%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP169-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 01:25:30 PM UTC 2026
% Result : Unsatisfiable 6.90s 1.51s
% Output : CNFRefutation 6.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of clauses : 56 ( 56 unt; 0 nHn; 17 RR)
% Number of literals : 56 ( 55 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t4,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t46,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t14,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(t24,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t14]) ).
cnf(t11,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t21,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
cnf(t3,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t36,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t3]) ).
cnf(t45,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t21,t36]) ).
cnf(t2,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t16,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t3874,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t45,t16]) ).
cnf(t109,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t3874]) ).
cnf(t110,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t109,t36]) ).
cnf(t128,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t110]) ).
cnf(t113,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t109,t109]) ).
cnf(t147,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t113]) ).
cnf(t3875,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t128,t147]) ).
cnf(t154,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t3875]) ).
cnf(t155,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t154]) ).
cnf(t157,plain,
multiply(X1,least_upper_bound(identity,X2)) = least_upper_bound(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t24,t155]) ).
cnf(t206,plain,
least_upper_bound(X1,multiply(X1,X2)) = multiply(X1,least_upper_bound(identity,X2)),
inference(orient,[status(thm)],[t157]) ).
cnf(t156,plain,
inverse(inverse(X1)) = multiply(X1,identity),
inference(cp,[status(thm)],[t155,t147]) ).
cnf(t3876,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t156,t155]) ).
cnf(t161,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t3876]) ).
cnf(t162,plain,
X1 = multiply(X2,multiply(inverse(X2),X1)),
inference(cp,[status(thm)],[t109,t161]) ).
cnf(t175,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t162]) ).
cnf(t210,plain,
multiply(X1,least_upper_bound(identity,multiply(inverse(X1),X2))) = least_upper_bound(X1,X2),
inference(cp,[status(thm)],[t206,t175]) ).
cnf(t3819,plain,
multiply(X1,least_upper_bound(identity,multiply(inverse(X1),X2))) = least_upper_bound(X1,X2),
inference(orient,[status(thm)],[t210]) ).
cnf(t15,axiom,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t31,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t15]) ).
cnf(t37,plain,
multiply(least_upper_bound(inverse(X1),X2),X1) = least_upper_bound(identity,multiply(X2,X1)),
inference(cp,[status(thm)],[t31,t36]) ).
cnf(t689,plain,
multiply(least_upper_bound(inverse(X1),X2),X1) = least_upper_bound(identity,multiply(X2,X1)),
inference(orient,[status(thm)],[t37]) ).
cnf(t7,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t20,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t8,axiom,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t3871,plain,
greatest_lower_bound(inverse(b),inverse(a)) = inverse(a),
inference(step,[status(thm)],[t8,t46]) ).
cnf(t60,plain,
greatest_lower_bound(inverse(b),inverse(a)) = inverse(a),
inference(orient,[status(thm)],[t3871]) ).
cnf(t62,plain,
inverse(b) = least_upper_bound(inverse(b),inverse(a)),
inference(cp,[status(thm)],[t20,t60]) ).
cnf(t87,plain,
least_upper_bound(inverse(b),inverse(a)) = inverse(b),
inference(orient,[status(thm)],[t62]) ).
cnf(t690,plain,
least_upper_bound(identity,multiply(inverse(a),b)) = multiply(inverse(b),b),
inference(cp,[status(thm)],[t689,t87]) ).
cnf(t3889,plain,
least_upper_bound(identity,multiply(inverse(a),b)) = identity,
inference(step,[status(thm)],[t690,t36]) ).
cnf(t717,plain,
least_upper_bound(identity,multiply(inverse(a),b)) = identity,
inference(orient,[status(thm)],[t3889]) ).
cnf(t3823,plain,
least_upper_bound(a,b) = multiply(a,identity),
inference(cp,[status(thm)],[t3819,t717]) ).
cnf(t6,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t63,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t4005,plain,
least_upper_bound(b,a) = multiply(a,identity),
inference(step,[status(thm)],[t3823,t63]) ).
cnf(t4006,plain,
least_upper_bound(b,a) = a,
inference(step,[status(thm)],[t4005,t155]) ).
cnf(t3862,plain,
least_upper_bound(b,a) = a,
inference(orient,[status(thm)],[t4006]) ).
cnf(t5,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t18,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(goal_0,negated_conjecture,
greatest_lower_bound(a,b) != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
greatest_lower_bound(a,b) != greatest_lower_bound(b,a),
inference(rw,[status(thm)],[goal_0,t46]) ).
cnf(g0_1,plain,
greatest_lower_bound(a,b) != greatest_lower_bound(b,least_upper_bound(b,a)),
inference(rw,[status(thm)],[g0_0,t3862]) ).
cnf(g0_2,plain,
greatest_lower_bound(a,b) != b,
inference(rw,[status(thm)],[g0_1,t18]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP169-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 13:57:03 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.90/1.51 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.90/1.51 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------