%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP123-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 : Tue Sep 29 10:12:39 AM UTC 2026
% Result : Satisfiable 4.80s 1.67s
% Output : Saturation 6.24s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(u46,axiom,
~ product(e_4,e_4,e_1) ).
cnf(u50,axiom,
~ product(e_3,e_4,e_1) ).
cnf(u55,axiom,
product(e_2,e_4,e_1) ).
cnf(u58,axiom,
~ product(e_1,e_4,e_1) ).
cnf(u64,axiom,
product(e_4,e_3,e_1) ).
cnf(u67,axiom,
~ product(e_3,e_3,e_1) ).
cnf(u71,axiom,
~ product(e_2,e_3,e_1) ).
cnf(u75,axiom,
~ product(e_1,e_3,e_1) ).
cnf(u80,axiom,
~ product(e_4,e_2,e_1) ).
cnf(u85,axiom,
product(e_3,e_2,e_1) ).
cnf(u88,axiom,
~ product(e_2,e_2,e_1) ).
cnf(u92,axiom,
~ product(e_1,e_2,e_1) ).
cnf(u200,axiom,
~ product(e_4,e_4,e_2) ).
cnf(u205,axiom,
product(e_3,e_4,e_2) ).
cnf(u208,axiom,
~ product(e_2,e_4,e_2) ).
cnf(u212,axiom,
~ product(e_1,e_4,e_2) ).
cnf(u219,axiom,
product(e_4,e_1,e_2) ).
cnf(u222,axiom,
~ product(e_3,e_1,e_2) ).
cnf(u226,axiom,
~ product(e_2,e_1,e_2) ).
cnf(u230,axiom,
~ product(e_1,e_1,e_2) ).
cnf(u235,negated_conjecture,
~ product(e_4,e_3,e_2) ).
cnf(u239,negated_conjecture,
~ product(e_3,e_3,e_2) ).
cnf(u243,negated_conjecture,
~ product(e_2,e_3,e_2) ).
cnf(u249,axiom,
product(e_1,e_3,e_2) ).
cnf(u639,axiom,
product(e_4,e_2,e_3) ).
cnf(u646,axiom,
~ product(e_2,e_2,e_3) ).
cnf(u650,axiom,
~ product(e_1,e_2,e_3) ).
cnf(u656,negated_conjecture,
~ product(e_4,e_4,e_3) ).
cnf(u660,negated_conjecture,
~ product(e_3,e_4,e_3) ).
cnf(u664,negated_conjecture,
~ product(e_2,e_4,e_3) ).
cnf(u669,negated_conjecture,
~ product(e_4,e_1,e_3) ).
cnf(u673,negated_conjecture,
~ product(e_3,e_1,e_3) ).
cnf(u677,negated_conjecture,
~ product(e_1,e_1,e_3) ).
cnf(u685,axiom,
product(e_1,e_4,e_3) ).
cnf(u839,negated_conjecture,
product(e_2,e_1,e_3) ).
cnf(u886,axiom,
~ product(e_4,e_2,e_4) ).
cnf(u890,axiom,
~ product(e_3,e_2,e_4) ).
cnf(u894,axiom,
~ product(e_2,e_2,e_4) ).
cnf(u899,axiom,
product(e_1,e_2,e_4) ).
cnf(u904,negated_conjecture,
~ product(e_4,e_3,e_4) ).
cnf(u908,negated_conjecture,
~ product(e_3,e_3,e_4) ).
cnf(u913,negated_conjecture,
product(e_2,e_3,e_4) ).
cnf(u917,negated_conjecture,
~ product(e_4,e_1,e_4) ).
cnf(u921,negated_conjecture,
~ product(e_2,e_1,e_4) ).
cnf(u925,negated_conjecture,
~ product(e_1,e_1,e_4) ).
cnf(u935,axiom,
product(e_3,e_1,e_4) ).
cnf(u939,axiom,
~ product(e_1,e_3,e_4) ).
cnf(u1343,axiom,
( ~ product(e_1,X0,e_2)
| equalish(X0,e_3) ) ).
cnf(u1481,negated_conjecture,
~ product(e_2,e_3,e_3) ).
cnf(u454,axiom,
( ~ group_element(X0)
| product(X0,e_4,e_1)
| product(X0,e_4,e_2)
| product(X0,e_4,e_3)
| product(X0,e_4,e_4) ) ).
cnf(element_1,axiom,
group_element(e_1) ).
cnf(u1196,negated_conjecture,
( ~ product(X0,e_1,e_2)
| ~ product(X0,X0,e_3)
| equalish(e_1,X0) ) ).
cnf(u184,axiom,
( ~ group_element(X0)
| product(X0,e_1,e_1)
| product(X0,e_2,e_1)
| product(X0,e_3,e_1)
| product(X0,e_4,e_1) ) ).
cnf(u1469,negated_conjecture,
( ~ product(e_4,e_2,X0)
| ~ product(e_1,X1,X2)
| ~ product(X2,X1,X0)
| equalish(X1,e_2) ) ).
cnf(u1278,axiom,
( ~ product(e_3,X0,e_1)
| equalish(X0,e_2) ) ).
cnf(product_left_cancellation,axiom,
( ~ product(X3,X1,X2)
| ~ product(X0,X1,X2)
| equalish(X0,X3) ) ).
cnf(u1501,axiom,
( ~ product(e_3,X0,e_4)
| equalish(X0,e_1) ) ).
cnf(u37,axiom,
( ~ group_element(X0)
| product(e_1,X0,e_2)
| product(e_2,X0,e_2)
| product(e_3,X0,e_2)
| product(e_4,X0,e_2) ) ).
cnf(u453,axiom,
( ~ group_element(X0)
| product(X0,e_3,e_1)
| product(X0,e_3,e_2)
| product(X0,e_3,e_3)
| product(X0,e_3,e_4) ) ).
cnf(u1395,axiom,
( ~ product(X0,e_4,e_3)
| equalish(X0,e_1) ) ).
cnf(u1468,negated_conjecture,
( ~ product(e_4,e_2,X0)
| ~ product(e_1,X1,X2)
| ~ product(X2,X1,X0)
| equalish(X2,e_4) ) ).
cnf(u1320,axiom,
( ~ product(e_4,e_1,X0)
| equalish(X0,e_2) ) ).
cnf(u1482,negated_conjecture,
( ~ product(e_1,X0,X1)
| ~ product(X1,X0,e_3)
| equalish(X0,e_2) ) ).
cnf(u1235,negated_conjecture,
( ~ product(e_2,e_2,X0)
| ~ product(e_1,e_4,X0) ) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2) ).
cnf(u452,axiom,
( ~ group_element(X0)
| product(X0,e_2,e_1)
| product(X0,e_2,e_2)
| product(X0,e_2,e_3)
| product(X0,e_2,e_4) ) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1) ).
cnf(u1367,negated_conjecture,
( ~ product(e_4,X1,X2)
| ~ product(e_3,e_2,X0)
| ~ product(X2,X1,X0)
| equalish(X1,e_2) ) ).
cnf(u1511,negated_conjecture,
~ product(e_1,e_2,e_2) ).
cnf(qg1_2,negated_conjecture,
( ~ product(X5,X4,X3)
| ~ product(X3,X4,X2)
| ~ product(X5,X1,X0)
| ~ product(X0,X1,X2)
| equalish(X1,X4) ) ).
cnf(u1282,negated_conjecture,
( ~ product(X0,e_2,e_3)
| ~ product(X0,X0,e_1)
| equalish(e_2,X0) ) ).
cnf(u1354,negated_conjecture,
( ~ product(e_1,X0,X1)
| ~ product(X1,X0,e_4)
| equalish(X0,e_3) ) ).
cnf(u1297,axiom,
( ~ product(e_3,X0,e_2)
| equalish(X0,e_4) ) ).
cnf(u1364,axiom,
( ~ product(e_4,X0,e_3)
| equalish(X0,e_2) ) ).
cnf(u1277,axiom,
( ~ product(e_3,e_2,X0)
| equalish(X0,e_1) ) ).
cnf(u1193,negated_conjecture,
( ~ product(X0,e_1,e_3)
| equalish(X0,e_2) ) ).
cnf(u1191,negated_conjecture,
( ~ product(e_2,e_1,X0)
| equalish(X0,e_3) ) ).
cnf(u1302,negated_conjecture,
( ~ product(X0,e_4,e_3)
| ~ product(X0,X0,e_2)
| equalish(e_3,X0) ) ).
cnf(u1205,negated_conjecture,
( ~ product(X0,e_3,e_2)
| ~ product(X0,X0,e_4)
| equalish(e_3,X0) ) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2) ).
cnf(u1467,axiom,
( ~ product(X0,e_2,e_4)
| equalish(X0,e_1) ) ).
cnf(row_surjectivity,axiom,
( ~ group_element(X1)
| ~ group_element(X0)
| product(e_1,X0,X1)
| product(e_2,X0,X1)
| product(e_3,X0,X1)
| product(e_4,X0,X1) ) ).
cnf(u1204,negated_conjecture,
( ~ product(e_4,e_3,X0)
| ~ product(e_2,X1,X2)
| ~ product(X2,X1,X0)
| equalish(X1,e_3) ) ).
cnf(u32,axiom,
( ~ product(X0,X1,X0)
| equalish(X1,X0) ) ).
cnf(u1491,negated_conjecture,
~ product(e_1,e_4,e_4) ).
cnf(u1381,negated_conjecture,
( ~ product(e_4,e_4,X0)
| ~ product(e_3,e_2,X0) ) ).
cnf(u1300,negated_conjecture,
( ~ product(e_3,X1,X2)
| ~ product(e_2,e_4,X0)
| ~ product(X2,X1,X0)
| equalish(X1,e_4) ) ).
cnf(u1200,negated_conjecture,
( ~ product(e_2,e_3,X0)
| equalish(X0,e_4) ) ).
cnf(u1246,negated_conjecture,
( ~ product(e_2,X0,X1)
| ~ product(X1,X0,e_1)
| equalish(X1,e_4) ) ).
cnf(u1366,negated_conjecture,
( ~ product(e_4,X1,X2)
| ~ product(e_3,e_2,X0)
| ~ product(X2,X1,X0)
| equalish(X2,e_3) ) ).
cnf(u1503,negated_conjecture,
( ~ product(e_4,e_1,X0)
| ~ product(e_3,X1,X2)
| ~ product(X2,X1,X0)
| equalish(X2,e_4) ) ).
cnf(element_3,axiom,
group_element(e_3) ).
cnf(u1324,negated_conjecture,
( ~ product(e_4,X1,X2)
| ~ product(e_2,e_1,X0)
| ~ product(X2,X1,X0)
| equalish(X1,e_1) ) ).
cnf(u1402,negated_conjecture,
~ product(e_3,e_4,e_4) ).
cnf(u1252,negated_conjecture,
( ~ product(X0,e_3,e_4)
| ~ product(X0,X0,e_1)
| equalish(e_3,X0) ) ).
cnf(u1363,axiom,
( ~ product(e_4,e_2,X0)
| equalish(X0,e_3) ) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3) ).
cnf(u36,axiom,
( ~ group_element(X0)
| product(e_1,X0,e_1)
| product(e_2,X0,e_1)
| product(e_3,X0,e_1)
| product(e_4,X0,e_1) ) ).
cnf(u1506,negated_conjecture,
( ~ product(X0,e_1,e_3)
| ~ product(X0,X0,e_4)
| equalish(e_3,X0) ) ).
cnf(u1334,negated_conjecture,
( ~ product(e_4,e_4,X0)
| ~ product(e_2,e_1,X0) ) ).
cnf(u31,axiom,
equalish(X0,X0) ).
cnf(u1397,negated_conjecture,
( ~ product(e_3,e_4,X0)
| ~ product(e_1,X1,X2)
| ~ product(X2,X1,X0)
| equalish(X1,e_4) ) ).
cnf(u34,axiom,
( ~ product(X0,X1,X1)
| equalish(X0,X1) ) ).
cnf(u1375,negated_conjecture,
~ product(e_2,e_1,e_1) ).
cnf(u1407,negated_conjecture,
( ~ product(e_1,X0,X1)
| ~ product(X1,X0,e_2)
| equalish(X1,e_3) ) ).
cnf(u1237,negated_conjecture,
( ~ product(e_3,e_1,X0)
| ~ product(e_1,e_4,X0) ) ).
cnf(u1202,negated_conjecture,
( ~ product(X0,e_3,e_4)
| equalish(X0,e_2) ) ).
cnf(u1372,negated_conjecture,
( ~ product(e_3,e_2,X0)
| ~ product(e_2,e_1,X0) ) ).
cnf(u1321,axiom,
( ~ product(e_4,X0,e_2)
| equalish(X0,e_1) ) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4) ).
cnf(u1411,negated_conjecture,
( ~ product(e_1,X0,X1)
| ~ product(X1,X0,e_2)
| equalish(X0,e_4) ) ).
cnf(product_total_function1,axiom,
( ~ group_element(X1)
| ~ group_element(X0)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3)
| product(X0,X1,e_4) ) ).
cnf(u1398,negated_conjecture,
( ~ product(X0,e_4,e_1)
| ~ product(X0,X0,e_3)
| equalish(e_4,X0) ) ).
cnf(u1296,axiom,
( ~ product(e_3,e_4,X0)
| equalish(X0,e_2) ) ).
cnf(u38,axiom,
( ~ group_element(X0)
| product(e_1,X0,e_3)
| product(e_2,X0,e_3)
| product(e_3,X0,e_3)
| product(e_4,X0,e_3) ) ).
cnf(u1224,axiom,
( ~ product(e_2,X0,e_1)
| equalish(X0,e_4) ) ).
cnf(u1528,negated_conjecture,
( ~ product(e_3,X0,X1)
| ~ product(X1,X0,e_2)
| equalish(X0,e_1) ) ).
cnf(u1325,negated_conjecture,
( ~ product(X0,e_1,e_4)
| ~ product(X0,X0,e_2)
| equalish(e_1,X0) ) ).
cnf(u1287,negated_conjecture,
( ~ product(e_3,e_3,X0)
| ~ product(e_1,e_2,X0) ) ).
cnf(u1393,axiom,
( ~ product(e_1,e_4,X0)
| equalish(X0,e_3) ) ).
cnf(u1310,negated_conjecture,
( ~ product(e_3,e_3,X0)
| ~ product(e_2,e_4,X0) ) ).
cnf(u1322,axiom,
( ~ product(X0,e_1,e_2)
| equalish(X0,e_4) ) ).
cnf(u1348,negated_conjecture,
( ~ product(X0,e_3,e_1)
| ~ product(X0,X0,e_2)
| equalish(e_1,X0) ) ).
cnf(u1283,negated_conjecture,
( ~ product(X0,e_2,e_3)
| ~ product(X0,X0,e_1)
| equalish(e_3,X0) ) ).
cnf(u1245,negated_conjecture,
( ~ product(e_2,X0,X1)
| ~ product(X1,X0,e_1)
| equalish(X0,e_3) ) ).
cnf(u1250,negated_conjecture,
( ~ product(e_4,X1,X2)
| ~ product(e_1,e_3,X0)
| ~ product(X2,X1,X0)
| equalish(X2,e_1) ) ).
cnf(u1369,negated_conjecture,
( ~ product(X0,e_2,e_4)
| ~ product(X0,X0,e_3)
| equalish(e_4,X0) ) ).
cnf(u1502,axiom,
( ~ product(X0,e_1,e_4)
| equalish(X0,e_3) ) ).
cnf(u1251,negated_conjecture,
( ~ product(e_4,X1,X2)
| ~ product(e_1,e_3,X0)
| ~ product(X2,X1,X0)
| equalish(X1,e_3) ) ).
cnf(product_idempotence,axiom,
product(X0,X0,X0) ).
cnf(u1194,negated_conjecture,
( ~ product(e_3,e_1,X0)
| ~ product(e_2,X1,X2)
| ~ product(X2,X1,X0)
| equalish(X2,e_3) ) ).
cnf(u1344,axiom,
( ~ product(X0,e_3,e_2)
| equalish(X0,e_1) ) ).
cnf(u26,negated_conjecture,
( ~ product(X3,X2,X1)
| ~ product(X0,X2,X3)
| ~ product(X0,X0,X1)
| equalish(X2,X0) ) ).
cnf(u1504,negated_conjecture,
( ~ product(e_4,e_1,X0)
| ~ product(e_3,X1,X2)
| ~ product(X2,X1,X0)
| equalish(X1,e_1) ) ).
cnf(u1493,negated_conjecture,
( ~ product(e_2,X0,X1)
| ~ product(X1,X0,e_4)
| equalish(X1,e_3) ) ).
cnf(u1280,negated_conjecture,
( ~ product(e_3,X1,X2)
| ~ product(e_1,e_2,X0)
| ~ product(X2,X1,X0)
| equalish(X2,e_1) ) ).
cnf(u1229,negated_conjecture,
( ~ product(X0,e_4,e_2)
| ~ product(X0,X0,e_1)
| equalish(e_2,X0) ) ).
cnf(u1500,axiom,
( ~ product(e_3,e_1,X0)
| equalish(X0,e_4) ) ).
cnf(u1298,axiom,
( ~ product(X0,e_4,e_2)
| equalish(X0,e_3) ) ).
cnf(u1370,negated_conjecture,
( ~ product(e_3,e_2,X0)
| ~ product(e_1,e_3,X0) ) ).
cnf(element_2,axiom,
group_element(e_2) ).
cnf(u1195,negated_conjecture,
( ~ product(e_3,e_1,X0)
| ~ product(e_2,X1,X2)
| ~ product(X2,X1,X0)
| equalish(X1,e_1) ) ).
cnf(u1301,negated_conjecture,
( ~ product(X0,e_4,e_3)
| ~ product(X0,X0,e_2)
| equalish(e_4,X0) ) ).
cnf(u1227,negated_conjecture,
( ~ product(e_2,X1,X2)
| ~ product(e_1,e_4,X0)
| ~ product(X2,X1,X0)
| equalish(X1,e_4) ) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3) ).
cnf(u1365,axiom,
( ~ product(X0,e_2,e_3)
| equalish(X0,e_4) ) ).
cnf(column_surjectivity,axiom,
( ~ group_element(X1)
| ~ group_element(X0)
| product(X0,e_1,X1)
| product(X0,e_2,X1)
| product(X0,e_3,X1)
| product(X0,e_4,X1) ) ).
cnf(u30,axiom,
( ~ product(X0,X0,X1)
| equalish(X1,X0) ) ).
cnf(u1471,negated_conjecture,
( ~ product(X0,e_2,e_1)
| ~ product(X0,X0,e_4)
| equalish(e_1,X0) ) ).
cnf(u1326,negated_conjecture,
( ~ product(X0,e_1,e_4)
| ~ product(X0,X0,e_2)
| equalish(e_4,X0) ) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2) ).
cnf(u451,axiom,
( ~ group_element(X0)
| product(X0,e_1,e_1)
| product(X0,e_1,e_2)
| product(X0,e_1,e_3)
| product(X0,e_1,e_4) ) ).
cnf(u1396,negated_conjecture,
( ~ product(e_3,e_4,X0)
| ~ product(e_1,X1,X2)
| ~ product(X2,X1,X0)
| equalish(X2,e_3) ) ).
cnf(u1223,axiom,
( ~ product(e_2,e_4,X0)
| equalish(X0,e_1) ) ).
cnf(u1507,negated_conjecture,
( ~ product(e_4,e_1,X0)
| ~ product(e_1,e_2,X0) ) ).
cnf(u1236,negated_conjecture,
( ~ product(e_4,e_3,X0)
| ~ product(e_1,e_4,X0) ) ).
cnf(element_4,axiom,
group_element(e_4) ).
cnf(u1327,negated_conjecture,
( ~ product(e_2,e_1,X0)
| ~ product(e_1,e_3,X0) ) ).
cnf(u1228,negated_conjecture,
( ~ product(X0,e_4,e_2)
| ~ product(X0,X0,e_1)
| equalish(e_4,X0) ) ).
cnf(u1203,negated_conjecture,
( ~ product(e_4,e_3,X0)
| ~ product(e_2,X1,X2)
| ~ product(X2,X1,X0)
| equalish(X2,e_4) ) ).
cnf(product_right_cancellation,axiom,
( ~ product(X0,X3,X2)
| ~ product(X0,X1,X2)
| equalish(X1,X3) ) ).
cnf(u1268,negated_conjecture,
( ~ product(e_4,e_4,X0)
| ~ product(e_1,e_3,X0) ) ).
cnf(u1476,negated_conjecture,
( ~ product(e_1,X0,X1)
| ~ product(X1,X0,e_3)
| equalish(X1,e_4) ) ).
cnf(qg1_1,negated_conjecture,
( ~ product(X5,X4,X3)
| ~ product(X3,X4,X2)
| ~ product(X5,X1,X0)
| ~ product(X0,X1,X2)
| equalish(X0,X3) ) ).
cnf(u1279,axiom,
( ~ product(X0,e_2,e_1)
| equalish(X0,e_3) ) ).
cnf(u1329,negated_conjecture,
~ product(e_1,e_3,e_3) ).
cnf(u1192,negated_conjecture,
( ~ product(e_2,X0,e_3)
| equalish(X0,e_1) ) ).
cnf(u1368,negated_conjecture,
( ~ product(X0,e_2,e_4)
| ~ product(X0,X0,e_3)
| equalish(e_2,X0) ) ).
cnf(u1249,axiom,
( ~ product(X0,e_3,e_1)
| equalish(X0,e_4) ) ).
cnf(u1472,negated_conjecture,
~ product(e_4,e_2,e_2) ).
cnf(u1253,negated_conjecture,
( ~ product(X0,e_3,e_4)
| ~ product(X0,X0,e_1)
| equalish(e_4,X0) ) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4) ).
cnf(u1394,axiom,
( ~ product(e_1,X0,e_3)
| equalish(X0,e_4) ) ).
cnf(u1323,negated_conjecture,
( ~ product(e_4,X1,X2)
| ~ product(e_2,e_1,X0)
| ~ product(X2,X1,X0)
| equalish(X2,e_2) ) ).
cnf(u1466,axiom,
( ~ product(e_1,X0,e_4)
| equalish(X0,e_2) ) ).
cnf(u1281,negated_conjecture,
( ~ product(e_3,X1,X2)
| ~ product(e_1,e_2,X0)
| ~ product(X2,X1,X0)
| equalish(X1,e_2) ) ).
cnf(u1492,negated_conjecture,
( ~ product(e_2,X0,X1)
| ~ product(X1,X0,e_4)
| equalish(X0,e_1) ) ).
cnf(u1351,negated_conjecture,
( ~ product(e_1,X0,X1)
| ~ product(X1,X0,e_4)
| equalish(X1,e_2) ) ).
cnf(u1303,negated_conjecture,
( ~ product(e_2,e_4,X0)
| ~ product(e_1,e_2,X0) ) ).
cnf(u1197,negated_conjecture,
( ~ product(X0,e_1,e_2)
| ~ product(X0,X0,e_3)
| equalish(e_2,X0) ) ).
cnf(u1226,negated_conjecture,
( ~ product(e_2,X1,X2)
| ~ product(e_1,e_4,X0)
| ~ product(X2,X1,X0)
| equalish(X2,e_1) ) ).
cnf(u1399,negated_conjecture,
( ~ product(X0,e_4,e_1)
| ~ product(X0,X0,e_3)
| equalish(e_1,X0) ) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1) ).
cnf(u1470,negated_conjecture,
( ~ product(X0,e_2,e_1)
| ~ product(X0,X0,e_4)
| equalish(e_2,X0) ) ).
cnf(u185,axiom,
( ~ group_element(X0)
| product(X0,e_1,e_2)
| product(X0,e_2,e_2)
| product(X0,e_3,e_2)
| product(X0,e_4,e_2) ) ).
cnf(u1299,negated_conjecture,
( ~ product(e_3,X1,X2)
| ~ product(e_2,e_4,X0)
| ~ product(X2,X1,X0)
| equalish(X2,e_2) ) ).
cnf(u1260,negated_conjecture,
~ product(e_3,e_1,e_1) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1) ).
cnf(u39,axiom,
( ~ group_element(X0)
| product(e_1,X0,e_4)
| product(e_2,X0,e_4)
| product(e_3,X0,e_4)
| product(e_4,X0,e_4) ) ).
cnf(u1225,axiom,
( ~ product(X0,e_4,e_1)
| equalish(X0,e_2) ) ).
cnf(u1248,axiom,
( ~ product(e_4,X0,e_1)
| equalish(X0,e_3) ) ).
cnf(u187,axiom,
( ~ group_element(X0)
| product(X0,e_1,e_4)
| product(X0,e_2,e_4)
| product(X0,e_3,e_4)
| product(X0,e_4,e_4) ) ).
cnf(u186,axiom,
( ~ group_element(X0)
| product(X0,e_1,e_3)
| product(X0,e_2,e_3)
| product(X0,e_3,e_3)
| product(X0,e_4,e_3) ) ).
cnf(u1206,negated_conjecture,
( ~ product(X0,e_3,e_2)
| ~ product(X0,X0,e_4)
| equalish(e_2,X0) ) ).
cnf(u1347,negated_conjecture,
( ~ product(X0,e_3,e_1)
| ~ product(X0,X0,e_2)
| equalish(e_3,X0) ) ).
cnf(product_total_function2,axiom,
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| equalish(X2,X3) ) ).
cnf(u1509,negated_conjecture,
( ~ product(e_4,e_1,X0)
| ~ product(e_2,e_4,X0) ) ).
cnf(u1505,negated_conjecture,
( ~ product(X0,e_1,e_3)
| ~ product(X0,X0,e_4)
| equalish(e_1,X0) ) ).
cnf(u1465,axiom,
( ~ product(e_1,e_2,X0)
| equalish(X0,e_4) ) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4) ).
cnf(u27,negated_conjecture,
( ~ product(X3,X2,X1)
| ~ product(X0,X2,X3)
| ~ product(X0,X0,X1)
| equalish(X3,X0) ) ).
cnf(u1345,negated_conjecture,
( ~ product(e_2,e_3,X0)
| ~ product(e_1,X1,X2)
| ~ product(X2,X1,X0)
| equalish(X2,e_2) ) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3) ).
cnf(u1346,negated_conjecture,
( ~ product(e_2,e_3,X0)
| ~ product(e_1,X1,X2)
| ~ product(X2,X1,X0)
| equalish(X1,e_3) ) ).
cnf(u1342,axiom,
( ~ product(e_1,e_3,X0)
| equalish(X0,e_2) ) ).
cnf(u1247,axiom,
( ~ product(e_4,e_3,X0)
| equalish(X0,e_1) ) ).
cnf(u1523,negated_conjecture,
( ~ product(e_3,X0,X1)
| ~ product(X1,X0,e_2)
| equalish(X1,e_4) ) ).
cnf(u1201,negated_conjecture,
( ~ product(e_2,X0,e_4)
| equalish(X0,e_3) ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP123-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n008.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 : Sun Sep 27 09:21:25 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.80/1.67 % (965342)Input is clausal, will run a generic CNF schedule.
% 4.80/1.67 % (965349)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1623205101:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.80/1.67 % (965352)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2779115427:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.80/1.67 % (965350)lrs+10_1_sil=8000:sp=occurrence:random_seed=1672663645:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.80/1.67 % (965348)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1887477422:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.80/1.67 % (965351)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4054451034:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.80/1.67 % (965353)dis-21_1_sil=8000:lcm=predicate:random_seed=2247777130:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 4.80/1.67 % (965347)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2793922635:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.80/1.67 % (965350)Refutation not found, incomplete strategy
% 4.80/1.67 % (965350)------------------------------
% 4.80/1.67 % (965350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.80/1.67 % (965350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.80/1.67 % (965350)CaDiCaL version: 2.1.3
% 4.80/1.67 % (965350)Termination reason: Refutation not found, incomplete strategy
% 4.80/1.67 % (965350)Time elapsed: 0.001 s
% 4.80/1.67 % (965350)Peak memory usage: 86 MB
% 4.80/1.67 % (965352)Refutation not found, incomplete strategy
% 4.80/1.67 % (965352)------------------------------
% 4.80/1.67 % (965352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.80/1.67 % (965352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.80/1.67 % (965352)CaDiCaL version: 2.1.3
% 4.80/1.67 % (965352)Termination reason: Refutation not found, incomplete strategy
% 4.80/1.67 % (965352)Time elapsed: 0.031 s
% 4.80/1.67 % (965352)Peak memory usage: 88 MB
% 4.80/1.67 % (965352)Instructions burned: 38 (million)
% 4.80/1.67 % (965351)Instruction limit reached!
% 4.80/1.67 % (965351)------------------------------
% 4.80/1.67 % (965351)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.80/1.67 % (965351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.80/1.67 % (965351)CaDiCaL version: 2.1.3
% 4.80/1.67 % (965351)Termination reason: Instruction limit
% 4.80/1.67 % (965351)Termination phase: Saturation
% 4.80/1.67 % (965351)Time elapsed: 0.062 s
% 4.80/1.67 % (965351)Peak memory usage: 88 MB
% 4.80/1.67 % (965351)Instructions burned: 115 (million)
% 4.80/1.67 % (965353)Instruction limit reached!
% 4.80/1.67 % (965353)------------------------------
% 4.80/1.67 % (965353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.80/1.67 % (965353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.80/1.67 % (965353)CaDiCaL version: 2.1.3
% 4.80/1.67 % (965353)Termination reason: Instruction limit
% 4.80/1.67 % (965353)Termination phase: Saturation
% 4.80/1.67 % (965353)Time elapsed: 0.073 s
% 4.80/1.67 % (965353)Peak memory usage: 89 MB
% 4.80/1.67 % (965353)Instructions burned: 118 (million)
% 4.80/1.67 % (965362)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2076890848:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 4.80/1.67 % (965361)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1617675536:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.80/1.67 % (965362)Refutation not found, incomplete strategy
% 4.80/1.67 % (965362)------------------------------
% 4.80/1.67 % (965362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.80/1.67 % (965362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.80/1.67 % (965362)CaDiCaL version: 2.1.3
% 4.80/1.67 % (965362)Termination reason: Refutation not found, incomplete strategy
% 4.80/1.67 % (965362)Time elapsed: 0.003 s
% 4.80/1.67 % (965362)Peak memory usage: 87 MB
% 4.80/1.67 % (965362)Instructions burned: 3 (million)
% 4.80/1.67 % (965350)------------------------------
% 4.80/1.67 % (965350)------------------------------
% 4.80/1.67 % (965352)------------------------------
% 4.80/1.67 % (965352)------------------------------
% 4.80/1.67 % (965361)Instruction limit reached!
% 4.80/1.67 % (965361)------------------------------
% 4.80/1.67 % (965361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.80/1.67 % (965361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.80/1.67 % (965361)CaDiCaL version: 2.1.3
% 4.80/1.67 % (965361)Termination reason: Instruction limit
% 4.80/1.67 % (965361)Termination phase: Saturation
% 4.80/1.67 % (965361)Time elapsed: 0.081 s
% 4.80/1.67 % (965361)Peak memory usage: 88 MB
% 4.80/1.67 % (965361)Instructions burned: 143 (million)
% 4.80/1.67 % (965365)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=275021549:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 4.80/1.67 % (965366)lrs+10_64_to=lpo:sil=8000:random_seed=853650148:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 4.80/1.67 % (965367)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3477333374:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 4.80/1.67 % (965366)First to succeed.
% 4.80/1.67 % (965366)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-965342"
% 4.80/1.67 % (965367)Refutation not found, incomplete strategy
% 4.80/1.67 % (965367)------------------------------
% 4.80/1.67 % (965367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.80/1.67 % (965367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.80/1.67 % (965367)CaDiCaL version: 2.1.3
% 4.80/1.67 % (965367)Termination reason: Refutation not found, incomplete strategy
% 4.80/1.67 % (965367)Time elapsed: 0.026 s
% 4.80/1.67 % (965367)Peak memory usage: 88 MB
% 4.80/1.67 % (965367)Instructions burned: 41 (million)
% 4.80/1.67 % (965362)------------------------------
% 4.80/1.67 % (965362)------------------------------
% 4.80/1.67 % (965365)Instruction limit reached!
% 4.80/1.67 % (965365)------------------------------
% 4.80/1.67 % (965365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.80/1.67 % (965365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.80/1.67 % (965365)CaDiCaL version: 2.1.3
% 4.80/1.67 % (965365)Termination reason: Instruction limit
% 4.80/1.67 % (965365)Termination phase: Saturation
% 4.80/1.67 % (965365)Time elapsed: 0.110 s
% 4.80/1.67 % (965365)Peak memory usage: 89 MB
% 4.80/1.67 % (965365)Instructions burned: 219 (million)
% 4.80/1.67 % (965371)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2966183702:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 4.80/1.67 % (965348)Refutation not found, incomplete strategy
% 4.80/1.67 % (965348)------------------------------
% 4.80/1.67 % (965348)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.80/1.67 % (965348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.80/1.67 % (965348)CaDiCaL version: 2.1.3
% 4.80/1.67 % (965348)Termination reason: Refutation not found, incomplete strategy
% 4.80/1.67 % (965348)Time elapsed: 0.598 s
% 4.80/1.67 % (965348)Peak memory usage: 127 MB
% 4.80/1.67 % (965348)Instructions burned: 907 (million)
% 4.80/1.67 % (965372)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3269533929:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 4.80/1.67 % (965371)Instruction limit reached!
% 4.80/1.67 % (965371)------------------------------
% 4.80/1.67 % (965371)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.80/1.67 % (965371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.80/1.67 % (965371)CaDiCaL version: 2.1.3
% 4.80/1.67 % (965371)Termination reason: Instruction limit
% 4.80/1.67 % (965371)Termination phase: Saturation
% 4.80/1.67 % (965371)Time elapsed: 0.094 s
% 4.80/1.67 % (965371)Peak memory usage: 89 MB
% 4.80/1.67 % (965371)Instructions burned: 158 (million)
% 4.80/1.67 % SZS status Satisfiable for theBenchmark
% 4.80/1.67 % SZS output start Saturation.
% See solution above
% 6.24/1.76 % SZS output start Definitions and Model Updates.
% 6.24/1.76 % SZS output end Definitions and Model Updates.
% 6.24/1.76 % (965366)------------------------------
% 6.24/1.76 % (965366)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.24/1.76 % (965366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.24/1.76 % (965366)CaDiCaL version: 2.1.3
% 6.24/1.76 % (965366)Termination reason: Satisfiable
% 6.24/1.76 % (965366)Time elapsed: 0.027 s
% 6.24/1.76 % (965366)Peak memory usage: 88 MB
% 6.24/1.76 % (965366)Instructions burned: 45 (million)
% 6.24/1.76 % (965366)------------------------------
% 6.24/1.76 % (965366)------------------------------
% 6.24/1.76 % (965342)Success in time 0.821 s
% 6.24/1.76 % Vampire exiting
%------------------------------------------------------------------------------