%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : CAT003-3 : 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 : n011.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 08:14:06 AM UTC 2026
% Result : Unsatisfiable 126.45s 126.78s
% Output : Proof 126.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of clauses : 34 ( 25 unt; 0 nHn; 32 RR)
% Number of literals : 52 ( 39 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_of_compose,axiom,
compose(X,compose(Y,Z)) = compose(compose(X,Y),Z),
file('CAT003-0.ax',associativity_of_compose) ).
cnf(epimorphism,hypothesis,
( X = Z
| compose(Z,compose(a,b)) != Y
| compose(X,compose(a,b)) != Y ),
file('theBenchmark.p',epimorphism) ).
cnf(ha_equals_ga,hypothesis,
compose(h,a) = compose(g,a),
file('theBenchmark.p',ha_equals_ga) ).
cnf(prove_g_equals_h,negated_conjecture,
g != h,
file('theBenchmark.p',prove_g_equals_h) ).
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_6,axiom,
( compose(Eq_x_0,Eq_x_1) = compose(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,
g != h,
inference(start,[status(thm),parent(0:0)],[prove_g_equals_h]) ).
cnf(t2,plain,
( compose(h,compose(a,b)) != compose(compose(g,a),b)
| compose(g,compose(a,b)) != compose(compose(g,a),b)
| g = h ),
inference(extension,[status(thm),parent(t1:1)],[epimorphism]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( compose(compose(compose(g,a),b),compose(a,b)) != compose(compose(compose(g,a),b),compose(a,b))
| compose(compose(g,compose(a,b)),compose(a,b)) != compose(compose(compose(g,a),b),compose(a,b))
| compose(g,compose(a,b)) = compose(compose(g,a),b) ),
inference(extension,[status(thm),parent(t2:2)],[epimorphism]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( compose(a,b) != compose(a,b)
| compose(g,compose(a,b)) != compose(compose(g,a),b)
| compose(compose(g,compose(a,b)),compose(a,b)) = compose(compose(compose(g,a),b),compose(a,b)) ),
inference(extension,[status(thm),parent(t4:2)],[equality_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
compose(g,compose(a,b)) = compose(compose(g,a),b),
inference(extension,[status(thm),parent(t6:2)],[associativity_of_compose]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
compose(a,b) = compose(a,b),
inference(extension,[status(thm),parent(t6:3)],[equality_1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
( compose(compose(compose(compose(g,a),b),compose(a,b)),compose(a,b)) != compose(compose(compose(compose(compose(g,a),b),compose(a,b)),a),b)
| compose(compose(compose(compose(g,a),b),compose(a,b)),compose(a,b)) != compose(compose(compose(compose(compose(g,a),b),compose(a,b)),a),b)
| compose(compose(compose(g,a),b),compose(a,b)) = compose(compose(compose(g,a),b),compose(a,b)) ),
inference(extension,[status(thm),parent(t4:3)],[epimorphism]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
cnf(t14,plain,
compose(compose(compose(compose(g,a),b),compose(a,b)),compose(a,b)) = compose(compose(compose(compose(compose(g,a),b),compose(a,b)),a),b),
inference(extension,[status(thm),parent(t12:2)],[associativity_of_compose]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
compose(compose(compose(compose(g,a),b),compose(a,b)),compose(a,b)) = compose(compose(compose(compose(compose(g,a),b),compose(a,b)),a),b),
inference(extension,[status(thm),parent(t12:3)],[associativity_of_compose]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
( compose(compose(h,a),b) != compose(compose(g,a),b)
| compose(h,compose(a,b)) != compose(compose(h,a),b)
| compose(h,compose(a,b)) = compose(compose(g,a),b) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t2:3]) ).
cnf(t20,plain,
compose(h,compose(a,b)) = compose(compose(h,a),b),
inference(extension,[status(thm),parent(t18:2)],[associativity_of_compose]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( b != b
| compose(h,a) != compose(g,a)
| compose(compose(h,a),b) = compose(compose(g,a),b) ),
inference(extension,[status(thm),parent(t18:3)],[equality_6]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
compose(h,a) = compose(g,a),
inference(extension,[status(thm),parent(t22:2)],[ha_equals_ga]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
b = b,
inference(extension,[status(thm),parent(t22:3)],[equality_1]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t22:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT003-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 13:57:55 UTC 2026
% 0.14/0.38 % CPUTime :
% 126.45/126.78 % SZS status Unsatisfiable for theBenchmark
% 126.45/126.78 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------