%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP159-1 : 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 : n005.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 08:41:29 AM UTC 2026
% Result : Unsatisfiable 19.54s 19.81s
% Output : Proof 19.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 12
% Syntax : Number of clauses : 67 ( 48 unt; 0 nHn; 55 RR)
% Number of literals : 100 ( 73 equ; 35 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 : 52 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('GRP004-2.ax',symmetry_of_glb) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_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_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(ax_mono2c_1,hypothesis,
greatest_lower_bound(a,b) = a,
file('theBenchmark.p',ax_mono2c_1) ).
cnf(prove_ax_mono2c,negated_conjecture,
least_upper_bound(multiply(c,a),multiply(c,b)) != multiply(c,b),
file('theBenchmark.p',prove_ax_mono2c) ).
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(c,a),multiply(c,b)) != multiply(c,b),
inference(start,[status(thm),parent(0:0)],[prove_ax_mono2c]) ).
cnf(t2,plain,
( least_upper_bound(multiply(greatest_lower_bound(c,least_upper_bound(c,U_343)),greatest_lower_bound(a,b)),multiply(greatest_lower_bound(c,least_upper_bound(c,U_351)),greatest_lower_bound(b,least_upper_bound(b,U_353)))) != multiply(c,b)
| least_upper_bound(multiply(c,a),multiply(c,b)) != least_upper_bound(multiply(greatest_lower_bound(c,least_upper_bound(c,U_343)),greatest_lower_bound(a,b)),multiply(greatest_lower_bound(c,least_upper_bound(c,U_351)),greatest_lower_bound(b,least_upper_bound(b,U_353))))
| least_upper_bound(multiply(c,a),multiply(c,b)) = multiply(c,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,
( multiply(c,b) != multiply(greatest_lower_bound(c,least_upper_bound(c,U_351)),greatest_lower_bound(b,least_upper_bound(b,U_353)))
| multiply(c,a) != multiply(greatest_lower_bound(c,least_upper_bound(c,U_343)),greatest_lower_bound(a,b))
| least_upper_bound(multiply(c,a),multiply(c,b)) = least_upper_bound(multiply(greatest_lower_bound(c,least_upper_bound(c,U_343)),greatest_lower_bound(a,b)),multiply(greatest_lower_bound(c,least_upper_bound(c,U_351)),greatest_lower_bound(b,least_upper_bound(b,U_353)))) ),
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,
( a != greatest_lower_bound(a,b)
| c != greatest_lower_bound(c,least_upper_bound(c,U_343))
| multiply(c,a) = multiply(greatest_lower_bound(c,least_upper_bound(c,U_343)),greatest_lower_bound(a,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,
( greatest_lower_bound(c,least_upper_bound(c,U_343)) != c
| c = greatest_lower_bound(c,least_upper_bound(c,U_343)) ),
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,
greatest_lower_bound(c,least_upper_bound(c,U_343)) = c,
inference(extension,[status(thm),parent(t8:2)],[glb_absorbtion]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( greatest_lower_bound(a,b) != a
| a = greatest_lower_bound(a,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,
greatest_lower_bound(a,b) = a,
inference(extension,[status(thm),parent(t12:2)],[ax_mono2c_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( b != greatest_lower_bound(b,least_upper_bound(b,U_353))
| c != greatest_lower_bound(c,least_upper_bound(c,U_351))
| multiply(c,b) = multiply(greatest_lower_bound(c,least_upper_bound(c,U_351)),greatest_lower_bound(b,least_upper_bound(b,U_353))) ),
inference(extension,[status(thm),parent(t4:3)],[equality_4]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t4:3]) ).
cnf(t18,plain,
( greatest_lower_bound(c,least_upper_bound(c,U_351)) != c
| c = greatest_lower_bound(c,least_upper_bound(c,U_351)) ),
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,
greatest_lower_bound(c,least_upper_bound(c,U_351)) = c,
inference(extension,[status(thm),parent(t18:2)],[glb_absorbtion]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( greatest_lower_bound(b,least_upper_bound(b,U_353)) != b
| b = greatest_lower_bound(b,least_upper_bound(b,U_353)) ),
inference(extension,[status(thm),parent(t16:3)],[equality_2]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t16:3]) ).
cnf(t24,plain,
greatest_lower_bound(b,least_upper_bound(b,U_353)) = b,
inference(extension,[status(thm),parent(t22:2)],[glb_absorbtion]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( least_upper_bound(multiply(c,greatest_lower_bound(b,a)),multiply(c,b)) != multiply(c,b)
| least_upper_bound(multiply(greatest_lower_bound(c,least_upper_bound(c,U_343)),greatest_lower_bound(a,b)),multiply(greatest_lower_bound(c,least_upper_bound(c,U_351)),greatest_lower_bound(b,least_upper_bound(b,U_353)))) != least_upper_bound(multiply(c,greatest_lower_bound(b,a)),multiply(c,b))
| least_upper_bound(multiply(greatest_lower_bound(c,least_upper_bound(c,U_343)),greatest_lower_bound(a,b)),multiply(greatest_lower_bound(c,least_upper_bound(c,U_351)),greatest_lower_bound(b,least_upper_bound(b,U_353)))) = multiply(c,b) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t2:3]) ).
cnf(t28,plain,
( multiply(greatest_lower_bound(c,least_upper_bound(c,U_351)),greatest_lower_bound(b,least_upper_bound(b,U_353))) != multiply(c,b)
| multiply(greatest_lower_bound(c,least_upper_bound(c,U_343)),greatest_lower_bound(a,b)) != multiply(c,greatest_lower_bound(b,a))
| least_upper_bound(multiply(greatest_lower_bound(c,least_upper_bound(c,U_343)),greatest_lower_bound(a,b)),multiply(greatest_lower_bound(c,least_upper_bound(c,U_351)),greatest_lower_bound(b,least_upper_bound(b,U_353)))) = least_upper_bound(multiply(c,greatest_lower_bound(b,a)),multiply(c,b)) ),
inference(extension,[status(thm),parent(t26:2)],[equality_7]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
( greatest_lower_bound(a,b) != greatest_lower_bound(b,a)
| greatest_lower_bound(c,least_upper_bound(c,U_343)) != c
| multiply(greatest_lower_bound(c,least_upper_bound(c,U_343)),greatest_lower_bound(a,b)) = multiply(c,greatest_lower_bound(b,a)) ),
inference(extension,[status(thm),parent(t28:2)],[equality_4]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
greatest_lower_bound(c,least_upper_bound(c,U_343)) = c,
inference(extension,[status(thm),parent(t30:2)],[glb_absorbtion]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(b,a),
inference(extension,[status(thm),parent(t30:3)],[symmetry_of_glb]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t30:3]) ).
cnf(t36,plain,
( greatest_lower_bound(b,least_upper_bound(b,U_353)) != b
| greatest_lower_bound(c,least_upper_bound(c,U_351)) != c
| multiply(greatest_lower_bound(c,least_upper_bound(c,U_351)),greatest_lower_bound(b,least_upper_bound(b,U_353))) = multiply(c,b) ),
inference(extension,[status(thm),parent(t28:3)],[equality_4]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t28:3]) ).
cnf(t38,plain,
greatest_lower_bound(c,least_upper_bound(c,U_351)) = c,
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,
greatest_lower_bound(b,least_upper_bound(b,U_353)) = b,
inference(extension,[status(thm),parent(t36:3)],[glb_absorbtion]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t36:3]) ).
cnf(t42,plain,
( least_upper_bound(greatest_lower_bound(multiply(c,b),multiply(c,a)),multiply(c,b)) != multiply(c,b)
| least_upper_bound(multiply(c,greatest_lower_bound(b,a)),multiply(c,b)) != least_upper_bound(greatest_lower_bound(multiply(c,b),multiply(c,a)),multiply(c,b))
| least_upper_bound(multiply(c,greatest_lower_bound(b,a)),multiply(c,b)) = multiply(c,b) ),
inference(extension,[status(thm),parent(t26:3)],[equality_3]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t26:3]) ).
cnf(t44,plain,
( multiply(c,b) != multiply(c,b)
| multiply(c,greatest_lower_bound(b,a)) != greatest_lower_bound(multiply(c,b),multiply(c,a))
| least_upper_bound(multiply(c,greatest_lower_bound(b,a)),multiply(c,b)) = least_upper_bound(greatest_lower_bound(multiply(c,b),multiply(c,a)),multiply(c,b)) ),
inference(extension,[status(thm),parent(t42:2)],[equality_7]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
multiply(c,greatest_lower_bound(b,a)) = greatest_lower_bound(multiply(c,b),multiply(c,a)),
inference(extension,[status(thm),parent(t44:2)],[monotony_glb1]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
multiply(c,b) = multiply(c,b),
inference(extension,[status(thm),parent(t44:3)],[equality_1]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t44:3]) ).
cnf(t50,plain,
( least_upper_bound(multiply(c,b),greatest_lower_bound(multiply(c,b),multiply(c,a))) != multiply(c,b)
| least_upper_bound(greatest_lower_bound(multiply(c,b),multiply(c,a)),multiply(c,b)) != least_upper_bound(multiply(c,b),greatest_lower_bound(multiply(c,b),multiply(c,a)))
| least_upper_bound(greatest_lower_bound(multiply(c,b),multiply(c,a)),multiply(c,b)) = multiply(c,b) ),
inference(extension,[status(thm),parent(t42:3)],[equality_3]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t42:3]) ).
cnf(t52,plain,
least_upper_bound(greatest_lower_bound(multiply(c,b),multiply(c,a)),multiply(c,b)) = least_upper_bound(multiply(c,b),greatest_lower_bound(multiply(c,b),multiply(c,a))),
inference(extension,[status(thm),parent(t50:2)],[symmetry_of_lub]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
least_upper_bound(multiply(c,b),greatest_lower_bound(multiply(c,b),multiply(c,a))) = multiply(c,b),
inference(extension,[status(thm),parent(t50:3)],[lub_absorbtion]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t50:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP159-1 : 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
% 0.09/0.38 % Computer : n005.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sat Sep 19 08:52:18 UTC 2026
% 0.09/0.39 % CPUTime :
% 19.54/19.81 % SZS status Unsatisfiable for theBenchmark
% 19.54/19.81 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------