(not(not(X1))),X2),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_36,c_0_54]) ).
cnf(c_0_57,plain,
is_a_theorem(implies(implies(not(X1),X2),or(X2,and(X1,X1)))),
inference(spm,[status(thm)],[c_0_47,c_0_55]) ).
cnf(c_0_58,plain,
not(and(X1,implies(X2,X3))) = implies(X1,and(X2,not(X3))),
inference(spm,[status(thm)],[c_0_22,c_0_22]) ).
cnf(c_0_59,plain,
is_a_theorem(implies(implies(not(not(not(X1))),X2),or(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_26]),c_0_39]) ).
cnf(c_0_60,plain,
is_a_theorem(implies(or(X1,X2),or(X2,and(X1,X1)))),
inference(spm,[status(thm)],[c_0_57,c_0_26]) ).
cnf(c_0_61,plain,
( ~ is_a_theorem(not(X2))
| ~ is_a_theorem(or(X2,X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_62,plain,
is_a_theorem(or(and(X1,X2),implies(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_33,c_0_48]) ).
cnf(c_0_63,plain,
not(and(X1,or(X2,X3))) = implies(X1,and(not(X2),not(X3))),
inference(spm,[status(thm)],[c_0_58,c_0_26]) ).
cnf(c_0_64,plain,
is_a_theorem(implies(or(not(not(X1)),X2),or(X2,X1))),
inference(spm,[status(thm)],[c_0_59,c_0_26]) ).
cnf(c_0_65,plain,
( ~ is_a_theorem(or(X2,X1))
| is_a_theorem(or(X1,and(X2,X2))) ),
inference(spm,[status(thm)],[c_0_30,c_0_60]) ).
cnf(c_0_66,plain,
( ~ is_a_theorem(not(X2))
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_61,c_0_51]) ).
cnf(c_0_67,plain,
( ~ is_a_theorem(not(and(X2,X1)))
| is_a_theorem(implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_68,plain,
is_a_theorem(not(and(not(X1),or(X1,X1)))),
inference(spm,[status(thm)],[c_0_37,c_0_63]) ).
cnf(c_0_69,plain,
( ~ is_a_theorem(or(not(not(X2)),X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_30,c_0_64]) ).
cnf(c_0_70,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(or(not(X1),and(X2,X2))) ),
inference(spm,[status(thm)],[c_0_65,c_0_51]) ).
cnf(c_0_71,plain,
( ~ is_a_theorem(not(X1))
| is_a_theorem(not(and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_66,c_0_46]) ).
cnf(c_0_72,plain,
is_a_theorem(implies(or(X1,X1),not(not(X1)))),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,plain,
( ~ is_a_theorem(implies(not(X2),X1))
| is_a_theorem(or(and(X1,X1),X2)) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,plain,
( ~ is_a_theorem(not(X1))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_71,c_0_22]) ).
cnf(c_0_75,plain,
( ~ is_a_theorem(or(X1,X1))
| is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_30,c_0_72]) ).
cnf(c_0_76,plain,
is_a_theorem(or(not(not(X1)),not(or(X1,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_72]),c_0_26]) ).
cnf(c_0_77,plain,
is_a_theorem(implies(not(X1),not(and(X1,X2)))),
inference(spm,[status(thm)],[c_0_53,c_0_46]) ).
cnf(c_0_78,plain,
( ~ is_a_theorem(or(X2,X1))
| is_a_theorem(or(and(X1,X1),X2)) ),
inference(spm,[status(thm)],[c_0_73,c_0_26]) ).
cnf(c_0_79,plain,
( ~ is_a_theorem(or(X1,X1))
| is_a_theorem(implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_80,plain,
is_a_theorem(or(not(or(X1,X1)),X1)),
inference(spm,[status(thm)],[c_0_69,c_0_76]) ).
cnf(c_0_81,plain,
is_a_theorem(implies(not(X1),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_77,c_0_22]) ).
cnf(c_0_82,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(or(X1,X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_51]),c_0_39]),c_0_26]) ).
cnf(c_0_83,plain,
( ~ is_a_theorem(or(X1,X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_79,c_0_26]) ).
cnf(c_0_84,plain,
is_a_theorem(or(and(X1,X1),not(or(X1,X1)))),
inference(spm,[status(thm)],[c_0_78,c_0_80]) ).
cnf(c_0_85,plain,
is_a_theorem(or(X1,implies(X1,X2))),
inference(spm,[status(thm)],[c_0_81,c_0_26]) ).
cnf(c_0_86,plain,
( ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(or(X2,X2))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_82]) ).
cnf(c_0_87,plain,
( ~ is_a_theorem(implies(X1,not(X1)))
| is_a_theorem(or(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_83,c_0_51]) ).
cnf(c_0_88,plain,
is_a_theorem(implies(implies(not(or(X1,X1)),X2),or(X2,and(X1,X1)))),
inference(spm,[status(thm)],[c_0_47,c_0_84]) ).
cnf(c_0_89,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),or(X3,X1))),
inference(spm,[status(thm)],[c_0_47,c_0_85]) ).
cnf(c_0_90,plain,
( ~ is_a_theorem(implies(X2,not(X2)))
| ~ is_a_theorem(implies(not(X2),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_91,plain,
is_a_theorem(implies(or(or(X1,X1),X2),or(X2,and(X1,X1)))),
inference(spm,[status(thm)],[c_0_88,c_0_26]) ).
cnf(c_0_92,plain,
is_a_theorem(implies(not(or(X1,X2)),not(implies(implies(X2,X3),X1)))),
inference(spm,[status(thm)],[c_0_53,c_0_89]) ).
cnf(c_0_93,plain,
( ~ is_a_theorem(or(X2,X1))
| ~ is_a_theorem(implies(X2,not(X2)))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_26]) ).
cnf(c_0_94,plain,
( ~ is_a_theorem(or(or(X2,X2),X1))
| is_a_theorem(or(X1,and(X2,X2))) ),
inference(spm,[status(thm)],[c_0_30,c_0_91]) ).
cnf(c_0_95,plain,
is_a_theorem(or(or(X1,X2),not(implies(implies(X2,X3),X1)))),
inference(spm,[status(thm)],[c_0_92,c_0_26]) ).
cnf(c_0_96,plain,
( ~ is_a_theorem(not(X2))
| is_a_theorem(implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_67,c_0_71]) ).
cnf(c_0_97,plain,
( ~ is_a_theorem(or(X2,X2))
| ~ is_a_theorem(or(not(X2),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_79]) ).
cnf(c_0_98,plain,
is_a_theorem(or(not(implies(implies(X1,X2),X1)),and(X1,X1))),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_99,plain,
( ~ is_a_theorem(not(X2))
| is_a_theorem(or(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_96,c_0_26]) ).
cnf(c_0_100,plain,
( ~ is_a_theorem(or(implies(implies(X1,X2),X1),implies(implies(X1,X2),X1)))
| is_a_theorem(and(X1,X1)) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_101,plain,
( ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(or(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_99,c_0_22]) ).
cnf(c_0_102,plain,
is_a_theorem(or(not(X1),or(X1,X2))),
inference(spm,[status(thm)],[c_0_85,c_0_26]) ).
cnf(c_0_103,plain,
( ~ is_a_theorem(implies(implies(X1,X2),X1))
| is_a_theorem(and(X1,X1)) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_104,plain,
is_a_theorem(implies(implies(or(X1,X2),X3),or(X3,not(X1)))),
inference(spm,[status(thm)],[c_0_47,c_0_102]) ).
cnf(c_0_105,plain,
( ~ is_a_theorem(and(X1,X2))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_46]) ).
cnf(c_0_106,plain,
is_a_theorem(and(implies(not(X1),not(X1)),implies(not(X1),not(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_26]),c_0_26]) ).
cnf(c_0_107,plain,
( ~ is_a_theorem(implies(not(X3),X1))
| is_a_theorem(implies(implies(X1,X2),or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_47,c_0_26]) ).
cnf(c_0_108,plain,
is_a_theorem(implies(not(X1),not(X1))),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_109,plain,
is_a_theorem(implies(implies(not(X1),X2),or(X2,X1))),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_110,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(spm,[status(thm)],[c_0_109,c_0_26]) ).
cnf(c_0_111,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_108]),c_0_39]),c_0_26]) ).
cnf(c_0_112,plain,
( ~ is_a_theorem(or(X2,X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_30,c_0_110]) ).
fof(c_0_113,negated_conjecture,
~ implies_2,
inference(assume_negation,[status(cth)],[hilbert_implies_2]) ).
cnf(c_0_114,plain,
is_a_theorem(implies(not(X1),not(or(X1,X1)))),
inference(spm,[status(thm)],[c_0_53,c_0_111]) ).
cnf(c_0_115,plain,
is_a_theorem(or(implies(X1,X2),X1)),
inference(spm,[status(thm)],[c_0_112,c_0_85]) ).
fof(c_0_116,negated_conjecture,
~ implies_2,
inference(fof_simplification,[status(thm)],[c_0_113]) ).
cnf(c_0_117,plain,
is_a_theorem(implies(implies(not(or(X1,X1)),X2),or(X2,X1))),
inference(spm,[status(thm)],[c_0_107,c_0_114]) ).
cnf(c_0_118,plain,
is_a_theorem(or(and(X1,X2),implies(X2,implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_33,c_0_115]) ).
fof(c_0_119,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_120,negated_conjecture,
~ implies_2,
inference(fof_nnf,[status(thm)],[c_0_116]) ).
cnf(c_0_121,plain,
is_a_theorem(implies(or(or(X1,X1),X2),or(X2,X1))),
inference(spm,[status(thm)],[c_0_117,c_0_26]) ).
cnf(c_0_122,plain,
is_a_theorem(or(implies(X1,implies(X2,X3)),and(X2,X1))),
inference(spm,[status(thm)],[c_0_112,c_0_118]) ).
cnf(c_0_123,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_119]) ).
cnf(c_0_124,negated_conjecture,
~ implies_2,
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_125,plain,
( ~ is_a_theorem(or(or(X2,X2),X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_30,c_0_121]) ).
cnf(c_0_126,plain,
is_a_theorem(or(or(X1,implies(X2,X3)),and(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_122,c_0_26]) ).
cnf(c_0_127,plain,
~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0))),
inference(sr,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_128,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_39]) ).
cnf(c_0_129,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_128])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL504+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n003.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 00:37:48 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.52 Running first-order theorem proving
% 0.25/0.52 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 75.23/19.53 % Version: 3.5.1
% 75.23/19.53 % Preprocessing class: FSMSSLSSSSSNFFN.
% 75.23/19.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 75.23/19.53 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 75.23/19.53 % Starting new_bool_3 with 300s (1) cores
% 75.23/19.53 % Starting new_bool_1 with 300s (1) cores
% 75.23/19.53 % Starting sh5l with 300s (1) cores
% 75.23/19.53 % new_bool_3 with pid 3022958 completed with status 9
% 75.23/19.53 % new_bool_1 with pid 3022959 completed with status 9
% 75.23/19.53 % sh5l with pid 3022960 completed with status 9
% 75.23/19.53 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 3022957 completed with status 0
% 75.23/19.53 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 75.23/19.53 % Preprocessing class: FSMSSLSSSSSNFFN.
% 75.23/19.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 75.23/19.53 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 75.23/19.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 75.23/19.53 % No SInE strategy applied
% 75.23/19.53 % Search class: FGUSF-FFMM21-MFFFFFNN
% 75.23/19.53 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 75.23/19.53 % Starting SubtermCWHack with 151s (1) cores
% 75.23/19.53 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 75.23/19.53 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 75.23/19.53 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 75.23/19.53 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 75.23/19.53 % U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 3022975 completed with status 0
% 75.23/19.53 % Result found by U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 75.23/19.53 % Preprocessing class: FSMSSLSSSSSNFFN.
% 75.23/19.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 75.23/19.53 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 75.23/19.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 75.23/19.53 % No SInE strategy applied
% 75.23/19.53 % Search class: FGUSF-FFMM21-MFFFFFNN
% 75.23/19.53 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 75.23/19.53 % Starting SubtermCWHack with 151s (1) cores
% 75.23/19.53 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 75.23/19.53 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 75.23/19.53 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 75.23/19.53 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 75.23/19.53 % Preprocessing time : 0.003 s
% 75.23/19.53 % Presaturation interreduction done
% 75.23/19.53
% 75.23/19.53 % Proof found!
% 75.23/19.53 % SZS status Theorem
% 75.23/19.53 % SZS output start CNFRefutation
% See solution above
% 75.23/19.53 % Parsed axioms : 43
% 75.23/19.53 % Removed by relevancy pruning/SinE : 0
% 75.23/19.53 % Initial clauses : 72
% 75.23/19.53 % Removed in clause preprocessing : 0
% 75.23/19.53 % Initial clauses in saturation : 72
% 75.23/19.53 % Processed clauses : 8087
% 75.23/19.53 % ...of these trivial : 1718
% 75.23/19.53 % ...subsumed : 3360
% 75.23/19.53 % ...remaining for further processing : 3009
% 75.23/19.53 % Other redundant clauses eliminated : 0
% 75.23/19.53 % Clauses deleted for lack of memory : 0
% 75.23/19.53 % Backward-subsumed : 65
% 75.23/19.53 % Backward-rewritten : 127
% 75.23/19.53 % Generated clauses : 578122
% 75.23/19.53 % ...of the previous two non-redundant : 549003
% 75.23/19.53 % ...aggressively subsumed : 0
% 75.23/19.53 % Contextual simplify-reflections : 0
% 75.23/19.53 % Paramodulations : 578122
% 75.23/19.53 % Factorizations : 0
% 75.23/19.53 % NegExts : 0
% 75.23/19.53 % Equation resolutions : 0
% 75.23/19.53 % Disequality decompositions : 0
% 75.23/19.53 % Total rewrite steps : 91599
% 75.23/19.53 % ...of those cached : 71261
% 75.23/19.53 % Propositional unsat checks : 0
% 75.23/19.53 % Propositional check models : 0
% 75.23/19.53 % Propositional check unsatisfiable : 0
% 75.23/19.53 % Propositional clauses : 0
% 75.23/19.53 % Propositional clauses after purity: 0
% 75.23/19.53 % Propositional unsat core size : 0
% 75.23/19.53 % Propositional preprocessing time : 0.000
% 75.23/19.53 % Propositional encoding time : 0.000
% 75.23/19.53 % Propositional solver time : 0.000
% 75.23/19.53 % Success case prop preproc time : 0.000
% 75.23/19.53 % Success case prop encoding time : 0.000
% 75.23/19.53 % Success case prop solver time : 0.000
% 75.23/19.53 % Current number of processed clauses : 2759
% 75.23/19.53 % Positive orientable unit clauses : 1762
% 75.23/19.53 % Positive unorientable unit clauses: 104
% 75.23/19.53 % Negative unit clauses : 3
% 75.23/19.53 % Non-unit-clauses : 890
% 75.23/19.53 % Current number of unprocessed clauses: 540906
% 75.23/19.53 % ...number of literals in the above : 660151
% 75.23/19.53 % Current number of archived formulas : 0
% 75.23/19.53 % Current number of archived clauses : 250
% 75.23/19.53 % Clause-clause subsumption calls (NU) : 88607
% 75.23/19.53 % Rec. Clause-clause subsumption calls : 88293
% 75.23/19.53 % Non-unit clause-clause subsumptions : 3339
% 75.23/19.53 % Unit Clause-clause subsumption calls : 5799
% 75.23/19.53 % Rewrite failures with RHS unbound : 0
% 75.23/19.53 % BW rewrite match attempts : 105708
% 75.23/19.53 % BW rewrite match successes : 190
% 75.23/19.53 % Condensation attempts : 0
% 75.23/19.53 % Condensation successes : 0
% 75.23/19.53 % Termbank termtop insertions : 15237816
% 75.23/19.53 % Search garbage collected termcells : 1092
% 75.23/19.53
% 75.23/19.53 % -------------------------------------------------
% 75.23/19.53 % User time : 17.938 s
% 75.23/19.53 % System time : 0.629 s
% 75.23/19.53 % Total time : 18.566 s
% 75.23/19.53 % Maximum resident set size: 3688 pages
% 75.23/19.53
% 75.23/19.53 % -------------------------------------------------
% 75.23/19.53 % User time : 90.200 s
% 75.23/19.53 % System time : 3.772 s
% 75.23/19.53 % Total time : 93.972 s
% 75.23/19.53 % Maximum resident set size: 4608 pages
% 75.23/19.53 % E exiting
%------------------------------------------------------------------------------