%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP166-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 01:25:29 PM UTC 2026
% Result : Unsatisfiable 4.83s 1.25s
% Output : CNFRefutation 4.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of clauses : 59 ( 59 unt; 0 nHn; 27 RR)
% Number of literals : 59 ( 58 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 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 : 57 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t6,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t59,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t7,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t21,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t8,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t80,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t83,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t21,t80]) ).
cnf(t114,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t83]) ).
cnf(t15,axiom,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t27,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t15]) ).
cnf(t17,axiom,
sFlat0 = multiply(a,b),
introduced(definition) ).
cnf(t39,plain,
multiply(a,b) = sFlat0,
inference(orient,[status(thm)],[t17]) ).
cnf(t44,plain,
multiply(a,least_upper_bound(b,X1)) = least_upper_bound(sFlat0,multiply(a,X1)),
inference(cp,[status(thm)],[t27,t39]) ).
cnf(t965,plain,
least_upper_bound(sFlat0,multiply(a,X1)) = multiply(a,least_upper_bound(b,X1)),
inference(orient,[status(thm)],[t44]) ).
cnf(t12,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)],[t12]) ).
cnf(t5,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t49,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t5]) ).
cnf(t58,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t24,t49]) ).
cnf(t4,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t19,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t1065,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t58,t19]) ).
cnf(t731,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t1065]) ).
cnf(t732,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t731,t49]) ).
cnf(t769,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t732]) ).
cnf(t737,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t731,t731]) ).
cnf(t805,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t737]) ).
cnf(t1066,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t769,t805]) ).
cnf(t814,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t1066]) ).
cnf(t815,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t814]) ).
cnf(t969,plain,
multiply(a,least_upper_bound(b,identity)) = least_upper_bound(sFlat0,a),
inference(cp,[status(thm)],[t965,t815]) ).
cnf(t1074,plain,
multiply(a,least_upper_bound(identity,b)) = least_upper_bound(sFlat0,a),
inference(step,[status(thm)],[t969,t80]) ).
cnf(t9,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t23,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t62,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)),
inference(cp,[status(thm)],[t23,t59]) ).
cnf(t96,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t62]) ).
cnf(t2,axiom,
greatest_lower_bound(b,identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t1011,plain,
greatest_lower_bound(identity,b) = identity,
inference(step,[status(thm)],[t2,t59]) ).
cnf(t78,plain,
greatest_lower_bound(identity,b) = identity,
inference(orient,[status(thm)],[t1011]) ).
cnf(t100,plain,
b = least_upper_bound(b,identity),
inference(cp,[status(thm)],[t96,t78]) ).
cnf(t1013,plain,
b = least_upper_bound(identity,b),
inference(step,[status(thm)],[t100,t80]) ).
cnf(t106,plain,
least_upper_bound(identity,b) = b,
inference(orient,[status(thm)],[t1013]) ).
cnf(t1075,plain,
multiply(a,b) = least_upper_bound(sFlat0,a),
inference(step,[status(thm)],[t1074,t106]) ).
cnf(t1076,plain,
sFlat0 = least_upper_bound(sFlat0,a),
inference(step,[status(thm)],[t1075,t39]) ).
cnf(t977,plain,
least_upper_bound(sFlat0,a) = sFlat0,
inference(orient,[status(thm)],[t1076]) ).
cnf(t985,plain,
a = greatest_lower_bound(a,sFlat0),
inference(cp,[status(thm)],[t114,t977]) ).
cnf(t1077,plain,
a = greatest_lower_bound(sFlat0,a),
inference(step,[status(thm)],[t985,t59]) ).
cnf(t18,axiom,
sFlat1 = greatest_lower_bound(a,multiply(a,b)),
introduced(definition) ).
cnf(t1008,plain,
sFlat1 = greatest_lower_bound(a,sFlat0),
inference(step,[status(thm)],[t18,t39]) ).
cnf(t1009,plain,
sFlat1 = greatest_lower_bound(sFlat0,a),
inference(step,[status(thm)],[t1008,t59]) ).
cnf(t73,plain,
greatest_lower_bound(sFlat0,a) = sFlat1,
inference(orient,[status(thm)],[t1009]) ).
cnf(t1078,plain,
a = sFlat1,
inference(step,[status(thm)],[t1077,t73]) ).
cnf(t987,plain,
a = sFlat1,
inference(orient,[status(thm)],[t1078]) ).
cnf(goal_0,negated_conjecture,
greatest_lower_bound(a,multiply(a,b)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
greatest_lower_bound(a,multiply(a,b)) != greatest_lower_bound(a,sFlat0),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
greatest_lower_bound(a,multiply(a,b)) != greatest_lower_bound(sFlat0,a),
inference(rw,[status(thm)],[g0_0,t59]) ).
cnf(g0_2,plain,
greatest_lower_bound(a,multiply(a,b)) != sFlat1,
inference(rw,[status(thm)],[g0_1]) ).
cnf(g0_3,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_2,t987]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP166-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 13:56:02 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.83/1.25 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.83/1.25 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------