%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEV566+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 18.74s 10.05s
% Output : CNFRefutation 18.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 9
% Syntax : Number of formulae : 79 ( 24 unt; 0 def)
% Number of atoms : 171 ( 45 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 133 ( 41 ~; 85 |; 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 : 106 ( 11 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_1242_1240,conjecture,
~ subq(u(m(p(u(n(e),n(s(n(e))))),n(p(s(n(e))))),s(a(s(n(e)),n(n(e))))),u(m(p(u(n(e),n(s(n(e))))),u(s(n(e)),n(p(s(n(e)))))),s(a(s(n(e)),n(n(e)))))) ).
fof(negated_conjecture,negated_conjecture,
~ ~ subq(u(m(p(u(n(e),n(s(n(e))))),n(p(s(n(e))))),s(a(s(n(e)),n(n(e))))),u(m(p(u(n(e),n(s(n(e))))),u(s(n(e)),n(p(s(n(e)))))),s(a(s(n(e)),n(n(e)))))),
inference(negate_conjecture,[status(cth)],[nsubq_1242_1240]) ).
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,
( X0 = X1
| ~ mem(X0,s(X1)) ),
inference(clausification,[status(esa)],[s_ax]) ).
cnf(c9,plain,
( X0 != X1
| mem(X0,s(X1)) ),
inference(clausification,[status(esa)],[s_ax]) ).
cnf(c10,plain,
( mem(X0,X2)
| mem(X0,X1)
| ~ 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(c14,plain,
( ~ mem(X0,X2)
| ~ mem(X0,m(X1,X2)) ),
inference(clausification,[status(esa)],[m_ax]) ).
cnf(c15,plain,
( mem(X0,X2)
| ~ mem(X0,X1)
| mem(X0,m(X1,X2)) ),
inference(clausification,[status(esa)],[m_ax]) ).
cnf(c16,plain,
a(X0,X1) = u(X0,s(X1)),
inference(clausification,[status(esa)],[a_def]) ).
cnf(c17,plain,
n(X0) = a(X0,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))))),n(p(s(n(e))))),s(a(s(n(e)),n(n(e))))),u(m(p(u(n(e),n(s(n(e))))),u(s(n(e)),n(p(s(n(e)))))),s(a(s(n(e)),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(u(X0,X1),X2)
| mem(sK3(u(X0,X1),X2),X0)
| mem(sK3(u(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[c10,c1]) ).
cnf(d8,plain,
( subq(u(X0,X1),X1)
| mem(sK3(u(X0,X1),X1),X0)
| subq(u(X0,X1),X1) ),
inference(resolution,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
subq(u(e,X0),X0),
inference(resolution,[status(thm)],[d8,c7]) ).
cnf(d10,plain,
subq(a(e,X0),s(X0)),
inference(superposition,[status(thm)],[c16,d9]) ).
cnf(d11,plain,
subq(n(e),s(e)),
inference(superposition,[status(thm)],[c17,d10]) ).
cnf(d12,plain,
( subq(X0,X0)
| subq(X0,X0) ),
inference(resolution,[status(thm)],[c2,c1]) ).
cnf(d13,plain,
( subq(X0,u(X1,X2))
| ~ mem(sK3(X0,u(X1,X2)),X1) ),
inference(resolution,[status(thm)],[c11,c2]) ).
cnf(d14,plain,
( subq(X0,u(X0,X1))
| subq(X0,u(X0,X1)) ),
inference(resolution,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
subq(X0,a(X0,X1)),
inference(superposition,[status(thm)],[c16,d14]) ).
cnf(d16,plain,
mem(X0,a(s(X0),X1)),
inference(resolution,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
( mem(X0,X1)
| ~ subq(n(X0),X1) ),
inference(resolution,[status(thm)],[d6,c0]) ).
cnf(d18,plain,
mem(X0,u(s(X0),X1)),
inference(resolution,[status(thm)],[d14,d1]) ).
cnf(d19,plain,
( mem(X2,X0)
| mem(X2,s(X1))
| ~ mem(X2,a(X0,X1)) ),
inference(superposition,[status(thm)],[c16,c10]) ).
cnf(d20,plain,
subq(a(m(p(u(n(e),n(s(n(e))))),n(p(s(n(e))))),a(s(n(e)),n(n(e)))),u(m(p(u(n(e),n(s(n(e))))),u(s(n(e)),n(p(s(n(e)))))),s(a(s(n(e)),n(n(e)))))),
inference(demodulation,[status(thm)],[c79,c16]) ).
cnf(d21,plain,
subq(a(m(p(u(n(e),n(s(n(e))))),n(p(s(n(e))))),a(s(n(e)),n(n(e)))),a(m(p(u(n(e),n(s(n(e))))),u(s(n(e)),n(p(s(n(e)))))),a(s(n(e)),n(n(e))))),
inference(demodulation,[status(thm)],[d20,c16]) ).
cnf(d22,plain,
( mem(X0,X3)
| ~ subq(u(X1,X2),X3)
| ~ mem(X0,X1) ),
inference(resolution,[status(thm)],[c11,c0]) ).
cnf(d23,plain,
( ~ mem(X3,X0)
| mem(X3,X2)
| ~ subq(a(X0,X1),X2) ),
inference(superposition,[status(thm)],[c16,d22]) ).
cnf(d24,plain,
( ~ mem(X0,m(p(u(n(e),n(s(n(e))))),n(p(s(n(e))))))
| mem(X0,a(m(p(u(n(e),n(s(n(e))))),u(s(n(e)),n(p(s(n(e)))))),a(s(n(e)),n(n(e))))) ),
inference(resolution,[status(thm)],[d23,d21]) ).
cnf(d25,plain,
( mem(X0,s(a(s(n(e)),n(n(e)))))
| mem(X0,m(p(u(n(e),n(s(n(e))))),u(s(n(e)),n(p(s(n(e)))))))
| ~ mem(X0,m(p(u(n(e),n(s(n(e))))),n(p(s(n(e)))))) ),
inference(resolution,[status(thm)],[d24,d19]) ).
cnf(d26,plain,
( ~ mem(X0,u(s(n(e)),n(p(s(n(e))))))
| ~ mem(X0,m(p(u(n(e),n(s(n(e))))),n(p(s(n(e))))))
| mem(X0,s(a(s(n(e)),n(n(e))))) ),
inference(resolution,[status(thm)],[d25,c14]) ).
cnf(d27,plain,
( ~ mem(X0,p(u(n(e),n(s(n(e))))))
| mem(X0,n(p(s(n(e)))))
| ~ mem(X0,u(s(n(e)),n(p(s(n(e))))))
| mem(X0,s(a(s(n(e)),n(n(e))))) ),
inference(resolution,[status(thm)],[d26,c15]) ).
cnf(d28,plain,
( ~ mem(n(e),p(u(n(e),n(s(n(e))))))
| mem(n(e),n(p(s(n(e)))))
| mem(n(e),s(a(s(n(e)),n(n(e))))) ),
inference(resolution,[status(thm)],[d27,d18]) ).
cnf(d29,plain,
( ~ subq(n(e),u(n(e),n(s(n(e)))))
| mem(n(e),n(p(s(n(e)))))
| mem(n(e),s(a(s(n(e)),n(n(e))))) ),
inference(resolution,[status(thm)],[d28,c19]) ).
cnf(d30,plain,
( mem(n(e),n(p(s(n(e)))))
| mem(n(e),s(a(s(n(e)),n(n(e))))) ),
inference(resolution,[status(thm)],[d14,d29]) ).
cnf(d31,plain,
( n(e) = a(s(n(e)),n(n(e)))
| mem(n(e),n(p(s(n(e))))) ),
inference(resolution,[status(thm)],[d30,c8]) ).
cnf(d32,plain,
( mem(X1,s(X0))
| mem(X1,X0)
| ~ mem(X1,n(X0)) ),
inference(superposition,[status(thm)],[c17,d19]) ).
cnf(d33,plain,
( n(e) = a(s(n(e)),n(n(e)))
| mem(n(e),s(p(s(n(e)))))
| mem(n(e),p(s(n(e)))) ),
inference(resolution,[status(thm)],[d32,d31]) ).
cnf(d34,plain,
( n(e) = p(s(n(e)))
| mem(n(e),p(s(n(e))))
| n(e) = a(s(n(e)),n(n(e))) ),
inference(resolution,[status(thm)],[d33,c8]) ).
cnf(d35,plain,
( subq(n(e),s(n(e)))
| n(e) = p(s(n(e)))
| n(e) = a(s(n(e)),n(n(e))) ),
inference(resolution,[status(thm)],[d34,c18]) ).
cnf(d36,plain,
( mem(e,s(n(e)))
| n(e) = p(s(n(e)))
| n(e) = a(s(n(e)),n(n(e))) ),
inference(resolution,[status(thm)],[d35,d17]) ).
cnf(d37,plain,
( e = n(e)
| n(e) = p(s(n(e)))
| n(e) = a(s(n(e)),n(n(e))) ),
inference(resolution,[status(thm)],[d36,c8]) ).
cnf(d38,plain,
( n(e) = p(s(n(e)))
| e = n(e)
| mem(n(e),n(e)) ),
inference(superposition,[status(thm)],[d37,d16]) ).
cnf(d39,plain,
( mem(n(e),X0)
| ~ subq(n(e),X0)
| n(e) = p(s(n(e)))
| e = n(e) ),
inference(resolution,[status(thm)],[d38,c0]) ).
cnf(d40,plain,
( mem(n(e),s(e))
| n(e) = p(s(n(e)))
| e = n(e) ),
inference(resolution,[status(thm)],[d39,d11]) ).
cnf(d41,plain,
( n(e) = e
| n(e) = p(s(n(e)))
| e = n(e) ),
inference(resolution,[status(thm)],[d40,c8]) ).
cnf(d42,plain,
( n(e) = e
| e = n(e)
| ~ subq(X0,s(n(e)))
| mem(X0,n(e)) ),
inference(superposition,[status(thm)],[d41,c19]) ).
cnf(d43,plain,
( mem(s(n(e)),n(e))
| n(e) = e
| e = n(e) ),
inference(resolution,[status(thm)],[d42,d12]) ).
cnf(d44,plain,
( mem(s(n(e)),X0)
| ~ subq(n(e),X0)
| n(e) = e
| e = n(e) ),
inference(resolution,[status(thm)],[d43,c0]) ).
cnf(d45,plain,
( s(n(e)) = X0
| ~ subq(n(e),s(X0))
| n(e) = e
| e = n(e) ),
inference(resolution,[status(thm)],[d44,c8]) ).
cnf(d46,plain,
( n(e) = e
| s(n(e)) = e
| e = n(e) ),
inference(resolution,[status(thm)],[d45,d11]) ).
cnf(d47,plain,
( n(e) = e
| e = n(e)
| mem(n(e),e) ),
inference(superposition,[status(thm)],[d46,d0]) ).
cnf(d48,plain,
( n(e) = e
| e = n(e) ),
inference(resolution,[status(thm)],[c7,d47]) ).
cnf(d49,plain,
( n(e) = e
| mem(e,e) ),
inference(superposition,[status(thm)],[d48,d6]) ).
cnf(d50,plain,
n(e) = e,
inference(resolution,[status(thm)],[c7,d49]) ).
cnf(d51,plain,
mem(e,e),
inference(superposition,[status(thm)],[d50,d6]) ).
cnf(d52,plain,
$false,
inference(resolution,[status(thm)],[c7,d51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV566+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.39 % Computer : n020.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sat Sep 26 11:18:25 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.74/10.05 % SZS status Theorem for theBenchmark.p
% 18.74/10.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------