%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP156-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 : Fri Sep 25 01:25:27 PM UTC 2026
% Result : Unsatisfiable 4.29s 1.40s
% Output : CNFRefutation 4.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 9 RR)
% Number of literals : 15 ( 14 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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 : 14 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t13,axiom,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t34,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(orient,[status(thm)],[t13]) ).
cnf(t2,axiom,
least_upper_bound(a,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t7,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t69,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t85,plain,
least_upper_bound(b,a) = b,
inference(step,[status(thm)],[t2,t69]) ).
cnf(t83,plain,
least_upper_bound(b,a) = b,
inference(orient,[status(thm)],[t85]) ).
cnf(t6,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t23,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(goal_0,negated_conjecture,
greatest_lower_bound(multiply(a,c),multiply(b,c)) != multiply(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(greatest_lower_bound(a,b),c) != multiply(a,c),
inference(rw,[status(thm)],[goal_0,t34]) ).
cnf(g0_1,plain,
multiply(greatest_lower_bound(a,least_upper_bound(b,a)),c) != multiply(a,c),
inference(rw,[status(thm)],[g0_0,t83]) ).
cnf(g0_2,plain,
multiply(greatest_lower_bound(a,least_upper_bound(a,b)),c) != multiply(a,c),
inference(rw,[status(thm)],[g0_1,t69]) ).
cnf(g0_3,plain,
multiply(a,c) != multiply(a,c),
inference(rw,[status(thm)],[g0_2,t23]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP156-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.56 % Computer : n009.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Wed Sep 23 13:53:14 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.29/1.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.29/1.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------