%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP155-1 : 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 : n016.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 08:41:28 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.41s
% Output : Proof 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of clauses : 20 ( 14 unt; 0 nHn; 18 RR)
% Number of literals : 30 ( 24 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(ax_mono1b,hypothesis,
greatest_lower_bound(a,b) = a,
file('theBenchmark.p',ax_mono1b) ).
cnf(prove_ax_mono1b,negated_conjecture,
greatest_lower_bound(multiply(a,c),multiply(b,c)) != multiply(a,c),
file('theBenchmark.p',prove_ax_mono1b) ).
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(t1,plain,
greatest_lower_bound(multiply(a,c),multiply(b,c)) != multiply(a,c),
inference(start,[status(thm),parent(0:0)],[prove_ax_mono1b]) ).
cnf(t2,plain,
( multiply(greatest_lower_bound(a,b),c) != multiply(a,c)
| greatest_lower_bound(multiply(a,c),multiply(b,c)) != multiply(greatest_lower_bound(a,b),c)
| greatest_lower_bound(multiply(a,c),multiply(b,c)) = multiply(a,c) ),
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(greatest_lower_bound(a,b),c) != greatest_lower_bound(multiply(a,c),multiply(b,c))
| greatest_lower_bound(multiply(a,c),multiply(b,c)) = multiply(greatest_lower_bound(a,b),c) ),
inference(extension,[status(thm),parent(t2:2)],[equality_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
multiply(greatest_lower_bound(a,b),c) = greatest_lower_bound(multiply(a,c),multiply(b,c)),
inference(extension,[status(thm),parent(t4:2)],[monotony_glb2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( c != c
| greatest_lower_bound(a,b) != a
| multiply(greatest_lower_bound(a,b),c) = multiply(a,c) ),
inference(extension,[status(thm),parent(t2:3)],[equality_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
greatest_lower_bound(a,b) = a,
inference(extension,[status(thm),parent(t8:2)],[ax_mono1b]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
c = c,
inference(extension,[status(thm),parent(t8:3)],[equality_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP155-1 : 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
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 08:57:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.41 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------