%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP126-3.005 : 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 : n012.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 1.34s 0.99s
% Output : Saturation 3.44s
% 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(u126,axiom,
~ cycle(e_3,e_2) ).
cnf(u130,axiom,
~ cycle(e_3,e_1) ).
cnf(u135,axiom,
cycle(e_3,e_0) ).
cnf(u143,axiom,
~ cycle(e_2,e_3) ).
cnf(u147,axiom,
~ cycle(e_2,e_2) ).
cnf(u152,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(u626,axiom,
product(e_5,e_1,e_4) ).
cnf(u629,axiom,
~ product(e_5,e_1,e_3) ).
cnf(u633,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(u667,axiom,
~ product(e_3,e_1,e_4) ).
cnf(u671,axiom,
~ product(e_3,e_1,e_3) ).
cnf(u676,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(u729,axiom,
( ~ next(e_5,X1)
| equalish(e_4,X1) ) ).
cnf(u740,axiom,
( ~ next(e_4,X1)
| equalish(e_5,X1) ) ).
cnf(u758,axiom,
( ~ cycle(e_3,X0)
| ~ greater(X0,e_0) ) ).
cnf(u820,axiom,
~ product(e_5,e_2,e_5) ).
cnf(u824,axiom,
~ product(e_5,e_2,e_4) ).
cnf(u829,axiom,
product(e_5,e_2,e_3) ).
cnf(u836,axiom,
~ product(e_5,e_2,e_1) ).
cnf(u841,axiom,
~ product(e_4,e_2,e_5) ).
cnf(u845,axiom,
~ product(e_4,e_2,e_4) ).
cnf(u849,axiom,
~ product(e_4,e_2,e_3) ).
cnf(u853,axiom,
~ product(e_4,e_2,e_2) ).
cnf(u858,axiom,
product(e_4,e_2,e_1) ).
cnf(u863,axiom,
product(e_3,e_2,e_5) ).
cnf(u866,axiom,
~ product(e_3,e_2,e_4) ).
cnf(u870,axiom,
~ product(e_3,e_2,e_3) ).
cnf(u874,axiom,
~ product(e_3,e_2,e_2) ).
cnf(u878,axiom,
~ product(e_3,e_2,e_1) ).
cnf(u883,axiom,
~ product(e_1,e_2,e_5) ).
cnf(u888,axiom,
product(e_1,e_2,e_4) ).
cnf(u891,axiom,
~ product(e_1,e_2,e_3) ).
cnf(u895,axiom,
~ product(e_1,e_2,e_2) ).
cnf(u899,axiom,
~ product(e_1,e_2,e_1) ).
cnf(u1002,axiom,
( ~ next(e_3,X1)
| equalish(e_4,X1) ) ).
cnf(u1038,axiom,
( ~ next(e_2,X1)
| equalish(e_3,X1) ) ).
cnf(u1073,axiom,
( ~ next(e_5,X1)
| equalish(e_3,X1) ) ).
cnf(u1082,axiom,
~ product(e_4,e_3,e_5) ).
cnf(u1086,axiom,
~ product(e_4,e_3,e_4) ).
cnf(u1090,axiom,
~ product(e_4,e_3,e_3) ).
cnf(u1095,axiom,
product(e_4,e_3,e_2) ).
cnf(u1098,axiom,
~ product(e_4,e_3,e_1) ).
cnf(u1103,axiom,
~ product(e_2,e_3,e_5) ).
cnf(u1108,axiom,
product(e_2,e_3,e_4) ).
cnf(u1111,axiom,
~ product(e_2,e_3,e_3) ).
cnf(u1115,axiom,
~ product(e_2,e_3,e_2) ).
cnf(u1119,axiom,
~ product(e_2,e_3,e_1) ).
cnf(u1125,axiom,
product(e_1,e_3,e_5) ).
cnf(u1128,axiom,
~ product(e_1,e_3,e_4) ).
cnf(u1132,axiom,
~ product(e_1,e_3,e_3) ).
cnf(u1136,axiom,
~ product(e_1,e_3,e_2) ).
cnf(u1140,axiom,
~ product(e_1,e_3,e_1) ).
cnf(u1195,axiom,
( ~ next(e_5,X1)
| equalish(e_2,X1) ) ).
cnf(u1330,axiom,
~ product(e_5,e_3,e_5) ).
cnf(u1334,axiom,
~ product(e_5,e_3,e_4) ).
cnf(u1338,axiom,
~ product(e_5,e_3,e_3) ).
cnf(u1342,axiom,
~ product(e_5,e_3,e_2) ).
cnf(u1347,axiom,
product(e_5,e_3,e_1) ).
cnf(u1578,axiom,
~ product(e_3,e_4,e_5) ).
cnf(u1582,axiom,
~ product(e_3,e_4,e_4) ).
cnf(u1586,axiom,
~ product(e_3,e_4,e_3) ).
cnf(u1590,axiom,
~ product(e_3,e_4,e_2) ).
cnf(u1595,axiom,
product(e_3,e_4,e_1) ).
cnf(u1600,axiom,
product(e_2,e_4,e_5) ).
cnf(u1603,axiom,
~ product(e_2,e_4,e_4) ).
cnf(u1607,axiom,
~ product(e_2,e_4,e_3) ).
cnf(u1611,axiom,
~ product(e_2,e_4,e_2) ).
cnf(u1615,axiom,
~ product(e_2,e_4,e_1) ).
cnf(u1840,axiom,
~ product(e_3,e_5,e_5) ).
cnf(u1845,axiom,
product(e_3,e_5,e_4) ).
cnf(u1848,axiom,
~ product(e_3,e_5,e_3) ).
cnf(u1852,axiom,
~ product(e_3,e_5,e_2) ).
cnf(u1856,axiom,
~ product(e_3,e_5,e_1) ).
cnf(u1861,axiom,
~ product(e_1,e_5,e_5) ).
cnf(u1865,axiom,
~ product(e_1,e_5,e_4) ).
cnf(u1869,axiom,
~ product(e_1,e_5,e_3) ).
cnf(u1874,axiom,
product(e_1,e_5,e_2) ).
cnf(u1877,axiom,
~ product(e_1,e_5,e_1) ).
cnf(u2043,axiom,
~ product(e_1,e_4,e_5) ).
cnf(u2047,axiom,
~ product(e_1,e_4,e_4) ).
cnf(u2052,axiom,
product(e_1,e_4,e_3) ).
cnf(u2055,axiom,
~ product(e_1,e_4,e_2) ).
cnf(u2059,axiom,
~ product(e_1,e_4,e_1) ).
cnf(u2427,axiom,
~ product(e_5,e_4,e_5) ).
cnf(u2431,axiom,
~ product(e_5,e_4,e_4) ).
cnf(u2435,axiom,
~ product(e_5,e_4,e_3) ).
cnf(u2440,axiom,
product(e_5,e_4,e_2) ).
cnf(u2443,axiom,
~ product(e_5,e_4,e_1) ).
cnf(u2448,axiom,
~ product(e_4,e_5,e_5) ).
cnf(u2452,axiom,
~ product(e_4,e_5,e_4) ).
cnf(u2457,axiom,
product(e_4,e_5,e_3) ).
cnf(u2460,axiom,
~ product(e_4,e_5,e_2) ).
cnf(u2464,axiom,
~ product(e_4,e_5,e_1) ).
cnf(u2492,axiom,
~ product(e_2,e_5,e_4) ).
cnf(u2496,axiom,
~ product(e_2,e_5,e_3) ).
cnf(u2505,axiom,
product(e_2,e_5,e_1) ).
cnf(u3359,axiom,
~ greater(e_0,e_2) ).
cnf(u3371,axiom,
~ greater(e_2,e_2) ).
cnf(product_left_cancellation,axiom,
( ~ product(X3,X1,X2)
| ~ product(X0,X1,X2)
| equalish(X0,X3) ) ).
cnf(u3206,axiom,
( ~ product(e_5,e_3,X0)
| equalish(X0,e_1) ) ).
cnf(e_5_is_not_e_2,axiom,
~ equalish(e_5,e_2) ).
cnf(u3407,axiom,
( ~ cycle(X0,X1)
| ~ next(X0,e_2)
| ~ greater(X1,e_0)
| ~ next(e_1,X2)
| equalish(X1,X2) ) ).
cnf(u3279,axiom,
( ~ product(e_1,e_5,X0)
| equalish(X0,e_2) ) ).
cnf(u3265,negated_conjecture,
( ~ product(e_1,e_5,X0)
| product(X0,e_4,e_5) ) ).
cnf(u2754,negated_conjecture,
( ~ product(e_4,e_5,X0)
| product(X0,e_2,e_5) ) ).
cnf(u2772,axiom,
( ~ product(e_2,e_3,X0)
| equalish(X0,e_4) ) ).
cnf(u74,axiom,
equalish(X0,X0) ).
cnf(u2849,axiom,
( ~ product(e_3,e_2,X0)
| equalish(X0,e_5) ) ).
cnf(u3263,axiom,
( ~ product(e_5,X0,e_4)
| equalish(X0,e_1) ) ).
cnf(u3043,axiom,
( ~ product(e_2,e_5,X0)
| equalish(X0,e_1) ) ).
cnf(u3113,axiom,
( ~ product(X0,e_5,e_4)
| equalish(X0,e_3) ) ).
cnf(u3277,axiom,
( ~ product(X0,e_5,e_2)
| 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(u726,axiom,
~ greater(e_4,e_5) ).
cnf(e_5_is_not_e_1,axiom,
~ equalish(e_5,e_1) ).
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(u3415,axiom,
( ~ cycle(X0,e_0)
| ~ next(X0,e_1)
| ~ greater(X0,e_2) ) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4) ).
cnf(u73,axiom,
( ~ product(X0,X0,X1)
| equalish(X1,X0) ) ).
cnf(u3428,axiom,
( ~ cycle(X0,e_0)
| ~ next(X0,e_3)
| ~ greater(X0,e_4) ) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1) ).
cnf(u2847,axiom,
( ~ product(X0,e_2,e_5)
| equalish(X0,e_3) ) ).
cnf(element_5,axiom,
group_element(e_5) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4) ).
cnf(cycle6,axiom,
( ~ product(X0,e_1,X1)
| ~ cycle(X0,e_0)
| ~ greater(X1,X0) ) ).
cnf(u2850,negated_conjecture,
( ~ product(e_2,e_3,X0)
| product(X0,e_5,e_3) ) ).
cnf(element_1,axiom,
group_element(e_1) ).
cnf(e_5_greater_e_3,axiom,
greater(e_5,e_3) ).
cnf(u2969,axiom,
( ~ product(e_3,e_4,X0)
| equalish(X0,e_1) ) ).
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(u3201,axiom,
( ~ product(e_4,e_1,X0)
| equalish(X0,e_5) ) ).
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(u2483,negated_conjecture,
( ~ product(e_1,e_2,X0)
| product(X0,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(e_0_then_e_1,axiom,
next(e_0,e_1) ).
cnf(u2921,axiom,
( ~ product(e_3,e_1,X0)
| equalish(X0,e_2) ) ).
cnf(u3267,axiom,
( ~ product(e_4,X0,e_1)
| equalish(X0,e_2) ) ).
cnf(u3269,negated_conjecture,
( ~ product(e_2,e_4,X0)
| product(X0,e_1,e_4) ) ).
cnf(u3272,axiom,
( ~ product(e_2,X0,e_5)
| equalish(X0,e_4) ) ).
cnf(u3266,axiom,
( ~ product(X0,e_2,e_1)
| equalish(X0,e_4) ) ).
cnf(u3406,axiom,
( ~ cycle(e_2,X0)
| equalish(X0,e_1) ) ).
cnf(u2794,axiom,
( ~ product(X0,e_5,e_3)
| equalish(X0,e_4) ) ).
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(u2967,axiom,
( ~ product(X0,e_4,e_1)
| equalish(X0,e_3) ) ).
cnf(u3204,axiom,
( ~ product(X0,e_3,e_1)
| equalish(X0,e_5) ) ).
cnf(u3212,axiom,
( ~ product(e_1,e_4,X0)
| equalish(X0,e_3) ) ).
cnf(u600,axiom,
~ next(e_5,e_3) ).
cnf(u2848,axiom,
( ~ product(e_3,X0,e_5)
| equalish(X0,e_2) ) ).
cnf(u2482,axiom,
( ~ product(e_2,e_1,X0)
| equalish(X0,e_3) ) ).
cnf(u2481,axiom,
( ~ product(e_2,X0,e_3)
| equalish(X0,e_1) ) ).
cnf(u2968,axiom,
( ~ product(e_3,X0,e_1)
| equalish(X0,e_4) ) ).
cnf(u1289,axiom,
~ greater(e_2,e_3) ).
cnf(e_3_then_e_4,axiom,
next(e_3,e_4) ).
cnf(u3429,axiom,
( ~ cycle(X0,e_0)
| ~ next(X0,e_3)
| ~ greater(X0,e_2) ) ).
cnf(u2795,axiom,
( ~ product(e_4,X0,e_3)
| equalish(X0,e_5) ) ).
cnf(u2770,axiom,
( ~ product(X0,e_3,e_4)
| equalish(X0,e_2) ) ).
cnf(u188,axiom,
( ~ cycle(X0,X1)
| ~ next(X0,e_1)
| ~ greater(X1,e_0)
| ~ next(e_0,X2)
| equalish(X1,X2) ) ).
cnf(qg4,negated_conjecture,
( ~ product(X1,X0,X3)
| ~ product(X0,X1,X2)
| product(X2,X3,X1) ) ).
cnf(product_idempotence,axiom,
product(X0,X0,X0) ).
cnf(u2797,negated_conjecture,
( ~ product(e_5,e_4,X0)
| product(X0,e_3,e_4) ) ).
cnf(e_5_is_not_e_3,axiom,
~ equalish(e_5,e_3) ).
cnf(u3188,axiom,
( ~ cycle(e_4,X0)
| equalish(X0,e_1) ) ).
cnf(product_total_function2,axiom,
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| equalish(X2,X3) ) ).
cnf(product_total_function1,axiom,
( ~ group_element(X1)
| ~ group_element(X0)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3)
| product(X0,X1,e_4)
| product(X0,X1,e_5) ) ).
cnf(u2950,axiom,
( ~ product(X0,e_2,e_4)
| equalish(X0,e_1) ) ).
cnf(e_2_is_not_e_5,axiom,
~ equalish(e_2,e_5) ).
cnf(u514,axiom,
~ next(e_5,e_1) ).
cnf(u3207,negated_conjecture,
( ~ product(e_3,e_5,X0)
| product(X0,e_1,e_5) ) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3) ).
cnf(u3414,axiom,
( ~ cycle(X0,e_0)
| ~ next(X0,e_5)
| ~ greater(X0,e_2) ) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3) ).
cnf(u3057,axiom,
( ~ cycle(e_3,X0)
| equalish(X0,e_0) ) ).
cnf(u2873,negated_conjecture,
( ~ product(e_2,e_5,X0)
| product(X0,e_3,e_5) ) ).
cnf(u3116,negated_conjecture,
( ~ product(e_5,e_3,X0)
| product(X0,e_4,e_3) ) ).
cnf(u75,axiom,
( ~ product(X0,X1,X0)
| equalish(X1,X0) ) ).
cnf(u2920,axiom,
( ~ product(e_3,X0,e_2)
| equalish(X0,e_1) ) ).
cnf(u2872,axiom,
( ~ product(e_5,e_2,X0)
| equalish(X0,e_3) ) ).
cnf(u3278,axiom,
( ~ product(e_1,X0,e_2)
| equalish(X0,e_5) ) ).
cnf(u2751,axiom,
( ~ product(X0,e_4,e_2)
| equalish(X0,e_5) ) ).
cnf(u3408,axiom,
( ~ cycle(X1,X2)
| ~ cycle(X0,e_0)
| ~ next(X0,e_2)
| ~ greater(X0,X1)
| ~ greater(X2,e_1) ) ).
cnf(u3213,negated_conjecture,
( ~ product(e_4,e_1,X0)
| product(X0,e_3,e_1) ) ).
cnf(u2871,axiom,
( ~ product(e_5,X0,e_3)
| equalish(X0,e_2) ) ).
cnf(u3058,axiom,
( ~ cycle(X0,X1)
| ~ next(X0,e_3)
| ~ greater(X1,e_0)
| ~ next(e_0,X2)
| equalish(X1,X2) ) ).
cnf(element_2,axiom,
group_element(e_2) ).
cnf(u77,axiom,
( ~ product(X0,X1,X1)
| equalish(X0,X1) ) ).
cnf(u3210,axiom,
( ~ product(X0,e_4,e_3)
| equalish(X0,e_1) ) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2) ).
cnf(e_1_is_not_e_5,axiom,
~ equalish(e_1,e_5) ).
cnf(u3196,axiom,
( ~ cycle(X0,e_0)
| ~ next(X0,e_1)
| ~ greater(X0,e_4) ) ).
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(u2955,axiom,
( ~ product(X0,e_3,e_2)
| equalish(X0,e_4) ) ).
cnf(u439,axiom,
( ~ cycle(X1,X2)
| ~ cycle(X0,e_0)
| ~ next(X0,e_5)
| ~ greater(X0,X1)
| ~ greater(X2,e_0) ) ).
cnf(u2753,axiom,
( ~ product(e_5,e_4,X0)
| equalish(X0,e_2) ) ).
cnf(e_4_greater_e_2,axiom,
greater(e_4,e_2) ).
cnf(cycle3,axiom,
cycle(e_5,e_0) ).
cnf(e_5_greater_e_0,axiom,
greater(e_5,e_0) ).
cnf(e_4_greater_e_0,axiom,
greater(e_4,e_0) ).
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(u2919,axiom,
( ~ product(X0,e_1,e_2)
| equalish(X0,e_3) ) ).
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(u2953,negated_conjecture,
( ~ product(e_2,e_1,X0)
| product(X0,e_4,e_1) ) ).
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(u2771,axiom,
( ~ product(e_2,X0,e_4)
| equalish(X0,e_3) ) ).
cnf(u3273,axiom,
( ~ product(e_2,e_4,X0)
| equalish(X0,e_5) ) ).
cnf(u3044,negated_conjecture,
( ~ product(e_5,e_2,X0)
| product(X0,e_1,e_2) ) ).
cnf(u3189,axiom,
( ~ cycle(X0,X1)
| ~ next(X0,e_4)
| ~ greater(X1,e_0)
| ~ next(e_1,X2)
| equalish(X1,X2) ) ).
cnf(u2957,axiom,
( ~ product(e_4,e_3,X0)
| equalish(X0,e_2) ) ).
cnf(u3205,axiom,
( ~ product(e_5,X0,e_1)
| equalish(X0,e_3) ) ).
cnf(u3202,negated_conjecture,
( ~ product(e_1,e_4,X0)
| product(X0,e_5,e_4) ) ).
cnf(u3190,axiom,
( ~ cycle(X1,X2)
| ~ cycle(X0,e_0)
| ~ next(X0,e_4)
| ~ greater(X0,X1)
| ~ greater(X2,e_1) ) ).
cnf(u3059,axiom,
( ~ cycle(X1,X2)
| ~ cycle(X0,e_0)
| ~ next(X0,e_3)
| ~ greater(X0,X1)
| ~ greater(X2,e_0) ) ).
cnf(u3199,axiom,
( ~ product(X0,e_1,e_5)
| equalish(X0,e_4) ) ).
cnf(u2480,axiom,
( ~ product(X0,e_1,e_3)
| equalish(X0,e_2) ) ).
cnf(u2952,axiom,
( ~ product(e_1,e_2,X0)
| equalish(X0,e_4) ) ).
cnf(u2796,axiom,
( ~ product(e_4,e_5,X0)
| equalish(X0,e_3) ) ).
cnf(u3114,axiom,
( ~ product(e_3,X0,e_4)
| equalish(X0,e_5) ) ).
cnf(u2961,axiom,
( ~ product(e_1,X0,e_5)
| equalish(X0,e_3) ) ).
cnf(u2962,axiom,
( ~ product(e_1,e_3,X0)
| equalish(X0,e_5) ) ).
cnf(u2773,negated_conjecture,
( ~ product(e_3,e_2,X0)
| product(X0,e_4,e_2) ) ).
cnf(u2958,negated_conjecture,
( ~ product(e_3,e_4,X0)
| product(X0,e_2,e_4) ) ).
cnf(u59,negated_conjecture,
( ~ product(X0,X0,X1)
| product(X1,X0,X0) ) ).
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(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1) ).
cnf(u3264,axiom,
( ~ product(e_5,e_1,X0)
| equalish(X0,e_4) ) ).
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(u3211,axiom,
( ~ product(e_1,X0,e_3)
| equalish(X0,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(u3041,axiom,
( ~ product(X0,e_5,e_1)
| equalish(X0,e_2) ) ).
cnf(e_4_greater_e_3,axiom,
greater(e_4,e_3) ).
cnf(u3262,axiom,
( ~ product(X0,e_1,e_4)
| equalish(X0,e_5) ) ).
cnf(e_5_greater_e_2,axiom,
greater(e_5,e_2) ).
cnf(u3115,axiom,
( ~ product(e_3,e_5,X0)
| equalish(X0,e_4) ) ).
cnf(u2870,axiom,
( ~ product(X0,e_2,e_3)
| equalish(X0,e_5) ) ).
cnf(u2960,axiom,
( ~ product(X0,e_3,e_5)
| equalish(X0,e_1) ) ).
cnf(u3268,axiom,
( ~ product(e_4,e_2,X0)
| equalish(X0,e_1) ) ).
cnf(u2970,negated_conjecture,
( ~ product(e_4,e_3,X0)
| product(X0,e_1,e_3) ) ).
cnf(u2956,axiom,
( ~ product(e_4,X0,e_2)
| equalish(X0,e_3) ) ).
cnf(u2752,axiom,
( ~ product(e_5,X0,e_2)
| equalish(X0,e_4) ) ).
cnf(u2951,axiom,
( ~ product(e_1,X0,e_4)
| equalish(X0,e_2) ) ).
cnf(u2963,negated_conjecture,
( ~ product(e_3,e_1,X0)
| product(X0,e_5,e_1) ) ).
cnf(u3195,axiom,
( ~ cycle(X0,e_0)
| ~ next(X0,e_5)
| ~ greater(X0,e_4) ) ).
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(u3042,axiom,
( ~ product(e_2,X0,e_1)
| 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(e_5_greater_e_4,axiom,
greater(e_5,e_4) ).
cnf(u3200,axiom,
( ~ product(e_4,X0,e_5)
| equalish(X0,e_1) ) ).
cnf(e_2_greater_e_1,axiom,
greater(e_2,e_1) ).
cnf(u2922,negated_conjecture,
( ~ product(e_1,e_3,X0)
| product(X0,e_2,e_3) ) ).
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(e_2_greater_e_0,axiom,
greater(e_2,e_0) ).
cnf(u3280,negated_conjecture,
( ~ product(e_5,e_1,X0)
| product(X0,e_2,e_1) ) ).
cnf(u3274,negated_conjecture,
( ~ product(e_4,e_2,X0)
| product(X0,e_5,e_2) ) ).
cnf(u3271,axiom,
( ~ product(X0,e_4,e_5)
| equalish(X0,e_2) ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP126-3.005 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sun Sep 27 09:25:35 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 1.34/0.99 % (2112785)Input is clausal, will run a generic CNF schedule.
% 1.34/0.99 % (2112792)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4032039424:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.34/0.99 % (2112790)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=372079870:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.34/0.99 % (2112791)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=907212217:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.34/0.99 % (2112793)lrs+10_1_sil=8000:sp=occurrence:random_seed=386075035:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.34/0.99 % (2112794)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3641762017:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.34/0.99 % (2112795)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3884358737:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.34/0.99 % (2112796)dis-21_1_sil=8000:lcm=predicate:random_seed=102812137: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)
% 1.34/0.99 % (2112793)Instruction limit reached!
% 1.34/0.99 % (2112793)------------------------------
% 1.34/0.99 % (2112793)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.34/0.99 % (2112793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.99 % (2112793)CaDiCaL version: 2.1.3
% 1.34/0.99 % (2112793)Termination reason: Instruction limit
% 1.34/0.99 % (2112793)Termination phase: Saturation
% 1.34/0.99 % (2112793)Time elapsed: 0.033 s
% 1.34/0.99 % (2112793)Peak memory usage: 88 MB
% 1.34/0.99 % (2112793)Instructions burned: 110 (million)
% 1.34/0.99 % (2112794)Instruction limit reached!
% 1.34/0.99 % (2112794)------------------------------
% 1.34/0.99 % (2112794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.34/0.99 % (2112794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.99 % (2112794)CaDiCaL version: 2.1.3
% 1.34/0.99 % (2112794)Termination reason: Instruction limit
% 1.34/0.99 % (2112794)Termination phase: Saturation
% 1.34/0.99 % (2112794)Time elapsed: 0.033 s
% 1.34/0.99 % (2112794)Peak memory usage: 88 MB
% 1.34/0.99 % (2112794)Instructions burned: 114 (million)
% 1.34/0.99 % (2112796)Instruction limit reached!
% 1.34/0.99 % (2112796)------------------------------
% 1.34/0.99 % (2112796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.34/0.99 % (2112796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.99 % (2112796)CaDiCaL version: 2.1.3
% 1.34/0.99 % (2112796)Termination reason: Instruction limit
% 1.34/0.99 % (2112796)Termination phase: Saturation
% 1.34/0.99 % (2112796)Time elapsed: 0.041 s
% 1.34/0.99 % (2112796)Peak memory usage: 89 MB
% 1.34/0.99 % (2112796)Instructions burned: 119 (million)
% 1.34/0.99 % (2112795)Instruction limit reached!
% 1.34/0.99 % (2112795)------------------------------
% 1.34/0.99 % (2112795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.34/0.99 % (2112795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.99 % (2112795)CaDiCaL version: 2.1.3
% 1.34/0.99 % (2112795)Termination reason: Instruction limit
% 1.34/0.99 % (2112795)Termination phase: Saturation
% 1.34/0.99 % (2112795)Time elapsed: 0.060 s
% 1.34/0.99 % (2112795)Peak memory usage: 89 MB
% 1.34/0.99 % (2112795)Instructions burned: 180 (million)
% 1.34/0.99 % (2112805)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1405707933:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2998 on theBenchmark for (2998ds/189Mi)
% 1.34/0.99 % (2112805)Refutation not found, incomplete strategy
% 1.34/0.99 % (2112805)------------------------------
% 1.34/0.99 % (2112805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.34/0.99 % (2112805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.99 % (2112805)CaDiCaL version: 2.1.3
% 1.34/0.99 % (2112805)Termination reason: Refutation not found, incomplete strategy
% 1.34/0.99 % (2112805)Time elapsed: 0.001 s
% 1.34/0.99 % (2112805)Peak memory usage: 87 MB
% 1.34/0.99 % (2112805)Instructions burned: 2 (million)
% 1.34/0.99 % (2112804)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=1845044680:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 1.34/0.99 % (2112806)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3987290377:st=4:i=219:sd=3:ss=axioms_2998 on theBenchmark for (2998ds/219Mi)
% 1.34/0.99 % (2112804)Instruction limit reached!
% 1.34/0.99 % (2112804)------------------------------
% 1.34/0.99 % (2112804)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.34/0.99 % (2112804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.99 % (2112804)CaDiCaL version: 2.1.3
% 1.34/0.99 % (2112804)Termination reason: Instruction limit
% 1.34/0.99 % (2112804)Termination phase: Saturation
% 1.34/0.99 % (2112804)Time elapsed: 0.039 s
% 1.34/0.99 % (2112804)Peak memory usage: 88 MB
% 1.34/0.99 % (2112804)Instructions burned: 143 (million)
% 1.34/0.99 % (2112807)lrs+10_64_to=lpo:sil=8000:random_seed=449837468:i=126:bd=preordered_2998 on theBenchmark for (2998ds/126Mi)
% 1.34/0.99 % (2112807)First to succeed.
% 1.34/0.99 % (2112807)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2112785"
% 1.34/0.99 % (2112806)Instruction limit reached!
% 1.34/0.99 % (2112806)------------------------------
% 1.34/0.99 % (2112806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.34/0.99 % (2112806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.99 % (2112806)CaDiCaL version: 2.1.3
% 1.34/0.99 % (2112806)Termination reason: Instruction limit
% 1.34/0.99 % (2112806)Termination phase: Saturation
% 1.34/0.99 % (2112806)Time elapsed: 0.065 s
% 1.34/0.99 % (2112806)Peak memory usage: 88 MB
% 1.34/0.99 % (2112806)Instructions burned: 221 (million)
% 1.34/0.99 % (2112805)------------------------------
% 1.34/0.99 % (2112805)------------------------------
% 1.34/0.99 % (2112811)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=4135340933:avsq=on:i=194:fgj=on:bd=preordered_2997 on theBenchmark for (2997ds/194Mi)
% 1.34/0.99 % (2112811)Instruction limit reached!
% 1.34/0.99 % (2112811)------------------------------
% 1.34/0.99 % (2112811)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.34/0.99 % (2112811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.99 % (2112811)CaDiCaL version: 2.1.3
% 1.34/0.99 % (2112811)Termination reason: Instruction limit
% 1.34/0.99 % (2112811)Termination phase: Saturation
% 1.34/0.99 % (2112811)Time elapsed: 0.049 s
% 1.34/0.99 % (2112811)Peak memory usage: 88 MB
% 1.34/0.99 % (2112811)Instructions burned: 197 (million)
% 1.34/0.99 % (2112813)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2105104877:i=157:gtg=all_2996 on theBenchmark for (2996ds/157Mi)
% 1.34/0.99 % (2112791)Refutation not found, incomplete strategy
% 1.34/0.99 % (2112791)------------------------------
% 1.34/0.99 % (2112791)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.34/0.99 % (2112791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.99 % (2112791)CaDiCaL version: 2.1.3
% 1.34/0.99 % (2112791)Termination reason: Refutation not found, incomplete strategy
% 1.34/0.99 % (2112791)Time elapsed: 0.349 s
% 1.34/0.99 % (2112791)Peak memory usage: 127 MB
% 1.34/0.99 % (2112791)Instructions burned: 938 (million)
% 1.34/0.99 % (2112815)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=2881507168:i=3394:sd=4:ss=included:sgt=64_2996 on theBenchmark for (2996ds/3394Mi)
% 1.34/0.99 % SZS status Satisfiable for theBenchmark
% 1.34/0.99 % SZS output start Saturation.
% See solution above
% 3.44/1.09 % SZS output start Definitions and Model Updates.
% 3.44/1.09 % SZS output end Definitions and Model Updates.
% 3.44/1.09 % (2112807)------------------------------
% 3.44/1.09 % (2112807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.09 % (2112807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.09 % (2112807)CaDiCaL version: 2.1.3
% 3.44/1.09 % (2112807)Termination reason: Satisfiable
% 3.44/1.09 % (2112807)Time elapsed: 0.030 s
% 3.44/1.09 % (2112807)Peak memory usage: 89 MB
% 3.44/1.09 % (2112807)Instructions burned: 84 (million)
% 3.44/1.09 % (2112807)------------------------------
% 3.44/1.09 % (2112807)------------------------------
% 3.44/1.09 % (2112785)Success in time 0.466 s
% 3.44/1.09 % Vampire exiting
%------------------------------------------------------------------------------