%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET041-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 08:31:44 AM UTC 2026
% Result : Unsatisfiable 21.41s 23.08s
% Output : CNFRefutation 21.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 10 unt; 0 nHn; 10 RR)
% Number of literals : 30 ( 6 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(two_sets_equal,axiom,
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ).
cnf(apply_for_composition1,axiom,
( subset(apply(X2,apply(X0,X1)),apply(compose(X2,X0),X1))
| ~ member(X1,'domain$uof'(X0))
| ~ function(X0) ) ).
cnf(apply_for_composition2,axiom,
( subset(apply(compose(X1,X0),X2),apply(X1,apply(X0,X2)))
| ~ function(X0) ) ).
cnf(a_function,hypothesis,
function('a$ufunction') ).
cnf(member_of_domain,hypothesis,
member(a,'domain$uof'('a$ufunction')) ).
cnf(prove_apply_for_composition3,negated_conjecture,
apply('another$ufunction',apply('a$ufunction',a)) != apply(compose('another$ufunction','a$ufunction'),a) ).
cnf(c3,plain,
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[two_sets_equal]) ).
cnf(c23,plain,
( subset(apply(X2,apply(X1,X0)),apply(compose(X2,X1),X0))
| ~ function(X1)
| ~ member(X0,'domain$uof'(X1)) ),
inference(clausification,[status(esa)],[apply_for_composition1]) ).
cnf(c24,plain,
( subset(apply(compose(X1,X0),X2),apply(X1,apply(X0,X2)))
| ~ function(X0) ),
inference(clausification,[status(esa)],[apply_for_composition2]) ).
cnf(c25,plain,
function('a$ufunction'),
inference(clausification,[status(esa)],[a_function]) ).
cnf(c26,plain,
member(a,'domain$uof'('a$ufunction')),
inference(clausification,[status(esa)],[member_of_domain]) ).
cnf(c27,plain,
apply(compose('another$ufunction','a$ufunction'),a) != apply('another$ufunction',apply('a$ufunction',a)),
inference(clausification,[status(esa)],[prove_apply_for_composition3]) ).
cnf(d0,plain,
( ~ function('a$ufunction')
| subset(apply(X0,apply('a$ufunction',a)),apply(compose(X0,'a$ufunction'),a)) ),
inference(resolution,[status(thm)],[c23,c26]) ).
cnf(d1,plain,
subset(apply(X0,apply('a$ufunction',a)),apply(compose(X0,'a$ufunction'),a)),
inference(resolution,[status(thm)],[c25,d0]) ).
cnf(d2,plain,
( ~ subset(apply(compose(X0,'a$ufunction'),a),apply(X0,apply('a$ufunction',a)))
| apply(compose(X0,'a$ufunction'),a) = apply(X0,apply('a$ufunction',a)) ),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
subset(apply(compose(X0,'a$ufunction'),X1),apply(X0,apply('a$ufunction',X1))),
inference(resolution,[status(thm)],[c24,c25]) ).
cnf(d4,plain,
apply(compose(X0,'a$ufunction'),a) = apply(X0,apply('a$ufunction',a)),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,c27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET041-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n002.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 07:01:35 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.41/23.08 % SZS status Unsatisfiable for theBenchmark.p
% 21.41/23.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------