%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP203-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 : Sun Sep 27 07:28:21 AM UTC 2026
% Result : Unsatisfiable 9.15s 1.69s
% Output : CNFRefutation 9.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 4
% Syntax : Number of formulae : 139 ( 139 unt; 0 def)
% Number of atoms : 139 ( 138 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 271 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(left_inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(left_inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(moufang3,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(multiply(VAR_0,VAR_1),VAR_0),VAR_2) = multiply(VAR_0,multiply(VAR_1,multiply(VAR_0,VAR_2))),
file('theBenchmark.p',moufang3) ).
cnf(c_3,plain,
multiply(multiply(multiply(A,B),A),C) = multiply(A,multiply(B,multiply(A,C))),
inference(clausify,[status(thm)],[moufang3]) ).
fof(prove_moufang2,axiom,
multiply(multiply(multiply(a,b),c),b) != multiply(a,multiply(b,multiply(c,b))),
file('theBenchmark.p',prove_moufang2) ).
cnf(c_4,plain,
multiply(multiply(multiply(a,b),c),b) != multiply(a,multiply(b,multiply(c,b))),
inference(clausify,[status(thm)],[prove_moufang2]) ).
cnf(c_1216,plain,
multiply(multiply(A,identity),B) = multiply(identity,multiply(A,multiply(identity,B))),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_1217,plain,
multiply(multiply(A,identity),B) = multiply(identity,multiply(A,B)),
inference(paramod,[status(thm)],[c_1,c_1216]) ).
cnf(c_5,plain,
multiply(multiply(A,identity),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_1,c_1217]) ).
cnf(c_1218,plain,
multiply(multiply(multiply(A,identity),A),B) = multiply(A,multiply(A,B)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_6,plain,
multiply(multiply(A,A),B) = multiply(A,multiply(A,B)),
inference(paramod,[status(thm)],[c_5,c_1218]) ).
cnf(c_1219,plain,
multiply(multiply(identity,left_inverse(A)),B) = multiply(left_inverse(A),multiply(A,multiply(left_inverse(A),B))),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_1220,plain,
multiply(left_inverse(A),B) = multiply(left_inverse(A),multiply(A,multiply(left_inverse(A),B))),
inference(paramod,[status(thm)],[c_1,c_1219]) ).
cnf(c_7,plain,
multiply(left_inverse(A),multiply(A,multiply(left_inverse(A),B))) = multiply(left_inverse(A),B),
inference(copy,[status(thm)],[c_1220]) ).
cnf(c_1221,plain,
multiply(identity,A) = multiply(left_inverse(identity),A),
inference(paramod,[status(thm)],[c_2,c_5]) ).
cnf(c_1222,plain,
A = multiply(left_inverse(identity),A),
inference(paramod,[status(thm)],[c_1,c_1221]) ).
cnf(c_9,plain,
multiply(left_inverse(identity),A) = A,
inference(copy,[status(thm)],[c_1222]) ).
cnf(c_1223,plain,
multiply(multiply(multiply(A,B),multiply(A,identity)),C) = multiply(multiply(A,identity),multiply(B,multiply(multiply(A,identity),C))),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_1224,plain,
multiply(multiply(multiply(A,B),multiply(A,identity)),C) = multiply(multiply(A,identity),multiply(B,multiply(A,C))),
inference(paramod,[status(thm)],[c_5,c_1223]) ).
cnf(c_10,plain,
multiply(multiply(multiply(A,B),multiply(A,identity)),C) = multiply(A,multiply(B,multiply(A,C))),
inference(paramod,[status(thm)],[c_5,c_1224]) ).
cnf(c_1225,plain,
multiply(multiply(A,multiply(B,multiply(A,identity))),C) = multiply(multiply(multiply(A,B),A),C),
inference(paramod,[status(thm)],[c_3,c_5]) ).
cnf(c_11,plain,
multiply(multiply(A,multiply(B,multiply(A,identity))),C) = multiply(A,multiply(B,multiply(A,C))),
inference(paramod,[status(thm)],[c_3,c_1225]) ).
cnf(c_1226,plain,
multiply(multiply(A,left_inverse(identity)),B) = multiply(left_inverse(identity),multiply(A,multiply(left_inverse(identity),B))),
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_1227,plain,
multiply(multiply(A,left_inverse(identity)),B) = multiply(left_inverse(identity),multiply(A,B)),
inference(paramod,[status(thm)],[c_9,c_1226]) ).
cnf(c_12,plain,
multiply(multiply(A,left_inverse(identity)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_9,c_1227]) ).
cnf(c_1228,plain,
multiply(identity,A) = multiply(left_inverse(left_inverse(identity)),A),
inference(paramod,[status(thm)],[c_2,c_12]) ).
cnf(c_1229,plain,
A = multiply(left_inverse(left_inverse(identity)),A),
inference(paramod,[status(thm)],[c_1,c_1228]) ).
cnf(c_13,plain,
multiply(left_inverse(left_inverse(identity)),A) = A,
inference(copy,[status(thm)],[c_1229]) ).
cnf(c_16,plain,
left_inverse(identity) = identity,
inference(paramod,[status(thm)],[c_13,c_2]) ).
cnf(c_1230,plain,
multiply(left_inverse(A),multiply(A,identity)) = multiply(left_inverse(A),A),
inference(paramod,[status(thm)],[c_2,c_7]) ).
cnf(c_23,plain,
multiply(left_inverse(A),multiply(A,identity)) = identity,
inference(paramod,[status(thm)],[c_2,c_1230]) ).
cnf(c_28,plain,
multiply(left_inverse(multiply(multiply(A,B),A)),multiply(A,multiply(B,multiply(A,identity)))) = identity,
inference(paramod,[status(thm)],[c_3,c_23]) ).
cnf(c_35,plain,
multiply(left_inverse(multiply(multiply(A,multiply(multiply(B,C),B)),A)),multiply(A,multiply(B,multiply(C,multiply(B,multiply(A,identity)))))) = identity,
inference(paramod,[status(thm)],[c_3,c_28]) ).
cnf(c_39,plain,
multiply(left_inverse(multiply(multiply(A,multiply(B,B)),A)),multiply(A,multiply(B,multiply(B,multiply(A,identity))))) = identity,
inference(paramod,[status(thm)],[c_6,c_28]) ).
cnf(c_41,plain,
multiply(left_inverse(multiply(multiply(A,left_inverse(A)),A)),multiply(A,identity)) = identity,
inference(paramod,[status(thm)],[c_23,c_28]) ).
cnf(c_1231,plain,
multiply(multiply(A,identity),B) = multiply(A,multiply(left_inverse(multiply(A,identity)),multiply(A,B))),
inference(paramod,[status(thm)],[c_2,c_11]) ).
cnf(c_1232,plain,
multiply(A,B) = multiply(A,multiply(left_inverse(multiply(A,identity)),multiply(A,B))),
inference(paramod,[status(thm)],[c_5,c_1231]) ).
cnf(c_53,plain,
multiply(A,multiply(left_inverse(multiply(A,identity)),multiply(A,B))) = multiply(A,B),
inference(copy,[status(thm)],[c_1232]) ).
cnf(c_1233,plain,
multiply(multiply(A,identity),B) = multiply(A,multiply(left_inverse(multiply(multiply(A,left_inverse(A)),A)),multiply(A,B))),
inference(paramod,[status(thm)],[c_41,c_11]) ).
cnf(c_1234,plain,
multiply(A,B) = multiply(A,multiply(left_inverse(multiply(multiply(A,left_inverse(A)),A)),multiply(A,B))),
inference(paramod,[status(thm)],[c_5,c_1233]) ).
cnf(c_57,plain,
multiply(A,multiply(left_inverse(multiply(multiply(A,left_inverse(A)),A)),multiply(A,B))) = multiply(A,B),
inference(copy,[status(thm)],[c_1234]) ).
cnf(c_1235,plain,
multiply(left_inverse(A),multiply(left_inverse(multiply(left_inverse(A),identity)),identity)) = multiply(left_inverse(A),A),
inference(paramod,[status(thm)],[c_2,c_53]) ).
cnf(c_66,plain,
multiply(left_inverse(A),multiply(left_inverse(multiply(left_inverse(A),identity)),identity)) = identity,
inference(paramod,[status(thm)],[c_2,c_1235]) ).
cnf(c_114,plain,
multiply(left_inverse(multiply(multiply(A,multiply(left_inverse(A),left_inverse(A))),A)),multiply(A,multiply(left_inverse(A),identity))) = identity,
inference(paramod,[status(thm)],[c_23,c_39]) ).
cnf(c_1236,plain,
multiply(left_inverse(multiply(multiply(left_inverse(multiply(left_inverse(A),identity)),multiply(left_inverse(A),left_inverse(A))),left_inverse(multiply(left_inverse(A),identity)))),multiply(left_inverse(multiply(left_inverse(A),identity)),multiply(left_inverse(A),identity))) = identity,
inference(paramod,[status(thm)],[c_66,c_39]) ).
cnf(c_116,plain,
multiply(left_inverse(multiply(multiply(left_inverse(multiply(left_inverse(A),identity)),multiply(left_inverse(A),left_inverse(A))),left_inverse(multiply(left_inverse(A),identity)))),identity) = identity,
inference(paramod,[status(thm)],[c_2,c_1236]) ).
cnf(c_1237,plain,
multiply(identity,A) = multiply(left_inverse(multiply(multiply(left_inverse(multiply(left_inverse(B),identity)),multiply(left_inverse(B),left_inverse(B))),left_inverse(multiply(left_inverse(B),identity)))),A),
inference(paramod,[status(thm)],[c_116,c_5]) ).
cnf(c_1238,plain,
A = multiply(left_inverse(multiply(multiply(left_inverse(multiply(left_inverse(B),identity)),multiply(left_inverse(B),left_inverse(B))),left_inverse(multiply(left_inverse(B),identity)))),A),
inference(paramod,[status(thm)],[c_1,c_1237]) ).
cnf(c_117,plain,
multiply(left_inverse(multiply(multiply(left_inverse(multiply(left_inverse(A),identity)),multiply(left_inverse(A),left_inverse(A))),left_inverse(multiply(left_inverse(A),identity)))),B) = B,
inference(copy,[status(thm)],[c_1238]) ).
cnf(c_123,plain,
multiply(multiply(left_inverse(multiply(left_inverse(A),identity)),multiply(left_inverse(A),left_inverse(A))),left_inverse(multiply(left_inverse(A),identity))) = identity,
inference(paramod,[status(thm)],[c_117,c_2]) ).
cnf(c_1239,plain,
multiply(identity,A) = multiply(left_inverse(multiply(left_inverse(B),identity)),multiply(multiply(left_inverse(B),left_inverse(B)),multiply(left_inverse(multiply(left_inverse(B),identity)),A))),
inference(paramod,[status(thm)],[c_123,c_3]) ).
cnf(c_1240,plain,
A = multiply(left_inverse(multiply(left_inverse(B),identity)),multiply(multiply(left_inverse(B),left_inverse(B)),multiply(left_inverse(multiply(left_inverse(B),identity)),A))),
inference(paramod,[status(thm)],[c_1,c_1239]) ).
cnf(c_1241,plain,
A = multiply(left_inverse(multiply(left_inverse(B),identity)),multiply(left_inverse(B),multiply(left_inverse(B),multiply(left_inverse(multiply(left_inverse(B),identity)),A)))),
inference(paramod,[status(thm)],[c_6,c_1240]) ).
cnf(c_124,plain,
multiply(left_inverse(multiply(left_inverse(A),identity)),multiply(left_inverse(A),multiply(left_inverse(A),multiply(left_inverse(multiply(left_inverse(A),identity)),B)))) = B,
inference(copy,[status(thm)],[c_1241]) ).
cnf(c_1242,plain,
multiply(left_inverse(multiply(left_inverse(A),identity)),multiply(multiply(left_inverse(A),identity),B)) = multiply(left_inverse(multiply(left_inverse(A),identity)),multiply(left_inverse(A),multiply(left_inverse(A),multiply(left_inverse(multiply(left_inverse(A),identity)),B)))),
inference(paramod,[status(thm)],[c_124,c_7]) ).
cnf(c_1243,plain,
multiply(left_inverse(multiply(left_inverse(A),identity)),multiply(left_inverse(A),B)) = multiply(left_inverse(multiply(left_inverse(A),identity)),multiply(left_inverse(A),multiply(left_inverse(A),multiply(left_inverse(multiply(left_inverse(A),identity)),B)))),
inference(paramod,[status(thm)],[c_5,c_1242]) ).
cnf(c_147,plain,
multiply(left_inverse(multiply(left_inverse(A),identity)),multiply(left_inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_124,c_1243]) ).
cnf(c_1244,plain,
multiply(left_inverse(multiply(left_inverse(A),identity)),multiply(multiply(left_inverse(A),identity),multiply(left_inverse(multiply(left_inverse(A),identity)),multiply(left_inverse(A),multiply(left_inverse(A),multiply(left_inverse(multiply(left_inverse(A),identity)),B)))))) = B,
inference(paramod,[status(thm)],[c_124,c_7]) ).
cnf(c_1245,plain,
multiply(left_inverse(multiply(left_inverse(A),identity)),multiply(multiply(left_inverse(A),identity),multiply(left_inverse(A),multiply(left_inverse(multiply(left_inverse(A),identity)),B)))) = B,
inference(paramod,[status(thm)],[c_147,c_1244]) ).
cnf(c_1246,plain,
multiply(left_inverse(multiply(left_inverse(A),identity)),multiply(left_inverse(A),multiply(left_inverse(A),multiply(left_inverse(multiply(left_inverse(A),identity)),B)))) = B,
inference(paramod,[status(thm)],[c_5,c_1245]) ).
cnf(c_148,plain,
multiply(left_inverse(A),multiply(left_inverse(multiply(left_inverse(A),identity)),B)) = B,
inference(paramod,[status(thm)],[c_147,c_1246]) ).
cnf(c_1247,plain,
multiply(left_inverse(multiply(left_inverse(A),identity)),multiply(left_inverse(A),multiply(left_inverse(A),multiply(left_inverse(multiply(left_inverse(A),identity)),B)))) = multiply(left_inverse(multiply(multiply(left_inverse(multiply(left_inverse(A),identity)),left_inverse(left_inverse(multiply(left_inverse(A),identity)))),left_inverse(multiply(left_inverse(A),identity)))),multiply(left_inverse(multiply(left_inverse(A),identity)),B)),
inference(paramod,[status(thm)],[c_57,c_124]) ).
cnf(c_1248,plain,
multiply(left_inverse(multiply(left_inverse(A),identity)),multiply(left_inverse(A),B)) = multiply(left_inverse(multiply(multiply(left_inverse(multiply(left_inverse(A),identity)),left_inverse(left_inverse(multiply(left_inverse(A),identity)))),left_inverse(multiply(left_inverse(A),identity)))),multiply(left_inverse(multiply(left_inverse(A),identity)),B)),
inference(paramod,[status(thm)],[c_148,c_1247]) ).
cnf(c_1249,plain,
B = multiply(left_inverse(multiply(multiply(left_inverse(multiply(left_inverse(A),identity)),left_inverse(left_inverse(multiply(left_inverse(A),identity)))),left_inverse(multiply(left_inverse(A),identity)))),multiply(left_inverse(multiply(left_inverse(A),identity)),B)),
inference(paramod,[status(thm)],[c_147,c_1248]) ).
cnf(c_156,plain,
multiply(left_inverse(multiply(multiply(left_inverse(multiply(left_inverse(A),identity)),left_inverse(left_inverse(multiply(left_inverse(A),identity)))),left_inverse(multiply(left_inverse(A),identity)))),multiply(left_inverse(multiply(left_inverse(A),identity)),B)) = B,
inference(copy,[status(thm)],[c_1249]) ).
cnf(c_172,plain,
multiply(left_inverse(multiply(multiply(A,multiply(multiply(left_inverse(A),B),left_inverse(A))),A)),multiply(A,multiply(left_inverse(A),multiply(B,identity)))) = identity,
inference(paramod,[status(thm)],[c_23,c_35]) ).
cnf(c_179,plain,
multiply(left_inverse(multiply(left_inverse(A),identity)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_147]) ).
cnf(c_1250,plain,
multiply(multiply(left_inverse(multiply(left_inverse(A),identity)),identity),multiply(left_inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_147,c_5]) ).
cnf(c_183,plain,
multiply(A,multiply(left_inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_179,c_1250]) ).
cnf(c_1251,plain,
multiply(left_inverse(multiply(left_inverse(A),identity)),identity) = multiply(A,identity),
inference(paramod,[status(thm)],[c_23,c_147]) ).
cnf(c_1252,plain,
A = multiply(A,identity),
inference(paramod,[status(thm)],[c_179,c_1251]) ).
cnf(c_185,plain,
multiply(A,identity) = A,
inference(copy,[status(thm)],[c_1252]) ).
cnf(c_1253,plain,
multiply(left_inverse(multiply(left_inverse(multiply(multiply(A,B),A)),identity)),identity) = multiply(A,multiply(B,multiply(A,identity))),
inference(paramod,[status(thm)],[c_28,c_147]) ).
cnf(c_1254,plain,
multiply(left_inverse(left_inverse(multiply(multiply(A,B),A))),identity) = multiply(A,multiply(B,multiply(A,identity))),
inference(paramod,[status(thm)],[c_185,c_1253]) ).
cnf(c_1255,plain,
left_inverse(left_inverse(multiply(multiply(A,B),A))) = multiply(A,multiply(B,multiply(A,identity))),
inference(paramod,[status(thm)],[c_185,c_1254]) ).
cnf(c_190,plain,
left_inverse(left_inverse(multiply(multiply(A,B),A))) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_185,c_1255]) ).
cnf(c_1256,plain,
multiply(multiply(A,multiply(left_inverse(multiply(left_inverse(B),identity)),identity)),C) = multiply(left_inverse(multiply(left_inverse(B),identity)),multiply(multiply(left_inverse(B),A),multiply(left_inverse(multiply(left_inverse(B),identity)),C))),
inference(paramod,[status(thm)],[c_147,c_10]) ).
cnf(c_1257,plain,
multiply(multiply(A,multiply(left_inverse(left_inverse(B)),identity)),C) = multiply(left_inverse(multiply(left_inverse(B),identity)),multiply(multiply(left_inverse(B),A),multiply(left_inverse(multiply(left_inverse(B),identity)),C))),
inference(paramod,[status(thm)],[c_185,c_1256]) ).
cnf(c_1258,plain,
multiply(multiply(A,left_inverse(left_inverse(B))),C) = multiply(left_inverse(multiply(left_inverse(B),identity)),multiply(multiply(left_inverse(B),A),multiply(left_inverse(multiply(left_inverse(B),identity)),C))),
inference(paramod,[status(thm)],[c_185,c_1257]) ).
cnf(c_1259,plain,
multiply(multiply(A,left_inverse(left_inverse(B))),C) = multiply(left_inverse(left_inverse(B)),multiply(multiply(left_inverse(B),A),multiply(left_inverse(multiply(left_inverse(B),identity)),C))),
inference(paramod,[status(thm)],[c_185,c_1258]) ).
cnf(c_1260,plain,
multiply(multiply(A,left_inverse(left_inverse(B))),C) = multiply(left_inverse(left_inverse(B)),multiply(multiply(left_inverse(B),A),multiply(left_inverse(left_inverse(B)),C))),
inference(paramod,[status(thm)],[c_185,c_1259]) ).
cnf(c_192,plain,
multiply(left_inverse(left_inverse(A)),multiply(multiply(left_inverse(A),B),multiply(left_inverse(left_inverse(A)),C))) = multiply(multiply(B,left_inverse(left_inverse(A))),C),
inference(copy,[status(thm)],[c_1260]) ).
cnf(c_1261,plain,
multiply(left_inverse(multiply(left_inverse(multiply(multiply(A,multiply(left_inverse(A),left_inverse(A))),A)),identity)),identity) = multiply(A,multiply(left_inverse(A),identity)),
inference(paramod,[status(thm)],[c_114,c_147]) ).
cnf(c_1262,plain,
multiply(left_inverse(multiply(left_inverse(multiply(left_inverse(A),A)),identity)),identity) = multiply(A,multiply(left_inverse(A),identity)),
inference(paramod,[status(thm)],[c_183,c_1261]) ).
cnf(c_1263,plain,
multiply(left_inverse(multiply(left_inverse(identity),identity)),identity) = multiply(A,multiply(left_inverse(A),identity)),
inference(paramod,[status(thm)],[c_2,c_1262]) ).
cnf(c_1264,plain,
multiply(left_inverse(multiply(identity,identity)),identity) = multiply(A,multiply(left_inverse(A),identity)),
inference(paramod,[status(thm)],[c_16,c_1263]) ).
cnf(c_1265,plain,
multiply(left_inverse(identity),identity) = multiply(A,multiply(left_inverse(A),identity)),
inference(paramod,[status(thm)],[c_185,c_1264]) ).
cnf(c_1266,plain,
multiply(identity,identity) = multiply(A,multiply(left_inverse(A),identity)),
inference(paramod,[status(thm)],[c_16,c_1265]) ).
cnf(c_1267,plain,
identity = multiply(A,multiply(left_inverse(A),identity)),
inference(paramod,[status(thm)],[c_185,c_1266]) ).
cnf(c_1268,plain,
identity = multiply(A,left_inverse(A)),
inference(paramod,[status(thm)],[c_185,c_1267]) ).
cnf(c_204,plain,
multiply(A,left_inverse(A)) = identity,
inference(copy,[status(thm)],[c_1268]) ).
cnf(c_1269,plain,
multiply(left_inverse(multiply(multiply(A,multiply(multiply(left_inverse(A),B),left_inverse(A))),A)),multiply(A,multiply(left_inverse(A),B))) = identity,
inference(paramod,[status(thm)],[c_185,c_172]) ).
cnf(c_209,plain,
multiply(left_inverse(multiply(multiply(A,multiply(multiply(left_inverse(A),B),left_inverse(A))),A)),B) = identity,
inference(paramod,[status(thm)],[c_183,c_1269]) ).
cnf(c_1270,plain,
multiply(left_inverse(left_inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_185,c_179]) ).
cnf(c_213,plain,
left_inverse(left_inverse(A)) = A,
inference(paramod,[status(thm)],[c_185,c_1270]) ).
cnf(c_1271,plain,
multiply(left_inverse(multiply(multiply(left_inverse(left_inverse(A)),left_inverse(left_inverse(multiply(left_inverse(A),identity)))),left_inverse(multiply(left_inverse(A),identity)))),multiply(left_inverse(multiply(left_inverse(A),identity)),B)) = B,
inference(paramod,[status(thm)],[c_185,c_156]) ).
cnf(c_1272,plain,
multiply(left_inverse(multiply(multiply(A,left_inverse(left_inverse(multiply(left_inverse(A),identity)))),left_inverse(multiply(left_inverse(A),identity)))),multiply(left_inverse(multiply(left_inverse(A),identity)),B)) = B,
inference(paramod,[status(thm)],[c_213,c_1271]) ).
cnf(c_1273,plain,
multiply(left_inverse(multiply(multiply(A,left_inverse(left_inverse(left_inverse(A)))),left_inverse(multiply(left_inverse(A),identity)))),multiply(left_inverse(multiply(left_inverse(A),identity)),B)) = B,
inference(paramod,[status(thm)],[c_185,c_1272]) ).
cnf(c_1274,plain,
multiply(left_inverse(multiply(multiply(A,left_inverse(A)),left_inverse(multiply(left_inverse(A),identity)))),multiply(left_inverse(multiply(left_inverse(A),identity)),B)) = B,
inference(paramod,[status(thm)],[c_213,c_1273]) ).
cnf(c_1275,plain,
multiply(left_inverse(multiply(identity,left_inverse(multiply(left_inverse(A),identity)))),multiply(left_inverse(multiply(left_inverse(A),identity)),B)) = B,
inference(paramod,[status(thm)],[c_204,c_1274]) ).
cnf(c_1276,plain,
multiply(left_inverse(multiply(identity,left_inverse(left_inverse(A)))),multiply(left_inverse(multiply(left_inverse(A),identity)),B)) = B,
inference(paramod,[status(thm)],[c_185,c_1275]) ).
cnf(c_1277,plain,
multiply(left_inverse(multiply(identity,A)),multiply(left_inverse(multiply(left_inverse(A),identity)),B)) = B,
inference(paramod,[status(thm)],[c_213,c_1276]) ).
cnf(c_1278,plain,
multiply(left_inverse(A),multiply(left_inverse(multiply(left_inverse(A),identity)),B)) = B,
inference(paramod,[status(thm)],[c_1,c_1277]) ).
cnf(c_1279,plain,
multiply(left_inverse(A),multiply(left_inverse(left_inverse(A)),B)) = B,
inference(paramod,[status(thm)],[c_185,c_1278]) ).
cnf(c_218,plain,
multiply(left_inverse(A),multiply(A,B)) = B,
inference(paramod,[status(thm)],[c_213,c_1279]) ).
cnf(c_227,plain,
multiply(multiply(A,multiply(B,A)),C) = multiply(A,multiply(B,multiply(A,C))),
inference(paramod,[status(thm)],[c_185,c_11]) ).
cnf(c_1280,plain,
multiply(A,multiply(multiply(left_inverse(A),B),multiply(left_inverse(left_inverse(A)),C))) = multiply(multiply(B,left_inverse(left_inverse(A))),C),
inference(paramod,[status(thm)],[c_213,c_192]) ).
cnf(c_1281,plain,
multiply(A,multiply(multiply(left_inverse(A),B),multiply(A,C))) = multiply(multiply(B,left_inverse(left_inverse(A))),C),
inference(paramod,[status(thm)],[c_213,c_1280]) ).
cnf(c_228,plain,
multiply(A,multiply(multiply(left_inverse(A),B),multiply(A,C))) = multiply(multiply(B,A),C),
inference(paramod,[status(thm)],[c_213,c_1281]) ).
cnf(c_231,plain,
multiply(multiply(A,B),A) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_213,c_190]) ).
cnf(c_1282,plain,
multiply(left_inverse(multiply(multiply(A,multiply(left_inverse(A),multiply(B,left_inverse(A)))),A)),B) = identity,
inference(paramod,[status(thm)],[c_231,c_209]) ).
cnf(c_232,plain,
multiply(left_inverse(multiply(multiply(A,left_inverse(B)),B)),A) = identity,
inference(paramod,[status(thm)],[c_183,c_1282]) ).
cnf(c_1283,plain,
multiply(left_inverse(left_inverse(multiply(multiply(A,left_inverse(B)),B))),identity) = A,
inference(paramod,[status(thm)],[c_232,c_218]) ).
cnf(c_1284,plain,
multiply(multiply(multiply(A,left_inverse(B)),B),identity) = A,
inference(paramod,[status(thm)],[c_213,c_1283]) ).
cnf(c_288,plain,
multiply(multiply(A,left_inverse(B)),B) = A,
inference(paramod,[status(thm)],[c_185,c_1284]) ).
cnf(c_292,plain,
multiply(multiply(A,B),left_inverse(B)) = A,
inference(paramod,[status(thm)],[c_213,c_288]) ).
cnf(c_302,plain,
multiply(left_inverse(multiply(A,B)),A) = left_inverse(B),
inference(paramod,[status(thm)],[c_292,c_218]) ).
cnf(c_1285,plain,
multiply(left_inverse(A),left_inverse(B)) = left_inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_218,c_302]) ).
cnf(c_312,plain,
left_inverse(multiply(A,B)) = multiply(left_inverse(B),left_inverse(A)),
inference(copy,[status(thm)],[c_1285]) ).
cnf(c_521,plain,
multiply(multiply(A,multiply(B,multiply(A,C))),left_inverse(C)) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_227,c_292]) ).
cnf(c_1286,plain,
multiply(left_inverse(A),multiply(multiply(left_inverse(left_inverse(A)),B),C)) = multiply(multiply(B,left_inverse(A)),multiply(A,C)),
inference(paramod,[status(thm)],[c_218,c_228]) ).
cnf(c_1287,plain,
multiply(left_inverse(A),multiply(multiply(A,B),C)) = multiply(multiply(B,left_inverse(A)),multiply(A,C)),
inference(paramod,[status(thm)],[c_213,c_1286]) ).
cnf(c_628,plain,
multiply(multiply(A,left_inverse(B)),multiply(B,C)) = multiply(left_inverse(B),multiply(multiply(B,A),C)),
inference(copy,[status(thm)],[c_1287]) ).
cnf(c_1288,plain,
multiply(A,multiply(multiply(B,left_inverse(A)),C)) = multiply(multiply(left_inverse(left_inverse(A)),B),multiply(left_inverse(A),C)),
inference(paramod,[status(thm)],[c_228,c_183]) ).
cnf(c_1289,plain,
multiply(A,multiply(multiply(B,left_inverse(A)),C)) = multiply(multiply(A,B),multiply(left_inverse(A),C)),
inference(paramod,[status(thm)],[c_213,c_1288]) ).
cnf(c_630,plain,
multiply(multiply(A,B),multiply(left_inverse(A),C)) = multiply(A,multiply(multiply(B,left_inverse(A)),C)),
inference(copy,[status(thm)],[c_1289]) ).
cnf(c_1290,plain,
multiply(multiply(A,multiply(B,C)),left_inverse(multiply(left_inverse(A),C))) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_183,c_521]) ).
cnf(c_1291,plain,
multiply(multiply(A,multiply(B,C)),multiply(left_inverse(C),left_inverse(left_inverse(A)))) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_312,c_1290]) ).
cnf(c_1123,plain,
multiply(multiply(A,multiply(B,C)),multiply(left_inverse(C),A)) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_213,c_1291]) ).
cnf(c_1292,plain,
multiply(multiply(A,B),multiply(left_inverse(left_inverse(C)),A)) = multiply(A,multiply(multiply(B,C),A)),
inference(paramod,[status(thm)],[c_292,c_1123]) ).
cnf(c_1156,plain,
multiply(multiply(A,B),multiply(C,A)) = multiply(A,multiply(multiply(B,C),A)),
inference(paramod,[status(thm)],[c_213,c_1292]) ).
cnf(c_1293,plain,
multiply(multiply(multiply(A,B),C),B) = multiply(multiply(A,B),multiply(multiply(C,left_inverse(A)),multiply(A,B))),
inference(paramod,[status(thm)],[c_218,c_1156]) ).
cnf(c_1294,plain,
multiply(multiply(multiply(A,B),C),B) = multiply(multiply(A,B),multiply(left_inverse(A),multiply(multiply(A,C),B))),
inference(paramod,[status(thm)],[c_628,c_1293]) ).
cnf(c_1295,plain,
multiply(multiply(multiply(A,B),C),B) = multiply(A,multiply(multiply(B,left_inverse(A)),multiply(multiply(A,C),B))),
inference(paramod,[status(thm)],[c_630,c_1294]) ).
cnf(c_1296,plain,
multiply(multiply(multiply(A,B),C),B) = multiply(A,multiply(B,multiply(multiply(left_inverse(A),multiply(A,C)),B))),
inference(paramod,[status(thm)],[c_1156,c_1295]) ).
cnf(c_1214,plain,
multiply(multiply(multiply(A,B),C),B) = multiply(A,multiply(B,multiply(C,B))),
inference(paramod,[status(thm)],[c_218,c_1296]) ).
cnf(c_1215,plain,
$false,
inference(resolve,[status(thm)],[c_1214,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP203-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n020.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 14:38:34 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 3145775 was started by sandbox on n020,
% 0.17/0.45 % Fri Sep 25 14:38:34 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 9.15/1.69
% 9.15/1.69 % Assigning unary symbol left_inverse kb_weight 0 and highest precedence (7).
% 9.15/1.69
% 9.15/1.69 % SZS status Unsatisfiable for theBenchmark
% 9.15/1.69
% 9.15/1.69 % Proof 1 at 0.90 (+ 0.31) seconds.
% 9.15/1.69 % Length of proof is 54.
% 9.15/1.69 % Level of proof is 22.
% 9.15/1.69 % Maximum clause weight is 99.000.
% 9.15/1.69 % Given clauses 153.
% 9.15/1.69
% 9.15/1.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------