%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP123-8.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 10:12:40 AM UTC 2026
% Result : Satisfiable 4.32s 1.59s
% Output : Saturation 5.73s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(u71,axiom,
~ cycle(e_3,e_3) ).
cnf(u75,axiom,
~ cycle(e_3,e_2) ).
cnf(u80,axiom,
cycle(e_3,e_1) ).
cnf(u88,axiom,
~ cycle(e_2,e_3) ).
cnf(u101,axiom,
cycle(e_2,e_0) ).
cnf(u105,axiom,
~ cycle(e_1,e_3) ).
cnf(u109,axiom,
~ cycle(e_1,e_2) ).
cnf(u113,axiom,
~ cycle(e_1,e_1) ).
cnf(u118,axiom,
cycle(e_1,e_0) ).
cnf(u140,axiom,
~ greater(e_0,e_0) ).
cnf(u144,axiom,
~ next(e_4,e_4) ).
cnf(u156,axiom,
~ next(e_2,e_4) ).
cnf(u161,axiom,
~ next(e_1,e_4) ).
cnf(u202,axiom,
~ next(e_3,e_1) ).
cnf(u210,axiom,
~ next(e_2,e_1) ).
cnf(u215,axiom,
~ next(e_1,e_1) ).
cnf(u227,axiom,
~ next(e_3,e_2) ).
cnf(u232,axiom,
~ next(e_2,e_2) ).
cnf(u280,axiom,
~ next(e_3,e_3) ).
cnf(u352,axiom,
~ greater(e_0,e_1) ).
cnf(u360,axiom,
~ greater(e_1,e_1) ).
cnf(u397,axiom,
~ product1(e_4,e_1,e_4) ).
cnf(u402,axiom,
product1(e_4,e_1,e_3) ).
cnf(u405,axiom,
~ product1(e_4,e_1,e_2) ).
cnf(u409,axiom,
~ product1(e_4,e_1,e_1) ).
cnf(u414,axiom,
~ product1(e_3,e_1,e_4) ).
cnf(u418,axiom,
~ product1(e_3,e_1,e_3) ).
cnf(u423,axiom,
product1(e_3,e_1,e_2) ).
cnf(u426,axiom,
~ product1(e_3,e_1,e_1) ).
cnf(u432,axiom,
product1(e_2,e_1,e_4) ).
cnf(u435,axiom,
~ product1(e_2,e_1,e_3) ).
cnf(u443,axiom,
~ product1(e_2,e_1,e_1) ).
cnf(u564,axiom,
~ product1(e_4,e_2,e_4) ).
cnf(u568,axiom,
~ product1(e_4,e_2,e_3) ).
cnf(u572,axiom,
~ product1(e_4,e_2,e_2) ).
cnf(u577,axiom,
product1(e_4,e_2,e_1) ).
cnf(u582,axiom,
product1(e_3,e_2,e_4) ).
cnf(u585,axiom,
~ product1(e_3,e_2,e_3) ).
cnf(u589,axiom,
~ product1(e_3,e_2,e_2) ).
cnf(u598,axiom,
~ product1(e_1,e_2,e_4) ).
cnf(u603,axiom,
product1(e_1,e_2,e_3) ).
cnf(u610,axiom,
~ product1(e_1,e_2,e_1) ).
cnf(u674,axiom,
~ product1(e_4,e_3,e_4) ).
cnf(u678,axiom,
~ product1(e_4,e_3,e_3) ).
cnf(u683,axiom,
product1(e_4,e_3,e_2) ).
cnf(u691,axiom,
~ product1(e_2,e_3,e_4) ).
cnf(u695,axiom,
~ product1(e_2,e_3,e_3) ).
cnf(u699,axiom,
~ product1(e_2,e_3,e_2) ).
cnf(u704,axiom,
product1(e_2,e_3,e_1) ).
cnf(u709,axiom,
product1(e_1,e_3,e_4) ).
cnf(u716,axiom,
~ product1(e_1,e_3,e_2) ).
cnf(u720,axiom,
~ product1(e_1,e_3,e_1) ).
cnf(u886,axiom,
~ product1(e_3,e_4,e_4) ).
cnf(u890,axiom,
~ product1(e_3,e_4,e_3) ).
cnf(u894,axiom,
~ product1(e_3,e_4,e_2) ).
cnf(u899,axiom,
product1(e_3,e_4,e_1) ).
cnf(u903,axiom,
~ product1(e_2,e_4,e_4) ).
cnf(u908,axiom,
product1(e_2,e_4,e_3) ).
cnf(u924,axiom,
~ product1(e_1,e_4,e_3) ).
cnf(u929,axiom,
product1(e_1,e_4,e_2) ).
cnf(u932,axiom,
~ product1(e_1,e_4,e_1) ).
cnf(u1087,axiom,
product2(e_3,e_1,e_4) ).
cnf(u1108,axiom,
product2(e_2,e_1,e_3) ).
cnf(u1115,axiom,
~ product2(e_2,e_1,e_1) ).
cnf(u1120,axiom,
( ~ product1(e_3,X0,e_2)
| equalish(X0,e_1) ) ).
cnf(e_2_then_e_3,axiom,
next(e_2,e_3) ).
cnf(u988,negated_conjecture,
( ~ product2(e_1,e_2,X0)
| equalish(X0,e_4) ) ).
cnf(element_1,axiom,
group_element(e_1) ).
cnf(u983,negated_conjecture,
( ~ product1(X0,e_4,e_3)
| product2(e_1,X0,e_4) ) ).
cnf(u986,negated_conjecture,
( ~ product2(X0,e_2,e_4)
| equalish(X0,e_1) ) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3) ).
cnf(u49,negated_conjecture,
( ~ product1(X0,X1,X1)
| product2(X1,X0,X1) ) ).
cnf(u531,negated_conjecture,
product2(e_4,e_3,e_1) ).
cnf(product1_right_cancellation,axiom,
( ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2)
| equalish(X1,X3) ) ).
cnf(u1131,negated_conjecture,
( ~ product2(e_3,e_2,X0)
| equalish(X0,e_1) ) ).
cnf(u995,axiom,
( ~ product1(e_4,X0,e_2)
| equalish(X0,e_3) ) ).
cnf(u63,axiom,
( ~ product2(X0,X1,X1)
| equalish(X0,X1) ) ).
cnf(e_3_greater_e_0,axiom,
greater(e_3,e_0) ).
cnf(u387,axiom,
( ~ group_element(X0)
| product1(X0,e_1,e_1)
| product1(X0,e_1,e_2)
| product1(X0,e_1,e_3)
| product1(X0,e_1,e_4) ) ).
cnf(e_3_greater_e_1,axiom,
greater(e_3,e_1) ).
cnf(u314,axiom,
( ~ cycle(X0,e_0)
| ~ next(X0,e_4)
| ~ greater(X0,e_3) ) ).
cnf(u317,axiom,
( ~ cycle(e_2,X0)
| equalish(X0,e_0) ) ).
cnf(element_4,axiom,
group_element(e_4) ).
cnf(u129,axiom,
( ~ cycle(X0,X1)
| ~ next(X0,e_4)
| ~ greater(X1,e_0)
| ~ next(e_0,X2)
| equalish(X1,X2) ) ).
cnf(u1050,axiom,
( ~ product1(X0,e_2,e_3)
| equalish(X0,e_1) ) ).
cnf(product2_total_function2,axiom,
( ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2)
| equalish(X2,X3) ) ).
cnf(u476,axiom,
( ~ group_element(X0)
| product2(X0,e_1,e_1)
| product2(X0,e_1,e_2)
| product2(X0,e_1,e_3)
| product2(X0,e_1,e_4) ) ).
cnf(u1046,axiom,
( ~ product1(e_3,X0,e_4)
| equalish(X0,e_2) ) ).
cnf(u1051,axiom,
( ~ product1(e_1,X0,e_3)
| equalish(X0,e_2) ) ).
cnf(u336,axiom,
( ~ cycle(X0,e_0)
| ~ next(X0,e_1)
| ~ greater(X0,e_3) ) ).
cnf(u51,axiom,
( ~ cycle(e_4,X0)
| equalish(X0,e_0) ) ).
cnf(u1024,negated_conjecture,
product2(e_1,e_4,e_3) ).
cnf(u1060,negated_conjecture,
product2(e_3,e_4,e_2) ).
cnf(e_4_greater_e_3,axiom,
greater(e_4,e_3) ).
cnf(u1143,axiom,
( ~ product1(X0,e_1,e_4)
| equalish(X0,e_2) ) ).
cnf(e_0_then_e_1,axiom,
next(e_0,e_1) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1) ).
cnf(u981,axiom,
( ~ product1(e_3,X0,e_1)
| equalish(X0,e_4) ) ).
cnf(u1154,negated_conjecture,
product2(e_4,e_2,e_3) ).
cnf(u1151,axiom,
( ~ product1(e_1,e_3,X0)
| equalish(X0,e_4) ) ).
cnf(u1067,negated_conjecture,
( ~ product2(X0,e_4,e_1)
| equalish(X0,e_2) ) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1) ).
cnf(u1157,negated_conjecture,
( ~ product2(e_4,e_2,X0)
| equalish(X0,e_3) ) ).
cnf(u1026,negated_conjecture,
( ~ product2(X0,e_4,e_3)
| equalish(X0,e_1) ) ).
cnf(u263,axiom,
( ~ cycle(X1,X2)
| ~ cycle(X0,e_0)
| ~ next(X0,e_1)
| ~ greater(X0,X1)
| ~ greater(X2,e_0) ) ).
cnf(u55,axiom,
( ~ product1(X0,X1,X0)
| equalish(X1,X0) ) ).
cnf(u1027,negated_conjecture,
( ~ product2(e_1,X0,e_3)
| equalish(X0,e_4) ) ).
cnf(u1134,negated_conjecture,
( ~ product2(e_4,e_3,X0)
| equalish(X0,e_1) ) ).
cnf(u980,axiom,
( ~ product1(X0,e_4,e_1)
| equalish(X0,e_3) ) ).
cnf(u1189,negated_conjecture,
( ~ product2(e_2,X0,e_4)
| equalish(X0,e_3) ) ).
cnf(u517,negated_conjecture,
product2(e_3,e_2,e_1) ).
cnf(u309,axiom,
( ~ cycle(e_3,X0)
| equalish(X0,e_1) ) ).
cnf(e_1_greater_e_0,axiom,
greater(e_1,e_0) ).
cnf(u749,negated_conjecture,
product2(e_1,e_3,e_2) ).
cnf(u1040,axiom,
( ~ product1(X0,e_2,e_1)
| equalish(X0,e_4) ) ).
cnf(u971,axiom,
( ~ product1(e_2,X0,e_3)
| equalish(X0,e_4) ) ).
cnf(e_4_greater_e_0,axiom,
greater(e_4,e_0) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2) ).
cnf(u1122,negated_conjecture,
( ~ product1(X0,e_1,e_3)
| product2(e_2,X0,e_1) ) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4) ).
cnf(product2_total_function1,axiom,
( ~ group_element(X1)
| ~ group_element(X0)
| product2(X0,X1,e_1)
| product2(X0,X1,e_2)
| product2(X0,X1,e_3)
| product2(X0,X1,e_4) ) ).
cnf(u1068,negated_conjecture,
( ~ product2(e_2,X0,e_1)
| equalish(X0,e_4) ) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4) ).
cnf(u1048,negated_conjecture,
( ~ product1(X0,e_2,e_3)
| product2(e_4,X0,e_2) ) ).
cnf(u1133,negated_conjecture,
( ~ product2(e_4,X0,e_1)
| equalish(X0,e_3) ) ).
cnf(u1014,axiom,
( ~ product1(X0,e_3,e_1)
| equalish(X0,e_2) ) ).
cnf(u1199,axiom,
( ~ product2(e_2,e_1,X0)
| equalish(X0,e_3) ) ).
cnf(u386,axiom,
~ greater(e_1,e_3) ).
cnf(u389,axiom,
( ~ group_element(X0)
| product1(X0,e_3,e_1)
| product1(X0,e_3,e_2)
| product1(X0,e_3,e_3)
| product1(X0,e_3,e_4) ) ).
cnf(u478,axiom,
( ~ group_element(X0)
| product2(X0,e_3,e_1)
| product2(X0,e_3,e_2)
| product2(X0,e_3,e_3)
| product2(X0,e_3,e_4) ) ).
cnf(e_3_greater_e_2,axiom,
greater(e_3,e_2) ).
cnf(u316,axiom,
( ~ next(e_0,X0)
| equalish(e_1,X0) ) ).
cnf(u311,axiom,
( ~ cycle(X1,X2)
| ~ cycle(X0,e_0)
| ~ next(X0,e_3)
| ~ greater(X0,X1)
| ~ greater(X2,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(u1076,axiom,
( ~ product1(X0,e_1,e_3)
| equalish(X0,e_4) ) ).
cnf(u1198,axiom,
( ~ product2(e_2,X0,e_3)
| equalish(X0,e_1) ) ).
cnf(product1_total_function1,axiom,
( ~ group_element(X1)
| ~ group_element(X0)
| product1(X0,X1,e_1)
| product1(X0,X1,e_2)
| product1(X0,X1,e_3)
| product1(X0,X1,e_4) ) ).
cnf(u1053,negated_conjecture,
( ~ product1(X0,e_2,e_1)
| product2(e_3,X0,e_2) ) ).
cnf(u261,axiom,
( ~ cycle(e_1,X0)
| equalish(X0,e_0) ) ).
cnf(u53,axiom,
( ~ product1(X0,X0,X1)
| equalish(X1,X0) ) ).
cnf(u1146,negated_conjecture,
( ~ product1(X0,e_1,e_2)
| product2(e_4,X0,e_1) ) ).
cnf(u390,axiom,
( ~ group_element(X0)
| product1(X0,e_4,e_1)
| product1(X0,e_4,e_2)
| product1(X0,e_4,e_3)
| product1(X0,e_4,e_4) ) ).
cnf(u1017,negated_conjecture,
( ~ product1(X0,e_3,e_2)
| product2(e_1,X0,e_3) ) ).
cnf(u1195,axiom,
( ~ product2(e_3,X0,e_4)
| equalish(X0,e_1) ) ).
cnf(u1033,negated_conjecture,
( ~ product2(e_1,e_3,X0)
| equalish(X0,e_2) ) ).
cnf(element_2,axiom,
group_element(e_2) ).
cnf(u1063,negated_conjecture,
( ~ product2(e_3,X0,e_2)
| equalish(X0,e_4) ) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2) ).
cnf(u987,negated_conjecture,
( ~ product2(e_1,X0,e_4)
| equalish(X0,e_2) ) ).
cnf(u1119,axiom,
( ~ product1(X0,e_1,e_2)
| equalish(X0,e_3) ) ).
cnf(u262,axiom,
( ~ cycle(X0,X1)
| ~ next(X0,e_1)
| ~ greater(X1,e_0)
| ~ next(e_0,X2)
| equalish(X1,X2) ) ).
cnf(u1015,axiom,
( ~ product1(e_2,X0,e_1)
| equalish(X0,e_3) ) ).
cnf(u1054,negated_conjecture,
( ~ product2(X0,e_1,e_2)
| equalish(X0,e_4) ) ).
cnf(product1_left_cancellation,axiom,
( ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2)
| equalish(X0,X3) ) ).
cnf(u1194,axiom,
( ~ product2(X0,e_1,e_4)
| equalish(X0,e_3) ) ).
cnf(e_3_then_e_4,axiom,
next(e_3,e_4) ).
cnf(u340,axiom,
~ next(e_4,e_1) ).
cnf(u1184,axiom,
( ~ product1(e_1,X0,e_2)
| equalish(X0,e_4) ) ).
cnf(e_4_greater_e_1,axiom,
greater(e_4,e_1) ).
cnf(u996,axiom,
( ~ product1(e_4,e_3,X0)
| equalish(X0,e_2) ) ).
cnf(e_1_then_e_2,axiom,
next(e_1,e_2) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3) ).
cnf(u982,axiom,
( ~ product1(e_3,e_4,X0)
| equalish(X0,e_1) ) ).
cnf(cycle3,axiom,
cycle(e_4,e_0) ).
cnf(product2_right_cancellation,axiom,
( ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2)
| equalish(X1,X3) ) ).
cnf(u997,negated_conjecture,
( ~ product1(X0,e_3,e_4)
| product2(e_2,X0,e_3) ) ).
cnf(u1077,axiom,
( ~ product1(e_4,X0,e_3)
| equalish(X0,e_1) ) ).
cnf(qg1a,negated_conjecture,
( ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2)
| product2(X3,X0,X1) ) ).
cnf(u1078,axiom,
( ~ product1(e_4,e_1,X0)
| equalish(X0,e_3) ) ).
cnf(u1062,negated_conjecture,
( ~ product2(X0,e_4,e_2)
| equalish(X0,e_3) ) ).
cnf(u1185,axiom,
( ~ product1(e_1,e_4,X0)
| equalish(X0,e_2) ) ).
cnf(u388,axiom,
( ~ group_element(X0)
| product1(X0,e_2,e_1)
| product1(X0,e_2,e_2)
| product1(X0,e_2,e_3)
| product1(X0,e_2,e_4) ) ).
cnf(u994,axiom,
( ~ product1(X0,e_3,e_2)
| equalish(X0,e_4) ) ).
cnf(u1043,negated_conjecture,
( ~ product1(X0,e_2,e_4)
| product2(e_1,X0,e_2) ) ).
cnf(u1190,negated_conjecture,
( ~ product2(e_2,e_3,X0)
| equalish(X0,e_4) ) ).
cnf(u1144,axiom,
( ~ product1(e_2,X0,e_4)
| equalish(X0,e_1) ) ).
cnf(u972,axiom,
( ~ product1(e_2,e_4,X0)
| equalish(X0,e_3) ) ).
cnf(e_2_greater_e_0,axiom,
greater(e_2,e_0) ).
cnf(u310,axiom,
( ~ cycle(X0,X1)
| ~ next(X0,e_3)
| ~ greater(X1,e_0)
| ~ next(e_1,X2)
| equalish(X1,X2) ) ).
cnf(u970,axiom,
( ~ product1(X0,e_4,e_3)
| equalish(X0,e_2) ) ).
cnf(u1042,axiom,
( ~ product1(e_4,e_2,X0)
| equalish(X0,e_1) ) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2) ).
cnf(u1183,axiom,
( ~ product1(X0,e_4,e_2)
| equalish(X0,e_1) ) ).
cnf(u1069,negated_conjecture,
( ~ product2(e_2,e_4,X0)
| equalish(X0,e_1) ) ).
cnf(element_3,axiom,
group_element(e_3) ).
cnf(u52,axiom,
equalish(e_0,e_0) ).
cnf(u1064,negated_conjecture,
( ~ product2(e_3,e_4,X0)
| equalish(X0,e_2) ) ).
cnf(u1129,negated_conjecture,
( ~ product2(X0,e_2,e_1)
| equalish(X0,e_3) ) ).
cnf(product2_idempotence,axiom,
product2(X0,X0,X0) ).
cnf(u59,axiom,
( ~ product2(X0,X0,X1)
| equalish(X1,X0) ) ).
cnf(u1056,negated_conjecture,
( ~ product2(e_4,e_1,X0)
| equalish(X0,e_2) ) ).
cnf(u1049,negated_conjecture,
product2(e_4,e_1,e_2) ).
cnf(u1016,axiom,
( ~ product1(e_2,e_3,X0)
| equalish(X0,e_1) ) ).
cnf(u1149,axiom,
( ~ product1(X0,e_3,e_4)
| equalish(X0,e_1) ) ).
cnf(e_2_greater_e_1,axiom,
greater(e_2,e_1) ).
cnf(u973,negated_conjecture,
( ~ product1(X0,e_4,e_2)
| product2(e_3,X0,e_4) ) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1) ).
cnf(u1028,negated_conjecture,
( ~ product2(e_1,e_4,X0)
| equalish(X0,e_3) ) ).
cnf(u1156,negated_conjecture,
( ~ product2(e_4,X0,e_3)
| equalish(X0,e_2) ) ).
cnf(u54,axiom,
equalish(X0,X0) ).
cnf(u1031,negated_conjecture,
( ~ product2(X0,e_3,e_2)
| equalish(X0,e_1) ) ).
cnf(u1197,axiom,
( ~ product2(X0,e_1,e_3)
| equalish(X0,e_2) ) ).
cnf(u1055,negated_conjecture,
( ~ product2(e_4,X0,e_2)
| equalish(X0,e_1) ) ).
cnf(e_4_greater_e_2,axiom,
greater(e_4,e_2) ).
cnf(u1145,axiom,
( ~ product1(e_2,e_1,X0)
| equalish(X0,e_4) ) ).
cnf(u1188,negated_conjecture,
( ~ product2(X0,e_3,e_4)
| equalish(X0,e_2) ) ).
cnf(u1150,axiom,
( ~ product1(e_1,X0,e_4)
| equalish(X0,e_3) ) ).
cnf(u1079,negated_conjecture,
( ~ product1(X0,e_1,e_4)
| product2(e_3,X0,e_1) ) ).
cnf(u1130,negated_conjecture,
( ~ product2(e_3,X0,e_1)
| equalish(X0,e_2) ) ).
cnf(u381,axiom,
( ~ cycle(X0,e_0)
| ~ next(X0,e_2)
| ~ greater(X0,e_3) ) ).
cnf(cycle2,axiom,
( ~ group_element(X0)
| cycle(X0,e_0)
| cycle(X0,e_1)
| cycle(X0,e_2)
| cycle(X0,e_3) ) ).
cnf(u1152,negated_conjecture,
( ~ product1(X0,e_3,e_1)
| product2(e_4,X0,e_3) ) ).
cnf(u1045,axiom,
( ~ product1(X0,e_2,e_4)
| equalish(X0,e_3) ) ).
cnf(product1_total_function2,axiom,
( ~ product1(X0,X1,X3)
| ~ product1(X0,X1,X2)
| equalish(X2,X3) ) ).
cnf(u542,negated_conjecture,
product2(e_2,e_4,e_1) ).
cnf(u318,axiom,
( ~ cycle(X0,X1)
| ~ next(X0,e_2)
| ~ greater(X1,e_0)
| ~ next(e_0,X2)
| equalish(X1,X2) ) ).
cnf(product1_idempotence,axiom,
product1(X0,X0,X0) ).
cnf(u477,axiom,
( ~ group_element(X0)
| product2(X0,e_2,e_1)
| product2(X0,e_2,e_2)
| product2(X0,e_2,e_3)
| product2(X0,e_2,e_4) ) ).
cnf(u174,axiom,
( ~ cycle(X1,X2)
| ~ cycle(X0,e_0)
| ~ next(X0,e_4)
| ~ greater(X0,X1)
| ~ greater(X2,e_0) ) ).
cnf(u57,axiom,
( ~ product1(X0,X1,X1)
| equalish(X0,X1) ) ).
cnf(u1132,negated_conjecture,
( ~ product2(X0,e_3,e_1)
| equalish(X0,e_4) ) ).
cnf(u1052,axiom,
( ~ product1(e_1,e_2,X0)
| equalish(X0,e_3) ) ).
cnf(u479,axiom,
( ~ group_element(X0)
| product2(X0,e_4,e_1)
| product2(X0,e_4,e_2)
| product2(X0,e_4,e_3)
| product2(X0,e_4,e_4) ) ).
cnf(u319,axiom,
( ~ cycle(X1,X2)
| ~ cycle(X0,e_0)
| ~ next(X0,e_2)
| ~ greater(X0,X1)
| ~ greater(X2,e_0) ) ).
cnf(u1032,negated_conjecture,
( ~ product2(e_1,X0,e_2)
| equalish(X0,e_3) ) ).
cnf(cycle1,axiom,
( ~ cycle(X0,X2)
| ~ cycle(X0,X1)
| equalish(X1,X2) ) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3) ).
cnf(u984,negated_conjecture,
product2(e_1,e_2,e_4) ).
cnf(u1121,axiom,
( ~ product1(e_3,e_1,X0)
| equalish(X0,e_2) ) ).
cnf(cycle4,axiom,
( ~ cycle(X2,X3)
| ~ cycle(X0,X1)
| ~ next(X0,X2)
| ~ greater(X1,e_0)
| ~ next(X3,X4)
| equalish(X1,X4) ) ).
cnf(product2_left_cancellation,axiom,
( ~ product2(X3,X1,X2)
| ~ product2(X0,X1,X2)
| equalish(X0,X3) ) ).
cnf(u1047,axiom,
( ~ product1(e_3,e_2,X0)
| equalish(X0,e_4) ) ).
cnf(u1155,negated_conjecture,
( ~ product2(X0,e_2,e_3)
| equalish(X0,e_4) ) ).
cnf(u1196,axiom,
( ~ product2(e_3,e_1,X0)
| equalish(X0,e_4) ) ).
cnf(u61,axiom,
( ~ product2(X0,X1,X0)
| equalish(X1,X0) ) ).
cnf(u385,axiom,
~ next(e_4,e_2) ).
cnf(u1186,negated_conjecture,
( ~ product1(X0,e_4,e_1)
| product2(e_2,X0,e_4) ) ).
cnf(u1041,axiom,
( ~ product1(e_4,X0,e_1)
| equalish(X0,e_2) ) ).
cnf(u1187,negated_conjecture,
product2(e_2,e_3,e_4) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP123-8.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:23:31 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 4.32/1.59 % (1392939)Input is clausal, will run a generic CNF schedule.
% 4.32/1.59 % (1393036)lrs+10_1_sil=8000:sp=occurrence:random_seed=4193694250:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.32/1.59 % (1393036)Instruction limit reached!
% 4.32/1.59 % (1393036)------------------------------
% 4.32/1.59 % (1393036)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.59 % (1393036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.59 % (1393036)CaDiCaL version: 2.1.3
% 4.32/1.59 % (1393036)Termination reason: Instruction limit
% 4.32/1.59 % (1393036)Termination phase: Saturation
% 4.32/1.59 % (1393036)Time elapsed: 0.033 s
% 4.32/1.59 % (1393036)Peak memory usage: 88 MB
% 4.32/1.59 % (1393036)Instructions burned: 107 (million)
% 4.32/1.59 % (1393032)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=1313543789:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.32/1.59 % (1393034)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2213305014:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.32/1.59 % (1393035)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=888963157:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.32/1.59 % (1393038)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2501693071:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.32/1.59 % (1393039)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3809956295:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.32/1.59 % (1393040)dis-21_1_sil=8000:lcm=predicate:random_seed=2261763608: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)
% 4.32/1.59 % (1393038)Instruction limit reached!
% 4.32/1.59 % (1393038)------------------------------
% 4.32/1.59 % (1393038)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.59 % (1393038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.59 % (1393038)CaDiCaL version: 2.1.3
% 4.32/1.59 % (1393038)Termination reason: Instruction limit
% 4.32/1.59 % (1393038)Termination phase: Saturation
% 4.32/1.59 % (1393038)Time elapsed: 0.036 s
% 4.32/1.59 % (1393038)Peak memory usage: 88 MB
% 4.32/1.59 % (1393038)Instructions burned: 118 (million)
% 4.32/1.59 % (1393040)Instruction limit reached!
% 4.32/1.59 % (1393040)------------------------------
% 4.32/1.59 % (1393040)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.59 % (1393040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.59 % (1393040)CaDiCaL version: 2.1.3
% 4.32/1.59 % (1393040)Termination reason: Instruction limit
% 4.32/1.59 % (1393040)Termination phase: Saturation
% 4.32/1.59 % (1393040)Time elapsed: 0.076 s
% 4.32/1.59 % (1393040)Peak memory usage: 89 MB
% 4.32/1.59 % (1393040)Instructions burned: 118 (million)
% 4.32/1.59 % (1393039)Instruction limit reached!
% 4.32/1.59 % (1393039)------------------------------
% 4.32/1.59 % (1393039)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.59 % (1393039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.59 % (1393039)CaDiCaL version: 2.1.3
% 4.32/1.59 % (1393039)Termination reason: Instruction limit
% 4.32/1.59 % (1393039)Termination phase: Saturation
% 4.32/1.59 % (1393039)Time elapsed: 0.116 s
% 4.32/1.59 % (1393039)Peak memory usage: 89 MB
% 4.32/1.59 % (1393039)Instructions burned: 180 (million)
% 4.32/1.59 % (1393060)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=2207945919:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 4.32/1.59 % (1393064)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=598785688: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)
% 4.32/1.59 % (1393064)Refutation not found, incomplete strategy
% 4.32/1.59 % (1393064)------------------------------
% 4.32/1.59 % (1393064)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.59 % (1393064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.59 % (1393064)CaDiCaL version: 2.1.3
% 4.32/1.59 % (1393064)Termination reason: Refutation not found, incomplete strategy
% 4.32/1.59 % (1393064)Time elapsed: 0.001 s
% 4.32/1.59 % (1393064)Peak memory usage: 87 MB
% 4.32/1.59 % (1393064)Instructions burned: 2 (million)
% 4.32/1.59 % (1393065)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1731824453:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.32/1.59 % (1393060)Instruction limit reached!
% 4.32/1.59 % (1393060)------------------------------
% 4.32/1.59 % (1393060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.59 % (1393060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.59 % (1393060)CaDiCaL version: 2.1.3
% 4.32/1.59 % (1393060)Termination reason: Instruction limit
% 4.32/1.59 % (1393060)Termination phase: Saturation
% 4.32/1.59 % (1393060)Time elapsed: 0.089 s
% 4.32/1.59 % (1393060)Peak memory usage: 89 MB
% 4.32/1.59 % (1393060)Instructions burned: 143 (million)
% 4.32/1.59 % (1393066)lrs+10_64_to=lpo:sil=8000:random_seed=969785230:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 4.32/1.59 % (1393064)------------------------------
% 4.32/1.59 % (1393064)------------------------------
% 4.32/1.59 % (1393066)First to succeed.
% 4.32/1.59 % (1393066)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1392939"
% 4.32/1.59 % (1393065)Instruction limit reached!
% 4.32/1.59 % (1393065)------------------------------
% 4.32/1.59 % (1393065)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.59 % (1393065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.59 % (1393065)CaDiCaL version: 2.1.3
% 4.32/1.59 % (1393065)Termination reason: Instruction limit
% 4.32/1.59 % (1393065)Termination phase: Saturation
% 4.32/1.59 % (1393065)Time elapsed: 0.127 s
% 4.32/1.59 % (1393065)Peak memory usage: 89 MB
% 4.32/1.59 % (1393065)Instructions burned: 220 (million)
% 4.32/1.59 % (1393074)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3121594905:avsq=on:i=194:fgj=on:bd=preordered_2996 on theBenchmark for (2996ds/194Mi)
% 4.32/1.59 % (1393082)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2276789978:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 4.32/1.59 % (1393082)Instruction limit reached!
% 4.32/1.59 % (1393082)------------------------------
% 4.32/1.59 % (1393082)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.59 % (1393082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.59 % (1393082)CaDiCaL version: 2.1.3
% 4.32/1.59 % (1393082)Termination reason: Instruction limit
% 4.32/1.59 % (1393082)Termination phase: Saturation
% 4.32/1.59 % (1393082)Time elapsed: 0.048 s
% 4.32/1.59 % (1393082)Peak memory usage: 89 MB
% 4.32/1.59 % (1393082)Instructions burned: 160 (million)
% 4.32/1.59 % (1393074)Instruction limit reached!
% 4.32/1.59 % (1393074)------------------------------
% 4.32/1.59 % (1393074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.59 % (1393074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.59 % (1393074)CaDiCaL version: 2.1.3
% 4.32/1.59 % (1393074)Termination reason: Instruction limit
% 4.32/1.59 % (1393074)Termination phase: Saturation
% 4.32/1.59 % (1393074)Time elapsed: 0.116 s
% 4.32/1.59 % (1393074)Peak memory usage: 88 MB
% 4.32/1.59 % (1393074)Instructions burned: 194 (million)
% 4.32/1.59 % (1393099)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=2281098834:i=3394:sd=4:ss=included:sgt=64_2994 on theBenchmark for (2994ds/3394Mi)
% 4.32/1.59 % SZS status Satisfiable for theBenchmark
% 4.32/1.59 % SZS output start Saturation.
% See solution above
% 5.73/1.78 % SZS output start Definitions and Model Updates.
% 5.73/1.78 for all inputs,
% 5.73/1.78 define product(X0,X1,X2) := $false
% 5.73/1.78 % SZS output end Definitions and Model Updates.
% 5.73/1.78 % (1393066)------------------------------
% 5.73/1.78 % (1393066)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.73/1.78 % (1393066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.78 % (1393066)CaDiCaL version: 2.1.3
% 5.73/1.78 % (1393066)Termination reason: Satisfiable
% 5.73/1.78 % (1393066)Time elapsed: 0.018 s
% 5.73/1.78 % (1393066)Peak memory usage: 88 MB
% 5.73/1.78 % (1393066)Instructions burned: 26 (million)
% 5.73/1.78 % (1393066)------------------------------
% 5.73/1.78 % (1393066)------------------------------
% 5.73/1.78 % (1392939)Success in time 0.73 s
% 5.73/1.78 % Vampire exiting
%------------------------------------------------------------------------------