%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COL075-2 : TPTP v9.3.1. Released v1.2.0.
% 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 : n026.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 08:14:31 AM UTC 2026
% Result : Unsatisfiable 0.16s 10.61s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of clauses : 28 ( 20 unt; 0 nHn; 25 RR)
% Number of literals : 42 ( 32 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(k_definition,axiom,
apply(apply(k,X),Y) = X,
file('theBenchmark.p',k_definition) ).
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,apply(k,Z)),apply(Y,Z)),
file('theBenchmark.p',abstraction) ).
cnf(prove_diagonal_combinator,negated_conjecture,
apply(apply(Y,b(Y)),c(Y)) != apply(b(Y),b(Y)),
file('theBenchmark.p',prove_diagonal_combinator) ).
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(equality_6,axiom,
( c(Eq_x_0) = c(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k))) != apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))),
inference(start,[status(thm),parent(0:0)],[prove_diagonal_combinator]) ).
cnf(t2,plain,
( apply(apply(apply(abstraction,apply(k,b(apply(apply(abstraction,abstraction),k)))),apply(k,b(apply(apply(abstraction,abstraction),k)))),c(apply(apply(abstraction,abstraction),k))) != apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k)))
| apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k))) != apply(apply(apply(abstraction,apply(k,b(apply(apply(abstraction,abstraction),k)))),apply(k,b(apply(apply(abstraction,abstraction),k)))),c(apply(apply(abstraction,abstraction),k)))
| apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k))) = apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))) ),
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,
( c(apply(apply(abstraction,abstraction),k)) != c(apply(apply(abstraction,abstraction),k))
| apply(apply(apply(abstraction,abstraction),k),b(apply(apply(abstraction,abstraction),k))) != apply(apply(abstraction,apply(k,b(apply(apply(abstraction,abstraction),k)))),apply(k,b(apply(apply(abstraction,abstraction),k))))
| apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k))) = apply(apply(apply(abstraction,apply(k,b(apply(apply(abstraction,abstraction),k)))),apply(k,b(apply(apply(abstraction,abstraction),k)))),c(apply(apply(abstraction,abstraction),k))) ),
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(apply(apply(abstraction,abstraction),k),b(apply(apply(abstraction,abstraction),k))) = apply(apply(abstraction,apply(k,b(apply(apply(abstraction,abstraction),k)))),apply(k,b(apply(apply(abstraction,abstraction),k)))),
inference(extension,[status(thm),parent(t4:2)],[abstraction]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( apply(apply(abstraction,abstraction),k) != apply(apply(abstraction,abstraction),k)
| c(apply(apply(abstraction,abstraction),k)) = c(apply(apply(abstraction,abstraction),k)) ),
inference(extension,[status(thm),parent(t4:3)],[equality_6]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
apply(apply(abstraction,abstraction),k) = apply(apply(abstraction,abstraction),k),
inference(extension,[status(thm),parent(t8:2)],[equality_1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( apply(apply(apply(k,b(apply(apply(abstraction,abstraction),k))),apply(k,c(apply(apply(abstraction,abstraction),k)))),apply(apply(k,b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k)))) != apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k)))
| apply(apply(apply(abstraction,apply(k,b(apply(apply(abstraction,abstraction),k)))),apply(k,b(apply(apply(abstraction,abstraction),k)))),c(apply(apply(abstraction,abstraction),k))) != apply(apply(apply(k,b(apply(apply(abstraction,abstraction),k))),apply(k,c(apply(apply(abstraction,abstraction),k)))),apply(apply(k,b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k))))
| apply(apply(apply(abstraction,apply(k,b(apply(apply(abstraction,abstraction),k)))),apply(k,b(apply(apply(abstraction,abstraction),k)))),c(apply(apply(abstraction,abstraction),k))) = apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:3]) ).
cnf(t14,plain,
apply(apply(apply(abstraction,apply(k,b(apply(apply(abstraction,abstraction),k)))),apply(k,b(apply(apply(abstraction,abstraction),k)))),c(apply(apply(abstraction,abstraction),k))) = apply(apply(apply(k,b(apply(apply(abstraction,abstraction),k))),apply(k,c(apply(apply(abstraction,abstraction),k)))),apply(apply(k,b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k)))),
inference(extension,[status(thm),parent(t12:2)],[abstraction]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( apply(apply(k,b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k))) != b(apply(apply(abstraction,abstraction),k))
| apply(apply(k,b(apply(apply(abstraction,abstraction),k))),apply(k,c(apply(apply(abstraction,abstraction),k)))) != b(apply(apply(abstraction,abstraction),k))
| apply(apply(apply(k,b(apply(apply(abstraction,abstraction),k))),apply(k,c(apply(apply(abstraction,abstraction),k)))),apply(apply(k,b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k)))) = apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))) ),
inference(extension,[status(thm),parent(t12:3)],[equality_4]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
apply(apply(k,b(apply(apply(abstraction,abstraction),k))),apply(k,c(apply(apply(abstraction,abstraction),k)))) = b(apply(apply(abstraction,abstraction),k)),
inference(extension,[status(thm),parent(t16:2)],[k_definition]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
apply(apply(k,b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k))) = b(apply(apply(abstraction,abstraction),k)),
inference(extension,[status(thm),parent(t16:3)],[k_definition]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL075-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 This is a CNF_UNS_RFO_PEQ_UEQ 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
% 0.11/10.39 % Computer : n026.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Sun Sep 20 14:52:03 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.16/10.61 % SZS status Unsatisfiable for theBenchmark
% 0.16/10.61 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------