%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COL019-1 : 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 : n004.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 08:14:21 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : Proof 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of clauses : 16 ( 13 unt; 0 nHn; 13 RR)
% Number of literals : 22 ( 17 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(s_definition,axiom,
apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)),
file('theBenchmark.p',s_definition) ).
cnf(b_definition,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('theBenchmark.p',b_definition) ).
cnf(t_definition,axiom,
apply(apply(t,X),Y) = apply(Y,X),
file('theBenchmark.p',t_definition) ).
cnf(prove_fixed_point,negated_conjecture,
Y != apply(combinator,Y),
file('theBenchmark.p',prove_fixed_point) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(t1,plain,
apply(apply(apply(s,t),apply(b,combinator)),apply(apply(s,t),apply(b,combinator))) != apply(combinator,apply(apply(apply(s,t),apply(b,combinator)),apply(apply(s,t),apply(b,combinator)))),
inference(start,[status(thm),parent(0:0)],[prove_fixed_point]) ).
cnf(t2,plain,
( apply(apply(t,apply(apply(s,t),apply(b,combinator))),apply(apply(b,combinator),apply(apply(s,t),apply(b,combinator)))) != apply(combinator,apply(apply(apply(s,t),apply(b,combinator)),apply(apply(s,t),apply(b,combinator))))
| apply(apply(apply(s,t),apply(b,combinator)),apply(apply(s,t),apply(b,combinator))) != apply(apply(t,apply(apply(s,t),apply(b,combinator))),apply(apply(b,combinator),apply(apply(s,t),apply(b,combinator))))
| apply(apply(apply(s,t),apply(b,combinator)),apply(apply(s,t),apply(b,combinator))) = apply(combinator,apply(apply(apply(s,t),apply(b,combinator)),apply(apply(s,t),apply(b,combinator)))) ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
apply(apply(apply(s,t),apply(b,combinator)),apply(apply(s,t),apply(b,combinator))) = apply(apply(t,apply(apply(s,t),apply(b,combinator))),apply(apply(b,combinator),apply(apply(s,t),apply(b,combinator)))),
inference(extension,[status(thm),parent(t2:2)],[s_definition]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( apply(apply(apply(b,combinator),apply(apply(s,t),apply(b,combinator))),apply(apply(s,t),apply(b,combinator))) != apply(combinator,apply(apply(apply(s,t),apply(b,combinator)),apply(apply(s,t),apply(b,combinator))))
| apply(apply(t,apply(apply(s,t),apply(b,combinator))),apply(apply(b,combinator),apply(apply(s,t),apply(b,combinator)))) != apply(apply(apply(b,combinator),apply(apply(s,t),apply(b,combinator))),apply(apply(s,t),apply(b,combinator)))
| apply(apply(t,apply(apply(s,t),apply(b,combinator))),apply(apply(b,combinator),apply(apply(s,t),apply(b,combinator)))) = apply(combinator,apply(apply(apply(s,t),apply(b,combinator)),apply(apply(s,t),apply(b,combinator)))) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
apply(apply(t,apply(apply(s,t),apply(b,combinator))),apply(apply(b,combinator),apply(apply(s,t),apply(b,combinator)))) = apply(apply(apply(b,combinator),apply(apply(s,t),apply(b,combinator))),apply(apply(s,t),apply(b,combinator))),
inference(extension,[status(thm),parent(t6:2)],[t_definition]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
apply(apply(apply(b,combinator),apply(apply(s,t),apply(b,combinator))),apply(apply(s,t),apply(b,combinator))) = apply(combinator,apply(apply(apply(s,t),apply(b,combinator)),apply(apply(s,t),apply(b,combinator)))),
inference(extension,[status(thm),parent(t6:3)],[b_definition]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL019-1 : 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
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 14:29:34 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------