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Vampire---5.0.1.SAT-Sat.s

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%------------------------------------------------------------------------------
% File     : Vampire---5.0.1
% Problem  : GRP128-3.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox2/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 10:12:57 AM UTC 2026

% Result   : Satisfiable 6.41s 2.00s
% Output   : Saturation 0.16s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
cnf(u51,axiom,
    ~ cycle(e_3,e_3) ).

cnf(u55,axiom,
    ~ cycle(e_3,e_2) ).

cnf(u60,axiom,
    cycle(e_3,e_1) ).

cnf(u63,axiom,
    ~ cycle(e_3,e_0) ).

cnf(u68,axiom,
    ~ cycle(e_2,e_3) ).

cnf(u73,axiom,
    cycle(e_2,e_2) ).

cnf(u76,axiom,
    ~ cycle(e_2,e_1) ).

cnf(u80,axiom,
    ~ cycle(e_2,e_0) ).

cnf(u85,axiom,
    ~ cycle(e_1,e_3) ).

cnf(u89,axiom,
    ~ cycle(e_1,e_2) ).

cnf(u93,axiom,
    ~ cycle(e_1,e_1) ).

cnf(u98,axiom,
    cycle(e_1,e_0) ).

cnf(u120,axiom,
    ~ greater(e_0,e_0) ).

cnf(u124,axiom,
    ~ next(e_4,e_4) ).

cnf(u136,axiom,
    ~ next(e_2,e_4) ).

cnf(u141,axiom,
    ~ next(e_1,e_4) ).

cnf(u166,axiom,
    ~ next(e_3,e_1) ).

cnf(u174,axiom,
    ~ next(e_2,e_1) ).

cnf(u179,axiom,
    ~ next(e_1,e_1) ).

cnf(u191,axiom,
    ~ next(e_3,e_2) ).

cnf(u196,axiom,
    ~ next(e_2,e_2) ).

cnf(u234,axiom,
    ~ next(e_3,e_3) ).

cnf(u243,axiom,
    ~ next(e_1,e_3) ).

cnf(u253,axiom,
    ~ greater(e_0,e_3) ).

cnf(u261,axiom,
    ~ greater(e_1,e_3) ).

cnf(u264,axiom,
    ( ~ cycle(X0,e_0)
    | ~ greater(X0,e_3)
    | ~ next(X0,e_1) ) ).

cnf(u269,axiom,
    ~ greater(e_2,e_3) ).

cnf(u272,axiom,
    ( ~ cycle(X0,e_0)
    | ~ greater(X0,e_2)
    | ~ next(X0,e_1) ) ).

cnf(u277,axiom,
    ~ greater(e_3,e_3) ).

cnf(u289,axiom,
    ~ greater(e_0,e_1) ).

cnf(u297,axiom,
    ~ greater(e_1,e_1) ).

cnf(u314,axiom,
    ~ greater(e_0,e_2) ).

cnf(u322,axiom,
    ~ greater(e_1,e_2) ).

cnf(u330,axiom,
    ~ greater(e_2,e_2) ).

cnf(u365,axiom,
    ~ product(e_4,e_1,e_4) ).

cnf(u369,axiom,
    ~ product(e_4,e_1,e_3) ).

cnf(u374,axiom,
    product(e_4,e_1,e_2) ).

cnf(u377,axiom,
    ~ product(e_4,e_1,e_1) ).

cnf(u383,axiom,
    product(e_3,e_1,e_4) ).

cnf(u386,axiom,
    ~ product(e_3,e_1,e_3) ).

cnf(u390,axiom,
    ~ product(e_3,e_1,e_2) ).

cnf(u394,axiom,
    ~ product(e_3,e_1,e_1) ).

cnf(u399,axiom,
    ~ product(e_2,e_1,e_4) ).

cnf(u404,axiom,
    product(e_2,e_1,e_3) ).

cnf(u407,axiom,
    ~ product(e_2,e_1,e_2) ).

cnf(u411,axiom,
    ~ product(e_2,e_1,e_1) ).

cnf(u416,axiom,
    ~ product(e_1,e_1,e_4) ).

cnf(u420,axiom,
    ~ product(e_1,e_1,e_3) ).

cnf(u429,axiom,
    product(e_1,e_1,e_1) ).

cnf(u440,axiom,
    ( ~ next(e_4,X1)
    | equalish(e_4,X1) ) ).

cnf(u443,axiom,
    ( ~ cycle(e_4,X0)
    | ~ greater(X0,e_0) ) ).

cnf(u510,axiom,
    ( ~ next(e_3,X1)
    | equalish(e_4,X1) ) ).

cnf(u529,axiom,
    ~ product(e_4,e_2,e_4) ).

cnf(u534,axiom,
    product(e_4,e_2,e_3) ).

cnf(u537,axiom,
    ~ product(e_4,e_2,e_2) ).

cnf(u541,axiom,
    ~ product(e_4,e_2,e_1) ).

cnf(u546,axiom,
    ~ product(e_3,e_2,e_4) ).

cnf(u550,axiom,
    ~ product(e_3,e_2,e_3) ).

cnf(u554,axiom,
    ~ product(e_3,e_2,e_2) ).

cnf(u559,axiom,
    product(e_3,e_2,e_1) ).

cnf(u572,axiom,
    product(e_2,e_2,e_2) ).

cnf(u581,axiom,
    product(e_1,e_2,e_4) ).

cnf(u584,axiom,
    ~ product(e_1,e_2,e_3) ).

cnf(u588,axiom,
    ~ product(e_1,e_2,e_2) ).

cnf(u592,axiom,
    ~ product(e_1,e_2,e_1) ).

cnf(u660,axiom,
    ( ~ cycle(e_1,X0)
    | ~ greater(X0,e_0) ) ).

cnf(u786,axiom,
    ~ product(e_4,e_3,e_4) ).

cnf(u790,axiom,
    ~ product(e_4,e_3,e_3) ).

cnf(u794,axiom,
    ~ product(e_4,e_3,e_2) ).

cnf(u799,axiom,
    product(e_4,e_3,e_1) ).

cnf(u808,axiom,
    product(e_3,e_3,e_3) ).

cnf(u815,axiom,
    ~ product(e_3,e_3,e_1) ).

cnf(u821,axiom,
    product(e_2,e_3,e_4) ).

cnf(u824,axiom,
    ~ product(e_2,e_3,e_3) ).

cnf(u828,axiom,
    ~ product(e_2,e_3,e_2) ).

cnf(u832,axiom,
    ~ product(e_2,e_3,e_1) ).

cnf(u837,axiom,
    ~ product(e_1,e_3,e_4) ).

cnf(u841,axiom,
    ~ product(e_1,e_3,e_3) ).

cnf(u846,axiom,
    product(e_1,e_3,e_2) ).

cnf(u849,axiom,
    ~ product(e_1,e_3,e_1) ).

cnf(u1019,axiom,
    product(e_4,e_4,e_4) ).

cnf(u1039,axiom,
    ~ product(e_3,e_4,e_3) ).

cnf(u1044,axiom,
    product(e_3,e_4,e_2) ).

cnf(u1047,axiom,
    ~ product(e_3,e_4,e_1) ).

cnf(u1065,axiom,
    product(e_2,e_4,e_1) ).

cnf(u1069,axiom,
    ~ product(e_1,e_4,e_4) ).

cnf(u1074,axiom,
    product(e_1,e_4,e_3) ).

cnf(u1077,axiom,
    ~ product(e_1,e_4,e_2) ).

cnf(u1081,axiom,
    ~ product(e_1,e_4,e_1) ).

cnf(u1317,axiom,
    ( ~ next(e_2,X1)
    | equalish(e_3,X1) ) ).

cnf(u1386,negated_conjecture,
    ( ~ product(X0,e_4,e_1)
    | product(X0,e_1,e_3) ) ).

cnf(u1505,axiom,
    ( ~ product(e_2,X0,e_4)
    | equalish(X0,e_3) ) ).

cnf(u952,axiom,
    ( ~ product(X0,e_3,e_3)
    | equalish(X0,e_3) ) ).

cnf(u1485,axiom,
    ( ~ product(e_1,X0,e_4)
    | equalish(X0,e_2) ) ).

cnf(u1324,axiom,
    ( ~ product(e_4,e_2,X0)
    | equalish(X0,e_3) ) ).

cnf(u1136,axiom,
    ( ~ product(e_2,X0,e_1)
    | equalish(X0,e_4) ) ).

cnf(u1435,axiom,
    ( ~ next(e_0,X0)
    | equalish(e_1,X0) ) ).

cnf(u1086,axiom,
    ( ~ product(e_4,e_4,X0)
    | equalish(X0,e_4) ) ).

cnf(u1437,axiom,
    ( ~ cycle(X0,X1)
    | ~ next(X0,e_1)
    | ~ greater(X1,e_0)
    | ~ next(e_0,X2)
    | equalish(X1,X2) ) ).

cnf(u1085,axiom,
    ( ~ product(e_4,X0,e_4)
    | equalish(X0,e_4) ) ).

cnf(u1314,negated_conjecture,
    ( ~ product(X0,e_1,e_2)
    | product(X0,e_2,e_3) ) ).

cnf(u1447,negated_conjecture,
    ( ~ product(X0,e_1,e_3)
    | product(X0,e_3,e_4) ) ).

cnf(u1433,axiom,
    ( ~ cycle(X0,e_0)
    | ~ next(X0,e_4)
    | ~ greater(X0,e_3) ) ).

cnf(u1542,negated_conjecture,
    ( ~ product(X0,e_4,e_3)
    | product(X0,e_3,e_2) ) ).

cnf(u880,axiom,
    ( ~ product(X0,e_2,e_2)
    | equalish(X0,e_2) ) ).

cnf(u1385,axiom,
    ( ~ product(e_1,e_4,X0)
    | equalish(X0,e_3) ) ).

cnf(u43,axiom,
    ( ~ cycle(e_4,X0)
    | equalish(X0,e_0) ) ).

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

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

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

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

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

cnf(u499,negated_conjecture,
    ( ~ product(X0,e_1,e_4)
    | product(X0,e_4,e_2) ) ).

cnf(cycle5,axiom,
    ( ~ cycle(X3,X4)
    | ~ cycle(X2,e_0)
    | ~ cycle(X0,X1)
    | ~ next(X2,X3)
    | ~ greater(X2,X0)
    | ~ greater(X1,X4) ) ).

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

cnf(e_4_greater_e_0,axiom,
    greater(e_4,e_0) ).

cnf(cycle7,axiom,
    ( ~ product(X0,e_1,X2)
    | ~ cycle(X0,X1)
    | ~ greater(X1,e_0)
    | ~ next(X0,X3)
    | equalish(X2,X3) ) ).

cnf(u1490,axiom,
    ( ~ product(e_4,X0,e_1)
    | equalish(X0,e_3) ) ).

cnf(u1279,axiom,
    equalish(e_2,e_2) ).

cnf(cycle1,axiom,
    ( ~ cycle(X0,X2)
    | ~ cycle(X0,X1)
    | equalish(X1,X2) ) ).

cnf(u1446,axiom,
    ( ~ product(e_3,e_1,X0)
    | equalish(X0,e_4) ) ).

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

cnf(u1636,axiom,
    ( ~ next(e_1,X0)
    | equalish(e_2,X0) ) ).

cnf(e_0_then_e_1,axiom,
    next(e_0,e_1) ).

cnf(u1428,axiom,
    ( ~ cycle(e_3,X0)
    | equalish(X0,e_1) ) ).

cnf(u1491,axiom,
    ( ~ product(e_4,e_3,X0)
    | equalish(X0,e_1) ) ).

cnf(u1313,axiom,
    ( ~ product(e_2,e_1,X0)
    | equalish(X0,e_3) ) ).

cnf(u1384,axiom,
    ( ~ product(e_1,X0,e_3)
    | equalish(X0,e_4) ) ).

cnf(u202,axiom,
    ( ~ cycle(X1,X2)
    | ~ cycle(X0,e_0)
    | ~ next(X0,e_4)
    | ~ greater(X0,X1)
    | ~ greater(X2,e_0) ) ).

cnf(u1138,negated_conjecture,
    ( ~ product(X0,e_4,e_2)
    | product(X0,e_2,e_1) ) ).

cnf(u1137,axiom,
    ( ~ product(e_2,e_4,X0)
    | equalish(X0,e_1) ) ).

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

cnf(u358,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(u496,axiom,
    ( ~ product(X0,e_1,e_2)
    | equalish(X0,e_4) ) ).

cnf(u1489,axiom,
    ( ~ product(X0,e_3,e_1)
    | equalish(X0,e_4) ) ).

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

cnf(u355,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(e_3_is_not_e_4,axiom,
    ~ equalish(e_3,e_4) ).

cnf(u1540,axiom,
    ( ~ product(e_3,X0,e_2)
    | equalish(X0,e_4) ) ).

cnf(u1322,axiom,
    ( ~ product(X0,e_2,e_3)
    | equalish(X0,e_4) ) ).

cnf(u1455,axiom,
    ( ~ product(e_1,e_1,X0)
    | equalish(X0,e_1) ) ).

cnf(u357,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(u1504,axiom,
    ( ~ product(X0,e_3,e_4)
    | equalish(X0,e_2) ) ).

cnf(u1269,axiom,
    equalish(e_1,e_1) ).

cnf(u1536,negated_conjecture,
    ( ~ product(X0,e_3,e_1)
    | product(X0,e_1,e_2) ) ).

cnf(u1460,axiom,
    ( ~ product(e_3,e_2,X0)
    | equalish(X0,e_1) ) ).

cnf(u1454,axiom,
    ( ~ product(e_1,X0,e_1)
    | equalish(X0,e_1) ) ).

cnf(u1383,axiom,
    ( ~ product(X0,e_4,e_3)
    | equalish(X0,e_1) ) ).

cnf(u1323,axiom,
    ( ~ product(e_4,X0,e_3)
    | equalish(X0,e_2) ) ).

cnf(u1325,negated_conjecture,
    ( ~ product(X0,e_2,e_4)
    | product(X0,e_4,e_3) ) ).

cnf(u462,axiom,
    ~ greater(e_2,e_4) ).

cnf(u1645,axiom,
    ( ~ cycle(X0,e_0)
    | ~ next(X0,e_3)
    | ~ greater(X0,e_2) ) ).

cnf(u1312,axiom,
    ( ~ product(e_2,X0,e_3)
    | equalish(X0,e_1) ) ).

cnf(u1629,axiom,
    ( ~ cycle(X0,X1)
    | ~ next(X0,e_2)
    | ~ greater(X1,e_0)
    | ~ next(e_2,X2)
    | equalish(X1,X2) ) ).

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

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

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

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

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

cnf(cycle2,axiom,
    ( ~ group_element(X0)
    | cycle(X0,e_0)
    | cycle(X0,e_1)
    | cycle(X0,e_2)
    | cycle(X0,e_3) ) ).

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

cnf(u1484,axiom,
    ( ~ product(X0,e_2,e_4)
    | equalish(X0,e_1) ) ).

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(u1635,axiom,
    ( ~ cycle(X0,e_0)
    | ~ next(X0,e_4)
    | ~ greater(X0,e_2) ) ).

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

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

cnf(u1135,axiom,
    ( ~ product(X0,e_4,e_1)
    | equalish(X0,e_2) ) ).

cnf(e_2_greater_e_0,axiom,
    greater(e_2,e_0) ).

cnf(u1541,axiom,
    ( ~ product(e_3,e_4,X0)
    | equalish(X0,e_2) ) ).

cnf(u954,axiom,
    ( ~ product(e_3,e_3,X0)
    | equalish(X0,e_3) ) ).

cnf(e_1_greater_e_0,axiom,
    greater(e_1,e_0) ).

cnf(u1436,axiom,
    ( ~ cycle(e_1,X0)
    | equalish(X0,e_0) ) ).

cnf(u1430,axiom,
    ( ~ cycle(X1,X2)
    | ~ cycle(X0,e_0)
    | ~ next(X0,e_3)
    | ~ greater(X0,X1)
    | ~ greater(X2,e_1) ) ).

cnf(u1535,axiom,
    ( ~ product(e_1,e_3,X0)
    | equalish(X0,e_2) ) ).

cnf(u1392,axiom,
    equalish(e_3,e_3) ).

cnf(u1534,axiom,
    ( ~ product(e_1,X0,e_2)
    | equalish(X0,e_3) ) ).

cnf(u1146,axiom,
    equalish(e_4,e_4) ).

cnf(u1311,axiom,
    ( ~ product(X0,e_1,e_3)
    | equalish(X0,e_2) ) ).

cnf(u1453,axiom,
    ( ~ product(X0,e_1,e_1)
    | equalish(X0,e_1) ) ).

cnf(u1487,negated_conjecture,
    ( ~ product(X0,e_2,e_1)
    | product(X0,e_1,e_4) ) ).

cnf(u1084,axiom,
    ( ~ product(X0,e_4,e_4)
    | equalish(X0,e_4) ) ).

cnf(u1429,axiom,
    ( ~ cycle(X0,X1)
    | ~ next(X0,e_3)
    | ~ greater(X1,e_0)
    | ~ next(e_1,X2)
    | equalish(X1,X2) ) ).

cnf(u498,axiom,
    ( ~ product(e_4,e_1,X0)
    | equalish(X0,e_2) ) ).

cnf(u109,axiom,
    ( ~ cycle(X0,X1)
    | ~ next(X0,e_4)
    | ~ greater(X1,e_0)
    | ~ next(e_0,X2)
    | equalish(X1,X2) ) ).

cnf(u882,axiom,
    ( ~ product(e_2,e_2,X0)
    | equalish(X0,e_2) ) ).

cnf(u1539,axiom,
    ( ~ product(X0,e_4,e_2)
    | equalish(X0,e_3) ) ).

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

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

cnf(u44,axiom,
    equalish(e_0,e_0) ).

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

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(u953,axiom,
    ( ~ product(e_3,X0,e_3)
    | equalish(X0,e_3) ) ).

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

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

cnf(u1506,axiom,
    ( ~ product(e_2,e_3,X0)
    | equalish(X0,e_4) ) ).

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

cnf(u1492,negated_conjecture,
    ( ~ product(X0,e_3,e_4)
    | product(X0,e_4,e_1) ) ).

cnf(cycle4,axiom,
    ( ~ cycle(X2,X3)
    | ~ cycle(X0,X1)
    | ~ next(X0,X2)
    | ~ greater(X1,e_0)
    | ~ next(X3,X4)
    | equalish(X1,X4) ) ).

cnf(cycle3,axiom,
    cycle(e_4,e_0) ).

cnf(u1486,axiom,
    ( ~ product(e_1,e_2,X0)
    | equalish(X0,e_4) ) ).

cnf(u1458,axiom,
    ( ~ product(X0,e_2,e_1)
    | equalish(X0,e_3) ) ).

cnf(u1444,axiom,
    ( ~ product(X0,e_1,e_4)
    | equalish(X0,e_3) ) ).

cnf(u1533,axiom,
    ( ~ product(X0,e_3,e_2)
    | equalish(X0,e_1) ) ).

cnf(u1438,axiom,
    ( ~ cycle(X1,X2)
    | ~ cycle(X0,e_0)
    | ~ next(X0,e_1)
    | ~ greater(X0,X1)
    | ~ greater(X2,e_0) ) ).

cnf(u1662,axiom,
    ~ next(e_4,e_1) ).

cnf(u881,axiom,
    ( ~ product(e_2,X0,e_2)
    | equalish(X0,e_2) ) ).

cnf(u1507,negated_conjecture,
    ( ~ product(X0,e_3,e_2)
    | product(X0,e_2,e_4) ) ).

cnf(u305,axiom,
    ~ next(e_4,e_3) ).

cnf(u1445,axiom,
    ( ~ product(e_3,X0,e_4)
    | equalish(X0,e_1) ) ).

cnf(u1459,axiom,
    ( ~ product(e_3,X0,e_1)
    | equalish(X0,e_2) ) ).

cnf(u1461,negated_conjecture,
    ( ~ product(X0,e_2,e_3)
    | product(X0,e_3,e_1) ) ).

cnf(u497,axiom,
    ( ~ product(e_4,X0,e_2)
    | equalish(X0,e_1) ) ).

cnf(u1630,axiom,
    ( ~ cycle(X1,X2)
    | ~ cycle(X0,e_0)
    | ~ next(X0,e_2)
    | ~ greater(X0,X1)
    | ~ greater(X2,e_2) ) ).

cnf(cycle6,axiom,
    ( ~ product(X0,e_1,X1)
    | ~ cycle(X0,e_0)
    | ~ greater(X1,X0) ) ).

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

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

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

cnf(e_3_greater_e_0,axiom,
    greater(e_3,e_0) ).

cnf(u356,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(u1628,axiom,
    ( ~ cycle(e_2,X0)
    | equalish(X0,e_2) ) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : GRP128-3.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05  % Command  : run_vampire /export/starexec/sandbox2/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 09:27:56 UTC 2026
% 0.09/0.35  % CPUTime  : 
% 0.09/0.35  Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41  Running first-order theorem proving
% 0.12/0.41  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
% 6.41/2.00  % (245599)Input is clausal, will run a generic CNF schedule.
% 6.41/2.00  % (245624)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1623737351:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.41/2.00  % (245619)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=2955986388:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.41/2.00  % (245621)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=599684574:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.41/2.00  % (245623)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3755751093:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.41/2.00  % (245620)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2842583161:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.41/2.00  % (245622)lrs+10_1_sil=8000:sp=occurrence:random_seed=3195957011:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.41/2.00  % (245626)dis-21_1_sil=8000:lcm=predicate:random_seed=3446353789: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)
% 6.41/2.00  % (245624)Instruction limit reached! 
% 6.41/2.00  % (245624)------------------------------
% 6.41/2.00  % (245624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/2.00  % (245624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/2.00  % (245624)CaDiCaL version: 2.1.3
% 6.41/2.00  % (245624)Termination reason: Instruction limit
% 6.41/2.00  % (245624)Termination phase: Saturation
% 6.41/2.00  % (245624)Time elapsed: 0.099 s
% 6.41/2.00  % (245624)Peak memory usage: 89 MB
% 6.41/2.00  % (245624)Instructions burned: 181 (million)
% 6.41/2.00  % (245623)Instruction limit reached! 
% 6.41/2.00  % (245623)------------------------------
% 6.41/2.00  % (245623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/2.00  % (245623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/2.00  % (245623)CaDiCaL version: 2.1.3
% 6.41/2.00  % (245623)Termination reason: Instruction limit
% 6.41/2.00  % (245623)Termination phase: Saturation
% 6.41/2.00  % (245623)Time elapsed: 0.095 s
% 6.41/2.00  % (245623)Peak memory usage: 88 MB
% 6.41/2.00  % (245623)Instructions burned: 114 (million)
% 6.41/2.00  % (245622)Instruction limit reached! 
% 6.41/2.00  % (245622)------------------------------
% 6.41/2.00  % (245622)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/2.00  % (245622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/2.00  % (245622)CaDiCaL version: 2.1.3
% 6.41/2.00  % (245622)Termination reason: Instruction limit
% 6.41/2.00  % (245622)Termination phase: Saturation
% 6.41/2.00  % (245622)Time elapsed: 0.096 s
% 6.41/2.00  % (245622)Peak memory usage: 88 MB
% 6.41/2.00  % (245622)Instructions burned: 107 (million)
% 6.41/2.00  % (245626)Instruction limit reached! 
% 6.41/2.00  % (245626)------------------------------
% 6.41/2.00  % (245626)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/2.00  % (245626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/2.00  % (245626)CaDiCaL version: 2.1.3
% 6.41/2.00  % (245626)Termination reason: Instruction limit
% 6.41/2.00  % (245626)Termination phase: Saturation
% 6.41/2.00  % (245626)Time elapsed: 0.120 s
% 6.41/2.00  % (245626)Peak memory usage: 89 MB
% 6.41/2.00  % (245626)Instructions burned: 117 (million)
% 6.41/2.00  % (245636)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=3299184576:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 6.41/2.00  % (245636)Instruction limit reached! 
% 6.41/2.00  % (245636)------------------------------
% 6.41/2.00  % (245636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/2.00  % (245636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/2.00  % (245636)CaDiCaL version: 2.1.3
% 6.41/2.00  % (245636)Termination reason: Instruction limit
% 6.41/2.00  % (245636)Termination phase: Saturation
% 6.41/2.00  % (245636)Time elapsed: 0.078 s
% 6.41/2.00  % (245636)Peak memory usage: 89 MB
% 6.41/2.00  % (245636)Instructions burned: 143 (million)
% 6.41/2.00  % (245638)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1168488924:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 6.41/2.00  % (245638)Refutation not found, incomplete strategy
% 6.41/2.00  % (245638)------------------------------
% 6.41/2.00  % (245638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/2.00  % (245638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/2.00  % (245638)CaDiCaL version: 2.1.3
% 6.41/2.00  % (245638)Termination reason: Refutation not found, incomplete strategy
% 6.41/2.00  % (245638)Time elapsed: 0.003 s
% 6.41/2.00  % (245638)Peak memory usage: 87 MB
% 6.41/2.00  % (245638)Instructions burned: 2 (million)
% 6.41/2.00  % (245639)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2239263066:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 6.41/2.00  % (245641)lrs+10_64_to=lpo:sil=8000:random_seed=4083242658:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 6.41/2.00  % (245641)First to succeed.
% 6.41/2.00  % (245641)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-245599"
% 6.41/2.00  % (245643)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=264383342:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 6.41/2.00  % (245643)Instruction limit reached! 
% 6.41/2.00  % (245643)------------------------------
% 6.41/2.00  % (245643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/2.00  % (245643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/2.00  % (245643)CaDiCaL version: 2.1.3
% 6.41/2.00  % (245643)Termination reason: Instruction limit
% 6.41/2.00  % (245643)Termination phase: Saturation
% 6.41/2.00  % (245643)Time elapsed: 0.063 s
% 6.41/2.00  % (245643)Peak memory usage: 87 MB
% 6.41/2.00  % (245643)Instructions burned: 194 (million)
% 6.41/2.00  % (245639)Instruction limit reached! 
% 6.41/2.00  % (245639)------------------------------
% 6.41/2.00  % (245639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/2.00  % (245639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/2.00  % (245639)CaDiCaL version: 2.1.3
% 6.41/2.00  % (245639)Termination reason: Instruction limit
% 6.41/2.00  % (245639)Termination phase: Saturation
% 6.41/2.00  % (245639)Time elapsed: 0.205 s
% 6.41/2.00  % (245639)Peak memory usage: 88 MB
% 6.41/2.00  % (245639)Instructions burned: 219 (million)
% 6.41/2.00  % (245650)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3287066259:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 6.41/2.00  % (245638)------------------------------
% 6.41/2.00  % (245638)------------------------------
% 6.41/2.00  % (245650)Instruction limit reached! 
% 6.41/2.00  % (245650)------------------------------
% 6.41/2.00  % (245650)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/2.00  % (245650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/2.00  % (245650)CaDiCaL version: 2.1.3
% 6.41/2.00  % (245650)Termination reason: Instruction limit
% 6.41/2.00  % (245650)Termination phase: Saturation
% 6.41/2.00  % (245650)Time elapsed: 0.076 s
% 6.41/2.00  % (245650)Peak memory usage: 89 MB
% 6.41/2.00  % (245650)Instructions burned: 157 (million)
% 6.41/2.00  % (245651)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=39865117:i=3394:sd=4:ss=included:sgt=64_2992 on theBenchmark for (2992ds/3394Mi)
% 6.41/2.00  % SZS status Satisfiable for theBenchmark
% 6.41/2.00  % SZS output start Saturation.
% See solution above
% 0.16/2.20  % SZS output start Definitions and Model Updates.
% 0.16/2.20  % SZS output end Definitions and Model Updates.
% 0.16/2.20  % (245641)------------------------------
% 0.16/2.20  % (245641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/2.20  % (245641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/2.20  % (245641)CaDiCaL version: 2.1.3
% 0.16/2.20  % (245641)Termination reason: Satisfiable
% 0.16/2.20  % (245641)Time elapsed: 0.040 s
% 0.16/2.20  % (245641)Peak memory usage: 88 MB
% 0.16/2.20  % (245641)Instructions burned: 36 (million)
% 0.16/2.20  % (245641)------------------------------
% 0.16/2.20  % (245641)------------------------------
% 0.16/2.20  % (245599)Success in time 1.029 s
% 0.16/2.20  % Vampire exiting
%------------------------------------------------------------------------------