%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COL013-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 08:14:20 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : Proof 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 2
% Syntax : Number of clauses : 5 ( 5 unt; 0 nHn; 4 RR)
% Number of literals : 5 ( 4 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 3 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(l_definition,axiom,
apply(apply(l,X),Y) = apply(X,apply(Y,Y)),
file('theBenchmark.p',l_definition) ).
cnf(prove_fixed_point,negated_conjecture,
Y != apply(combinator,Y),
file('theBenchmark.p',prove_fixed_point) ).
cnf(t1,plain,
apply(apply(l,combinator),apply(l,combinator)) != apply(combinator,apply(apply(l,combinator),apply(l,combinator))),
inference(start,[status(thm),parent(0:0)],[prove_fixed_point]) ).
cnf(t2,plain,
apply(apply(l,combinator),apply(l,combinator)) = apply(combinator,apply(apply(l,combinator),apply(l,combinator))),
inference(extension,[status(thm),parent(t1:1)],[l_definition]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_PEQ_UEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.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 : Sun Sep 20 14:33:57 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------