%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP058-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 07:26:53 AM UTC 2026
% Result : Unsatisfiable 3.48s 1.42s
% Output : CNFRefutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 2
% Syntax : Number of formulae : 123 ( 118 unt; 0 def)
% Number of atoms : 132 ( 131 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 15 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 422 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : multiply(VAR_0,inverse(multiply(VAR_1,multiply(multiply(multiply(VAR_2,inverse(VAR_2)),inverse(multiply(VAR_3,VAR_1))),VAR_0)))) = VAR_3,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A)))) = D,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(prove_these_axioms,axiom,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('theBenchmark.p',prove_these_axioms) ).
cnf(c_2,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(clausify,[status(thm)],[prove_these_axioms]) ).
cnf(c_3,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ),
inference(copy,[status(thm)],[c_2]) ).
cnf(c_4,plain,
multiply(A,inverse(multiply(inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),E))),multiply(multiply(multiply(F,inverse(F)),inverse(D)),A)))) = E,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,D))),multiply(E,inverse(E))),multiply(C,A)))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
multiply(inverse(multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,A))),multiply(multiply(D,inverse(D)),inverse(multiply(E,F)))))),inverse(multiply(F,C))) = E,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_8,plain,
multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(B)),inverse(C)),multiply(D,inverse(D))),multiply(E,A)))) = inverse(multiply(F,multiply(multiply(multiply(V6,inverse(V6)),inverse(multiply(C,F))),E))),
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_1279,plain,
multiply(A,inverse(multiply(multiply(B,multiply(C,inverse(C))),multiply(D,A)))) = multiply(multiply(multiply(E,inverse(E)),inverse(multiply(B,D))),multiply(F,inverse(F))),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_19,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,C))),multiply(D,inverse(D))) = multiply(E,inverse(multiply(multiply(B,multiply(F,inverse(F))),multiply(C,E)))),
inference(copy,[status(thm)],[c_1279]) ).
cnf(c_34,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,inverse(multiply(multiply(D,multiply(E,inverse(E))),multiply(B,C))))))) = D,
inference(paramod,[status(thm)],[c_19,c_1]) ).
cnf(c_96,plain,
multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(C,multiply(D,inverse(D))),multiply(A,B)))))),inverse(multiply(inverse(E),C))) = E,
inference(paramod,[status(thm)],[c_34,c_1]) ).
cnf(c_1280,plain,
multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(C,multiply(D,inverse(D))),multiply(A,B)))))),inverse(multiply(inverse(multiply(E,multiply(multiply(multiply(F,inverse(F)),inverse(multiply(multiply(V6,inverse(V6)),E))),V7))),C))) = V7,
inference(paramod,[status(thm)],[c_34,c_4]) ).
cnf(c_102,plain,
multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(multiply(C,inverse(C)),A))),D)) = D,
inference(paramod,[status(thm)],[c_96,c_1280]) ).
cnf(c_155,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(paramod,[status(thm)],[c_102,c_1]) ).
cnf(c_1281,plain,
multiply(A,B) = inverse(multiply(C,multiply(multiply(multiply(D,inverse(D)),inverse(multiply(B,C))),multiply(multiply(E,inverse(E)),inverse(multiply(multiply(F,inverse(F)),A)))))),
inference(paramod,[status(thm)],[c_1,c_102]) ).
cnf(c_158,plain,
inverse(multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,A))),multiply(multiply(D,inverse(D)),inverse(multiply(multiply(E,inverse(E)),F)))))) = multiply(F,C),
inference(copy,[status(thm)],[c_1281]) ).
cnf(c_197,plain,
multiply(A,inverse(multiply(inverse(B),multiply(multiply(C,inverse(C)),A)))) = B,
inference(paramod,[status(thm)],[c_155,c_1]) ).
cnf(c_203,plain,
multiply(A,inverse(multiply(multiply(multiply(B,inverse(B)),multiply(C,inverse(C))),multiply(D,A)))) = inverse(D),
inference(paramod,[status(thm)],[c_155,c_5]) ).
cnf(c_217,plain,
multiply(inverse(multiply(A,inverse(A))),multiply(multiply(B,inverse(B)),C)) = C,
inference(paramod,[status(thm)],[c_155,c_102]) ).
cnf(c_246,plain,
multiply(inverse(multiply(A,inverse(A))),inverse(multiply(inverse(B),multiply(C,inverse(C))))) = B,
inference(paramod,[status(thm)],[c_155,c_197]) ).
cnf(c_271,plain,
multiply(inverse(multiply(A,inverse(A))),multiply(B,inverse(B))) = inverse(multiply(C,inverse(C))),
inference(paramod,[status(thm)],[c_155,c_217]) ).
cnf(c_1282,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(multiply(B,inverse(B))),multiply(multiply(C,inverse(C)),inverse(multiply(multiply(D,multiply(E,inverse(E))),inverse(multiply(F,inverse(F))))))))) = D,
inference(paramod,[status(thm)],[c_271,c_34]) ).
cnf(c_393,plain,
multiply(multiply(A,inverse(A)),inverse(inverse(multiply(multiply(B,multiply(C,inverse(C))),inverse(multiply(D,inverse(D))))))) = B,
inference(paramod,[status(thm)],[c_217,c_1282]) ).
cnf(c_409,plain,
inverse(multiply(A,inverse(A))) = inverse(multiply(B,inverse(B))),
inference(paramod,[status(thm)],[c_271,c_217]) ).
cnf(c_442,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))) = multiply(C,inverse(C)),
inference(paramod,[status(thm)],[c_409,c_155]) ).
cnf(c_1283,plain,
multiply(inverse(multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,A))),multiply(multiply(D,inverse(D)),inverse(multiply(multiply(E,inverse(E)),inverse(multiply(F,inverse(F))))))))),inverse(multiply(inverse(V6),C))) = V6,
inference(paramod,[status(thm)],[c_442,c_6]) ).
cnf(c_471,plain,
multiply(multiply(inverse(multiply(A,inverse(A))),B),inverse(multiply(inverse(C),B))) = C,
inference(paramod,[status(thm)],[c_158,c_1283]) ).
cnf(c_1284,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(multiply(C,multiply(multiply(multiply(D,inverse(D)),inverse(multiply(E,C))),B)))))) = multiply(multiply(F,inverse(F)),inverse(E)),
inference(paramod,[status(thm)],[c_8,c_34]) ).
cnf(c_538,plain,
multiply(multiply(A,inverse(A)),inverse(B)) = multiply(multiply(C,inverse(C)),inverse(B)),
inference(paramod,[status(thm)],[c_1,c_1284]) ).
cnf(c_643,plain,
multiply(A,inverse(multiply(inverse(inverse(multiply(B,inverse(B)))),multiply(C,A)))) = inverse(C),
inference(paramod,[status(thm)],[c_471,c_1]) ).
cnf(c_686,plain,
multiply(A,inverse(multiply(inverse(B),inverse(multiply(inverse(A),multiply(C,inverse(C))))))) = B,
inference(paramod,[status(thm)],[c_246,c_471]) ).
cnf(c_694,plain,
multiply(multiply(inverse(multiply(A,inverse(A))),inverse(inverse(B))),inverse(multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(D)))))) = B,
inference(paramod,[status(thm)],[c_442,c_471]) ).
cnf(c_1285,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(multiply(multiply(B,inverse(B)),inverse(C)))),multiply(D,inverse(D))) = multiply(E,inverse(multiply(multiply(multiply(F,inverse(F)),multiply(V6,inverse(V6))),multiply(inverse(C),E)))),
inference(paramod,[status(thm)],[c_538,c_19]) ).
cnf(c_709,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(multiply(multiply(B,inverse(B)),inverse(C)))),multiply(D,inverse(D))) = inverse(inverse(C)),
inference(paramod,[status(thm)],[c_203,c_1285]) ).
cnf(c_1286,plain,
multiply(A,inverse(B)) = multiply(multiply(C,inverse(C)),inverse(multiply(B,inverse(A)))),
inference(paramod,[status(thm)],[c_1,c_686]) ).
cnf(c_785,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(C)))) = multiply(C,inverse(B)),
inference(copy,[status(thm)],[c_1286]) ).
cnf(c_1287,plain,
multiply(A,B) = inverse(multiply(inverse(B),inverse(multiply(inverse(multiply(multiply(C,inverse(C)),inverse(multiply(multiply(D,inverse(D)),A)))),multiply(E,inverse(E)))))),
inference(paramod,[status(thm)],[c_686,c_102]) ).
cnf(c_807,plain,
inverse(multiply(inverse(A),inverse(multiply(inverse(multiply(multiply(B,inverse(B)),inverse(multiply(multiply(C,inverse(C)),D)))),multiply(E,inverse(E)))))) = multiply(D,A),
inference(copy,[status(thm)],[c_1287]) ).
cnf(c_1288,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(B),inverse(inverse(multiply(C,inverse(C))))))) = B,
inference(paramod,[status(thm)],[c_217,c_686]) ).
cnf(c_811,plain,
multiply(inverse(multiply(A,inverse(A))),inverse(inverse(B))) = B,
inference(paramod,[status(thm)],[c_785,c_1288]) ).
cnf(c_838,plain,
multiply(multiply(A,inverse(multiply(B,inverse(B)))),multiply(C,inverse(C))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_785,c_709]) ).
cnf(c_1289,plain,
multiply(B,inverse(multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(D)))))) = B,
inference(paramod,[status(thm)],[c_811,c_694]) ).
cnf(c_841,plain,
multiply(A,inverse(multiply(B,inverse(B)))) = A,
inference(paramod,[status(thm)],[c_785,c_1289]) ).
cnf(c_872,plain,
multiply(A,multiply(B,inverse(B))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_841,c_838]) ).
cnf(c_885,plain,
multiply(multiply(A,inverse(A)),inverse(inverse(multiply(B,multiply(C,inverse(C)))))) = B,
inference(paramod,[status(thm)],[c_841,c_393]) ).
cnf(c_1039,plain,
multiply(A,inverse(multiply(inverse(inverse(inverse(B))),multiply(multiply(multiply(C,inverse(C)),inverse(D)),A)))) = inverse(multiply(multiply(E,inverse(E)),inverse(multiply(D,B)))),
inference(paramod,[status(thm)],[c_872,c_4]) ).
cnf(c_1048,plain,
multiply(inverse(A),inverse(inverse(inverse(multiply(multiply(multiply(B,inverse(B)),inverse(multiply(A,C))),multiply(D,inverse(D))))))) = C,
inference(paramod,[status(thm)],[c_872,c_5]) ).
cnf(c_1290,plain,
inverse(inverse(multiply(multiply(A,inverse(A)),inverse(multiply(B,C))))) = multiply(D,inverse(multiply(multiply(B,multiply(E,inverse(E))),multiply(C,D)))),
inference(paramod,[status(thm)],[c_872,c_19]) ).
cnf(c_1052,plain,
multiply(A,inverse(multiply(multiply(B,multiply(C,inverse(C))),multiply(D,A)))) = inverse(inverse(multiply(multiply(E,inverse(E)),inverse(multiply(B,D))))),
inference(copy,[status(thm)],[c_1290]) ).
cnf(c_1053,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,C))),multiply(D,inverse(D))) = multiply(E,inverse(multiply(inverse(inverse(B)),multiply(C,E)))),
inference(paramod,[status(thm)],[c_872,c_19]) ).
cnf(c_1055,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,C))),multiply(D,inverse(D))) = multiply(inverse(C),inverse(inverse(inverse(multiply(B,multiply(E,inverse(E))))))),
inference(paramod,[status(thm)],[c_872,c_19]) ).
cnf(c_1291,plain,
multiply(inverse(multiply(A,inverse(A))),inverse(inverse(inverse(inverse(B))))) = B,
inference(paramod,[status(thm)],[c_872,c_197]) ).
cnf(c_1081,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_811,c_1291]) ).
cnf(c_1086,plain,
multiply(inverse(multiply(A,inverse(A))),multiply(multiply(inverse(B),multiply(B,multiply(C,inverse(C)))),D)) = D,
inference(paramod,[status(thm)],[c_872,c_217]) ).
cnf(c_1292,plain,
multiply(A,multiply(multiply(B,inverse(B)),inverse(multiply(C,inverse(C))))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_409,c_872]) ).
cnf(c_1293,plain,
multiply(A,multiply(B,inverse(B))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_841,c_1292]) ).
cnf(c_1109,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(paramod,[status(thm)],[c_1081,c_1293]) ).
cnf(c_1294,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(inverse(multiply(B,inverse(B)))),inverse(inverse(C))))) = inverse(C),
inference(paramod,[status(thm)],[c_872,c_643]) ).
cnf(c_1295,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(multiply(B,inverse(B)),inverse(inverse(C))))) = inverse(C),
inference(paramod,[status(thm)],[c_1081,c_1294]) ).
cnf(c_1126,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(multiply(B,inverse(B)),C))) = inverse(C),
inference(paramod,[status(thm)],[c_1081,c_1295]) ).
cnf(c_1296,plain,
multiply(A,multiply(inverse(B),multiply(B,multiply(C,inverse(C))))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_872,c_872]) ).
cnf(c_1297,plain,
multiply(A,multiply(inverse(B),B)) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_1109,c_1296]) ).
cnf(c_1139,plain,
multiply(A,multiply(inverse(B),B)) = A,
inference(paramod,[status(thm)],[c_1081,c_1297]) ).
cnf(c_1298,plain,
inverse(multiply(inverse(A),inverse(multiply(inverse(inverse(D)),multiply(E,inverse(E)))))) = multiply(D,A),
inference(paramod,[status(thm)],[c_1126,c_807]) ).
cnf(c_1299,plain,
inverse(multiply(inverse(A),inverse(multiply(D,multiply(E,inverse(E)))))) = multiply(D,A),
inference(paramod,[status(thm)],[c_1081,c_1298]) ).
cnf(c_1141,plain,
inverse(multiply(inverse(A),inverse(B))) = multiply(B,A),
inference(paramod,[status(thm)],[c_1109,c_1299]) ).
cnf(c_1300,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,C))) = multiply(inverse(C),inverse(inverse(inverse(multiply(B,multiply(E,inverse(E))))))),
inference(paramod,[status(thm)],[c_1109,c_1055]) ).
cnf(c_1301,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,C))) = multiply(inverse(C),inverse(inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_1109,c_1300]) ).
cnf(c_1152,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,C))) = multiply(inverse(C),inverse(B)),
inference(paramod,[status(thm)],[c_1081,c_1301]) ).
cnf(c_1302,plain,
multiply(multiply(inverse(C),inverse(B)),multiply(D,inverse(D))) = multiply(E,inverse(multiply(inverse(inverse(B)),multiply(C,E)))),
inference(paramod,[status(thm)],[c_1152,c_1053]) ).
cnf(c_1303,plain,
multiply(inverse(C),inverse(B)) = multiply(E,inverse(multiply(inverse(inverse(B)),multiply(C,E)))),
inference(paramod,[status(thm)],[c_1109,c_1302]) ).
cnf(c_1304,plain,
multiply(inverse(C),inverse(B)) = multiply(E,inverse(multiply(B,multiply(C,E)))),
inference(paramod,[status(thm)],[c_1081,c_1303]) ).
cnf(c_1153,plain,
multiply(A,inverse(multiply(B,multiply(C,A)))) = multiply(inverse(C),inverse(B)),
inference(copy,[status(thm)],[c_1304]) ).
cnf(c_1305,plain,
multiply(A,inverse(multiply(B,multiply(D,A)))) = inverse(inverse(multiply(multiply(E,inverse(E)),inverse(multiply(B,D))))),
inference(paramod,[status(thm)],[c_1109,c_1052]) ).
cnf(c_1306,plain,
multiply(inverse(D),inverse(B)) = inverse(inverse(multiply(multiply(E,inverse(E)),inverse(multiply(B,D))))),
inference(paramod,[status(thm)],[c_1153,c_1305]) ).
cnf(c_1307,plain,
multiply(inverse(D),inverse(B)) = inverse(inverse(multiply(inverse(D),inverse(B)))),
inference(paramod,[status(thm)],[c_1152,c_1306]) ).
cnf(c_1308,plain,
multiply(inverse(D),inverse(B)) = inverse(multiply(B,D)),
inference(paramod,[status(thm)],[c_1141,c_1307]) ).
cnf(c_1154,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_1308]) ).
cnf(c_1309,plain,
multiply(inverse(A),inverse(inverse(inverse(multiply(multiply(multiply(B,inverse(B)),multiply(inverse(C),inverse(A))),multiply(D,inverse(D))))))) = C,
inference(paramod,[status(thm)],[c_1154,c_1048]) ).
cnf(c_1310,plain,
multiply(inverse(A),inverse(inverse(inverse(multiply(multiply(B,inverse(B)),multiply(inverse(C),inverse(A))))))) = C,
inference(paramod,[status(thm)],[c_1109,c_1309]) ).
cnf(c_1311,plain,
multiply(inverse(A),inverse(inverse(multiply(inverse(multiply(inverse(C),inverse(A))),inverse(multiply(B,inverse(B))))))) = C,
inference(paramod,[status(thm)],[c_1154,c_1310]) ).
cnf(c_1312,plain,
multiply(inverse(A),inverse(inverse(multiply(multiply(inverse(inverse(A)),inverse(inverse(C))),inverse(multiply(B,inverse(B))))))) = C,
inference(paramod,[status(thm)],[c_1154,c_1311]) ).
cnf(c_1313,plain,
multiply(inverse(A),inverse(inverse(multiply(multiply(A,inverse(inverse(C))),inverse(multiply(B,inverse(B))))))) = C,
inference(paramod,[status(thm)],[c_1081,c_1312]) ).
cnf(c_1314,plain,
multiply(inverse(A),inverse(inverse(multiply(multiply(A,C),inverse(multiply(B,inverse(B))))))) = C,
inference(paramod,[status(thm)],[c_1081,c_1313]) ).
cnf(c_1315,plain,
multiply(inverse(A),inverse(inverse(multiply(multiply(A,C),multiply(inverse(inverse(B)),inverse(B)))))) = C,
inference(paramod,[status(thm)],[c_1154,c_1314]) ).
cnf(c_1316,plain,
multiply(inverse(A),inverse(inverse(multiply(multiply(A,C),multiply(B,inverse(B)))))) = C,
inference(paramod,[status(thm)],[c_1081,c_1315]) ).
cnf(c_1317,plain,
multiply(inverse(A),inverse(inverse(multiply(A,C)))) = C,
inference(paramod,[status(thm)],[c_1109,c_1316]) ).
cnf(c_1318,plain,
multiply(inverse(A),inverse(multiply(inverse(C),inverse(A)))) = C,
inference(paramod,[status(thm)],[c_1154,c_1317]) ).
cnf(c_1319,plain,
multiply(inverse(A),multiply(inverse(inverse(A)),inverse(inverse(C)))) = C,
inference(paramod,[status(thm)],[c_1154,c_1318]) ).
cnf(c_1320,plain,
multiply(inverse(A),multiply(A,inverse(inverse(C)))) = C,
inference(paramod,[status(thm)],[c_1081,c_1319]) ).
cnf(c_1156,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(paramod,[status(thm)],[c_1081,c_1320]) ).
cnf(c_1321,plain,
multiply(A,inverse(multiply(inverse(B),multiply(multiply(multiply(C,inverse(C)),inverse(D)),A)))) = inverse(multiply(multiply(E,inverse(E)),inverse(multiply(D,B)))),
inference(paramod,[status(thm)],[c_1081,c_1039]) ).
cnf(c_1322,plain,
multiply(A,multiply(inverse(multiply(multiply(multiply(C,inverse(C)),inverse(D)),A)),inverse(inverse(B)))) = inverse(multiply(multiply(E,inverse(E)),inverse(multiply(D,B)))),
inference(paramod,[status(thm)],[c_1154,c_1321]) ).
cnf(c_1323,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(C,inverse(C)),inverse(D)))),inverse(inverse(B)))) = inverse(multiply(multiply(E,inverse(E)),inverse(multiply(D,B)))),
inference(paramod,[status(thm)],[c_1154,c_1322]) ).
cnf(c_1324,plain,
multiply(A,multiply(multiply(inverse(A),multiply(inverse(inverse(D)),inverse(multiply(C,inverse(C))))),inverse(inverse(B)))) = inverse(multiply(multiply(E,inverse(E)),inverse(multiply(D,B)))),
inference(paramod,[status(thm)],[c_1154,c_1323]) ).
cnf(c_1325,plain,
multiply(A,multiply(multiply(inverse(A),multiply(D,inverse(multiply(C,inverse(C))))),inverse(inverse(B)))) = inverse(multiply(multiply(E,inverse(E)),inverse(multiply(D,B)))),
inference(paramod,[status(thm)],[c_1081,c_1324]) ).
cnf(c_1326,plain,
multiply(A,multiply(multiply(inverse(A),multiply(D,multiply(inverse(inverse(C)),inverse(C)))),inverse(inverse(B)))) = inverse(multiply(multiply(E,inverse(E)),inverse(multiply(D,B)))),
inference(paramod,[status(thm)],[c_1154,c_1325]) ).
cnf(c_1327,plain,
multiply(A,multiply(multiply(inverse(A),multiply(D,multiply(C,inverse(C)))),inverse(inverse(B)))) = inverse(multiply(multiply(E,inverse(E)),inverse(multiply(D,B)))),
inference(paramod,[status(thm)],[c_1081,c_1326]) ).
cnf(c_1328,plain,
multiply(A,multiply(multiply(inverse(A),D),inverse(inverse(B)))) = inverse(multiply(multiply(E,inverse(E)),inverse(multiply(D,B)))),
inference(paramod,[status(thm)],[c_1109,c_1327]) ).
cnf(c_1329,plain,
multiply(A,multiply(multiply(inverse(A),D),B)) = inverse(multiply(multiply(E,inverse(E)),inverse(multiply(D,B)))),
inference(paramod,[status(thm)],[c_1081,c_1328]) ).
cnf(c_1330,plain,
multiply(A,multiply(multiply(inverse(A),D),B)) = inverse(multiply(multiply(E,inverse(E)),multiply(inverse(B),inverse(D)))),
inference(paramod,[status(thm)],[c_1154,c_1329]) ).
cnf(c_1331,plain,
multiply(A,multiply(multiply(inverse(A),D),B)) = multiply(inverse(multiply(inverse(B),inverse(D))),inverse(multiply(E,inverse(E)))),
inference(paramod,[status(thm)],[c_1154,c_1330]) ).
cnf(c_1332,plain,
multiply(A,multiply(multiply(inverse(A),D),B)) = multiply(multiply(inverse(inverse(D)),inverse(inverse(B))),inverse(multiply(E,inverse(E)))),
inference(paramod,[status(thm)],[c_1154,c_1331]) ).
cnf(c_1333,plain,
multiply(A,multiply(multiply(inverse(A),D),B)) = multiply(multiply(D,inverse(inverse(B))),inverse(multiply(E,inverse(E)))),
inference(paramod,[status(thm)],[c_1081,c_1332]) ).
cnf(c_1334,plain,
multiply(A,multiply(multiply(inverse(A),D),B)) = multiply(multiply(D,B),inverse(multiply(E,inverse(E)))),
inference(paramod,[status(thm)],[c_1081,c_1333]) ).
cnf(c_1335,plain,
multiply(A,multiply(multiply(inverse(A),D),B)) = multiply(multiply(D,B),multiply(inverse(inverse(E)),inverse(E))),
inference(paramod,[status(thm)],[c_1154,c_1334]) ).
cnf(c_1336,plain,
multiply(A,multiply(multiply(inverse(A),D),B)) = multiply(multiply(D,B),multiply(E,inverse(E))),
inference(paramod,[status(thm)],[c_1081,c_1335]) ).
cnf(c_1160,plain,
multiply(A,multiply(multiply(inverse(A),B),C)) = multiply(B,C),
inference(paramod,[status(thm)],[c_1109,c_1336]) ).
cnf(c_1337,plain,
multiply(multiply(A,inverse(A)),inverse(inverse(B))) = B,
inference(paramod,[status(thm)],[c_1109,c_885]) ).
cnf(c_1183,plain,
multiply(multiply(A,inverse(A)),B) = B,
inference(paramod,[status(thm)],[c_1081,c_1337]) ).
cnf(c_1338,plain,
multiply(multiply(inverse(inverse(A)),inverse(A)),multiply(multiply(inverse(B),multiply(B,multiply(C,inverse(C)))),D)) = D,
inference(paramod,[status(thm)],[c_1154,c_1086]) ).
cnf(c_1339,plain,
multiply(multiply(A,inverse(A)),multiply(multiply(inverse(B),multiply(B,multiply(C,inverse(C)))),D)) = D,
inference(paramod,[status(thm)],[c_1081,c_1338]) ).
cnf(c_1340,plain,
multiply(multiply(A,inverse(A)),multiply(multiply(inverse(B),B),D)) = D,
inference(paramod,[status(thm)],[c_1109,c_1339]) ).
cnf(c_1221,plain,
multiply(multiply(inverse(A),A),B) = B,
inference(paramod,[status(thm)],[c_1183,c_1340]) ).
cnf(c_1341,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ),
inference(paramod,[status(thm)],[c_1221,c_3]) ).
cnf(c_1265,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ),
inference(copy,[status(thm)],[c_1341]) ).
cnf(c_1271,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(paramod,[status(thm)],[c_1139,c_1156]) ).
cnf(c_1272,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(resolve,[status(thm)],[c_1271,c_1265]) ).
cnf(c_1342,plain,
multiply(A,multiply(B,C)) = multiply(multiply(A,B),C),
inference(paramod,[status(thm)],[c_1156,c_1160]) ).
cnf(c_1277,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(copy,[status(thm)],[c_1342]) ).
cnf(c_1278,plain,
$false,
inference(resolve,[status(thm)],[c_1277,c_1272]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP058-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.44 % Computer : n013.cluster.edu
% 0.08/0.44 % Model : x86_64 x86_64
% 0.08/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.44 % Memory : 8046.5625MB
% 0.08/0.44 % OS : Linux 6.8.0-71-generic
% 0.08/0.44 % CPULimit : 300
% 0.08/0.44 % WCLimit : 300
% 0.08/0.44 % DateTime : Fri Sep 25 14:19:36 UTC 2026
% 0.08/0.45 % CPUTime :
% 0.08/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.45 % Process 597297 was started by sandbox on n013,
% 0.08/0.45 % Fri Sep 25 14:19:36 2026
% 0.08/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.45
% 0.08/0.45 % From the command line: assign(max_seconds, 300).
% 3.48/1.42
% 3.48/1.42 % SZS status Unsatisfiable for theBenchmark
% 3.48/1.42
% 3.48/1.42 % Proof 1 at 0.36 (+ 0.07) seconds.
% 3.48/1.42 % Length of proof is 57.
% 3.48/1.42 % Level of proof is 25.
% 3.48/1.42 % Maximum clause weight is 34.000.
% 3.48/1.42 % Given clauses 37.
% 3.48/1.42
% 3.48/1.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------