%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COL058-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n001.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 08:14:26 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.49s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 35 ( 25 unt; 0 nHn; 33 RR)
% Number of literals : 53 ( 39 equ; 20 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 : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(lark_exists,axiom,
response(response(lark,X1),X2) = response(X1,response(X2,X2)),
file('theBenchmark.p',lark_exists) ).
cnf(prove_the_bird_exists,negated_conjecture,
response(X,X) != X,
file('theBenchmark.p',prove_the_bird_exists) ).
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_4,axiom,
( response(Eq_x_0,Eq_x_1) = response(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,
response(response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))) != response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),
inference(start,[status(thm),parent(0:0)],[prove_the_bird_exists]) ).
cnf(t2,plain,
( response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))) != response(response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))))
| response(response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))) = response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))) ),
inference(extension,[status(thm),parent(t1:1)],[equality_2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( response(response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))) != response(response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))))
| response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))) != response(response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))))
| response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))) = response(response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))) ),
inference(extension,[status(thm),parent(t2:2)],[equality_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))) = response(response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))),
inference(extension,[status(thm),parent(t4:2)],[lark_exists]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))) != response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))
| response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))) != response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))
| response(response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))) = response(response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))) ),
inference(extension,[status(thm),parent(t4:3)],[equality_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( response(response(lark,response(lark,lark)),response(lark,response(lark,lark))) != response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))
| response(response(lark,response(lark,lark)),response(lark,response(lark,lark))) != response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))
| response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))) = response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))) ),
inference(extension,[status(thm),parent(t8:2)],[equality_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))) != response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))
| response(response(lark,response(lark,lark)),response(lark,response(lark,lark))) != response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))
| response(response(lark,response(lark,lark)),response(lark,response(lark,lark))) = response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))) ),
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,
response(response(lark,response(lark,lark)),response(lark,response(lark,lark))) = response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),
inference(extension,[status(thm),parent(t12:2)],[lark_exists]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))) = response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),
inference(extension,[status(thm),parent(t12:3)],[lark_exists]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
response(response(lark,response(lark,lark)),response(lark,response(lark,lark))) = response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),
inference(extension,[status(thm),parent(t10:3)],[lark_exists]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t10:3]) ).
cnf(t20,plain,
( response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))) != response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))
| response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))) != response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))))
| response(response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))) = response(response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))) ),
inference(extension,[status(thm),parent(t8:3)],[equality_4]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t8:3]) ).
cnf(t22,plain,
response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))) = response(lark,response(response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),response(response(lark,response(lark,lark)),response(lark,response(lark,lark))))),
inference(extension,[status(thm),parent(t20:2)],[lark_exists]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( response(response(lark,response(lark,lark)),response(lark,response(lark,lark))) != response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))
| response(lark,lark) != response(lark,lark)
| response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))) = response(response(lark,lark),response(response(lark,response(lark,lark)),response(lark,response(lark,lark)))) ),
inference(extension,[status(thm),parent(t20:3)],[equality_4]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
response(lark,lark) = response(lark,lark),
inference(extension,[status(thm),parent(t24:2)],[equality_1]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
response(response(lark,response(lark,lark)),response(lark,response(lark,lark))) = response(response(lark,response(lark,lark)),response(lark,response(lark,lark))),
inference(extension,[status(thm),parent(t24:3)],[equality_1]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL058-1 : 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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 14:45:42 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.23/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.49 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------