%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COL056-1 : 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 : n015.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 32.37s 32.70s
% Output : Proof 32.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 48 ( 33 unt; 0 nHn; 46 RR)
% Number of literals : 71 ( 52 equ; 25 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(composer_exists,axiom,
response(compose(X,Y),W) = response(X,response(Y,W)),
file('theBenchmark.p',composer_exists) ).
cnf(a_to_b_responds_c,hypothesis,
response(a,b) = c,
file('theBenchmark.p',a_to_b_responds_c) ).
cnf(a_to_c_responds_b,hypothesis,
response(a,c) = b,
file('theBenchmark.p',a_to_c_responds_b) ).
cnf(prove_there_exists_a_happy_bird,negated_conjecture,
response(W,V) != V,
file('theBenchmark.p',prove_there_exists_a_happy_bird) ).
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,
( 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(compose(a,a),response(a,c)) != response(a,c),
inference(start,[status(thm),parent(0:0)],[prove_there_exists_a_happy_bird]) ).
cnf(t2,plain,
( response(a,c) != response(compose(a,a),response(a,c))
| response(compose(a,a),response(a,c)) = response(a,c) ),
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,
( b != response(compose(a,a),response(a,c))
| response(a,c) != b
| response(a,c) = response(compose(a,a),response(a,c)) ),
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(a,c) = b,
inference(extension,[status(thm),parent(t4:2)],[a_to_c_responds_b]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( response(compose(a,a),response(a,c)) != b
| b = response(compose(a,a),response(a,c)) ),
inference(extension,[status(thm),parent(t4:3)],[equality_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( response(a,response(a,response(a,c))) != b
| response(compose(a,a),response(a,c)) != response(a,response(a,response(a,c)))
| response(compose(a,a),response(a,c)) = 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,
response(compose(a,a),response(a,c)) = response(a,response(a,response(a,c))),
inference(extension,[status(thm),parent(t10:2)],[composer_exists]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( b != response(a,response(a,response(a,c)))
| response(a,response(a,response(a,c))) = b ),
inference(extension,[status(thm),parent(t10:3)],[equality_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
( response(a,c) != response(a,response(a,response(a,c)))
| b != response(a,c)
| b = response(a,response(a,response(a,c))) ),
inference(extension,[status(thm),parent(t14:2)],[equality_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( response(a,c) != b
| b = response(a,c) ),
inference(extension,[status(thm),parent(t16:2)],[equality_2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
response(a,c) = b,
inference(extension,[status(thm),parent(t18:2)],[a_to_c_responds_b]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(l9,lemma,
b = response(a,c),
inference(lemma,[status(cth),parent(t16:2),below(t14:2)],[t16:2]) ).
cnf(t22,plain,
( c != response(a,response(a,c))
| a != a
| response(a,c) = response(a,response(a,response(a,c))) ),
inference(extension,[status(thm),parent(t16:3)],[equality_5]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t16:3]) ).
cnf(t24,plain,
( a != a
| a = a ),
inference(extension,[status(thm),parent(t22:2)],[equality_2]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
a = a,
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(a,b) != response(a,response(a,c))
| c != response(a,b)
| c = response(a,response(a,c)) ),
inference(extension,[status(thm),parent(t22:3)],[equality_3]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t22:3]) ).
cnf(t30,plain,
( response(a,b) != c
| c = response(a,b) ),
inference(extension,[status(thm),parent(t28:2)],[equality_2]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
response(a,b) = c,
inference(extension,[status(thm),parent(t30:2)],[a_to_b_responds_c]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
( b != response(a,c)
| a != a
| response(a,b) = response(a,response(a,c)) ),
inference(extension,[status(thm),parent(t28:3)],[equality_5]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t28:3]) ).
cnf(t36,plain,
a = a,
inference(extension,[status(thm),parent(t34:2)],[equality_1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
b = response(a,c),
inference(lemma_extension,[status(thm),parent(t34:3)],[l9:1]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t34:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL056-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 This is a CNF_UNS_RFO_PEQ_UEQ problem
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.47 % Computer : n015.cluster.edu
% 0.18/0.47 % Model : x86_64 x86_64
% 0.18/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.47 % Memory : 8046.5625MB
% 0.18/0.47 % OS : Linux 6.8.0-71-generic
% 0.18/0.47 % CPULimit : 300
% 0.18/0.47 % WCLimit : 300
% 0.18/0.47 % DateTime : Sun Sep 20 14:41:35 UTC 2026
% 0.18/0.48 % CPUTime :
% 32.37/32.70 % SZS status Unsatisfiable for theBenchmark
% 32.37/32.70 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------