%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP127-3.005 : 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 10:12:56 AM UTC 2026
% Result : Satisfiable 4.59s 1.55s
% Output : Saturation 5.67s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(u67,axiom,
~ greater(e_1,e_1) ).
cnf(u70,axiom,
cycle(e_1,e_0) ).
cnf(u85,axiom,
( ~ cycle(e_1,X0)
| ~ greater(X0,e_0) ) ).
cnf(u97,axiom,
~ cycle(e_4,e_4) ).
cnf(u101,axiom,
~ cycle(e_4,e_3) ).
cnf(u105,axiom,
~ cycle(e_4,e_2) ).
cnf(u110,axiom,
cycle(e_4,e_1) ).
cnf(u113,axiom,
~ cycle(e_4,e_0) ).
cnf(u118,axiom,
~ cycle(e_3,e_4) ).
cnf(u122,axiom,
~ cycle(e_3,e_3) ).
cnf(u127,axiom,
cycle(e_3,e_2) ).
cnf(u130,axiom,
~ cycle(e_3,e_1) ).
cnf(u134,axiom,
~ cycle(e_3,e_0) ).
cnf(u139,axiom,
~ cycle(e_2,e_4) ).
cnf(u144,axiom,
cycle(e_2,e_3) ).
cnf(u147,axiom,
~ cycle(e_2,e_2) ).
cnf(u151,axiom,
~ cycle(e_2,e_1) ).
cnf(u155,axiom,
~ cycle(e_2,e_0) ).
cnf(u160,axiom,
~ cycle(e_1,e_4) ).
cnf(u209,axiom,
~ next(e_3,e_5) ).
cnf(u214,axiom,
~ next(e_2,e_5) ).
cnf(u259,axiom,
~ next(e_4,e_3) ).
cnf(u267,axiom,
~ next(e_3,e_3) ).
cnf(u286,axiom,
~ next(e_4,e_2) ).
cnf(u294,axiom,
~ next(e_3,e_2) ).
cnf(u299,axiom,
~ next(e_2,e_2) ).
cnf(u314,axiom,
~ next(e_3,e_1) ).
cnf(u319,axiom,
~ next(e_2,e_1) ).
cnf(u332,axiom,
~ next(e_4,e_4) ).
cnf(u341,axiom,
~ next(e_2,e_4) ).
cnf(u385,axiom,
( ~ next(e_0,X0)
| equalish(e_1,X0) ) ).
cnf(u489,axiom,
~ greater(e_1,e_4) ).
cnf(u493,axiom,
~ next(e_1,e_5) ).
cnf(u500,axiom,
~ greater(e_1,e_3) ).
cnf(u520,axiom,
~ next(e_1,e_1) ).
cnf(u527,axiom,
~ greater(e_1,e_2) ).
cnf(u537,axiom,
~ greater(e_0,e_1) ).
cnf(u621,axiom,
~ product(e_5,e_1,e_5) ).
cnf(u625,axiom,
~ product(e_5,e_1,e_4) ).
cnf(u629,axiom,
~ product(e_5,e_1,e_3) ).
cnf(u634,axiom,
product(e_5,e_1,e_2) ).
cnf(u637,axiom,
~ product(e_5,e_1,e_1) ).
cnf(u643,axiom,
product(e_4,e_1,e_5) ).
cnf(u646,axiom,
~ product(e_4,e_1,e_4) ).
cnf(u650,axiom,
~ product(e_4,e_1,e_3) ).
cnf(u654,axiom,
~ product(e_4,e_1,e_2) ).
cnf(u658,axiom,
~ product(e_4,e_1,e_1) ).
cnf(u663,axiom,
~ product(e_3,e_1,e_5) ).
cnf(u668,axiom,
product(e_3,e_1,e_4) ).
cnf(u671,axiom,
~ product(e_3,e_1,e_3) ).
cnf(u675,axiom,
~ product(e_3,e_1,e_2) ).
cnf(u679,axiom,
~ product(e_3,e_1,e_1) ).
cnf(u684,axiom,
~ product(e_2,e_1,e_5) ).
cnf(u688,axiom,
~ product(e_2,e_1,e_4) ).
cnf(u693,axiom,
product(e_2,e_1,e_3) ).
cnf(u696,axiom,
~ product(e_2,e_1,e_2) ).
cnf(u700,axiom,
~ product(e_2,e_1,e_1) ).
cnf(u730,axiom,
( ~ next(e_5,X1)
| equalish(e_4,X1) ) ).
cnf(u741,axiom,
( ~ next(e_4,X1)
| equalish(e_5,X1) ) ).
cnf(u821,axiom,
~ product(e_5,e_2,e_5) ).
cnf(u825,axiom,
~ product(e_5,e_2,e_4) ).
cnf(u829,axiom,
~ product(e_5,e_2,e_3) ).
cnf(u833,axiom,
~ product(e_5,e_2,e_2) ).
cnf(u838,axiom,
product(e_5,e_2,e_1) ).
cnf(u842,axiom,
~ product(e_4,e_2,e_5) ).
cnf(u846,axiom,
~ product(e_4,e_2,e_4) ).
cnf(u851,axiom,
product(e_4,e_2,e_3) ).
cnf(u854,axiom,
~ product(e_4,e_2,e_2) ).
cnf(u858,axiom,
~ product(e_4,e_2,e_1) ).
cnf(u864,axiom,
product(e_3,e_2,e_5) ).
cnf(u867,axiom,
~ product(e_3,e_2,e_4) ).
cnf(u871,axiom,
~ product(e_3,e_2,e_3) ).
cnf(u875,axiom,
~ product(e_3,e_2,e_2) ).
cnf(u879,axiom,
~ product(e_3,e_2,e_1) ).
cnf(u884,axiom,
~ product(e_1,e_2,e_5) ).
cnf(u889,axiom,
product(e_1,e_2,e_4) ).
cnf(u892,axiom,
~ product(e_1,e_2,e_3) ).
cnf(u896,axiom,
~ product(e_1,e_2,e_2) ).
cnf(u900,axiom,
~ product(e_1,e_2,e_1) ).
cnf(u941,axiom,
( ~ next(e_2,X1)
| equalish(e_3,X1) ) ).
cnf(u1055,axiom,
( ~ next(e_5,X1)
| equalish(e_3,X1) ) ).
cnf(u1066,axiom,
( ~ next(e_5,X1)
| equalish(e_2,X1) ) ).
cnf(u1114,axiom,
~ product(e_5,e_3,e_5) ).
cnf(u1119,axiom,
product(e_5,e_3,e_4) ).
cnf(u1122,axiom,
~ product(e_5,e_3,e_3) ).
cnf(u1126,axiom,
~ product(e_5,e_3,e_2) ).
cnf(u1130,axiom,
~ product(e_5,e_3,e_1) ).
cnf(u1135,axiom,
~ product(e_4,e_3,e_5) ).
cnf(u1139,axiom,
~ product(e_4,e_3,e_4) ).
cnf(u1143,axiom,
~ product(e_4,e_3,e_3) ).
cnf(u1148,axiom,
product(e_4,e_3,e_2) ).
cnf(u1151,axiom,
~ product(e_4,e_3,e_1) ).
cnf(u1156,axiom,
~ product(e_2,e_3,e_5) ).
cnf(u1160,axiom,
~ product(e_2,e_3,e_4) ).
cnf(u1164,axiom,
~ product(e_2,e_3,e_3) ).
cnf(u1168,axiom,
~ product(e_2,e_3,e_2) ).
cnf(u1173,axiom,
product(e_2,e_3,e_1) ).
cnf(u1178,axiom,
product(e_1,e_3,e_5) ).
cnf(u1181,axiom,
~ product(e_1,e_3,e_4) ).
cnf(u1185,axiom,
~ product(e_1,e_3,e_3) ).
cnf(u1189,axiom,
~ product(e_1,e_3,e_2) ).
cnf(u1193,axiom,
~ product(e_1,e_3,e_1) ).
cnf(u1421,axiom,
~ product(e_5,e_4,e_5) ).
cnf(u1425,axiom,
~ product(e_5,e_4,e_4) ).
cnf(u1430,axiom,
product(e_5,e_4,e_3) ).
cnf(u1433,axiom,
~ product(e_5,e_4,e_2) ).
cnf(u1437,axiom,
~ product(e_5,e_4,e_1) ).
cnf(u1442,axiom,
~ product(e_3,e_4,e_5) ).
cnf(u1446,axiom,
~ product(e_3,e_4,e_4) ).
cnf(u1450,axiom,
~ product(e_3,e_4,e_3) ).
cnf(u1454,axiom,
~ product(e_3,e_4,e_2) ).
cnf(u1459,axiom,
product(e_3,e_4,e_1) ).
cnf(u1464,axiom,
product(e_2,e_4,e_5) ).
cnf(u1467,axiom,
~ product(e_2,e_4,e_4) ).
cnf(u1471,axiom,
~ product(e_2,e_4,e_3) ).
cnf(u1475,axiom,
~ product(e_2,e_4,e_2) ).
cnf(u1479,axiom,
~ product(e_2,e_4,e_1) ).
cnf(u1484,axiom,
~ product(e_1,e_4,e_5) ).
cnf(u1488,axiom,
~ product(e_1,e_4,e_4) ).
cnf(u1497,axiom,
product(e_1,e_4,e_2) ).
cnf(u1500,axiom,
~ product(e_1,e_4,e_1) ).
cnf(u1738,axiom,
~ product(e_4,e_5,e_5) ).
cnf(u1742,axiom,
~ product(e_4,e_5,e_4) ).
cnf(u1746,axiom,
~ product(e_4,e_5,e_3) ).
cnf(u1750,axiom,
~ product(e_4,e_5,e_2) ).
cnf(u1755,axiom,
product(e_4,e_5,e_1) ).
cnf(u1759,axiom,
~ product(e_3,e_5,e_5) ).
cnf(u1763,axiom,
~ product(e_3,e_5,e_4) ).
cnf(u1767,axiom,
~ product(e_3,e_5,e_3) ).
cnf(u1772,axiom,
product(e_3,e_5,e_2) ).
cnf(u1775,axiom,
~ product(e_3,e_5,e_1) ).
cnf(u1785,axiom,
product(e_2,e_5,e_4) ).
cnf(u1788,axiom,
~ product(e_2,e_5,e_3) ).
cnf(u1792,axiom,
~ product(e_2,e_5,e_2) ).
cnf(u1796,axiom,
~ product(e_2,e_5,e_1) ).
cnf(u1801,axiom,
~ product(e_1,e_5,e_5) ).
cnf(u1805,axiom,
~ product(e_1,e_5,e_4) ).
cnf(u1810,axiom,
product(e_1,e_5,e_3) ).
cnf(u1813,axiom,
~ product(e_1,e_5,e_2) ).
cnf(u1817,axiom,
~ product(e_1,e_5,e_1) ).
cnf(u2147,axiom,
( ~ next(e_3,X1)
| equalish(e_4,X1) ) ).
cnf(u3127,axiom,
~ greater(e_0,e_3) ).
cnf(u3135,axiom,
~ greater(e_2,e_3) ).
cnf(u3143,axiom,
~ greater(e_3,e_3) ).
cnf(u3165,axiom,
~ greater(e_0,e_2) ).
cnf(u3173,axiom,
~ greater(e_2,e_2) ).
cnf(u2657,axiom,
( ~ cycle(X0,X1)
| ~ next(X0,e_4)
| ~ greater(X1,e_0)
| ~ next(e_1,X2)
| equalish(X1,X2) ) ).
cnf(u2941,axiom,
( ~ product(e_3,e_4,X0)
| equalish(X0,e_1) ) ).
cnf(u2994,axiom,
( ~ product(e_2,X0,e_4)
| equalish(X0,e_5) ) ).
cnf(product_left_cancellation,axiom,
( ~ product(X3,X1,X2)
| ~ product(X0,X1,X2)
| equalish(X0,X3) ) ).
cnf(u2885,negated_conjecture,
( ~ product(e_2,X0,e_5)
| product(e_1,e_2,X0) ) ).
cnf(e_5_is_not_e_2,axiom,
~ equalish(e_5,e_2) ).
cnf(u2749,axiom,
( ~ product(e_4,e_3,X0)
| equalish(X0,e_2) ) ).
cnf(u2935,axiom,
( ~ product(e_5,e_4,X0)
| equalish(X0,e_3) ) ).
cnf(u2971,axiom,
( ~ product(X0,e_5,e_1)
| equalish(X0,e_4) ) ).
cnf(u2936,negated_conjecture,
( ~ product(e_4,X0,e_5)
| product(e_3,e_4,X0) ) ).
cnf(u2727,axiom,
( ~ product(e_4,e_2,X0)
| equalish(X0,e_3) ) ).
cnf(u2883,axiom,
( ~ product(e_5,X0,e_1)
| equalish(X0,e_2) ) ).
cnf(u2893,axiom,
( ~ product(e_1,X0,e_4)
| equalish(X0,e_2) ) ).
cnf(u2932,negated_conjecture,
( ~ product(e_3,X0,e_1)
| product(e_5,e_3,X0) ) ).
cnf(u74,axiom,
equalish(X0,X0) ).
cnf(u2728,negated_conjecture,
( ~ product(e_2,X0,e_4)
| product(e_3,e_2,X0) ) ).
cnf(u2725,axiom,
( ~ product(X0,e_2,e_3)
| equalish(X0,e_4) ) ).
cnf(u2942,negated_conjecture,
( ~ product(e_4,X0,e_3)
| product(e_1,e_4,X0) ) ).
cnf(u2995,axiom,
( ~ product(e_2,e_5,X0)
| equalish(X0,e_4) ) ).
cnf(u2940,axiom,
( ~ product(e_3,X0,e_1)
| equalish(X0,e_4) ) ).
cnf(u2907,axiom,
( ~ product(e_2,e_3,X0)
| equalish(X0,e_1) ) ).
cnf(cycle5,axiom,
( ~ cycle(X3,X4)
| ~ cycle(X2,e_0)
| ~ cycle(X0,X1)
| ~ next(X2,X3)
| ~ greater(X2,X0)
| ~ greater(X1,X4) ) ).
cnf(u2888,axiom,
( ~ product(e_3,e_2,X0)
| equalish(X0,e_5) ) ).
cnf(e_5_is_not_e_1,axiom,
~ equalish(e_5,e_1) ).
cnf(u2945,axiom,
( ~ product(X0,e_4,e_5)
| equalish(X0,e_2) ) ).
cnf(e_5_is_not_e_4,axiom,
~ equalish(e_5,e_4) ).
cnf(u436,axiom,
( ~ cycle(X1,X2)
| ~ cycle(X0,e_0)
| ~ next(X0,e_1)
| ~ greater(X0,X1)
| ~ greater(X2,e_0) ) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4) ).
cnf(u73,axiom,
( ~ product(X0,X0,X1)
| equalish(X1,X0) ) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2) ).
cnf(u2898,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(element_5,axiom,
group_element(e_5) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4) ).
cnf(u2954,negated_conjecture,
( ~ product(e_4,X0,e_1)
| product(e_2,e_4,X0) ) ).
cnf(cycle6,axiom,
( ~ product(X0,e_1,X1)
| ~ cycle(X0,e_0)
| ~ greater(X1,X0) ) ).
cnf(u2894,axiom,
( ~ product(e_1,e_2,X0)
| equalish(X0,e_4) ) ).
cnf(element_1,axiom,
group_element(e_1) ).
cnf(e_5_greater_e_3,axiom,
greater(e_5,e_3) ).
cnf(cycle2,axiom,
( ~ group_element(X0)
| cycle(X0,e_0)
| cycle(X0,e_1)
| cycle(X0,e_2)
| cycle(X0,e_3)
| cycle(X0,e_4) ) ).
cnf(cycle1,axiom,
( ~ cycle(X0,X2)
| ~ cycle(X0,X1)
| equalish(X1,X2) ) ).
cnf(e_3_greater_e_0,axiom,
greater(e_3,e_0) ).
cnf(u610,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(e_3_greater_e_2,axiom,
greater(e_3,e_2) ).
cnf(u609,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(e_1_then_e_2,axiom,
next(e_1,e_2) ).
cnf(u2897,axiom,
( ~ product(X0,e_3,e_4)
| equalish(X0,e_5) ) ).
cnf(u2726,axiom,
( ~ product(e_4,X0,e_3)
| equalish(X0,e_2) ) ).
cnf(e_0_then_e_1,axiom,
next(e_0,e_1) ).
cnf(u2988,axiom,
( ~ product(e_3,X0,e_2)
| equalish(X0,e_5) ) ).
cnf(u2946,axiom,
( ~ product(e_2,X0,e_5)
| equalish(X0,e_4) ) ).
cnf(u3101,axiom,
( ~ next(e_1,X0)
| equalish(e_2,X0) ) ).
cnf(u2973,axiom,
( ~ product(e_4,e_5,X0)
| equalish(X0,e_1) ) ).
cnf(u2929,axiom,
( ~ product(X0,e_3,e_5)
| equalish(X0,e_1) ) ).
cnf(u2887,axiom,
( ~ product(e_3,X0,e_5)
| equalish(X0,e_2) ) ).
cnf(u611,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(u2925,axiom,
( ~ product(e_3,X0,e_4)
| equalish(X0,e_1) ) ).
cnf(u2947,axiom,
( ~ product(e_2,e_4,X0)
| equalish(X0,e_5) ) ).
cnf(u2895,negated_conjecture,
( ~ product(e_2,X0,e_1)
| product(e_4,e_2,X0) ) ).
cnf(e_3_then_e_4,axiom,
next(e_3,e_4) ).
cnf(u2914,axiom,
( ~ cycle(X1,X2)
| ~ cycle(X0,e_0)
| ~ next(X0,e_3)
| ~ greater(X0,X1)
| ~ greater(X2,e_2) ) ).
cnf(u2927,negated_conjecture,
( ~ product(e_1,X0,e_3)
| product(e_4,e_1,X0) ) ).
cnf(u2889,negated_conjecture,
( ~ product(e_2,X0,e_3)
| product(e_5,e_2,X0) ) ).
cnf(u2906,axiom,
( ~ product(e_2,X0,e_1)
| equalish(X0,e_3) ) ).
cnf(u2974,negated_conjecture,
( ~ product(e_5,X0,e_4)
| product(e_1,e_5,X0) ) ).
cnf(u188,axiom,
( ~ cycle(X0,X1)
| ~ next(X0,e_1)
| ~ greater(X1,e_0)
| ~ next(e_0,X2)
| equalish(X1,X2) ) ).
cnf(u2713,axiom,
( ~ cycle(X0,e_0)
| ~ next(X0,e_5)
| ~ greater(X0,e_2) ) ).
cnf(qg3,negated_conjecture,
( ~ product(X2,X0,X3)
| ~ product(X0,X1,X2)
| product(X3,X0,X1) ) ).
cnf(u2926,axiom,
( ~ product(e_3,e_1,X0)
| equalish(X0,e_4) ) ).
cnf(product_idempotence,axiom,
product(X0,X0,X0) ).
cnf(e_5_is_not_e_3,axiom,
~ equalish(e_5,e_3) ).
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(u2878,negated_conjecture,
( ~ product(e_1,X0,e_2)
| product(e_3,e_1,X0) ) ).
cnf(e_2_is_not_e_5,axiom,
~ equalish(e_2,e_5) ).
cnf(u3012,negated_conjecture,
( ~ product(e_5,X0,e_1)
| product(e_3,e_5,X0) ) ).
cnf(u514,axiom,
~ next(e_5,e_1) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3) ).
cnf(u2934,axiom,
( ~ product(e_5,X0,e_3)
| equalish(X0,e_4) ) ).
cnf(u2919,axiom,
( ~ cycle(X0,e_0)
| ~ next(X0,e_5)
| ~ greater(X0,e_3) ) ).
cnf(u3108,axiom,
( ~ cycle(X0,e_0)
| ~ next(X0,e_4)
| ~ greater(X0,e_3) ) ).
cnf(u2920,axiom,
( ~ cycle(X0,e_0)
| ~ next(X0,e_1)
| ~ greater(X0,e_3) ) ).
cnf(u3178,axiom,
( ~ cycle(X0,e_0)
| ~ next(X0,e_3)
| ~ greater(X0,e_2) ) ).
cnf(u2748,axiom,
( ~ product(e_4,X0,e_2)
| equalish(X0,e_3) ) ).
cnf(u2892,axiom,
( ~ product(X0,e_2,e_4)
| equalish(X0,e_1) ) ).
cnf(u549,axiom,
~ next(e_5,e_4) ).
cnf(u2899,axiom,
( ~ product(e_5,e_3,X0)
| equalish(X0,e_4) ) ).
cnf(u2708,axiom,
( ~ cycle(X1,X2)
| ~ cycle(X0,e_0)
| ~ next(X0,e_2)
| ~ greater(X0,X1)
| ~ greater(X2,e_3) ) ).
cnf(u2868,negated_conjecture,
( ~ product(e_1,X0,e_5)
| product(e_2,e_1,X0) ) ).
cnf(u2930,axiom,
( ~ product(e_1,X0,e_5)
| equalish(X0,e_3) ) ).
cnf(u2714,axiom,
( ~ cycle(X0,e_0)
| ~ next(X0,e_1)
| ~ greater(X0,e_2) ) ).
cnf(u2695,axiom,
( ~ product(e_4,e_1,X0)
| equalish(X0,e_5) ) ).
cnf(u75,axiom,
( ~ product(X0,X1,X0)
| equalish(X1,X0) ) ).
cnf(u77,axiom,
( ~ product(X0,X1,X1)
| equalish(X0,X1) ) ).
cnf(u2931,axiom,
( ~ product(e_1,e_3,X0)
| equalish(X0,e_5) ) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2) ).
cnf(u2876,axiom,
( ~ product(e_2,X0,e_3)
| equalish(X0,e_1) ) ).
cnf(e_1_is_not_e_5,axiom,
~ equalish(e_1,e_5) ).
cnf(cycle7,axiom,
( ~ product(X0,e_1,X2)
| ~ cycle(X0,X1)
| ~ greater(X1,e_0)
| ~ next(X0,X3)
| equalish(X2,X3) ) ).
cnf(element_3,axiom,
group_element(e_3) ).
cnf(element_2,axiom,
group_element(e_2) ).
cnf(u2693,axiom,
( ~ product(X0,e_1,e_5)
| equalish(X0,e_4) ) ).
cnf(e_4_greater_e_2,axiom,
greater(e_4,e_2) ).
cnf(cycle3,axiom,
cycle(e_5,e_0) ).
cnf(e_4_greater_e_0,axiom,
greater(e_4,e_0) ).
cnf(e_5_greater_e_0,axiom,
greater(e_5,e_0) ).
cnf(u2939,axiom,
( ~ product(X0,e_4,e_1)
| equalish(X0,e_3) ) ).
cnf(e_3_greater_e_1,axiom,
greater(e_3,e_1) ).
cnf(e_2_then_e_3,axiom,
next(e_2,e_3) ).
cnf(u2953,axiom,
( ~ product(e_1,e_4,X0)
| equalish(X0,e_2) ) ).
cnf(e_1_greater_e_0,axiom,
greater(e_1,e_0) ).
cnf(u485,axiom,
~ next(e_5,e_5) ).
cnf(e_4_then_e_5,axiom,
next(e_4,e_5) ).
cnf(u2877,axiom,
( ~ product(e_2,e_1,X0)
| equalish(X0,e_3) ) ).
cnf(u2905,axiom,
( ~ product(X0,e_3,e_1)
| equalish(X0,e_2) ) ).
cnf(u2750,negated_conjecture,
( ~ product(e_3,X0,e_4)
| product(e_2,e_3,X0) ) ).
cnf(u2924,axiom,
( ~ product(X0,e_1,e_4)
| equalish(X0,e_3) ) ).
cnf(u2996,negated_conjecture,
( ~ product(e_5,X0,e_2)
| product(e_4,e_5,X0) ) ).
cnf(u3009,axiom,
( ~ product(X0,e_5,e_3)
| equalish(X0,e_1) ) ).
cnf(u2972,axiom,
( ~ product(e_4,X0,e_1)
| equalish(X0,e_5) ) ).
cnf(u2951,axiom,
( ~ product(X0,e_4,e_2)
| equalish(X0,e_1) ) ).
cnf(u2865,axiom,
( ~ product(X0,e_1,e_2)
| equalish(X0,e_5) ) ).
cnf(u3185,axiom,
~ next(e_5,e_3) ).
cnf(u2987,axiom,
( ~ product(X0,e_5,e_2)
| equalish(X0,e_3) ) ).
cnf(u2694,axiom,
( ~ product(e_4,X0,e_5)
| equalish(X0,e_1) ) ).
cnf(u3109,axiom,
( ~ cycle(X0,e_0)
| ~ next(X0,e_4)
| ~ greater(X0,e_2) ) ).
cnf(u2952,axiom,
( ~ product(e_1,X0,e_2)
| equalish(X0,e_4) ) ).
cnf(u2747,axiom,
( ~ product(X0,e_3,e_2)
| equalish(X0,e_4) ) ).
cnf(u2882,axiom,
( ~ product(X0,e_2,e_1)
| equalish(X0,e_5) ) ).
cnf(u59,negated_conjecture,
( ~ product(X0,X1,X0)
| product(X0,X0,X1) ) ).
cnf(u62,axiom,
equalish(e_0,e_0) ).
cnf(u61,axiom,
( ~ cycle(e_5,X0)
| equalish(X0,e_0) ) ).
cnf(e_4_is_not_e_5,axiom,
~ equalish(e_4,e_5) ).
cnf(product_right_cancellation,axiom,
( ~ product(X0,X3,X2)
| ~ product(X0,X1,X2)
| equalish(X1,X3) ) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2) ).
cnf(u2706,axiom,
( ~ cycle(e_2,X0)
| equalish(X0,e_3) ) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1) ).
cnf(u2886,axiom,
( ~ product(X0,e_2,e_5)
| equalish(X0,e_3) ) ).
cnf(u2866,axiom,
( ~ product(e_5,X0,e_2)
| equalish(X0,e_1) ) ).
cnf(e_3_is_not_e_5,axiom,
~ equalish(e_3,e_5) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4) ).
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(cycle4,axiom,
( ~ cycle(X2,X3)
| ~ cycle(X0,X1)
| ~ next(X0,X2)
| ~ greater(X1,e_0)
| ~ next(X3,X4)
| equalish(X1,X4) ) ).
cnf(element_4,axiom,
group_element(e_4) ).
cnf(e_4_greater_e_3,axiom,
greater(e_4,e_3) ).
cnf(e_5_greater_e_2,axiom,
greater(e_5,e_2) ).
cnf(u2948,negated_conjecture,
( ~ product(e_4,X0,e_2)
| product(e_5,e_4,X0) ) ).
cnf(u2933,axiom,
( ~ product(X0,e_4,e_3)
| equalish(X0,e_5) ) ).
cnf(u2707,axiom,
( ~ cycle(X0,X1)
| ~ next(X0,e_2)
| ~ greater(X1,e_0)
| ~ next(e_3,X2)
| equalish(X1,X2) ) ).
cnf(u2989,axiom,
( ~ product(e_3,e_5,X0)
| equalish(X0,e_2) ) ).
cnf(u2900,negated_conjecture,
( ~ product(e_3,X0,e_5)
| product(e_4,e_3,X0) ) ).
cnf(u2696,negated_conjecture,
( ~ product(e_1,X0,e_4)
| product(e_5,e_1,X0) ) ).
cnf(u1063,axiom,
~ greater(e_2,e_5) ).
cnf(u3011,axiom,
( ~ product(e_1,e_5,X0)
| equalish(X0,e_3) ) ).
cnf(u2912,axiom,
( ~ cycle(e_3,X0)
| equalish(X0,e_2) ) ).
cnf(u2664,axiom,
( ~ cycle(X0,e_0)
| ~ next(X0,e_1)
| ~ greater(X0,e_4) ) ).
cnf(u2908,negated_conjecture,
( ~ product(e_3,X0,e_2)
| product(e_1,e_3,X0) ) ).
cnf(u2993,axiom,
( ~ product(X0,e_5,e_4)
| equalish(X0,e_2) ) ).
cnf(u187,axiom,
~ greater(e_0,e_0) ).
cnf(u612,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(u3010,axiom,
( ~ product(e_1,X0,e_3)
| equalish(X0,e_5) ) ).
cnf(u189,axiom,
( ~ cycle(e_1,X0)
| equalish(X0,e_0) ) ).
cnf(u176,axiom,
( ~ cycle(X0,X1)
| ~ next(X0,e_5)
| ~ greater(X1,e_0)
| ~ next(e_0,X2)
| equalish(X1,X2) ) ).
cnf(u2656,axiom,
( ~ cycle(e_4,X0)
| equalish(X0,e_1) ) ).
cnf(u2663,axiom,
( ~ cycle(X0,e_0)
| ~ next(X0,e_5)
| ~ greater(X0,e_4) ) ).
cnf(e_5_greater_e_4,axiom,
greater(e_5,e_4) ).
cnf(e_2_greater_e_1,axiom,
greater(e_2,e_1) ).
cnf(e_5_greater_e_1,axiom,
greater(e_5,e_1) ).
cnf(e_4_greater_e_1,axiom,
greater(e_4,e_1) ).
cnf(u2913,axiom,
( ~ cycle(X0,X1)
| ~ next(X0,e_3)
| ~ greater(X1,e_0)
| ~ next(e_2,X2)
| equalish(X1,X2) ) ).
cnf(u2867,axiom,
( ~ product(e_5,e_1,X0)
| equalish(X0,e_2) ) ).
cnf(e_2_greater_e_0,axiom,
greater(e_2,e_0) ).
cnf(u2884,axiom,
( ~ product(e_5,e_2,X0)
| equalish(X0,e_1) ) ).
cnf(u2990,negated_conjecture,
( ~ product(e_5,X0,e_3)
| product(e_2,e_5,X0) ) ).
cnf(u439,axiom,
( ~ cycle(X1,X2)
| ~ cycle(X0,e_0)
| ~ next(X0,e_5)
| ~ greater(X0,X1)
| ~ greater(X2,e_0) ) ).
cnf(u613,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(u2875,axiom,
( ~ product(X0,e_1,e_3)
| equalish(X0,e_2) ) ).
cnf(u2658,axiom,
( ~ cycle(X1,X2)
| ~ cycle(X0,e_0)
| ~ next(X0,e_4)
| ~ greater(X0,X1)
| ~ greater(X2,e_1) ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP127-3.005 : 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 09:28:25 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 Running first-order theorem proving
% 0.11/0.38 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
% 4.59/1.55 % (246848)Input is clausal, will run a generic CNF schedule.
% 4.59/1.55 % (246857)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1456666940:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.59/1.55 % (246857)Instruction limit reached!
% 4.59/1.55 % (246857)------------------------------
% 4.59/1.55 % (246857)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.55 % (246857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.55 % (246857)CaDiCaL version: 2.1.3
% 4.59/1.55 % (246857)Termination reason: Instruction limit
% 4.59/1.55 % (246857)Termination phase: Saturation
% 4.59/1.55 % (246857)Time elapsed: 0.033 s
% 4.59/1.55 % (246857)Peak memory usage: 88 MB
% 4.59/1.55 % (246857)Instructions burned: 114 (million)
% 4.59/1.55 % (246858)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1262007097:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.59/1.55 % (246853)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=3260641647:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.59/1.55 % (246854)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3842171110:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.59/1.55 % (246856)lrs+10_1_sil=8000:sp=occurrence:random_seed=2612938970:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.59/1.55 % (246859)dis-21_1_sil=8000:lcm=predicate:random_seed=1335641220: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)
% 4.59/1.55 % (246855)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=869875979:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.59/1.55 % (246858)Instruction limit reached!
% 4.59/1.55 % (246858)------------------------------
% 4.59/1.55 % (246858)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.55 % (246858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.55 % (246858)CaDiCaL version: 2.1.3
% 4.59/1.55 % (246858)Termination reason: Instruction limit
% 4.59/1.55 % (246858)Termination phase: Saturation
% 4.59/1.55 % (246858)Time elapsed: 0.059 s
% 4.59/1.55 % (246858)Peak memory usage: 89 MB
% 4.59/1.55 % (246858)Instructions burned: 183 (million)
% 4.59/1.55 % (246856)Instruction limit reached!
% 4.59/1.55 % (246856)------------------------------
% 4.59/1.55 % (246856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.55 % (246856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.55 % (246856)CaDiCaL version: 2.1.3
% 4.59/1.55 % (246856)Termination reason: Instruction limit
% 4.59/1.55 % (246856)Termination phase: Saturation
% 4.59/1.55 % (246856)Time elapsed: 0.062 s
% 4.59/1.55 % (246856)Peak memory usage: 88 MB
% 4.59/1.55 % (246856)Instructions burned: 107 (million)
% 4.59/1.55 % (246859)Instruction limit reached!
% 4.59/1.55 % (246859)------------------------------
% 4.59/1.55 % (246859)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.55 % (246859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.55 % (246859)CaDiCaL version: 2.1.3
% 4.59/1.55 % (246859)Termination reason: Instruction limit
% 4.59/1.55 % (246859)Termination phase: Saturation
% 4.59/1.55 % (246859)Time elapsed: 0.076 s
% 4.59/1.55 % (246859)Peak memory usage: 89 MB
% 4.59/1.55 % (246859)Instructions burned: 118 (million)
% 4.59/1.55 % (246861)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=1832095390:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 4.59/1.55 % (246868)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3299191655: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)
% 4.59/1.55 % (246868)Refutation not found, incomplete strategy
% 4.59/1.55 % (246868)------------------------------
% 4.59/1.55 % (246868)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.55 % (246868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.55 % (246868)CaDiCaL version: 2.1.3
% 4.59/1.55 % (246868)Termination reason: Refutation not found, incomplete strategy
% 4.59/1.55 % (246868)Time elapsed: 0.001 s
% 4.59/1.55 % (246868)Peak memory usage: 87 MB
% 4.59/1.55 % (246868)Instructions burned: 2 (million)
% 4.59/1.55 % (246869)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2875981130:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.59/1.55 % (246861)Instruction limit reached!
% 4.59/1.55 % (246861)------------------------------
% 4.59/1.55 % (246861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.55 % (246861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.55 % (246861)CaDiCaL version: 2.1.3
% 4.59/1.55 % (246861)Termination reason: Instruction limit
% 4.59/1.55 % (246861)Termination phase: Saturation
% 4.59/1.55 % (246861)Time elapsed: 0.086 s
% 4.59/1.55 % (246861)Peak memory usage: 89 MB
% 4.59/1.55 % (246861)Instructions burned: 143 (million)
% 4.59/1.55 % (246870)lrs+10_64_to=lpo:sil=8000:random_seed=2227706344:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 4.59/1.55 % (246870)First to succeed.
% 4.59/1.55 % (246870)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-246848"
% 4.59/1.55 % (246868)------------------------------
% 4.59/1.55 % (246868)------------------------------
% 4.59/1.55 % (246869)Instruction limit reached!
% 4.59/1.55 % (246869)------------------------------
% 4.59/1.55 % (246869)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.55 % (246869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.55 % (246869)CaDiCaL version: 2.1.3
% 4.59/1.55 % (246869)Termination reason: Instruction limit
% 4.59/1.55 % (246869)Termination phase: Saturation
% 4.59/1.55 % (246869)Time elapsed: 0.123 s
% 4.59/1.55 % (246869)Peak memory usage: 88 MB
% 4.59/1.55 % (246869)Instructions burned: 220 (million)
% 4.59/1.55 % (246874)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2180094197:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 4.59/1.55 % (246876)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3898457589:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 4.59/1.55 % (246874)Instruction limit reached!
% 4.59/1.55 % (246874)------------------------------
% 4.59/1.55 % (246874)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.55 % (246874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.55 % (246874)CaDiCaL version: 2.1.3
% 4.59/1.55 % (246874)Termination reason: Instruction limit
% 4.59/1.55 % (246874)Termination phase: Saturation
% 4.59/1.55 % (246874)Time elapsed: 0.096 s
% 4.59/1.55 % (246874)Peak memory usage: 88 MB
% 4.59/1.55 % (246874)Instructions burned: 194 (million)
% 4.59/1.55 % (246876)Instruction limit reached!
% 4.59/1.55 % (246876)------------------------------
% 4.59/1.55 % (246876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.55 % (246876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.55 % (246876)CaDiCaL version: 2.1.3
% 4.59/1.55 % (246876)Termination reason: Instruction limit
% 4.59/1.55 % (246876)Termination phase: Saturation
% 4.59/1.55 % (246876)Time elapsed: 0.048 s
% 4.59/1.55 % (246876)Peak memory usage: 89 MB
% 4.59/1.55 % (246876)Instructions burned: 161 (million)
% 4.59/1.55 % (246877)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=2411378192:i=3394:sd=4:ss=included:sgt=64_2994 on theBenchmark for (2994ds/3394Mi)
% 4.59/1.55 % SZS status Satisfiable for theBenchmark
% 4.59/1.55 % SZS output start Saturation.
% See solution above
% 5.67/1.75 % SZS output start Definitions and Model Updates.
% 5.67/1.75 % SZS output end Definitions and Model Updates.
% 5.67/1.75 % (246870)------------------------------
% 5.67/1.75 % (246870)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.67/1.75 % (246870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.67/1.75 % (246870)CaDiCaL version: 2.1.3
% 5.67/1.75 % (246870)Termination reason: Satisfiable
% 5.67/1.75 % (246870)Time elapsed: 0.053 s
% 5.67/1.75 % (246870)Peak memory usage: 89 MB
% 5.67/1.75 % (246870)Instructions burned: 81 (million)
% 5.67/1.75 % (246870)------------------------------
% 5.67/1.75 % (246870)------------------------------
% 5.67/1.75 % (246848)Success in time 0.723 s
% 5.67/1.75 % Vampire exiting
%------------------------------------------------------------------------------