%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : CAT001-4 : 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 : n016.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 08:14:05 AM UTC 2026
% Result : Unsatisfiable 20.22s 20.50s
% Output : Proof 20.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 37 ( 26 unt; 0 nHn; 35 RR)
% Number of literals : 57 ( 43 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 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 : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_of_compose,axiom,
compose(X,compose(Y,Z)) = compose(compose(X,Y),Z),
file('CAT004-0.ax',associativity_of_compose) ).
cnf(monomorphism,hypothesis,
( X = Z
| compose(compose(a,b),Z) != Y
| compose(compose(a,b),X) != Y ),
file('theBenchmark.p',monomorphism) ).
cnf(bh_equals_bg,hypothesis,
compose(b,h) = compose(b,g),
file('theBenchmark.p',bh_equals_bg) ).
cnf(prove_h_equals_g,negated_conjecture,
h != g,
file('theBenchmark.p',prove_h_equals_g) ).
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_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,
h != g,
inference(start,[status(thm),parent(0:0)],[prove_h_equals_g]) ).
cnf(t2,plain,
( compose(compose(a,b),g) != compose(a,compose(b,g))
| compose(compose(a,b),h) != compose(a,compose(b,g))
| h = g ),
inference(extension,[status(thm),parent(t1:1)],[monomorphism]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( compose(a,compose(b,h)) != compose(a,compose(b,g))
| compose(compose(a,b),h) != compose(a,compose(b,h))
| compose(compose(a,b),h) = compose(a,compose(b,g)) ),
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,
( compose(a,compose(b,h)) != compose(compose(a,b),h)
| compose(compose(a,b),h) = compose(a,compose(b,h)) ),
inference(extension,[status(thm),parent(t4:2)],[equality_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
compose(a,compose(b,h)) = compose(compose(a,b),h),
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(b,h) != compose(b,g)
| a != a
| compose(a,compose(b,h)) = compose(a,compose(b,g)) ),
inference(extension,[status(thm),parent(t4:3)],[equality_6]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:3]) ).
cnf(t12,plain,
a = a,
inference(extension,[status(thm),parent(t10:2)],[equality_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
compose(b,h) = compose(b,g),
inference(extension,[status(thm),parent(t10:3)],[bh_equals_bg]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
( compose(compose(a,b),compose(a,compose(b,g))) != compose(compose(a,b),compose(compose(a,b),g))
| compose(compose(a,b),compose(compose(a,b),g)) != compose(compose(a,b),compose(compose(a,b),g))
| compose(compose(a,b),g) = compose(a,compose(b,g)) ),
inference(extension,[status(thm),parent(t2:3)],[monomorphism]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:3]) ).
cnf(t18,plain,
( compose(compose(a,b),compose(compose(a,b),compose(compose(a,b),g))) != compose(compose(compose(a,b),compose(a,b)),compose(compose(a,b),g))
| compose(compose(a,b),compose(compose(a,b),compose(compose(a,b),g))) != compose(compose(compose(a,b),compose(a,b)),compose(compose(a,b),g))
| compose(compose(a,b),compose(compose(a,b),g)) = compose(compose(a,b),compose(compose(a,b),g)) ),
inference(extension,[status(thm),parent(t16:2)],[monomorphism]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
compose(compose(a,b),compose(compose(a,b),compose(compose(a,b),g))) = compose(compose(compose(a,b),compose(a,b)),compose(compose(a,b),g)),
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,
compose(compose(a,b),compose(compose(a,b),compose(compose(a,b),g))) = compose(compose(compose(a,b),compose(a,b)),compose(compose(a,b),g)),
inference(extension,[status(thm),parent(t18:3)],[associativity_of_compose]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
( compose(a,compose(b,g)) != compose(compose(a,b),g)
| compose(a,b) != compose(a,b)
| compose(compose(a,b),compose(a,compose(b,g))) = compose(compose(a,b),compose(compose(a,b),g)) ),
inference(extension,[status(thm),parent(t16:3)],[equality_6]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t16:3]) ).
cnf(t26,plain,
compose(a,b) = compose(a,b),
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,
compose(a,compose(b,g)) = compose(compose(a,b),g),
inference(extension,[status(thm),parent(t24:3)],[associativity_of_compose]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT001-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40 % Computer : n016.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 20 14:01:21 UTC 2026
% 0.12/0.40 % CPUTime :
% 20.22/20.50 % SZS status Unsatisfiable for theBenchmark
% 20.22/20.50 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------