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Vampire---5.0.1.SAT-Sat.s

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%------------------------------------------------------------------------------
% File     : Vampire---5.0.1
% Problem  : GRP127-2.005 : TPTP v9.3.1. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n003.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 10:12:46 AM UTC 2026

% Result   : Satisfiable 4.41s 1.54s
% Output   : Saturation 5.57s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
cnf(u72,axiom,
    ~ product(e_5,e_1,e_4) ).

cnf(u76,axiom,
    ~ product(e_5,e_1,e_3) ).

cnf(u81,axiom,
    product(e_5,e_1,e_2) ).

cnf(u84,axiom,
    ~ product(e_5,e_1,e_1) ).

cnf(u90,axiom,
    product(e_4,e_1,e_5) ).

cnf(u93,axiom,
    ~ product(e_4,e_1,e_4) ).

cnf(u97,axiom,
    ~ product(e_4,e_1,e_3) ).

cnf(u101,axiom,
    ~ product(e_4,e_1,e_2) ).

cnf(u105,axiom,
    ~ product(e_4,e_1,e_1) ).

cnf(u110,axiom,
    ~ product(e_3,e_1,e_5) ).

cnf(u115,axiom,
    product(e_3,e_1,e_4) ).

cnf(u118,axiom,
    ~ product(e_3,e_1,e_3) ).

cnf(u122,axiom,
    ~ product(e_3,e_1,e_2) ).

cnf(u126,axiom,
    ~ product(e_3,e_1,e_1) ).

cnf(u131,axiom,
    ~ product(e_2,e_1,e_5) ).

cnf(u135,axiom,
    ~ product(e_2,e_1,e_4) ).

cnf(u140,axiom,
    product(e_2,e_1,e_3) ).

cnf(u143,axiom,
    ~ product(e_2,e_1,e_2) ).

cnf(u147,axiom,
    ~ product(e_2,e_1,e_1) ).

cnf(u184,axiom,
    ~ product(e_5,e_2,e_5) ).

cnf(u188,axiom,
    ~ product(e_5,e_2,e_4) ).

cnf(u192,axiom,
    ~ product(e_5,e_2,e_3) ).

cnf(u196,axiom,
    ~ product(e_5,e_2,e_2) ).

cnf(u201,axiom,
    product(e_5,e_2,e_1) ).

cnf(u205,axiom,
    ~ product(e_4,e_2,e_5) ).

cnf(u209,axiom,
    ~ product(e_4,e_2,e_4) ).

cnf(u214,axiom,
    product(e_4,e_2,e_3) ).

cnf(u217,axiom,
    ~ product(e_4,e_2,e_2) ).

cnf(u221,axiom,
    ~ product(e_4,e_2,e_1) ).

cnf(u227,axiom,
    product(e_3,e_2,e_5) ).

cnf(u230,axiom,
    ~ product(e_3,e_2,e_4) ).

cnf(u234,axiom,
    ~ product(e_3,e_2,e_3) ).

cnf(u238,axiom,
    ~ product(e_3,e_2,e_2) ).

cnf(u242,axiom,
    ~ product(e_3,e_2,e_1) ).

cnf(u247,axiom,
    ~ product(e_1,e_2,e_5) ).

cnf(u252,axiom,
    product(e_1,e_2,e_4) ).

cnf(u255,axiom,
    ~ product(e_1,e_2,e_3) ).

cnf(u259,axiom,
    ~ product(e_1,e_2,e_2) ).

cnf(u263,axiom,
    ~ product(e_1,e_2,e_1) ).

cnf(u422,axiom,
    ~ product(e_5,e_3,e_5) ).

cnf(u427,axiom,
    product(e_5,e_3,e_4) ).

cnf(u430,axiom,
    ~ product(e_5,e_3,e_3) ).

cnf(u434,axiom,
    ~ product(e_5,e_3,e_2) ).

cnf(u438,axiom,
    ~ product(e_5,e_3,e_1) ).

cnf(u443,axiom,
    ~ product(e_4,e_3,e_5) ).

cnf(u447,axiom,
    ~ product(e_4,e_3,e_4) ).

cnf(u451,axiom,
    ~ product(e_4,e_3,e_3) ).

cnf(u456,axiom,
    product(e_4,e_3,e_2) ).

cnf(u459,axiom,
    ~ product(e_4,e_3,e_1) ).

cnf(u464,axiom,
    ~ product(e_2,e_3,e_5) ).

cnf(u468,axiom,
    ~ product(e_2,e_3,e_4) ).

cnf(u472,axiom,
    ~ product(e_2,e_3,e_3) ).

cnf(u476,axiom,
    ~ product(e_2,e_3,e_2) ).

cnf(u481,axiom,
    product(e_2,e_3,e_1) ).

cnf(u486,axiom,
    product(e_1,e_3,e_5) ).

cnf(u489,axiom,
    ~ product(e_1,e_3,e_4) ).

cnf(u493,axiom,
    ~ product(e_1,e_3,e_3) ).

cnf(u497,axiom,
    ~ product(e_1,e_3,e_2) ).

cnf(u501,axiom,
    ~ product(e_1,e_3,e_1) ).

cnf(u685,axiom,
    ~ product(e_5,e_4,e_5) ).

cnf(u689,axiom,
    ~ product(e_5,e_4,e_4) ).

cnf(u694,axiom,
    product(e_5,e_4,e_3) ).

cnf(u697,axiom,
    ~ product(e_5,e_4,e_2) ).

cnf(u701,axiom,
    ~ product(e_5,e_4,e_1) ).

cnf(u706,axiom,
    ~ product(e_3,e_4,e_5) ).

cnf(u710,axiom,
    ~ product(e_3,e_4,e_4) ).

cnf(u714,axiom,
    ~ product(e_3,e_4,e_3) ).

cnf(u718,axiom,
    ~ product(e_3,e_4,e_2) ).

cnf(u723,axiom,
    product(e_3,e_4,e_1) ).

cnf(u728,axiom,
    product(e_2,e_4,e_5) ).

cnf(u731,axiom,
    ~ product(e_2,e_4,e_4) ).

cnf(u735,axiom,
    ~ product(e_2,e_4,e_3) ).

cnf(u739,axiom,
    ~ product(e_2,e_4,e_2) ).

cnf(u743,axiom,
    ~ product(e_2,e_4,e_1) ).

cnf(u748,axiom,
    ~ product(e_1,e_4,e_5) ).

cnf(u752,axiom,
    ~ product(e_1,e_4,e_4) ).

cnf(u756,axiom,
    ~ product(e_1,e_4,e_3) ).

cnf(u761,axiom,
    product(e_1,e_4,e_2) ).

cnf(u764,axiom,
    ~ product(e_1,e_4,e_1) ).

cnf(u970,axiom,
    ~ product(e_4,e_5,e_5) ).

cnf(u974,axiom,
    ~ product(e_4,e_5,e_4) ).

cnf(u978,axiom,
    ~ product(e_4,e_5,e_3) ).

cnf(u982,axiom,
    ~ product(e_4,e_5,e_2) ).

cnf(u987,axiom,
    product(e_4,e_5,e_1) ).

cnf(u995,axiom,
    ~ product(e_3,e_5,e_4) ).

cnf(u999,axiom,
    ~ product(e_3,e_5,e_3) ).

cnf(u1004,axiom,
    product(e_3,e_5,e_2) ).

cnf(u1012,axiom,
    ~ product(e_2,e_5,e_5) ).

cnf(u1017,axiom,
    product(e_2,e_5,e_4) ).

cnf(u1042,axiom,
    product(e_1,e_5,e_3) ).

cnf(u1045,axiom,
    ~ product(e_1,e_5,e_2) ).

cnf(u1525,axiom,
    ~ next(e_2,e_2) ).

cnf(u1386,axiom,
    ( ~ product(e_5,e_4,X0)
    | equalish(X0,e_3) ) ).

cnf(u1416,axiom,
    ( ~ product(X0,e_4,e_2)
    | equalish(X0,e_1) ) ).

cnf(u1372,negated_conjecture,
    ( ~ product(e_2,X0,e_1)
    | product(e_4,e_2,X0) ) ).

cnf(u56,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)
    | product(X0,e_1,e_5) ) ).

cnf(u1366,negated_conjecture,
    ( ~ product(e_2,X0,e_3)
    | product(e_5,e_2,X0) ) ).

cnf(u1524,axiom,
    ~ next(e_2,e_1) ).

cnf(u50,axiom,
    ( ~ product(X0,X0,X1)
    | equalish(X1,X0) ) ).

cnf(u1348,negated_conjecture,
    ( ~ product(e_1,X0,e_5)
    | product(e_2,e_1,X0) ) ).

cnf(u1470,negated_conjecture,
    ( ~ product(e_5,X0,e_4)
    | product(e_1,e_5,X0) ) ).

cnf(u506,axiom,
    ( ~ product(X0,e_1,e_3)
    | equalish(X0,e_2) ) ).

cnf(u1387,negated_conjecture,
    ( ~ product(e_4,X0,e_5)
    | product(e_3,e_4,X0) ) ).

cnf(u508,axiom,
    ( ~ product(e_2,e_1,X0)
    | equalish(X0,e_3) ) ).

cnf(u1119,axiom,
    ( ~ product(e_3,X0,e_4)
    | equalish(X0,e_1) ) ).

cnf(u1399,negated_conjecture,
    ( ~ product(e_4,X0,e_2)
    | product(e_5,e_4,X0) ) ).

cnf(u1385,axiom,
    ( ~ product(e_5,X0,e_3)
    | equalish(X0,e_4) ) ).

cnf(u1363,axiom,
    ( ~ product(X0,e_2,e_5)
    | equalish(X0,e_3) ) ).

cnf(u1365,axiom,
    ( ~ product(e_3,e_2,X0)
    | equalish(X0,e_5) ) ).

cnf(e_2_is_not_e_1,axiom,
    ~ equalish(e_2,e_1) ).

cnf(u49,axiom,
    ( ~ greater(e_1,X0)
    | ~ next(e_1,X0) ) ).

cnf(u52,axiom,
    ( ~ product(X0,X1,X0)
    | equalish(X1,X0) ) ).

cnf(product_right_cancellation,axiom,
    ( ~ product(X0,X3,X2)
    | ~ product(X0,X1,X2)
    | equalish(X1,X3) ) ).

cnf(qg3,negated_conjecture,
    ( ~ product(X2,X0,X3)
    | ~ product(X0,X1,X2)
    | product(X3,X0,X1) ) ).

cnf(product_idempotence,axiom,
    product(X0,X0,X0) ).

cnf(e_3_is_not_e_5,axiom,
    ~ equalish(e_3,e_5) ).

cnf(u1514,axiom,
    ( ~ product(e_1,e_5,X0)
    | equalish(X0,e_3) ) ).

cnf(e_5_is_not_e_3,axiom,
    ~ equalish(e_5,e_3) ).

cnf(e_2_is_not_e_3,axiom,
    ~ equalish(e_2,e_3) ).

cnf(u505,axiom,
    ( ~ greater(e_3,X0)
    | ~ next(e_2,X0) ) ).

cnf(u1344,axiom,
    ( ~ greater(e_2,X0)
    | ~ next(e_5,X0) ) ).

cnf(e_2_is_not_e_5,axiom,
    ~ equalish(e_2,e_5) ).

cnf(element_4,axiom,
    group_element(e_4) ).

cnf(e_1_is_not_e_3,axiom,
    ~ equalish(e_1,e_3) ).

cnf(e_1_is_not_e_2,axiom,
    ~ equalish(e_1,e_2) ).

cnf(e_5_greater_e_1,axiom,
    greater(e_5,e_1) ).

cnf(u1490,axiom,
    ( ~ product(e_3,X0,e_2)
    | equalish(X0,e_5) ) ).

cnf(no_redundancy,axiom,
    ( ~ product(X0,e_1,X1)
    | ~ next(X0,X2)
    | ~ greater(X1,X2) ) ).

cnf(e_2_then_e_3,axiom,
    next(e_2,e_3) ).

cnf(e_1_then_e_2,axiom,
    next(e_1,e_2) ).

cnf(u1398,axiom,
    ( ~ product(e_2,e_4,X0)
    | equalish(X0,e_5) ) ).

cnf(u1515,negated_conjecture,
    ( ~ product(e_5,X0,e_1)
    | product(e_3,e_5,X0) ) ).

cnf(u1375,axiom,
    ( ~ product(e_4,X0,e_2)
    | equalish(X0,e_3) ) ).

cnf(u1361,negated_conjecture,
    ( ~ product(e_2,X0,e_4)
    | product(e_3,e_2,X0) ) ).

cnf(u1467,axiom,
    ( ~ product(X0,e_5,e_1)
    | equalish(X0,e_4) ) ).

cnf(u1380,axiom,
    ( ~ product(X0,e_3,e_5)
    | equalish(X0,e_1) ) ).

cnf(u1513,axiom,
    ( ~ product(e_1,X0,e_3)
    | equalish(X0,e_5) ) ).

cnf(u620,axiom,
    ( ~ product(e_5,e_3,X0)
    | equalish(X0,e_4) ) ).

cnf(u1374,axiom,
    ( ~ product(X0,e_3,e_2)
    | equalish(X0,e_4) ) ).

cnf(u1491,axiom,
    ( ~ product(e_3,e_5,X0)
    | equalish(X0,e_2) ) ).

cnf(u1351,axiom,
    ( ~ product(e_4,X0,e_5)
    | equalish(X0,e_1) ) ).

cnf(u174,axiom,
    ~ next(e_4,e_2) ).

cnf(u173,axiom,
    ~ next(e_4,e_1) ).

cnf(e_4_then_e_5,axiom,
    next(e_4,e_5) ).

cnf(u1120,axiom,
    ( ~ product(e_3,e_1,X0)
    | equalish(X0,e_4) ) ).

cnf(u1418,axiom,
    ( ~ product(e_1,e_4,X0)
    | equalish(X0,e_2) ) ).

cnf(u1381,axiom,
    ( ~ product(e_1,X0,e_5)
    | equalish(X0,e_3) ) ).

cnf(u58,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)
    | product(X0,e_3,e_5) ) ).

cnf(u409,axiom,
    ~ next(e_3,e_3) ).

cnf(u57,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)
    | product(X0,e_2,e_5) ) ).

cnf(u1376,axiom,
    ( ~ product(e_4,e_3,X0)
    | equalish(X0,e_2) ) ).

cnf(u60,axiom,
    ( ~ group_element(X0)
    | product(X0,e_5,e_1)
    | product(X0,e_5,e_2)
    | product(X0,e_5,e_3)
    | product(X0,e_5,e_4)
    | product(X0,e_5,e_5) ) ).

cnf(u51,axiom,
    equalish(X0,X0) ).

cnf(u1370,axiom,
    ( ~ product(e_1,X0,e_4)
    | equalish(X0,e_2) ) ).

cnf(u54,axiom,
    ( ~ product(X0,X1,X1)
    | equalish(X0,X1) ) ).

cnf(u1356,axiom,
    ( ~ product(e_5,e_2,X0)
    | equalish(X0,e_1) ) ).

cnf(u1489,axiom,
    ( ~ product(X0,e_5,e_2)
    | equalish(X0,e_3) ) ).

cnf(e_5_is_not_e_4,axiom,
    ~ equalish(e_5,e_4) ).

cnf(u47,negated_conjecture,
    ( ~ product(X0,X1,X0)
    | product(X0,X0,X1) ) ).

cnf(u1350,axiom,
    ( ~ product(X0,e_1,e_5)
    | equalish(X0,e_4) ) ).

cnf(u1508,axiom,
    ( ~ product(e_2,e_5,X0)
    | equalish(X0,e_4) ) ).

cnf(e_4_is_not_e_2,axiom,
    ~ equalish(e_4,e_2) ).

cnf(u1118,axiom,
    ( ~ product(X0,e_1,e_4)
    | equalish(X0,e_3) ) ).

cnf(u1352,axiom,
    ( ~ product(e_4,e_1,X0)
    | equalish(X0,e_5) ) ).

cnf(u1117,axiom,
    ( ~ greater(e_4,X0)
    | ~ next(e_3,X0) ) ).

cnf(u1346,axiom,
    ( ~ product(e_5,X0,e_2)
    | equalish(X0,e_1) ) ).

cnf(u1127,axiom,
    ( ~ product(e_2,e_3,X0)
    | equalish(X0,e_1) ) ).

cnf(u1419,negated_conjecture,
    ( ~ product(e_4,X0,e_1)
    | product(e_2,e_4,X0) ) ).

cnf(u618,axiom,
    ( ~ product(X0,e_3,e_4)
    | equalish(X0,e_5) ) ).

cnf(u1393,negated_conjecture,
    ( ~ product(e_4,X0,e_3)
    | product(e_1,e_4,X0) ) ).

cnf(u1371,axiom,
    ( ~ product(e_1,e_2,X0)
    | equalish(X0,e_4) ) ).

cnf(u1417,axiom,
    ( ~ product(e_1,X0,e_2)
    | equalish(X0,e_4) ) ).

cnf(u1383,negated_conjecture,
    ( ~ product(e_3,X0,e_1)
    | product(e_5,e_3,X0) ) ).

cnf(u1369,axiom,
    ( ~ product(X0,e_2,e_4)
    | equalish(X0,e_1) ) ).

cnf(u1347,axiom,
    ( ~ product(e_5,e_1,X0)
    | equalish(X0,e_2) ) ).

cnf(u1349,axiom,
    ( ~ greater(e_5,X0)
    | ~ next(e_4,X0) ) ).

cnf(u619,axiom,
    ( ~ product(e_5,X0,e_4)
    | equalish(X0,e_3) ) ).

cnf(e_4_is_not_e_1,axiom,
    ~ equalish(e_4,e_1) ).

cnf(e_4_is_not_e_5,axiom,
    ~ equalish(e_4,e_5) ).

cnf(u507,axiom,
    ( ~ product(e_2,X0,e_3)
    | equalish(X0,e_1) ) ).

cnf(e_2_is_not_e_4,axiom,
    ~ equalish(e_2,e_4) ).

cnf(e_3_is_not_e_2,axiom,
    ~ equalish(e_3,e_2) ).

cnf(u509,negated_conjecture,
    ( ~ product(e_1,X0,e_2)
    | product(e_3,e_1,X0) ) ).

cnf(e_3_is_not_e_1,axiom,
    ~ equalish(e_3,e_1) ).

cnf(element_1,axiom,
    group_element(e_1) ).

cnf(e_1_is_not_e_4,axiom,
    ~ equalish(e_1,e_4) ).

cnf(e_4_greater_e_2,axiom,
    greater(e_4,e_2) ).

cnf(e_3_greater_e_2,axiom,
    greater(e_3,e_2) ).

cnf(u175,axiom,
    ~ next(e_4,e_3) ).

cnf(e_4_greater_e_3,axiom,
    greater(e_4,e_3) ).

cnf(e_3_then_e_4,axiom,
    next(e_3,e_4) ).

cnf(e_3_greater_e_1,axiom,
    greater(e_3,e_1) ).

cnf(e_2_greater_e_1,axiom,
    greater(e_2,e_1) ).

cnf(u1382,axiom,
    ( ~ product(e_1,e_3,X0)
    | equalish(X0,e_5) ) ).

cnf(u1359,axiom,
    ( ~ product(e_4,X0,e_3)
    | equalish(X0,e_2) ) ).

cnf(u1384,axiom,
    ( ~ product(X0,e_4,e_3)
    | equalish(X0,e_5) ) ).

cnf(u1345,axiom,
    ( ~ product(X0,e_1,e_2)
    | equalish(X0,e_5) ) ).

cnf(u1364,axiom,
    ( ~ product(e_3,X0,e_5)
    | equalish(X0,e_2) ) ).

cnf(u1358,axiom,
    ( ~ product(X0,e_2,e_3)
    | equalish(X0,e_4) ) ).

cnf(u1126,axiom,
    ( ~ product(e_2,X0,e_1)
    | equalish(X0,e_3) ) ).

cnf(u1125,axiom,
    ( ~ product(X0,e_3,e_1)
    | equalish(X0,e_2) ) ).

cnf(u1128,negated_conjecture,
    ( ~ product(e_3,X0,e_2)
    | product(e_1,e_3,X0) ) ).

cnf(u1121,negated_conjecture,
    ( ~ product(e_1,X0,e_3)
    | product(e_4,e_1,X0) ) ).

cnf(u59,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)
    | product(X0,e_4,e_5) ) ).

cnf(u407,axiom,
    ~ next(e_3,e_1) ).

cnf(product_total_function2,axiom,
    ( ~ product(X0,X1,X3)
    | ~ product(X0,X1,X2)
    | equalish(X2,X3) ) ).

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)
    | product(X0,X1,e_5) ) ).

cnf(u1360,axiom,
    ( ~ product(e_4,e_2,X0)
    | equalish(X0,e_3) ) ).

cnf(product_left_cancellation,axiom,
    ( ~ product(X3,X1,X2)
    | ~ product(X0,X1,X2)
    | equalish(X0,X3) ) ).

cnf(e_4_is_not_e_3,axiom,
    ~ equalish(e_4,e_3) ).

cnf(u1354,axiom,
    ( ~ product(X0,e_2,e_1)
    | equalish(X0,e_5) ) ).

cnf(e_5_is_not_e_2,axiom,
    ~ equalish(e_5,e_2) ).

cnf(u1512,axiom,
    ( ~ product(X0,e_5,e_3)
    | equalish(X0,e_1) ) ).

cnf(e_5_is_not_e_1,axiom,
    ~ equalish(e_5,e_1) ).

cnf(u1468,axiom,
    ( ~ product(e_4,X0,e_1)
    | equalish(X0,e_5) ) ).

cnf(e_1_is_not_e_5,axiom,
    ~ equalish(e_1,e_5) ).

cnf(u1506,axiom,
    ( ~ product(X0,e_5,e_4)
    | equalish(X0,e_2) ) ).

cnf(e_3_is_not_e_4,axiom,
    ~ equalish(e_3,e_4) ).

cnf(u1492,negated_conjecture,
    ( ~ product(e_5,X0,e_3)
    | product(e_2,e_5,X0) ) ).

cnf(element_3,axiom,
    group_element(e_3) ).

cnf(element_2,axiom,
    group_element(e_2) ).

cnf(u1469,axiom,
    ( ~ product(e_4,e_5,X0)
    | equalish(X0,e_1) ) ).

cnf(u621,negated_conjecture,
    ( ~ product(e_3,X0,e_5)
    | product(e_4,e_3,X0) ) ).

cnf(u1391,axiom,
    ( ~ product(e_3,X0,e_1)
    | equalish(X0,e_4) ) ).

cnf(u1377,negated_conjecture,
    ( ~ product(e_3,X0,e_4)
    | product(e_2,e_3,X0) ) ).

cnf(u1355,axiom,
    ( ~ product(e_5,X0,e_1)
    | equalish(X0,e_2) ) ).

cnf(u1396,axiom,
    ( ~ product(X0,e_4,e_5)
    | equalish(X0,e_2) ) ).

cnf(u1529,axiom,
    ~ next(e_5,e_1) ).

cnf(u1357,negated_conjecture,
    ( ~ product(e_2,X0,e_5)
    | product(e_1,e_2,X0) ) ).

cnf(u1390,axiom,
    ( ~ product(X0,e_4,e_1)
    | equalish(X0,e_3) ) ).

cnf(u1507,axiom,
    ( ~ product(e_2,X0,e_4)
    | equalish(X0,e_5) ) ).

cnf(u1509,negated_conjecture,
    ( ~ product(e_5,X0,e_2)
    | product(e_4,e_5,X0) ) ).

cnf(u1353,negated_conjecture,
    ( ~ product(e_1,X0,e_4)
    | product(e_5,e_1,X0) ) ).

cnf(u408,axiom,
    ~ next(e_3,e_2) ).

cnf(u176,axiom,
    ~ next(e_4,e_4) ).

cnf(element_5,axiom,
    group_element(e_5) ).

cnf(e_5_greater_e_2,axiom,
    greater(e_5,e_2) ).

cnf(e_5_greater_e_4,axiom,
    greater(e_5,e_4) ).

cnf(e_5_greater_e_3,axiom,
    greater(e_5,e_3) ).

cnf(e_4_greater_e_1,axiom,
    greater(e_4,e_1) ).

cnf(u1397,axiom,
    ( ~ product(e_2,X0,e_5)
    | equalish(X0,e_4) ) ).

cnf(u1392,axiom,
    ( ~ product(e_3,e_4,X0)
    | equalish(X0,e_1) ) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : GRP127-2.005 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35  % Computer : n003.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 : Sun Sep 27 09:27:25 UTC 2026
% 0.09/0.36  % CPUTime  : 
% 0.09/0.36  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39  Running first-order theorem proving
% 0.12/0.39  Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.41/1.54  % (244369)Input is clausal, will run a generic CNF schedule.
% 4.41/1.54  % (244374)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=975884089:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.41/1.54  % (244376)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2556193281:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.41/1.54  % (244378)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=809133801:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.41/1.54  % (244380)dis-21_1_sil=8000:lcm=predicate:random_seed=2132010632: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)
% 4.41/1.54  % (244375)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3745338128:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.41/1.54  % (244377)lrs+10_1_sil=8000:sp=occurrence:random_seed=223915986:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.41/1.54  % (244379)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3825726793:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.41/1.54  % (244378)Instruction limit reached! 
% 4.41/1.54  % (244378)------------------------------
% 4.41/1.54  % (244378)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.54  % (244378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.54  % (244378)CaDiCaL version: 2.1.3
% 4.41/1.54  % (244378)Termination reason: Instruction limit
% 4.41/1.54  % (244378)Termination phase: Saturation
% 4.41/1.54  % (244378)Time elapsed: 0.058 s
% 4.41/1.54  % (244378)Peak memory usage: 87 MB
% 4.41/1.54  % (244378)Instructions burned: 114 (million)
% 4.41/1.54  % (244377)Instruction limit reached! 
% 4.41/1.54  % (244377)------------------------------
% 4.41/1.54  % (244377)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.54  % (244377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.54  % (244377)CaDiCaL version: 2.1.3
% 4.41/1.54  % (244377)Termination reason: Instruction limit
% 4.41/1.54  % (244377)Termination phase: Saturation
% 4.41/1.54  % (244377)Time elapsed: 0.058 s
% 4.41/1.54  % (244377)Peak memory usage: 88 MB
% 4.41/1.54  % (244377)Instructions burned: 107 (million)
% 4.41/1.54  % (244380)Instruction limit reached! 
% 4.41/1.54  % (244380)------------------------------
% 4.41/1.54  % (244380)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.54  % (244380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.54  % (244380)CaDiCaL version: 2.1.3
% 4.41/1.54  % (244380)Termination reason: Instruction limit
% 4.41/1.54  % (244380)Termination phase: Saturation
% 4.41/1.54  % (244380)Time elapsed: 0.077 s
% 4.41/1.54  % (244380)Peak memory usage: 88 MB
% 4.41/1.54  % (244380)Instructions burned: 118 (million)
% 4.41/1.54  % (244379)Instruction limit reached! 
% 4.41/1.54  % (244379)------------------------------
% 4.41/1.54  % (244379)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.54  % (244379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.54  % (244379)CaDiCaL version: 2.1.3
% 4.41/1.54  % (244379)Termination reason: Instruction limit
% 4.41/1.54  % (244379)Termination phase: Saturation
% 4.41/1.54  % (244379)Time elapsed: 0.111 s
% 4.41/1.54  % (244379)Peak memory usage: 88 MB
% 4.41/1.54  % (244379)Instructions burned: 181 (million)
% 4.41/1.54  % (244389)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=783759919: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)
% 4.41/1.54  % (244388)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=868187024:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.41/1.54  % (244389)Refutation not found, incomplete strategy
% 4.41/1.54  % (244389)------------------------------
% 4.41/1.54  % (244389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.54  % (244389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.54  % (244389)CaDiCaL version: 2.1.3
% 4.41/1.54  % (244389)Termination reason: Refutation not found, incomplete strategy
% 4.41/1.54  % (244389)Time elapsed: 0.002 s
% 4.41/1.54  % (244389)Peak memory usage: 87 MB
% 4.41/1.54  % (244389)Instructions burned: 1 (million)
% 4.41/1.54  % (244390)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1493273330:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.41/1.54  % (244391)lrs+10_64_to=lpo:sil=8000:random_seed=977047220:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 4.41/1.54  % (244391)First to succeed.
% 4.41/1.54  % (244391)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-244369"
% 4.41/1.54  % (244388)Instruction limit reached! 
% 4.41/1.54  % (244388)------------------------------
% 4.41/1.54  % (244388)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.54  % (244388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.54  % (244388)CaDiCaL version: 2.1.3
% 4.41/1.54  % (244388)Termination reason: Instruction limit
% 4.41/1.54  % (244388)Termination phase: Saturation
% 4.41/1.54  % (244388)Time elapsed: 0.085 s
% 4.41/1.54  % (244388)Peak memory usage: 88 MB
% 4.41/1.54  % (244388)Instructions burned: 143 (million)
% 4.41/1.54  % (244390)Instruction limit reached! 
% 4.41/1.54  % (244390)------------------------------
% 4.41/1.54  % (244390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.54  % (244390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.54  % (244390)CaDiCaL version: 2.1.3
% 4.41/1.54  % (244390)Termination reason: Instruction limit
% 4.41/1.54  % (244390)Termination phase: Saturation
% 4.41/1.54  % (244390)Time elapsed: 0.120 s
% 4.41/1.54  % (244390)Peak memory usage: 88 MB
% 4.41/1.54  % (244390)Instructions burned: 220 (million)
% 4.41/1.54  % (244389)------------------------------
% 4.41/1.54  % (244389)------------------------------
% 4.41/1.54  % (244396)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=671357352:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 4.41/1.54  % (244397)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2691167624:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 4.41/1.54  % SZS status Satisfiable for theBenchmark
% 4.41/1.54  % SZS output start Saturation.
% See solution above
% 5.57/1.73  % SZS output start Definitions and Model Updates.
% 5.57/1.73  % SZS output end Definitions and Model Updates.
% 5.57/1.73  % (244391)------------------------------
% 5.57/1.73  % (244391)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.57/1.73  % (244391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.73  % (244391)CaDiCaL version: 2.1.3
% 5.57/1.73  % (244391)Termination reason: Satisfiable
% 5.57/1.73  % (244391)Time elapsed: 0.024 s
% 5.57/1.73  % (244391)Peak memory usage: 88 MB
% 5.57/1.73  % (244391)Instructions burned: 38 (million)
% 5.57/1.73  % (244391)------------------------------
% 5.57/1.73  % (244391)------------------------------
% 5.57/1.73  % (244369)Success in time 0.71 s
% 5.57/1.73  % Vampire exiting
%------------------------------------------------------------------------------