%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWX187+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 : n007.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 09:15:35 AM UTC 2026
% Result : Theorem 36.53s 14.10s
% Output : CNFRefutation 36.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 31 unt; 0 def)
% Number of atoms : 136 ( 94 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 139 ( 61 ~; 67 |; 0 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 169 ( 8 sgn 16 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_001,axiom,
! [X0,X1] : head(cons(X0,X1)) = X0 ).
fof(axiom_005,axiom,
! [X0] : s(X0) != z ).
fof(axiom_007,axiom,
! [X0,X1] : length(cons(X0,X1)) = s(length(X1)) ).
fof(axiom_008,axiom,
! [X0,X1] :
( x2(s(X0),s(X1))
<=> x2(X0,X1) ) ).
fof(axiom_010,axiom,
! [X0] : x2(z,s(X0)) ).
fof(axiom_012,axiom,
! [X0] : x(nil,X0) = X0 ).
fof(axiom_013,axiom,
! [X0,X1,X2] : x(cons(X1,X2),X0) = cons(X1,x(X2,X0)) ).
fof(axiom_015,axiom,
! [X0,X1,X2] : rotate(s(X0),cons(X1,X2)) = rotate(X0,x(X2,cons(X1,nil))) ).
fof(axiom_016,axiom,
! [X0] : rotate(z,X0) = X0 ).
fof(goal_017,conjecture,
? [X0,X1,X2,X3] :
~ ( x2(X0,length(X3))
=> ( x2(X1,length(X2))
=> ( X3 = X2
=> ( rotate(s(z),X3) != X3
=> ( rotate(X0,X3) = rotate(X1,X2)
=> X0 = X1 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1,X2,X3] :
~ ( x2(X0,length(X3))
=> ( x2(X1,length(X2))
=> ( X3 = X2
=> ( rotate(s(z),X3) != X3
=> ( rotate(X0,X3) = rotate(X1,X2)
=> X0 = X1 ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[goal_017]) ).
cnf(c0,plain,
head(cons(X0,X1)) = X0,
inference(clausification,[status(esa)],[axiom_001]) ).
cnf(c4,plain,
s(X0) != z,
inference(clausification,[status(esa)],[axiom_005]) ).
cnf(c6,plain,
s(length(X0)) = length(cons(X1,X0)),
inference(clausification,[status(esa)],[axiom_007]) ).
cnf(c8,plain,
( ~ x2(X0,X1)
| x2(s(X0),s(X1)) ),
inference(clausification,[status(esa)],[axiom_008]) ).
cnf(c10,plain,
x2(z,s(X0)),
inference(clausification,[status(esa)],[axiom_010]) ).
cnf(c12,plain,
x(nil,X0) = X0,
inference(clausification,[status(esa)],[axiom_012]) ).
cnf(c13,plain,
cons(X0,x(X1,X2)) = x(cons(X0,X1),X2),
inference(clausification,[status(esa)],[axiom_013]) ).
cnf(c15,plain,
rotate(X0,x(X1,cons(X2,nil))) = rotate(s(X0),cons(X2,X1)),
inference(clausification,[status(esa)],[axiom_015]) ).
cnf(c16,plain,
rotate(z,X0) = X0,
inference(clausification,[status(esa)],[axiom_016]) ).
cnf(c17,plain,
( X0 = X3
| rotate(X0,X1) != rotate(X3,X2)
| ~ x2(X3,length(X2))
| X1 != X2
| rotate(s(z),X2) = X2
| ~ x2(X0,length(X1)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
rotate(s(z),cons(X1,X0)) = x(X0,cons(X1,nil)),
inference(superposition,[status(thm)],[c15,c16]) ).
cnf(d1,plain,
( ~ x2(X1,length(X2))
| ~ x2(X0,length(X2))
| rotate(s(z),X2) = X2
| rotate(X0,X2) != rotate(X1,X2)
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[c17]) ).
cnf(d2,plain,
( ~ x2(X1,length(X0))
| ~ x2(z,length(X0))
| rotate(s(z),X0) = X0
| X1 = z
| rotate(X1,X0) != X0 ),
inference(superposition,[status(thm)],[c16,d1]) ).
cnf(d3,plain,
x(X0,cons(X1,nil)) = rotate(s(z),cons(X1,X0)),
inference(superposition,[status(thm)],[c16,c15]) ).
cnf(d4,plain,
rotate(X3,cons(X0,x(X1,cons(X2,nil)))) = rotate(s(X3),cons(X2,cons(X0,X1))),
inference(superposition,[status(thm)],[c13,c15]) ).
cnf(d5,plain,
x(x(X1,cons(X2,nil)),cons(X0,nil)) = rotate(s(s(z)),cons(X2,cons(X0,X1))),
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
x(cons(X0,x(X1,cons(X2,nil))),cons(X3,nil)) = rotate(s(s(z)),cons(X2,cons(X3,cons(X0,X1)))),
inference(superposition,[status(thm)],[c13,d5]) ).
cnf(d7,plain,
cons(X0,x(x(X1,cons(X2,nil)),cons(X3,nil))) = rotate(s(s(z)),cons(X2,cons(X3,cons(X0,X1)))),
inference(demodulation,[status(thm)],[d6,c13]) ).
cnf(d8,plain,
cons(X3,rotate(s(s(z)),cons(X1,cons(X2,X0)))) = rotate(s(s(z)),cons(X1,cons(X2,cons(X3,X0)))),
inference(demodulation,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ x2(z,length(cons(X0,cons(X1,cons(X2,X3)))))
| ~ x2(s(s(z)),length(cons(X0,cons(X1,cons(X2,X3)))))
| rotate(s(z),cons(X0,cons(X1,cons(X2,X3)))) = cons(X0,cons(X1,cons(X2,X3)))
| s(s(z)) = z
| cons(X2,rotate(s(s(z)),cons(X0,cons(X1,X3)))) != cons(X0,cons(X1,cons(X2,X3))) ),
inference(superposition,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
( ~ x2(z,length(cons(X0,cons(X1,cons(X2,X3)))))
| ~ x2(s(s(z)),length(cons(X0,cons(X1,cons(X2,X3)))))
| x(cons(X1,cons(X2,X3)),cons(X0,nil)) = cons(X0,cons(X1,cons(X2,X3)))
| s(s(z)) = z
| cons(X2,rotate(s(s(z)),cons(X0,cons(X1,X3)))) != cons(X0,cons(X1,cons(X2,X3))) ),
inference(demodulation,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
( ~ x2(z,length(cons(X3,cons(X0,cons(X1,X2)))))
| ~ x2(s(s(z)),length(cons(X3,cons(X0,cons(X1,X2)))))
| cons(X0,x(cons(X1,X2),cons(X3,nil))) = cons(X3,cons(X0,cons(X1,X2)))
| s(s(z)) = z
| cons(X1,rotate(s(s(z)),cons(X3,cons(X0,X2)))) != cons(X3,cons(X0,cons(X1,X2))) ),
inference(demodulation,[status(thm)],[d10,c13]) ).
cnf(d12,plain,
( ~ x2(z,length(cons(X2,cons(X3,cons(X0,X1)))))
| ~ x2(s(s(z)),length(cons(X2,cons(X3,cons(X0,X1)))))
| cons(X3,cons(X0,x(X1,cons(X2,nil)))) = cons(X2,cons(X3,cons(X0,X1)))
| s(s(z)) = z
| cons(X0,rotate(s(s(z)),cons(X2,cons(X3,X1)))) != cons(X2,cons(X3,cons(X0,X1))) ),
inference(demodulation,[status(thm)],[d11,c13]) ).
cnf(d13,plain,
( ~ x2(z,length(cons(X0,cons(X1,cons(X2,X3)))))
| ~ x2(s(s(z)),s(length(cons(X1,cons(X2,X3)))))
| cons(X1,cons(X2,x(X3,cons(X0,nil)))) = cons(X0,cons(X1,cons(X2,X3)))
| s(s(z)) = z
| cons(X2,rotate(s(s(z)),cons(X0,cons(X1,X3)))) != cons(X0,cons(X1,cons(X2,X3))) ),
inference(demodulation,[status(thm)],[d12,c6]) ).
cnf(d14,plain,
( ~ x2(z,length(cons(X3,cons(X0,cons(X1,X2)))))
| ~ x2(s(s(z)),s(s(length(cons(X1,X2)))))
| cons(X0,cons(X1,x(X2,cons(X3,nil)))) = cons(X3,cons(X0,cons(X1,X2)))
| s(s(z)) = z
| cons(X1,rotate(s(s(z)),cons(X3,cons(X0,X2)))) != cons(X3,cons(X0,cons(X1,X2))) ),
inference(demodulation,[status(thm)],[d13,c6]) ).
cnf(d15,plain,
( ~ x2(z,length(cons(X2,cons(X3,cons(X0,X1)))))
| ~ x2(s(s(z)),s(s(s(length(X1)))))
| cons(X3,cons(X0,x(X1,cons(X2,nil)))) = cons(X2,cons(X3,cons(X0,X1)))
| s(s(z)) = z
| cons(X0,rotate(s(s(z)),cons(X2,cons(X3,X1)))) != cons(X2,cons(X3,cons(X0,X1))) ),
inference(demodulation,[status(thm)],[d14,c6]) ).
cnf(d16,plain,
( ~ x2(z,s(length(cons(X1,cons(X2,X3)))))
| ~ x2(s(s(z)),s(s(s(length(X3)))))
| cons(X1,cons(X2,x(X3,cons(X0,nil)))) = cons(X0,cons(X1,cons(X2,X3)))
| s(s(z)) = z
| cons(X2,rotate(s(s(z)),cons(X0,cons(X1,X3)))) != cons(X0,cons(X1,cons(X2,X3))) ),
inference(demodulation,[status(thm)],[d15,c6]) ).
cnf(d17,plain,
( ~ x2(z,s(s(length(cons(X1,X2)))))
| ~ x2(s(s(z)),s(s(s(length(X2)))))
| cons(X0,cons(X1,x(X2,cons(X3,nil)))) = cons(X3,cons(X0,cons(X1,X2)))
| s(s(z)) = z
| cons(X1,rotate(s(s(z)),cons(X3,cons(X0,X2)))) != cons(X3,cons(X0,cons(X1,X2))) ),
inference(demodulation,[status(thm)],[d16,c6]) ).
cnf(d18,plain,
( ~ x2(z,s(s(s(length(X1)))))
| ~ x2(s(s(z)),s(s(s(length(X1)))))
| cons(X3,cons(X0,x(X1,cons(X2,nil)))) = cons(X2,cons(X3,cons(X0,X1)))
| s(s(z)) = z
| cons(X0,rotate(s(s(z)),cons(X2,cons(X3,X1)))) != cons(X2,cons(X3,cons(X0,X1))) ),
inference(demodulation,[status(thm)],[d17,c6]) ).
cnf(d19,plain,
( ~ x2(z,s(s(s(length(X3)))))
| ~ x2(s(s(z)),s(s(s(length(X3)))))
| cons(X2,cons(X0,x(X3,cons(X1,nil)))) = cons(X1,cons(X2,cons(X0,X3)))
| cons(X0,rotate(s(s(z)),cons(X1,cons(X2,X3)))) != cons(X1,cons(X2,cons(X0,X3))) ),
inference(resolution,[status(thm)],[c4,d18]) ).
cnf(d20,plain,
( ~ x2(s(s(z)),s(s(s(length(X2)))))
| cons(X1,rotate(s(s(z)),cons(X3,cons(X0,X2)))) != cons(X3,cons(X0,cons(X1,X2)))
| cons(X0,cons(X1,x(X2,cons(X3,nil)))) = cons(X3,cons(X0,cons(X1,X2))) ),
inference(resolution,[status(thm)],[c10,d19]) ).
cnf(d21,plain,
x2(s(z),s(s(X0))),
inference(resolution,[status(thm)],[c8,c10]) ).
cnf(d22,plain,
x2(s(s(z)),s(s(s(X0)))),
inference(resolution,[status(thm)],[d21,c8]) ).
cnf(d23,plain,
( cons(X2,cons(X0,x(X3,cons(X1,nil)))) = cons(X1,cons(X2,cons(X0,X3)))
| cons(X0,rotate(s(s(z)),cons(X1,cons(X2,X3)))) != cons(X1,cons(X2,cons(X0,X3))) ),
inference(resolution,[status(thm)],[d22,d20]) ).
cnf(d24,plain,
rotate(X3,cons(X4,cons(X0,x(X1,cons(X2,nil))))) = rotate(s(X3),cons(X2,cons(X4,cons(X0,X1)))),
inference(superposition,[status(thm)],[c13,d4]) ).
cnf(d25,plain,
rotate(X1,cons(X2,cons(X3,cons(X0,nil)))) = rotate(s(X1),cons(X0,cons(X2,cons(X3,nil)))),
inference(superposition,[status(thm)],[c12,d24]) ).
cnf(d26,plain,
( cons(X1,cons(X3,x(cons(X2,nil),cons(X0,nil)))) = cons(X0,cons(X1,cons(X3,cons(X2,nil))))
| cons(X3,rotate(s(z),cons(X1,cons(X2,cons(X0,nil))))) != cons(X0,cons(X1,cons(X3,cons(X2,nil)))) ),
inference(superposition,[status(thm)],[d25,d23]) ).
cnf(d27,plain,
( cons(X0,cons(X3,x(cons(X1,nil),cons(X2,nil)))) = cons(X2,cons(X0,cons(X3,cons(X1,nil))))
| cons(X3,x(cons(X1,cons(X2,nil)),cons(X0,nil))) != cons(X2,cons(X0,cons(X3,cons(X1,nil)))) ),
inference(demodulation,[status(thm)],[d26,d0]) ).
cnf(d28,plain,
( cons(X2,cons(X3,x(cons(X0,nil),cons(X1,nil)))) = cons(X1,cons(X2,cons(X3,cons(X0,nil))))
| cons(X3,cons(X0,x(cons(X1,nil),cons(X2,nil)))) != cons(X1,cons(X2,cons(X3,cons(X0,nil)))) ),
inference(demodulation,[status(thm)],[d27,c13]) ).
cnf(d29,plain,
( cons(X1,cons(X2,x(cons(X3,nil),cons(X0,nil)))) = cons(X0,cons(X1,cons(X2,cons(X3,nil))))
| cons(X2,cons(X3,cons(X0,x(nil,cons(X1,nil))))) != cons(X0,cons(X1,cons(X2,cons(X3,nil)))) ),
inference(demodulation,[status(thm)],[d28,c13]) ).
cnf(d30,plain,
( cons(X0,cons(X1,x(cons(X2,nil),cons(X3,nil)))) = cons(X3,cons(X0,cons(X1,cons(X2,nil))))
| cons(X1,cons(X2,cons(X3,cons(X0,nil)))) != cons(X3,cons(X0,cons(X1,cons(X2,nil)))) ),
inference(demodulation,[status(thm)],[d29,c12]) ).
cnf(d31,plain,
( cons(X3,cons(X2,cons(X0,x(nil,cons(X1,nil))))) = cons(X1,cons(X3,cons(X2,cons(X0,nil))))
| cons(X2,cons(X0,cons(X1,cons(X3,nil)))) != cons(X1,cons(X3,cons(X2,cons(X0,nil)))) ),
inference(demodulation,[status(thm)],[d30,c13]) ).
cnf(d32,plain,
( cons(X3,cons(X1,cons(X2,cons(X0,nil)))) = cons(X0,cons(X3,cons(X1,cons(X2,nil))))
| cons(X1,cons(X2,cons(X0,cons(X3,nil)))) != cons(X0,cons(X3,cons(X1,cons(X2,nil)))) ),
inference(demodulation,[status(thm)],[d31,c12]) ).
cnf(d33,plain,
cons(X0,cons(X1,cons(X0,cons(X1,nil)))) = cons(X1,cons(X0,cons(X1,cons(X0,nil)))),
inference(equality_resolution,[status(thm)],[d32]) ).
cnf(d34,plain,
head(cons(X1,cons(X0,cons(X1,cons(X0,nil))))) = X0,
inference(superposition,[status(thm)],[d33,c0]) ).
cnf(d35,plain,
X0 = X1,
inference(demodulation,[status(thm)],[d34,c0]) ).
cnf(d36,plain,
$false,
inference(resolution,[status(thm)],[d35,c4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWX187+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/5.44 % Computer : n007.cluster.edu
% 0.19/5.44 % Model : x86_64 x86_64
% 0.19/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.44 % Memory : 8046.5625MB
% 0.19/5.44 % OS : Linux 6.8.0-71-generic
% 0.19/5.44 % CPULimit : 300
% 0.19/5.44 % WCLimit : 300
% 0.19/5.44 % DateTime : Sat Sep 26 16:49:00 UTC 2026
% 0.19/5.45 % CPUTime :
% 0.19/5.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.53/14.10 % SZS status Theorem for theBenchmark.p
% 36.53/14.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------