%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP143-1 : 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 : 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 08:41:27 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of clauses : 22 ( 17 unt; 0 nHn; 18 RR)
% Number of literals : 32 ( 25 equ; 12 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 0 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(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z),
file('GRP004-2.ax',associativity_of_glb) ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X,X) = X,
file('GRP004-2.ax',idempotence_of_gld) ).
cnf(prove_ax_glb2b,negated_conjecture,
greatest_lower_bound(greatest_lower_bound(a,b),a) != greatest_lower_bound(a,b),
file('theBenchmark.p',prove_ax_glb2b) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
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_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(t1,plain,
greatest_lower_bound(greatest_lower_bound(a,b),a) != greatest_lower_bound(a,b),
inference(start,[status(thm),parent(0:0)],[prove_ax_glb2b]) ).
cnf(t2,plain,
( greatest_lower_bound(a,greatest_lower_bound(a,b)) != greatest_lower_bound(a,b)
| greatest_lower_bound(greatest_lower_bound(a,b),a) != greatest_lower_bound(a,greatest_lower_bound(a,b))
| greatest_lower_bound(greatest_lower_bound(a,b),a) = greatest_lower_bound(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,
greatest_lower_bound(greatest_lower_bound(a,b),a) = greatest_lower_bound(a,greatest_lower_bound(a,b)),
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,
( greatest_lower_bound(greatest_lower_bound(a,a),b) != greatest_lower_bound(a,b)
| greatest_lower_bound(a,greatest_lower_bound(a,b)) != greatest_lower_bound(greatest_lower_bound(a,a),b)
| greatest_lower_bound(a,greatest_lower_bound(a,b)) = greatest_lower_bound(a,b) ),
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,
greatest_lower_bound(a,greatest_lower_bound(a,b)) = greatest_lower_bound(greatest_lower_bound(a,a),b),
inference(extension,[status(thm),parent(t6:2)],[associativity_of_glb]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( b != b
| greatest_lower_bound(a,a) != a
| greatest_lower_bound(greatest_lower_bound(a,a),b) = greatest_lower_bound(a,b) ),
inference(extension,[status(thm),parent(t6:3)],[equality_6]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
greatest_lower_bound(a,a) = a,
inference(extension,[status(thm),parent(t10:2)],[idempotence_of_gld]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
b = b,
inference(extension,[status(thm),parent(t10:3)],[equality_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP143-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 This is a CNF_UNS_RFO_PEQ_UEQ problem
% 0.00/0.03 % 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 : n003.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 08:53:27 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------