%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP186-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 01:25:37 PM UTC 2026
% Result : Unsatisfiable 5.62s 1.40s
% Output : CNFRefutation 5.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 4 RR)
% Number of literals : 31 ( 30 equ; 3 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 : 44 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t13,axiom,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t23,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
cnf(t3,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t35,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t3]) ).
cnf(t10,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t20,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(t44,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t20,t35]) ).
cnf(t2,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t15,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t772,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t44,t15]) ).
cnf(t101,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t772]) ).
cnf(t102,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t101,t35]) ).
cnf(t120,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t102]) ).
cnf(t105,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t101,t101]) ).
cnf(t139,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t105]) ).
cnf(t773,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t120,t139]) ).
cnf(t146,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t773]) ).
cnf(t147,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t146]) ).
cnf(t148,plain,
inverse(inverse(X1)) = multiply(X1,identity),
inference(cp,[status(thm)],[t147,t139]) ).
cnf(t774,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t148,t147]) ).
cnf(t153,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t774]) ).
cnf(t155,plain,
identity = multiply(X1,inverse(X1)),
inference(cp,[status(thm)],[t35,t153]) ).
cnf(t156,plain,
multiply(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t155]) ).
cnf(t162,plain,
multiply(X1,least_upper_bound(inverse(X1),X2)) = least_upper_bound(identity,multiply(X1,X2)),
inference(cp,[status(thm)],[t23,t156]) ).
cnf(t744,plain,
multiply(X1,least_upper_bound(inverse(X1),X2)) = least_upper_bound(identity,multiply(X1,X2)),
inference(orient,[status(thm)],[t162]) ).
cnf(t6,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t59,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(goal_0,negated_conjecture,
multiply(a,least_upper_bound(inverse(a),b)) != least_upper_bound(multiply(a,b),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
least_upper_bound(identity,multiply(a,b)) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[goal_0,t744]) ).
cnf(g0_1,plain,
least_upper_bound(identity,multiply(a,b)) != least_upper_bound(identity,multiply(a,b)),
inference(rw,[status(thm)],[g0_0,t59]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP186-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 14:04:04 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.62/1.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.62/1.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------