%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP184-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 01:25:36 PM UTC 2026
% Result : Unsatisfiable 6.34s 1.57s
% Output : CNFRefutation 6.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 13
% Syntax : Number of clauses : 90 ( 90 unt; 0 nHn; 44 RR)
% Number of literals : 90 ( 89 equ; 12 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; 5 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t6,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t89,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t15,axiom,
sFlat0 = least_upper_bound(a,identity),
introduced(definition) ).
cnf(t1738,plain,
sFlat0 = least_upper_bound(identity,a),
inference(step,[status(thm)],[t15,t89]) ).
cnf(t103,plain,
least_upper_bound(identity,a) = sFlat0,
inference(orient,[status(thm)],[t1738]) ).
cnf(t4,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t70,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t16,axiom,
sFlat1 = greatest_lower_bound(a,identity),
introduced(definition) ).
cnf(t1737,plain,
sFlat1 = greatest_lower_bound(identity,a),
inference(step,[status(thm)],[t16,t70]) ).
cnf(t86,plain,
greatest_lower_bound(identity,a) = sFlat1,
inference(orient,[status(thm)],[t1737]) ).
cnf(t17,axiom,
sFlat2 = inverse(greatest_lower_bound(a,identity)),
introduced(definition) ).
cnf(t1739,plain,
sFlat2 = inverse(greatest_lower_bound(identity,a)),
inference(step,[status(thm)],[t17,t70]) ).
cnf(t1740,plain,
sFlat2 = inverse(sFlat1),
inference(step,[status(thm)],[t1739,t86]) ).
cnf(t106,plain,
inverse(sFlat1) = sFlat2,
inference(orient,[status(thm)],[t1740]) ).
cnf(t14,axiom,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t35,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t14]) ).
cnf(t2,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t20,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t36,plain,
multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t35,t20]) ).
cnf(t719,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(identity,X2),X1),
inference(orient,[status(thm)],[t36]) ).
cnf(t10,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t25,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(t3,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t50,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t3]) ).
cnf(t59,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t25,t50]) ).
cnf(t1771,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t59,t20]) ).
cnf(t690,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t1771]) ).
cnf(t11,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(t26,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
cnf(t694,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t690,t50]) ).
cnf(t800,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t694]) ).
cnf(t697,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t690,t690]) ).
cnf(t846,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t697]) ).
cnf(t1776,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t800,t846]) ).
cnf(t855,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t1776]) ).
cnf(t856,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t855]) ).
cnf(t861,plain,
multiply(X1,greatest_lower_bound(identity,X2)) = greatest_lower_bound(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t26,t856]) ).
cnf(t1308,plain,
greatest_lower_bound(X1,multiply(X1,X2)) = multiply(X1,greatest_lower_bound(identity,X2)),
inference(orient,[status(thm)],[t861]) ).
cnf(t12,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(t29,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(orient,[status(thm)],[t12]) ).
cnf(t30,plain,
multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t29,t20]) ).
cnf(t281,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(greatest_lower_bound(identity,X2),X1),
inference(orient,[status(thm)],[t30]) ).
cnf(t1309,plain,
multiply(X1,greatest_lower_bound(identity,X1)) = multiply(greatest_lower_bound(identity,X1),X1),
inference(cp,[status(thm)],[t1308,t281]) ).
cnf(t1439,plain,
multiply(greatest_lower_bound(identity,X1),X1) = multiply(X1,greatest_lower_bound(identity,X1)),
inference(orient,[status(thm)],[t1309]) ).
cnf(t1448,plain,
multiply(a,greatest_lower_bound(identity,a)) = multiply(sFlat1,a),
inference(cp,[status(thm)],[t1439,t86]) ).
cnf(t1812,plain,
multiply(a,sFlat1) = multiply(sFlat1,a),
inference(step,[status(thm)],[t1448,t86]) ).
cnf(t1467,plain,
multiply(a,sFlat1) = multiply(sFlat1,a),
inference(orient,[status(thm)],[t1812]) ).
cnf(t1481,plain,
multiply(a,multiply(sFlat1,X1)) = multiply(multiply(sFlat1,a),X1),
inference(cp,[status(thm)],[t25,t1467]) ).
cnf(t1827,plain,
multiply(a,multiply(sFlat1,X1)) = multiply(sFlat1,multiply(a,X1)),
inference(step,[status(thm)],[t1481,t25]) ).
cnf(t1676,plain,
multiply(a,multiply(sFlat1,X1)) = multiply(sFlat1,multiply(a,X1)),
inference(orient,[status(thm)],[t1827]) ).
cnf(t107,plain,
identity = multiply(sFlat2,sFlat1),
inference(cp,[status(thm)],[t50,t106]) ).
cnf(t114,plain,
multiply(sFlat2,sFlat1) = identity,
inference(orient,[status(thm)],[t107]) ).
cnf(t123,plain,
multiply(sFlat2,multiply(sFlat1,X1)) = multiply(identity,X1),
inference(cp,[status(thm)],[t25,t114]) ).
cnf(t1745,plain,
multiply(sFlat2,multiply(sFlat1,X1)) = X1,
inference(step,[status(thm)],[t123,t20]) ).
cnf(t154,plain,
multiply(sFlat2,multiply(sFlat1,X1)) = X1,
inference(orient,[status(thm)],[t1745]) ).
cnf(t693,plain,
multiply(sFlat1,X1) = multiply(inverse(sFlat2),X1),
inference(cp,[status(thm)],[t690,t154]) ).
cnf(t753,plain,
multiply(inverse(sFlat2),X1) = multiply(sFlat1,X1),
inference(orient,[status(thm)],[t693]) ).
cnf(t754,plain,
multiply(sFlat1,sFlat2) = identity,
inference(cp,[status(thm)],[t753,t50]) ).
cnf(t764,plain,
multiply(sFlat1,sFlat2) = identity,
inference(orient,[status(thm)],[t754]) ).
cnf(t1678,plain,
multiply(sFlat1,multiply(a,sFlat2)) = multiply(a,identity),
inference(cp,[status(thm)],[t1676,t764]) ).
cnf(t1828,plain,
multiply(sFlat1,multiply(a,sFlat2)) = a,
inference(step,[status(thm)],[t1678,t856]) ).
cnf(t1692,plain,
multiply(sFlat1,multiply(a,sFlat2)) = a,
inference(orient,[status(thm)],[t1828]) ).
cnf(t1695,plain,
multiply(a,sFlat2) = multiply(inverse(sFlat1),a),
inference(cp,[status(thm)],[t690,t1692]) ).
cnf(t1829,plain,
multiply(a,sFlat2) = multiply(sFlat2,a),
inference(step,[status(thm)],[t1695,t106]) ).
cnf(t1707,plain,
multiply(a,sFlat2) = multiply(sFlat2,a),
inference(orient,[status(thm)],[t1829]) ).
cnf(t1710,plain,
multiply(least_upper_bound(identity,a),sFlat2) = least_upper_bound(sFlat2,multiply(sFlat2,a)),
inference(cp,[status(thm)],[t719,t1707]) ).
cnf(t1830,plain,
multiply(sFlat0,sFlat2) = least_upper_bound(sFlat2,multiply(sFlat2,a)),
inference(step,[status(thm)],[t1710,t103]) ).
cnf(t13,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(t28,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
cnf(t766,plain,
sFlat2 = multiply(inverse(sFlat1),identity),
inference(cp,[status(thm)],[t690,t764]) ).
cnf(t1773,plain,
sFlat2 = multiply(sFlat2,identity),
inference(step,[status(thm)],[t766,t106]) ).
cnf(t789,plain,
multiply(sFlat2,identity) = sFlat2,
inference(orient,[status(thm)],[t1773]) ).
cnf(t796,plain,
multiply(sFlat2,least_upper_bound(identity,X1)) = least_upper_bound(sFlat2,multiply(sFlat2,X1)),
inference(cp,[status(thm)],[t28,t789]) ).
cnf(t1261,plain,
least_upper_bound(sFlat2,multiply(sFlat2,X1)) = multiply(sFlat2,least_upper_bound(identity,X1)),
inference(orient,[status(thm)],[t796]) ).
cnf(t1831,plain,
multiply(sFlat0,sFlat2) = multiply(sFlat2,least_upper_bound(identity,a)),
inference(step,[status(thm)],[t1830,t1261]) ).
cnf(t1832,plain,
multiply(sFlat0,sFlat2) = multiply(sFlat2,sFlat0),
inference(step,[status(thm)],[t1831,t103]) ).
cnf(t1721,plain,
multiply(sFlat2,sFlat0) = multiply(sFlat0,sFlat2),
inference(orient,[status(thm)],[t1832]) ).
cnf(goal_0,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(rw,[status(thm)],[goal_0,t89]) ).
cnf(g0_1,plain,
multiply(sFlat0,inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(rw,[status(thm)],[g0_0,t103]) ).
cnf(g0_2,plain,
multiply(sFlat0,inverse(greatest_lower_bound(identity,a))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(rw,[status(thm)],[g0_1,t70]) ).
cnf(g0_3,plain,
multiply(sFlat0,inverse(sFlat1)) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(rw,[status(thm)],[g0_2,t86]) ).
cnf(g0_4,plain,
multiply(sFlat0,sFlat2) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(rw,[status(thm)],[g0_3,t106]) ).
cnf(g0_5,plain,
multiply(sFlat0,sFlat2) != multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(a,identity)),
inference(rw,[status(thm)],[g0_4,t70]) ).
cnf(g0_6,plain,
multiply(sFlat0,sFlat2) != multiply(inverse(sFlat1),least_upper_bound(a,identity)),
inference(rw,[status(thm)],[g0_5,t86]) ).
cnf(g0_7,plain,
multiply(sFlat0,sFlat2) != multiply(sFlat2,least_upper_bound(a,identity)),
inference(rw,[status(thm)],[g0_6,t106]) ).
cnf(g0_8,plain,
multiply(sFlat0,sFlat2) != multiply(sFlat2,least_upper_bound(identity,a)),
inference(rw,[status(thm)],[g0_7,t89]) ).
cnf(g0_9,plain,
multiply(sFlat0,sFlat2) != multiply(sFlat2,sFlat0),
inference(rw,[status(thm)],[g0_8,t103]) ).
cnf(g0_10,plain,
multiply(sFlat0,sFlat2) != multiply(sFlat0,sFlat2),
inference(rw,[status(thm)],[g0_9,t1721]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP184-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 14:02:59 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.34/1.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.34/1.57 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------