%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEV572+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 : n017.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 08:48:55 AM UTC 2026
% Result : Theorem 7.99s 6.88s
% Output : CNFRefutation 7.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 7
% Syntax : Number of formulae : 74 ( 23 unt; 0 def)
% Number of atoms : 214 ( 88 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 174 ( 34 ~; 136 |; 0 &)
% ( 3 <=>; 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 : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 92 ( 11 sgn 12 !; 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(a_def,axiom,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)) ).
fof(n_def,axiom,
! [X0] : n(X0) = a(X0,X0) ).
fof(nsubq_4703_4702,conjecture,
~ subq(u(u(u(s(s(s(n(e)))),n(n(s(n(e))))),n(a(n(e),n(n(e))))),s(a(s(s(n(e))),n(n(e))))),u(a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e)))),a(s(n(n(e))),a(s(s(n(e))),n(n(e)))))) ).
fof(negated_conjecture,negated_conjecture,
~ ~ subq(u(u(u(s(s(s(n(e)))),n(n(s(n(e))))),n(a(n(e),n(n(e))))),s(a(s(s(n(e))),n(n(e))))),u(a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e)))),a(s(n(n(e))),a(s(s(n(e))),n(n(e)))))),
inference(negate_conjecture,[status(cth)],[nsubq_4703_4702]) ).
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(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(c79,plain,
subq(u(u(u(s(s(s(n(e)))),n(n(s(n(e))))),n(a(n(e),n(n(e))))),s(a(s(s(n(e))),n(n(e))))),u(a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e)))),a(s(n(n(e))),a(s(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(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,n(s(X0))),
inference(resolution,[status(thm)],[d10,d1]) ).
cnf(d14,plain,
mem(X0,a(n(X0),X1)),
inference(resolution,[status(thm)],[d11,d9]) ).
cnf(d15,plain,
mem(X0,a(s(X0),X1)),
inference(resolution,[status(thm)],[d9,d1]) ).
cnf(d16,plain,
( mem(X2,X0)
| mem(X2,s(X1))
| ~ mem(X2,a(X0,X1)) ),
inference(superposition,[status(thm)],[c16,c10]) ).
cnf(d17,plain,
( mem(X1,s(X0))
| mem(X1,X0)
| ~ mem(X1,n(X0)) ),
inference(superposition,[status(thm)],[c17,d16]) ).
cnf(d18,plain,
( ~ mem(X2,X0)
| mem(X2,a(X0,X1)) ),
inference(superposition,[status(thm)],[c16,c11]) ).
cnf(d19,plain,
( ~ mem(X1,X0)
| mem(X1,n(X0)) ),
inference(superposition,[status(thm)],[c17,d18]) ).
cnf(d20,plain,
subq(a(u(u(s(s(s(n(e)))),n(n(s(n(e))))),n(a(n(e),n(n(e))))),a(s(s(n(e))),n(n(e)))),u(a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e)))),a(s(n(n(e))),a(s(s(n(e))),n(n(e)))))),
inference(demodulation,[status(thm)],[c79,c16]) ).
cnf(d21,plain,
( mem(X0,X3)
| ~ subq(u(X1,X2),X3)
| ~ mem(X0,X1) ),
inference(resolution,[status(thm)],[c11,c0]) ).
cnf(d22,plain,
( ~ mem(X3,X0)
| mem(X3,X2)
| ~ subq(a(X0,X1),X2) ),
inference(superposition,[status(thm)],[c16,d21]) ).
cnf(d23,plain,
( ~ mem(X0,u(u(s(s(s(n(e)))),n(n(s(n(e))))),n(a(n(e),n(n(e))))))
| mem(X0,u(a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e)))),a(s(n(n(e))),a(s(s(n(e))),n(n(e)))))) ),
inference(resolution,[status(thm)],[d22,d20]) ).
cnf(d24,plain,
( mem(X0,a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e)))))
| mem(X0,a(s(n(n(e))),a(s(s(n(e))),n(n(e)))))
| ~ mem(X0,u(u(s(s(s(n(e)))),n(n(s(n(e))))),n(a(n(e),n(n(e)))))) ),
inference(resolution,[status(thm)],[d23,c10]) ).
cnf(d25,plain,
( ~ mem(X0,n(a(n(e),n(n(e)))))
| mem(X0,a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e)))))
| mem(X0,a(s(n(n(e))),a(s(s(n(e))),n(n(e))))) ),
inference(resolution,[status(thm)],[d24,c12]) ).
cnf(d26,plain,
( mem(X0,s(a(n(e),n(n(e)))))
| mem(X0,u(s(s(s(n(e)))),n(n(s(n(e))))))
| ~ mem(X0,n(a(n(e),n(n(e)))))
| mem(X0,a(s(n(n(e))),a(s(s(n(e))),n(n(e))))) ),
inference(resolution,[status(thm)],[d25,d16]) ).
cnf(d27,plain,
( mem(X0,s(a(s(s(n(e))),n(n(e)))))
| mem(X0,s(n(n(e))))
| ~ mem(X0,n(a(n(e),n(n(e)))))
| mem(X0,u(s(s(s(n(e)))),n(n(s(n(e))))))
| mem(X0,s(a(n(e),n(n(e))))) ),
inference(resolution,[status(thm)],[d26,d16]) ).
cnf(d28,plain,
( mem(X0,s(s(s(n(e)))))
| mem(X0,n(n(s(n(e)))))
| ~ mem(X0,n(a(n(e),n(n(e)))))
| mem(X0,s(n(n(e))))
| mem(X0,s(a(n(e),n(n(e)))))
| mem(X0,s(a(s(s(n(e))),n(n(e))))) ),
inference(resolution,[status(thm)],[d27,c10]) ).
cnf(d29,plain,
( X0 = a(s(s(n(e))),n(n(e)))
| mem(X0,n(n(s(n(e)))))
| ~ mem(X0,n(a(n(e),n(n(e)))))
| mem(X0,s(n(n(e))))
| mem(X0,s(a(n(e),n(n(e)))))
| mem(X0,s(s(s(n(e))))) ),
inference(resolution,[status(thm)],[d28,c8]) ).
cnf(d30,plain,
( ~ mem(X0,a(n(e),n(n(e))))
| mem(X0,n(n(s(n(e)))))
| mem(X0,s(n(n(e))))
| mem(X0,s(a(n(e),n(n(e)))))
| mem(X0,s(s(s(n(e)))))
| X0 = a(s(s(n(e))),n(n(e))) ),
inference(resolution,[status(thm)],[d29,d19]) ).
cnf(d31,plain,
( X0 = a(n(e),n(n(e)))
| mem(X0,n(n(s(n(e)))))
| ~ mem(X0,a(n(e),n(n(e))))
| mem(X0,s(n(n(e))))
| mem(X0,s(s(s(n(e)))))
| X0 = a(s(s(n(e))),n(n(e))) ),
inference(resolution,[status(thm)],[d30,c8]) ).
cnf(d32,plain,
( mem(e,n(n(s(n(e)))))
| mem(e,s(n(n(e))))
| mem(e,s(s(s(n(e)))))
| e = a(n(e),n(n(e)))
| e = a(s(s(n(e))),n(n(e))) ),
inference(resolution,[status(thm)],[d31,d14]) ).
cnf(d33,plain,
( e = s(s(n(e)))
| mem(e,n(n(s(n(e)))))
| mem(e,s(n(n(e))))
| e = a(n(e),n(n(e)))
| e = a(s(s(n(e))),n(n(e))) ),
inference(resolution,[status(thm)],[d32,c8]) ).
cnf(d34,plain,
( mem(e,s(n(s(n(e)))))
| mem(e,n(s(n(e))))
| mem(e,s(n(n(e))))
| e = a(n(e),n(n(e)))
| e = a(s(s(n(e))),n(n(e)))
| e = s(s(n(e))) ),
inference(resolution,[status(thm)],[d33,d17]) ).
cnf(d35,plain,
( e = n(s(n(e)))
| mem(e,n(s(n(e))))
| mem(e,s(n(n(e))))
| e = a(n(e),n(n(e)))
| e = a(s(s(n(e))),n(n(e)))
| e = s(s(n(e))) ),
inference(resolution,[status(thm)],[d34,c8]) ).
cnf(d36,plain,
( e = n(n(e))
| mem(e,n(s(n(e))))
| e = n(s(n(e)))
| e = a(n(e),n(n(e)))
| e = a(s(s(n(e))),n(n(e)))
| e = s(s(n(e))) ),
inference(resolution,[status(thm)],[d35,c8]) ).
cnf(d37,plain,
( mem(e,s(s(n(e))))
| mem(e,s(n(e)))
| e = n(n(e))
| e = n(s(n(e)))
| e = a(n(e),n(n(e)))
| e = a(s(s(n(e))),n(n(e)))
| e = s(s(n(e))) ),
inference(resolution,[status(thm)],[d36,d17]) ).
cnf(d38,plain,
( e = s(n(e))
| mem(e,s(n(e)))
| e = n(n(e))
| e = n(s(n(e)))
| e = a(n(e),n(n(e)))
| e = a(s(s(n(e))),n(n(e)))
| e = s(s(n(e))) ),
inference(resolution,[status(thm)],[d37,c8]) ).
cnf(d39,plain,
( e = n(e)
| e = n(n(e))
| e = n(s(n(e)))
| e = a(n(e),n(n(e)))
| e = a(s(s(n(e))),n(n(e)))
| e = s(n(e))
| e = s(s(n(e))) ),
inference(resolution,[status(thm)],[d38,c8]) ).
cnf(d40,plain,
( e = n(n(e))
| e = n(s(n(e)))
| e = n(e)
| e = a(n(e),n(n(e)))
| e = s(n(e))
| e = s(s(n(e)))
| mem(s(n(e)),e) ),
inference(superposition,[status(thm)],[d39,d15]) ).
cnf(d41,plain,
( e = n(n(e))
| e = n(s(n(e)))
| e = n(e)
| e = a(n(e),n(n(e)))
| e = s(n(e))
| e = s(s(n(e))) ),
inference(resolution,[status(thm)],[c7,d40]) ).
cnf(d42,plain,
( e = n(n(e))
| e = n(s(n(e)))
| e = n(e)
| e = s(n(e))
| e = s(s(n(e)))
| mem(e,e) ),
inference(superposition,[status(thm)],[d41,d14]) ).
cnf(d43,plain,
( e = n(n(e))
| e = n(s(n(e)))
| e = n(e)
| e = s(n(e))
| e = s(s(n(e))) ),
inference(resolution,[status(thm)],[c7,d42]) ).
cnf(d44,plain,
( e = n(n(e))
| e = n(s(n(e)))
| e = n(e)
| e = s(n(e))
| mem(s(n(e)),e) ),
inference(superposition,[status(thm)],[d43,d0]) ).
cnf(d45,plain,
( e = n(n(e))
| e = n(s(n(e)))
| e = n(e)
| e = s(n(e)) ),
inference(resolution,[status(thm)],[c7,d44]) ).
cnf(d46,plain,
( e = n(n(e))
| e = n(e)
| e = s(n(e))
| mem(n(e),e) ),
inference(superposition,[status(thm)],[d45,d13]) ).
cnf(d47,plain,
( e = n(n(e))
| e = n(e)
| e = s(n(e)) ),
inference(resolution,[status(thm)],[c7,d46]) ).
cnf(d48,plain,
( e = n(n(e))
| e = n(e)
| mem(n(e),e) ),
inference(superposition,[status(thm)],[d47,d0]) ).
cnf(d49,plain,
( e = n(n(e))
| e = n(e) ),
inference(resolution,[status(thm)],[c7,d48]) ).
cnf(d50,plain,
( e = n(e)
| mem(e,e) ),
inference(superposition,[status(thm)],[d49,d12]) ).
cnf(d51,plain,
e = n(e),
inference(resolution,[status(thm)],[c7,d50]) ).
cnf(d52,plain,
mem(e,e),
inference(superposition,[status(thm)],[d51,d6]) ).
cnf(d53,plain,
$false,
inference(resolution,[status(thm)],[c7,d52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV572+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.58 % Computer : n017.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Sat Sep 26 11:13:05 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.99/6.88 % SZS status Theorem for theBenchmark.p
% 7.99/6.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------