%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP175-3 : 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 : n017.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 08:41:31 AM UTC 2026
% Result : Unsatisfiable 37.33s 42.68s
% Output : Proof 37.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 18
% Syntax : Number of clauses : 177 ( 122 unt; 0 nHn; 154 RR)
% Number of literals : 265 ( 186 equ; 90 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('GRP004-2.ax',symmetry_of_glb) ).
cnf(idempotence_of_lub,axiom,
least_upper_bound(X,X) = X,
file('GRP004-2.ax',idempotence_of_lub) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('GRP004-2.ax',lub_absorbtion) ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
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(monotony_glb1,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)),
file('GRP004-2.ax',monotony_lub2) ).
cnf(p06c_1,hypothesis,
least_upper_bound(identity,b) = b,
file('theBenchmark.p',p06c_1) ).
cnf(prove_p06c,negated_conjecture,
greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != identity,
file('theBenchmark.p',prove_p06c) ).
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_5,axiom,
( inverse(Eq_x_0) = inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( greatest_lower_bound(Eq_x_0,Eq_x_1) = greatest_lower_bound(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,
greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != identity,
inference(start,[status(thm),parent(0:0)],[prove_p06c]) ).
cnf(t2,plain,
( greatest_lower_bound(multiply(inverse(a),multiply(b,a)),identity) != identity
| greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != greatest_lower_bound(multiply(inverse(a),multiply(b,a)),identity)
| greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) = identity ),
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,
greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) = greatest_lower_bound(multiply(inverse(a),multiply(b,a)),identity),
inference(extension,[status(thm),parent(t2:2)],[symmetry_of_glb]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( identity != greatest_lower_bound(multiply(inverse(a),multiply(b,a)),identity)
| greatest_lower_bound(multiply(inverse(a),multiply(b,a)),identity) = identity ),
inference(extension,[status(thm),parent(t2:3)],[equality_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a)))))) != greatest_lower_bound(multiply(inverse(a),multiply(b,a)),identity)
| identity != greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a))))))
| identity = greatest_lower_bound(multiply(inverse(a),multiply(b,a)),identity) ),
inference(extension,[status(thm),parent(t6:2)],[equality_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a)))))) != identity
| identity = greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a)))))) ),
inference(extension,[status(thm),parent(t8:2)],[equality_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a)))))) = identity,
inference(extension,[status(thm),parent(t10:2)],[glb_absorbtion]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( greatest_lower_bound(multiply(inverse(a),multiply(b,a)),identity) != greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a))))))
| greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a)))))) = greatest_lower_bound(multiply(inverse(a),multiply(b,a)),identity) ),
inference(extension,[status(thm),parent(t8:3)],[equality_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t8:3]) ).
cnf(t16,plain,
( greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a))))))
| greatest_lower_bound(multiply(inverse(a),multiply(b,a)),identity) != greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a)))
| greatest_lower_bound(multiply(inverse(a),multiply(b,a)),identity) = greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a)))))) ),
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,
greatest_lower_bound(multiply(inverse(a),multiply(b,a)),identity) = greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))),
inference(extension,[status(thm),parent(t16:2)],[symmetry_of_glb]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( multiply(inverse(a),multiply(b,a)) != least_upper_bound(identity,multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a)))))
| identity != identity
| greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) = greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a)))))) ),
inference(extension,[status(thm),parent(t16:3)],[equality_6]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,U_453)) != identity
| identity != greatest_lower_bound(identity,least_upper_bound(identity,U_453))
| identity = identity ),
inference(extension,[status(thm),parent(t20:2)],[equality_3]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,U_453)) != identity
| identity = greatest_lower_bound(identity,least_upper_bound(identity,U_453)) ),
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,
greatest_lower_bound(identity,least_upper_bound(identity,U_453)) = identity,
inference(extension,[status(thm),parent(t24:2)],[glb_absorbtion]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
greatest_lower_bound(identity,least_upper_bound(identity,U_453)) = identity,
inference(extension,[status(thm),parent(t22:3)],[glb_absorbtion]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t22:3]) ).
cnf(t30,plain,
( multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_487))),multiply(least_upper_bound(identity,b),greatest_lower_bound(a,least_upper_bound(a,a)))) != least_upper_bound(identity,multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a)))))
| multiply(inverse(a),multiply(b,a)) != multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_487))),multiply(least_upper_bound(identity,b),greatest_lower_bound(a,least_upper_bound(a,a))))
| multiply(inverse(a),multiply(b,a)) = least_upper_bound(identity,multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a))))) ),
inference(extension,[status(thm),parent(t20:3)],[equality_3]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t20:3]) ).
cnf(t32,plain,
( multiply(b,a) != multiply(least_upper_bound(identity,b),greatest_lower_bound(a,least_upper_bound(a,a)))
| inverse(a) != inverse(greatest_lower_bound(a,least_upper_bound(a,U_487)))
| multiply(inverse(a),multiply(b,a)) = multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_487))),multiply(least_upper_bound(identity,b),greatest_lower_bound(a,least_upper_bound(a,a)))) ),
inference(extension,[status(thm),parent(t30:2)],[equality_4]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
( a != greatest_lower_bound(a,least_upper_bound(a,U_487))
| inverse(a) = inverse(greatest_lower_bound(a,least_upper_bound(a,U_487))) ),
inference(extension,[status(thm),parent(t32:2)],[equality_5]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
( greatest_lower_bound(a,least_upper_bound(a,U_487)) != a
| a = greatest_lower_bound(a,least_upper_bound(a,U_487)) ),
inference(extension,[status(thm),parent(t34:2)],[equality_2]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
greatest_lower_bound(a,least_upper_bound(a,U_487)) = a,
inference(extension,[status(thm),parent(t36:2)],[glb_absorbtion]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
( a != greatest_lower_bound(a,least_upper_bound(a,a))
| b != least_upper_bound(identity,b)
| multiply(b,a) = multiply(least_upper_bound(identity,b),greatest_lower_bound(a,least_upper_bound(a,a))) ),
inference(extension,[status(thm),parent(t32:3)],[equality_4]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t32:3]) ).
cnf(t42,plain,
( least_upper_bound(identity,b) != b
| b = least_upper_bound(identity,b) ),
inference(extension,[status(thm),parent(t40:2)],[equality_2]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
least_upper_bound(identity,b) = b,
inference(extension,[status(thm),parent(t42:2)],[p06c_1]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
( greatest_lower_bound(a,least_upper_bound(a,a)) != a
| a = greatest_lower_bound(a,least_upper_bound(a,a)) ),
inference(extension,[status(thm),parent(t40:3)],[equality_2]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t40:3]) ).
cnf(t48,plain,
greatest_lower_bound(a,least_upper_bound(a,a)) = a,
inference(extension,[status(thm),parent(t46:2)],[glb_absorbtion]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
cnf(t50,plain,
( multiply(inverse(a),least_upper_bound(multiply(identity,greatest_lower_bound(a,least_upper_bound(a,a))),multiply(b,greatest_lower_bound(a,least_upper_bound(a,a))))) != least_upper_bound(identity,multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a)))))
| multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_487))),multiply(least_upper_bound(identity,b),greatest_lower_bound(a,least_upper_bound(a,a)))) != multiply(inverse(a),least_upper_bound(multiply(identity,greatest_lower_bound(a,least_upper_bound(a,a))),multiply(b,greatest_lower_bound(a,least_upper_bound(a,a)))))
| multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_487))),multiply(least_upper_bound(identity,b),greatest_lower_bound(a,least_upper_bound(a,a)))) = least_upper_bound(identity,multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a))))) ),
inference(extension,[status(thm),parent(t30:3)],[equality_3]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t30:3]) ).
cnf(t52,plain,
( multiply(least_upper_bound(identity,b),greatest_lower_bound(a,least_upper_bound(a,a))) != least_upper_bound(multiply(identity,greatest_lower_bound(a,least_upper_bound(a,a))),multiply(b,greatest_lower_bound(a,least_upper_bound(a,a))))
| inverse(greatest_lower_bound(a,least_upper_bound(a,U_487))) != inverse(a)
| multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_487))),multiply(least_upper_bound(identity,b),greatest_lower_bound(a,least_upper_bound(a,a)))) = multiply(inverse(a),least_upper_bound(multiply(identity,greatest_lower_bound(a,least_upper_bound(a,a))),multiply(b,greatest_lower_bound(a,least_upper_bound(a,a))))) ),
inference(extension,[status(thm),parent(t50:2)],[equality_4]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
( greatest_lower_bound(a,least_upper_bound(a,U_487)) != a
| inverse(greatest_lower_bound(a,least_upper_bound(a,U_487))) = inverse(a) ),
inference(extension,[status(thm),parent(t52:2)],[equality_5]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
cnf(t56,plain,
greatest_lower_bound(a,least_upper_bound(a,U_487)) = a,
inference(extension,[status(thm),parent(t54:2)],[glb_absorbtion]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
multiply(least_upper_bound(identity,b),greatest_lower_bound(a,least_upper_bound(a,a))) = least_upper_bound(multiply(identity,greatest_lower_bound(a,least_upper_bound(a,a))),multiply(b,greatest_lower_bound(a,least_upper_bound(a,a)))),
inference(extension,[status(thm),parent(t52:3)],[monotony_lub2]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t52:3]) ).
cnf(t60,plain,
( least_upper_bound(multiply(inverse(a),multiply(identity,greatest_lower_bound(a,least_upper_bound(a,a)))),multiply(inverse(a),multiply(b,greatest_lower_bound(a,least_upper_bound(a,a))))) != least_upper_bound(identity,multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a)))))
| multiply(inverse(a),least_upper_bound(multiply(identity,greatest_lower_bound(a,least_upper_bound(a,a))),multiply(b,greatest_lower_bound(a,least_upper_bound(a,a))))) != least_upper_bound(multiply(inverse(a),multiply(identity,greatest_lower_bound(a,least_upper_bound(a,a)))),multiply(inverse(a),multiply(b,greatest_lower_bound(a,least_upper_bound(a,a)))))
| multiply(inverse(a),least_upper_bound(multiply(identity,greatest_lower_bound(a,least_upper_bound(a,a))),multiply(b,greatest_lower_bound(a,least_upper_bound(a,a))))) = least_upper_bound(identity,multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a))))) ),
inference(extension,[status(thm),parent(t50:3)],[equality_3]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t50:3]) ).
cnf(t62,plain,
multiply(inverse(a),least_upper_bound(multiply(identity,greatest_lower_bound(a,least_upper_bound(a,a))),multiply(b,greatest_lower_bound(a,least_upper_bound(a,a))))) = least_upper_bound(multiply(inverse(a),multiply(identity,greatest_lower_bound(a,least_upper_bound(a,a)))),multiply(inverse(a),multiply(b,greatest_lower_bound(a,least_upper_bound(a,a))))),
inference(extension,[status(thm),parent(t60:2)],[monotony_lub1]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t60:2]) ).
cnf(t64,plain,
( multiply(inverse(a),multiply(b,greatest_lower_bound(a,least_upper_bound(a,a)))) != multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a))))
| multiply(inverse(a),multiply(identity,greatest_lower_bound(a,least_upper_bound(a,a)))) != identity
| least_upper_bound(multiply(inverse(a),multiply(identity,greatest_lower_bound(a,least_upper_bound(a,a)))),multiply(inverse(a),multiply(b,greatest_lower_bound(a,least_upper_bound(a,a))))) = least_upper_bound(identity,multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a))))) ),
inference(extension,[status(thm),parent(t60:3)],[equality_7]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t60:3]) ).
cnf(t66,plain,
( multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),greatest_lower_bound(multiply(identity,a),multiply(identity,least_upper_bound(a,a)))) != identity
| multiply(inverse(a),multiply(identity,greatest_lower_bound(a,least_upper_bound(a,a)))) != multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),greatest_lower_bound(multiply(identity,a),multiply(identity,least_upper_bound(a,a))))
| multiply(inverse(a),multiply(identity,greatest_lower_bound(a,least_upper_bound(a,a)))) = identity ),
inference(extension,[status(thm),parent(t64:2)],[equality_3]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t64:2]) ).
cnf(t68,plain,
( multiply(identity,greatest_lower_bound(a,least_upper_bound(a,a))) != greatest_lower_bound(multiply(identity,a),multiply(identity,least_upper_bound(a,a)))
| inverse(a) != inverse(greatest_lower_bound(a,least_upper_bound(a,U_589)))
| multiply(inverse(a),multiply(identity,greatest_lower_bound(a,least_upper_bound(a,a)))) = multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),greatest_lower_bound(multiply(identity,a),multiply(identity,least_upper_bound(a,a)))) ),
inference(extension,[status(thm),parent(t66:2)],[equality_4]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t66:2]) ).
cnf(t70,plain,
( a != greatest_lower_bound(a,least_upper_bound(a,U_589))
| inverse(a) = inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))) ),
inference(extension,[status(thm),parent(t68:2)],[equality_5]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t68:2]) ).
cnf(t72,plain,
( greatest_lower_bound(a,least_upper_bound(a,U_589)) != a
| a = greatest_lower_bound(a,least_upper_bound(a,U_589)) ),
inference(extension,[status(thm),parent(t70:2)],[equality_2]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t70:2]) ).
cnf(t74,plain,
greatest_lower_bound(a,least_upper_bound(a,U_589)) = a,
inference(extension,[status(thm),parent(t72:2)],[glb_absorbtion]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t72:2]) ).
cnf(t76,plain,
multiply(identity,greatest_lower_bound(a,least_upper_bound(a,a))) = greatest_lower_bound(multiply(identity,a),multiply(identity,least_upper_bound(a,a))),
inference(extension,[status(thm),parent(t68:3)],[monotony_glb1]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t68:3]) ).
cnf(t78,plain,
( greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a)),multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a)))) != identity
| multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),greatest_lower_bound(multiply(identity,a),multiply(identity,least_upper_bound(a,a)))) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a)),multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a))))
| multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),greatest_lower_bound(multiply(identity,a),multiply(identity,least_upper_bound(a,a)))) = identity ),
inference(extension,[status(thm),parent(t66:3)],[equality_3]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t66:3]) ).
cnf(t80,plain,
multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),greatest_lower_bound(multiply(identity,a),multiply(identity,least_upper_bound(a,a)))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a)),multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a)))),
inference(extension,[status(thm),parent(t78:2)],[monotony_glb1]) ).
cnf(t81,plain,
$false,
inference(connection,[status(thm),parent(t80:1)],[t80:1,t78:2]) ).
cnf(t82,plain,
( greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a))),multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a))) != identity
| greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a)),multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a)))) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a))),multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a)))
| greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a)),multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a)))) = identity ),
inference(extension,[status(thm),parent(t78:3)],[equality_3]) ).
cnf(t83,plain,
$false,
inference(connection,[status(thm),parent(t82:1)],[t82:1,t78:3]) ).
cnf(t84,plain,
greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a)),multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a)))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a))),multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a))),
inference(extension,[status(thm),parent(t82:2)],[symmetry_of_glb]) ).
cnf(t85,plain,
$false,
inference(connection,[status(thm),parent(t84:1)],[t84:1,t82:2]) ).
cnf(t86,plain,
( identity != greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a))),multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a)))
| greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a))),multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a))) = identity ),
inference(extension,[status(thm),parent(t82:3)],[equality_2]) ).
cnf(t87,plain,
$false,
inference(connection,[status(thm),parent(t86:1)],[t86:1,t82:3]) ).
cnf(t88,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(identity,U_598))) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a))),multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a)))
| identity != greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(identity,U_598)))
| identity = greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a))),multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a))) ),
inference(extension,[status(thm),parent(t86:2)],[equality_3]) ).
cnf(t89,plain,
$false,
inference(connection,[status(thm),parent(t88:1)],[t88:1,t86:2]) ).
cnf(t90,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(identity,U_598))) != identity
| identity = greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(identity,U_598))) ),
inference(extension,[status(thm),parent(t88:2)],[equality_2]) ).
cnf(t91,plain,
$false,
inference(connection,[status(thm),parent(t90:1)],[t90:1,t88:2]) ).
cnf(t92,plain,
greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(identity,U_598))) = identity,
inference(extension,[status(thm),parent(t90:2)],[glb_absorbtion]) ).
cnf(t93,plain,
$false,
inference(connection,[status(thm),parent(t92:1)],[t92:1,t90:2]) ).
cnf(t94,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,U_598)) != multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a))
| identity != multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a)))
| greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(identity,U_598))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a))),multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a))) ),
inference(extension,[status(thm),parent(t88:3)],[equality_6]) ).
cnf(t95,plain,
$false,
inference(connection,[status(thm),parent(t94:1)],[t94:1,t88:3]) ).
cnf(t96,plain,
( multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a))) != identity
| identity = multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a))) ),
inference(extension,[status(thm),parent(t94:2)],[equality_2]) ).
cnf(t97,plain,
$false,
inference(connection,[status(thm),parent(t96:1)],[t96:1,t94:2]) ).
cnf(t98,plain,
( multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(identity,a))) != identity
| multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a))) != multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(identity,a)))
| multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a))) = identity ),
inference(extension,[status(thm),parent(t96:2)],[equality_3]) ).
cnf(t99,plain,
$false,
inference(connection,[status(thm),parent(t98:1)],[t98:1,t96:2]) ).
cnf(t100,plain,
( multiply(identity,least_upper_bound(a,a)) != least_upper_bound(multiply(identity,a),multiply(identity,a))
| inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))) != inverse(a)
| multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,least_upper_bound(a,a))) = multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(identity,a))) ),
inference(extension,[status(thm),parent(t98:2)],[equality_4]) ).
cnf(t101,plain,
$false,
inference(connection,[status(thm),parent(t100:1)],[t100:1,t98:2]) ).
cnf(t102,plain,
( greatest_lower_bound(a,least_upper_bound(a,U_589)) != a
| inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))) = inverse(a) ),
inference(extension,[status(thm),parent(t100:2)],[equality_5]) ).
cnf(t103,plain,
$false,
inference(connection,[status(thm),parent(t102:1)],[t102:1,t100:2]) ).
cnf(t104,plain,
greatest_lower_bound(a,least_upper_bound(a,U_589)) = a,
inference(extension,[status(thm),parent(t102:2)],[glb_absorbtion]) ).
cnf(t105,plain,
$false,
inference(connection,[status(thm),parent(t104:1)],[t104:1,t102:2]) ).
cnf(t106,plain,
multiply(identity,least_upper_bound(a,a)) = least_upper_bound(multiply(identity,a),multiply(identity,a)),
inference(extension,[status(thm),parent(t100:3)],[monotony_lub1]) ).
cnf(t107,plain,
$false,
inference(connection,[status(thm),parent(t106:1)],[t106:1,t100:3]) ).
cnf(t108,plain,
( least_upper_bound(multiply(inverse(a),multiply(identity,a)),multiply(inverse(a),multiply(identity,a))) != identity
| multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(identity,a))) != least_upper_bound(multiply(inverse(a),multiply(identity,a)),multiply(inverse(a),multiply(identity,a)))
| multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(identity,a))) = identity ),
inference(extension,[status(thm),parent(t98:3)],[equality_3]) ).
cnf(t109,plain,
$false,
inference(connection,[status(thm),parent(t108:1)],[t108:1,t98:3]) ).
cnf(t110,plain,
multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(identity,a))) = least_upper_bound(multiply(inverse(a),multiply(identity,a)),multiply(inverse(a),multiply(identity,a))),
inference(extension,[status(thm),parent(t108:2)],[monotony_lub1]) ).
cnf(t111,plain,
$false,
inference(connection,[status(thm),parent(t110:1)],[t110:1,t108:2]) ).
cnf(t112,plain,
( multiply(inverse(a),multiply(identity,a)) != identity
| least_upper_bound(multiply(inverse(a),multiply(identity,a)),multiply(inverse(a),multiply(identity,a))) != multiply(inverse(a),multiply(identity,a))
| least_upper_bound(multiply(inverse(a),multiply(identity,a)),multiply(inverse(a),multiply(identity,a))) = identity ),
inference(extension,[status(thm),parent(t108:3)],[equality_3]) ).
cnf(t113,plain,
$false,
inference(connection,[status(thm),parent(t112:1)],[t112:1,t108:3]) ).
cnf(t114,plain,
least_upper_bound(multiply(inverse(a),multiply(identity,a)),multiply(inverse(a),multiply(identity,a))) = multiply(inverse(a),multiply(identity,a)),
inference(extension,[status(thm),parent(t112:2)],[idempotence_of_lub]) ).
cnf(t115,plain,
$false,
inference(connection,[status(thm),parent(t114:1)],[t114:1,t112:2]) ).
cnf(t116,plain,
( multiply(inverse(a),a) != identity
| multiply(inverse(a),multiply(identity,a)) != multiply(inverse(a),a)
| multiply(inverse(a),multiply(identity,a)) = identity ),
inference(extension,[status(thm),parent(t112:3)],[equality_3]) ).
cnf(t117,plain,
$false,
inference(connection,[status(thm),parent(t116:1)],[t116:1,t112:3]) ).
cnf(t118,plain,
( multiply(identity,a) != a
| inverse(a) != inverse(a)
| multiply(inverse(a),multiply(identity,a)) = multiply(inverse(a),a) ),
inference(extension,[status(thm),parent(t116:2)],[equality_4]) ).
cnf(t119,plain,
$false,
inference(connection,[status(thm),parent(t118:1)],[t118:1,t116:2]) ).
cnf(t120,plain,
inverse(a) = inverse(a),
inference(extension,[status(thm),parent(t118:2)],[equality_1]) ).
cnf(t121,plain,
$false,
inference(connection,[status(thm),parent(t120:1)],[t120:1,t118:2]) ).
cnf(t122,plain,
multiply(identity,a) = a,
inference(extension,[status(thm),parent(t118:3)],[left_identity]) ).
cnf(t123,plain,
$false,
inference(connection,[status(thm),parent(t122:1)],[t122:1,t118:3]) ).
cnf(t124,plain,
multiply(inverse(a),a) = identity,
inference(extension,[status(thm),parent(t116:3)],[left_inverse]) ).
cnf(t125,plain,
$false,
inference(connection,[status(thm),parent(t124:1)],[t124:1,t116:3]) ).
cnf(t126,plain,
( multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a)) != least_upper_bound(identity,greatest_lower_bound(identity,U_598))
| least_upper_bound(identity,greatest_lower_bound(identity,U_598)) = multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a)) ),
inference(extension,[status(thm),parent(t94:3)],[equality_2]) ).
cnf(t127,plain,
$false,
inference(connection,[status(thm),parent(t126:1)],[t126:1,t94:3]) ).
cnf(t128,plain,
( multiply(inverse(a),a) != least_upper_bound(identity,greatest_lower_bound(identity,U_598))
| multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a)) != multiply(inverse(a),a)
| multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a)) = least_upper_bound(identity,greatest_lower_bound(identity,U_598)) ),
inference(extension,[status(thm),parent(t126:2)],[equality_3]) ).
cnf(t129,plain,
$false,
inference(connection,[status(thm),parent(t128:1)],[t128:1,t126:2]) ).
cnf(t130,plain,
( multiply(identity,a) != a
| inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))) != inverse(a)
| multiply(inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))),multiply(identity,a)) = multiply(inverse(a),a) ),
inference(extension,[status(thm),parent(t128:2)],[equality_4]) ).
cnf(t131,plain,
$false,
inference(connection,[status(thm),parent(t130:1)],[t130:1,t128:2]) ).
cnf(t132,plain,
( greatest_lower_bound(a,least_upper_bound(a,U_589)) != a
| inverse(greatest_lower_bound(a,least_upper_bound(a,U_589))) = inverse(a) ),
inference(extension,[status(thm),parent(t130:2)],[equality_5]) ).
cnf(t133,plain,
$false,
inference(connection,[status(thm),parent(t132:1)],[t132:1,t130:2]) ).
cnf(t134,plain,
greatest_lower_bound(a,least_upper_bound(a,U_589)) = a,
inference(extension,[status(thm),parent(t132:2)],[glb_absorbtion]) ).
cnf(t135,plain,
$false,
inference(connection,[status(thm),parent(t134:1)],[t134:1,t132:2]) ).
cnf(t136,plain,
multiply(identity,a) = a,
inference(extension,[status(thm),parent(t130:3)],[left_identity]) ).
cnf(t137,plain,
$false,
inference(connection,[status(thm),parent(t136:1)],[t136:1,t130:3]) ).
cnf(t138,plain,
( identity != least_upper_bound(identity,greatest_lower_bound(identity,U_598))
| multiply(inverse(a),a) != identity
| multiply(inverse(a),a) = least_upper_bound(identity,greatest_lower_bound(identity,U_598)) ),
inference(extension,[status(thm),parent(t128:3)],[equality_3]) ).
cnf(t139,plain,
$false,
inference(connection,[status(thm),parent(t138:1)],[t138:1,t128:3]) ).
cnf(t140,plain,
multiply(inverse(a),a) = identity,
inference(extension,[status(thm),parent(t138:2)],[left_inverse]) ).
cnf(t141,plain,
$false,
inference(connection,[status(thm),parent(t140:1)],[t140:1,t138:2]) ).
cnf(t142,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,U_598)) != identity
| identity = least_upper_bound(identity,greatest_lower_bound(identity,U_598)) ),
inference(extension,[status(thm),parent(t138:3)],[equality_2]) ).
cnf(t143,plain,
$false,
inference(connection,[status(thm),parent(t142:1)],[t142:1,t138:3]) ).
cnf(t144,plain,
least_upper_bound(identity,greatest_lower_bound(identity,U_598)) = identity,
inference(extension,[status(thm),parent(t142:2)],[lub_absorbtion]) ).
cnf(t145,plain,
$false,
inference(connection,[status(thm),parent(t144:1)],[t144:1,t142:2]) ).
cnf(t146,plain,
( multiply(b,greatest_lower_bound(a,least_upper_bound(a,a))) != greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a)))
| inverse(a) != inverse(a)
| multiply(inverse(a),multiply(b,greatest_lower_bound(a,least_upper_bound(a,a)))) = multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a)))) ),
inference(extension,[status(thm),parent(t64:3)],[equality_4]) ).
cnf(t147,plain,
$false,
inference(connection,[status(thm),parent(t146:1)],[t146:1,t64:3]) ).
cnf(t148,plain,
( a != a
| inverse(a) = inverse(a) ),
inference(extension,[status(thm),parent(t146:2)],[equality_5]) ).
cnf(t149,plain,
$false,
inference(connection,[status(thm),parent(t148:1)],[t148:1,t146:2]) ).
cnf(t150,plain,
( greatest_lower_bound(a,least_upper_bound(a,U_613)) != a
| a != greatest_lower_bound(a,least_upper_bound(a,U_613))
| a = a ),
inference(extension,[status(thm),parent(t148:2)],[equality_3]) ).
cnf(t151,plain,
$false,
inference(connection,[status(thm),parent(t150:1)],[t150:1,t148:2]) ).
cnf(t152,plain,
( greatest_lower_bound(a,least_upper_bound(a,U_613)) != a
| a = greatest_lower_bound(a,least_upper_bound(a,U_613)) ),
inference(extension,[status(thm),parent(t150:2)],[equality_2]) ).
cnf(t153,plain,
$false,
inference(connection,[status(thm),parent(t152:1)],[t152:1,t150:2]) ).
cnf(t154,plain,
greatest_lower_bound(a,least_upper_bound(a,U_613)) = a,
inference(extension,[status(thm),parent(t152:2)],[glb_absorbtion]) ).
cnf(t155,plain,
$false,
inference(connection,[status(thm),parent(t154:1)],[t154:1,t152:2]) ).
cnf(t156,plain,
greatest_lower_bound(a,least_upper_bound(a,U_613)) = a,
inference(extension,[status(thm),parent(t150:3)],[glb_absorbtion]) ).
cnf(t157,plain,
$false,
inference(connection,[status(thm),parent(t156:1)],[t156:1,t150:3]) ).
cnf(t158,plain,
multiply(b,greatest_lower_bound(a,least_upper_bound(a,a))) = greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(a,a))),
inference(extension,[status(thm),parent(t146:3)],[monotony_glb1]) ).
cnf(t159,plain,
$false,
inference(connection,[status(thm),parent(t158:1)],[t158:1,t146:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP175-3 : 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
% 0.09/5.39 % Computer : n017.cluster.edu
% 0.09/5.39 % Model : x86_64 x86_64
% 0.09/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.39 % Memory : 8046.5625MB
% 0.09/5.39 % OS : Linux 6.8.0-71-generic
% 0.09/5.39 % CPULimit : 300
% 0.09/5.39 % WCLimit : 300
% 0.09/5.39 % DateTime : Sat Sep 19 08:51:02 UTC 2026
% 0.09/5.39 % CPUTime :
% 37.33/42.68 % SZS status Unsatisfiable for theBenchmark
% 37.33/42.68 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------