%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEV565+1 : TPTP v9.3.1. Released v9.1.0.
% 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 08:48:54 AM UTC 2026
% Result : Theorem 56.97s 14.92s
% Output : CNFRefutation 56.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 9
% Syntax : Number of formulae : 83 ( 22 unt; 0 def)
% Number of atoms : 229 ( 76 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 191 ( 45 ~; 139 |; 1 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 116 ( 10 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subq_def,axiom,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( mem(X2,X0)
=> mem(X2,X1) ) ) ).
fof(e_ax,axiom,
! [X0] : ~ mem(X0,e) ).
fof(s_ax,axiom,
! [X0,X1] :
( mem(X0,s(X1))
<=> X0 = X1 ) ).
fof(u_ax,axiom,
! [X0,X1,X2] :
( mem(X0,u(X1,X2))
<=> ( mem(X0,X2)
| mem(X0,X1) ) ) ).
fof(m_ax,axiom,
! [X0,X1,X2] :
( mem(X0,m(X1,X2))
<=> ( ~ mem(X0,X2)
& mem(X0,X1) ) ) ).
fof(a_def,axiom,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)) ).
fof(n_def,axiom,
! [X0] : n(X0) = a(X0,X0) ).
fof(p_ax,axiom,
! [X0,X1] :
( mem(X0,p(X1))
<=> subq(X0,X1) ) ).
fof(nsubq_2252_2248,conjecture,
~ subq(u(m(p(u(n(e),n(s(n(e))))),p(p(s(n(e))))),s(n(n(n(e))))),u(a(a(s(n(n(e))),n(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(n(e)))))) ).
fof(negated_conjecture,negated_conjecture,
~ ~ subq(u(m(p(u(n(e),n(s(n(e))))),p(p(s(n(e))))),s(n(n(n(e))))),u(a(a(s(n(n(e))),n(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(n(e)))))),
inference(negate_conjecture,[status(cth)],[nsubq_2252_2248]) ).
cnf(c0,plain,
( mem(X2,X1)
| ~ mem(X2,X0)
| ~ subq(X0,X1) ),
inference(clausification,[status(esa)],[subq_def]) ).
cnf(c1,plain,
( mem(sK3(X0,X1),X0)
| subq(X0,X1) ),
inference(clausification,[status(esa)],[subq_def]) ).
cnf(c2,plain,
( ~ mem(sK3(X0,X1),X1)
| subq(X0,X1) ),
inference(clausification,[status(esa)],[subq_def]) ).
cnf(c7,plain,
~ mem(X0,e),
inference(clausification,[status(esa)],[e_ax]) ).
cnf(c8,plain,
( X1 = X0
| ~ mem(X0,s(X1)) ),
inference(clausification,[status(esa)],[s_ax]) ).
cnf(c9,plain,
( X1 != X0
| mem(X0,s(X1)) ),
inference(clausification,[status(esa)],[s_ax]) ).
cnf(c10,plain,
( mem(X0,X1)
| mem(X0,X2)
| ~ mem(X0,u(X1,X2)) ),
inference(clausification,[status(esa)],[u_ax]) ).
cnf(c11,plain,
( ~ mem(X0,X1)
| mem(X0,u(X1,X2)) ),
inference(clausification,[status(esa)],[u_ax]) ).
cnf(c12,plain,
( ~ mem(X0,X2)
| mem(X0,u(X1,X2)) ),
inference(clausification,[status(esa)],[u_ax]) ).
cnf(c15,plain,
( ~ mem(X0,X1)
| mem(X0,X2)
| mem(X0,m(X1,X2)) ),
inference(clausification,[status(esa)],[m_ax]) ).
cnf(c16,plain,
u(X0,s(X1)) = a(X0,X1),
inference(clausification,[status(esa)],[a_def]) ).
cnf(c17,plain,
a(X0,X0) = n(X0),
inference(clausification,[status(esa)],[n_def]) ).
cnf(c18,plain,
( subq(X0,X1)
| ~ mem(X0,p(X1)) ),
inference(clausification,[status(esa)],[p_ax]) ).
cnf(c19,plain,
( ~ subq(X0,X1)
| mem(X0,p(X1)) ),
inference(clausification,[status(esa)],[p_ax]) ).
cnf(c79,plain,
subq(u(m(p(u(n(e),n(s(n(e))))),p(p(s(n(e))))),s(n(n(n(e))))),u(a(a(s(n(n(e))),n(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(n(e)))))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
mem(X0,s(X0)),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(d1,plain,
( mem(X0,X1)
| ~ subq(s(X0),X1) ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
( subq(X0,u(X1,X2))
| ~ mem(sK3(X0,u(X1,X2)),X2) ),
inference(resolution,[status(thm)],[c12,c2]) ).
cnf(d3,plain,
( subq(X0,u(X1,X0))
| subq(X0,u(X1,X0)) ),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
mem(X0,u(X1,s(X0))),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
mem(X1,a(X0,X1)),
inference(demodulation,[status(thm)],[d4,c16]) ).
cnf(d6,plain,
mem(X0,n(X0)),
inference(superposition,[status(thm)],[c17,d5]) ).
cnf(d7,plain,
( subq(X0,u(X1,X2))
| ~ mem(sK3(X0,u(X1,X2)),X1) ),
inference(resolution,[status(thm)],[c11,c2]) ).
cnf(d8,plain,
( subq(X0,u(X0,X1))
| subq(X0,u(X0,X1)) ),
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
subq(X0,a(X0,X1)),
inference(superposition,[status(thm)],[c16,d8]) ).
cnf(d10,plain,
subq(X0,n(X0)),
inference(superposition,[status(thm)],[c17,d9]) ).
cnf(d11,plain,
( mem(X0,X1)
| ~ subq(n(X0),X1) ),
inference(resolution,[status(thm)],[d6,c0]) ).
cnf(d12,plain,
mem(X0,n(n(X0))),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( mem(X0,X1)
| ~ subq(n(n(X0)),X1) ),
inference(resolution,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
mem(X0,n(n(n(X0)))),
inference(resolution,[status(thm)],[d13,d10]) ).
cnf(d15,plain,
mem(X0,u(n(X0),X1)),
inference(resolution,[status(thm)],[d11,d8]) ).
cnf(d16,plain,
( subq(X0,X0)
| subq(X0,X0) ),
inference(resolution,[status(thm)],[c2,c1]) ).
cnf(d17,plain,
( mem(sK3(X0,X1),X2)
| ~ subq(X0,X2)
| subq(X0,X1) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d18,plain,
( subq(X0,u(X1,X2))
| ~ subq(X0,X1)
| subq(X0,u(X1,X2)) ),
inference(resolution,[status(thm)],[d7,d17]) ).
cnf(d19,plain,
( ~ subq(X2,X0)
| subq(X2,a(X0,X1)) ),
inference(superposition,[status(thm)],[c16,d18]) ).
cnf(d20,plain,
( ~ subq(X1,X0)
| subq(X1,n(X0)) ),
inference(superposition,[status(thm)],[c17,d19]) ).
cnf(d21,plain,
( subq(X0,u(X1,X2))
| ~ subq(X0,X2)
| subq(X0,u(X1,X2)) ),
inference(resolution,[status(thm)],[d2,d17]) ).
cnf(d22,plain,
( mem(X2,X0)
| mem(X2,s(X1))
| ~ mem(X2,a(X0,X1)) ),
inference(superposition,[status(thm)],[c16,c10]) ).
cnf(d23,plain,
subq(a(m(p(u(n(e),n(s(n(e))))),p(p(s(n(e))))),n(n(n(e)))),u(a(a(s(n(n(e))),n(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(n(e)))))),
inference(demodulation,[status(thm)],[c79,c16]) ).
cnf(d24,plain,
subq(a(m(p(u(n(e),n(s(n(e))))),p(p(s(n(e))))),n(n(n(e)))),a(a(a(s(n(n(e))),n(s(n(e)))),u(n(e),n(s(n(e))))),n(n(n(e))))),
inference(demodulation,[status(thm)],[d23,c16]) ).
cnf(d25,plain,
( ~ mem(X2,X0)
| mem(X2,a(X0,X1)) ),
inference(superposition,[status(thm)],[c16,c11]) ).
cnf(d26,plain,
( mem(X0,X3)
| ~ subq(a(X1,X2),X3)
| ~ mem(X0,X1) ),
inference(resolution,[status(thm)],[d25,c0]) ).
cnf(d27,plain,
( ~ mem(X0,m(p(u(n(e),n(s(n(e))))),p(p(s(n(e))))))
| mem(X0,a(a(a(s(n(n(e))),n(s(n(e)))),u(n(e),n(s(n(e))))),n(n(n(e))))) ),
inference(resolution,[status(thm)],[d26,d24]) ).
cnf(d28,plain,
( mem(X0,s(n(n(n(e)))))
| mem(X0,a(a(s(n(n(e))),n(s(n(e)))),u(n(e),n(s(n(e))))))
| ~ mem(X0,m(p(u(n(e),n(s(n(e))))),p(p(s(n(e)))))) ),
inference(resolution,[status(thm)],[d27,d22]) ).
cnf(d29,plain,
( mem(X0,s(u(n(e),n(s(n(e))))))
| mem(X0,a(s(n(n(e))),n(s(n(e)))))
| ~ mem(X0,m(p(u(n(e),n(s(n(e))))),p(p(s(n(e))))))
| mem(X0,s(n(n(n(e))))) ),
inference(resolution,[status(thm)],[d28,d22]) ).
cnf(d30,plain,
( ~ mem(X0,p(u(n(e),n(s(n(e))))))
| mem(X0,p(p(s(n(e)))))
| mem(X0,a(s(n(n(e))),n(s(n(e)))))
| mem(X0,s(n(n(n(e)))))
| mem(X0,s(u(n(e),n(s(n(e)))))) ),
inference(resolution,[status(thm)],[d29,c15]) ).
cnf(d31,plain,
( mem(X0,s(n(s(n(e)))))
| mem(X0,s(n(n(e))))
| mem(X0,p(p(s(n(e)))))
| ~ mem(X0,p(u(n(e),n(s(n(e))))))
| mem(X0,s(n(n(n(e)))))
| mem(X0,s(u(n(e),n(s(n(e)))))) ),
inference(resolution,[status(thm)],[d30,d22]) ).
cnf(d32,plain,
( ~ subq(X0,u(n(e),n(s(n(e)))))
| mem(X0,p(p(s(n(e)))))
| mem(X0,s(n(n(n(e)))))
| mem(X0,s(n(n(e))))
| mem(X0,s(n(s(n(e)))))
| mem(X0,s(u(n(e),n(s(n(e)))))) ),
inference(resolution,[status(thm)],[d31,c19]) ).
cnf(d33,plain,
( u(n(e),n(s(n(e)))) = X0
| mem(X0,p(p(s(n(e)))))
| mem(X0,s(n(n(n(e)))))
| mem(X0,s(n(n(e))))
| mem(X0,s(n(s(n(e)))))
| ~ subq(X0,u(n(e),n(s(n(e))))) ),
inference(resolution,[status(thm)],[d32,c8]) ).
cnf(d34,plain,
( ~ subq(X0,n(s(n(e))))
| mem(X0,p(p(s(n(e)))))
| mem(X0,s(n(n(n(e)))))
| mem(X0,s(n(n(e))))
| mem(X0,s(n(s(n(e)))))
| u(n(e),n(s(n(e)))) = X0 ),
inference(resolution,[status(thm)],[d33,d21]) ).
cnf(d35,plain,
( subq(X0,p(s(n(e))))
| mem(X0,s(n(n(n(e)))))
| mem(X0,s(n(n(e))))
| mem(X0,s(n(s(n(e)))))
| ~ subq(X0,n(s(n(e))))
| u(n(e),n(s(n(e)))) = X0 ),
inference(resolution,[status(thm)],[d34,c18]) ).
cnf(d36,plain,
( n(n(n(e))) = X0
| mem(X0,s(n(n(e))))
| mem(X0,s(n(s(n(e)))))
| subq(X0,p(s(n(e))))
| ~ subq(X0,n(s(n(e))))
| u(n(e),n(s(n(e)))) = X0 ),
inference(resolution,[status(thm)],[d35,c8]) ).
cnf(d37,plain,
( n(s(n(e))) = X0
| mem(X0,s(n(n(e))))
| subq(X0,p(s(n(e))))
| ~ subq(X0,n(s(n(e))))
| n(n(n(e))) = X0
| u(n(e),n(s(n(e)))) = X0 ),
inference(resolution,[status(thm)],[d36,c8]) ).
cnf(d38,plain,
( ~ subq(X0,s(n(e)))
| mem(X0,s(n(n(e))))
| subq(X0,p(s(n(e))))
| n(n(n(e))) = X0
| n(s(n(e))) = X0
| u(n(e),n(s(n(e)))) = X0 ),
inference(resolution,[status(thm)],[d37,d20]) ).
cnf(d39,plain,
( n(n(e)) = X0
| subq(X0,p(s(n(e))))
| ~ subq(X0,s(n(e)))
| n(n(n(e))) = X0
| n(s(n(e))) = X0
| u(n(e),n(s(n(e)))) = X0 ),
inference(resolution,[status(thm)],[d38,c8]) ).
cnf(d40,plain,
( mem(X0,p(s(n(e))))
| ~ subq(s(X0),s(n(e)))
| n(n(n(e))) = s(X0)
| n(n(e)) = s(X0)
| n(s(n(e))) = s(X0)
| u(n(e),n(s(n(e)))) = s(X0) ),
inference(resolution,[status(thm)],[d39,d1]) ).
cnf(d41,plain,
( mem(n(e),p(s(n(e))))
| n(n(n(e))) = s(n(e))
| n(n(e)) = s(n(e))
| n(s(n(e))) = s(n(e))
| u(n(e),n(s(n(e)))) = s(n(e)) ),
inference(resolution,[status(thm)],[d40,d16]) ).
cnf(d42,plain,
( subq(n(e),s(n(e)))
| n(n(n(e))) = s(n(e))
| n(n(e)) = s(n(e))
| n(s(n(e))) = s(n(e))
| u(n(e),n(s(n(e)))) = s(n(e)) ),
inference(resolution,[status(thm)],[d41,c18]) ).
cnf(d43,plain,
( mem(e,s(n(e)))
| n(n(n(e))) = s(n(e))
| n(n(e)) = s(n(e))
| n(s(n(e))) = s(n(e))
| u(n(e),n(s(n(e)))) = s(n(e)) ),
inference(resolution,[status(thm)],[d42,d11]) ).
cnf(d44,plain,
( n(e) = e
| n(n(n(e))) = s(n(e))
| n(n(e)) = s(n(e))
| n(s(n(e))) = s(n(e))
| u(n(e),n(s(n(e)))) = s(n(e)) ),
inference(resolution,[status(thm)],[d43,c8]) ).
cnf(d45,plain,
( n(n(n(e))) = s(n(e))
| n(n(e)) = s(n(e))
| n(s(n(e))) = s(n(e))
| n(e) = e
| mem(e,s(n(e))) ),
inference(superposition,[status(thm)],[d44,d15]) ).
cnf(d46,plain,
( n(e) = e
| n(n(n(e))) = s(n(e))
| n(n(e)) = s(n(e))
| n(s(n(e))) = s(n(e))
| n(e) = e ),
inference(resolution,[status(thm)],[d45,c8]) ).
cnf(d47,plain,
( n(n(e)) = s(n(e))
| n(s(n(e))) = s(n(e))
| n(e) = e
| mem(e,s(n(e))) ),
inference(superposition,[status(thm)],[d46,d14]) ).
cnf(d48,plain,
( n(e) = e
| n(n(e)) = s(n(e))
| n(s(n(e))) = s(n(e))
| n(e) = e ),
inference(resolution,[status(thm)],[d47,c8]) ).
cnf(d49,plain,
( n(n(e)) = s(n(e))
| n(e) = e
| mem(s(n(e)),s(n(e))) ),
inference(superposition,[status(thm)],[d48,d6]) ).
cnf(d50,plain,
( n(e) = s(n(e))
| n(n(e)) = s(n(e))
| n(e) = e ),
inference(resolution,[status(thm)],[d49,c8]) ).
cnf(d51,plain,
( n(e) = s(n(e))
| n(e) = e
| mem(e,s(n(e))) ),
inference(superposition,[status(thm)],[d50,d12]) ).
cnf(d52,plain,
( n(e) = e
| n(e) = s(n(e))
| n(e) = e ),
inference(resolution,[status(thm)],[d51,c8]) ).
cnf(d53,plain,
( n(e) = e
| n(n(e)) = s(n(e))
| n(e) = e
| n(n(e)) = s(n(e)) ),
inference(superposition,[status(thm)],[d52,d48]) ).
cnf(d54,plain,
( n(e) = e
| mem(e,s(n(e))) ),
inference(superposition,[status(thm)],[d53,d12]) ).
cnf(d55,plain,
( n(e) = e
| n(e) = e ),
inference(resolution,[status(thm)],[d54,c8]) ).
cnf(d56,plain,
mem(e,e),
inference(superposition,[status(thm)],[d55,d6]) ).
cnf(d57,plain,
$false,
inference(resolution,[status(thm)],[c7,d56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEV565+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n007.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 11:15:08 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 56.97/14.92 % SZS status Theorem for theBenchmark.p
% 56.97/14.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------