%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP130-2.005 : 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 : n006.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 10:13:00 AM UTC 2026
% Result : Satisfiable 4.87s 1.62s
% Output : Saturation 5.97s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(u58,axiom,
~ product(e_5,e_1,e_5) ).
cnf(u62,axiom,
~ product(e_5,e_1,e_4) ).
cnf(u66,axiom,
~ product(e_5,e_1,e_3) ).
cnf(u71,axiom,
product(e_5,e_1,e_2) ).
cnf(u74,axiom,
~ product(e_5,e_1,e_1) ).
cnf(u80,axiom,
product(e_4,e_1,e_5) ).
cnf(u83,axiom,
~ product(e_4,e_1,e_4) ).
cnf(u87,axiom,
~ product(e_4,e_1,e_3) ).
cnf(u91,axiom,
~ product(e_4,e_1,e_2) ).
cnf(u95,axiom,
~ product(e_4,e_1,e_1) ).
cnf(u100,axiom,
~ product(e_3,e_1,e_5) ).
cnf(u105,axiom,
product(e_3,e_1,e_4) ).
cnf(u108,axiom,
~ product(e_3,e_1,e_3) ).
cnf(u112,axiom,
~ product(e_3,e_1,e_2) ).
cnf(u116,axiom,
~ product(e_3,e_1,e_1) ).
cnf(u121,axiom,
~ product(e_2,e_1,e_5) ).
cnf(u125,axiom,
~ product(e_2,e_1,e_4) ).
cnf(u130,axiom,
product(e_2,e_1,e_3) ).
cnf(u133,axiom,
~ product(e_2,e_1,e_2) ).
cnf(u137,axiom,
~ product(e_2,e_1,e_1) ).
cnf(u142,axiom,
~ product(e_1,e_1,e_5) ).
cnf(u146,axiom,
~ product(e_1,e_1,e_4) ).
cnf(u150,axiom,
~ product(e_1,e_1,e_3) ).
cnf(u154,axiom,
~ product(e_1,e_1,e_2) ).
cnf(u159,axiom,
product(e_1,e_1,e_1) ).
cnf(u206,axiom,
~ product(e_5,e_2,e_5) ).
cnf(u211,axiom,
product(e_5,e_2,e_4) ).
cnf(u214,axiom,
~ product(e_5,e_2,e_3) ).
cnf(u218,axiom,
~ product(e_5,e_2,e_2) ).
cnf(u222,axiom,
~ product(e_5,e_2,e_1) ).
cnf(u227,axiom,
~ product(e_4,e_2,e_5) ).
cnf(u231,axiom,
~ product(e_4,e_2,e_4) ).
cnf(u235,axiom,
~ product(e_4,e_2,e_3) ).
cnf(u239,axiom,
~ product(e_4,e_2,e_2) ).
cnf(u244,axiom,
product(e_4,e_2,e_1) ).
cnf(u249,axiom,
product(e_3,e_2,e_5) ).
cnf(u252,axiom,
~ product(e_3,e_2,e_4) ).
cnf(u256,axiom,
~ product(e_3,e_2,e_3) ).
cnf(u260,axiom,
~ product(e_3,e_2,e_2) ).
cnf(u264,axiom,
~ product(e_3,e_2,e_1) ).
cnf(u269,axiom,
~ product(e_2,e_2,e_5) ).
cnf(u273,axiom,
~ product(e_2,e_2,e_4) ).
cnf(u277,axiom,
~ product(e_2,e_2,e_3) ).
cnf(u282,axiom,
product(e_2,e_2,e_2) ).
cnf(u285,axiom,
~ product(e_2,e_2,e_1) ).
cnf(u290,axiom,
~ product(e_1,e_2,e_5) ).
cnf(u294,axiom,
~ product(e_1,e_2,e_4) ).
cnf(u299,axiom,
product(e_1,e_2,e_3) ).
cnf(u302,axiom,
~ product(e_1,e_2,e_2) ).
cnf(u306,axiom,
~ product(e_1,e_2,e_1) ).
cnf(u445,axiom,
~ product(e_4,e_3,e_5) ).
cnf(u449,axiom,
~ product(e_4,e_3,e_4) ).
cnf(u453,axiom,
~ product(e_4,e_3,e_3) ).
cnf(u458,axiom,
product(e_4,e_3,e_2) ).
cnf(u461,axiom,
~ product(e_4,e_3,e_1) ).
cnf(u468,axiom,
product(e_2,e_3,e_5) ).
cnf(u471,axiom,
~ product(e_2,e_3,e_4) ).
cnf(u475,axiom,
~ product(e_2,e_3,e_3) ).
cnf(u479,axiom,
~ product(e_2,e_3,e_2) ).
cnf(u483,axiom,
~ product(e_2,e_3,e_1) ).
cnf(u488,axiom,
~ product(e_1,e_3,e_5) ).
cnf(u493,axiom,
product(e_1,e_3,e_4) ).
cnf(u496,axiom,
~ product(e_1,e_3,e_3) ).
cnf(u500,axiom,
~ product(e_1,e_3,e_2) ).
cnf(u504,axiom,
~ product(e_1,e_3,e_1) ).
cnf(u509,negated_conjecture,
~ product(e_5,e_3,e_5) ).
cnf(u513,negated_conjecture,
~ product(e_5,e_3,e_4) ).
cnf(u517,negated_conjecture,
~ product(e_5,e_3,e_3) ).
cnf(u522,negated_conjecture,
product(e_5,e_3,e_1) ).
cnf(u526,negated_conjecture,
~ product(e_3,e_3,e_5) ).
cnf(u530,negated_conjecture,
~ product(e_3,e_3,e_4) ).
cnf(u535,negated_conjecture,
product(e_3,e_3,e_3) ).
cnf(u538,negated_conjecture,
~ product(e_3,e_3,e_2) ).
cnf(u543,axiom,
~ product(e_5,e_3,e_2) ).
cnf(u548,axiom,
~ product(e_3,e_3,e_1) ).
cnf(u694,axiom,
~ product(e_5,e_4,e_5) ).
cnf(u698,axiom,
~ product(e_5,e_4,e_4) ).
cnf(u703,axiom,
product(e_5,e_4,e_3) ).
cnf(u706,axiom,
~ product(e_5,e_4,e_2) ).
cnf(u710,axiom,
~ product(e_5,e_4,e_1) ).
cnf(u715,axiom,
~ product(e_4,e_4,e_5) ).
cnf(u720,axiom,
product(e_4,e_4,e_4) ).
cnf(u723,axiom,
~ product(e_4,e_4,e_3) ).
cnf(u727,axiom,
~ product(e_4,e_4,e_2) ).
cnf(u731,axiom,
~ product(e_4,e_4,e_1) ).
cnf(u736,axiom,
~ product(e_3,e_4,e_5) ).
cnf(u740,axiom,
~ product(e_3,e_4,e_4) ).
cnf(u744,axiom,
~ product(e_3,e_4,e_3) ).
cnf(u749,axiom,
product(e_3,e_4,e_2) ).
cnf(u752,axiom,
~ product(e_3,e_4,e_1) ).
cnf(u757,axiom,
~ product(e_2,e_4,e_5) ).
cnf(u761,axiom,
~ product(e_2,e_4,e_4) ).
cnf(u765,axiom,
~ product(e_2,e_4,e_3) ).
cnf(u769,axiom,
~ product(e_2,e_4,e_2) ).
cnf(u774,axiom,
product(e_2,e_4,e_1) ).
cnf(u779,axiom,
product(e_1,e_4,e_5) ).
cnf(u782,axiom,
~ product(e_1,e_4,e_4) ).
cnf(u786,axiom,
~ product(e_1,e_4,e_3) ).
cnf(u790,axiom,
~ product(e_1,e_4,e_2) ).
cnf(u794,axiom,
~ product(e_1,e_4,e_1) ).
cnf(u916,axiom,
product(e_5,e_5,e_5) ).
cnf(u919,axiom,
~ product(e_5,e_5,e_4) ).
cnf(u923,axiom,
~ product(e_5,e_5,e_3) ).
cnf(u927,axiom,
~ product(e_5,e_5,e_2) ).
cnf(u931,axiom,
~ product(e_5,e_5,e_1) ).
cnf(u936,axiom,
~ product(e_4,e_5,e_5) ).
cnf(u940,axiom,
~ product(e_4,e_5,e_4) ).
cnf(u945,axiom,
product(e_4,e_5,e_3) ).
cnf(u948,axiom,
~ product(e_4,e_5,e_2) ).
cnf(u952,axiom,
~ product(e_4,e_5,e_1) ).
cnf(u957,axiom,
~ product(e_3,e_5,e_5) ).
cnf(u961,axiom,
~ product(e_3,e_5,e_4) ).
cnf(u965,axiom,
~ product(e_3,e_5,e_3) ).
cnf(u969,axiom,
~ product(e_3,e_5,e_2) ).
cnf(u974,axiom,
product(e_3,e_5,e_1) ).
cnf(u978,axiom,
~ product(e_2,e_5,e_5) ).
cnf(u983,axiom,
product(e_2,e_5,e_4) ).
cnf(u986,axiom,
~ product(e_2,e_5,e_3) ).
cnf(u990,axiom,
~ product(e_2,e_5,e_2) ).
cnf(u994,axiom,
~ product(e_2,e_5,e_1) ).
cnf(u999,axiom,
~ product(e_1,e_5,e_5) ).
cnf(u1003,axiom,
~ product(e_1,e_5,e_4) ).
cnf(u1007,axiom,
~ product(e_1,e_5,e_3) ).
cnf(u1012,axiom,
product(e_1,e_5,e_2) ).
cnf(u1015,axiom,
~ product(e_1,e_5,e_1) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2) ).
cnf(u3675,axiom,
( ~ greater(e_5,X0)
| ~ next(e_4,X0) ) ).
cnf(e_3_is_not_e_5,axiom,
~ equalish(e_3,e_5) ).
cnf(e_5_is_not_e_2,axiom,
~ equalish(e_5,e_2) ).
cnf(u3714,axiom,
( ~ product(X0,e_4,e_4)
| equalish(X0,e_4) ) ).
cnf(u3625,axiom,
( ~ product(e_3,X0,e_5)
| equalish(X0,e_2) ) ).
cnf(u189,axiom,
~ next(e_4,e_1) ).
cnf(u3505,axiom,
( ~ greater(e_4,X0)
| ~ next(e_3,X0) ) ).
cnf(u2780,axiom,
equalish(e_4,e_4) ).
cnf(u3626,axiom,
( ~ product(e_3,e_2,X0)
| equalish(X0,e_5) ) ).
cnf(u3507,axiom,
( ~ product(e_3,X0,e_4)
| equalish(X0,e_1) ) ).
cnf(u3771,axiom,
~ next(e_5,e_1) ).
cnf(u3663,negated_conjecture,
( ~ product(e_5,e_3,X0)
| equalish(X0,e_1) ) ).
cnf(u3678,axiom,
( ~ product(e_4,e_1,X0)
| equalish(X0,e_5) ) ).
cnf(u3684,negated_conjecture,
( ~ product(e_4,X0,e_2)
| product(e_1,X0,e_4) ) ).
cnf(u3701,negated_conjecture,
( ~ product(e_2,X0,e_3)
| product(e_5,X0,e_2) ) ).
cnf(u3682,axiom,
( ~ product(e_4,X0,e_1)
| equalish(X0,e_2) ) ).
cnf(u3699,axiom,
( ~ product(e_2,X0,e_5)
| equalish(X0,e_3) ) ).
cnf(e_4_greater_e_1,axiom,
greater(e_4,e_1) ).
cnf(e_2_greater_e_1,axiom,
greater(e_2,e_1) ).
cnf(element_1,axiom,
group_element(e_1) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3) ).
cnf(qg3,negated_conjecture,
( ~ product(X0,X2,X3)
| ~ product(X0,X1,X2)
| product(X3,X1,X0) ) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3) ).
cnf(u3627,negated_conjecture,
( ~ product(e_3,X0,e_2)
| product(e_5,X0,e_3) ) ).
cnf(u190,axiom,
~ next(e_4,e_2) ).
cnf(u3740,axiom,
( ~ product(e_3,X0,e_1)
| equalish(X0,e_5) ) ).
cnf(u3511,axiom,
( ~ greater(e_3,X0)
| ~ next(e_2,X0) ) ).
cnf(u50,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(u3515,negated_conjecture,
( ~ product(e_2,X0,e_1)
| product(e_3,X0,e_2) ) ).
cnf(u3518,axiom,
( ~ product(e_1,X0,e_1)
| equalish(X0,e_1) ) ).
cnf(u3662,negated_conjecture,
( ~ product(e_5,X0,e_1)
| equalish(X0,e_3) ) ).
cnf(u3685,axiom,
( ~ product(X0,e_2,e_2)
| equalish(X0,e_2) ) ).
cnf(u3683,axiom,
( ~ product(e_4,e_2,X0)
| equalish(X0,e_1) ) ).
cnf(u3672,axiom,
( ~ product(e_5,e_1,X0)
| equalish(X0,e_2) ) ).
cnf(u3522,axiom,
( ~ product(e_5,X0,e_4)
| equalish(X0,e_2) ) ).
cnf(u3686,axiom,
( ~ product(e_2,X0,e_2)
| equalish(X0,e_2) ) ).
cnf(u3692,negated_conjecture,
( ~ product(e_1,X0,e_2)
| product(e_3,X0,e_1) ) ).
cnf(e_3_greater_e_1,axiom,
greater(e_3,e_1) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1) ).
cnf(u3593,axiom,
( ~ product(e_5,X0,e_5)
| equalish(X0,e_5) ) ).
cnf(element_4,axiom,
group_element(e_4) ).
cnf(u46,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(u3715,axiom,
( ~ product(e_4,X0,e_4)
| equalish(X0,e_4) ) ).
cnf(u3613,negated_conjecture,
( ~ product(X0,e_3,e_3)
| equalish(X0,e_3) ) ).
cnf(u3594,axiom,
( ~ product(e_5,e_5,X0)
| equalish(X0,e_5) ) ).
cnf(element_2,axiom,
group_element(e_2) ).
cnf(u3735,axiom,
( ~ product(e_4,e_5,X0)
| equalish(X0,e_3) ) ).
cnf(product_left_cancellation,axiom,
( ~ product(X3,X1,X2)
| ~ product(X0,X1,X2)
| equalish(X0,X3) ) ).
cnf(u3724,axiom,
( ~ product(e_2,X0,e_1)
| equalish(X0,e_4) ) ).
cnf(u3741,axiom,
( ~ product(e_3,e_5,X0)
| equalish(X0,e_1) ) ).
cnf(u3739,axiom,
( ~ product(X0,e_5,e_1)
| equalish(X0,e_3) ) ).
cnf(u3728,axiom,
( ~ product(e_1,X0,e_5)
| equalish(X0,e_4) ) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2) ).
cnf(u3519,axiom,
( ~ product(e_1,e_1,X0)
| equalish(X0,e_1) ) ).
cnf(u3506,axiom,
( ~ product(X0,e_1,e_4)
| equalish(X0,e_3) ) ).
cnf(u3669,axiom,
( ~ greater(e_2,X0)
| ~ next(e_5,X0) ) ).
cnf(u191,axiom,
~ next(e_4,e_3) ).
cnf(u3670,axiom,
( ~ product(X0,e_1,e_2)
| equalish(X0,e_5) ) ).
cnf(u3676,axiom,
( ~ product(X0,e_1,e_5)
| equalish(X0,e_4) ) ).
cnf(u358,axiom,
~ next(e_3,e_3) ).
cnf(u356,axiom,
~ next(e_3,e_1) ).
cnf(u3568,negated_conjecture,
( ~ product(e_3,X0,e_4)
| product(e_2,X0,e_3) ) ).
cnf(e_5_greater_e_3,axiom,
greater(e_5,e_3) ).
cnf(u3705,axiom,
( ~ product(e_1,e_3,X0)
| equalish(X0,e_4) ) ).
cnf(e_3_then_e_4,axiom,
next(e_3,e_4) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2) ).
cnf(u3706,negated_conjecture,
( ~ product(e_1,X0,e_3)
| product(e_4,X0,e_1) ) ).
cnf(e_1_then_e_2,axiom,
next(e_1,e_2) ).
cnf(e_2_is_not_e_5,axiom,
~ equalish(e_2,e_5) ).
cnf(u3725,axiom,
( ~ product(e_2,e_4,X0)
| equalish(X0,e_1) ) ).
cnf(u3615,negated_conjecture,
( ~ product(e_3,e_3,X0)
| equalish(X0,e_3) ) ).
cnf(product_right_cancellation,axiom,
( ~ product(X0,X3,X2)
| ~ product(X0,X1,X2)
| equalish(X1,X3) ) ).
cnf(u3723,axiom,
( ~ product(X0,e_4,e_1)
| equalish(X0,e_2) ) ).
cnf(u3712,negated_conjecture,
( ~ product(e_5,X0,e_4)
| product(e_3,X0,e_5) ) ).
cnf(element_3,axiom,
group_element(e_3) ).
cnf(u3729,axiom,
( ~ product(e_1,e_4,X0)
| equalish(X0,e_5) ) ).
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(u47,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(u2882,axiom,
equalish(e_2,e_2) ).
cnf(u3514,axiom,
( ~ product(e_2,e_1,X0)
| equalish(X0,e_3) ) ).
cnf(u3524,negated_conjecture,
( ~ product(e_5,X0,e_2)
| product(e_4,X0,e_5) ) ).
cnf(u2758,axiom,
equalish(e_5,e_5) ).
cnf(u3761,axiom,
( ~ product(X0,e_5,e_2)
| equalish(X0,e_1) ) ).
cnf(u357,axiom,
~ next(e_3,e_2) ).
cnf(u380,axiom,
~ next(e_2,e_2) ).
cnf(u2779,axiom,
equalish(e_1,e_1) ).
cnf(u3565,axiom,
( ~ product(X0,e_4,e_2)
| equalish(X0,e_3) ) ).
cnf(u3689,axiom,
( ~ product(X0,e_2,e_3)
| equalish(X0,e_1) ) ).
cnf(u3703,axiom,
( ~ product(X0,e_3,e_4)
| equalish(X0,e_1) ) ).
cnf(e_5_greater_e_4,axiom,
greater(e_5,e_4) ).
cnf(u3709,axiom,
( ~ product(X0,e_4,e_3)
| equalish(X0,e_5) ) ).
cnf(u3690,axiom,
( ~ product(e_1,X0,e_3)
| equalish(X0,e_2) ) ).
cnf(u3696,axiom,
( ~ product(e_4,e_3,X0)
| equalish(X0,e_2) ) ).
cnf(e_4_greater_e_3,axiom,
greater(e_4,e_3) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4) ).
cnf(e_2_then_e_3,axiom,
next(e_2,e_3) ).
cnf(u3614,negated_conjecture,
( ~ product(e_3,X0,e_3)
| equalish(X0,e_3) ) ).
cnf(u3727,axiom,
( ~ product(X0,e_4,e_5)
| equalish(X0,e_1) ) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1) ).
cnf(u3742,negated_conjecture,
( ~ product(e_3,X0,e_5)
| product(e_1,X0,e_3) ) ).
cnf(u3624,axiom,
( ~ product(X0,e_2,e_5)
| equalish(X0,e_3) ) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4) ).
cnf(u3748,axiom,
( ~ product(e_2,e_5,X0)
| equalish(X0,e_4) ) ).
cnf(product_total_function2,axiom,
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| equalish(X2,X3) ) ).
cnf(u3763,axiom,
( ~ product(e_1,e_5,X0)
| equalish(X0,e_2) ) ).
cnf(e_5_is_not_e_4,axiom,
~ equalish(e_5,e_4) ).
cnf(u3508,axiom,
( ~ product(e_3,e_1,X0)
| equalish(X0,e_4) ) ).
cnf(u3764,negated_conjecture,
( ~ product(e_1,X0,e_5)
| product(e_2,X0,e_1) ) ).
cnf(u3762,axiom,
( ~ product(e_1,X0,e_2)
| equalish(X0,e_5) ) ).
cnf(u3512,axiom,
( ~ product(X0,e_1,e_3)
| equalish(X0,e_2) ) ).
cnf(u3673,negated_conjecture,
( ~ product(e_5,X0,e_1)
| product(e_2,X0,e_5) ) ).
cnf(u3687,axiom,
( ~ product(e_2,e_2,X0)
| equalish(X0,e_2) ) ).
cnf(u3691,axiom,
( ~ product(e_1,e_2,X0)
| equalish(X0,e_3) ) ).
cnf(u3697,negated_conjecture,
( ~ product(e_4,X0,e_3)
| product(e_2,X0,e_4) ) ).
cnf(u3711,axiom,
( ~ product(e_5,e_4,X0)
| equalish(X0,e_3) ) ).
cnf(e_5_greater_e_2,axiom,
greater(e_5,e_2) ).
cnf(e_3_greater_e_2,axiom,
greater(e_3,e_2) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3) ).
cnf(e_4_is_not_e_5,axiom,
~ equalish(e_4,e_5) ).
cnf(u3726,negated_conjecture,
( ~ product(e_2,X0,e_4)
| product(e_1,X0,e_2) ) ).
cnf(no_redundancy,axiom,
( ~ product(X0,e_1,X1)
| ~ next(X0,X2)
| ~ greater(X1,X2) ) ).
cnf(u3749,negated_conjecture,
( ~ product(e_2,X0,e_5)
| product(e_4,X0,e_2) ) ).
cnf(u3730,negated_conjecture,
( ~ product(e_1,X0,e_4)
| product(e_5,X0,e_1) ) ).
cnf(u3747,axiom,
( ~ product(e_2,X0,e_4)
| equalish(X0,e_5) ) ).
cnf(u3736,negated_conjecture,
( ~ product(e_4,X0,e_5)
| product(e_3,X0,e_4) ) ).
cnf(u49,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(e_1_is_not_e_5,axiom,
~ equalish(e_1,e_5) ).
cnf(u3746,axiom,
( ~ product(X0,e_5,e_4)
| equalish(X0,e_2) ) ).
cnf(u3516,axiom,
( ~ greater(e_1,X0)
| ~ next(e_1,X0) ) ).
cnf(u3509,negated_conjecture,
( ~ product(e_3,X0,e_1)
| product(e_4,X0,e_3) ) ).
cnf(u3513,axiom,
( ~ product(e_2,X0,e_3)
| equalish(X0,e_1) ) ).
cnf(u192,axiom,
~ next(e_4,e_4) ).
cnf(u3671,axiom,
( ~ product(e_5,X0,e_2)
| equalish(X0,e_1) ) ).
cnf(u3677,axiom,
( ~ product(e_4,X0,e_5)
| equalish(X0,e_1) ) ).
cnf(u3664,negated_conjecture,
( ~ product(e_5,X0,e_3)
| product(e_1,X0,e_5) ) ).
cnf(u3681,axiom,
( ~ product(X0,e_2,e_1)
| equalish(X0,e_4) ) ).
cnf(u3695,axiom,
( ~ product(e_4,X0,e_2)
| equalish(X0,e_3) ) ).
cnf(u3710,axiom,
( ~ product(e_5,X0,e_3)
| equalish(X0,e_4) ) ).
cnf(u3566,axiom,
( ~ product(e_3,X0,e_2)
| equalish(X0,e_4) ) ).
cnf(element_5,axiom,
group_element(e_5) ).
cnf(u3592,axiom,
( ~ product(X0,e_5,e_5)
| equalish(X0,e_5) ) ).
cnf(u3716,axiom,
( ~ product(e_4,e_4,X0)
| equalish(X0,e_4) ) ).
cnf(u3733,axiom,
( ~ product(X0,e_5,e_3)
| equalish(X0,e_4) ) ).
cnf(e_4_greater_e_2,axiom,
greater(e_4,e_2) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1) ).
cnf(u3734,axiom,
( ~ product(e_4,X0,e_3)
| equalish(X0,e_5) ) ).
cnf(e_5_greater_e_1,axiom,
greater(e_5,e_1) ).
cnf(e_5_is_not_e_3,axiom,
~ equalish(e_5,e_3) ).
cnf(e_5_is_not_e_1,axiom,
~ equalish(e_5,e_1) ).
cnf(u48,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(u3517,axiom,
( ~ product(X0,e_1,e_1)
| equalish(X0,e_1) ) ).
cnf(u3521,axiom,
( ~ product(X0,e_2,e_4)
| equalish(X0,e_5) ) ).
cnf(u3661,negated_conjecture,
( ~ product(X0,e_3,e_1)
| equalish(X0,e_5) ) ).
cnf(u3523,axiom,
( ~ product(e_5,e_2,X0)
| equalish(X0,e_4) ) ).
cnf(u3679,negated_conjecture,
( ~ product(e_4,X0,e_1)
| product(e_5,X0,e_4) ) ).
cnf(u3694,axiom,
( ~ product(X0,e_3,e_2)
| equalish(X0,e_4) ) ).
cnf(u3700,axiom,
( ~ product(e_2,e_3,X0)
| equalish(X0,e_5) ) ).
cnf(u3567,axiom,
( ~ product(e_3,e_4,X0)
| equalish(X0,e_2) ) ).
cnf(u3698,axiom,
( ~ product(X0,e_3,e_5)
| equalish(X0,e_2) ) ).
cnf(e_4_then_e_5,axiom,
next(e_4,e_5) ).
cnf(u3704,axiom,
( ~ product(e_1,X0,e_4)
| equalish(X0,e_3) ) ).
cnf(u379,axiom,
~ next(e_2,e_1) ).
cnf(u2778,axiom,
equalish(e_3,e_3) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP130-2.005 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n006.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 09:27:55 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 4.87/1.62 % (2728908)Input is clausal, will run a generic CNF schedule.
% 4.87/1.62 % (2728915)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1774301481:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.87/1.62 % (2728913)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=416799548:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.87/1.62 % (2728917)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3102245942:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.87/1.62 % (2728916)lrs+10_1_sil=8000:sp=occurrence:random_seed=1431139167:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.87/1.62 % (2728919)dis-21_1_sil=8000:lcm=predicate:random_seed=436429848: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)
% 4.87/1.62 % (2728914)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2378163559:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.87/1.62 % (2728918)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=8206649:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.87/1.62 % (2728916)Instruction limit reached!
% 4.87/1.62 % (2728916)------------------------------
% 4.87/1.62 % (2728916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.87/1.62 % (2728916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.87/1.62 % (2728916)CaDiCaL version: 2.1.3
% 4.87/1.62 % (2728916)Termination reason: Instruction limit
% 4.87/1.62 % (2728916)Termination phase: Saturation
% 4.87/1.62 % (2728916)Time elapsed: 0.056 s
% 4.87/1.62 % (2728916)Peak memory usage: 88 MB
% 4.87/1.62 % (2728916)Instructions burned: 109 (million)
% 4.87/1.62 % (2728917)Instruction limit reached!
% 4.87/1.62 % (2728917)------------------------------
% 4.87/1.62 % (2728917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.87/1.62 % (2728917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.87/1.62 % (2728917)CaDiCaL version: 2.1.3
% 4.87/1.62 % (2728917)Termination reason: Instruction limit
% 4.87/1.62 % (2728917)Termination phase: Saturation
% 4.87/1.62 % (2728917)Time elapsed: 0.061 s
% 4.87/1.62 % (2728917)Peak memory usage: 88 MB
% 4.87/1.62 % (2728917)Instructions burned: 115 (million)
% 4.87/1.62 % (2728919)Instruction limit reached!
% 4.87/1.62 % (2728919)------------------------------
% 4.87/1.62 % (2728919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.87/1.62 % (2728919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.87/1.62 % (2728919)CaDiCaL version: 2.1.3
% 4.87/1.62 % (2728919)Termination reason: Instruction limit
% 4.87/1.62 % (2728919)Termination phase: Saturation
% 4.87/1.62 % (2728919)Time elapsed: 0.075 s
% 4.87/1.62 % (2728919)Peak memory usage: 88 MB
% 4.87/1.62 % (2728919)Instructions burned: 118 (million)
% 4.87/1.62 % (2728918)Instruction limit reached!
% 4.87/1.62 % (2728918)------------------------------
% 4.87/1.62 % (2728918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.87/1.62 % (2728918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.87/1.62 % (2728918)CaDiCaL version: 2.1.3
% 4.87/1.62 % (2728918)Termination reason: Instruction limit
% 4.87/1.62 % (2728918)Termination phase: Saturation
% 4.87/1.62 % (2728918)Time elapsed: 0.107 s
% 4.87/1.62 % (2728918)Peak memory usage: 89 MB
% 4.87/1.62 % (2728918)Instructions burned: 180 (million)
% 4.87/1.62 % (2728928)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3796204274: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)
% 4.87/1.62 % (2728927)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=663228956:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.87/1.62 % (2728928)Refutation not found, incomplete strategy
% 4.87/1.62 % (2728928)------------------------------
% 4.87/1.62 % (2728928)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.87/1.62 % (2728928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.87/1.62 % (2728928)CaDiCaL version: 2.1.3
% 4.87/1.62 % (2728928)Termination reason: Refutation not found, incomplete strategy
% 4.87/1.62 % (2728928)Time elapsed: 0.002 s
% 4.87/1.62 % (2728928)Peak memory usage: 87 MB
% 4.87/1.62 % (2728928)Instructions burned: 1 (million)
% 4.87/1.62 % (2728929)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3017278441:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.87/1.62 % (2728930)lrs+10_64_to=lpo:sil=8000:random_seed=3283334011:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 4.87/1.62 % (2728927)Instruction limit reached!
% 4.87/1.62 % (2728927)------------------------------
% 4.87/1.62 % (2728927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.87/1.62 % (2728927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.87/1.62 % (2728927)CaDiCaL version: 2.1.3
% 4.87/1.62 % (2728927)Termination reason: Instruction limit
% 4.87/1.62 % (2728927)Termination phase: Saturation
% 4.87/1.62 % (2728927)Time elapsed: 0.082 s
% 4.87/1.62 % (2728927)Peak memory usage: 88 MB
% 4.87/1.62 % (2728927)Instructions burned: 144 (million)
% 4.87/1.62 % (2728930)First to succeed.
% 4.87/1.62 % (2728930)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2728908"
% 4.87/1.62 % (2728929)Instruction limit reached!
% 4.87/1.62 % (2728929)------------------------------
% 4.87/1.62 % (2728929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.87/1.62 % (2728929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.87/1.62 % (2728929)CaDiCaL version: 2.1.3
% 4.87/1.62 % (2728929)Termination reason: Instruction limit
% 4.87/1.62 % (2728929)Termination phase: Saturation
% 4.87/1.62 % (2728929)Time elapsed: 0.121 s
% 4.87/1.62 % (2728929)Peak memory usage: 88 MB
% 4.87/1.62 % (2728929)Instructions burned: 220 (million)
% 4.87/1.62 % (2728928)------------------------------
% 4.87/1.62 % (2728928)------------------------------
% 4.87/1.62 % (2728935)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1270061008:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 4.87/1.62 % (2728936)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1690415016:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 4.87/1.62 % (2728935)Instruction limit reached!
% 4.87/1.62 % (2728935)------------------------------
% 4.87/1.62 % (2728935)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.87/1.62 % (2728935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.87/1.62 % (2728935)CaDiCaL version: 2.1.3
% 4.87/1.62 % (2728935)Termination reason: Instruction limit
% 4.87/1.62 % (2728935)Termination phase: Saturation
% 4.87/1.62 % (2728935)Time elapsed: 0.073 s
% 4.87/1.62 % (2728935)Peak memory usage: 87 MB
% 4.87/1.62 % (2728935)Instructions burned: 194 (million)
% 4.87/1.62 % SZS status Satisfiable for theBenchmark
% 4.87/1.62 % SZS output start Saturation.
% See solution above
% 5.97/1.82 % SZS output start Definitions and Model Updates.
% 5.97/1.82 % SZS output end Definitions and Model Updates.
% 5.97/1.82 % (2728930)------------------------------
% 5.97/1.82 % (2728930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.82 % (2728930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.82 % (2728930)CaDiCaL version: 2.1.3
% 5.97/1.82 % (2728930)Termination reason: Satisfiable
% 5.97/1.82 % (2728930)Time elapsed: 0.072 s
% 5.97/1.82 % (2728930)Peak memory usage: 88 MB
% 5.97/1.82 % (2728930)Instructions burned: 119 (million)
% 5.97/1.82 % (2728930)------------------------------
% 5.97/1.82 % (2728930)------------------------------
% 5.97/1.82 % (2728908)Success in time 0.753 s
% 5.97/1.82 % Vampire exiting
%------------------------------------------------------------------------------