%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COL009-1 : 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 : n018.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 08:14:19 AM UTC 2026
% Result : Unsatisfiable 0.23s 5.72s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 21 ( 16 unt; 0 nHn; 18 RR)
% Number of literals : 31 ( 24 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_definition,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('theBenchmark.p',b_definition) ).
cnf(l2_definition,axiom,
apply(apply(l2,X),Y) = apply(Y,apply(X,X)),
file('theBenchmark.p',l2_definition) ).
cnf(prove_fixed_point,negated_conjecture,
Y != apply(combinator,Y),
file('theBenchmark.p',prove_fixed_point) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
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(equality_4,axiom,
( apply(Eq_x_0,Eq_x_1) = apply(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(apply(b,apply(b,combinator)),l2),apply(apply(b,apply(b,combinator)),l2))) != apply(combinator,apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(apply(b,apply(b,combinator)),l2),apply(apply(b,apply(b,combinator)),l2)))),
inference(start,[status(thm),parent(0:0)],[prove_fixed_point]) ).
cnf(t2,plain,
( apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2)))) != apply(combinator,apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(apply(b,apply(b,combinator)),l2),apply(apply(b,apply(b,combinator)),l2))))
| apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(apply(b,apply(b,combinator)),l2),apply(apply(b,apply(b,combinator)),l2))) != apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))))
| apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(apply(b,apply(b,combinator)),l2),apply(apply(b,apply(b,combinator)),l2))) = apply(combinator,apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(apply(b,apply(b,combinator)),l2),apply(apply(b,apply(b,combinator)),l2)))) ),
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(b,apply(b,combinator)),l2),apply(apply(b,apply(b,combinator)),l2)) != apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2)))
| apply(l2,apply(apply(b,apply(b,combinator)),l2)) != apply(l2,apply(apply(b,apply(b,combinator)),l2))
| apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(apply(b,apply(b,combinator)),l2),apply(apply(b,apply(b,combinator)),l2))) = apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2)))) ),
inference(extension,[status(thm),parent(t2:2)],[equality_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
apply(l2,apply(apply(b,apply(b,combinator)),l2)) = apply(l2,apply(apply(b,apply(b,combinator)),l2)),
inference(extension,[status(thm),parent(t4:2)],[equality_1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
apply(apply(apply(b,apply(b,combinator)),l2),apply(apply(b,apply(b,combinator)),l2)) = apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))),
inference(extension,[status(thm),parent(t4:3)],[b_definition]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( apply(apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))),apply(apply(apply(b,apply(b,combinator)),l2),apply(apply(b,apply(b,combinator)),l2))) != apply(combinator,apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(apply(b,apply(b,combinator)),l2),apply(apply(b,apply(b,combinator)),l2))))
| apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2)))) != apply(apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))),apply(apply(apply(b,apply(b,combinator)),l2),apply(apply(b,apply(b,combinator)),l2)))
| apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2)))) = apply(combinator,apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(apply(b,apply(b,combinator)),l2),apply(apply(b,apply(b,combinator)),l2)))) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2)))) = apply(apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))),apply(apply(apply(b,apply(b,combinator)),l2),apply(apply(b,apply(b,combinator)),l2))),
inference(extension,[status(thm),parent(t10:2)],[l2_definition]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
apply(apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))),apply(apply(apply(b,apply(b,combinator)),l2),apply(apply(b,apply(b,combinator)),l2))) = apply(combinator,apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(apply(b,apply(b,combinator)),l2),apply(apply(b,apply(b,combinator)),l2)))),
inference(extension,[status(thm),parent(t10:3)],[b_definition]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 This is a CNF_UNS_RFO_PEQ_UEQ problem
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/5.45 % Computer : n018.cluster.edu
% 0.19/5.45 % Model : x86_64 x86_64
% 0.19/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.45 % Memory : 8046.5625MB
% 0.19/5.45 % OS : Linux 6.8.0-71-generic
% 0.19/5.45 % CPULimit : 300
% 0.19/5.45 % WCLimit : 300
% 0.19/5.45 % DateTime : Sun Sep 20 14:29:04 UTC 2026
% 0.19/5.45 % CPUTime :
% 0.23/5.72 % SZS status Unsatisfiable for theBenchmark
% 0.23/5.72 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------