%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COL080-2 : TPTP v9.3.1. Released v1.2.0.
% 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 08:14:31 AM UTC 2026
% Result : Unsatisfiable 194.24s 194.53s
% Output : Proof 194.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 41 ( 27 unt; 0 nHn; 38 RR)
% Number of literals : 62 ( 46 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 11 ( 3 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 : 17 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(k_definition,axiom,
apply(k(X),Y) = X,
file('theBenchmark.p',k_definition) ).
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)),
file('theBenchmark.p',abstraction) ).
cnf(extensionality2,axiom,
( apply(X,n(X,Y)) != apply(Y,n(X,Y))
| X = Y ),
file('theBenchmark.p',extensionality2) ).
cnf(prove_TRC2b,negated_conjecture,
k(b) != apply(abstraction,apply(abstraction,k(b))),
file('theBenchmark.p',prove_TRC2b) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
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_5,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,
k(b) != apply(abstraction,apply(abstraction,k(b))),
inference(start,[status(thm),parent(0:0)],[prove_TRC2b]) ).
cnf(t2,plain,
( apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b))))) != apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b)))))
| k(b) = apply(abstraction,apply(abstraction,k(b))) ),
inference(extension,[status(thm),parent(t1:1)],[extensionality2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))) != apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b)))))
| apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b))))) = apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))) ),
inference(extension,[status(thm),parent(t2:2)],[equality_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( b != apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b)))))
| apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))) != b
| apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))) = apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b))))) ),
inference(extension,[status(thm),parent(t4:2)],[equality_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( apply(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)) != apply(b,n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b))
| apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))) = b ),
inference(extension,[status(thm),parent(t6:2)],[extensionality2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( apply(apply(k(b),k(apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)))),apply(k(n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)),apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)))) != apply(b,n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b))
| apply(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)) != apply(apply(k(b),k(apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)))),apply(k(n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)),apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b))))
| apply(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)) = apply(b,n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)) ),
inference(extension,[status(thm),parent(t8:2)],[equality_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( apply(apply(apply(abstraction,k(b)),k(n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b))),apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b))) != apply(apply(k(b),k(apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)))),apply(k(n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)),apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b))))
| apply(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)) != apply(apply(apply(abstraction,k(b)),k(n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b))),apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)))
| apply(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)) = apply(apply(k(b),k(apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)))),apply(k(n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)),apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)))) ),
inference(extension,[status(thm),parent(t10:2)],[equality_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
apply(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)) = apply(apply(apply(abstraction,k(b)),k(n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b))),apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b))),
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(apply(abstraction,k(b)),k(n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b))),apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b))) = apply(apply(k(b),k(apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)))),apply(k(n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)),apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)))),
inference(extension,[status(thm),parent(t12:3)],[abstraction]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
( apply(k(n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)),apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b))) != n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)
| apply(k(b),k(apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)))) != b
| apply(apply(k(b),k(apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)))),apply(k(n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)),apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)))) = apply(b,n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)) ),
inference(extension,[status(thm),parent(t10:3)],[equality_5]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t10:3]) ).
cnf(t20,plain,
apply(k(b),k(apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)))) = b,
inference(extension,[status(thm),parent(t18:2)],[k_definition]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
apply(k(n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b)),apply(n(k(b),apply(abstraction,apply(abstraction,k(b)))),n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b))) = n(apply(apply(abstraction,apply(abstraction,k(b))),n(k(b),apply(abstraction,apply(abstraction,k(b))))),b),
inference(extension,[status(thm),parent(t18:3)],[k_definition]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
( apply(b,n(b,apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b))))))) != apply(apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b))))),n(b,apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b)))))))
| b = apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b))))) ),
inference(extension,[status(thm),parent(t6:3)],[extensionality2]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t6:3]) ).
cnf(t26,plain,
( apply(apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b))))),n(b,apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b))))))) != apply(b,n(b,apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b)))))))
| apply(b,n(b,apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b))))))) = apply(apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b))))),n(b,apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b))))))) ),
inference(extension,[status(thm),parent(t24:2)],[equality_2]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( n(b,apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b)))))) != n(b,apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b))))))
| apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b))))) != b
| apply(apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b))))),n(b,apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b))))))) = apply(b,n(b,apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b))))))) ),
inference(extension,[status(thm),parent(t26:2)],[equality_5]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b))))) = b,
inference(extension,[status(thm),parent(t28:2)],[k_definition]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
n(b,apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b)))))) = n(b,apply(k(b),n(k(b),apply(abstraction,apply(abstraction,k(b)))))),
inference(extension,[status(thm),parent(t28:3)],[equality_1]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL080-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 This is a CNF_UNS_RFO_PEQ_NUE problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n006.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 20 14:49:57 UTC 2026
% 0.08/0.34 % CPUTime :
% 194.24/194.53 % SZS status Unsatisfiable for theBenchmark
% 194.24/194.53 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------