%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWX210+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 : n010.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 09:15:39 AM UTC 2026
% Result : Theorem 173.00s 45.68s
% Output : CNFRefutation 173.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 28
% Syntax : Number of formulae : 170 ( 109 unt; 0 def)
% Number of atoms : 281 ( 159 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 213 ( 102 ~; 95 |; 1 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 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 : 271 ( 78 sgn 51 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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_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_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] : rec(X0,cons(a,cons(b,cons(b,cons(a,nil))))) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] : rec(X0,cons(a,cons(b,cons(b,cons(a,nil))))),
inference(negate_conjecture,[status(cth)],[goal_050]) ).
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(c13,plain,
atom(X0) != nil2,
inference(clausification,[status(esa)],[axiom_014]) ).
cnf(c14,plain,
x(X0,X1) != nil2,
inference(clausification,[status(esa)],[axiom_015]) ).
cnf(c15,plain,
y(X0,X1) != nil2,
inference(clausification,[status(esa)],[axiom_016]) ).
cnf(c16,plain,
star(X0) != nil2,
inference(clausification,[status(esa)],[axiom_017]) ).
cnf(c17,plain,
atom(X0) != eps,
inference(clausification,[status(esa)],[axiom_018]) ).
cnf(c18,plain,
x(X0,X1) != eps,
inference(clausification,[status(esa)],[axiom_019]) ).
cnf(c19,plain,
y(X0,X1) != eps,
inference(clausification,[status(esa)],[axiom_020]) ).
cnf(c20,plain,
star(X0) != eps,
inference(clausification,[status(esa)],[axiom_021]) ).
cnf(c21,plain,
x(X0,X1) != atom(X2),
inference(clausification,[status(esa)],[axiom_022]) ).
cnf(c22,plain,
y(X0,X1) != atom(X2),
inference(clausification,[status(esa)],[axiom_023]) ).
cnf(c23,plain,
star(X0) != atom(X1),
inference(clausification,[status(esa)],[axiom_024]) ).
cnf(c35,plain,
( y(proj12(X0),proj22(X0)) = X0
| x(proj1(X0),proj2(X0)) = X0
| X0 = eps
| star(proj1Star(X0)) = X0
| ~ eps2(X0) ),
inference(clausification,[status(esa)],[axiom_036]) ).
cnf(c36,plain,
eps2(eps),
inference(clausification,[status(esa)],[axiom_037]) ).
cnf(c37,plain,
( eps2(X0)
| eps2(X1)
| ~ 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(c42,plain,
( ~ eps2(X0)
| ~ eps2(X1)
| 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,
( star(proj1Star(X0)) = X0
| step(X0,X1) = nil2
| x(proj1(X0),proj2(X0)) = X0
| atom(proj1Atom(X0)) = X0
| y(proj12(X0),proj22(X0)) = X0 ),
inference(clausification,[status(esa)],[axiom_041]) ).
cnf(c45,plain,
( step(atom(X1),X0) = eps
| X0 != X1 ),
inference(clausification,[status(esa)],[axiom_042]) ).
cnf(c47,plain,
x(step(X0,X1),step(X2,X1)) = step(x(X0,X2),X1),
inference(clausification,[status(esa)],[axiom_044]) ).
cnf(c48,plain,
( x(y(step(X0,X1),X2),step(X2,X1)) = step(y(X0,X2),X1)
| ~ eps2(X0) ),
inference(clausification,[status(esa)],[axiom_045]) ).
cnf(c49,plain,
( x(y(step(X0,X1),X2),nil2) = step(y(X0,X2),X1)
| eps2(X0) ),
inference(clausification,[status(esa)],[axiom_046]) ).
cnf(c50,plain,
y(step(X0,X1),star(X0)) = step(star(X0),X1),
inference(clausification,[status(esa)],[axiom_047]) ).
cnf(c52,plain,
( ~ eps2(X0)
| rec(X0,nil) ),
inference(clausification,[status(esa)],[axiom_048]) ).
cnf(c54,plain,
( ~ rec(step(X0,X1),X2)
| rec(X0,cons(X1,X2)) ),
inference(clausification,[status(esa)],[axiom_049]) ).
cnf(c55,plain,
~ rec(X0,cons(a,cons(b,cons(b,cons(a,nil))))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
x(y(step(star(X0),X1),X2),step(X2,X1)) = step(y(star(X0),X2),X1),
inference(resolution,[status(thm)],[c48,c43]) ).
cnf(d1,plain,
proj1(step(x(X0,X2),X1)) = step(X0,X1),
inference(superposition,[status(thm)],[c47,c7]) ).
cnf(d2,plain,
( step(X0,X1) = nil2
| star(proj1Star(X0)) = X0
| x(proj1(X0),proj2(X0)) = X0
| atom(proj1Atom(X0)) = X0
| X0 != nil2 ),
inference(superposition,[status(thm)],[c44,c15]) ).
cnf(d3,plain,
( step(nil2,X0) = nil2
| star(proj1Star(nil2)) = nil2
| x(proj1(nil2),proj2(nil2)) = nil2
| atom(proj1Atom(nil2)) = nil2 ),
inference(equality_resolution,[status(thm)],[d2]) ).
cnf(d4,plain,
( step(nil2,X0) = nil2
| star(proj1Star(nil2)) = nil2
| x(proj1(nil2),proj2(nil2)) = nil2 ),
inference(resolution,[status(thm)],[c13,d3]) ).
cnf(d5,plain,
( step(nil2,X0) = nil2
| x(proj1(nil2),proj2(nil2)) = nil2 ),
inference(resolution,[status(thm)],[c16,d4]) ).
cnf(d6,plain,
step(nil2,X0) = nil2,
inference(resolution,[status(thm)],[c14,d5]) ).
cnf(d7,plain,
( ~ eps2(step(X0,X1))
| rec(X0,cons(X1,nil)) ),
inference(resolution,[status(thm)],[c54,c52]) ).
cnf(d8,plain,
( rec(X0,cons(X1,cons(X2,nil)))
| ~ eps2(step(step(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d7,c54]) ).
cnf(d9,plain,
step(atom(X0),X0) = eps,
inference(equality_resolution,[status(thm)],[c45]) ).
cnf(d10,plain,
( rec(atom(X0),cons(X0,X1))
| ~ rec(eps,X1) ),
inference(superposition,[status(thm)],[d9,c54]) ).
cnf(d11,plain,
~ rec(eps,cons(b,cons(b,cons(a,nil)))),
inference(resolution,[status(thm)],[d10,c55]) ).
cnf(d12,plain,
( star(proj1Star(X0)) = X0
| y(proj12(X0),proj22(X0)) = X0
| x(proj1(X0),proj2(X0)) = X0
| atom(proj1Atom(X0)) = X0
| rec(X0,cons(X1,X2))
| ~ rec(nil2,X2) ),
inference(superposition,[status(thm)],[c44,c54]) ).
cnf(d13,plain,
( ~ rec(nil2,cons(b,cons(a,nil)))
| star(proj1Star(eps)) = eps
| y(proj12(eps),proj22(eps)) = eps
| x(proj1(eps),proj2(eps)) = eps
| atom(proj1Atom(eps)) = eps ),
inference(resolution,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
( ~ rec(nil2,cons(b,cons(a,nil)))
| star(proj1Star(eps)) = eps
| y(proj12(eps),proj22(eps)) = eps
| x(proj1(eps),proj2(eps)) = eps ),
inference(resolution,[status(thm)],[c17,d13]) ).
cnf(d15,plain,
( ~ rec(nil2,cons(b,cons(a,nil)))
| y(proj12(eps),proj22(eps)) = eps
| x(proj1(eps),proj2(eps)) = eps ),
inference(resolution,[status(thm)],[c20,d14]) ).
cnf(d16,plain,
( ~ rec(nil2,cons(b,cons(a,nil)))
| y(proj12(eps),proj22(eps)) = eps ),
inference(resolution,[status(thm)],[c18,d15]) ).
cnf(d17,plain,
~ rec(nil2,cons(b,cons(a,nil))),
inference(resolution,[status(thm)],[c19,d16]) ).
cnf(d18,plain,
~ eps2(step(step(nil2,b),a)),
inference(resolution,[status(thm)],[d17,d8]) ).
cnf(d19,plain,
x(y(step(step(step(nil2,b),a),X0),X1),nil2) = step(y(step(step(nil2,b),a),X1),X0),
inference(resolution,[status(thm)],[d18,c49]) ).
cnf(d20,plain,
x(y(step(step(nil2,a),X0),X1),nil2) = step(y(step(step(nil2,b),a),X1),X0),
inference(demodulation,[status(thm)],[d19,d6]) ).
cnf(d21,plain,
x(y(step(nil2,X0),X1),nil2) = step(y(step(step(nil2,b),a),X1),X0),
inference(demodulation,[status(thm)],[d20,d6]) ).
cnf(d22,plain,
x(y(nil2,X1),nil2) = step(y(step(step(nil2,b),a),X1),X0),
inference(demodulation,[status(thm)],[d21,d6]) ).
cnf(d23,plain,
x(y(nil2,X0),nil2) = step(y(step(nil2,a),X0),X1),
inference(demodulation,[status(thm)],[d22,d6]) ).
cnf(d24,plain,
x(y(nil2,X0),nil2) = step(y(nil2,X0),X1),
inference(demodulation,[status(thm)],[d23,d6]) ).
cnf(d25,plain,
x(step(star(step(step(nil2,b),a)),X0),nil2) = step(y(step(step(nil2,b),a),star(step(step(nil2,b),a))),X0),
inference(superposition,[status(thm)],[c50,d19]) ).
cnf(d26,plain,
x(step(star(step(nil2,a)),X0),nil2) = step(y(step(step(nil2,b),a),star(step(step(nil2,b),a))),X0),
inference(demodulation,[status(thm)],[d25,d6]) ).
cnf(d27,plain,
x(step(star(nil2),X0),nil2) = step(y(step(step(nil2,b),a),star(step(step(nil2,b),a))),X0),
inference(demodulation,[status(thm)],[d26,d6]) ).
cnf(d28,plain,
x(step(star(nil2),X0),nil2) = step(y(step(nil2,a),star(step(step(nil2,b),a))),X0),
inference(demodulation,[status(thm)],[d27,d6]) ).
cnf(d29,plain,
x(step(star(nil2),X0),nil2) = step(y(nil2,star(step(step(nil2,b),a))),X0),
inference(demodulation,[status(thm)],[d28,d6]) ).
cnf(d30,plain,
x(step(star(nil2),X0),nil2) = step(y(nil2,star(step(nil2,a))),X0),
inference(demodulation,[status(thm)],[d29,d6]) ).
cnf(d31,plain,
x(step(star(nil2),X0),nil2) = step(y(nil2,star(nil2)),X0),
inference(demodulation,[status(thm)],[d30,d6]) ).
cnf(d32,plain,
x(step(star(nil2),X0),nil2) = x(y(nil2,star(nil2)),nil2),
inference(demodulation,[status(thm)],[d31,d24]) ).
cnf(d33,plain,
proj1(x(y(nil2,star(nil2)),nil2)) = step(star(nil2),X0),
inference(superposition,[status(thm)],[d32,c7]) ).
cnf(d34,plain,
y(nil2,star(nil2)) = step(star(nil2),X0),
inference(demodulation,[status(thm)],[d33,c7]) ).
cnf(d35,plain,
x(step(X1,X0),y(nil2,star(nil2))) = step(x(X1,star(nil2)),X0),
inference(superposition,[status(thm)],[d34,c47]) ).
cnf(d36,plain,
( step(X0,X1) = nil2
| star(proj1Star(X0)) = X0
| x(proj1(X0),proj2(X0)) = X0
| atom(proj1Atom(X0)) = X0
| X0 != eps ),
inference(superposition,[status(thm)],[c44,c19]) ).
cnf(d37,plain,
( step(eps,X0) = nil2
| star(proj1Star(eps)) = eps
| x(proj1(eps),proj2(eps)) = eps
| atom(proj1Atom(eps)) = eps ),
inference(equality_resolution,[status(thm)],[d36]) ).
cnf(d38,plain,
( step(eps,X0) = nil2
| star(proj1Star(eps)) = eps
| x(proj1(eps),proj2(eps)) = eps ),
inference(resolution,[status(thm)],[c17,d37]) ).
cnf(d39,plain,
( step(eps,X0) = nil2
| x(proj1(eps),proj2(eps)) = eps ),
inference(resolution,[status(thm)],[c20,d38]) ).
cnf(d40,plain,
step(eps,X0) = nil2,
inference(resolution,[status(thm)],[c18,d39]) ).
cnf(d41,plain,
x(nil2,y(nil2,star(nil2))) = step(x(eps,star(nil2)),X0),
inference(superposition,[status(thm)],[d40,d35]) ).
cnf(d42,plain,
proj1(x(nil2,y(nil2,star(nil2)))) = step(eps,X0),
inference(superposition,[status(thm)],[d41,d1]) ).
cnf(d43,plain,
nil2 = step(eps,X0),
inference(demodulation,[status(thm)],[d42,c7]) ).
cnf(d44,plain,
x(y(step(star(X1),X0),eps),nil2) = step(y(star(X1),eps),X0),
inference(superposition,[status(thm)],[d43,d0]) ).
cnf(d45,plain,
( ~ eps2(y(step(star(X0),X1),eps))
| eps2(step(y(star(X0),eps),X1)) ),
inference(superposition,[status(thm)],[d44,c38]) ).
cnf(d46,plain,
proj2(step(x(X0,X2),X1)) = step(X2,X1),
inference(superposition,[status(thm)],[c47,c8]) ).
cnf(d47,plain,
x(eps,step(X1,X0)) = step(x(atom(X0),X1),X0),
inference(superposition,[status(thm)],[d9,c47]) ).
cnf(d48,plain,
proj2(x(eps,step(X1,X0))) = step(X1,X0),
inference(superposition,[status(thm)],[d47,d46]) ).
cnf(d49,plain,
step(X0,X1) = step(X0,X1),
inference(demodulation,[status(thm)],[d48,c8]) ).
cnf(d50,plain,
y(eps,star(atom(X0))) = step(star(atom(X0)),X0),
inference(superposition,[status(thm)],[d9,c50]) ).
cnf(d51,plain,
step(star(atom(X0)),X0) = y(eps,star(atom(X0))),
inference(superposition,[status(thm)],[d50,d49]) ).
cnf(d52,plain,
( eps2(step(y(star(atom(X0)),eps),X0))
| ~ eps2(y(y(eps,star(atom(X0))),eps)) ),
inference(superposition,[status(thm)],[d51,d45]) ).
cnf(d53,plain,
( ~ eps2(step(star(X0),X1))
| ~ eps2(eps)
| eps2(step(y(star(X0),eps),X1)) ),
inference(resolution,[status(thm)],[d45,c42]) ).
cnf(d54,plain,
( ~ eps2(step(star(X0),X1))
| eps2(step(y(star(X0),eps),X1)) ),
inference(resolution,[status(thm)],[c36,d53]) ).
cnf(d55,plain,
( eps2(y(step(star(X0),X1),eps))
| eps2(nil2)
| ~ eps2(step(y(star(X0),eps),X1)) ),
inference(superposition,[status(thm)],[d44,c37]) ).
cnf(d56,plain,
~ eps2(step(nil2,a)),
inference(demodulation,[status(thm)],[d18,d6]) ).
cnf(d57,plain,
~ eps2(nil2),
inference(demodulation,[status(thm)],[d56,d6]) ).
cnf(d58,plain,
( ~ eps2(step(y(star(X0),eps),X1))
| eps2(y(step(star(X0),X1),eps)) ),
inference(resolution,[status(thm)],[d57,d55]) ).
cnf(d59,plain,
( ~ eps2(step(star(X0),X1))
| eps2(y(step(star(X0),X1),eps)) ),
inference(resolution,[status(thm)],[d58,d54]) ).
cnf(d60,plain,
( ~ eps2(step(star(atom(X0)),X0))
| eps2(y(y(eps,star(atom(X0))),eps)) ),
inference(superposition,[status(thm)],[d51,d59]) ).
cnf(d61,plain,
( ~ eps2(y(eps,star(atom(X0))))
| eps2(y(y(eps,star(atom(X0))),eps)) ),
inference(demodulation,[status(thm)],[d60,d50]) ).
cnf(d62,plain,
( ~ eps2(step(X0,X1))
| ~ eps2(star(X0))
| eps2(step(star(X0),X1)) ),
inference(superposition,[status(thm)],[c50,c42]) ).
cnf(d63,plain,
( eps2(step(star(X0),X1))
| ~ eps2(step(X0,X1)) ),
inference(resolution,[status(thm)],[c43,d62]) ).
cnf(d64,plain,
( ~ eps2(step(atom(X0),X0))
| eps2(y(eps,star(atom(X0)))) ),
inference(superposition,[status(thm)],[d50,d63]) ).
cnf(d65,plain,
( ~ eps2(eps)
| eps2(y(eps,star(atom(X0)))) ),
inference(demodulation,[status(thm)],[d64,d9]) ).
cnf(d66,plain,
eps2(y(eps,star(atom(X0)))),
inference(resolution,[status(thm)],[c36,d65]) ).
cnf(d67,plain,
eps2(y(y(eps,star(atom(X0))),eps)),
inference(resolution,[status(thm)],[d66,d61]) ).
cnf(d68,plain,
eps2(step(y(star(atom(X0)),eps),X0)),
inference(resolution,[status(thm)],[d67,d52]) ).
cnf(d69,plain,
x(y(step(eps,X0),X1),step(X1,X0)) = step(y(eps,X1),X0),
inference(resolution,[status(thm)],[c48,c36]) ).
cnf(d70,plain,
( ~ eps2(step(X1,X0))
| eps2(step(y(eps,X1),X0)) ),
inference(superposition,[status(thm)],[d69,c39]) ).
cnf(d71,plain,
proj12(step(star(X0),X1)) = step(X0,X1),
inference(superposition,[status(thm)],[c50,c9]) ).
cnf(d72,plain,
proj12(y(nil2,star(nil2))) = step(nil2,X0),
inference(superposition,[status(thm)],[d34,d71]) ).
cnf(d73,plain,
nil2 = step(nil2,X0),
inference(demodulation,[status(thm)],[d72,c9]) ).
cnf(d74,plain,
x(step(X1,X0),nil2) = step(x(X1,nil2),X0),
inference(superposition,[status(thm)],[d73,c47]) ).
cnf(d75,plain,
( ~ eps2(step(X2,X1))
| eps2(step(x(X0,X2),X1)) ),
inference(superposition,[status(thm)],[c47,c39]) ).
cnf(d76,plain,
( ~ eps2(step(step(X1,X0),X2))
| eps2(step(step(y(eps,X1),X0),X2)) ),
inference(superposition,[status(thm)],[d69,d75]) ).
cnf(d77,plain,
x(nil2,step(X1,X0)) = step(x(nil2,X1),X0),
inference(superposition,[status(thm)],[d73,c47]) ).
cnf(d78,plain,
x(nil2,step(X1,X0)) = step(x(eps,X1),X0),
inference(superposition,[status(thm)],[d43,c47]) ).
cnf(d79,plain,
( rec(X0,cons(X1,cons(X2,cons(X3,nil))))
| ~ eps2(step(step(step(X0,X1),X2),X3)) ),
inference(resolution,[status(thm)],[d8,c54]) ).
cnf(d80,plain,
( rec(x(atom(X0),X1),cons(X0,X2))
| ~ rec(x(eps,step(X1,X0)),X2) ),
inference(superposition,[status(thm)],[d47,c54]) ).
cnf(d81,plain,
~ rec(x(eps,step(X0,a)),cons(b,cons(b,cons(a,nil)))),
inference(resolution,[status(thm)],[d80,c55]) ).
cnf(d82,plain,
~ eps2(step(step(step(x(eps,step(X0,a)),b),b),a)),
inference(resolution,[status(thm)],[d81,d79]) ).
cnf(d83,plain,
~ eps2(step(step(x(nil2,step(step(X0,a),b)),b),a)),
inference(demodulation,[status(thm)],[d82,d78]) ).
cnf(d84,plain,
~ eps2(step(x(nil2,step(step(step(X0,a),b),b)),a)),
inference(demodulation,[status(thm)],[d83,d77]) ).
cnf(d85,plain,
~ eps2(x(nil2,step(step(step(step(X0,a),b),b),a))),
inference(demodulation,[status(thm)],[d84,d77]) ).
cnf(d86,plain,
~ eps2(step(step(step(step(X0,a),b),b),a)),
inference(resolution,[status(thm)],[d85,c39]) ).
cnf(d87,plain,
( star(proj1Star(X0)) = X0
| y(proj12(X0),proj22(X0)) = X0
| x(proj1(X0),proj2(X0)) = X0
| X0 = eps
| x(y(step(X0,X1),X2),nil2) = step(y(X0,X2),X1) ),
inference(resolution,[status(thm)],[c49,c35]) ).
cnf(d88,plain,
( star(proj1Star(atom(X0))) = atom(X0)
| y(proj12(atom(X0)),proj22(atom(X0))) = atom(X0)
| x(proj1(atom(X0)),proj2(atom(X0))) = atom(X0)
| atom(X0) = eps
| x(y(eps,X1),nil2) = step(y(atom(X0),X1),X0) ),
inference(superposition,[status(thm)],[d9,d87]) ).
cnf(d89,plain,
( star(proj1Star(atom(X0))) = atom(X0)
| y(proj12(atom(X0)),proj22(atom(X0))) = atom(X0)
| x(y(eps,X1),nil2) = step(y(atom(X0),X1),X0)
| x(proj1(atom(X0)),proj2(atom(X0))) = atom(X0) ),
inference(resolution,[status(thm)],[c17,d88]) ).
cnf(d90,plain,
( y(proj12(atom(X0)),proj22(atom(X0))) = atom(X0)
| x(y(eps,X1),nil2) = step(y(atom(X0),X1),X0)
| x(proj1(atom(X0)),proj2(atom(X0))) = atom(X0) ),
inference(resolution,[status(thm)],[c23,d89]) ).
cnf(d91,plain,
( y(proj12(atom(X1)),proj22(atom(X1))) = atom(X1)
| x(y(eps,X0),nil2) = step(y(atom(X1),X0),X1) ),
inference(resolution,[status(thm)],[c21,d90]) ).
cnf(d92,plain,
x(y(eps,X0),nil2) = step(y(atom(X1),X0),X1),
inference(resolution,[status(thm)],[c22,d91]) ).
cnf(d93,plain,
~ eps2(step(step(step(x(y(eps,X0),nil2),b),b),a)),
inference(superposition,[status(thm)],[d92,d86]) ).
cnf(d94,plain,
~ eps2(step(step(x(step(y(eps,X0),b),nil2),b),a)),
inference(demodulation,[status(thm)],[d93,d74]) ).
cnf(d95,plain,
~ eps2(step(x(step(step(y(eps,X0),b),b),nil2),a)),
inference(demodulation,[status(thm)],[d94,d74]) ).
cnf(d96,plain,
~ eps2(x(step(step(step(y(eps,X0),b),b),a),nil2)),
inference(demodulation,[status(thm)],[d95,d74]) ).
cnf(d97,plain,
~ eps2(step(step(step(y(eps,X0),b),b),a)),
inference(resolution,[status(thm)],[d96,c38]) ).
cnf(d98,plain,
( ~ eps2(step(step(X2,X1),X3))
| eps2(step(step(x(X0,X2),X1),X3)) ),
inference(superposition,[status(thm)],[c47,d75]) ).
cnf(d99,plain,
( ~ eps2(step(step(step(X1,X0),X2),X3))
| eps2(step(step(step(y(eps,X1),X0),X2),X3)) ),
inference(superposition,[status(thm)],[d69,d98]) ).
cnf(d100,plain,
~ eps2(step(step(step(X0,b),b),a)),
inference(resolution,[status(thm)],[d99,d97]) ).
cnf(d101,plain,
~ eps2(step(step(x(y(eps,X0),nil2),b),a)),
inference(superposition,[status(thm)],[d92,d100]) ).
cnf(d102,plain,
~ eps2(step(x(step(y(eps,X0),b),nil2),a)),
inference(demodulation,[status(thm)],[d101,d74]) ).
cnf(d103,plain,
~ eps2(x(step(step(y(eps,X0),b),a),nil2)),
inference(demodulation,[status(thm)],[d102,d74]) ).
cnf(d104,plain,
~ eps2(step(step(y(eps,X0),b),a)),
inference(resolution,[status(thm)],[d103,c38]) ).
cnf(d105,plain,
~ eps2(step(step(X0,b),a)),
inference(resolution,[status(thm)],[d104,d76]) ).
cnf(d106,plain,
~ eps2(step(x(y(eps,X0),nil2),a)),
inference(superposition,[status(thm)],[d92,d105]) ).
cnf(d107,plain,
~ eps2(x(step(y(eps,X0),a),nil2)),
inference(demodulation,[status(thm)],[d106,d74]) ).
cnf(d108,plain,
~ eps2(step(y(eps,X0),a)),
inference(resolution,[status(thm)],[d107,c38]) ).
cnf(d109,plain,
~ eps2(step(X0,a)),
inference(resolution,[status(thm)],[d108,d70]) ).
cnf(d110,plain,
$false,
inference(resolution,[status(thm)],[d109,d68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX210+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/20.43 % Computer : n010.cluster.edu
% 0.14/20.43 % Model : x86_64 x86_64
% 0.14/20.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/20.43 % Memory : 8046.5625MB
% 0.14/20.43 % OS : Linux 6.8.0-71-generic
% 0.14/20.43 % CPULimit : 300
% 0.14/20.43 % WCLimit : 300
% 0.14/20.43 % DateTime : Sat Sep 26 16:56:52 UTC 2026
% 0.14/20.43 % CPUTime :
% 0.14/20.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 173.00/45.68 % SZS status Theorem for theBenchmark.p
% 173.00/45.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------