%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP169-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 : Fri Sep 25 01:25:30 PM UTC 2026
% Result : Unsatisfiable 3.37s 6.13s
% Output : CNFRefutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 11
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 19 RR)
% Number of literals : 60 ( 59 equ; 6 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 : 76 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t6,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t46,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t12,axiom,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t24,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t12]) ).
cnf(t11,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
cnf(t16,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t3839,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t45,t16]) ).
cnf(t108,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t3839]) ).
cnf(t109,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t108,t36]) ).
cnf(t127,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t109]) ).
cnf(t112,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t108,t108]) ).
cnf(t146,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t112]) ).
cnf(t3840,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t127,t146]) ).
cnf(t153,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t3840]) ).
cnf(t154,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t153]) ).
cnf(t156,plain,
multiply(X1,greatest_lower_bound(identity,X2)) = greatest_lower_bound(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t24,t154]) ).
cnf(t205,plain,
greatest_lower_bound(X1,multiply(X1,X2)) = multiply(X1,greatest_lower_bound(identity,X2)),
inference(orient,[status(thm)],[t156]) ).
cnf(t155,plain,
inverse(inverse(X1)) = multiply(X1,identity),
inference(cp,[status(thm)],[t154,t146]) ).
cnf(t3841,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t155,t154]) ).
cnf(t160,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t3841]) ).
cnf(t161,plain,
X1 = multiply(X2,multiply(inverse(X2),X1)),
inference(cp,[status(thm)],[t108,t160]) ).
cnf(t174,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t161]) ).
cnf(t209,plain,
multiply(X1,greatest_lower_bound(identity,multiply(inverse(X1),X2))) = greatest_lower_bound(X1,X2),
inference(cp,[status(thm)],[t205,t174]) ).
cnf(t3784,plain,
multiply(X1,greatest_lower_bound(identity,multiply(inverse(X1),X2))) = greatest_lower_bound(X1,X2),
inference(orient,[status(thm)],[t209]) ).
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(t31,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(orient,[status(thm)],[t13]) ).
cnf(t37,plain,
multiply(greatest_lower_bound(inverse(X1),X2),X1) = greatest_lower_bound(identity,multiply(X2,X1)),
inference(cp,[status(thm)],[t31,t36]) ).
cnf(t688,plain,
multiply(greatest_lower_bound(inverse(X1),X2),X1) = greatest_lower_bound(identity,multiply(X2,X1)),
inference(orient,[status(thm)],[t37]) ).
cnf(t5,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t20,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t49,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t20,t46]) ).
cnf(t76,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t49]) ).
cnf(t8,axiom,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t3835,plain,
least_upper_bound(inverse(b),inverse(a)) = inverse(b),
inference(step,[status(thm)],[t8,t46]) ).
cnf(t60,plain,
least_upper_bound(inverse(b),inverse(a)) = inverse(b),
inference(orient,[status(thm)],[t3835]) ).
cnf(t79,plain,
inverse(a) = greatest_lower_bound(inverse(a),inverse(b)),
inference(cp,[status(thm)],[t76,t60]) ).
cnf(t4,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t62,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t3836,plain,
inverse(a) = greatest_lower_bound(inverse(b),inverse(a)),
inference(step,[status(thm)],[t79,t62]) ).
cnf(t87,plain,
greatest_lower_bound(inverse(b),inverse(a)) = inverse(a),
inference(orient,[status(thm)],[t3836]) ).
cnf(t689,plain,
greatest_lower_bound(identity,multiply(inverse(a),b)) = multiply(inverse(a),b),
inference(cp,[status(thm)],[t688,t87]) ).
cnf(t716,plain,
greatest_lower_bound(identity,multiply(inverse(a),b)) = multiply(inverse(a),b),
inference(orient,[status(thm)],[t689]) ).
cnf(t3788,plain,
greatest_lower_bound(a,b) = multiply(a,multiply(inverse(a),b)),
inference(cp,[status(thm)],[t3784,t716]) ).
cnf(t3970,plain,
greatest_lower_bound(b,a) = multiply(a,multiply(inverse(a),b)),
inference(step,[status(thm)],[t3788,t62]) ).
cnf(t3971,plain,
greatest_lower_bound(b,a) = b,
inference(step,[status(thm)],[t3970,t174]) ).
cnf(t3827,plain,
greatest_lower_bound(b,a) = b,
inference(orient,[status(thm)],[t3971]) ).
cnf(t7,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t18,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(goal_0,negated_conjecture,
least_upper_bound(a,b) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
least_upper_bound(a,b) != least_upper_bound(b,a),
inference(rw,[status(thm)],[goal_0,t46]) ).
cnf(g0_1,plain,
least_upper_bound(a,b) != least_upper_bound(greatest_lower_bound(b,a),a),
inference(rw,[status(thm)],[g0_0,t3827]) ).
cnf(g0_2,plain,
least_upper_bound(a,b) != least_upper_bound(greatest_lower_bound(a,b),a),
inference(rw,[status(thm)],[g0_1,t62]) ).
cnf(g0_3,plain,
least_upper_bound(a,b) != least_upper_bound(a,greatest_lower_bound(a,b)),
inference(rw,[status(thm)],[g0_2,t46]) ).
cnf(g0_4,plain,
least_upper_bound(a,b) != a,
inference(rw,[status(thm)],[g0_3,t18]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP169-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/5.37 % Computer : n003.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Wed Sep 23 13:58:41 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.37/6.13 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.37/6.13 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------