%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWX212+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 : n014.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 09:15:40 AM UTC 2026
% Result : Theorem 152.20s 44.68s
% Output : CNFRefutation 152.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 31
% Syntax : Number of formulae : 183 ( 70 unt; 0 def)
% Number of atoms : 375 ( 153 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 329 ( 137 ~; 173 |; 1 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-2 aty)
% Number of variables : 361 ( 83 sgn 53 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_004,axiom,
a != b ).
fof(axiom_008,axiom,
! [X0,X1] : proj1(x(X0,X1)) = X0 ).
fof(axiom_009,axiom,
! [X0,X1] : proj2(x(X0,X1)) = X1 ).
fof(axiom_010,axiom,
! [X0,X1] : proj12(y(X0,X1)) = X0 ).
fof(axiom_013,axiom,
nil2 != eps ).
fof(axiom_014,axiom,
! [X0] : nil2 != atom(X0) ).
fof(axiom_015,axiom,
! [X0,X1] : nil2 != x(X0,X1) ).
fof(axiom_016,axiom,
! [X0,X1] : nil2 != y(X0,X1) ).
fof(axiom_017,axiom,
! [X0] : nil2 != star(X0) ).
fof(axiom_018,axiom,
! [X0] : eps != atom(X0) ).
fof(axiom_019,axiom,
! [X0,X1] : eps != x(X0,X1) ).
fof(axiom_020,axiom,
! [X0,X1] : eps != y(X0,X1) ).
fof(axiom_021,axiom,
! [X0] : eps != star(X0) ).
fof(axiom_022,axiom,
! [X0,X1,X2] : atom(X0) != x(X1,X2) ).
fof(axiom_023,axiom,
! [X0,X1,X2] : atom(X0) != y(X1,X2) ).
fof(axiom_024,axiom,
! [X0,X1] : atom(X0) != star(X1) ).
fof(axiom_036,axiom,
! [X0] :
( X0 != eps
=> ( X0 != x(proj1(X0),proj2(X0))
=> ( X0 != y(proj12(X0),proj22(X0))
=> ( X0 != star(proj1Star(X0))
=> ~ eps2(X0) ) ) ) ) ).
fof(axiom_037,axiom,
eps2(eps) ).
fof(axiom_038,axiom,
! [X0,X1] :
( eps2(x(X0,X1))
<=> ( eps2(X1)
| eps2(X0) ) ) ).
fof(axiom_039,axiom,
! [X0,X1] :
( eps2(y(X0,X1))
<=> ( eps2(X1)
& eps2(X0) ) ) ).
fof(axiom_040,axiom,
! [X0] : eps2(star(X0)) ).
fof(axiom_041,axiom,
! [X0,X1] :
( X0 != atom(proj1Atom(X0))
=> ( X0 != x(proj1(X0),proj2(X0))
=> ( X0 != y(proj12(X0),proj22(X0))
=> ( X0 != star(proj1Star(X0))
=> step(X0,X1) = nil2 ) ) ) ) ).
fof(axiom_042,axiom,
! [X0,X1] :
( X1 = X0
=> step(atom(X1),X0) = eps ) ).
fof(axiom_043,axiom,
! [X0,X1] :
( X1 != X0
=> step(atom(X1),X0) = nil2 ) ).
fof(axiom_044,axiom,
! [X0,X1,X2] : step(x(X1,X2),X0) = x(step(X1,X0),step(X2,X0)) ).
fof(axiom_045,axiom,
! [X0,X1,X2] :
( eps2(X1)
=> step(y(X1,X2),X0) = x(y(step(X1,X0),X2),step(X2,X0)) ) ).
fof(axiom_046,axiom,
! [X0,X1,X2] :
( ~ eps2(X1)
=> step(y(X1,X2),X0) = x(y(step(X1,X0),X2),nil2) ) ).
fof(axiom_047,axiom,
! [X0,X1] : step(star(X1),X0) = y(step(X1,X0),star(X1)) ).
fof(axiom_048,axiom,
! [X0] :
( rec(X0,nil)
<=> eps2(X0) ) ).
fof(axiom_049,axiom,
! [X0,X1,X2] :
( rec(X0,cons(X1,X2))
<=> rec(step(X0,X1),X2) ) ).
fof(goal_050,conjecture,
? [X0,X1,X2] :
~ ( rec(y(X0,X1),X2)
<=> rec(y(X1,X0),X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1,X2] :
~ ( rec(y(X0,X1),X2)
<=> rec(y(X1,X0),X2) ),
inference(negate_conjecture,[status(cth)],[goal_050]) ).
cnf(c3,plain,
a != b,
inference(clausification,[status(esa)],[axiom_004]) ).
cnf(c7,plain,
proj1(x(X0,X1)) = X0,
inference(clausification,[status(esa)],[axiom_008]) ).
cnf(c8,plain,
proj2(x(X0,X1)) = X1,
inference(clausification,[status(esa)],[axiom_009]) ).
cnf(c9,plain,
proj12(y(X0,X1)) = X0,
inference(clausification,[status(esa)],[axiom_010]) ).
cnf(c12,plain,
nil2 != eps,
inference(clausification,[status(esa)],[axiom_013]) ).
cnf(c13,plain,
nil2 != atom(X0),
inference(clausification,[status(esa)],[axiom_014]) ).
cnf(c14,plain,
nil2 != x(X0,X1),
inference(clausification,[status(esa)],[axiom_015]) ).
cnf(c15,plain,
nil2 != y(X0,X1),
inference(clausification,[status(esa)],[axiom_016]) ).
cnf(c16,plain,
nil2 != star(X0),
inference(clausification,[status(esa)],[axiom_017]) ).
cnf(c17,plain,
eps != atom(X0),
inference(clausification,[status(esa)],[axiom_018]) ).
cnf(c18,plain,
eps != x(X0,X1),
inference(clausification,[status(esa)],[axiom_019]) ).
cnf(c19,plain,
eps != y(X0,X1),
inference(clausification,[status(esa)],[axiom_020]) ).
cnf(c20,plain,
eps != star(X0),
inference(clausification,[status(esa)],[axiom_021]) ).
cnf(c21,plain,
atom(X0) != x(X1,X2),
inference(clausification,[status(esa)],[axiom_022]) ).
cnf(c22,plain,
atom(X0) != y(X1,X2),
inference(clausification,[status(esa)],[axiom_023]) ).
cnf(c23,plain,
atom(X0) != star(X1),
inference(clausification,[status(esa)],[axiom_024]) ).
cnf(c35,plain,
( X0 = y(proj12(X0),proj22(X0))
| X0 = eps
| X0 = x(proj1(X0),proj2(X0))
| ~ eps2(X0)
| X0 = star(proj1Star(X0)) ),
inference(clausification,[status(esa)],[axiom_036]) ).
cnf(c36,plain,
eps2(eps),
inference(clausification,[status(esa)],[axiom_037]) ).
cnf(c37,plain,
( eps2(X1)
| eps2(X0)
| ~ eps2(x(X0,X1)) ),
inference(clausification,[status(esa)],[axiom_038]) ).
cnf(c38,plain,
( ~ eps2(X0)
| eps2(x(X0,X1)) ),
inference(clausification,[status(esa)],[axiom_038]) ).
cnf(c39,plain,
( ~ eps2(X1)
| eps2(x(X0,X1)) ),
inference(clausification,[status(esa)],[axiom_038]) ).
cnf(c40,plain,
( eps2(X0)
| ~ eps2(y(X0,X1)) ),
inference(clausification,[status(esa)],[axiom_039]) ).
cnf(c41,plain,
( eps2(X1)
| ~ eps2(y(X0,X1)) ),
inference(clausification,[status(esa)],[axiom_039]) ).
cnf(c42,plain,
( ~ eps2(X1)
| ~ eps2(X0)
| eps2(y(X0,X1)) ),
inference(clausification,[status(esa)],[axiom_039]) ).
cnf(c43,plain,
eps2(star(X0)),
inference(clausification,[status(esa)],[axiom_040]) ).
cnf(c44,plain,
( X0 = y(proj12(X0),proj22(X0))
| X0 = x(proj1(X0),proj2(X0))
| step(X0,X1) = nil2
| X0 = atom(proj1Atom(X0))
| X0 = star(proj1Star(X0)) ),
inference(clausification,[status(esa)],[axiom_041]) ).
cnf(c45,plain,
( step(atom(X0),X1) = eps
| X0 != X1 ),
inference(clausification,[status(esa)],[axiom_042]) ).
cnf(c46,plain,
( step(atom(X0),X1) = nil2
| X0 = X1 ),
inference(clausification,[status(esa)],[axiom_043]) ).
cnf(c47,plain,
step(x(X0,X1),X2) = x(step(X0,X2),step(X1,X2)),
inference(clausification,[status(esa)],[axiom_044]) ).
cnf(c48,plain,
( step(y(X0,X1),X2) = x(y(step(X0,X2),X1),step(X1,X2))
| ~ eps2(X0) ),
inference(clausification,[status(esa)],[axiom_045]) ).
cnf(c49,plain,
( step(y(X0,X1),X2) = x(y(step(X0,X2),X1),nil2)
| eps2(X0) ),
inference(clausification,[status(esa)],[axiom_046]) ).
cnf(c50,plain,
step(star(X0),X1) = y(step(X0,X1),star(X0)),
inference(clausification,[status(esa)],[axiom_047]) ).
cnf(c51,plain,
( eps2(X0)
| ~ rec(X0,nil) ),
inference(clausification,[status(esa)],[axiom_048]) ).
cnf(c52,plain,
( ~ eps2(X0)
| rec(X0,nil) ),
inference(clausification,[status(esa)],[axiom_048]) ).
cnf(c53,plain,
( rec(step(X0,X1),X2)
| ~ rec(X0,cons(X1,X2)) ),
inference(clausification,[status(esa)],[axiom_049]) ).
cnf(c54,plain,
( ~ rec(step(X0,X1),X2)
| rec(X0,cons(X1,X2)) ),
inference(clausification,[status(esa)],[axiom_049]) ).
cnf(c55,plain,
( rec(y(X1,X0),X2)
| ~ rec(y(X0,X1),X2) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( step(X0,X1) = nil2
| X0 = star(proj1Star(X0))
| X0 = x(proj1(X0),proj2(X0))
| X0 = atom(proj1Atom(X0))
| eps != X0 ),
inference(superposition,[status(thm)],[c44,c19]) ).
cnf(d1,plain,
( step(eps,X0) = nil2
| eps = star(proj1Star(eps))
| eps = x(proj1(eps),proj2(eps))
| eps = atom(proj1Atom(eps)) ),
inference(equality_resolution,[status(thm)],[d0]) ).
cnf(d2,plain,
( step(eps,X0) = nil2
| eps = star(proj1Star(eps))
| eps = x(proj1(eps),proj2(eps)) ),
inference(resolution,[status(thm)],[c17,d1]) ).
cnf(d3,plain,
( step(eps,X0) = nil2
| eps = x(proj1(eps),proj2(eps)) ),
inference(resolution,[status(thm)],[c20,d2]) ).
cnf(d4,plain,
step(eps,X0) = nil2,
inference(resolution,[status(thm)],[c18,d3]) ).
cnf(d5,plain,
( step(X0,X1) = nil2
| X0 = star(proj1Star(X0))
| X0 = x(proj1(X0),proj2(X0))
| X0 = atom(proj1Atom(X0))
| nil2 != X0 ),
inference(superposition,[status(thm)],[c44,c15]) ).
cnf(d6,plain,
( step(nil2,X0) = nil2
| nil2 = star(proj1Star(nil2))
| nil2 = x(proj1(nil2),proj2(nil2))
| nil2 = atom(proj1Atom(nil2)) ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
( step(nil2,X0) = nil2
| nil2 = star(proj1Star(nil2))
| nil2 = x(proj1(nil2),proj2(nil2)) ),
inference(resolution,[status(thm)],[c13,d6]) ).
cnf(d8,plain,
( step(nil2,X0) = nil2
| nil2 = x(proj1(nil2),proj2(nil2)) ),
inference(resolution,[status(thm)],[c16,d7]) ).
cnf(d9,plain,
step(nil2,X0) = nil2,
inference(resolution,[status(thm)],[c14,d8]) ).
cnf(d10,plain,
proj2(step(x(X0,X2),X1)) = step(X2,X1),
inference(superposition,[status(thm)],[c47,c8]) ).
cnf(d11,plain,
proj2(step(step(x(X0,X2),X1),X3)) = step(step(X2,X1),X3),
inference(superposition,[status(thm)],[c47,d10]) ).
cnf(d12,plain,
proj1(step(x(X0,X2),X1)) = step(X0,X1),
inference(superposition,[status(thm)],[c47,c7]) ).
cnf(d13,plain,
step(atom(X0),X0) = eps,
inference(equality_resolution,[status(thm)],[c45]) ).
cnf(d14,plain,
( eps2(atom(X0))
| step(y(atom(X0),X1),X0) = x(y(eps,X1),nil2) ),
inference(superposition,[status(thm)],[d13,c49]) ).
cnf(d15,plain,
( rec(y(X1,X0),nil)
| ~ eps2(y(X0,X1)) ),
inference(resolution,[status(thm)],[c52,c55]) ).
cnf(d16,plain,
( ~ eps2(y(X1,X0))
| eps2(y(X0,X1)) ),
inference(resolution,[status(thm)],[c51,d15]) ).
cnf(d17,plain,
( eps2(y(star(X0),step(X0,X1)))
| ~ eps2(step(star(X0),X1)) ),
inference(superposition,[status(thm)],[c50,d16]) ).
cnf(d18,plain,
( eps2(step(X0,X1))
| ~ eps2(step(star(X0),X1)) ),
inference(resolution,[status(thm)],[d17,c41]) ).
cnf(d19,plain,
( ~ eps2(y(star(X0),step(X0,X1)))
| rec(step(star(X0),X1),nil) ),
inference(superposition,[status(thm)],[c50,d15]) ).
cnf(d20,plain,
step(star(atom(X0)),X0) = y(eps,star(atom(X0))),
inference(superposition,[status(thm)],[d13,c50]) ).
cnf(d21,plain,
( rec(step(star(star(atom(X0))),X0),nil)
| ~ eps2(y(star(star(atom(X0))),y(eps,star(atom(X0))))) ),
inference(superposition,[status(thm)],[d20,d19]) ).
cnf(d22,plain,
( ~ eps2(star(star(atom(X0))))
| ~ eps2(y(eps,star(atom(X0))))
| rec(step(star(star(atom(X0))),X0),nil) ),
inference(resolution,[status(thm)],[d21,c42]) ).
cnf(d23,plain,
( rec(step(star(star(atom(X0))),X0),nil)
| ~ eps2(y(eps,star(atom(X0)))) ),
inference(resolution,[status(thm)],[c43,d22]) ).
cnf(d24,plain,
( ~ eps2(step(star(atom(X0)),X0))
| eps2(y(star(atom(X0)),eps)) ),
inference(superposition,[status(thm)],[d13,d17]) ).
cnf(d25,plain,
( ~ eps2(star(X0))
| ~ eps2(step(X0,X1))
| rec(step(star(X0),X1),nil) ),
inference(resolution,[status(thm)],[d19,c42]) ).
cnf(d26,plain,
( rec(step(star(X0),X1),nil)
| ~ eps2(step(X0,X1)) ),
inference(resolution,[status(thm)],[c43,d25]) ).
cnf(d27,plain,
( eps2(step(star(X0),X1))
| ~ eps2(step(X0,X1)) ),
inference(resolution,[status(thm)],[d26,c51]) ).
cnf(d28,plain,
( eps2(y(star(atom(X0)),eps))
| ~ eps2(step(atom(X0),X0)) ),
inference(resolution,[status(thm)],[d27,d24]) ).
cnf(d29,plain,
( ~ eps2(eps)
| eps2(y(star(atom(X0)),eps)) ),
inference(demodulation,[status(thm)],[d28,d13]) ).
cnf(d30,plain,
eps2(y(star(atom(X0)),eps)),
inference(resolution,[status(thm)],[c36,d29]) ).
cnf(d31,plain,
eps2(y(eps,star(atom(X0)))),
inference(resolution,[status(thm)],[d30,d16]) ).
cnf(d32,plain,
rec(step(star(star(atom(X0))),X0),nil),
inference(resolution,[status(thm)],[d31,d23]) ).
cnf(d33,plain,
eps2(step(star(star(atom(X0))),X0)),
inference(resolution,[status(thm)],[d32,c51]) ).
cnf(d34,plain,
( ~ eps2(X0)
| X0 = eps
| X0 = star(proj1Star(X0))
| X0 = x(proj1(X0),proj2(X0))
| atom(X1) != X0 ),
inference(superposition,[status(thm)],[c35,c22]) ).
cnf(d35,plain,
( ~ eps2(atom(X0))
| atom(X0) = eps
| atom(X0) = star(proj1Star(atom(X0)))
| atom(X0) = x(proj1(atom(X0)),proj2(atom(X0))) ),
inference(equality_resolution,[status(thm)],[d34]) ).
cnf(d36,plain,
( ~ eps2(atom(X0))
| atom(X0) = eps
| atom(X0) = x(proj1(atom(X0)),proj2(atom(X0))) ),
inference(resolution,[status(thm)],[c23,d35]) ).
cnf(d37,plain,
( ~ eps2(atom(X0))
| atom(X0) = eps ),
inference(resolution,[status(thm)],[c21,d36]) ).
cnf(d38,plain,
( ~ eps2(atom(X0))
| eps2(step(star(star(eps)),X0)) ),
inference(superposition,[status(thm)],[d37,d33]) ).
cnf(d39,plain,
( eps2(step(star(eps),X0))
| ~ eps2(atom(X0)) ),
inference(resolution,[status(thm)],[d38,d18]) ).
cnf(d40,plain,
( eps2(step(eps,X0))
| ~ eps2(atom(X0)) ),
inference(resolution,[status(thm)],[d39,d18]) ).
cnf(d41,plain,
( eps2(nil2)
| ~ eps2(atom(X0)) ),
inference(demodulation,[status(thm)],[d40,d4]) ).
cnf(d42,plain,
( ~ eps2(X0)
| X0 = eps
| X0 = star(proj1Star(X0))
| X0 = x(proj1(X0),proj2(X0))
| nil2 != X0 ),
inference(superposition,[status(thm)],[c35,c15]) ).
cnf(d43,plain,
( ~ eps2(nil2)
| nil2 = eps
| nil2 = star(proj1Star(nil2))
| nil2 = x(proj1(nil2),proj2(nil2)) ),
inference(equality_resolution,[status(thm)],[d42]) ).
cnf(d44,plain,
( ~ eps2(nil2)
| nil2 = star(proj1Star(nil2))
| nil2 = x(proj1(nil2),proj2(nil2)) ),
inference(resolution,[status(thm)],[c12,d43]) ).
cnf(d45,plain,
( ~ eps2(nil2)
| nil2 = x(proj1(nil2),proj2(nil2)) ),
inference(resolution,[status(thm)],[c16,d44]) ).
cnf(d46,plain,
~ eps2(nil2),
inference(resolution,[status(thm)],[c14,d45]) ).
cnf(d47,plain,
~ eps2(atom(X0)),
inference(resolution,[status(thm)],[d46,d41]) ).
cnf(d48,plain,
step(y(atom(X0),X1),X0) = x(y(eps,X1),nil2),
inference(resolution,[status(thm)],[d47,d14]) ).
cnf(d49,plain,
step(x(X2,y(atom(X0),X1)),X0) = x(step(X2,X0),x(y(eps,X1),nil2)),
inference(superposition,[status(thm)],[d48,c47]) ).
cnf(d50,plain,
step(x(eps,y(atom(X0),X1)),X0) = x(nil2,x(y(eps,X1),nil2)),
inference(superposition,[status(thm)],[d4,d49]) ).
cnf(d51,plain,
proj1(x(nil2,x(y(eps,X1),nil2))) = step(eps,X0),
inference(superposition,[status(thm)],[d50,d12]) ).
cnf(d52,plain,
nil2 = step(eps,X1),
inference(demodulation,[status(thm)],[d51,c7]) ).
cnf(d53,plain,
step(x(X1,eps),X0) = x(step(X1,X0),nil2),
inference(superposition,[status(thm)],[d52,c47]) ).
cnf(d54,plain,
proj2(step(x(step(X0,X1),nil2),X2)) = step(step(eps,X1),X2),
inference(superposition,[status(thm)],[d53,d11]) ).
cnf(d55,plain,
step(nil2,X2) = step(step(eps,X1),X2),
inference(demodulation,[status(thm)],[d54,d10]) ).
cnf(d56,plain,
nil2 = step(step(eps,X1),X0),
inference(demodulation,[status(thm)],[d55,d9]) ).
cnf(d57,plain,
nil2 = step(nil2,X1),
inference(demodulation,[status(thm)],[d56,d4]) ).
cnf(d58,plain,
( eps2(nil2)
| step(y(nil2,X1),X0) = x(y(nil2,X1),nil2) ),
inference(superposition,[status(thm)],[d57,c49]) ).
cnf(d59,plain,
step(y(nil2,X0),X1) = x(y(nil2,X0),nil2),
inference(resolution,[status(thm)],[d46,d58]) ).
cnf(d60,plain,
( ~ eps2(step(X0,X1))
| rec(X0,cons(X1,nil)) ),
inference(resolution,[status(thm)],[c54,c52]) ).
cnf(d61,plain,
( rec(y(X1,X0),cons(X2,nil))
| ~ eps2(step(y(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d60,c55]) ).
cnf(d62,plain,
( rec(step(y(X1,X0),X2),nil)
| ~ eps2(step(y(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d61,c53]) ).
cnf(d63,plain,
( eps2(step(y(X1,X0),X2))
| ~ eps2(step(y(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d62,c51]) ).
cnf(d64,plain,
( eps2(step(X0,X1))
| eps2(step(X2,X1))
| ~ eps2(step(x(X0,X2),X1)) ),
inference(superposition,[status(thm)],[c47,c37]) ).
cnf(d65,plain,
( eps2(X0)
| eps2(step(y(step(X0,X1),X2),X3))
| eps2(step(nil2,X3))
| ~ eps2(step(step(y(X0,X2),X1),X3)) ),
inference(superposition,[status(thm)],[c49,d64]) ).
cnf(d66,plain,
( ~ eps2(step(step(y(X1,X3),X2),X0))
| eps2(nil2)
| eps2(step(y(step(X1,X2),X3),X0))
| eps2(X1) ),
inference(demodulation,[status(thm)],[d65,d9]) ).
cnf(d67,plain,
( ~ eps2(step(step(y(X0,X2),X1),X3))
| eps2(step(y(step(X0,X1),X2),X3))
| eps2(X0) ),
inference(resolution,[status(thm)],[d46,d66]) ).
cnf(d68,plain,
step(x(X1,nil2),X0) = x(step(X1,X0),nil2),
inference(superposition,[status(thm)],[d57,c47]) ).
cnf(d69,plain,
( rec(X0,cons(X1,cons(X2,nil)))
| ~ eps2(step(step(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d60,c54]) ).
cnf(d70,plain,
( rec(y(X1,X0),cons(X2,cons(X3,nil)))
| ~ eps2(step(step(y(X0,X1),X2),X3)) ),
inference(resolution,[status(thm)],[d69,c55]) ).
cnf(d71,plain,
( rec(step(y(X1,X0),X2),cons(X3,nil))
| ~ eps2(step(step(y(X0,X1),X2),X3)) ),
inference(resolution,[status(thm)],[d70,c53]) ).
cnf(d72,plain,
( rec(step(step(y(X1,X0),X2),X3),nil)
| ~ eps2(step(step(y(X0,X1),X2),X3)) ),
inference(resolution,[status(thm)],[d71,c53]) ).
cnf(d73,plain,
( eps2(step(step(y(X1,X0),X2),X3))
| ~ eps2(step(step(y(X0,X1),X2),X3)) ),
inference(resolution,[status(thm)],[d72,c51]) ).
cnf(d74,plain,
( eps2(step(step(y(X0,nil2),X1),X2))
| ~ eps2(step(x(y(nil2,X0),nil2),X2)) ),
inference(superposition,[status(thm)],[d59,d73]) ).
cnf(d75,plain,
( eps2(step(step(y(X0,nil2),X2),X1))
| ~ eps2(x(step(y(nil2,X0),X1),nil2)) ),
inference(demodulation,[status(thm)],[d74,d68]) ).
cnf(d76,plain,
( eps2(step(step(y(X0,nil2),X2),X1))
| ~ eps2(x(x(y(nil2,X0),nil2),nil2)) ),
inference(demodulation,[status(thm)],[d75,d59]) ).
cnf(d77,plain,
( ~ eps2(x(y(nil2,X0),nil2))
| eps2(step(step(y(X0,nil2),X1),X2)) ),
inference(resolution,[status(thm)],[d76,c38]) ).
cnf(d78,plain,
( eps2(step(y(step(X0,X1),nil2),X2))
| eps2(X0)
| ~ eps2(x(y(nil2,X0),nil2)) ),
inference(resolution,[status(thm)],[d77,d67]) ).
cnf(d79,plain,
( eps2(step(y(nil2,step(X0,X1)),X2))
| ~ eps2(x(y(nil2,X0),nil2))
| eps2(X0) ),
inference(resolution,[status(thm)],[d78,d63]) ).
cnf(d80,plain,
( eps2(x(y(nil2,step(X0,X1)),nil2))
| ~ eps2(x(y(nil2,X0),nil2))
| eps2(X0) ),
inference(demodulation,[status(thm)],[d79,d59]) ).
cnf(d81,plain,
( eps2(y(nil2,step(X0,X1)))
| eps2(nil2)
| ~ eps2(x(y(nil2,X0),nil2))
| eps2(X0) ),
inference(resolution,[status(thm)],[d80,c37]) ).
cnf(d82,plain,
( eps2(y(nil2,step(X0,X1)))
| ~ eps2(x(y(nil2,X0),nil2))
| eps2(X0) ),
inference(resolution,[status(thm)],[d46,d81]) ).
cnf(d83,plain,
( ~ eps2(X0)
| ~ eps2(step(X2,X1))
| eps2(step(y(X0,X2),X1)) ),
inference(superposition,[status(thm)],[c48,c39]) ).
cnf(d84,plain,
( ~ eps2(step(y(X1,atom(X0)),X0))
| rec(x(y(eps,X1),nil2),nil) ),
inference(superposition,[status(thm)],[d48,d62]) ).
cnf(d85,plain,
( ~ eps2(step(atom(X1),X1))
| ~ eps2(X0)
| rec(x(y(eps,X0),nil2),nil) ),
inference(resolution,[status(thm)],[d84,d83]) ).
cnf(d86,plain,
( rec(x(y(eps,X1),nil2),nil)
| ~ eps2(eps)
| ~ eps2(X1) ),
inference(demodulation,[status(thm)],[d85,d13]) ).
cnf(d87,plain,
( rec(x(y(eps,X0),nil2),nil)
| ~ eps2(X0) ),
inference(resolution,[status(thm)],[c36,d86]) ).
cnf(d88,plain,
( rec(y(atom(X0),X1),cons(X0,X2))
| ~ rec(x(y(eps,X1),nil2),X2) ),
inference(superposition,[status(thm)],[d48,c54]) ).
cnf(d89,plain,
( rec(y(X0,atom(X2)),cons(X2,X1))
| ~ rec(x(y(eps,X0),nil2),X1) ),
inference(resolution,[status(thm)],[d88,c55]) ).
cnf(d90,plain,
( rec(step(y(X0,atom(X2)),X2),X1)
| ~ rec(x(y(eps,X0),nil2),X1) ),
inference(resolution,[status(thm)],[d89,c53]) ).
cnf(d91,plain,
( eps2(step(y(X0,atom(X1)),X1))
| ~ rec(x(y(eps,X0),nil2),nil) ),
inference(resolution,[status(thm)],[d90,c51]) ).
cnf(d92,plain,
( ~ eps2(X0)
| eps2(step(y(X0,atom(X1)),X1)) ),
inference(resolution,[status(thm)],[d91,d87]) ).
cnf(d93,plain,
( ~ eps2(step(X0,X1))
| eps2(step(x(X0,X2),X1)) ),
inference(superposition,[status(thm)],[c47,c38]) ).
cnf(d94,plain,
( eps2(X0)
| ~ eps2(step(y(step(X0,X1),X2),X3))
| eps2(step(step(y(X0,X2),X1),X3)) ),
inference(superposition,[status(thm)],[c49,d93]) ).
cnf(d95,plain,
( ~ eps2(step(X0,X2))
| eps2(step(step(y(X0,atom(X1)),X2),X1))
| eps2(X0) ),
inference(resolution,[status(thm)],[d94,d92]) ).
cnf(d96,plain,
( eps2(step(step(y(atom(X2),X0),X1),X2))
| ~ eps2(step(X0,X1))
| eps2(X0) ),
inference(resolution,[status(thm)],[d95,d73]) ).
cnf(d97,plain,
( X0 = X1
| eps2(atom(X0))
| step(y(atom(X0),X2),X1) = x(y(nil2,X2),nil2) ),
inference(superposition,[status(thm)],[c46,c49]) ).
cnf(d98,plain,
( step(y(atom(X0),X2),X1) = x(y(nil2,X2),nil2)
| X0 = X1 ),
inference(resolution,[status(thm)],[d47,d97]) ).
cnf(d99,plain,
( X0 = X2
| ~ eps2(step(X1,X2))
| eps2(X1)
| eps2(step(x(y(nil2,X1),nil2),X0)) ),
inference(superposition,[status(thm)],[d98,d96]) ).
cnf(d100,plain,
( eps2(x(step(y(nil2,X0),X1),nil2))
| ~ eps2(step(X0,X2))
| eps2(X0)
| X1 = X2 ),
inference(demodulation,[status(thm)],[d99,d68]) ).
cnf(d101,plain,
( ~ eps2(step(X0,X2))
| eps2(x(x(y(nil2,X0),nil2),nil2))
| eps2(X0)
| X1 = X2 ),
inference(demodulation,[status(thm)],[d100,d59]) ).
cnf(d102,plain,
( eps2(x(y(nil2,X2),nil2))
| eps2(nil2)
| ~ eps2(step(X2,X1))
| eps2(X2)
| X0 = X1 ),
inference(resolution,[status(thm)],[d101,c37]) ).
cnf(d103,plain,
( ~ eps2(step(X2,X1))
| eps2(x(y(nil2,X2),nil2))
| eps2(X2)
| X0 = X1 ),
inference(resolution,[status(thm)],[d46,d102]) ).
cnf(d104,plain,
( eps2(y(nil2,step(X2,X3)))
| eps2(X2)
| ~ eps2(step(X2,X1))
| eps2(X2)
| X0 = X1 ),
inference(resolution,[status(thm)],[d103,d82]) ).
cnf(d105,plain,
( eps2(nil2)
| ~ eps2(step(X2,X1))
| eps2(X2)
| X0 = X1 ),
inference(resolution,[status(thm)],[d104,c40]) ).
cnf(d106,plain,
( ~ eps2(step(X2,X1))
| eps2(X2)
| X0 = X1 ),
inference(resolution,[status(thm)],[d46,d105]) ).
cnf(d107,plain,
proj12(step(star(X0),X1)) = step(X0,X1),
inference(superposition,[status(thm)],[c50,c9]) ).
cnf(d108,plain,
proj12(y(eps,star(atom(X0)))) = step(atom(X0),X0),
inference(superposition,[status(thm)],[d20,d107]) ).
cnf(d109,plain,
eps = step(atom(X0),X0),
inference(demodulation,[status(thm)],[d108,c9]) ).
cnf(d110,plain,
( eps2(atom(X0))
| X1 = X0
| ~ eps2(eps) ),
inference(superposition,[status(thm)],[d109,d106]) ).
cnf(d111,plain,
( eps2(atom(X1))
| X0 = X1 ),
inference(resolution,[status(thm)],[c36,d110]) ).
cnf(d112,plain,
X0 = X1,
inference(resolution,[status(thm)],[d47,d111]) ).
cnf(d113,plain,
$false,
inference(resolution,[status(thm)],[d112,c3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWX212+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
% 0.16/0.44 % Computer : n014.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.45 % CPULimit : 300
% 0.16/0.45 % WCLimit : 300
% 0.16/0.45 % DateTime : Sat Sep 26 16:56:31 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 152.20/44.68 % SZS status Theorem for theBenchmark.p
% 152.20/44.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------