%------------------------------------------------------------------------------
% File : E---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 : n026.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 03:14:15 PM UTC 2026
% Result : Theorem 1.75s 0.76s
% Output : CNFRefutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 18
% Syntax : Number of formulae : 95 ( 47 unt; 0 def)
% Number of atoms : 257 ( 57 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 243 ( 81 ~; 143 |; 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 : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 148 ( 8 sgn 54 !; 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(axiom_004,axiom,
! [X1] : proj1S(s(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
fof(c_0_18,plain,
! [X36,X37] : rev(cons(X36,X37)) = append(rev(X37),cons(X36,nil)),
inference(variable_rename,[status(thm)],[axiom_021]) ).
fof(c_0_19,plain,
! [X32] : append(nil,X32) = X32,
inference(variable_rename,[status(thm)],[axiom_018]) ).
cnf(c_0_20,plain,
rev(cons(X1,X2)) = append(rev(X2),cons(X1,nil)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
rev(nil) = nil,
inference(split_conjunct,[status(thm)],[axiom_020]) ).
cnf(c_0_22,plain,
append(nil,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_23,plain,
! [X33,X34,X35] : append(cons(X34,X35),X33) = cons(X34,append(X35,X33)),
inference(variable_rename,[status(thm)],[axiom_019]) ).
fof(c_0_24,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_25,plain,
rev(cons(X1,nil)) = cons(X1,nil),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_26,plain,
append(cons(X1,X2),X3) = cons(X1,append(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_27,negated_conjecture,
! [X38] :
( leqNat(lengthNat(X38),s(s(s(z))))
| ~ unique(X38)
| ~ sorted(rev(X38)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
fof(c_0_28,plain,
! [X24,X25] : lengthNat(cons(X24,X25)) = s(lengthNat(X25)),
inference(variable_rename,[status(thm)],[axiom_013]) ).
cnf(c_0_29,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_20,c_0_25]),c_0_26]),c_0_22]) ).
cnf(c_0_30,negated_conjecture,
( ~ unique(X1)
| ~ sorted(rev(X1))
| leqNat(lengthNat(X1),s(s(s(z)))) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,plain,
lengthNat(cons(X1,X2)) = s(lengthNat(X2)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,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_20,c_0_29]),c_0_26]),c_0_26]),c_0_22]) ).
fof(c_0_33,plain,
! [X3,X7] :
( unique(cons(X3,X7))
<=> ( unique(X7)
& ~ elemNat(X3,X7) ) ),
inference(fof_simplification,[status(thm)],[axiom_017]) ).
cnf(c_0_34,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_30,c_0_31]) ).
cnf(c_0_35,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_20,c_0_32]),c_0_26]),c_0_26]),c_0_26]),c_0_22]) ).
cnf(c_0_36,plain,
lengthNat(nil) = z,
inference(split_conjunct,[status(thm)],[axiom_012]) ).
fof(c_0_37,plain,
! [X30,X31] :
( ( unique(cons(X30,X31))
| ~ unique(X31)
| elemNat(X30,X31) )
& ( ~ unique(cons(X30,X31))
| unique(X31) )
& ( ~ unique(cons(X30,X31))
| ~ elemNat(X30,X31) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])]) ).
cnf(c_0_38,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_34,c_0_35]),c_0_31]),c_0_31]),c_0_31]),c_0_36]) ).
cnf(c_0_39,plain,
( ~ unique(X2)
| unique(cons(X1,X2))
| elemNat(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_40,plain,
! [X21,X22,X23] :
( ( sorted(cons(X21,cons(X22,X23)))
| ~ sorted(cons(X22,X23))
| ~ leqNat(X21,X22) )
& ( ~ sorted(cons(X21,cons(X22,X23)))
| sorted(cons(X22,X23)) )
& ( ~ sorted(cons(X21,cons(X22,X23)))
| leqNat(X21,X22) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_011])])])]) ).
cnf(c_0_41,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_38,c_0_39]) ).
cnf(c_0_42,plain,
( ~ sorted(cons(X2,X3))
| ~ leqNat(X1,X2)
| sorted(cons(X1,cons(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_43,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_41,c_0_42]) ).
cnf(c_0_44,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_43,c_0_39]) ).
cnf(c_0_45,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_44,c_0_42]) ).
fof(c_0_46,plain,
! [X20] : sorted(cons(X20,nil)),
inference(variable_rename,[status(thm)],[axiom_010]) ).
fof(c_0_47,plain,
! [X1] : ~ elemNat(X1,nil),
inference(fof_simplification,[status(thm)],[axiom_014]) ).
cnf(c_0_48,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_34,c_0_29]),c_0_31]),c_0_36]) ).
cnf(c_0_49,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_45,c_0_39]) ).
cnf(c_0_50,plain,
sorted(cons(X1,nil)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_51,plain,
! [X26] : ~ elemNat(X26,nil),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_47])]) ).
cnf(c_0_52,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_48,c_0_39]) ).
cnf(c_0_53,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_49,c_0_42]),c_0_50])]) ).
cnf(c_0_54,plain,
unique(nil),
inference(split_conjunct,[status(thm)],[axiom_016]) ).
cnf(c_0_55,plain,
~ elemNat(X1,nil),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_56,plain,
! [X16] : leqNat(z,X16),
inference(variable_rename,[status(thm)],[axiom_006]) ).
cnf(c_0_57,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_52,c_0_42]),c_0_50])]) ).
cnf(c_0_58,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_53,c_0_39]),c_0_54])]),c_0_55]) ).
cnf(c_0_59,plain,
leqNat(z,X1),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
fof(c_0_60,plain,
! [X18,X19] :
( ( leqNat(s(X18),s(X19))
| ~ leqNat(X18,X19) )
& ( leqNat(X18,X19)
| ~ leqNat(s(X18),s(X19)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_008])])]) ).
fof(c_0_61,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_62,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_57,c_0_39]),c_0_54])]),c_0_55]) ).
fof(c_0_63,plain,
! [X1] : z != s(X1),
inference(fof_simplification,[status(thm)],[axiom_005]) ).
cnf(c_0_64,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_58,c_0_59]) ).
cnf(c_0_65,plain,
( ~ leqNat(X1,X2)
| leqNat(s(X1),s(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_66,plain,
( ~ elemNat(X1,cons(X2,X3))
| elemNat(X1,X3)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( leqNat(s(s(z)),s(s(s(z))))
| elemNat(X1,cons(z,nil)) ),
inference(spm,[status(thm)],[c_0_62,c_0_59]) ).
fof(c_0_68,plain,
! [X15] : z != s(X15),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_63])]) ).
cnf(c_0_69,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_64,c_0_65]) ).
cnf(c_0_70,negated_conjecture,
( leqNat(s(s(z)),s(s(s(z))))
| X1 = z ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_55]) ).
cnf(c_0_71,plain,
z != s(X1),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_72,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_69,c_0_65]) ).
cnf(c_0_73,plain,
( ~ leqNat(s(X1),s(X2))
| leqNat(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_74,negated_conjecture,
leqNat(s(s(z)),s(s(s(z)))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_70]),c_0_71]) ).
cnf(c_0_75,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_72,c_0_59]) ).
cnf(c_0_76,negated_conjecture,
leqNat(s(z),s(s(z))),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_77,negated_conjecture,
( leqNat(s(s(s(s(z)))),s(s(s(z))))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(s(z),cons(z,nil)))
| elemNat(s(s(s(z))),cons(s(s(z)),cons(s(z),cons(z,nil)))) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
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(z)),cons(s(z),cons(z,nil)))
| elemNat(s(s(s(z))),cons(s(z),cons(z,nil)))
| s(s(s(z))) = s(s(z)) ),
inference(spm,[status(thm)],[c_0_66,c_0_77]) ).
cnf(c_0_79,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)))
| elemNat(s(s(s(z))),cons(s(z),cons(z,nil)))
| s(s(s(z))) = s(s(z)) ),
inference(spm,[status(thm)],[c_0_73,c_0_78]) ).
cnf(c_0_80,negated_conjecture,
( leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(s(z))),cons(z,nil))
| elemNat(s(s(z)),cons(s(z),cons(z,nil)))
| s(s(s(z))) = s(z)
| s(s(s(z))) = s(s(z)) ),
inference(spm,[status(thm)],[c_0_66,c_0_79]) ).
cnf(c_0_81,negated_conjecture,
( leqNat(s(s(s(z))),s(s(z)))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(z,nil))
| elemNat(s(s(s(z))),cons(z,nil))
| s(s(z)) = s(z)
| s(s(s(z))) = s(z)
| s(s(s(z))) = s(s(z)) ),
inference(spm,[status(thm)],[c_0_66,c_0_80]) ).
cnf(c_0_82,negated_conjecture,
( leqNat(s(s(z)),s(z))
| elemNat(s(z),cons(z,nil))
| elemNat(s(s(z)),cons(z,nil))
| elemNat(s(s(s(z))),cons(z,nil))
| s(s(z)) = s(z)
| s(s(s(z))) = s(z)
| s(s(s(z))) = s(s(z)) ),
inference(spm,[status(thm)],[c_0_73,c_0_81]) ).
fof(c_0_83,plain,
! [X4] : ~ leqNat(s(X4),z),
inference(fof_simplification,[status(thm)],[axiom_007]) ).
cnf(c_0_84,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)
| s(s(s(z))) = s(z)
| s(s(s(z))) = s(s(z)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_82]),c_0_71]),c_0_55]) ).
fof(c_0_85,plain,
! [X17] : ~ leqNat(s(X17),z),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_83])]) ).
cnf(c_0_86,negated_conjecture,
( leqNat(s(s(z)),s(z))
| elemNat(s(z),cons(z,nil))
| s(s(z)) = s(z)
| s(s(s(z))) = s(z)
| s(s(s(z))) = s(s(z)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_84]),c_0_71]),c_0_55]) ).
cnf(c_0_87,plain,
~ leqNat(s(X1),z),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
fof(c_0_88,plain,
! [X14] : proj1S(s(X14)) = X14,
inference(variable_rename,[status(thm)],[axiom_004]) ).
cnf(c_0_89,negated_conjecture,
( elemNat(s(z),cons(z,nil))
| s(s(z)) = s(z)
| s(s(s(z))) = s(z)
| s(s(s(z))) = s(s(z)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_86]),c_0_87]) ).
cnf(c_0_90,plain,
proj1S(s(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_91,negated_conjecture,
( s(s(z)) = s(z)
| s(s(s(z))) = s(z)
| s(s(s(z))) = s(s(z)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_89]),c_0_71]),c_0_55]) ).
cnf(c_0_92,negated_conjecture,
( s(s(z)) = s(z)
| s(s(s(z))) = s(z) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_90])]) ).
cnf(c_0_93,negated_conjecture,
s(s(z)) = s(z),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_92]),c_0_90]),c_0_71]) ).
cnf(c_0_94,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_93]),c_0_90]),c_0_71]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX203+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n026.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 10:36:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.45 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
% 1.75/0.76 % Version: 3.5.1
% 1.75/0.76 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.75/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.75/0.76 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.75/0.76 % Starting new_bool_3 with 300s (1) cores
% 1.75/0.76 % Starting new_bool_1 with 300s (1) cores
% 1.75/0.76 % Starting sh5l with 300s (1) cores
% 1.75/0.76 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2044850 completed with status 0
% 1.75/0.76 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.75/0.76 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.75/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.75/0.76 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.75/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.75/0.76 % No SInE strategy applied
% 1.75/0.76 % Search class: FGHSM-FFSS21-MFFFFFNN
% 1.75/0.76 % partial match(1): FGHSM-FFSF21-MFFFFFNN
% 1.75/0.76 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.75/0.76 % Starting SubtermCWHack with 136s (1) cores
% 1.75/0.76 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.75/0.76 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 1.75/0.76 % Starting new_bool_3 with 136s (1) cores
% 1.75/0.76 % Starting new_bool_1 with 136s (1) cores
% 1.75/0.76 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 2044857 completed with status 0
% 1.75/0.76 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 1.75/0.76 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.75/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.75/0.76 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.75/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.75/0.76 % No SInE strategy applied
% 1.75/0.76 % Search class: FGHSM-FFSS21-MFFFFFNN
% 1.75/0.76 % partial match(1): FGHSM-FFSF21-MFFFFFNN
% 1.75/0.76 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.75/0.76 % Starting SubtermCWHack with 136s (1) cores
% 1.75/0.76 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.75/0.76 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 1.75/0.76 % Preprocessing time : 0.002 s
% 1.75/0.76 % Presaturation interreduction done
% 1.75/0.76
% 1.75/0.76 % Proof found!
% 1.75/0.76 % SZS status Theorem
% 1.75/0.76 % SZS output start CNFRefutation
% See solution above
% 1.75/0.77 % Parsed axioms : 22
% 1.75/0.77 % Removed by relevancy pruning/SinE : 0
% 1.75/0.77 % Initial clauses : 29
% 1.75/0.77 % Removed in clause preprocessing : 0
% 1.75/0.77 % Initial clauses in saturation : 29
% 1.75/0.77 % Processed clauses : 877
% 1.75/0.77 % ...of these trivial : 5
% 1.75/0.77 % ...subsumed : 332
% 1.75/0.77 % ...remaining for further processing : 540
% 1.75/0.77 % Other redundant clauses eliminated : 1
% 1.75/0.77 % Clauses deleted for lack of memory : 0
% 1.75/0.77 % Backward-subsumed : 339
% 1.75/0.77 % Backward-rewritten : 105
% 1.75/0.77 % Generated clauses : 7751
% 1.75/0.77 % ...of the previous two non-redundant : 6400
% 1.75/0.77 % ...aggressively subsumed : 0
% 1.75/0.77 % Contextual simplify-reflections : 2
% 1.75/0.77 % Paramodulations : 7730
% 1.75/0.77 % Factorizations : 18
% 1.75/0.77 % NegExts : 0
% 1.75/0.77 % Equation resolutions : 3
% 1.75/0.77 % Disequality decompositions : 0
% 1.75/0.77 % Total rewrite steps : 3349
% 1.75/0.77 % ...of those cached : 3184
% 1.75/0.77 % Propositional unsat checks : 0
% 1.75/0.77 % Propositional check models : 0
% 1.75/0.77 % Propositional check unsatisfiable : 0
% 1.75/0.77 % Propositional clauses : 0
% 1.75/0.77 % Propositional clauses after purity: 0
% 1.75/0.77 % Propositional unsat core size : 0
% 1.75/0.77 % Propositional preprocessing time : 0.000
% 1.75/0.77 % Propositional encoding time : 0.000
% 1.75/0.77 % Propositional solver time : 0.000
% 1.75/0.77 % Success case prop preproc time : 0.000
% 1.75/0.77 % Success case prop encoding time : 0.000
% 1.75/0.77 % Success case prop solver time : 0.000
% 1.75/0.77 % Current number of processed clauses : 66
% 1.75/0.77 % Positive orientable unit clauses : 27
% 1.75/0.77 % Positive unorientable unit clauses: 0
% 1.75/0.77 % Negative unit clauses : 4
% 1.75/0.77 % Non-unit-clauses : 35
% 1.75/0.77 % Current number of unprocessed clauses: 106
% 1.75/0.77 % ...number of literals in the above : 681
% 1.75/0.77 % Current number of archived formulas : 0
% 1.75/0.77 % Current number of archived clauses : 473
% 1.75/0.77 % Clause-clause subsumption calls (NU) : 30465
% 1.75/0.77 % Rec. Clause-clause subsumption calls : 4202
% 1.75/0.77 % Non-unit clause-clause subsumptions : 519
% 1.75/0.77 % Unit Clause-clause subsumption calls : 192
% 1.75/0.77 % Rewrite failures with RHS unbound : 0
% 1.75/0.77 % BW rewrite match attempts : 50
% 1.75/0.77 % BW rewrite match successes : 7
% 1.75/0.77 % Condensation attempts : 0
% 1.75/0.77 % Condensation successes : 0
% 1.75/0.77 % Termbank termtop insertions : 306315
% 1.75/0.77 % Search garbage collected termcells : 162
% 1.75/0.77
% 1.75/0.77 % -------------------------------------------------
% 1.75/0.77 % User time : 0.217 s
% 1.75/0.77 % System time : 0.008 s
% 1.75/0.77 % Total time : 0.225 s
% 1.75/0.77 % Maximum resident set size: 3648 pages
% 1.75/0.77
% 1.75/0.77 % -------------------------------------------------
% 1.75/0.77 % User time : 1.124 s
% 1.75/0.77 % System time : 0.059 s
% 1.75/0.77 % Total time : 1.183 s
% 1.75/0.77 % Maximum resident set size: 4864 pages
% 1.75/0.77 % E exiting
%------------------------------------------------------------------------------