%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP489-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 01:27:10 PM UTC 2026
% Result : Unsatisfiable 6.21s 1.31s
% Output : CNFRefutation 6.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 99
% Number of leaves : 5
% Syntax : Number of clauses : 185 ( 185 unt; 0 nHn; 8 RR)
% Number of literals : 185 ( 184 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 290 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t2,axiom,
double_divide(double_divide(X1,X2),identity) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t0,axiom,
double_divide(X1,identity) = inverse(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t7,plain,
double_divide(X1,identity) = inverse(X1),
inference(orient,[status(thm)],[t0]) ).
cnf(t1315,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(step,[status(thm)],[t2,t7]) ).
cnf(t10,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(orient,[status(thm)],[t1315]) ).
cnf(t3,axiom,
double_divide(X1,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X1,identity),double_divide(X2,X3))),X2),identity)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t4,plain,
double_divide(X1,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X1,identity),double_divide(X2,X3))),X2),identity)) = X3,
inference(orient,[status(thm)],[t3]) ).
cnf(t1313,plain,
double_divide(X1,inverse(double_divide(double_divide(identity,double_divide(double_divide(X1,identity),double_divide(X2,X3))),X2))) = X3,
inference(step,[status(thm)],[t4,t7]) ).
cnf(t1314,plain,
double_divide(X1,inverse(double_divide(double_divide(identity,double_divide(inverse(X1),double_divide(X2,X3))),X2))) = X3,
inference(step,[status(thm)],[t1313,t7]) ).
cnf(t8,plain,
double_divide(X1,inverse(double_divide(double_divide(identity,double_divide(inverse(X1),double_divide(X2,X3))),X2))) = X3,
inference(rw,[status(thm)],[t1314]) ).
cnf(t1316,plain,
double_divide(X1,multiply(X2,double_divide(identity,double_divide(inverse(X1),double_divide(X2,X3))))) = X3,
inference(step,[status(thm)],[t8,t10]) ).
cnf(t69,plain,
double_divide(X1,multiply(X2,double_divide(identity,double_divide(inverse(X1),double_divide(X2,X3))))) = X3,
inference(orient,[status(thm)],[t1316]) ).
cnf(t11,plain,
multiply(identity,X1) = inverse(inverse(X1)),
inference(cp,[status(thm)],[t10,t7]) ).
cnf(t14,plain,
inverse(inverse(X1)) = multiply(identity,X1),
inference(orient,[status(thm)],[t11]) ).
cnf(t1,axiom,
double_divide(X1,inverse(X1)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t9,plain,
double_divide(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t1]) ).
cnf(t75,plain,
inverse(X1) = double_divide(X2,multiply(X1,double_divide(identity,double_divide(inverse(X2),identity)))),
inference(cp,[status(thm)],[t69,t9]) ).
cnf(t1317,plain,
inverse(X1) = double_divide(X2,multiply(X1,double_divide(identity,inverse(inverse(X2))))),
inference(step,[status(thm)],[t75,t7]) ).
cnf(t1318,plain,
inverse(X1) = double_divide(X2,multiply(X1,double_divide(identity,multiply(identity,X2)))),
inference(step,[status(thm)],[t1317,t14]) ).
cnf(t86,plain,
double_divide(X1,multiply(X2,double_divide(identity,multiply(identity,X1)))) = inverse(X2),
inference(orient,[status(thm)],[t1318]) ).
cnf(t12,plain,
multiply(inverse(X1),X1) = inverse(identity),
inference(cp,[status(thm)],[t10,t9]) ).
cnf(t18,plain,
multiply(inverse(X1),X1) = inverse(identity),
inference(orient,[status(thm)],[t12]) ).
cnf(t19,plain,
inverse(identity) = multiply(multiply(X1,X2),double_divide(X2,X1)),
inference(cp,[status(thm)],[t18,t10]) ).
cnf(t38,plain,
multiply(multiply(X1,X2),double_divide(X2,X1)) = inverse(identity),
inference(orient,[status(thm)],[t19]) ).
cnf(t87,plain,
inverse(multiply(multiply(identity,X1),identity)) = double_divide(X1,inverse(identity)),
inference(cp,[status(thm)],[t86,t38]) ).
cnf(t98,plain,
inverse(multiply(multiply(identity,X1),identity)) = double_divide(X1,inverse(identity)),
inference(orient,[status(thm)],[t87]) ).
cnf(t104,plain,
multiply(identity,multiply(multiply(identity,X1),identity)) = inverse(double_divide(X1,inverse(identity))),
inference(cp,[status(thm)],[t14,t98]) ).
cnf(t1319,plain,
multiply(identity,multiply(multiply(identity,X1),identity)) = multiply(inverse(identity),X1),
inference(step,[status(thm)],[t104,t10]) ).
cnf(t112,plain,
multiply(identity,multiply(multiply(identity,X1),identity)) = multiply(inverse(identity),X1),
inference(orient,[status(thm)],[t1319]) ).
cnf(t15,plain,
multiply(identity,double_divide(X1,X2)) = inverse(multiply(X2,X1)),
inference(cp,[status(thm)],[t14,t10]) ).
cnf(t29,plain,
multiply(identity,double_divide(X1,X2)) = inverse(multiply(X2,X1)),
inference(orient,[status(thm)],[t15]) ).
cnf(t89,plain,
inverse(identity) = double_divide(X1,inverse(multiply(multiply(identity,X1),identity))),
inference(cp,[status(thm)],[t86,t29]) ).
cnf(t1320,plain,
inverse(identity) = double_divide(X1,double_divide(X1,inverse(identity))),
inference(step,[status(thm)],[t89,t98]) ).
cnf(t117,plain,
double_divide(X1,double_divide(X1,inverse(identity))) = inverse(identity),
inference(orient,[status(thm)],[t1320]) ).
cnf(t122,plain,
inverse(identity) = double_divide(X1,multiply(inverse(X1),double_divide(identity,inverse(identity)))),
inference(cp,[status(thm)],[t69,t117]) ).
cnf(t1321,plain,
inverse(identity) = double_divide(X1,multiply(inverse(X1),identity)),
inference(step,[status(thm)],[t122,t9]) ).
cnf(t124,plain,
double_divide(X1,multiply(inverse(X1),identity)) = inverse(identity),
inference(orient,[status(thm)],[t1321]) ).
cnf(t125,plain,
inverse(identity) = double_divide(identity,inverse(identity)),
inference(cp,[status(thm)],[t124,t18]) ).
cnf(t1322,plain,
inverse(identity) = identity,
inference(step,[status(thm)],[t125,t9]) ).
cnf(t135,plain,
inverse(identity) = identity,
inference(orient,[status(thm)],[t1322]) ).
cnf(t1339,plain,
multiply(identity,multiply(multiply(identity,X1),identity)) = multiply(identity,X1),
inference(step,[status(thm)],[t112,t135]) ).
cnf(t150,plain,
multiply(identity,multiply(multiply(identity,X1),identity)) = multiply(identity,X1),
inference(orient,[status(thm)],[t1339]) ).
cnf(t1323,plain,
multiply(inverse(X1),X1) = identity,
inference(step,[status(thm)],[t18,t135]) ).
cnf(t136,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t1323]) ).
cnf(t156,plain,
identity = multiply(identity,identity),
inference(cp,[status(thm)],[t136,t135]) ).
cnf(t166,plain,
multiply(identity,identity) = identity,
inference(orient,[status(thm)],[t156]) ).
cnf(t167,plain,
inverse(X1) = double_divide(identity,multiply(X1,double_divide(identity,identity))),
inference(cp,[status(thm)],[t86,t166]) ).
cnf(t1343,plain,
inverse(X1) = double_divide(identity,multiply(X1,inverse(identity))),
inference(step,[status(thm)],[t167,t7]) ).
cnf(t1344,plain,
inverse(X1) = double_divide(identity,multiply(X1,identity)),
inference(step,[status(thm)],[t1343,t135]) ).
cnf(t168,plain,
double_divide(identity,multiply(X1,identity)) = inverse(X1),
inference(orient,[status(thm)],[t1344]) ).
cnf(t172,plain,
multiply(multiply(X1,identity),identity) = inverse(inverse(X1)),
inference(cp,[status(thm)],[t10,t168]) ).
cnf(t1345,plain,
multiply(multiply(X1,identity),identity) = multiply(identity,X1),
inference(step,[status(thm)],[t172,t14]) ).
cnf(t174,plain,
multiply(multiply(X1,identity),identity) = multiply(identity,X1),
inference(orient,[status(thm)],[t1345]) ).
cnf(t176,plain,
inverse(multiply(X1,identity)) = double_divide(identity,multiply(identity,X1)),
inference(cp,[status(thm)],[t168,t174]) ).
cnf(t177,plain,
double_divide(identity,multiply(identity,X1)) = inverse(multiply(X1,identity)),
inference(orient,[status(thm)],[t176]) ).
cnf(t183,plain,
inverse(multiply(multiply(identity,X1),identity)) = multiply(identity,inverse(multiply(X1,identity))),
inference(cp,[status(thm)],[t29,t177]) ).
cnf(t1335,plain,
inverse(multiply(multiply(identity,X1),identity)) = double_divide(X1,identity),
inference(step,[status(thm)],[t98,t135]) ).
cnf(t1336,plain,
inverse(multiply(multiply(identity,X1),identity)) = inverse(X1),
inference(step,[status(thm)],[t1335,t7]) ).
cnf(t148,plain,
inverse(multiply(multiply(identity,X1),identity)) = inverse(X1),
inference(orient,[status(thm)],[t1336]) ).
cnf(t1347,plain,
inverse(X1) = multiply(identity,inverse(multiply(X1,identity))),
inference(step,[status(thm)],[t183,t148]) ).
cnf(t187,plain,
multiply(identity,inverse(multiply(X1,identity))) = inverse(X1),
inference(orient,[status(thm)],[t1347]) ).
cnf(t197,plain,
multiply(identity,inverse(multiply(X1,identity))) = multiply(identity,multiply(inverse(X1),identity)),
inference(cp,[status(thm)],[t150,t187]) ).
cnf(t1348,plain,
inverse(X1) = multiply(identity,multiply(inverse(X1),identity)),
inference(step,[status(thm)],[t197,t187]) ).
cnf(t209,plain,
multiply(identity,multiply(inverse(X1),identity)) = inverse(X1),
inference(orient,[status(thm)],[t1348]) ).
cnf(t210,plain,
inverse(double_divide(X1,X2)) = multiply(identity,multiply(multiply(X2,X1),identity)),
inference(cp,[status(thm)],[t209,t10]) ).
cnf(t1381,plain,
multiply(X2,X1) = multiply(identity,multiply(multiply(X2,X1),identity)),
inference(step,[status(thm)],[t210,t10]) ).
cnf(t295,plain,
multiply(identity,multiply(multiply(X1,X2),identity)) = multiply(X1,X2),
inference(orient,[status(thm)],[t1381]) ).
cnf(t296,plain,
multiply(X1,identity) = multiply(identity,multiply(identity,X1)),
inference(cp,[status(thm)],[t295,t174]) ).
cnf(t211,plain,
inverse(multiply(multiply(inverse(X1),identity),identity)) = double_divide(identity,inverse(X1)),
inference(cp,[status(thm)],[t177,t209]) ).
cnf(t1349,plain,
inverse(multiply(identity,inverse(X1))) = double_divide(identity,inverse(X1)),
inference(step,[status(thm)],[t211,t174]) ).
cnf(t17,plain,
multiply(identity,inverse(X1)) = inverse(multiply(identity,X1)),
inference(cp,[status(thm)],[t14,t14]) ).
cnf(t21,plain,
inverse(multiply(identity,X1)) = multiply(identity,inverse(X1)),
inference(orient,[status(thm)],[t17]) ).
cnf(t1350,plain,
multiply(identity,inverse(inverse(X1))) = double_divide(identity,inverse(X1)),
inference(step,[status(thm)],[t1349,t21]) ).
cnf(t1351,plain,
multiply(identity,multiply(identity,X1)) = double_divide(identity,inverse(X1)),
inference(step,[status(thm)],[t1350,t14]) ).
cnf(t216,plain,
multiply(identity,multiply(identity,X1)) = double_divide(identity,inverse(X1)),
inference(orient,[status(thm)],[t1351]) ).
cnf(t1382,plain,
multiply(X1,identity) = double_divide(identity,inverse(X1)),
inference(step,[status(thm)],[t296,t216]) ).
cnf(t302,plain,
double_divide(identity,inverse(X1)) = multiply(X1,identity),
inference(orient,[status(thm)],[t1382]) ).
cnf(t305,plain,
multiply(double_divide(X1,X2),identity) = double_divide(identity,multiply(X2,X1)),
inference(cp,[status(thm)],[t302,t10]) ).
cnf(t309,plain,
double_divide(identity,multiply(X1,X2)) = multiply(double_divide(X2,X1),identity),
inference(orient,[status(thm)],[t305]) ).
cnf(t1346,plain,
double_divide(X1,multiply(X2,inverse(multiply(X1,identity)))) = inverse(X2),
inference(step,[status(thm)],[t86,t177]) ).
cnf(t186,plain,
double_divide(X1,multiply(X2,inverse(multiply(X1,identity)))) = inverse(X2),
inference(rw,[status(thm)],[t1346]) ).
cnf(t224,plain,
multiply(identity,inverse(multiply(identity,X1))) = inverse(double_divide(identity,inverse(X1))),
inference(cp,[status(thm)],[t21,t216]) ).
cnf(t1362,plain,
multiply(identity,multiply(identity,inverse(X1))) = inverse(double_divide(identity,inverse(X1))),
inference(step,[status(thm)],[t224,t21]) ).
cnf(t1363,plain,
double_divide(identity,inverse(inverse(X1))) = inverse(double_divide(identity,inverse(X1))),
inference(step,[status(thm)],[t1362,t216]) ).
cnf(t1364,plain,
double_divide(identity,multiply(identity,X1)) = inverse(double_divide(identity,inverse(X1))),
inference(step,[status(thm)],[t1363,t14]) ).
cnf(t1365,plain,
inverse(multiply(X1,identity)) = inverse(double_divide(identity,inverse(X1))),
inference(step,[status(thm)],[t1364,t177]) ).
cnf(t1366,plain,
inverse(multiply(X1,identity)) = multiply(inverse(X1),identity),
inference(step,[status(thm)],[t1365,t10]) ).
cnf(t233,plain,
inverse(multiply(X1,identity)) = multiply(inverse(X1),identity),
inference(orient,[status(thm)],[t1366]) ).
cnf(t1415,plain,
double_divide(X1,multiply(X2,multiply(inverse(X1),identity))) = inverse(X2),
inference(step,[status(thm)],[t186,t233]) ).
cnf(t463,plain,
double_divide(X1,multiply(X2,multiply(inverse(X1),identity))) = inverse(X2),
inference(orient,[status(thm)],[t1415]) ).
cnf(t133,plain,
multiply(multiply(inverse(X1),identity),X1) = inverse(inverse(identity)),
inference(cp,[status(thm)],[t10,t124]) ).
cnf(t1372,plain,
multiply(multiply(inverse(X1),identity),X1) = multiply(identity,identity),
inference(step,[status(thm)],[t133,t14]) ).
cnf(t1373,plain,
multiply(multiply(inverse(X1),identity),X1) = identity,
inference(step,[status(thm)],[t1372,t166]) ).
cnf(t262,plain,
multiply(multiply(inverse(X1),identity),X1) = identity,
inference(orient,[status(thm)],[t1373]) ).
cnf(t464,plain,
inverse(multiply(inverse(multiply(inverse(X1),identity)),identity)) = double_divide(X1,identity),
inference(cp,[status(thm)],[t463,t262]) ).
cnf(t1416,plain,
multiply(inverse(inverse(multiply(inverse(X1),identity))),identity) = double_divide(X1,identity),
inference(step,[status(thm)],[t464,t233]) ).
cnf(t1417,plain,
multiply(multiply(identity,multiply(inverse(X1),identity)),identity) = double_divide(X1,identity),
inference(step,[status(thm)],[t1416,t14]) ).
cnf(t1418,plain,
multiply(inverse(X1),identity) = double_divide(X1,identity),
inference(step,[status(thm)],[t1417,t209]) ).
cnf(t1419,plain,
multiply(inverse(X1),identity) = inverse(X1),
inference(step,[status(thm)],[t1418,t7]) ).
cnf(t476,plain,
multiply(inverse(X1),identity) = inverse(X1),
inference(orient,[status(thm)],[t1419]) ).
cnf(t481,plain,
multiply(double_divide(identity,inverse(X1)),identity) = double_divide(identity,inverse(X1)),
inference(cp,[status(thm)],[t309,t476]) ).
cnf(t219,plain,
inverse(multiply(multiply(identity,X1),identity)) = double_divide(identity,double_divide(identity,inverse(X1))),
inference(cp,[status(thm)],[t177,t216]) ).
cnf(t1371,plain,
inverse(X1) = double_divide(identity,double_divide(identity,inverse(X1))),
inference(step,[status(thm)],[t219,t148]) ).
cnf(t246,plain,
double_divide(identity,double_divide(identity,inverse(X1))) = inverse(X1),
inference(orient,[status(thm)],[t1371]) ).
cnf(t250,plain,
multiply(double_divide(identity,inverse(X1)),identity) = inverse(inverse(X1)),
inference(cp,[status(thm)],[t10,t246]) ).
cnf(t1375,plain,
multiply(double_divide(identity,inverse(X1)),identity) = multiply(identity,X1),
inference(step,[status(thm)],[t250,t14]) ).
cnf(t274,plain,
multiply(double_divide(identity,inverse(X1)),identity) = multiply(identity,X1),
inference(orient,[status(thm)],[t1375]) ).
cnf(t1436,plain,
multiply(identity,X1) = double_divide(identity,inverse(X1)),
inference(step,[status(thm)],[t481,t274]) ).
cnf(t1437,plain,
multiply(identity,X1) = multiply(X1,identity),
inference(step,[status(thm)],[t1436,t302]) ).
cnf(t508,plain,
multiply(identity,X1) = multiply(X1,identity),
inference(orient,[status(thm)],[t1437]) ).
cnf(t1438,plain,
double_divide(identity,multiply(X1,X2)) = multiply(identity,double_divide(X2,X1)),
inference(step,[status(thm)],[t309,t508]) ).
cnf(t1439,plain,
double_divide(identity,multiply(X1,X2)) = inverse(multiply(X1,X2)),
inference(step,[status(thm)],[t1438,t29]) ).
cnf(t509,plain,
double_divide(identity,multiply(X1,X2)) = inverse(multiply(X1,X2)),
inference(orient,[status(thm)],[t1439]) ).
cnf(t70,plain,
X1 = double_divide(X2,inverse(multiply(double_divide(inverse(X2),double_divide(identity,X1)),identity))),
inference(cp,[status(thm)],[t69,t29]) ).
cnf(t1420,plain,
inverse(multiply(X1,identity)) = inverse(X1),
inference(step,[status(thm)],[t233,t476]) ).
cnf(t477,plain,
inverse(multiply(X1,identity)) = inverse(X1),
inference(orient,[status(thm)],[t1420]) ).
cnf(t1468,plain,
X1 = double_divide(X2,inverse(double_divide(inverse(X2),double_divide(identity,X1)))),
inference(step,[status(thm)],[t70,t477]) ).
cnf(t1469,plain,
X1 = double_divide(X2,multiply(double_divide(identity,X1),inverse(X2))),
inference(step,[status(thm)],[t1468,t10]) ).
cnf(t1427,plain,
double_divide(X1,multiply(X2,inverse(X1))) = inverse(X2),
inference(step,[status(thm)],[t463,t476]) ).
cnf(t496,plain,
double_divide(X1,multiply(X2,inverse(X1))) = inverse(X2),
inference(rw,[status(thm)],[t1427]) ).
cnf(t563,plain,
double_divide(X1,multiply(X2,inverse(X1))) = inverse(X2),
inference(orient,[status(thm)],[t496]) ).
cnf(t1470,plain,
X1 = inverse(double_divide(identity,X1)),
inference(step,[status(thm)],[t1469,t563]) ).
cnf(t1471,plain,
X1 = multiply(X1,identity),
inference(step,[status(thm)],[t1470,t10]) ).
cnf(t912,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t1471]) ).
cnf(t923,plain,
inverse(multiply(X1,identity)) = double_divide(identity,X1),
inference(cp,[status(thm)],[t509,t912]) ).
cnf(t1496,plain,
inverse(X1) = double_divide(identity,X1),
inference(step,[status(thm)],[t923,t477]) ).
cnf(t955,plain,
double_divide(identity,X1) = inverse(X1),
inference(orient,[status(thm)],[t1496]) ).
cnf(t1497,plain,
double_divide(X1,multiply(X2,inverse(double_divide(inverse(X1),double_divide(X2,X3))))) = X3,
inference(step,[status(thm)],[t69,t955]) ).
cnf(t1498,plain,
double_divide(X1,multiply(X2,multiply(double_divide(X2,X3),inverse(X1)))) = X3,
inference(step,[status(thm)],[t1497,t10]) ).
cnf(t957,plain,
double_divide(X1,multiply(X2,multiply(double_divide(X2,X3),inverse(X1)))) = X3,
inference(rw,[status(thm)],[t1498]) ).
cnf(t999,plain,
double_divide(X1,multiply(X2,multiply(double_divide(X2,X3),inverse(X1)))) = X3,
inference(orient,[status(thm)],[t957]) ).
cnf(t1000,plain,
X1 = inverse(multiply(X2,multiply(double_divide(X2,X1),inverse(identity)))),
inference(cp,[status(thm)],[t999,t955]) ).
cnf(t571,plain,
multiply(multiply(X1,inverse(X2)),X2) = inverse(inverse(X1)),
inference(cp,[status(thm)],[t10,t563]) ).
cnf(t1448,plain,
multiply(multiply(X1,inverse(X2)),X2) = multiply(identity,X1),
inference(step,[status(thm)],[t571,t14]) ).
cnf(t573,plain,
multiply(multiply(X1,inverse(X2)),X2) = multiply(identity,X1),
inference(orient,[status(thm)],[t1448]) ).
cnf(t582,plain,
inverse(multiply(X1,inverse(inverse(X2)))) = double_divide(X2,multiply(identity,X1)),
inference(cp,[status(thm)],[t563,t573]) ).
cnf(t1455,plain,
inverse(multiply(X1,multiply(identity,X2))) = double_divide(X2,multiply(identity,X1)),
inference(step,[status(thm)],[t582,t14]) ).
cnf(t632,plain,
inverse(multiply(X1,multiply(identity,X2))) = double_divide(X2,multiply(identity,X1)),
inference(orient,[status(thm)],[t1455]) ).
cnf(t581,plain,
multiply(identity,multiply(X1,inverse(inverse(X2)))) = multiply(multiply(identity,X1),X2),
inference(cp,[status(thm)],[t573,t573]) ).
cnf(t482,plain,
multiply(identity,inverse(X1)) = multiply(inverse(X1),identity),
inference(cp,[status(thm)],[t174,t476]) ).
cnf(t1428,plain,
multiply(identity,inverse(X1)) = inverse(X1),
inference(step,[status(thm)],[t482,t476]) ).
cnf(t497,plain,
multiply(identity,inverse(X1)) = inverse(X1),
inference(orient,[status(thm)],[t1428]) ).
cnf(t500,plain,
inverse(double_divide(X1,X2)) = multiply(identity,multiply(X2,X1)),
inference(cp,[status(thm)],[t497,t10]) ).
cnf(t1442,plain,
multiply(X2,X1) = multiply(identity,multiply(X2,X1)),
inference(step,[status(thm)],[t500,t10]) ).
cnf(t533,plain,
multiply(identity,multiply(X1,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t1442]) ).
cnf(t1449,plain,
multiply(X1,inverse(inverse(X2))) = multiply(multiply(identity,X1),X2),
inference(step,[status(thm)],[t581,t533]) ).
cnf(t1450,plain,
multiply(X1,multiply(identity,X2)) = multiply(multiply(identity,X1),X2),
inference(step,[status(thm)],[t1449,t14]) ).
cnf(t583,plain,
multiply(multiply(identity,X1),X2) = multiply(X1,multiply(identity,X2)),
inference(orient,[status(thm)],[t1450]) ).
cnf(t588,plain,
multiply(inverse(X1),multiply(identity,X2)) = multiply(inverse(X1),X2),
inference(cp,[status(thm)],[t583,t497]) ).
cnf(t618,plain,
multiply(inverse(X1),multiply(identity,X2)) = multiply(inverse(X1),X2),
inference(orient,[status(thm)],[t588]) ).
cnf(t635,plain,
double_divide(X1,multiply(identity,inverse(X2))) = inverse(multiply(inverse(X2),X1)),
inference(cp,[status(thm)],[t632,t618]) ).
cnf(t1456,plain,
double_divide(X1,inverse(X2)) = inverse(multiply(inverse(X2),X1)),
inference(step,[status(thm)],[t635,t497]) ).
cnf(t656,plain,
inverse(multiply(inverse(X1),X2)) = double_divide(X2,inverse(X1)),
inference(orient,[status(thm)],[t1456]) ).
cnf(t663,plain,
double_divide(X1,inverse(double_divide(X2,X3))) = inverse(multiply(multiply(X3,X2),X1)),
inference(cp,[status(thm)],[t656,t10]) ).
cnf(t1459,plain,
double_divide(X1,multiply(X3,X2)) = inverse(multiply(multiply(X3,X2),X1)),
inference(step,[status(thm)],[t663,t10]) ).
cnf(t726,plain,
inverse(multiply(multiply(X1,X2),X3)) = double_divide(X3,multiply(X1,X2)),
inference(orient,[status(thm)],[t1459]) ).
cnf(t929,plain,
double_divide(X1,multiply(X2,identity)) = inverse(multiply(X2,X1)),
inference(cp,[status(thm)],[t726,t912]) ).
cnf(t1499,plain,
double_divide(X1,X2) = inverse(multiply(X2,X1)),
inference(step,[status(thm)],[t929,t912]) ).
cnf(t960,plain,
inverse(multiply(X1,X2)) = double_divide(X2,X1),
inference(orient,[status(thm)],[t1499]) ).
cnf(t1501,plain,
X1 = double_divide(multiply(double_divide(X2,X1),inverse(identity)),X2),
inference(step,[status(thm)],[t1000,t960]) ).
cnf(t1502,plain,
X1 = double_divide(multiply(double_divide(X2,X1),identity),X2),
inference(step,[status(thm)],[t1501,t135]) ).
cnf(t1503,plain,
X1 = double_divide(double_divide(X2,X1),X2),
inference(step,[status(thm)],[t1502,t912]) ).
cnf(t1021,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(orient,[status(thm)],[t1503]) ).
cnf(t1027,plain,
X1 = double_divide(X2,double_divide(X1,X2)),
inference(cp,[status(thm)],[t1021,t1021]) ).
cnf(t1038,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(orient,[status(thm)],[t1027]) ).
cnf(t1048,plain,
multiply(double_divide(X1,X2),X2) = inverse(X1),
inference(cp,[status(thm)],[t10,t1038]) ).
cnf(t1081,plain,
multiply(double_divide(X1,X2),X2) = inverse(X1),
inference(orient,[status(thm)],[t1048]) ).
cnf(t1032,plain,
multiply(X1,double_divide(X1,X2)) = inverse(X2),
inference(cp,[status(thm)],[t10,t1021]) ).
cnf(t1072,plain,
multiply(X1,double_divide(X1,X2)) = inverse(X2),
inference(orient,[status(thm)],[t1032]) ).
cnf(t1022,plain,
multiply(X1,inverse(X2)) = double_divide(inverse(X1),X2),
inference(cp,[status(thm)],[t1021,t563]) ).
cnf(t1054,plain,
double_divide(inverse(X1),X2) = multiply(X1,inverse(X2)),
inference(orient,[status(thm)],[t1022]) ).
cnf(t1059,plain,
multiply(double_divide(X1,X2),inverse(X3)) = double_divide(multiply(X2,X1),X3),
inference(cp,[status(thm)],[t1054,t10]) ).
cnf(t1139,plain,
multiply(double_divide(X1,X2),inverse(X3)) = double_divide(multiply(X2,X1),X3),
inference(orient,[status(thm)],[t1059]) ).
cnf(t1508,plain,
double_divide(X1,multiply(X2,double_divide(multiply(X3,X2),X1))) = X3,
inference(step,[status(thm)],[t999,t1139]) ).
cnf(t1142,plain,
double_divide(X1,multiply(X2,double_divide(multiply(X3,X2),X1))) = X3,
inference(rw,[status(thm)],[t1508]) ).
cnf(t1210,plain,
double_divide(X1,multiply(X2,double_divide(multiply(X3,X2),X1))) = X3,
inference(orient,[status(thm)],[t1142]) ).
cnf(t1233,plain,
inverse(multiply(X1,double_divide(multiply(X2,X1),X3))) = multiply(X3,X2),
inference(cp,[status(thm)],[t1072,t1210]) ).
cnf(t1509,plain,
double_divide(double_divide(multiply(X2,X1),X3),X1) = multiply(X3,X2),
inference(step,[status(thm)],[t1233,t960]) ).
cnf(t1248,plain,
double_divide(double_divide(multiply(X1,X2),X3),X2) = multiply(X3,X1),
inference(orient,[status(thm)],[t1509]) ).
cnf(t1268,plain,
inverse(double_divide(multiply(X1,X2),X3)) = multiply(multiply(X3,X1),X2),
inference(cp,[status(thm)],[t1081,t1248]) ).
cnf(t1510,plain,
multiply(X3,multiply(X1,X2)) = multiply(multiply(X3,X1),X2),
inference(step,[status(thm)],[t1268,t10]) ).
cnf(t1285,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t1510]) ).
cnf(goal_0,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(rw,[status(thm)],[goal_0,t1285]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP489-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n018.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 14:55:48 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.21/1.31 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.21/1.31 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------