%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET041-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 : Thu Sep 24 08:56:03 AM UTC 2026
% Result : Unsatisfiable 30.35s 30.63s
% Output : Proof 30.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 13 unt; 0 nHn; 17 RR)
% Number of literals : 29 ( 4 equ; 12 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 : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(two_sets_equal,axiom,
( X = Y
| ~ subset(Y,X)
| ~ subset(X,Y) ),
file('theBenchmark.p',two_sets_equal) ).
cnf(apply_for_composition1,axiom,
( subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X))
| ~ member(X,domain_of(Xf))
| ~ function(Xf) ),
file('theBenchmark.p',apply_for_composition1) ).
cnf(apply_for_composition2,axiom,
( subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X)))
| ~ function(Xf) ),
file('theBenchmark.p',apply_for_composition2) ).
cnf(a_function,hypothesis,
function(a_function),
file('theBenchmark.p',a_function) ).
cnf(member_of_domain,hypothesis,
member(a,domain_of(a_function)),
file('theBenchmark.p',member_of_domain) ).
cnf(prove_apply_for_composition3,negated_conjecture,
apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
file('theBenchmark.p',prove_apply_for_composition3) ).
cnf(t1,plain,
apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
inference(start,[status(thm),parent(0:0)],[prove_apply_for_composition3]) ).
cnf(t2,plain,
( ~ subset(apply(compose(another_function,a_function),a),apply(another_function,apply(a_function,a)))
| ~ subset(apply(another_function,apply(a_function,a)),apply(compose(another_function,a_function),a))
| apply(another_function,apply(a_function,a)) = apply(compose(another_function,a_function),a) ),
inference(extension,[status(thm),parent(t1:1)],[two_sets_equal]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ member(a,domain_of(a_function))
| ~ function(a_function)
| subset(apply(another_function,apply(a_function,a)),apply(compose(another_function,a_function),a)) ),
inference(extension,[status(thm),parent(t2:2)],[apply_for_composition1]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
function(a_function),
inference(extension,[status(thm),parent(t4:2)],[a_function]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
member(a,domain_of(a_function)),
inference(extension,[status(thm),parent(t4:3)],[member_of_domain]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( ~ function(a_function)
| subset(apply(compose(another_function,a_function),a),apply(another_function,apply(a_function,a))) ),
inference(extension,[status(thm),parent(t2:3)],[apply_for_composition2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
function(a_function),
inference(extension,[status(thm),parent(t10:2)],[a_function]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET041-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 21:33:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 30.35/30.63 % SZS status Unsatisfiable for theBenchmark
% 30.35/30.63 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------