%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP186-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 : n003.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 08:41:34 AM UTC 2026
% Result : Unsatisfiable 22.74s 23.24s
% Output : Proof 22.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of clauses : 59 ( 41 unt; 0 nHn; 54 RR)
% Number of literals : 89 ( 65 equ; 32 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(p23x_2,hypothesis,
inverse(inverse(X)) = X,
file('theBenchmark.p',p23x_2) ).
cnf(prove_p23x,negated_conjecture,
least_upper_bound(multiply(a,b),identity) != multiply(a,least_upper_bound(inverse(a),b)),
file('theBenchmark.p',prove_p23x) ).
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,
( multiply(Eq_x_0,Eq_x_1) = multiply(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( least_upper_bound(Eq_x_0,Eq_x_1) = least_upper_bound(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,
least_upper_bound(multiply(a,b),identity) != multiply(a,least_upper_bound(inverse(a),b)),
inference(start,[status(thm),parent(0:0)],[prove_p23x]) ).
cnf(t2,plain,
( least_upper_bound(multiply(inverse(inverse(a)),inverse(inverse(b))),identity) != multiply(a,least_upper_bound(inverse(a),b))
| least_upper_bound(multiply(a,b),identity) != least_upper_bound(multiply(inverse(inverse(a)),inverse(inverse(b))),identity)
| least_upper_bound(multiply(a,b),identity) = multiply(a,least_upper_bound(inverse(a),b)) ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( identity != identity
| multiply(a,b) != multiply(inverse(inverse(a)),inverse(inverse(b)))
| least_upper_bound(multiply(a,b),identity) = least_upper_bound(multiply(inverse(inverse(a)),inverse(inverse(b))),identity) ),
inference(extension,[status(thm),parent(t2:2)],[equality_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( b != inverse(inverse(b))
| a != inverse(inverse(a))
| multiply(a,b) = multiply(inverse(inverse(a)),inverse(inverse(b))) ),
inference(extension,[status(thm),parent(t4:2)],[equality_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( inverse(inverse(a)) != a
| a = inverse(inverse(a)) ),
inference(extension,[status(thm),parent(t6:2)],[equality_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
inverse(inverse(a)) = a,
inference(extension,[status(thm),parent(t8:2)],[p23x_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( inverse(inverse(b)) != b
| b = inverse(inverse(b)) ),
inference(extension,[status(thm),parent(t6:3)],[equality_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t6:3]) ).
cnf(t14,plain,
inverse(inverse(b)) = b,
inference(extension,[status(thm),parent(t12:2)],[p23x_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( inverse(inverse(identity)) != identity
| identity != inverse(inverse(identity))
| identity = identity ),
inference(extension,[status(thm),parent(t4:3)],[equality_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t4:3]) ).
cnf(t18,plain,
( inverse(inverse(identity)) != identity
| identity = inverse(inverse(identity)) ),
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,
inverse(inverse(identity)) = identity,
inference(extension,[status(thm),parent(t18:2)],[p23x_2]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
inverse(inverse(identity)) = identity,
inference(extension,[status(thm),parent(t16:3)],[p23x_2]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t16:3]) ).
cnf(t24,plain,
( least_upper_bound(multiply(inverse(inverse(a)),b),multiply(inverse(inverse(a)),inverse(a))) != multiply(a,least_upper_bound(inverse(a),b))
| least_upper_bound(multiply(inverse(inverse(a)),inverse(inverse(b))),identity) != least_upper_bound(multiply(inverse(inverse(a)),b),multiply(inverse(inverse(a)),inverse(a)))
| least_upper_bound(multiply(inverse(inverse(a)),inverse(inverse(b))),identity) = multiply(a,least_upper_bound(inverse(a),b)) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t2:3]) ).
cnf(t26,plain,
( identity != multiply(inverse(inverse(a)),inverse(a))
| multiply(inverse(inverse(a)),inverse(inverse(b))) != multiply(inverse(inverse(a)),b)
| least_upper_bound(multiply(inverse(inverse(a)),inverse(inverse(b))),identity) = least_upper_bound(multiply(inverse(inverse(a)),b),multiply(inverse(inverse(a)),inverse(a))) ),
inference(extension,[status(thm),parent(t24:2)],[equality_7]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( inverse(inverse(b)) != b
| inverse(inverse(a)) != inverse(inverse(a))
| multiply(inverse(inverse(a)),inverse(inverse(b))) = multiply(inverse(inverse(a)),b) ),
inference(extension,[status(thm),parent(t26:2)],[equality_4]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
inverse(inverse(a)) = inverse(inverse(a)),
inference(extension,[status(thm),parent(t28:2)],[equality_1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
inverse(inverse(b)) = b,
inference(extension,[status(thm),parent(t28:3)],[p23x_2]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(t34,plain,
( multiply(inverse(inverse(a)),inverse(a)) != identity
| identity = multiply(inverse(inverse(a)),inverse(a)) ),
inference(extension,[status(thm),parent(t26:3)],[equality_2]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t26:3]) ).
cnf(t36,plain,
multiply(inverse(inverse(a)),inverse(a)) = identity,
inference(extension,[status(thm),parent(t34:2)],[left_inverse]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
( multiply(inverse(inverse(a)),least_upper_bound(b,inverse(a))) != multiply(a,least_upper_bound(inverse(a),b))
| least_upper_bound(multiply(inverse(inverse(a)),b),multiply(inverse(inverse(a)),inverse(a))) != multiply(inverse(inverse(a)),least_upper_bound(b,inverse(a)))
| least_upper_bound(multiply(inverse(inverse(a)),b),multiply(inverse(inverse(a)),inverse(a))) = multiply(a,least_upper_bound(inverse(a),b)) ),
inference(extension,[status(thm),parent(t24:3)],[equality_3]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t24:3]) ).
cnf(t40,plain,
( multiply(inverse(inverse(a)),least_upper_bound(b,inverse(a))) != least_upper_bound(multiply(inverse(inverse(a)),b),multiply(inverse(inverse(a)),inverse(a)))
| least_upper_bound(multiply(inverse(inverse(a)),b),multiply(inverse(inverse(a)),inverse(a))) = multiply(inverse(inverse(a)),least_upper_bound(b,inverse(a))) ),
inference(extension,[status(thm),parent(t38:2)],[equality_2]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
multiply(inverse(inverse(a)),least_upper_bound(b,inverse(a))) = least_upper_bound(multiply(inverse(inverse(a)),b),multiply(inverse(inverse(a)),inverse(a))),
inference(extension,[status(thm),parent(t40:2)],[monotony_lub1]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
( least_upper_bound(b,inverse(a)) != least_upper_bound(inverse(a),b)
| inverse(inverse(a)) != a
| multiply(inverse(inverse(a)),least_upper_bound(b,inverse(a))) = multiply(a,least_upper_bound(inverse(a),b)) ),
inference(extension,[status(thm),parent(t38:3)],[equality_4]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t38:3]) ).
cnf(t46,plain,
inverse(inverse(a)) = a,
inference(extension,[status(thm),parent(t44:2)],[p23x_2]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
least_upper_bound(b,inverse(a)) = least_upper_bound(inverse(a),b),
inference(extension,[status(thm),parent(t44:3)],[symmetry_of_lub]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t44:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP186-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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
% 0.10/0.57 % Computer : n003.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Sat Sep 19 09:00:28 UTC 2026
% 0.10/0.57 % CPUTime :
% 22.74/23.24 % SZS status Unsatisfiable for theBenchmark
% 22.74/23.24 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------