%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP168-1 : 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 : n026.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 08:41:30 AM UTC 2026
% Result : Unsatisfiable 30.15s 30.63s
% Output : Proof 30.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 11
% Syntax : Number of clauses : 74 ( 50 unt; 0 nHn; 63 RR)
% Number of literals : 112 ( 81 equ; 40 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
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_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(p01a_1,hypothesis,
least_upper_bound(a,b) = b,
file('theBenchmark.p',p01a_1) ).
cnf(prove_p01a,negated_conjecture,
least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) != multiply(inverse(c),multiply(b,c)),
file('theBenchmark.p',prove_p01a) ).
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_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(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) != multiply(inverse(c),multiply(b,c)),
inference(start,[status(thm),parent(0:0)],[prove_p01a]) ).
cnf(t2,plain,
( multiply(inverse(c),multiply(b,c)) != least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c)))
| least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) = multiply(inverse(c),multiply(b,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,
( multiply(inverse(greatest_lower_bound(c,least_upper_bound(c,U_329))),multiply(least_upper_bound(a,b),greatest_lower_bound(c,least_upper_bound(c,U_370)))) != least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c)))
| multiply(inverse(c),multiply(b,c)) != multiply(inverse(greatest_lower_bound(c,least_upper_bound(c,U_329))),multiply(least_upper_bound(a,b),greatest_lower_bound(c,least_upper_bound(c,U_370))))
| multiply(inverse(c),multiply(b,c)) = least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,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,
( multiply(b,c) != multiply(least_upper_bound(a,b),greatest_lower_bound(c,least_upper_bound(c,U_370)))
| inverse(c) != inverse(greatest_lower_bound(c,least_upper_bound(c,U_329)))
| multiply(inverse(c),multiply(b,c)) = multiply(inverse(greatest_lower_bound(c,least_upper_bound(c,U_329))),multiply(least_upper_bound(a,b),greatest_lower_bound(c,least_upper_bound(c,U_370)))) ),
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,
( c != greatest_lower_bound(c,least_upper_bound(c,U_329))
| inverse(c) = inverse(greatest_lower_bound(c,least_upper_bound(c,U_329))) ),
inference(extension,[status(thm),parent(t6:2)],[equality_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( greatest_lower_bound(c,least_upper_bound(c,U_329)) != c
| c = greatest_lower_bound(c,least_upper_bound(c,U_329)) ),
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(c,least_upper_bound(c,U_329)) = c,
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,
( c != greatest_lower_bound(c,least_upper_bound(c,U_370))
| b != least_upper_bound(a,b)
| multiply(b,c) = multiply(least_upper_bound(a,b),greatest_lower_bound(c,least_upper_bound(c,U_370))) ),
inference(extension,[status(thm),parent(t6:3)],[equality_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t6:3]) ).
cnf(t16,plain,
( least_upper_bound(a,b) != b
| b = least_upper_bound(a,b) ),
inference(extension,[status(thm),parent(t14:2)],[equality_2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
least_upper_bound(a,b) = b,
inference(extension,[status(thm),parent(t16:2)],[p01a_1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( greatest_lower_bound(c,least_upper_bound(c,U_370)) != c
| c = greatest_lower_bound(c,least_upper_bound(c,U_370)) ),
inference(extension,[status(thm),parent(t14:3)],[equality_2]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t14:3]) ).
cnf(t22,plain,
greatest_lower_bound(c,least_upper_bound(c,U_370)) = c,
inference(extension,[status(thm),parent(t20:2)],[glb_absorbtion]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( multiply(inverse(c),least_upper_bound(multiply(a,greatest_lower_bound(c,least_upper_bound(c,U_370))),multiply(b,greatest_lower_bound(c,least_upper_bound(c,U_370))))) != least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c)))
| multiply(inverse(greatest_lower_bound(c,least_upper_bound(c,U_329))),multiply(least_upper_bound(a,b),greatest_lower_bound(c,least_upper_bound(c,U_370)))) != multiply(inverse(c),least_upper_bound(multiply(a,greatest_lower_bound(c,least_upper_bound(c,U_370))),multiply(b,greatest_lower_bound(c,least_upper_bound(c,U_370)))))
| multiply(inverse(greatest_lower_bound(c,least_upper_bound(c,U_329))),multiply(least_upper_bound(a,b),greatest_lower_bound(c,least_upper_bound(c,U_370)))) = least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) ),
inference(extension,[status(thm),parent(t4:3)],[equality_3]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t4:3]) ).
cnf(t26,plain,
( multiply(least_upper_bound(a,b),greatest_lower_bound(c,least_upper_bound(c,U_370))) != least_upper_bound(multiply(a,greatest_lower_bound(c,least_upper_bound(c,U_370))),multiply(b,greatest_lower_bound(c,least_upper_bound(c,U_370))))
| inverse(greatest_lower_bound(c,least_upper_bound(c,U_329))) != inverse(c)
| multiply(inverse(greatest_lower_bound(c,least_upper_bound(c,U_329))),multiply(least_upper_bound(a,b),greatest_lower_bound(c,least_upper_bound(c,U_370)))) = multiply(inverse(c),least_upper_bound(multiply(a,greatest_lower_bound(c,least_upper_bound(c,U_370))),multiply(b,greatest_lower_bound(c,least_upper_bound(c,U_370))))) ),
inference(extension,[status(thm),parent(t24:2)],[equality_4]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( greatest_lower_bound(c,least_upper_bound(c,U_329)) != c
| inverse(greatest_lower_bound(c,least_upper_bound(c,U_329))) = inverse(c) ),
inference(extension,[status(thm),parent(t26:2)],[equality_5]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
greatest_lower_bound(c,least_upper_bound(c,U_329)) = c,
inference(extension,[status(thm),parent(t28:2)],[glb_absorbtion]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
multiply(least_upper_bound(a,b),greatest_lower_bound(c,least_upper_bound(c,U_370))) = least_upper_bound(multiply(a,greatest_lower_bound(c,least_upper_bound(c,U_370))),multiply(b,greatest_lower_bound(c,least_upper_bound(c,U_370)))),
inference(extension,[status(thm),parent(t26:3)],[monotony_lub2]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t26:3]) ).
cnf(t34,plain,
( least_upper_bound(multiply(inverse(c),multiply(a,greatest_lower_bound(c,least_upper_bound(c,U_370)))),multiply(inverse(c),multiply(b,greatest_lower_bound(c,least_upper_bound(c,U_370))))) != least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c)))
| multiply(inverse(c),least_upper_bound(multiply(a,greatest_lower_bound(c,least_upper_bound(c,U_370))),multiply(b,greatest_lower_bound(c,least_upper_bound(c,U_370))))) != least_upper_bound(multiply(inverse(c),multiply(a,greatest_lower_bound(c,least_upper_bound(c,U_370)))),multiply(inverse(c),multiply(b,greatest_lower_bound(c,least_upper_bound(c,U_370)))))
| multiply(inverse(c),least_upper_bound(multiply(a,greatest_lower_bound(c,least_upper_bound(c,U_370))),multiply(b,greatest_lower_bound(c,least_upper_bound(c,U_370))))) = least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) ),
inference(extension,[status(thm),parent(t24:3)],[equality_3]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t24:3]) ).
cnf(t36,plain,
multiply(inverse(c),least_upper_bound(multiply(a,greatest_lower_bound(c,least_upper_bound(c,U_370))),multiply(b,greatest_lower_bound(c,least_upper_bound(c,U_370))))) = least_upper_bound(multiply(inverse(c),multiply(a,greatest_lower_bound(c,least_upper_bound(c,U_370)))),multiply(inverse(c),multiply(b,greatest_lower_bound(c,least_upper_bound(c,U_370))))),
inference(extension,[status(thm),parent(t34:2)],[monotony_lub1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
( multiply(inverse(c),multiply(b,greatest_lower_bound(c,least_upper_bound(c,U_370)))) != multiply(inverse(c),multiply(b,c))
| multiply(inverse(c),multiply(a,greatest_lower_bound(c,least_upper_bound(c,U_370)))) != multiply(inverse(c),multiply(a,c))
| least_upper_bound(multiply(inverse(c),multiply(a,greatest_lower_bound(c,least_upper_bound(c,U_370)))),multiply(inverse(c),multiply(b,greatest_lower_bound(c,least_upper_bound(c,U_370))))) = least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) ),
inference(extension,[status(thm),parent(t34:3)],[equality_7]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t34:3]) ).
cnf(t40,plain,
( multiply(a,greatest_lower_bound(c,least_upper_bound(c,U_370))) != multiply(a,c)
| inverse(c) != inverse(c)
| multiply(inverse(c),multiply(a,greatest_lower_bound(c,least_upper_bound(c,U_370)))) = multiply(inverse(c),multiply(a,c)) ),
inference(extension,[status(thm),parent(t38:2)],[equality_4]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
( c != c
| inverse(c) = inverse(c) ),
inference(extension,[status(thm),parent(t40:2)],[equality_5]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
c = c,
inference(extension,[status(thm),parent(t42:2)],[equality_1]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
( greatest_lower_bound(c,least_upper_bound(c,U_370)) != c
| a != a
| multiply(a,greatest_lower_bound(c,least_upper_bound(c,U_370))) = multiply(a,c) ),
inference(extension,[status(thm),parent(t40:3)],[equality_4]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t40:3]) ).
cnf(t48,plain,
a = a,
inference(extension,[status(thm),parent(t46:2)],[equality_1]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
cnf(t50,plain,
greatest_lower_bound(c,least_upper_bound(c,U_370)) = c,
inference(extension,[status(thm),parent(t46:3)],[glb_absorbtion]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t46:3]) ).
cnf(t52,plain,
( multiply(b,greatest_lower_bound(c,least_upper_bound(c,U_370))) != multiply(b,c)
| inverse(c) != inverse(c)
| multiply(inverse(c),multiply(b,greatest_lower_bound(c,least_upper_bound(c,U_370)))) = multiply(inverse(c),multiply(b,c)) ),
inference(extension,[status(thm),parent(t38:3)],[equality_4]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t38:3]) ).
cnf(t54,plain,
( c != c
| inverse(c) = inverse(c) ),
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,
c = c,
inference(extension,[status(thm),parent(t54:2)],[equality_1]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
( greatest_lower_bound(c,least_upper_bound(c,U_370)) != c
| b != b
| multiply(b,greatest_lower_bound(c,least_upper_bound(c,U_370))) = multiply(b,c) ),
inference(extension,[status(thm),parent(t52:3)],[equality_4]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t52:3]) ).
cnf(t60,plain,
b = b,
inference(extension,[status(thm),parent(t58:2)],[equality_1]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t58:2]) ).
cnf(t62,plain,
greatest_lower_bound(c,least_upper_bound(c,U_370)) = c,
inference(extension,[status(thm),parent(t58:3)],[glb_absorbtion]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t58:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP168-1 : 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
% 0.11/0.59 % Computer : n026.cluster.edu
% 0.11/0.59 % Model : x86_64 x86_64
% 0.11/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.59 % Memory : 8046.5625MB
% 0.11/0.59 % OS : Linux 6.8.0-71-generic
% 0.11/0.59 % CPULimit : 300
% 0.11/0.59 % WCLimit : 300
% 0.11/0.59 % DateTime : Sat Sep 19 08:55:52 UTC 2026
% 0.11/0.59 % CPUTime :
% 30.15/30.63 % SZS status Unsatisfiable for theBenchmark
% 30.15/30.63 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------