%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP190-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 01:25:38 PM UTC 2026
% Result : Unsatisfiable 5.85s 1.27s
% Output : CNFRefutation 5.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of clauses : 67 ( 67 unt; 0 nHn; 30 RR)
% Number of literals : 67 ( 66 equ; 9 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 64 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t17,axiom,
sFlat1 = inverse(b),
introduced(definition) ).
cnf(t86,plain,
inverse(b) = sFlat1,
inference(orient,[status(thm)],[t17]) ).
cnf(t11,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t24,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
cnf(t4,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t39,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t4]) ).
cnf(t48,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t24,t39]) ).
cnf(t3,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t19,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t929,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t48,t19]) ).
cnf(t409,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t929]) ).
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(t27,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t12]) ).
cnf(t87,plain,
identity = multiply(sFlat1,b),
inference(cp,[status(thm)],[t39,t86]) ).
cnf(t100,plain,
multiply(sFlat1,b) = identity,
inference(orient,[status(thm)],[t87]) ).
cnf(t105,plain,
multiply(sFlat1,greatest_lower_bound(b,X1)) = greatest_lower_bound(identity,multiply(sFlat1,X1)),
inference(cp,[status(thm)],[t27,t100]) ).
cnf(t872,plain,
greatest_lower_bound(identity,multiply(sFlat1,X1)) = multiply(sFlat1,greatest_lower_bound(b,X1)),
inference(orient,[status(thm)],[t105]) ).
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(t16,axiom,
sFlat0 = inverse(a),
introduced(definition) ).
cnf(t83,plain,
inverse(a) = sFlat0,
inference(orient,[status(thm)],[t16]) ).
cnf(t84,plain,
identity = multiply(sFlat0,a),
inference(cp,[status(thm)],[t39,t83]) ).
cnf(t90,plain,
multiply(sFlat0,a) = identity,
inference(orient,[status(thm)],[t84]) ).
cnf(t91,plain,
multiply(greatest_lower_bound(sFlat0,X1),a) = greatest_lower_bound(identity,multiply(X1,a)),
inference(cp,[status(thm)],[t34,t90]) ).
cnf(t724,plain,
greatest_lower_bound(identity,multiply(X1,a)) = multiply(greatest_lower_bound(sFlat0,X1),a),
inference(orient,[status(thm)],[t91]) ).
cnf(t873,plain,
multiply(sFlat1,greatest_lower_bound(b,a)) = multiply(greatest_lower_bound(sFlat0,sFlat1),a),
inference(cp,[status(thm)],[t872,t724]) ).
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(t2,axiom,
least_upper_bound(a,b) = a,
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(t49,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t902,plain,
least_upper_bound(b,a) = a,
inference(step,[status(thm)],[t2,t49]) ).
cnf(t66,plain,
least_upper_bound(b,a) = a,
inference(orient,[status(thm)],[t902]) ).
cnf(t68,plain,
b = greatest_lower_bound(b,a),
inference(cp,[status(thm)],[t23,t66]) ).
cnf(t88,plain,
greatest_lower_bound(b,a) = b,
inference(orient,[status(thm)],[t68]) ).
cnf(t948,plain,
multiply(sFlat1,b) = multiply(greatest_lower_bound(sFlat0,sFlat1),a),
inference(step,[status(thm)],[t873,t88]) ).
cnf(t949,plain,
identity = multiply(greatest_lower_bound(sFlat0,sFlat1),a),
inference(step,[status(thm)],[t948,t100]) ).
cnf(t881,plain,
multiply(greatest_lower_bound(sFlat0,sFlat1),a) = identity,
inference(orient,[status(thm)],[t949]) ).
cnf(t883,plain,
a = multiply(inverse(greatest_lower_bound(sFlat0,sFlat1)),identity),
inference(cp,[status(thm)],[t409,t881]) ).
cnf(t416,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t409,t39]) ).
cnf(t546,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t416]) ).
cnf(t419,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t409,t409]) ).
cnf(t587,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t419]) ).
cnf(t934,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t546,t587]) ).
cnf(t595,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t934]) ).
cnf(t596,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t595]) ).
cnf(t950,plain,
a = inverse(greatest_lower_bound(sFlat0,sFlat1)),
inference(step,[status(thm)],[t883,t596]) ).
cnf(t896,plain,
inverse(greatest_lower_bound(sFlat0,sFlat1)) = a,
inference(orient,[status(thm)],[t950]) ).
cnf(t5,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t69,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t597,plain,
inverse(inverse(X1)) = multiply(X1,identity),
inference(cp,[status(thm)],[t596,t587]) ).
cnf(t937,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t597,t596]) ).
cnf(t606,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t937]) ).
cnf(t8,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t21,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t72,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)),
inference(cp,[status(thm)],[t21,t69]) ).
cnf(t123,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t72]) ).
cnf(goal_0,negated_conjecture,
least_upper_bound(inverse(a),inverse(b)) != inverse(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
sFlat1 != inverse(b),
inference(rw,[status(thm)],[goal_0,t86]) ).
cnf(g0_1,plain,
sFlat1 != least_upper_bound(inverse(inverse(greatest_lower_bound(sFlat0,sFlat1))),inverse(b)),
inference(rw,[status(thm)],[g0_0,t896]) ).
cnf(g0_2,plain,
sFlat1 != least_upper_bound(inverse(inverse(greatest_lower_bound(sFlat1,sFlat0))),inverse(b)),
inference(rw,[status(thm)],[g0_1,t69]) ).
cnf(g0_3,plain,
sFlat1 != least_upper_bound(inverse(b),inverse(inverse(greatest_lower_bound(sFlat1,sFlat0)))),
inference(rw,[status(thm)],[g0_2,t49]) ).
cnf(g0_4,plain,
sFlat1 != least_upper_bound(inverse(b),greatest_lower_bound(sFlat1,sFlat0)),
inference(rw,[status(thm)],[g0_3,t606]) ).
cnf(g0_5,plain,
sFlat1 != least_upper_bound(inverse(b),greatest_lower_bound(sFlat0,sFlat1)),
inference(rw,[status(thm)],[g0_4,t69]) ).
cnf(g0_6,plain,
sFlat1 != least_upper_bound(sFlat1,greatest_lower_bound(sFlat0,sFlat1)),
inference(rw,[status(thm)],[g0_5,t86]) ).
cnf(g0_7,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_6,t123]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP190-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 14:08:08 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.85/1.27 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.85/1.27 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------