%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWX203+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 : Sun Sep 27 09:15:38 AM UTC 2026
% Result : Theorem 27.74s 4.28s
% Output : CNFRefutation 27.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 64
% Number of leaves : 18
% Syntax : Number of formulae : 105 ( 43 unt; 0 def)
% Number of atoms : 440 ( 196 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 496 ( 161 ~; 325 |; 2 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 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 : 274 ( 9 sgn 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_004,axiom,
! [X0] : proj1S(s(X0)) = X0 ).
fof(axiom_005,axiom,
! [X0] : z != s(X0) ).
fof(axiom_006,axiom,
! [X0] : leqNat(z,X0) ).
fof(axiom_007,axiom,
! [X0] : ~ leqNat(s(X0),z) ).
fof(axiom_008,axiom,
! [X0,X1] :
( leqNat(s(X0),s(X1))
<=> leqNat(X0,X1) ) ).
fof(axiom_010,axiom,
! [X0] : sorted(cons(X0,nil)) ).
fof(axiom_011,axiom,
! [X0,X1,X2] :
( sorted(cons(X0,cons(X1,X2)))
<=> ( sorted(cons(X1,X2))
& leqNat(X0,X1) ) ) ).
fof(axiom_012,axiom,
lengthNat(nil) = z ).
fof(axiom_013,axiom,
! [X0,X1] : lengthNat(cons(X0,X1)) = s(lengthNat(X1)) ).
fof(axiom_014,axiom,
! [X0] : ~ elemNat(X0,nil) ).
fof(axiom_015,axiom,
! [X0,X1,X2] :
( elemNat(X0,cons(X1,X2))
<=> ( elemNat(X0,X2)
| X0 = X1 ) ) ).
fof(axiom_016,axiom,
unique(nil) ).
fof(axiom_017,axiom,
! [X0,X1] :
( unique(cons(X0,X1))
<=> ( unique(X1)
& ~ elemNat(X0,X1) ) ) ).
fof(axiom_018,axiom,
! [X0] : append(nil,X0) = X0 ).
fof(axiom_019,axiom,
! [X0,X1,X2] : append(cons(X1,X2),X0) = cons(X1,append(X2,X0)) ).
fof(axiom_020,axiom,
rev(nil) = nil ).
fof(axiom_021,axiom,
! [X0,X1] : rev(cons(X0,X1)) = append(rev(X1),cons(X0,nil)) ).
fof(goal_022,conjecture,
? [X0] :
~ ( sorted(rev(X0))
=> ( unique(X0)
=> leqNat(lengthNat(X0),s(s(s(z)))) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] :
~ ( sorted(rev(X0))
=> ( unique(X0)
=> leqNat(lengthNat(X0),s(s(s(z)))) ) ),
inference(negate_conjecture,[status(cth)],[goal_022]) ).
cnf(c3,plain,
proj1S(s(X0)) = X0,
inference(clausification,[status(esa)],[axiom_004]) ).
cnf(c4,plain,
z != s(X0),
inference(clausification,[status(esa)],[axiom_005]) ).
cnf(c5,plain,
leqNat(z,X0),
inference(clausification,[status(esa)],[axiom_006]) ).
cnf(c6,plain,
~ leqNat(s(X0),z),
inference(clausification,[status(esa)],[axiom_007]) ).
cnf(c7,plain,
( leqNat(X0,X1)
| ~ leqNat(s(X0),s(X1)) ),
inference(clausification,[status(esa)],[axiom_008]) ).
cnf(c8,plain,
( ~ leqNat(X0,X1)
| leqNat(s(X0),s(X1)) ),
inference(clausification,[status(esa)],[axiom_008]) ).
cnf(c10,plain,
sorted(cons(X0,nil)),
inference(clausification,[status(esa)],[axiom_010]) ).
cnf(c13,plain,
( ~ sorted(cons(X1,X2))
| ~ leqNat(X0,X1)
| sorted(cons(X0,cons(X1,X2))) ),
inference(clausification,[status(esa)],[axiom_011]) ).
cnf(c14,plain,
lengthNat(nil) = z,
inference(clausification,[status(esa)],[axiom_012]) ).
cnf(c15,plain,
lengthNat(cons(X0,X1)) = s(lengthNat(X1)),
inference(clausification,[status(esa)],[axiom_013]) ).
cnf(c16,plain,
~ elemNat(X0,nil),
inference(clausification,[status(esa)],[axiom_014]) ).
cnf(c17,plain,
( elemNat(X0,X2)
| X0 = X1
| ~ elemNat(X0,cons(X1,X2)) ),
inference(clausification,[status(esa)],[axiom_015]) ).
cnf(c20,plain,
unique(nil),
inference(clausification,[status(esa)],[axiom_016]) ).
cnf(c23,plain,
( ~ unique(X1)
| elemNat(X0,X1)
| unique(cons(X0,X1)) ),
inference(clausification,[status(esa)],[axiom_017]) ).
cnf(c24,plain,
append(nil,X0) = X0,
inference(clausification,[status(esa)],[axiom_018]) ).
cnf(c25,plain,
append(cons(X0,X1),X2) = cons(X0,append(X1,X2)),
inference(clausification,[status(esa)],[axiom_019]) ).
cnf(c26,plain,
rev(nil) = nil,
inference(clausification,[status(esa)],[axiom_020]) ).
cnf(c27,plain,
rev(cons(X0,X1)) = append(rev(X1),cons(X0,nil)),
inference(clausification,[status(esa)],[axiom_021]) ).
cnf(c28,plain,
( leqNat(lengthNat(X0),s(s(s(z))))
| ~ unique(X0)
| ~ sorted(rev(X0)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ unique(cons(X0,X1))
| ~ sorted(rev(cons(X0,X1)))
| leqNat(s(lengthNat(X1)),s(s(s(z)))) ),
inference(superposition,[status(thm)],[c15,c28]) ).
cnf(d1,plain,
( ~ unique(cons(X2,cons(X0,X1)))
| ~ sorted(rev(cons(X2,cons(X0,X1))))
| leqNat(s(s(lengthNat(X1))),s(s(s(z)))) ),
inference(superposition,[status(thm)],[c15,d0]) ).
cnf(d2,plain,
( ~ unique(cons(X2,cons(X3,cons(X0,X1))))
| ~ sorted(rev(cons(X2,cons(X3,cons(X0,X1)))))
| leqNat(s(s(s(lengthNat(X1)))),s(s(s(z)))) ),
inference(superposition,[status(thm)],[c15,d1]) ).
cnf(d3,plain,
( leqNat(s(s(lengthNat(X3))),s(s(z)))
| ~ unique(cons(X0,cons(X1,cons(X2,X3))))
| ~ sorted(rev(cons(X0,cons(X1,cons(X2,X3))))) ),
inference(resolution,[status(thm)],[d2,c7]) ).
cnf(d4,plain,
rev(cons(X0,nil)) = append(nil,cons(X0,nil)),
inference(superposition,[status(thm)],[c26,c27]) ).
cnf(d5,plain,
rev(cons(X0,nil)) = cons(X0,nil),
inference(demodulation,[status(thm)],[d4,c24]) ).
cnf(d6,plain,
rev(cons(X1,cons(X0,nil))) = append(cons(X0,nil),cons(X1,nil)),
inference(superposition,[status(thm)],[d5,c27]) ).
cnf(d7,plain,
rev(cons(X1,cons(X0,nil))) = cons(X0,append(nil,cons(X1,nil))),
inference(demodulation,[status(thm)],[d6,c25]) ).
cnf(d8,plain,
rev(cons(X0,cons(X1,nil))) = cons(X1,cons(X0,nil)),
inference(demodulation,[status(thm)],[d7,c24]) ).
cnf(d9,plain,
rev(cons(X2,cons(X0,cons(X1,nil)))) = append(cons(X1,cons(X0,nil)),cons(X2,nil)),
inference(superposition,[status(thm)],[d8,c27]) ).
cnf(d10,plain,
rev(cons(X2,cons(X1,cons(X0,nil)))) = cons(X0,append(cons(X1,nil),cons(X2,nil))),
inference(demodulation,[status(thm)],[d9,c25]) ).
cnf(d11,plain,
rev(cons(X1,cons(X0,cons(X2,nil)))) = cons(X2,cons(X0,append(nil,cons(X1,nil)))),
inference(demodulation,[status(thm)],[d10,c25]) ).
cnf(d12,plain,
rev(cons(X0,cons(X1,cons(X2,nil)))) = cons(X2,cons(X1,cons(X0,nil))),
inference(demodulation,[status(thm)],[d11,c24]) ).
cnf(d13,plain,
rev(cons(X3,cons(X0,cons(X1,cons(X2,nil))))) = append(cons(X2,cons(X1,cons(X0,nil))),cons(X3,nil)),
inference(superposition,[status(thm)],[d12,c27]) ).
cnf(d14,plain,
rev(cons(X3,cons(X2,cons(X1,cons(X0,nil))))) = cons(X0,append(cons(X1,cons(X2,nil)),cons(X3,nil))),
inference(demodulation,[status(thm)],[d13,c25]) ).
cnf(d15,plain,
rev(cons(X2,cons(X1,cons(X0,cons(X3,nil))))) = cons(X3,cons(X0,append(cons(X1,nil),cons(X2,nil)))),
inference(demodulation,[status(thm)],[d14,c25]) ).
cnf(d16,plain,
rev(cons(X1,cons(X0,cons(X2,cons(X3,nil))))) = cons(X3,cons(X2,cons(X0,append(nil,cons(X1,nil))))),
inference(demodulation,[status(thm)],[d15,c25]) ).
cnf(d17,plain,
rev(cons(X0,cons(X1,cons(X2,cons(X3,nil))))) = cons(X3,cons(X2,cons(X1,cons(X0,nil)))),
inference(demodulation,[status(thm)],[d16,c24]) ).
cnf(d18,plain,
( ~ unique(cons(X0,cons(X1,cons(X2,cons(X3,nil)))))
| leqNat(s(s(lengthNat(cons(X3,nil)))),s(s(z)))
| ~ sorted(cons(X3,cons(X2,cons(X1,cons(X0,nil))))) ),
inference(superposition,[status(thm)],[d17,d3]) ).
cnf(d19,plain,
( ~ unique(cons(X3,cons(X2,cons(X1,cons(X0,nil)))))
| ~ sorted(cons(X0,cons(X1,cons(X2,cons(X3,nil)))))
| leqNat(s(s(s(lengthNat(nil)))),s(s(z))) ),
inference(demodulation,[status(thm)],[d18,c15]) ).
cnf(d20,plain,
( ~ unique(cons(X3,cons(X2,cons(X1,cons(X0,nil)))))
| ~ sorted(cons(X0,cons(X1,cons(X2,cons(X3,nil)))))
| leqNat(s(s(s(z))),s(s(z))) ),
inference(demodulation,[status(thm)],[d19,c14]) ).
cnf(d21,plain,
( ~ unique(cons(X2,cons(X1,cons(X0,nil))))
| elemNat(X3,cons(X2,cons(X1,cons(X0,nil))))
| ~ sorted(cons(X0,cons(X1,cons(X2,cons(X3,nil)))))
| leqNat(s(s(s(z))),s(s(z))) ),
inference(resolution,[status(thm)],[d20,c23]) ).
cnf(d22,plain,
( ~ sorted(cons(X2,cons(X1,cons(X0,nil))))
| ~ leqNat(X3,X2)
| ~ unique(cons(X1,cons(X2,cons(X3,nil))))
| elemNat(X0,cons(X1,cons(X2,cons(X3,nil))))
| leqNat(s(s(s(z))),s(s(z))) ),
inference(resolution,[status(thm)],[d21,c13]) ).
cnf(d23,plain,
( elemNat(X3,cons(X1,cons(X0,nil)))
| X3 = X2
| ~ unique(cons(X2,cons(X1,cons(X0,nil))))
| ~ sorted(cons(X1,cons(X2,cons(X3,nil))))
| leqNat(s(s(s(z))),s(s(z)))
| ~ leqNat(X0,X1) ),
inference(resolution,[status(thm)],[d22,c17]) ).
cnf(d24,plain,
( ~ unique(cons(X3,cons(X2,nil)))
| elemNat(X1,cons(X3,cons(X2,nil)))
| elemNat(X0,cons(X3,cons(X2,nil)))
| ~ sorted(cons(X3,cons(X1,cons(X0,nil))))
| leqNat(s(s(s(z))),s(s(z)))
| ~ leqNat(X2,X3)
| X0 = X1 ),
inference(resolution,[status(thm)],[d23,c23]) ).
cnf(d25,plain,
( ~ sorted(cons(X1,cons(X0,nil)))
| ~ leqNat(X3,X1)
| ~ unique(cons(X3,cons(X2,nil)))
| elemNat(X0,cons(X3,cons(X2,nil)))
| elemNat(X1,cons(X3,cons(X2,nil)))
| leqNat(s(s(s(z))),s(s(z)))
| ~ leqNat(X2,X3)
| X0 = X1 ),
inference(resolution,[status(thm)],[d24,c13]) ).
cnf(d26,plain,
( leqNat(s(s(z)),s(z))
| ~ unique(cons(X2,cons(X3,nil)))
| elemNat(X0,cons(X2,cons(X3,nil)))
| elemNat(X1,cons(X2,cons(X3,nil)))
| ~ sorted(cons(X1,cons(X0,nil)))
| ~ leqNat(X3,X2)
| ~ leqNat(X2,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[d25,c7]) ).
cnf(d27,plain,
( elemNat(X0,cons(X2,nil))
| X0 = X3
| ~ unique(cons(X3,cons(X2,nil)))
| elemNat(X1,cons(X3,cons(X2,nil)))
| ~ sorted(cons(X1,cons(X0,nil)))
| leqNat(s(s(z)),s(z))
| ~ leqNat(X3,X1)
| ~ leqNat(X2,X3)
| X0 = X1 ),
inference(resolution,[status(thm)],[d26,c17]) ).
cnf(d28,plain,
( elemNat(X2,cons(X3,nil))
| X2 = X1
| ~ unique(cons(X1,cons(X3,nil)))
| elemNat(X0,cons(X3,nil))
| ~ sorted(cons(X2,cons(X0,nil)))
| leqNat(s(s(z)),s(z))
| ~ leqNat(X3,X1)
| ~ leqNat(X1,X2)
| X0 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[d27,c17]) ).
cnf(d29,plain,
( ~ unique(cons(X3,nil))
| elemNat(X1,cons(X3,nil))
| elemNat(X2,cons(X3,nil))
| elemNat(X0,cons(X3,nil))
| ~ sorted(cons(X0,cons(X2,nil)))
| leqNat(s(s(z)),s(z))
| ~ leqNat(X1,X0)
| ~ leqNat(X3,X1)
| X2 = X1
| X2 = X0
| X0 = X1 ),
inference(resolution,[status(thm)],[d28,c23]) ).
cnf(d30,plain,
( ~ sorted(cons(X0,nil))
| ~ leqNat(X2,X0)
| ~ unique(cons(X3,nil))
| elemNat(X2,cons(X3,nil))
| elemNat(X1,cons(X3,nil))
| elemNat(X0,cons(X3,nil))
| leqNat(s(s(z)),s(z))
| ~ leqNat(X1,X2)
| ~ leqNat(X3,X1)
| X2 = X1
| X0 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[d29,c13]) ).
cnf(d31,plain,
( ~ unique(cons(X3,nil))
| elemNat(X2,cons(X3,nil))
| elemNat(X1,cons(X3,nil))
| elemNat(X0,cons(X3,nil))
| leqNat(s(s(z)),s(z))
| ~ leqNat(X1,X0)
| ~ leqNat(X0,X2)
| ~ leqNat(X3,X1)
| X2 = X1
| X2 = X0
| X0 = X1 ),
inference(resolution,[status(thm)],[c10,d30]) ).
cnf(d32,plain,
( leqNat(s(z),z)
| ~ unique(cons(X3,nil))
| elemNat(X2,cons(X3,nil))
| elemNat(X1,cons(X3,nil))
| elemNat(X0,cons(X3,nil))
| ~ leqNat(X2,X0)
| ~ leqNat(X1,X2)
| ~ leqNat(X3,X1)
| X2 = X1
| X0 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[d31,c7]) ).
cnf(d33,plain,
( ~ unique(cons(X3,nil))
| elemNat(X2,cons(X3,nil))
| elemNat(X1,cons(X3,nil))
| elemNat(X0,cons(X3,nil))
| ~ leqNat(X1,X0)
| ~ leqNat(X0,X2)
| ~ leqNat(X3,X1)
| X2 = X1
| X2 = X0
| X0 = X1 ),
inference(resolution,[status(thm)],[c6,d32]) ).
cnf(d34,plain,
( elemNat(X2,nil)
| X2 = X3
| ~ unique(cons(X3,nil))
| elemNat(X1,cons(X3,nil))
| elemNat(X0,cons(X3,nil))
| ~ leqNat(X2,X0)
| ~ leqNat(X1,X2)
| ~ leqNat(X3,X1)
| X2 = X1
| X0 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[d33,c17]) ).
cnf(d35,plain,
( ~ unique(cons(X1,nil))
| elemNat(X3,cons(X1,nil))
| elemNat(X2,cons(X1,nil))
| ~ leqNat(X2,X0)
| ~ leqNat(X0,X3)
| ~ leqNat(X1,X2)
| X3 = X2
| X3 = X0
| X0 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[c16,d34]) ).
cnf(d36,plain,
( elemNat(X1,nil)
| X1 = X3
| ~ unique(cons(X3,nil))
| elemNat(X0,cons(X3,nil))
| ~ leqNat(X2,X0)
| ~ leqNat(X3,X1)
| ~ leqNat(X1,X2)
| X2 = X3
| X2 = X1
| X0 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[d35,c17]) ).
cnf(d37,plain,
( ~ unique(cons(X1,nil))
| elemNat(X3,cons(X1,nil))
| ~ leqNat(X2,X0)
| ~ leqNat(X0,X3)
| ~ leqNat(X1,X2)
| X3 = X2
| X3 = X0
| X2 = X1
| X0 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[c16,d36]) ).
cnf(d38,plain,
( elemNat(X0,nil)
| X0 = X3
| ~ unique(cons(X3,nil))
| ~ leqNat(X2,X0)
| ~ leqNat(X3,X1)
| ~ leqNat(X1,X2)
| X2 = X3
| X2 = X1
| X1 = X3
| X0 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[d37,c17]) ).
cnf(d39,plain,
( ~ unique(cons(X1,nil))
| ~ leqNat(X2,X0)
| ~ leqNat(X0,X3)
| ~ leqNat(X1,X2)
| X3 = X2
| X3 = X0
| X3 = X1
| X2 = X1
| X0 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[c16,d38]) ).
cnf(d40,plain,
( ~ unique(nil)
| elemNat(X2,nil)
| ~ leqNat(X3,X0)
| ~ leqNat(X2,X1)
| ~ leqNat(X1,X3)
| X3 = X2
| X3 = X1
| X1 = X2
| X0 = X3
| X0 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[d39,c23]) ).
cnf(d41,plain,
( elemNat(X1,nil)
| ~ leqNat(X2,X0)
| ~ leqNat(X1,X2)
| ~ leqNat(X0,X3)
| X3 = X2
| X3 = X1
| X3 = X0
| X2 = X1
| X0 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[c20,d40]) ).
cnf(d42,plain,
( ~ leqNat(X3,X0)
| ~ leqNat(X2,X1)
| ~ leqNat(X1,X3)
| X3 = X2
| X3 = X1
| X1 = X2
| X0 = X3
| X0 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[c16,d41]) ).
cnf(d43,plain,
( ~ leqNat(X2,X0)
| ~ leqNat(X1,s(X2))
| ~ leqNat(s(X0),X3)
| X3 = s(X2)
| X3 = X1
| X3 = s(X0)
| s(X2) = X1
| s(X0) = s(X2)
| s(X0) = X1 ),
inference(resolution,[status(thm)],[d42,c8]) ).
cnf(d44,plain,
( ~ leqNat(s(X0),X2)
| ~ leqNat(X3,s(X1))
| ~ leqNat(X1,X0)
| s(X0) = X3
| s(X1) = X3
| X2 = s(X0)
| X2 = s(X1)
| X2 = X3
| proj1S(s(X1)) = X0 ),
inference(superposition,[status(thm)],[d43,c3]) ).
cnf(d45,plain,
( ~ leqNat(s(X3),X1)
| ~ leqNat(X0,X3)
| ~ leqNat(X2,s(X0))
| s(X3) = X2
| s(X0) = X2
| X0 = X3
| X1 = s(X3)
| X1 = s(X0)
| X1 = X2 ),
inference(demodulation,[status(thm)],[d44,c3]) ).
cnf(d46,plain,
( ~ leqNat(X3,X0)
| ~ leqNat(X2,X3)
| ~ leqNat(X1,s(X2))
| s(X3) = X1
| s(X2) = X1
| X2 = X3
| s(X0) = s(X3)
| s(X0) = s(X2)
| s(X0) = X1 ),
inference(resolution,[status(thm)],[d45,c8]) ).
cnf(d47,plain,
( ~ leqNat(X3,s(X1))
| ~ leqNat(X1,X2)
| ~ leqNat(X2,X0)
| s(X0) = s(X2)
| s(X0) = X3
| s(X1) = X3
| s(X2) = X3
| X1 = X2
| proj1S(s(X1)) = X0 ),
inference(superposition,[status(thm)],[d46,c3]) ).
cnf(d48,plain,
( ~ leqNat(X0,X1)
| ~ leqNat(X1,X2)
| ~ leqNat(X3,s(X0))
| s(X2) = s(X1)
| s(X2) = X3
| s(X0) = X3
| s(X1) = X3
| X0 = X2
| X0 = X1 ),
inference(demodulation,[status(thm)],[d47,c3]) ).
cnf(d49,plain,
( ~ leqNat(X2,X1)
| ~ leqNat(X1,X0)
| ~ leqNat(X3,s(X2))
| s(X0) = X3
| s(X2) = X3
| s(X1) = X3
| X2 = X0
| X2 = X1
| proj1S(s(X1)) = X0 ),
inference(superposition,[status(thm)],[d48,c3]) ).
cnf(d50,plain,
( ~ leqNat(X0,X2)
| ~ leqNat(X1,X0)
| ~ leqNat(X3,s(X1))
| s(X2) = X3
| s(X0) = X3
| s(X1) = X3
| X0 = X2
| X1 = X2
| X1 = X0 ),
inference(demodulation,[status(thm)],[d49,c3]) ).
cnf(d51,plain,
( ~ leqNat(X1,X2)
| ~ leqNat(X0,X1)
| s(X2) = z
| s(X1) = z
| s(X0) = z
| X1 = X2
| X0 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[d50,c5]) ).
cnf(d52,plain,
( ~ leqNat(X0,X1)
| ~ leqNat(X1,X2)
| s(X1) = z
| s(X2) = z
| X0 = X1
| X0 = X2
| X1 = X2
| ~ leqNat(z,z) ),
inference(superposition,[status(thm)],[d51,c6]) ).
cnf(d53,plain,
( ~ leqNat(X2,X0)
| ~ leqNat(X0,X1)
| s(X0) = z
| s(X1) = z
| X2 = X0
| X2 = X1
| X0 = X1 ),
inference(resolution,[status(thm)],[c5,d52]) ).
cnf(d54,plain,
( ~ leqNat(X0,X2)
| ~ leqNat(X1,X0)
| s(X2) = z
| X0 = X2
| X1 = X0
| X1 = X2
| ~ leqNat(z,z) ),
inference(superposition,[status(thm)],[d53,c6]) ).
cnf(d55,plain,
( ~ leqNat(X2,X1)
| ~ leqNat(X0,X2)
| s(X1) = z
| X2 = X1
| X0 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[c5,d54]) ).
cnf(d56,plain,
( ~ leqNat(X2,X1)
| ~ leqNat(X1,X0)
| X2 = X0
| X2 = X1
| X1 = X0
| ~ leqNat(z,z) ),
inference(superposition,[status(thm)],[d55,c6]) ).
cnf(d57,plain,
( ~ leqNat(X1,X2)
| ~ leqNat(X0,X1)
| X1 = X2
| X0 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[c5,d56]) ).
cnf(d58,plain,
( ~ leqNat(X0,X1)
| z = X0
| z = X1
| X0 = X1 ),
inference(resolution,[status(thm)],[d57,c5]) ).
cnf(d59,plain,
( ~ leqNat(X0,X1)
| z = s(X0)
| z = s(X1)
| s(X0) = s(X1) ),
inference(resolution,[status(thm)],[d58,c8]) ).
cnf(d60,plain,
( ~ leqNat(X0,X1)
| z = s(X0)
| s(X0) = s(X1) ),
inference(resolution,[status(thm)],[c4,d59]) ).
cnf(d61,plain,
( ~ leqNat(X0,X1)
| z = s(X0)
| proj1S(s(X1)) = X0 ),
inference(superposition,[status(thm)],[d60,c3]) ).
cnf(d62,plain,
( ~ leqNat(X1,X0)
| z = s(X1)
| X0 = X1 ),
inference(demodulation,[status(thm)],[d61,c3]) ).
cnf(d63,plain,
( ~ leqNat(X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c4,d62]) ).
cnf(d64,plain,
X0 = z,
inference(resolution,[status(thm)],[d63,c5]) ).
cnf(d65,plain,
leqNat(X0,X1),
inference(superposition,[status(thm)],[d64,c5]) ).
cnf(d66,plain,
$false,
inference(resolution,[status(thm)],[d65,c6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX203+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.36 % Computer : n009.cluster.edu
% 0.06/0.36 % Model : x86_64 x86_64
% 0.06/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.36 % Memory : 8046.5625MB
% 0.06/0.36 % OS : Linux 6.8.0-71-generic
% 0.06/0.36 % CPULimit : 300
% 0.06/0.36 % WCLimit : 300
% 0.06/0.36 % DateTime : Sat Sep 26 16:54:59 UTC 2026
% 0.06/0.36 % CPUTime :
% 0.06/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.74/4.28 % SZS status Theorem for theBenchmark.p
% 27.74/4.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------