%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWX203+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 03:14:44 PM UTC 2026
% Result : Theorem 1.36s 0.63s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 17
% Syntax : Number of formulae : 120 ( 44 unt; 0 def)
% Number of atoms : 366 ( 53 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 348 ( 102 ~; 227 |; 10 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 197 ( 16 sgn 52 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_021,axiom,
! [X3,X7] : rev(cons(X3,X7)) = append(rev(X7),cons(X3,nil)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
fof(axiom_018,axiom,
! [X3] : append(nil,X3) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
fof(axiom_020,axiom,
rev(nil) = nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
fof(axiom_019,axiom,
! [X3,X4,X7] : append(cons(X4,X7),X3) = cons(X4,append(X7,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
fof(goal_022,conjecture,
? [X7] :
~ ( sorted(rev(X7))
=> ( unique(X7)
=> leqNat(lengthNat(X7),s(s(s(z)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_022) ).
fof(axiom_013,axiom,
! [X3,X7] : lengthNat(cons(X3,X7)) = s(lengthNat(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
fof(axiom_017,axiom,
! [X3,X7] :
( unique(cons(X3,X7))
<=> ( unique(X7)
& ~ elemNat(X3,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
fof(axiom_012,axiom,
lengthNat(nil) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
fof(axiom_011,axiom,
! [X3,X6,X7] :
( sorted(cons(X3,cons(X6,X7)))
<=> ( sorted(cons(X6,X7))
& leqNat(X3,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
fof(axiom_010,axiom,
! [X3] : sorted(cons(X3,nil)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
fof(axiom_014,axiom,
! [X1] : ~ elemNat(X1,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
fof(axiom_016,axiom,
unique(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
fof(axiom_006,axiom,
! [X3] : leqNat(z,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
fof(axiom_008,axiom,
! [X4,X5] :
( leqNat(s(X4),s(X5))
<=> leqNat(X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
fof(axiom_015,axiom,
! [X1,X4,X7] :
( elemNat(X1,cons(X4,X7))
<=> ( elemNat(X1,X7)
| X1 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
fof(axiom_005,axiom,
! [X1] : z != s(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
fof(axiom_007,axiom,
! [X4] : ~ leqNat(s(X4),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
fof(c_0_17,plain,
! [X22,X23] : rev(cons(X22,X23)) = append(rev(X23),cons(X22,nil)),
inference(variable_rename,[status(thm)],[axiom_021]) ).
fof(c_0_18,plain,
! [X30] : append(nil,X30) = X30,
inference(variable_rename,[status(thm)],[axiom_018]) ).
cnf(c_0_19,plain,
rev(cons(X1,X2)) = append(rev(X2),cons(X1,nil)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,plain,
rev(nil) = nil,
inference(split_conjunct,[status(thm)],[axiom_020]) ).
cnf(c_0_21,plain,
append(nil,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_22,plain,
! [X31,X32,X33] : append(cons(X32,X33),X31) = cons(X32,append(X33,X31)),
inference(variable_rename,[status(thm)],[axiom_019]) ).
fof(c_0_23,negated_conjecture,
~ ? [X7] :
~ ( sorted(rev(X7))
=> ( unique(X7)
=> leqNat(lengthNat(X7),s(s(s(z)))) ) ),
inference(assume_negation,[status(cth)],[goal_022]) ).
cnf(c_0_24,plain,
rev(cons(X1,nil)) = cons(X1,nil),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_25,plain,
append(cons(X1,X2),X3) = cons(X1,append(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_26,negated_conjecture,
! [X8] :
( leqNat(lengthNat(X8),s(s(s(z))))
| ~ unique(X8)
| ~ sorted(rev(X8)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
fof(c_0_27,plain,
! [X17,X18] : lengthNat(cons(X17,X18)) = s(lengthNat(X18)),
inference(variable_rename,[status(thm)],[axiom_013]) ).
cnf(c_0_28,plain,
rev(cons(X1,cons(X2,nil))) = cons(X2,cons(X1,nil)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_24]),c_0_25]),c_0_21]) ).
cnf(c_0_29,negated_conjecture,
( ~ unique(X1)
| ~ sorted(rev(X1))
| leqNat(lengthNat(X1),s(s(s(z)))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
lengthNat(cons(X1,X2)) = s(lengthNat(X2)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,plain,
rev(cons(X1,cons(X2,cons(X3,nil)))) = cons(X3,cons(X2,cons(X1,nil))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_28]),c_0_25]),c_0_25]),c_0_21]) ).
fof(c_0_32,plain,
! [X3,X7] :
( unique(cons(X3,X7))
<=> ( unique(X7)
& ~ elemNat(X3,X7) ) ),
inference(fof_simplification,[status(thm)],[axiom_017]) ).
cnf(c_0_33,negated_conjecture,
( ~ sorted(rev(cons(X2,X1)))
| ~ unique(cons(X2,X1))
| leqNat(s(lengthNat(X1)),s(s(s(z)))) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
rev(cons(X1,cons(X2,cons(X3,cons(X4,nil))))) = cons(X4,cons(X3,cons(X2,cons(X1,nil)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_31]),c_0_25]),c_0_25]),c_0_25]),c_0_21]) ).
cnf(c_0_35,plain,
lengthNat(nil) = z,
inference(split_conjunct,[status(thm)],[axiom_012]) ).
fof(c_0_36,plain,
! [X19,X20] :
( ( unique(cons(X19,X20))
| ~ unique(X20)
| elemNat(X19,X20) )
& ( ~ unique(cons(X19,X20))
| unique(X20) )
& ( ~ unique(cons(X19,X20))
| ~ elemNat(X19,X20) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])]) ).
cnf(c_0_37,negated_conjecture,
( ~ sorted(cons(X4,cons(X3,cons(X2,cons(X1,nil)))))
| ~ unique(cons(X1,cons(X2,cons(X3,cons(X4,nil)))))
| leqNat(s(s(s(s(z)))),s(s(s(z)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_30]),c_0_30]),c_0_30]),c_0_35]) ).
cnf(c_0_38,plain,
( ~ unique(X2)
| unique(cons(X1,X2))
| elemNat(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_39,plain,
! [X13,X14,X15] :
( ( sorted(cons(X13,cons(X14,X15)))
| ~ sorted(cons(X14,X15))
| ~ leqNat(X13,X14) )
& ( ~ sorted(cons(X13,cons(X14,X15)))
| sorted(cons(X14,X15)) )
& ( ~ sorted(cons(X13,cons(X14,X15)))
| leqNat(X13,X14) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_011])])])]) ).
cnf(c_0_40,negated_conjecture,
( ~ sorted(cons(X4,cons(X3,cons(X2,cons(X1,nil)))))
| ~ unique(cons(X2,cons(X3,cons(X4,nil))))
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| elemNat(X1,cons(X2,cons(X3,cons(X4,nil)))) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,plain,
( ~ sorted(cons(X2,X3))
| ~ leqNat(X1,X2)
| sorted(cons(X1,cons(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( ~ leqNat(X4,X3)
| ~ sorted(cons(X3,cons(X2,cons(X1,nil))))
| ~ unique(cons(X2,cons(X3,cons(X4,nil))))
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| elemNat(X1,cons(X2,cons(X3,cons(X4,nil)))) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_43,negated_conjecture,
( ~ leqNat(X4,X3)
| ~ sorted(cons(X3,cons(X2,cons(X1,nil))))
| ~ unique(cons(X3,cons(X4,nil)))
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| elemNat(X2,cons(X3,cons(X4,nil)))
| elemNat(X1,cons(X2,cons(X3,cons(X4,nil)))) ),
inference(spm,[status(thm)],[c_0_42,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( ~ leqNat(X3,X2)
| ~ leqNat(X4,X3)
| ~ sorted(cons(X2,cons(X1,nil)))
| ~ unique(cons(X3,cons(X4,nil)))
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| elemNat(X2,cons(X3,cons(X4,nil)))
| elemNat(X1,cons(X2,cons(X3,cons(X4,nil)))) ),
inference(spm,[status(thm)],[c_0_43,c_0_41]) ).
fof(c_0_45,plain,
! [X21] : sorted(cons(X21,nil)),
inference(variable_rename,[status(thm)],[axiom_010]) ).
fof(c_0_46,plain,
! [X1] : ~ elemNat(X1,nil),
inference(fof_simplification,[status(thm)],[axiom_014]) ).
cnf(c_0_47,negated_conjecture,
( ~ leqNat(X3,X2)
| ~ leqNat(X4,X3)
| ~ sorted(cons(X2,cons(X1,nil)))
| ~ unique(cons(X4,nil))
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| elemNat(X3,cons(X4,nil))
| elemNat(X2,cons(X3,cons(X4,nil)))
| elemNat(X1,cons(X2,cons(X3,cons(X4,nil)))) ),
inference(spm,[status(thm)],[c_0_44,c_0_38]) ).
cnf(c_0_48,plain,
sorted(cons(X1,nil)),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_49,plain,
! [X26] : ~ elemNat(X26,nil),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_46])]) ).
cnf(c_0_50,negated_conjecture,
( ~ leqNat(X2,X1)
| ~ leqNat(X3,X2)
| ~ leqNat(X4,X3)
| ~ unique(cons(X4,nil))
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| elemNat(X3,cons(X4,nil))
| elemNat(X2,cons(X3,cons(X4,nil)))
| elemNat(X1,cons(X2,cons(X3,cons(X4,nil)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_41]),c_0_48])]) ).
cnf(c_0_51,plain,
unique(nil),
inference(split_conjunct,[status(thm)],[axiom_016]) ).
cnf(c_0_52,plain,
~ elemNat(X1,nil),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
fof(c_0_53,plain,
! [X9] : leqNat(z,X9),
inference(variable_rename,[status(thm)],[axiom_006]) ).
cnf(c_0_54,negated_conjecture,
( ~ leqNat(X2,X1)
| ~ leqNat(X3,X2)
| ~ leqNat(X4,X3)
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| elemNat(X3,cons(X4,nil))
| elemNat(X2,cons(X3,cons(X4,nil)))
| elemNat(X1,cons(X2,cons(X3,cons(X4,nil)))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_38]),c_0_51])]),c_0_52]) ).
cnf(c_0_55,plain,
leqNat(z,X1),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_56,plain,
! [X11,X12] :
( ( leqNat(s(X11),s(X12))
| ~ leqNat(X11,X12) )
& ( leqNat(X11,X12)
| ~ leqNat(s(X11),s(X12)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_008])])]) ).
cnf(c_0_57,negated_conjecture,
( ~ leqNat(X2,X1)
| ~ leqNat(X3,X2)
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| elemNat(X3,cons(z,nil))
| elemNat(X2,cons(X3,cons(z,nil)))
| elemNat(X1,cons(X2,cons(X3,cons(z,nil)))) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_58,plain,
( ~ leqNat(X1,X2)
| leqNat(s(X1),s(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_59,negated_conjecture,
( ~ sorted(cons(X3,cons(X2,cons(X1,nil))))
| ~ unique(cons(X1,cons(X2,cons(X3,nil))))
| leqNat(s(s(s(z))),s(s(s(z)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_31]),c_0_30]),c_0_30]),c_0_35]) ).
cnf(c_0_60,negated_conjecture,
( ~ leqNat(X3,X2)
| ~ leqNat(s(X2),X1)
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| elemNat(s(X3),cons(z,nil))
| elemNat(s(X2),cons(s(X3),cons(z,nil)))
| elemNat(X1,cons(s(X2),cons(s(X3),cons(z,nil)))) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_61,negated_conjecture,
( ~ sorted(cons(X3,cons(X2,cons(X1,nil))))
| ~ unique(cons(X2,cons(X3,nil)))
| leqNat(s(s(s(z))),s(s(s(z))))
| elemNat(X1,cons(X2,cons(X3,nil))) ),
inference(spm,[status(thm)],[c_0_59,c_0_38]) ).
cnf(c_0_62,negated_conjecture,
( ~ leqNat(X2,X1)
| ~ leqNat(X3,X2)
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| elemNat(s(X3),cons(z,nil))
| elemNat(s(X2),cons(s(X3),cons(z,nil)))
| elemNat(s(X1),cons(s(X2),cons(s(X3),cons(z,nil)))) ),
inference(spm,[status(thm)],[c_0_60,c_0_58]) ).
cnf(c_0_63,negated_conjecture,
( ~ leqNat(X3,X2)
| ~ sorted(cons(X2,cons(X1,nil)))
| ~ unique(cons(X2,cons(X3,nil)))
| leqNat(s(s(s(z))),s(s(s(z))))
| elemNat(X1,cons(X2,cons(X3,nil))) ),
inference(spm,[status(thm)],[c_0_61,c_0_41]) ).
cnf(c_0_64,negated_conjecture,
( ~ sorted(cons(X2,cons(X1,nil)))
| ~ unique(cons(X1,cons(X2,nil)))
| leqNat(s(s(z)),s(s(s(z)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_28]),c_0_30]),c_0_35]) ).
fof(c_0_65,plain,
! [X27,X28,X29] :
( ( elemNat(X27,cons(X28,X29))
| ~ elemNat(X27,X29) )
& ( elemNat(X27,cons(X28,X29))
| X27 != X28 )
& ( elemNat(X27,X29)
| X27 = X28
| ~ elemNat(X27,cons(X28,X29)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_015])])])]) ).
cnf(c_0_66,negated_conjecture,
( ~ leqNat(X2,X1)
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| elemNat(s(z),cons(z,nil))
| elemNat(s(X2),cons(s(z),cons(z,nil)))
| elemNat(s(X1),cons(s(X2),cons(s(z),cons(z,nil)))) ),
inference(spm,[status(thm)],[c_0_62,c_0_55]) ).
cnf(c_0_67,negated_conjecture,
( ~ leqNat(X3,X2)
| ~ sorted(cons(X2,cons(X1,nil)))
| ~ unique(cons(X3,nil))
| leqNat(s(s(s(z))),s(s(s(z))))
| elemNat(X2,cons(X3,nil))
| elemNat(X1,cons(X2,cons(X3,nil))) ),
inference(spm,[status(thm)],[c_0_63,c_0_38]) ).
cnf(c_0_68,negated_conjecture,
( ~ sorted(cons(X2,cons(X1,nil)))
| ~ unique(cons(X2,nil))
| leqNat(s(s(z)),s(s(s(z))))
| elemNat(X1,cons(X2,nil)) ),
inference(spm,[status(thm)],[c_0_64,c_0_38]) ).
cnf(c_0_69,plain,
( ~ elemNat(X1,cons(X2,X3))
| elemNat(X1,X3)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_70,negated_conjecture,
( ~ leqNat(X2,X1)
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(X2)),cons(s(z),cons(z,nil)))
| elemNat(s(s(X1)),cons(s(s(X2)),cons(s(z),cons(z,nil)))) ),
inference(spm,[status(thm)],[c_0_66,c_0_58]) ).
cnf(c_0_71,negated_conjecture,
( ~ leqNat(X2,X1)
| ~ leqNat(X3,X2)
| ~ unique(cons(X3,nil))
| leqNat(s(s(s(z))),s(s(s(z))))
| elemNat(X2,cons(X3,nil))
| elemNat(X1,cons(X2,cons(X3,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_41]),c_0_48])]) ).
cnf(c_0_72,negated_conjecture,
( ~ leqNat(X2,X1)
| ~ unique(cons(X2,nil))
| leqNat(s(s(z)),s(s(s(z))))
| elemNat(X1,cons(X2,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_41]),c_0_48])]) ).
cnf(c_0_73,negated_conjecture,
( ~ leqNat(X2,X1)
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(X1)),cons(s(z),cons(z,nil)))
| elemNat(s(s(X2)),cons(s(z),cons(z,nil)))
| s(s(X1)) = s(s(X2)) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,negated_conjecture,
( ~ leqNat(X2,X1)
| ~ leqNat(X3,X2)
| leqNat(s(s(s(z))),s(s(s(z))))
| elemNat(X2,cons(X3,nil))
| elemNat(X1,cons(X2,cons(X3,nil))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_38]),c_0_51])]),c_0_52]) ).
cnf(c_0_75,negated_conjecture,
( ~ leqNat(X2,X1)
| leqNat(s(s(z)),s(s(s(z))))
| elemNat(X1,cons(X2,nil)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_38]),c_0_51])]),c_0_52]) ).
fof(c_0_76,plain,
! [X1] : z != s(X1),
inference(fof_simplification,[status(thm)],[axiom_005]) ).
cnf(c_0_77,plain,
( ~ leqNat(s(X1),s(X2))
| leqNat(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_78,negated_conjecture,
( leqNat(s(s(s(s(z)))),s(s(s(z))))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(X1)),cons(s(z),cons(z,nil)))
| elemNat(s(s(z)),cons(s(z),cons(z,nil)))
| s(s(X1)) = s(s(z)) ),
inference(spm,[status(thm)],[c_0_73,c_0_55]) ).
cnf(c_0_79,negated_conjecture,
( ~ leqNat(X2,X1)
| leqNat(s(s(s(z))),s(s(s(z))))
| elemNat(X2,cons(z,nil))
| elemNat(X1,cons(X2,cons(z,nil))) ),
inference(spm,[status(thm)],[c_0_74,c_0_55]) ).
cnf(c_0_80,negated_conjecture,
( leqNat(s(s(z)),s(s(s(z))))
| elemNat(X1,cons(z,nil)) ),
inference(spm,[status(thm)],[c_0_75,c_0_55]) ).
fof(c_0_81,plain,
! [X16] : z != s(X16),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_76])]) ).
cnf(c_0_82,negated_conjecture,
( leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(X1)),cons(s(z),cons(z,nil)))
| elemNat(s(s(z)),cons(s(z),cons(z,nil)))
| s(s(X1)) = s(s(z)) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_83,negated_conjecture,
( ~ leqNat(X2,X1)
| leqNat(s(s(s(z))),s(s(s(z))))
| elemNat(s(X2),cons(z,nil))
| elemNat(s(X1),cons(s(X2),cons(z,nil))) ),
inference(spm,[status(thm)],[c_0_79,c_0_58]) ).
cnf(c_0_84,negated_conjecture,
( leqNat(s(s(z)),s(s(s(z))))
| X1 = z ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_80]),c_0_52]) ).
cnf(c_0_85,plain,
z != s(X1),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_86,negated_conjecture,
( leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(X1)),cons(z,nil))
| elemNat(s(s(z)),cons(s(z),cons(z,nil)))
| s(s(X1)) = s(z)
| s(s(X1)) = s(s(z)) ),
inference(spm,[status(thm)],[c_0_69,c_0_82]) ).
cnf(c_0_87,negated_conjecture,
( leqNat(s(s(s(z))),s(s(s(z))))
| elemNat(s(z),cons(z,nil))
| elemNat(s(X1),cons(s(z),cons(z,nil))) ),
inference(spm,[status(thm)],[c_0_83,c_0_55]) ).
cnf(c_0_88,negated_conjecture,
leqNat(s(s(z)),s(s(s(z)))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_84]),c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(s(z),cons(z,nil)))
| s(s(X1)) = s(z)
| s(s(X1)) = s(s(z)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_86]),c_0_85]),c_0_52]) ).
cnf(c_0_90,negated_conjecture,
( leqNat(s(s(z)),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(X1),cons(s(z),cons(z,nil))) ),
inference(spm,[status(thm)],[c_0_77,c_0_87]) ).
cnf(c_0_91,negated_conjecture,
( leqNat(s(s(X1)),s(s(s(X1))))
| leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(s(z),cons(z,nil)))
| s(s(X1)) = s(z) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_92,negated_conjecture,
( leqNat(s(s(z)),s(s(z)))
| elemNat(s(X1),cons(z,nil))
| elemNat(s(z),cons(z,nil))
| s(X1) = s(z) ),
inference(spm,[status(thm)],[c_0_69,c_0_90]) ).
cnf(c_0_93,negated_conjecture,
( leqNat(s(X1),s(s(X1)))
| leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(s(z),cons(z,nil)))
| s(s(X1)) = s(z) ),
inference(spm,[status(thm)],[c_0_77,c_0_91]) ).
cnf(c_0_94,negated_conjecture,
( leqNat(s(s(z)),s(s(z)))
| elemNat(s(z),cons(z,nil))
| s(X1) = s(z) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_92]),c_0_85]),c_0_52]) ).
cnf(c_0_95,negated_conjecture,
( leqNat(X1,s(X1))
| leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(s(z),cons(z,nil)))
| s(s(X1)) = s(z) ),
inference(spm,[status(thm)],[c_0_77,c_0_93]) ).
cnf(c_0_96,negated_conjecture,
( leqNat(s(z),s(z))
| elemNat(s(z),cons(z,nil))
| s(X1) = s(z) ),
inference(spm,[status(thm)],[c_0_77,c_0_94]) ).
cnf(c_0_97,negated_conjecture,
( leqNat(X1,s(X1))
| leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(s(z),cons(z,nil)))
| s(s(s(X1))) = s(z) ),
inference(spm,[status(thm)],[c_0_77,c_0_95]) ).
cnf(c_0_98,negated_conjecture,
( leqNat(s(z),s(z))
| s(X1) = s(z) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_96]),c_0_85]),c_0_52]) ).
fof(c_0_99,plain,
! [X4] : ~ leqNat(s(X4),z),
inference(fof_simplification,[status(thm)],[axiom_007]) ).
cnf(c_0_100,negated_conjecture,
( leqNat(X1,s(X1))
| leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(s(z),cons(z,nil)))
| s(s(s(s(X1)))) = s(z) ),
inference(spm,[status(thm)],[c_0_77,c_0_97]) ).
cnf(c_0_101,negated_conjecture,
( leqNat(s(X1),s(X2))
| leqNat(s(z),s(z)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_98]),c_0_55])]) ).
fof(c_0_102,plain,
! [X10] : ~ leqNat(s(X10),z),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_99])]) ).
cnf(c_0_103,negated_conjecture,
( ~ leqNat(s(z),s(X2))
| leqNat(X1,s(X1))
| leqNat(s(s(s(X1))),X2)
| leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(s(z),cons(z,nil))) ),
inference(spm,[status(thm)],[c_0_77,c_0_100]) ).
cnf(c_0_104,negated_conjecture,
leqNat(s(z),s(z)),
inference(ef,[status(thm)],[c_0_101]) ).
cnf(c_0_105,plain,
~ leqNat(s(X1),z),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_106,negated_conjecture,
( leqNat(X1,s(X1))
| leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(s(z),cons(z,nil))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_105]) ).
cnf(c_0_107,negated_conjecture,
( leqNat(s(X1),s(s(z)))
| leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(s(z),cons(z,nil)))
| s(s(X1)) = s(z) ),
inference(spm,[status(thm)],[c_0_106,c_0_89]) ).
cnf(c_0_108,negated_conjecture,
( leqNat(X1,s(z))
| leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(s(z),cons(z,nil)))
| s(s(X1)) = s(z) ),
inference(spm,[status(thm)],[c_0_77,c_0_107]) ).
cnf(c_0_109,negated_conjecture,
( leqNat(X1,z)
| leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(s(z),cons(z,nil)))
| s(s(s(X1))) = s(z) ),
inference(spm,[status(thm)],[c_0_77,c_0_108]) ).
cnf(c_0_110,negated_conjecture,
( leqNat(X1,z)
| leqNat(s(s(X1)),s(z))
| leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(s(z),cons(z,nil))) ),
inference(spm,[status(thm)],[c_0_106,c_0_109]) ).
cnf(c_0_111,negated_conjecture,
( leqNat(X1,z)
| leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(s(z),cons(z,nil))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_110]),c_0_105]) ).
cnf(c_0_112,negated_conjecture,
( leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(s(z),cons(z,nil))) ),
inference(spm,[status(thm)],[c_0_105,c_0_111]) ).
cnf(c_0_113,negated_conjecture,
( leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(z,nil))
| s(s(z)) = s(z) ),
inference(spm,[status(thm)],[c_0_69,c_0_112]) ).
cnf(c_0_114,negated_conjecture,
( leqNat(s(s(z)),s(z))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(z,nil))
| s(s(z)) = s(z) ),
inference(spm,[status(thm)],[c_0_77,c_0_113]) ).
cnf(c_0_115,negated_conjecture,
( leqNat(s(s(z)),s(z))
| elemNat(s(z),cons(z,nil))
| s(s(z)) = s(z) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_114]),c_0_85]),c_0_52]) ).
cnf(c_0_116,negated_conjecture,
( elemNat(s(z),cons(z,nil))
| s(s(z)) = s(z) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_115]),c_0_105]) ).
cnf(c_0_117,negated_conjecture,
s(s(z)) = s(z),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_116]),c_0_85]),c_0_52]) ).
cnf(c_0_118,negated_conjecture,
( ~ leqNat(s(z),s(X1))
| leqNat(s(z),X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_117]) ).
cnf(c_0_119,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_104]),c_0_105]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX203+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 10:36:51 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.40 Running first-order theorem proving
% 0.03/0.40 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
% 1.36/0.63 % Version: 3.5.1
% 1.36/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.36/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.36/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.36/0.63 % Starting new_bool_3 with 300s (1) cores
% 1.36/0.63 % Starting new_bool_1 with 300s (1) cores
% 1.36/0.63 % Starting sh5l with 300s (1) cores
% 1.36/0.63 % new_bool_3 with pid 1251852 completed with status 0
% 1.36/0.63 % Result found by new_bool_3
% 1.36/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.36/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.36/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.36/0.63 % Starting new_bool_3 with 300s (1) cores
% 1.36/0.63 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.36/0.63 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.36/0.63 % Search class: FGHSM-FFSS21-MFFFFFNN
% 1.36/0.63 % partial match(1): FGHSM-FFSF21-MFFFFFNN
% 1.36/0.63 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.36/0.63 % Starting SubtermCWHack with 31s (1) cores
% 1.36/0.63 % SubtermCWHack with pid 1251858 completed with status 0
% 1.36/0.63 % Result found by SubtermCWHack
% 1.36/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.36/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.36/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.36/0.63 % Starting new_bool_3 with 300s (1) cores
% 1.36/0.63 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.36/0.63 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.36/0.63 % Search class: FGHSM-FFSS21-MFFFFFNN
% 1.36/0.63 % partial match(1): FGHSM-FFSF21-MFFFFFNN
% 1.36/0.63 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.36/0.63 % Starting SubtermCWHack with 31s (1) cores
% 1.36/0.63 % Preprocessing time : 0.001 s
% 1.36/0.63
% 1.36/0.63 % Proof found!
% 1.36/0.63 % SZS status Theorem
% 1.36/0.63 % SZS output start CNFRefutation
% See solution above
% 1.36/0.63 % Parsed axioms : 22
% 1.36/0.63 % Removed by relevancy pruning/SinE : 3
% 1.36/0.63 % Initial clauses : 26
% 1.36/0.63 % Removed in clause preprocessing : 0
% 1.36/0.63 % Initial clauses in saturation : 26
% 1.36/0.63 % Processed clauses : 1108
% 1.36/0.63 % ...of these trivial : 5
% 1.36/0.63 % ...subsumed : 479
% 1.36/0.63 % ...remaining for further processing : 624
% 1.36/0.63 % Other redundant clauses eliminated : 1
% 1.36/0.63 % Clauses deleted for lack of memory : 0
% 1.36/0.63 % Backward-subsumed : 431
% 1.36/0.63 % Backward-rewritten : 107
% 1.36/0.63 % Generated clauses : 9189
% 1.36/0.63 % ...of the previous two non-redundant : 7182
% 1.36/0.63 % ...aggressively subsumed : 0
% 1.36/0.63 % Contextual simplify-reflections : 0
% 1.36/0.63 % Paramodulations : 9123
% 1.36/0.63 % Factorizations : 65
% 1.36/0.63 % NegExts : 0
% 1.36/0.63 % Equation resolutions : 1
% 1.36/0.63 % Disequality decompositions : 0
% 1.36/0.63 % Total rewrite steps : 4199
% 1.36/0.63 % ...of those cached : 3951
% 1.36/0.63 % Propositional unsat checks : 0
% 1.36/0.63 % Propositional check models : 0
% 1.36/0.63 % Propositional check unsatisfiable : 0
% 1.36/0.63 % Propositional clauses : 0
% 1.36/0.63 % Propositional clauses after purity: 0
% 1.36/0.63 % Propositional unsat core size : 0
% 1.36/0.63 % Propositional preprocessing time : 0.000
% 1.36/0.63 % Propositional encoding time : 0.000
% 1.36/0.63 % Propositional solver time : 0.000
% 1.36/0.63 % Success case prop preproc time : 0.000
% 1.36/0.63 % Success case prop encoding time : 0.000
% 1.36/0.63 % Success case prop solver time : 0.000
% 1.36/0.63 % Current number of processed clauses : 85
% 1.36/0.63 % Positive orientable unit clauses : 27
% 1.36/0.63 % Positive unorientable unit clauses: 0
% 1.36/0.63 % Negative unit clauses : 4
% 1.36/0.63 % Non-unit-clauses : 54
% 1.36/0.63 % Current number of unprocessed clauses: 686
% 1.36/0.63 % ...number of literals in the above : 5002
% 1.36/0.63 % Current number of archived formulas : 0
% 1.36/0.63 % Current number of archived clauses : 538
% 1.36/0.63 % Clause-clause subsumption calls (NU) : 27863
% 1.36/0.63 % Rec. Clause-clause subsumption calls : 5182
% 1.36/0.63 % Non-unit clause-clause subsumptions : 734
% 1.36/0.63 % Unit Clause-clause subsumption calls : 175
% 1.36/0.63 % Rewrite failures with RHS unbound : 0
% 1.36/0.63 % BW rewrite match attempts : 85
% 1.36/0.63 % BW rewrite match successes : 7
% 1.36/0.63 % Condensation attempts : 0
% 1.36/0.63 % Condensation successes : 0
% 1.36/0.63 % Termbank termtop insertions : 377871
% 1.36/0.63 % Search garbage collected termcells : 175
% 1.36/0.63
% 1.36/0.63 % -------------------------------------------------
% 1.36/0.63 % User time : 0.188 s
% 1.36/0.63 % System time : 0.005 s
% 1.36/0.63 % Total time : 0.194 s
% 1.36/0.63 % Maximum resident set size: 3648 pages
% 1.36/0.63
% 1.36/0.63 % -------------------------------------------------
% 1.36/0.63 % User time : 0.191 s
% 1.36/0.63 % System time : 0.009 s
% 1.36/0.63 % Total time : 0.200 s
% 1.36/0.63 % Maximum resident set size: 4608 pages
% 1.36/0.63 % E exiting
%------------------------------------------------------------------------------