%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYN966+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 : n013.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 09:34:25 AM UTC 2026
% Result : Theorem 12.94s 2.31s
% Output : CNFRefutation 12.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 6 unt; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 34 ( 12 ~; 14 |; 0 &)
% ( 4 <=>; 4 =>; 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 : 23 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
( ! [X0,X1] :
( eq(X0,X1)
<=> ! [X2] :
( 'a$umember$uof'(X2,X0)
<=> 'a$umember$uof'(X2,X1) ) )
=> ! [X3,X4] :
( eq(X3,X4)
=> eq(X4,X3) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ! [X0,X1] :
( eq(X0,X1)
<=> ! [X2] :
( 'a$umember$uof'(X2,X0)
<=> 'a$umember$uof'(X2,X1) ) )
=> ! [X3,X4] :
( eq(X3,X4)
=> eq(X4,X3) ) ),
inference(negate_conjecture,[status(cth)],[prove_this]) ).
cnf(c0,plain,
( 'a$umember$uof'(X2,X1)
| ~ 'a$umember$uof'(X2,X0)
| ~ eq(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c1,plain,
( ~ 'a$umember$uof'(X2,X1)
| 'a$umember$uof'(X2,X0)
| ~ eq(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)
| eq(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)
| eq(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c6,plain,
eq(sK4,sK5),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c7,plain,
~ eq(sK5,sK4),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'a$umember$uof'(X0,sK4)
| 'a$umember$uof'(X0,sK5) ),
inference(resolution,[status(thm)],[c0,c6]) ).
cnf(d1,plain,
( 'a$umember$uof'(sK3(X0,sK4),sK5)
| eq(X0,sK4)
| 'a$umember$uof'(sK3(X0,sK4),X0) ),
inference(resolution,[status(thm)],[c3,d0]) ).
cnf(d2,plain,
( eq(sK5,sK4)
| 'a$umember$uof'(sK3(sK5,sK4),sK5) ),
inference(factoring,[status(thm)],[d1]) ).
cnf(d3,plain,
'a$umember$uof'(sK3(sK5,sK4),sK5),
inference(resolution,[status(thm)],[c7,d2]) ).
cnf(d4,plain,
( eq(sK5,sK4)
| ~ 'a$umember$uof'(sK3(sK5,sK4),sK4) ),
inference(resolution,[status(thm)],[d3,c4]) ).
cnf(d5,plain,
~ 'a$umember$uof'(sK3(sK5,sK4),sK4),
inference(resolution,[status(thm)],[c7,d4]) ).
cnf(d6,plain,
( 'a$umember$uof'(X0,sK4)
| ~ 'a$umember$uof'(X0,sK5) ),
inference(resolution,[status(thm)],[c1,c6]) ).
cnf(d7,plain,
'a$umember$uof'(sK3(sK5,sK4),sK4),
inference(resolution,[status(thm)],[d3,d6]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN966+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n013.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 18:51:37 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.94/2.31 % SZS status Theorem for theBenchmark.p
% 12.94/2.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------