%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP126-4.005 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 10:12:45 AM UTC 2026
% Result : Satisfiable 5.04s 1.68s
% Output : Saturation 6.43s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(u60,axiom,
~ product(e_5,e_5,e_1) ).
cnf(u64,axiom,
~ product(e_4,e_5,e_1) ).
cnf(u68,axiom,
~ product(e_3,e_5,e_1) ).
cnf(u73,axiom,
product(e_2,e_5,e_1) ).
cnf(u76,axiom,
~ product(e_1,e_5,e_1) ).
cnf(u82,axiom,
product(e_5,e_4,e_1) ).
cnf(u85,axiom,
~ product(e_4,e_4,e_1) ).
cnf(u89,axiom,
~ product(e_3,e_4,e_1) ).
cnf(u93,axiom,
~ product(e_2,e_4,e_1) ).
cnf(u97,axiom,
~ product(e_1,e_4,e_1) ).
cnf(u102,axiom,
~ product(e_5,e_3,e_1) ).
cnf(u107,axiom,
product(e_4,e_3,e_1) ).
cnf(u110,axiom,
~ product(e_3,e_3,e_1) ).
cnf(u114,axiom,
~ product(e_2,e_3,e_1) ).
cnf(u118,axiom,
~ product(e_1,e_3,e_1) ).
cnf(u123,axiom,
~ product(e_5,e_2,e_1) ).
cnf(u127,axiom,
~ product(e_4,e_2,e_1) ).
cnf(u132,axiom,
product(e_3,e_2,e_1) ).
cnf(u135,axiom,
~ product(e_2,e_2,e_1) ).
cnf(u139,axiom,
~ product(e_1,e_2,e_1) ).
cnf(u263,axiom,
~ product(e_5,e_5,e_2) ).
cnf(u268,axiom,
product(e_4,e_5,e_2) ).
cnf(u271,axiom,
~ product(e_3,e_5,e_2) ).
cnf(u275,axiom,
~ product(e_2,e_5,e_2) ).
cnf(u279,axiom,
~ product(e_1,e_5,e_2) ).
cnf(u284,axiom,
~ product(e_5,e_4,e_2) ).
cnf(u288,axiom,
~ product(e_4,e_4,e_2) ).
cnf(u292,axiom,
~ product(e_3,e_4,e_2) ).
cnf(u296,axiom,
~ product(e_2,e_4,e_2) ).
cnf(u301,axiom,
product(e_1,e_4,e_2) ).
cnf(u306,axiom,
product(e_5,e_3,e_2) ).
cnf(u309,axiom,
~ product(e_4,e_3,e_2) ).
cnf(u313,axiom,
~ product(e_3,e_3,e_2) ).
cnf(u317,axiom,
~ product(e_2,e_3,e_2) ).
cnf(u321,axiom,
~ product(e_1,e_3,e_2) ).
cnf(u326,axiom,
~ product(e_5,e_1,e_2) ).
cnf(u330,axiom,
~ product(e_4,e_1,e_2) ).
cnf(u335,axiom,
product(e_3,e_1,e_2) ).
cnf(u338,axiom,
~ product(e_2,e_1,e_2) ).
cnf(u342,axiom,
~ product(e_1,e_1,e_2) ).
cnf(u621,axiom,
~ product(e_5,e_5,e_3) ).
cnf(u625,axiom,
~ product(e_4,e_5,e_3) ).
cnf(u629,axiom,
~ product(e_3,e_5,e_3) ).
cnf(u633,axiom,
~ product(e_2,e_5,e_3) ).
cnf(u638,axiom,
product(e_1,e_5,e_3) ).
cnf(u642,axiom,
~ product(e_5,e_4,e_3) ).
cnf(u646,axiom,
~ product(e_4,e_4,e_3) ).
cnf(u650,axiom,
~ product(e_3,e_4,e_3) ).
cnf(u655,axiom,
product(e_2,e_4,e_3) ).
cnf(u658,axiom,
~ product(e_1,e_4,e_3) ).
cnf(u664,axiom,
product(e_5,e_2,e_3) ).
cnf(u667,axiom,
~ product(e_4,e_2,e_3) ).
cnf(u671,axiom,
~ product(e_3,e_2,e_3) ).
cnf(u675,axiom,
~ product(e_2,e_2,e_3) ).
cnf(u679,axiom,
~ product(e_1,e_2,e_3) ).
cnf(u684,axiom,
~ product(e_5,e_1,e_3) ).
cnf(u689,axiom,
product(e_4,e_1,e_3) ).
cnf(u692,axiom,
~ product(e_3,e_1,e_3) ).
cnf(u696,axiom,
~ product(e_2,e_1,e_3) ).
cnf(u700,axiom,
~ product(e_1,e_1,e_3) ).
cnf(u866,axiom,
~ product(e_5,e_5,e_4) ).
cnf(u870,axiom,
~ product(e_4,e_5,e_4) ).
cnf(u875,axiom,
product(e_3,e_5,e_4) ).
cnf(u878,axiom,
~ product(e_2,e_5,e_4) ).
cnf(u882,axiom,
~ product(e_1,e_5,e_4) ).
cnf(u887,axiom,
~ product(e_5,e_3,e_4) ).
cnf(u891,axiom,
~ product(e_4,e_3,e_4) ).
cnf(u895,axiom,
~ product(e_3,e_3,e_4) ).
cnf(u900,axiom,
product(e_2,e_3,e_4) ).
cnf(u903,axiom,
~ product(e_1,e_3,e_4) ).
cnf(u908,axiom,
~ product(e_5,e_2,e_4) ).
cnf(u912,axiom,
~ product(e_4,e_2,e_4) ).
cnf(u916,axiom,
~ product(e_3,e_2,e_4) ).
cnf(u920,axiom,
~ product(e_2,e_2,e_4) ).
cnf(u925,axiom,
product(e_1,e_2,e_4) ).
cnf(u930,axiom,
product(e_5,e_1,e_4) ).
cnf(u933,axiom,
~ product(e_4,e_1,e_4) ).
cnf(u937,axiom,
~ product(e_3,e_1,e_4) ).
cnf(u941,axiom,
~ product(e_2,e_1,e_4) ).
cnf(u1108,axiom,
~ product(e_5,e_2,e_5) ).
cnf(u1113,axiom,
product(e_4,e_2,e_5) ).
cnf(u1116,axiom,
~ product(e_3,e_2,e_5) ).
cnf(u1124,axiom,
~ product(e_1,e_2,e_5) ).
cnf(u1129,axiom,
~ product(e_5,e_1,e_5) ).
cnf(u1133,axiom,
~ product(e_4,e_1,e_5) ).
cnf(u1137,axiom,
~ product(e_3,e_1,e_5) ).
cnf(u1142,axiom,
product(e_2,e_1,e_5) ).
cnf(u1181,axiom,
~ product(e_5,e_3,e_5) ).
cnf(u1185,axiom,
~ product(e_4,e_3,e_5) ).
cnf(u1189,axiom,
~ product(e_3,e_3,e_5) ).
cnf(u1193,axiom,
~ product(e_2,e_3,e_5) ).
cnf(u1198,axiom,
product(e_1,e_3,e_5) ).
cnf(u1291,axiom,
~ product(e_5,e_4,e_5) ).
cnf(u1295,axiom,
~ product(e_4,e_4,e_5) ).
cnf(u1300,axiom,
product(e_3,e_4,e_5) ).
cnf(u1303,axiom,
~ product(e_2,e_4,e_5) ).
cnf(u1307,axiom,
~ product(e_1,e_4,e_5) ).
cnf(u1478,axiom,
~ product(e_1,e_2,e_2) ).
cnf(u1705,axiom,
~ product(e_1,e_3,e_3) ).
cnf(u1873,axiom,
~ product(e_2,e_4,e_4) ).
cnf(u1998,axiom,
~ product(e_2,e_3,e_3) ).
cnf(u2453,negated_conjecture,
( ~ product(e_3,X0,e_5)
| product(X0,e_3,e_1) ) ).
cnf(u2519,axiom,
( ~ product(X0,e_3,e_4)
| equalish(X0,e_2) ) ).
cnf(u2427,axiom,
( ~ product(e_5,X0,e_1)
| equalish(X0,e_4) ) ).
cnf(u2626,negated_conjecture,
( ~ product(e_2,e_1,X0)
| product(X0,e_4,e_1) ) ).
cnf(u50,axiom,
( ~ group_element(X0)
| product(e_1,X0,e_3)
| product(e_2,X0,e_3)
| product(e_3,X0,e_3)
| product(e_4,X0,e_3)
| product(e_5,X0,e_3) ) ).
cnf(u2429,negated_conjecture,
( ~ product(e_4,e_5,X0)
| product(X0,e_1,e_5) ) ).
cnf(u2897,axiom,
( ~ product(e_3,X0,e_5)
| equalish(X0,e_4) ) ).
cnf(u2444,negated_conjecture,
( ~ product(X0,e_2,e_1)
| product(e_2,X0,e_4) ) ).
cnf(u2438,negated_conjecture,
( ~ product(e_1,X0,e_3)
| product(X0,e_1,e_4) ) ).
cnf(u2520,axiom,
( ~ product(e_2,X0,e_4)
| equalish(X0,e_3) ) ).
cnf(u2625,axiom,
( ~ product(e_1,e_2,X0)
| equalish(X0,e_4) ) ).
cnf(u2898,axiom,
( ~ product(e_3,e_4,X0)
| equalish(X0,e_5) ) ).
cnf(u2472,negated_conjecture,
( ~ product(e_4,X0,e_5)
| product(X0,e_4,e_3) ) ).
cnf(u2449,axiom,
( ~ product(e_1,X0,e_3)
| equalish(X0,e_5) ) ).
cnf(u49,axiom,
( ~ group_element(X0)
| product(e_1,X0,e_2)
| product(e_2,X0,e_2)
| product(e_3,X0,e_2)
| product(e_4,X0,e_2)
| product(e_5,X0,e_2) ) ).
cnf(u2331,negated_conjecture,
( ~ product(e_2,X0,e_3)
| product(X0,e_2,e_5) ) ).
cnf(u52,axiom,
( ~ group_element(X0)
| product(e_1,X0,e_5)
| product(e_2,X0,e_5)
| product(e_3,X0,e_5)
| product(e_4,X0,e_5)
| product(e_5,X0,e_5) ) ).
cnf(u2342,negated_conjecture,
( ~ product(e_3,X0,e_2)
| product(X0,e_3,e_5) ) ).
cnf(u43,axiom,
equalish(X0,X0) ).
cnf(u46,axiom,
( ~ product(X0,X1,X1)
| equalish(X0,X1) ) ).
cnf(u2462,negated_conjecture,
( ~ product(e_3,X0,e_1)
| product(X0,e_3,e_4) ) ).
cnf(u2702,axiom,
( ~ product(X0,e_2,e_5)
| equalish(X0,e_4) ) ).
cnf(u2433,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(u2289,axiom,
( ~ product(e_2,X0,e_3)
| equalish(X0,e_4) ) ).
cnf(e_5_is_not_e_1,axiom,
~ equalish(e_5,e_1) ).
cnf(u2457,axiom,
( ~ product(X0,e_1,e_3)
| equalish(X0,e_4) ) ).
cnf(e_4_is_not_e_5,axiom,
~ equalish(e_4,e_5) ).
cnf(u2426,axiom,
( ~ product(X0,e_4,e_1)
| equalish(X0,e_5) ) ).
cnf(e_5_is_not_e_3,axiom,
~ equalish(e_5,e_3) ).
cnf(u2210,negated_conjecture,
( ~ product(e_2,X0,e_1)
| product(X0,e_2,e_3) ) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1) ).
cnf(e_3_is_not_e_5,axiom,
~ equalish(e_3,e_5) ).
cnf(element_4,axiom,
group_element(e_4) ).
cnf(u2207,axiom,
( ~ product(e_3,e_1,X0)
| equalish(X0,e_2) ) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3) ).
cnf(column_surjectivity,axiom,
( ~ group_element(X1)
| ~ group_element(X0)
| product(X0,e_1,X1)
| product(X0,e_2,X1)
| product(X0,e_3,X1)
| product(X0,e_4,X1)
| product(X0,e_5,X1) ) ).
cnf(row_surjectivity,axiom,
( ~ group_element(X1)
| ~ group_element(X0)
| product(e_1,X0,X1)
| product(e_2,X0,X1)
| product(e_3,X0,X1)
| product(e_4,X0,X1)
| product(e_5,X0,X1) ) ).
cnf(u2638,negated_conjecture,
( ~ product(e_4,X0,e_1)
| product(X0,e_4,e_5) ) ).
cnf(u2330,negated_conjecture,
( ~ product(X0,e_2,e_5)
| product(e_2,X0,e_3) ) ).
cnf(u2030,axiom,
( ~ product(X0,e_5,e_1)
| equalish(X0,e_2) ) ).
cnf(u2854,negated_conjecture,
( ~ product(e_3,e_1,X0)
| product(X0,e_5,e_1) ) ).
cnf(u2523,negated_conjecture,
( ~ product(X0,e_4,e_2)
| product(e_4,X0,e_3) ) ).
cnf(u458,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(u2522,negated_conjecture,
( ~ product(e_3,e_2,X0)
| product(X0,e_4,e_2) ) ).
cnf(u460,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(u2633,axiom,
( ~ product(X0,e_1,e_4)
| equalish(X0,e_5) ) ).
cnf(u2460,negated_conjecture,
( ~ product(e_1,e_4,X0)
| product(X0,e_3,e_4) ) ).
cnf(u2896,axiom,
( ~ product(X0,e_4,e_5)
| equalish(X0,e_3) ) ).
cnf(u2247,negated_conjecture,
( ~ product(X0,e_2,e_4)
| product(e_2,X0,e_5) ) ).
cnf(u215,axiom,
( ~ group_element(X0)
| product(X0,e_1,e_4)
| product(X0,e_2,e_4)
| product(X0,e_3,e_4)
| product(X0,e_4,e_4)
| product(X0,e_5,e_4) ) ).
cnf(u2852,axiom,
( ~ product(e_1,X0,e_5)
| equalish(X0,e_3) ) ).
cnf(u2628,negated_conjecture,
( ~ product(e_4,X0,e_2)
| product(X0,e_4,e_1) ) ).
cnf(u2206,axiom,
( ~ product(e_3,X0,e_2)
| equalish(X0,e_1) ) ).
cnf(u2428,axiom,
( ~ product(e_5,e_4,X0)
| equalish(X0,e_1) ) ).
cnf(u2899,negated_conjecture,
( ~ product(e_4,e_3,X0)
| product(X0,e_5,e_3) ) ).
cnf(qg4_2,negated_conjecture,
( ~ product(X3,X2,X0)
| product(X0,X1,X2)
| ~ product(X1,X0,X3) ) ).
cnf(u2459,axiom,
( ~ product(e_4,e_1,X0)
| equalish(X0,e_3) ) ).
cnf(u2784,negated_conjecture,
( ~ product(e_1,e_2,X0)
| product(X0,e_5,e_2) ) ).
cnf(u2290,axiom,
( ~ product(e_2,e_4,X0)
| equalish(X0,e_3) ) ).
cnf(u2322,negated_conjecture,
( ~ product(e_2,e_3,X0)
| product(X0,e_1,e_3) ) ).
cnf(u2321,axiom,
( ~ product(e_3,e_2,X0)
| equalish(X0,e_1) ) ).
cnf(u2292,negated_conjecture,
( ~ product(X0,e_3,e_2)
| product(e_3,X0,e_4) ) ).
cnf(u2324,negated_conjecture,
( ~ product(e_1,X0,e_2)
| product(X0,e_1,e_3) ) ).
cnf(u2441,axiom,
( ~ product(e_1,X0,e_2)
| equalish(X0,e_4) ) ).
cnf(u2035,negated_conjecture,
( ~ product(e_1,X0,e_5)
| product(X0,e_1,e_2) ) ).
cnf(u2436,negated_conjecture,
( ~ product(e_3,e_4,X0)
| product(X0,e_1,e_4) ) ).
cnf(u2431,negated_conjecture,
( ~ product(e_1,X0,e_4)
| product(X0,e_1,e_5) ) ).
cnf(u2435,axiom,
( ~ product(e_4,e_3,X0)
| equalish(X0,e_1) ) ).
cnf(u51,axiom,
( ~ group_element(X0)
| product(e_1,X0,e_4)
| product(e_2,X0,e_4)
| product(e_3,X0,e_4)
| product(e_4,X0,e_4)
| product(e_5,X0,e_4) ) ).
cnf(u2437,negated_conjecture,
( ~ product(X0,e_1,e_4)
| product(e_1,X0,e_3) ) ).
cnf(product_idempotence,axiom,
product(X0,X0,X0) ).
cnf(u2637,negated_conjecture,
( ~ product(X0,e_4,e_5)
| product(e_4,X0,e_1) ) ).
cnf(u2339,axiom,
( ~ product(e_5,e_2,X0)
| equalish(X0,e_3) ) ).
cnf(u2341,negated_conjecture,
( ~ product(X0,e_3,e_5)
| product(e_3,X0,e_2) ) ).
cnf(u2319,axiom,
( ~ product(X0,e_2,e_1)
| equalish(X0,e_3) ) ).
cnf(u2246,negated_conjecture,
( ~ product(e_5,e_4,X0)
| product(X0,e_2,e_4) ) ).
cnf(u2328,axiom,
( ~ product(e_5,e_3,X0)
| equalish(X0,e_2) ) ).
cnf(u2440,axiom,
( ~ product(X0,e_4,e_2)
| equalish(X0,e_1) ) ).
cnf(u2450,axiom,
( ~ product(e_1,e_5,X0)
| equalish(X0,e_3) ) ).
cnf(product_left_cancellation,axiom,
( ~ product(X3,X1,X2)
| ~ product(X0,X1,X2)
| equalish(X0,X3) ) ).
cnf(u36,negated_conjecture,
( ~ product(X0,X0,X1)
| product(X1,X0,X0) ) ).
cnf(u2452,negated_conjecture,
( ~ product(X0,e_3,e_1)
| product(e_3,X0,e_5) ) ).
cnf(u2326,axiom,
( ~ product(X0,e_3,e_2)
| equalish(X0,e_5) ) ).
cnf(u2248,negated_conjecture,
( ~ product(e_2,X0,e_5)
| product(X0,e_2,e_4) ) ).
cnf(e_5_is_not_e_2,axiom,
~ equalish(e_5,e_2) ).
cnf(u216,axiom,
( ~ group_element(X0)
| product(X0,e_1,e_5)
| product(X0,e_2,e_5)
| product(X0,e_3,e_5)
| product(X0,e_4,e_5)
| product(X0,e_5,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(u2445,negated_conjecture,
( ~ product(e_2,X0,e_4)
| product(X0,e_2,e_1) ) ).
cnf(e_5_is_not_e_4,axiom,
~ equalish(e_5,e_4) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4) ).
cnf(u2244,axiom,
( ~ product(e_4,X0,e_2)
| equalish(X0,e_5) ) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2) ).
cnf(u212,axiom,
( ~ group_element(X0)
| product(X0,e_1,e_1)
| product(X0,e_2,e_1)
| product(X0,e_3,e_1)
| product(X0,e_4,e_1)
| product(X0,e_5,e_1) ) ).
cnf(u2521,axiom,
( ~ product(e_2,e_3,X0)
| equalish(X0,e_4) ) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2) ).
cnf(element_5,axiom,
group_element(e_5) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4) ).
cnf(u2705,negated_conjecture,
( ~ product(e_2,e_4,X0)
| product(X0,e_5,e_4) ) ).
cnf(qg4_1,negated_conjecture,
( ~ product(X2,X3,X1)
| product(X0,X1,X2)
| ~ product(X1,X0,X3) ) ).
cnf(element_2,axiom,
group_element(e_2) ).
cnf(element_1,axiom,
group_element(e_1) ).
cnf(u2451,negated_conjecture,
( ~ product(e_5,e_1,X0)
| product(X0,e_3,e_1) ) ).
cnf(u2467,axiom,
( ~ product(X0,e_5,e_4)
| equalish(X0,e_3) ) ).
cnf(u2034,negated_conjecture,
( ~ product(X0,e_1,e_2)
| product(e_1,X0,e_5) ) ).
cnf(u2205,axiom,
( ~ product(X0,e_1,e_2)
| equalish(X0,e_3) ) ).
cnf(u2634,axiom,
( ~ product(e_5,X0,e_4)
| equalish(X0,e_1) ) ).
cnf(u2853,axiom,
( ~ product(e_1,e_3,X0)
| equalish(X0,e_5) ) ).
cnf(u2703,axiom,
( ~ product(e_4,X0,e_5)
| equalish(X0,e_2) ) ).
cnf(u2448,axiom,
( ~ product(X0,e_5,e_3)
| equalish(X0,e_1) ) ).
cnf(u2627,negated_conjecture,
( ~ product(X0,e_4,e_1)
| product(e_4,X0,e_2) ) ).
cnf(u2783,axiom,
( ~ product(e_2,e_1,X0)
| equalish(X0,e_5) ) ).
cnf(u2458,axiom,
( ~ product(e_4,X0,e_3)
| equalish(X0,e_1) ) ).
cnf(u2442,axiom,
( ~ product(e_1,e_4,X0)
| equalish(X0,e_2) ) ).
cnf(u2338,axiom,
( ~ product(e_5,X0,e_3)
| equalish(X0,e_2) ) ).
cnf(u2337,axiom,
( ~ product(X0,e_2,e_3)
| equalish(X0,e_5) ) ).
cnf(u2340,negated_conjecture,
( ~ product(e_2,e_5,X0)
| product(X0,e_3,e_5) ) ).
cnf(u2635,axiom,
( ~ product(e_5,e_1,X0)
| equalish(X0,e_4) ) ).
cnf(u2208,negated_conjecture,
( ~ product(e_1,e_3,X0)
| product(X0,e_2,e_3) ) ).
cnf(u2033,negated_conjecture,
( ~ product(e_5,e_2,X0)
| product(X0,e_1,e_2) ) ).
cnf(u459,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(u2624,axiom,
( ~ product(e_1,X0,e_4)
| equalish(X0,e_2) ) ).
cnf(u461,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(u2291,negated_conjecture,
( ~ product(e_4,e_2,X0)
| product(X0,e_3,e_2) ) ).
cnf(u2461,negated_conjecture,
( ~ product(X0,e_3,e_4)
| product(e_3,X0,e_1) ) ).
cnf(u2293,negated_conjecture,
( ~ product(e_3,X0,e_4)
| product(X0,e_3,e_2) ) ).
cnf(u2623,axiom,
( ~ product(X0,e_2,e_4)
| equalish(X0,e_1) ) ).
cnf(u2443,negated_conjecture,
( ~ product(e_4,e_1,X0)
| product(X0,e_2,e_1) ) ).
cnf(u2851,axiom,
( ~ product(X0,e_3,e_5)
| equalish(X0,e_1) ) ).
cnf(u2785,negated_conjecture,
( ~ product(X0,e_5,e_2)
| product(e_5,X0,e_1) ) ).
cnf(u48,axiom,
( ~ group_element(X0)
| product(e_1,X0,e_1)
| product(e_2,X0,e_1)
| product(e_3,X0,e_1)
| product(e_4,X0,e_1)
| product(e_5,X0,e_1) ) ).
cnf(u42,axiom,
( ~ product(X0,X0,X1)
| equalish(X1,X0) ) ).
cnf(u2706,negated_conjecture,
( ~ product(X0,e_5,e_4)
| product(e_5,X0,e_2) ) ).
cnf(u2781,axiom,
( ~ product(X0,e_1,e_5)
| equalish(X0,e_2) ) ).
cnf(u2430,negated_conjecture,
( ~ product(X0,e_1,e_5)
| product(e_1,X0,e_4) ) ).
cnf(u44,axiom,
( ~ product(X0,X1,X0)
| equalish(X1,X0) ) ).
cnf(qg4,negated_conjecture,
( ~ product(X1,X0,X3)
| ~ product(X0,X1,X2)
| product(X2,X3,X1) ) ).
cnf(u2524,negated_conjecture,
( ~ product(e_4,X0,e_3)
| product(X0,e_4,e_2) ) ).
cnf(u38,negated_conjecture,
( ~ product(X1,X0,X1)
| product(X0,X1,X1) ) ).
cnf(u37,negated_conjecture,
( ~ product(X1,X0,X0)
| product(X0,X1,X0) ) ).
cnf(u2031,axiom,
( ~ product(e_2,X0,e_1)
| equalish(X0,e_5) ) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3) ).
cnf(product_total_function2,axiom,
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| equalish(X2,X3) ) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1) ).
cnf(u2209,negated_conjecture,
( ~ product(X0,e_2,e_3)
| product(e_2,X0,e_1) ) ).
cnf(e_2_is_not_e_5,axiom,
~ equalish(e_2,e_5) ).
cnf(u2329,negated_conjecture,
( ~ product(e_3,e_5,X0)
| product(X0,e_2,e_5) ) ).
cnf(u2323,negated_conjecture,
( ~ product(X0,e_1,e_3)
| product(e_1,X0,e_2) ) ).
cnf(u2707,negated_conjecture,
( ~ product(e_5,X0,e_2)
| product(X0,e_5,e_4) ) ).
cnf(u2900,negated_conjecture,
( ~ product(X0,e_5,e_3)
| product(e_5,X0,e_4) ) ).
cnf(u2856,negated_conjecture,
( ~ product(e_5,X0,e_3)
| product(X0,e_5,e_1) ) ).
cnf(u2636,negated_conjecture,
( ~ product(e_1,e_5,X0)
| product(X0,e_4,e_5) ) ).
cnf(u2470,negated_conjecture,
( ~ product(e_5,e_3,X0)
| product(X0,e_4,e_3) ) ).
cnf(u2468,axiom,
( ~ product(e_3,X0,e_4)
| equalish(X0,e_5) ) ).
cnf(u2288,axiom,
( ~ product(X0,e_4,e_3)
| equalish(X0,e_2) ) ).
cnf(u2320,axiom,
( ~ product(e_3,X0,e_1)
| equalish(X0,e_2) ) ).
cnf(u2704,axiom,
( ~ product(e_4,e_2,X0)
| equalish(X0,e_5) ) ).
cnf(u457,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(u2243,axiom,
( ~ product(X0,e_5,e_2)
| equalish(X0,e_4) ) ).
cnf(u2434,axiom,
( ~ product(e_4,X0,e_1)
| equalish(X0,e_3) ) ).
cnf(u2855,negated_conjecture,
( ~ product(X0,e_5,e_1)
| product(e_5,X0,e_3) ) ).
cnf(u214,axiom,
( ~ group_element(X0)
| product(X0,e_1,e_3)
| product(X0,e_2,e_3)
| product(X0,e_3,e_3)
| product(X0,e_4,e_3)
| product(X0,e_5,e_3) ) ).
cnf(u2245,axiom,
( ~ product(e_4,e_5,X0)
| equalish(X0,e_2) ) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4) ).
cnf(u213,axiom,
( ~ group_element(X0)
| product(X0,e_1,e_2)
| product(X0,e_2,e_2)
| product(X0,e_3,e_2)
| product(X0,e_4,e_2)
| product(X0,e_5,e_2) ) ).
cnf(u2327,axiom,
( ~ product(e_5,X0,e_2)
| equalish(X0,e_3) ) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3) ).
cnf(u2469,axiom,
( ~ product(e_3,e_5,X0)
| equalish(X0,e_4) ) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1) ).
cnf(e_1_is_not_e_5,axiom,
~ equalish(e_1,e_5) ).
cnf(u2901,negated_conjecture,
( ~ product(e_5,X0,e_4)
| product(X0,e_5,e_3) ) ).
cnf(element_3,axiom,
group_element(e_3) ).
cnf(u2032,axiom,
( ~ product(e_2,e_5,X0)
| equalish(X0,e_1) ) ).
cnf(u2786,negated_conjecture,
( ~ product(e_5,X0,e_1)
| product(X0,e_5,e_2) ) ).
cnf(u2471,negated_conjecture,
( ~ product(X0,e_4,e_3)
| product(e_4,X0,e_5) ) ).
cnf(u2782,axiom,
( ~ product(e_2,X0,e_5)
| equalish(X0,e_1) ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP126-4.005 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n007.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 09:23:40 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 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
% 5.04/1.68 % (1153448)Input is clausal, will run a generic CNF schedule.
% 5.04/1.68 % (1153454)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3642816573:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.04/1.68 % (1153458)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=594550277:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.04/1.68 % (1153456)lrs+10_1_sil=8000:sp=occurrence:random_seed=750937493:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.04/1.68 % (1153457)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3480093360:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.04/1.68 % (1153455)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3628992503:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.04/1.68 % (1153453)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=1023291596:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.04/1.68 % (1153456)Refutation not found, incomplete strategy
% 5.04/1.68 % (1153456)------------------------------
% 5.04/1.68 % (1153456)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.68 % (1153456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.68 % (1153456)CaDiCaL version: 2.1.3
% 5.04/1.68 % (1153456)Termination reason: Refutation not found, incomplete strategy
% 5.04/1.68 % (1153456)Time elapsed: 0.001 s
% 5.04/1.68 % (1153456)Peak memory usage: 87 MB
% 5.04/1.68 % (1153459)dis-21_1_sil=8000:lcm=predicate:random_seed=945981259: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)
% 5.04/1.68 % (1153457)Instruction limit reached!
% 5.04/1.68 % (1153457)------------------------------
% 5.04/1.68 % (1153457)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.68 % (1153457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.68 % (1153457)CaDiCaL version: 2.1.3
% 5.04/1.68 % (1153457)Termination reason: Instruction limit
% 5.04/1.68 % (1153457)Termination phase: Saturation
% 5.04/1.68 % (1153457)Time elapsed: 0.055 s
% 5.04/1.68 % (1153457)Peak memory usage: 87 MB
% 5.04/1.68 % (1153457)Instructions burned: 115 (million)
% 5.04/1.68 % (1153459)Instruction limit reached!
% 5.04/1.68 % (1153459)------------------------------
% 5.04/1.68 % (1153459)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.68 % (1153459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.68 % (1153459)CaDiCaL version: 2.1.3
% 5.04/1.68 % (1153459)Termination reason: Instruction limit
% 5.04/1.68 % (1153459)Termination phase: Saturation
% 5.04/1.68 % (1153459)Time elapsed: 0.072 s
% 5.04/1.68 % (1153459)Peak memory usage: 89 MB
% 5.04/1.68 % (1153459)Instructions burned: 117 (million)
% 5.04/1.68 % (1153458)Instruction limit reached!
% 5.04/1.68 % (1153458)------------------------------
% 5.04/1.68 % (1153458)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.68 % (1153458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.68 % (1153458)CaDiCaL version: 2.1.3
% 5.04/1.68 % (1153458)Termination reason: Instruction limit
% 5.04/1.68 % (1153458)Termination phase: Saturation
% 5.04/1.68 % (1153458)Time elapsed: 0.112 s
% 5.04/1.68 % (1153458)Peak memory usage: 89 MB
% 5.04/1.68 % (1153458)Instructions burned: 181 (million)
% 5.04/1.68 % (1153467)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=1936305509:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.04/1.68 % (1153468)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2517804511: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)
% 5.04/1.68 % (1153468)Refutation not found, incomplete strategy
% 5.04/1.68 % (1153468)------------------------------
% 5.04/1.68 % (1153468)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.68 % (1153468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.68 % (1153468)CaDiCaL version: 2.1.3
% 5.04/1.68 % (1153468)Termination reason: Refutation not found, incomplete strategy
% 5.04/1.68 % (1153468)Time elapsed: 0.002 s
% 5.04/1.68 % (1153468)Peak memory usage: 87 MB
% 5.04/1.68 % (1153468)Instructions burned: 2 (million)
% 5.04/1.68 % (1153456)------------------------------
% 5.04/1.68 % (1153456)------------------------------
% 5.04/1.68 % (1153469)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1361598977:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.04/1.68 % (1153467)Instruction limit reached!
% 5.04/1.68 % (1153467)------------------------------
% 5.04/1.68 % (1153467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.68 % (1153467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.68 % (1153467)CaDiCaL version: 2.1.3
% 5.04/1.68 % (1153467)Termination reason: Instruction limit
% 5.04/1.68 % (1153467)Termination phase: Saturation
% 5.04/1.68 % (1153467)Time elapsed: 0.086 s
% 5.04/1.68 % (1153467)Peak memory usage: 89 MB
% 5.04/1.68 % (1153467)Instructions burned: 144 (million)
% 5.04/1.68 % (1153454)Refutation not found, incomplete strategy
% 5.04/1.68 % (1153454)------------------------------
% 5.04/1.68 % (1153454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.68 % (1153454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.68 % (1153454)CaDiCaL version: 2.1.3
% 5.04/1.68 % (1153454)Termination reason: Refutation not found, incomplete strategy
% 5.04/1.68 % (1153454)Time elapsed: 0.369 s
% 5.04/1.68 % (1153454)Peak memory usage: 128 MB
% 5.04/1.68 % (1153454)Instructions burned: 921 (million)
% 5.04/1.68 % (1153469)Instruction limit reached!
% 5.04/1.68 % (1153469)------------------------------
% 5.04/1.68 % (1153469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.68 % (1153469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.68 % (1153469)CaDiCaL version: 2.1.3
% 5.04/1.68 % (1153469)Termination reason: Instruction limit
% 5.04/1.68 % (1153469)Termination phase: Saturation
% 5.04/1.68 % (1153469)Time elapsed: 0.105 s
% 5.04/1.68 % (1153469)Peak memory usage: 88 MB
% 5.04/1.68 % (1153469)Instructions burned: 221 (million)
% 5.04/1.68 % (1153473)lrs+10_64_to=lpo:sil=8000:random_seed=3996040862:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 5.04/1.68 % (1153474)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2198296067:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.04/1.68 % (1153473)First to succeed.
% 5.04/1.68 % (1153473)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1153448"
% 5.04/1.68 % (1153468)------------------------------
% 5.04/1.68 % (1153468)------------------------------
% 5.04/1.68 % (1153454)------------------------------
% 5.04/1.68 % (1153454)------------------------------
% 5.04/1.68 % (1153475)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=211580111:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 5.04/1.68 % (1153474)Instruction limit reached!
% 5.04/1.68 % (1153474)------------------------------
% 5.04/1.68 % (1153474)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.68 % (1153474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.68 % (1153474)CaDiCaL version: 2.1.3
% 5.04/1.68 % (1153474)Termination reason: Instruction limit
% 5.04/1.68 % (1153474)Termination phase: Saturation
% 5.04/1.68 % (1153474)Time elapsed: 0.099 s
% 5.04/1.68 % (1153474)Peak memory usage: 88 MB
% 5.04/1.68 % (1153474)Instructions burned: 194 (million)
% 5.04/1.68 % (1153479)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=536626409:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 5.04/1.68 % (1153479)Refutation not found, incomplete strategy
% 5.04/1.68 % (1153479)------------------------------
% 5.04/1.68 % (1153479)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.68 % (1153479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.68 % (1153479)CaDiCaL version: 2.1.3
% 5.04/1.68 % (1153479)Termination reason: Refutation not found, incomplete strategy
% 5.04/1.68 % (1153479)Time elapsed: 0.003 s
% 5.04/1.68 % (1153479)Peak memory usage: 87 MB
% 5.04/1.68 % (1153479)Instructions burned: 10 (million)
% 5.04/1.68 % (1153478)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=415570478:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 5.04/1.68 % (1153475)Instruction limit reached!
% 5.04/1.68 % (1153475)------------------------------
% 5.04/1.68 % (1153475)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.68 % (1153475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.68 % (1153475)CaDiCaL version: 2.1.3
% 5.04/1.68 % (1153475)Termination reason: Instruction limit
% 5.04/1.68 % (1153475)Termination phase: Saturation
% 5.04/1.68 % (1153475)Time elapsed: 0.093 s
% 5.04/1.68 % (1153475)Peak memory usage: 89 MB
% 5.04/1.68 % (1153475)Instructions burned: 158 (million)
% 5.04/1.68 % (1153481)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=2840649708:i=107_2993 on theBenchmark for (2993ds/107Mi)
% 5.04/1.68 % SZS status Satisfiable for theBenchmark
% 5.04/1.68 % SZS output start Saturation.
% See solution above
% 6.43/1.87 % SZS output start Definitions and Model Updates.
% 6.43/1.87 % SZS output end Definitions and Model Updates.
% 6.43/1.87 % (1153473)------------------------------
% 6.43/1.87 % (1153473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.43/1.87 % (1153473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.43/1.87 % (1153473)CaDiCaL version: 2.1.3
% 6.43/1.87 % (1153473)Termination reason: Satisfiable
% 6.43/1.87 % (1153473)Time elapsed: 0.055 s
% 6.43/1.87 % (1153473)Peak memory usage: 88 MB
% 6.43/1.87 % (1153473)Instructions burned: 89 (million)
% 6.43/1.87 % (1153473)------------------------------
% 6.43/1.87 % (1153473)------------------------------
% 6.43/1.87 % (1153448)Success in time 0.826 s
% 6.43/1.87 % Vampire exiting
%------------------------------------------------------------------------------