%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET788+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 08:33:14 AM UTC 2026
% Result : Theorem 12.65s 2.06s
% Output : CNFRefutation 12.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 25 ( 5 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 55 ( 17 ~; 30 |; 0 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
( ! [X0,X1] :
( equalish(X0,X1)
<=> ! [X2] :
( 'a$umember$uof'(X2,X0)
<=> 'a$umember$uof'(X2,X1) ) )
=> ! [X0,X1] :
( equalish(X0,X1)
<=> equalish(X1,X0) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ! [X0,X1] :
( equalish(X0,X1)
<=> ! [X2] :
( 'a$umember$uof'(X2,X0)
<=> 'a$umember$uof'(X2,X1) ) )
=> ! [X0,X1] :
( equalish(X0,X1)
<=> equalish(X1,X0) ) ),
inference(negate_conjecture,[status(cth)],[prove_this]) ).
cnf(c0,plain,
( 'a$umember$uof'(X2,X1)
| ~ 'a$umember$uof'(X2,X0)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c1,plain,
( ~ 'a$umember$uof'(X2,X1)
| 'a$umember$uof'(X2,X0)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c3,plain,
( 'a$umember$uof'(sK3(X0,X1),X1)
| 'a$umember$uof'(sK3(X0,X1),X0)
| equalish(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c4,plain,
( ~ 'a$umember$uof'(sK3(X0,X1),X0)
| ~ 'a$umember$uof'(sK3(X0,X1),X1)
| equalish(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c7,plain,
( equalish(sK5,sK4)
| equalish(sK4,sK5) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c8,plain,
( ~ equalish(sK4,sK5)
| ~ equalish(sK5,sK4) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( equalish(sK4,sK5)
| ~ 'a$umember$uof'(X0,sK5)
| 'a$umember$uof'(X0,sK4) ),
inference(resolution,[status(thm)],[c0,c7]) ).
cnf(d1,plain,
( equalish(sK4,sK5)
| 'a$umember$uof'(sK3(X0,sK5),sK4)
| equalish(X0,sK5)
| 'a$umember$uof'(sK3(X0,sK5),X0) ),
inference(resolution,[status(thm)],[c3,d0]) ).
cnf(d2,plain,
( equalish(sK4,sK5)
| equalish(sK4,sK5)
| 'a$umember$uof'(sK3(sK4,sK5),sK4) ),
inference(factoring,[status(thm)],[d1]) ).
cnf(d3,plain,
( equalish(sK4,sK5)
| ~ 'a$umember$uof'(sK3(sK4,sK5),sK5)
| equalish(sK4,sK5) ),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
( equalish(sK4,sK5)
| ~ 'a$umember$uof'(X0,sK4)
| 'a$umember$uof'(X0,sK5) ),
inference(resolution,[status(thm)],[c1,c7]) ).
cnf(d5,plain,
( equalish(sK4,sK5)
| 'a$umember$uof'(sK3(sK4,sK5),sK5)
| equalish(sK4,sK5) ),
inference(resolution,[status(thm)],[d2,d4]) ).
cnf(d6,plain,
( equalish(sK4,sK5)
| equalish(sK4,sK5) ),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( ~ 'a$umember$uof'(X0,sK4)
| 'a$umember$uof'(X0,sK5) ),
inference(resolution,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
( ~ 'a$umember$uof'(X0,sK5)
| 'a$umember$uof'(X0,sK4) ),
inference(resolution,[status(thm)],[d6,c1]) ).
cnf(d9,plain,
( equalish(sK5,X0)
| 'a$umember$uof'(sK3(sK5,X0),X0)
| 'a$umember$uof'(sK3(sK5,X0),sK4) ),
inference(resolution,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
( equalish(sK5,sK4)
| 'a$umember$uof'(sK3(sK5,sK4),sK4) ),
inference(factoring,[status(thm)],[d9]) ).
cnf(d11,plain,
~ equalish(sK5,sK4),
inference(resolution,[status(thm)],[d6,c8]) ).
cnf(d12,plain,
'a$umember$uof'(sK3(sK5,sK4),sK4),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
'a$umember$uof'(sK3(sK5,sK4),sK5),
inference(resolution,[status(thm)],[d12,d7]) ).
cnf(d14,plain,
( equalish(sK5,sK4)
| ~ 'a$umember$uof'(sK3(sK5,sK4),sK4) ),
inference(resolution,[status(thm)],[d13,c4]) ).
cnf(d15,plain,
~ 'a$umember$uof'(sK3(sK5,sK4),sK4),
inference(resolution,[status(thm)],[d11,d14]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[d12,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET788+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 08:16:02 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.65/2.06 % SZS status Theorem for theBenchmark.p
% 12.65/2.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------