%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP166-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 : n006.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 7.46s 7.74s
% Output : Proof 7.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of clauses : 41 ( 29 unt; 0 nHn; 37 RR)
% Number of literals : 62 ( 47 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
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(lat3a_2,hypothesis,
least_upper_bound(b,identity) = b,
file('theBenchmark.p',lat3a_2) ).
cnf(prove_lat3a,negated_conjecture,
least_upper_bound(a,multiply(b,a)) != multiply(b,a),
file('theBenchmark.p',prove_lat3a) ).
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(a,multiply(b,a)) != multiply(b,a),
inference(start,[status(thm),parent(0:0)],[prove_lat3a]) ).
cnf(t2,plain,
( least_upper_bound(multiply(b,a),a) != multiply(b,a)
| least_upper_bound(a,multiply(b,a)) != least_upper_bound(multiply(b,a),a)
| least_upper_bound(a,multiply(b,a)) = multiply(b,a) ),
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,
least_upper_bound(a,multiply(b,a)) = least_upper_bound(multiply(b,a),a),
inference(extension,[status(thm),parent(t2:2)],[symmetry_of_lub]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( least_upper_bound(multiply(b,a),multiply(identity,a)) != multiply(b,a)
| least_upper_bound(multiply(b,a),a) != least_upper_bound(multiply(b,a),multiply(identity,a))
| least_upper_bound(multiply(b,a),a) = multiply(b,a) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( a != multiply(identity,a)
| multiply(b,a) != multiply(b,a)
| least_upper_bound(multiply(b,a),a) = least_upper_bound(multiply(b,a),multiply(identity,a)) ),
inference(extension,[status(thm),parent(t6:2)],[equality_7]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( a != a
| b != b
| multiply(b,a) = multiply(b,a) ),
inference(extension,[status(thm),parent(t8:2)],[equality_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
b = b,
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,
a = a,
inference(extension,[status(thm),parent(t10:3)],[equality_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
( multiply(identity,a) != a
| a = multiply(identity,a) ),
inference(extension,[status(thm),parent(t8:3)],[equality_2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t8:3]) ).
cnf(t18,plain,
multiply(identity,a) = a,
inference(extension,[status(thm),parent(t16:2)],[left_identity]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( multiply(least_upper_bound(b,identity),a) != multiply(b,a)
| least_upper_bound(multiply(b,a),multiply(identity,a)) != multiply(least_upper_bound(b,identity),a)
| least_upper_bound(multiply(b,a),multiply(identity,a)) = multiply(b,a) ),
inference(extension,[status(thm),parent(t6:3)],[equality_3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t6:3]) ).
cnf(t22,plain,
( multiply(least_upper_bound(b,identity),a) != least_upper_bound(multiply(b,a),multiply(identity,a))
| least_upper_bound(multiply(b,a),multiply(identity,a)) = multiply(least_upper_bound(b,identity),a) ),
inference(extension,[status(thm),parent(t20:2)],[equality_2]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
multiply(least_upper_bound(b,identity),a) = least_upper_bound(multiply(b,a),multiply(identity,a)),
inference(extension,[status(thm),parent(t22:2)],[monotony_lub2]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( a != a
| least_upper_bound(b,identity) != b
| multiply(least_upper_bound(b,identity),a) = multiply(b,a) ),
inference(extension,[status(thm),parent(t20:3)],[equality_4]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t20:3]) ).
cnf(t28,plain,
least_upper_bound(b,identity) = b,
inference(extension,[status(thm),parent(t26:2)],[lat3a_2]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
a = a,
inference(extension,[status(thm),parent(t26:3)],[equality_1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t26:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP166-3 : 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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 08:52:42 UTC 2026
% 0.08/0.35 % CPUTime :
% 7.46/7.74 % SZS status Unsatisfiable for theBenchmark
% 7.46/7.74 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------