%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP191-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 01:25:39 PM UTC 2026
% Result : Unsatisfiable 5.36s 1.48s
% Output : CNFRefutation 5.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of clauses : 62 ( 62 unt; 0 nHn; 33 RR)
% Number of literals : 62 ( 61 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t5,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t49,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t5]) ).
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(t896,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t48,t19]) ).
cnf(t408,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t896]) ).
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(t28,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(t85,plain,
inverse(a) = sFlat0,
inference(orient,[status(thm)],[t16]) ).
cnf(t86,plain,
identity = multiply(sFlat0,a),
inference(cp,[status(thm)],[t39,t85]) ).
cnf(t97,plain,
multiply(sFlat0,a) = identity,
inference(orient,[status(thm)],[t86]) ).
cnf(t100,plain,
multiply(greatest_lower_bound(sFlat0,X1),a) = greatest_lower_bound(identity,multiply(X1,a)),
inference(cp,[status(thm)],[t28,t97]) ).
cnf(t841,plain,
greatest_lower_bound(identity,multiply(X1,a)) = multiply(greatest_lower_bound(sFlat0,X1),a),
inference(orient,[status(thm)],[t100]) ).
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(t25,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t12]) ).
cnf(t17,axiom,
sFlat1 = inverse(b),
introduced(definition) ).
cnf(t82,plain,
inverse(b) = sFlat1,
inference(orient,[status(thm)],[t17]) ).
cnf(t83,plain,
identity = multiply(sFlat1,b),
inference(cp,[status(thm)],[t39,t82]) ).
cnf(t87,plain,
multiply(sFlat1,b) = identity,
inference(orient,[status(thm)],[t83]) ).
cnf(t94,plain,
multiply(sFlat1,greatest_lower_bound(b,X1)) = greatest_lower_bound(identity,multiply(sFlat1,X1)),
inference(cp,[status(thm)],[t25,t87]) ).
cnf(t788,plain,
greatest_lower_bound(identity,multiply(sFlat1,X1)) = multiply(sFlat1,greatest_lower_bound(b,X1)),
inference(orient,[status(thm)],[t94]) ).
cnf(t842,plain,
multiply(greatest_lower_bound(sFlat0,sFlat1),a) = multiply(sFlat1,greatest_lower_bound(b,a)),
inference(cp,[status(thm)],[t841,t788]) ).
cnf(t18,axiom,
sFlat2 = greatest_lower_bound(inverse(a),inverse(b)),
introduced(definition) ).
cnf(t865,plain,
sFlat2 = greatest_lower_bound(inverse(b),inverse(a)),
inference(step,[status(thm)],[t18,t49]) ).
cnf(t63,plain,
greatest_lower_bound(inverse(b),inverse(a)) = sFlat2,
inference(orient,[status(thm)],[t865]) ).
cnf(t867,plain,
greatest_lower_bound(sFlat1,inverse(a)) = sFlat2,
inference(step,[status(thm)],[t63,t82]) ).
cnf(t84,plain,
greatest_lower_bound(sFlat1,inverse(a)) = sFlat2,
inference(rw,[status(thm)],[t867]) ).
cnf(t868,plain,
greatest_lower_bound(sFlat1,sFlat0) = sFlat2,
inference(step,[status(thm)],[t84,t85]) ).
cnf(t869,plain,
greatest_lower_bound(sFlat0,sFlat1) = sFlat2,
inference(step,[status(thm)],[t868,t49]) ).
cnf(t107,plain,
greatest_lower_bound(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t869]) ).
cnf(t916,plain,
multiply(sFlat2,a) = multiply(sFlat1,greatest_lower_bound(b,a)),
inference(step,[status(thm)],[t842,t107]) ).
cnf(t1,axiom,
greatest_lower_bound(a,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t866,plain,
greatest_lower_bound(b,a) = b,
inference(step,[status(thm)],[t1,t49]) ).
cnf(t66,plain,
greatest_lower_bound(b,a) = b,
inference(orient,[status(thm)],[t866]) ).
cnf(t917,plain,
multiply(sFlat2,a) = multiply(sFlat1,b),
inference(step,[status(thm)],[t916,t66]) ).
cnf(t918,plain,
multiply(sFlat2,a) = identity,
inference(step,[status(thm)],[t917,t87]) ).
cnf(t846,plain,
multiply(sFlat2,a) = identity,
inference(orient,[status(thm)],[t918]) ).
cnf(t848,plain,
a = multiply(inverse(sFlat2),identity),
inference(cp,[status(thm)],[t408,t846]) ).
cnf(t415,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t408,t39]) ).
cnf(t545,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t415]) ).
cnf(t418,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t408,t408]) ).
cnf(t586,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t418]) ).
cnf(t901,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t545,t586]) ).
cnf(t594,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t901]) ).
cnf(t595,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t594]) ).
cnf(t919,plain,
a = inverse(sFlat2),
inference(step,[status(thm)],[t848,t595]) ).
cnf(t859,plain,
inverse(sFlat2) = a,
inference(orient,[status(thm)],[t919]) ).
cnf(t596,plain,
inverse(inverse(X1)) = multiply(X1,identity),
inference(cp,[status(thm)],[t595,t586]) ).
cnf(t904,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t596,t595]) ).
cnf(t605,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t904]) ).
cnf(goal_0,negated_conjecture,
greatest_lower_bound(inverse(a),inverse(b)) != inverse(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
greatest_lower_bound(inverse(b),inverse(a)) != inverse(a),
inference(rw,[status(thm)],[goal_0,t49]) ).
cnf(g0_1,plain,
sFlat2 != inverse(a),
inference(rw,[status(thm)],[g0_0]) ).
cnf(g0_2,plain,
sFlat2 != inverse(inverse(sFlat2)),
inference(rw,[status(thm)],[g0_1,t859]) ).
cnf(g0_3,plain,
sFlat2 != sFlat2,
inference(rw,[status(thm)],[g0_2,t605]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP191-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.37 % Computer : n001.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Wed Sep 23 14:10:50 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.36/1.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.36/1.48 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------