%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWX199+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:15:37 AM UTC 2026
% Result : Theorem 25.39s 4.72s
% Output : CNFRefutation 25.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 15 unt; 0 def)
% Number of atoms : 84 ( 46 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 90 ( 46 ~; 38 |; 0 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 97 ( 8 sgn 15 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_001,axiom,
! [X0,X1] : head(cons(X0,X1)) = X0 ).
fof(axiom_002,axiom,
! [X0,X1] : tail(cons(X0,X1)) = X1 ).
fof(axiom_005,axiom,
! [X0] : z != s(X0) ).
fof(axiom_006,axiom,
! [X0] : leqNat(z,X0) ).
fof(axiom_008,axiom,
! [X0,X1] :
( leqNat(s(X0),s(X1))
<=> leqNat(X0,X1) ) ).
fof(axiom_009,axiom,
! [X0] : merge(nil,X0) = X0 ).
fof(axiom_010,axiom,
! [X0,X1] : merge(cons(X0,X1),nil) = cons(X0,X1) ).
fof(axiom_011,axiom,
! [X0,X1,X2,X3] :
( leqNat(X0,X2)
=> merge(cons(X0,X1),cons(X2,X3)) = cons(X0,merge(X1,cons(X2,X3))) ) ).
fof(goal_013,conjecture,
? [X0,X1,X2] :
~ ( merge(X0,X1) = merge(X1,X0)
=> ( merge(X0,X2) = merge(X2,X0)
=> merge(X1,X2) = merge(X2,X1) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1,X2] :
~ ( merge(X0,X1) = merge(X1,X0)
=> ( merge(X0,X2) = merge(X2,X0)
=> merge(X1,X2) = merge(X2,X1) ) ),
inference(negate_conjecture,[status(cth)],[goal_013]) ).
cnf(c0,plain,
head(cons(X0,X1)) = X0,
inference(clausification,[status(esa)],[axiom_001]) ).
cnf(c1,plain,
tail(cons(X0,X1)) = X1,
inference(clausification,[status(esa)],[axiom_002]) ).
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(c8,plain,
( ~ leqNat(X0,X1)
| leqNat(s(X0),s(X1)) ),
inference(clausification,[status(esa)],[axiom_008]) ).
cnf(c9,plain,
merge(nil,X0) = X0,
inference(clausification,[status(esa)],[axiom_009]) ).
cnf(c10,plain,
merge(cons(X0,X1),nil) = cons(X0,X1),
inference(clausification,[status(esa)],[axiom_010]) ).
cnf(c11,plain,
( merge(cons(X0,X2),cons(X1,X3)) = cons(X0,merge(X2,cons(X1,X3)))
| ~ leqNat(X0,X1) ),
inference(clausification,[status(esa)],[axiom_011]) ).
cnf(c13,plain,
( merge(X1,X2) = merge(X2,X1)
| merge(X0,X2) != merge(X2,X0)
| merge(X0,X1) != merge(X1,X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( merge(nil,X1) != merge(X1,nil)
| merge(X0,X1) = merge(X1,X0)
| X0 != merge(X0,nil) ),
inference(superposition,[status(thm)],[c9,c13]) ).
cnf(d1,plain,
( X0 != merge(X0,nil)
| merge(X1,X0) = merge(X0,X1)
| X1 != merge(X1,nil) ),
inference(demodulation,[status(thm)],[d0,c9]) ).
cnf(d2,plain,
( merge(X2,cons(X0,X1)) = merge(cons(X0,X1),X2)
| X2 != merge(X2,nil)
| cons(X0,X1) != cons(X0,X1) ),
inference(superposition,[status(thm)],[c10,d1]) ).
cnf(d3,plain,
( merge(X0,cons(X1,X2)) = merge(cons(X1,X2),X0)
| X0 != merge(X0,nil) ),
inference(equality_resolution,[status(thm)],[d2]) ).
cnf(d4,plain,
( merge(cons(X0,X1),cons(X2,X3)) = merge(cons(X2,X3),cons(X0,X1))
| cons(X0,X1) != cons(X0,X1) ),
inference(superposition,[status(thm)],[c10,d3]) ).
cnf(d5,plain,
merge(cons(X0,X1),cons(X2,X3)) = merge(cons(X2,X3),cons(X0,X1)),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
( ~ leqNat(X0,X2)
| cons(X0,merge(X1,cons(X2,X3))) = merge(cons(X2,X3),cons(X0,X1)) ),
inference(superposition,[status(thm)],[c11,d5]) ).
cnf(d7,plain,
( ~ leqNat(X2,X0)
| ~ leqNat(X0,X2)
| cons(X2,merge(X3,cons(X0,X1))) = cons(X0,merge(X1,cons(X2,X3))) ),
inference(superposition,[status(thm)],[d6,c11]) ).
cnf(d8,plain,
( ~ leqNat(X0,X2)
| ~ leqNat(X2,X0)
| cons(X2,cons(X0,X1)) = cons(X0,merge(X1,cons(X2,nil))) ),
inference(superposition,[status(thm)],[c9,d7]) ).
cnf(d9,plain,
( ~ leqNat(X0,X2)
| ~ leqNat(X2,X0)
| tail(cons(X2,cons(X0,X1))) = merge(X1,cons(X2,nil)) ),
inference(superposition,[status(thm)],[d8,c1]) ).
cnf(d10,plain,
( ~ leqNat(X1,X0)
| ~ leqNat(X0,X1)
| cons(X1,X2) = merge(X2,cons(X0,nil)) ),
inference(demodulation,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
( ~ leqNat(X0,X2)
| ~ leqNat(X2,X0)
| head(merge(X1,cons(X2,nil))) = X0 ),
inference(superposition,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
( ~ leqNat(X3,X2)
| ~ leqNat(X2,X3)
| head(merge(cons(X2,nil),cons(X0,X1))) = X3 ),
inference(superposition,[status(thm)],[d5,d11]) ).
cnf(d13,plain,
( ~ leqNat(X0,X2)
| ~ leqNat(X2,X0)
| ~ leqNat(X3,X1)
| ~ leqNat(X1,X3)
| X2 = X3 ),
inference(superposition,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
( ~ leqNat(X2,X1)
| ~ leqNat(X0,z)
| ~ leqNat(X1,X2)
| X0 = X1 ),
inference(resolution,[status(thm)],[d13,c5]) ).
cnf(d15,plain,
( ~ leqNat(X0,X1)
| ~ leqNat(X1,X0)
| z = X0 ),
inference(resolution,[status(thm)],[d14,c5]) ).
cnf(d16,plain,
( ~ leqNat(X0,X1)
| ~ leqNat(s(X1),s(X0))
| z = s(X0) ),
inference(resolution,[status(thm)],[d15,c8]) ).
cnf(d17,plain,
( ~ leqNat(s(X1),s(X0))
| ~ leqNat(X0,X1) ),
inference(resolution,[status(thm)],[c4,d16]) ).
cnf(d18,plain,
( ~ leqNat(X1,X0)
| ~ leqNat(X0,X1) ),
inference(resolution,[status(thm)],[d17,c8]) ).
cnf(d19,plain,
~ leqNat(X0,z),
inference(resolution,[status(thm)],[d18,c5]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[d19,c5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX199+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n011.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 16:54:14 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.39/4.72 % SZS status Theorem for theBenchmark.p
% 25.39/4.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------