%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP051-1 : 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 : n005.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 07:26:34 AM UTC 2026
% Result : Unsatisfiable 13.94s 2.40s
% Output : CNFRefutation 13.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 68
% Number of leaves : 2
% Syntax : Number of formulae : 253 ( 248 unt; 0 def)
% Number of atoms : 261 ( 260 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 14 ( 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 : 963 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(inverse(multiply(VAR_0,inverse(multiply(VAR_1,VAR_2)))),multiply(VAR_0,inverse(VAR_2))),inverse(multiply(inverse(VAR_2),VAR_2))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(C),C))) = B,
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_3575,plain,
multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))) = multiply(inverse(multiply(D,inverse(multiply(B,C)))),multiply(D,inverse(C))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_4,plain,
multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))) = multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),
inference(copy,[status(thm)],[c_3575]) ).
cnf(c_5,plain,
multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(C))),inverse(multiply(inverse(C),C))) = inverse(C),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_7,plain,
multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(C),C))) = B,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_8,plain,
multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),C))),C)))),multiply(A,inverse(C))) = B,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_9,plain,
multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(C))) = multiply(multiply(inverse(multiply(D,inverse(inverse(C)))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_10,plain,
multiply(inverse(multiply(A,inverse(multiply(multiply(inverse(B),B),C)))),multiply(A,inverse(C))) = multiply(multiply(inverse(D),multiply(multiply(inverse(multiply(E,inverse(multiply(D,B)))),multiply(E,inverse(B))),inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_12,plain,
multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(multiply(B,C)))),multiply(D,inverse(C))),
inference(paramod,[status(thm)],[c_4,c_4]) ).
cnf(c_23,plain,
multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))),inverse(multiply(inverse(multiply(C,inverse(D))),multiply(C,inverse(D))))) = inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(inverse(D),D))),D)))),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_3576,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))) = multiply(inverse(multiply(E,inverse(multiply(inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(inverse(D),D))),D)))),multiply(C,inverse(D)))))),multiply(E,inverse(multiply(C,inverse(D))))),
inference(paramod,[status(thm)],[c_8,c_12]) ).
cnf(c_25,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))) = multiply(inverse(multiply(E,inverse(B))),multiply(E,inverse(multiply(C,inverse(D))))),
inference(paramod,[status(thm)],[c_8,c_3576]) ).
cnf(c_3577,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(B,multiply(C,inverse(D)))))),multiply(A,inverse(multiply(C,inverse(D))))),inverse(multiply(inverse(multiply(C,inverse(D))),multiply(C,inverse(D))))) = B,
inference(paramod,[status(thm)],[c_25,c_1]) ).
cnf(c_26,plain,
inverse(multiply(A,inverse(multiply(multiply(multiply(B,multiply(A,inverse(C))),inverse(multiply(inverse(C),C))),C)))) = B,
inference(paramod,[status(thm)],[c_23,c_3577]) ).
cnf(c_3578,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(multiply(multiply(inverse(multiply(E,inverse(multiply(C,F)))),multiply(E,inverse(F))),inverse(multiply(inverse(F),F)))))),
inference(paramod,[status(thm)],[c_1,c_25]) ).
cnf(c_29,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(C))),
inference(paramod,[status(thm)],[c_1,c_3578]) ).
cnf(c_3579,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(multiply(E,inverse(multiply(multiply(multiply(B,multiply(E,inverse(F))),inverse(multiply(inverse(F),F))),F)))))),multiply(D,inverse(C))),
inference(paramod,[status(thm)],[c_26,c_29]) ).
cnf(c_43,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(C))) = multiply(inverse(multiply(D,B)),multiply(D,inverse(C))),
inference(paramod,[status(thm)],[c_26,c_3579]) ).
cnf(c_48,plain,
multiply(multiply(multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(C),C))) = multiply(D,inverse(multiply(multiply(multiply(B,multiply(D,inverse(E))),inverse(multiply(inverse(E),E))),E))),
inference(paramod,[status(thm)],[c_26,c_7]) ).
cnf(c_49,plain,
multiply(multiply(multiply(A,multiply(B,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(C),C))) = multiply(multiply(multiply(A,multiply(B,inverse(D))),inverse(multiply(inverse(D),D))),D),
inference(paramod,[status(thm)],[c_26,c_7]) ).
cnf(c_50,plain,
multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(C))) = multiply(inverse(D),multiply(multiply(inverse(multiply(E,inverse(multiply(D,C)))),multiply(E,inverse(C))),inverse(C))),
inference(paramod,[status(thm)],[c_9,c_9]) ).
cnf(c_3580,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,inverse(multiply(E,inverse(multiply(multiply(multiply(C,multiply(E,inverse(F))),inverse(multiply(inverse(F),F))),F)))))),
inference(paramod,[status(thm)],[c_26,c_43]) ).
cnf(c_55,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(paramod,[status(thm)],[c_26,c_3580]) ).
cnf(c_58,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(B,C)),multiply(B,D))))),multiply(A,inverse(multiply(E,D)))),inverse(multiply(inverse(multiply(E,D)),multiply(E,D)))) = inverse(multiply(E,C)),
inference(paramod,[status(thm)],[c_55,c_1]) ).
cnf(c_59,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(B,multiply(C,D))))),multiply(A,inverse(multiply(C,D)))),inverse(multiply(inverse(multiply(E,D)),multiply(E,D)))) = B,
inference(paramod,[status(thm)],[c_55,c_1]) ).
cnf(c_3581,plain,
multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),D)) = multiply(inverse(multiply(E,inverse(multiply(inverse(C),C)))),multiply(E,D)),
inference(paramod,[status(thm)],[c_1,c_55]) ).
cnf(c_60,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,C)) = multiply(inverse(D),multiply(multiply(inverse(multiply(E,inverse(multiply(D,B)))),multiply(E,inverse(B))),C)),
inference(copy,[status(thm)],[c_3581]) ).
cnf(c_62,plain,
multiply(multiply(inverse(inverse(multiply(A,B))),multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(multiply(D,B)),multiply(D,E))))),multiply(C,inverse(multiply(A,E)))),inverse(multiply(A,E)))),inverse(multiply(inverse(multiply(A,E)),multiply(A,E)))) = inverse(multiply(A,E)),
inference(paramod,[status(thm)],[c_55,c_5]) ).
cnf(c_3582,plain,
multiply(A,multiply(B,C)) = multiply(inverse(multiply(D,inverse(multiply(multiply(multiply(A,multiply(B,inverse(E))),inverse(multiply(inverse(E),E))),E)))),multiply(D,C)),
inference(paramod,[status(thm)],[c_26,c_55]) ).
cnf(c_71,plain,
multiply(inverse(multiply(A,inverse(multiply(multiply(multiply(B,multiply(C,inverse(D))),inverse(multiply(inverse(D),D))),D)))),multiply(A,E)) = multiply(B,multiply(C,E)),
inference(copy,[status(thm)],[c_3582]) ).
cnf(c_73,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),E)) = multiply(inverse(multiply(F,multiply(D,C))),multiply(F,E)),
inference(paramod,[status(thm)],[c_55,c_55]) ).
cnf(c_74,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(multiply(F,C)),multiply(F,multiply(A,E))),
inference(paramod,[status(thm)],[c_55,c_55]) ).
cnf(c_3583,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(B,multiply(C,D))),multiply(B,E))))),multiply(A,inverse(multiply(inverse(multiply(C,F)),E)))),inverse(multiply(inverse(multiply(inverse(multiply(C,F)),E)),multiply(inverse(multiply(C,F)),E)))) = inverse(multiply(inverse(multiply(V6,F)),multiply(V6,D))),
inference(paramod,[status(thm)],[c_73,c_1]) ).
cnf(c_75,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = inverse(multiply(inverse(multiply(D,B)),multiply(D,C))),
inference(paramod,[status(thm)],[c_58,c_3583]) ).
cnf(c_122,plain,
inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E)))) = inverse(multiply(inverse(multiply(F,C)),multiply(F,multiply(A,E)))),
inference(paramod,[status(thm)],[c_55,c_75]) ).
cnf(c_3584,plain,
multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(inverse(multiply(E,inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(F,C)),inverse(V6))),inverse(multiply(inverse(V6),V6))),V6)))),multiply(E,multiply(F,D))),
inference(paramod,[status(thm)],[c_26,c_74]) ).
cnf(c_140,plain,
multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(A,multiply(inverse(multiply(E,C)),multiply(E,D))),
inference(paramod,[status(thm)],[c_71,c_3584]) ).
cnf(c_150,plain,
multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,D))) = multiply(inverse(multiply(E,multiply(F,C))),multiply(E,multiply(F,D))),
inference(paramod,[status(thm)],[c_74,c_73]) ).
cnf(c_574,plain,
multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))),inverse(multiply(inverse(multiply(E,inverse(D))),multiply(E,inverse(D))))) = inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(inverse(D),D))),D)))),
inference(paramod,[status(thm)],[c_55,c_23]) ).
cnf(c_1144,plain,
multiply(A,inverse(multiply(inverse(multiply(B,C)),multiply(B,C)))) = multiply(A,inverse(multiply(inverse(multiply(D,C)),multiply(D,C)))),
inference(paramod,[status(thm)],[c_8,c_59]) ).
cnf(c_1149,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(B,C)),multiply(B,D))))),multiply(A,inverse(multiply(E,D)))),inverse(multiply(inverse(multiply(F,D)),multiply(F,D)))) = inverse(multiply(E,C)),
inference(paramod,[status(thm)],[c_55,c_59]) ).
cnf(c_1175,plain,
multiply(A,inverse(multiply(multiply(multiply(B,multiply(A,inverse(C))),inverse(multiply(inverse(C),C))),C))) = multiply(D,inverse(multiply(multiply(multiply(B,multiply(D,inverse(E))),inverse(multiply(inverse(E),E))),E))),
inference(paramod,[status(thm)],[c_48,c_48]) ).
cnf(c_3585,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(C),C))) = multiply(multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(E))),inverse(multiply(inverse(E),E))),E),
inference(paramod,[status(thm)],[c_4,c_49]) ).
cnf(c_3586,plain,
B = multiply(multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(E))),inverse(multiply(inverse(E),E))),E),
inference(paramod,[status(thm)],[c_1,c_3585]) ).
cnf(c_1177,plain,
multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))),inverse(multiply(inverse(C),C))),C) = B,
inference(copy,[status(thm)],[c_3586]) ).
cnf(c_1181,plain,
multiply(multiply(multiply(inverse(multiply(A,B)),multiply(A,inverse(C))),inverse(multiply(inverse(C),C))),C) = multiply(D,inverse(multiply(multiply(multiply(B,multiply(D,inverse(E))),inverse(multiply(inverse(E),E))),E))),
inference(paramod,[status(thm)],[c_49,c_48]) ).
cnf(c_1182,plain,
multiply(multiply(multiply(A,multiply(B,inverse(C))),inverse(multiply(inverse(C),C))),C) = multiply(multiply(multiply(A,multiply(B,inverse(D))),inverse(multiply(inverse(D),D))),D),
inference(paramod,[status(thm)],[c_49,c_49]) ).
cnf(c_3587,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(D,inverse(C))),multiply(D,inverse(E))),inverse(multiply(inverse(E),E))),E)))),inverse(multiply(inverse(multiply(F,E)),multiply(F,E)))) = B,
inference(paramod,[status(thm)],[c_1177,c_59]) ).
cnf(c_1350,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(multiply(D,E)),multiply(D,E)))) = B,
inference(paramod,[status(thm)],[c_1177,c_3587]) ).
cnf(c_3588,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(B,multiply(C,D))))),multiply(A,inverse(multiply(C,D)))),inverse(multiply(inverse(E),multiply(multiply(multiply(inverse(multiply(F,inverse(E))),multiply(F,inverse(D))),inverse(multiply(inverse(D),D))),D)))) = B,
inference(paramod,[status(thm)],[c_1177,c_59]) ).
cnf(c_1352,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(B,multiply(C,D))))),multiply(A,inverse(multiply(C,D)))),inverse(multiply(inverse(E),E))) = B,
inference(paramod,[status(thm)],[c_1177,c_3588]) ).
cnf(c_3589,plain,
multiply(A,inverse(multiply(inverse(B),multiply(multiply(multiply(inverse(multiply(C,inverse(B))),multiply(C,inverse(D))),inverse(multiply(inverse(D),D))),D)))) = multiply(A,inverse(multiply(inverse(multiply(E,D)),multiply(E,D)))),
inference(paramod,[status(thm)],[c_1177,c_1144]) ).
cnf(c_3590,plain,
multiply(A,inverse(multiply(inverse(B),B))) = multiply(A,inverse(multiply(inverse(multiply(E,D)),multiply(E,D)))),
inference(paramod,[status(thm)],[c_1177,c_3589]) ).
cnf(c_1354,plain,
multiply(A,inverse(multiply(inverse(multiply(B,C)),multiply(B,C)))) = multiply(A,inverse(multiply(inverse(D),D))),
inference(copy,[status(thm)],[c_3590]) ).
cnf(c_1361,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(B,C)),multiply(B,C))))),multiply(A,inverse(D))),inverse(multiply(inverse(D),D))) = inverse(D),
inference(paramod,[status(thm)],[c_1354,c_1]) ).
cnf(c_3591,plain,
multiply(A,inverse(multiply(inverse(B),multiply(multiply(inverse(multiply(C,inverse(multiply(B,D)))),multiply(C,inverse(D))),inverse(multiply(inverse(D),D)))))) = multiply(A,inverse(multiply(inverse(E),E))),
inference(paramod,[status(thm)],[c_1,c_1354]) ).
cnf(c_1364,plain,
multiply(A,inverse(multiply(inverse(B),B))) = multiply(A,inverse(multiply(inverse(C),C))),
inference(paramod,[status(thm)],[c_1,c_3591]) ).
cnf(c_3592,plain,
multiply(inverse(multiply(A,inverse(multiply(multiply(inverse(B),B),C)))),multiply(A,inverse(C))) = multiply(multiply(inverse(multiply(D,inverse(multiply(inverse(multiply(E,F)),multiply(E,F))))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),
inference(paramod,[status(thm)],[c_1354,c_4]) ).
cnf(c_1368,plain,
multiply(inverse(multiply(A,inverse(multiply(multiply(inverse(B),B),C)))),multiply(A,inverse(C))) = inverse(inverse(multiply(inverse(C),C))),
inference(paramod,[status(thm)],[c_1361,c_3592]) ).
cnf(c_3593,plain,
multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,multiply(inverse(C),C))))),multiply(B,inverse(multiply(inverse(C),C)))),inverse(multiply(inverse(multiply(D,E)),multiply(D,E))))),inverse(multiply(inverse(multiply(inverse(C),C)),multiply(inverse(C),C)))) = inverse(multiply(inverse(C),C)),
inference(paramod,[status(thm)],[c_1354,c_5]) ).
cnf(c_1375,plain,
multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(B),B)))) = inverse(multiply(inverse(B),B)),
inference(paramod,[status(thm)],[c_1350,c_3593]) ).
cnf(c_1379,plain,
multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(multiply(inverse(C),C)),multiply(inverse(C),C)))),multiply(inverse(C),C))))),multiply(A,inverse(multiply(inverse(multiply(D,E)),multiply(D,E))))) = B,
inference(paramod,[status(thm)],[c_1354,c_8]) ).
cnf(c_3594,plain,
multiply(A,inverse(multiply(B,multiply(C,inverse(multiply(multiply(multiply(B,multiply(C,inverse(D))),inverse(multiply(inverse(D),D))),D)))))) = multiply(A,inverse(multiply(inverse(E),E))),
inference(paramod,[status(thm)],[c_26,c_1354]) ).
cnf(c_1385,plain,
multiply(A,inverse(multiply(inverse(B),B))) = multiply(A,inverse(multiply(C,multiply(D,inverse(multiply(multiply(multiply(C,multiply(D,inverse(E))),inverse(multiply(inverse(E),E))),E)))))),
inference(copy,[status(thm)],[c_3594]) ).
cnf(c_3595,plain,
multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,multiply(inverse(multiply(C,D)),multiply(C,D)))))),multiply(B,inverse(multiply(inverse(multiply(C,D)),multiply(C,D))))),inverse(multiply(inverse(E),E)))) = multiply(inverse(F),multiply(multiply(inverse(multiply(V6,inverse(multiply(F,multiply(inverse(multiply(C,D)),multiply(C,D)))))),multiply(V6,inverse(multiply(inverse(multiply(C,D)),multiply(C,D))))),inverse(multiply(inverse(multiply(C,D)),multiply(C,D))))),
inference(paramod,[status(thm)],[c_1354,c_50]) ).
cnf(c_3596,plain,
multiply(inverse(A),A) = multiply(inverse(F),multiply(multiply(inverse(multiply(V6,inverse(multiply(F,multiply(inverse(multiply(C,D)),multiply(C,D)))))),multiply(V6,inverse(multiply(inverse(multiply(C,D)),multiply(C,D))))),inverse(multiply(inverse(multiply(C,D)),multiply(C,D))))),
inference(paramod,[status(thm)],[c_1352,c_3595]) ).
cnf(c_1508,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(paramod,[status(thm)],[c_1350,c_3596]) ).
cnf(c_1515,plain,
multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(inverse(multiply(C,D)),multiply(C,D))))),inverse(multiply(inverse(multiply(inverse(E),E)),multiply(inverse(E),E)))),multiply(inverse(E),E)) = B,
inference(paramod,[status(thm)],[c_1354,c_1177]) ).
cnf(c_1518,plain,
multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(multiply(D,E)),multiply(D,E)))) = B,
inference(paramod,[status(thm)],[c_1354,c_1177]) ).
cnf(c_3597,plain,
inverse(inverse(multiply(inverse(C),C))) = multiply(multiply(inverse(D),multiply(multiply(inverse(multiply(E,inverse(multiply(D,B)))),multiply(E,inverse(B))),inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),
inference(paramod,[status(thm)],[c_1368,c_10]) ).
cnf(c_1524,plain,
multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(inverse(multiply(inverse(D),D))))),inverse(multiply(inverse(inverse(multiply(inverse(D),D))),inverse(multiply(inverse(D),D))))) = inverse(inverse(multiply(inverse(D),D))),
inference(copy,[status(thm)],[c_3597]) ).
cnf(c_1525,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2 ),
inference(resolve,[status(thm)],[c_1508,c_3]) ).
cnf(c_1533,plain,
multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))) = multiply(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(inverse(B)),inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),
inference(paramod,[status(thm)],[c_1508,c_4]) ).
cnf(c_1534,plain,
multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))) = multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(inverse(multiply(inverse(E),E))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),
inference(paramod,[status(thm)],[c_1508,c_4]) ).
cnf(c_1536,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),B)),B)))),multiply(A,inverse(B))) = multiply(multiply(inverse(C),C),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),
inference(paramod,[status(thm)],[c_1508,c_4]) ).
cnf(c_1539,plain,
multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))) = multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(E),E))),
inference(paramod,[status(thm)],[c_1508,c_4]) ).
cnf(c_1547,plain,
inverse(multiply(inverse(inverse(A)),inverse(multiply(multiply(multiply(B,multiply(inverse(C),C)),inverse(multiply(inverse(A),A))),A)))) = B,
inference(paramod,[status(thm)],[c_1508,c_26]) ).
cnf(c_1560,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(paramod,[status(thm)],[c_1508,c_55]) ).
cnf(c_1561,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(C),C)) = multiply(inverse(multiply(D,B)),multiply(D,A)),
inference(paramod,[status(thm)],[c_1508,c_55]) ).
cnf(c_1683,plain,
multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),B) = B,
inference(paramod,[status(thm)],[c_1508,c_1177]) ).
cnf(c_3598,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(B,C)),multiply(B,C))))),multiply(A,D)) = multiply(inverse(inverse(multiply(B,E))),multiply(multiply(inverse(multiply(F,inverse(multiply(inverse(multiply(V6,E)),multiply(V6,C))))),multiply(F,inverse(multiply(B,C)))),D)),
inference(paramod,[status(thm)],[c_55,c_60]) ).
cnf(c_1783,plain,
multiply(inverse(inverse(multiply(A,B))),multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(multiply(D,B)),multiply(D,E))))),multiply(C,inverse(multiply(A,E)))),F)) = multiply(inverse(multiply(V6,inverse(multiply(inverse(multiply(A,E)),multiply(A,E))))),multiply(V6,F)),
inference(copy,[status(thm)],[c_3598]) ).
cnf(c_1794,plain,
multiply(inverse(multiply(A,multiply(inverse(B),C))),multiply(A,multiply(inverse(multiply(D,inverse(multiply(inverse(E),E)))),multiply(D,F)))) = multiply(inverse(multiply(V6,multiply(V7,C))),multiply(V6,multiply(V7,multiply(multiply(inverse(multiply(V8,inverse(multiply(B,E)))),multiply(V8,inverse(E))),F)))),
inference(paramod,[status(thm)],[c_60,c_150]) ).
cnf(c_1825,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,C)) = multiply(inverse(D),multiply(multiply(inverse(multiply(inverse(E),E)),multiply(inverse(inverse(multiply(D,B))),inverse(B))),C)),
inference(paramod,[status(thm)],[c_1508,c_60]) ).
cnf(c_2549,plain,
multiply(multiply(inverse(inverse(multiply(A,B))),multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(multiply(D,B)),multiply(D,E))))),multiply(C,inverse(multiply(A,E)))),inverse(multiply(A,E)))),inverse(multiply(inverse(F),F))) = inverse(multiply(A,E)),
inference(paramod,[status(thm)],[c_1508,c_62]) ).
cnf(c_2920,plain,
multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),C)),B) = multiply(inverse(multiply(D,C)),multiply(D,B)),
inference(paramod,[status(thm)],[c_1683,c_55]) ).
cnf(c_2927,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),E)) = multiply(inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(E),E))),multiply(D,C))),E),
inference(paramod,[status(thm)],[c_1683,c_73]) ).
cnf(c_2931,plain,
inverse(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),C)),B)) = inverse(multiply(inverse(multiply(D,C)),multiply(D,B))),
inference(paramod,[status(thm)],[c_1683,c_75]) ).
cnf(c_2937,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(A,E)),multiply(A,E)))),C)),multiply(A,E)),
inference(paramod,[status(thm)],[c_1683,c_74]) ).
cnf(c_2940,plain,
multiply(A,multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(C),C))),D)),C)) = multiply(A,multiply(inverse(multiply(E,D)),multiply(E,C))),
inference(paramod,[status(thm)],[c_1683,c_140]) ).
cnf(c_2993,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,multiply(C,D)))),multiply(inverse(multiply(inverse(multiply(C,E)),B)),multiply(inverse(multiply(F,E)),multiply(F,D)))),inverse(multiply(inverse(V6),V6))),V6) = V6,
inference(paramod,[status(thm)],[c_122,c_1683]) ).
cnf(c_3031,plain,
multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),C) = C,
inference(paramod,[status(thm)],[c_1508,c_1683]) ).
cnf(c_3599,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),C)) = multiply(inverse(B),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(B),B))),C)),
inference(paramod,[status(thm)],[c_1683,c_1560]) ).
cnf(c_3037,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),C)) = multiply(inverse(B),C),
inference(paramod,[status(thm)],[c_3031,c_3599]) ).
cnf(c_3600,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(C),C)) = multiply(inverse(B),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(B),B))),A)),
inference(paramod,[status(thm)],[c_1683,c_1561]) ).
cnf(c_3040,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(C),C)) = multiply(inverse(B),A),
inference(paramod,[status(thm)],[c_3031,c_3600]) ).
cnf(c_3601,plain,
multiply(A,multiply(inverse(D),C)) = multiply(A,multiply(inverse(multiply(E,D)),multiply(E,C))),
inference(paramod,[status(thm)],[c_3031,c_2940]) ).
cnf(c_3072,plain,
multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(A,multiply(inverse(C),D)),
inference(copy,[status(thm)],[c_3601]) ).
cnf(c_3602,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),E)) = multiply(inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(A,E)),multiply(A,E)))),C)),multiply(A,E)),
inference(paramod,[status(thm)],[c_3072,c_2937]) ).
cnf(c_3073,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),D)) = multiply(inverse(C),multiply(A,D)),
inference(paramod,[status(thm)],[c_3031,c_3602]) ).
cnf(c_3603,plain,
inverse(multiply(inverse(C),B)) = inverse(multiply(inverse(multiply(D,C)),multiply(D,B))),
inference(paramod,[status(thm)],[c_3031,c_2931]) ).
cnf(c_3075,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = inverse(multiply(inverse(B),C)),
inference(copy,[status(thm)],[c_3603]) ).
cnf(c_3604,plain,
multiply(inverse(multiply(inverse(B),C)),multiply(inverse(multiply(D,B)),E)) = multiply(inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(E),E))),multiply(D,C))),E),
inference(paramod,[status(thm)],[c_3075,c_2927]) ).
cnf(c_3076,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,A)),D)) = multiply(inverse(multiply(C,B)),D),
inference(paramod,[status(thm)],[c_3031,c_3604]) ).
cnf(c_3605,plain,
multiply(inverse(C),B) = multiply(inverse(multiply(D,C)),multiply(D,B)),
inference(paramod,[status(thm)],[c_3031,c_2920]) ).
cnf(c_3078,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(B),C),
inference(copy,[status(thm)],[c_3605]) ).
cnf(c_3606,plain,
multiply(inverse(inverse(multiply(inverse(B),B))),C) = multiply(inverse(D),multiply(multiply(inverse(multiply(inverse(E),E)),multiply(inverse(inverse(multiply(D,B))),inverse(B))),C)),
inference(paramod,[status(thm)],[c_3078,c_1825]) ).
cnf(c_3607,plain,
multiply(inverse(inverse(multiply(inverse(B),B))),C) = multiply(inverse(D),multiply(multiply(inverse(inverse(multiply(D,B))),inverse(B)),C)),
inference(paramod,[status(thm)],[c_3037,c_3606]) ).
cnf(c_3125,plain,
multiply(inverse(A),multiply(multiply(inverse(inverse(multiply(A,B))),inverse(B)),C)) = multiply(inverse(inverse(multiply(inverse(B),B))),C),
inference(copy,[status(thm)],[c_3607]) ).
cnf(c_3608,plain,
multiply(inverse(inverse(multiply(B,C))),inverse(C)) = multiply(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(inverse(B)),inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),
inference(paramod,[status(thm)],[c_3078,c_1533]) ).
cnf(c_3609,plain,
multiply(inverse(inverse(multiply(B,C))),inverse(C)) = multiply(multiply(inverse(inverse(B)),inverse(inverse(multiply(inverse(C),C)))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),
inference(paramod,[status(thm)],[c_3037,c_3608]) ).
cnf(c_3134,plain,
multiply(multiply(inverse(inverse(A)),inverse(inverse(multiply(inverse(B),B)))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))) = multiply(inverse(inverse(multiply(A,B))),inverse(B)),
inference(copy,[status(thm)],[c_3609]) ).
cnf(c_3610,plain,
multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(inverse(D),D)))),inverse(multiply(inverse(multiply(inverse(E),E)),multiply(inverse(E),E)))),multiply(inverse(E),E)) = B,
inference(paramod,[status(thm)],[c_3078,c_1515]) ).
cnf(c_3611,plain,
multiply(multiply(multiply(inverse(inverse(B)),inverse(multiply(inverse(D),D))),inverse(multiply(inverse(multiply(inverse(E),E)),multiply(inverse(E),E)))),multiply(inverse(E),E)) = B,
inference(paramod,[status(thm)],[c_3078,c_3610]) ).
cnf(c_3136,plain,
multiply(multiply(multiply(inverse(inverse(A)),inverse(multiply(inverse(B),B))),inverse(multiply(inverse(C),C))),multiply(inverse(C),C)) = A,
inference(paramod,[status(thm)],[c_3078,c_3611]) ).
cnf(c_3612,plain,
multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),C))),multiply(inverse(C),C))))),multiply(A,inverse(multiply(inverse(multiply(D,E)),multiply(D,E))))) = B,
inference(paramod,[status(thm)],[c_3078,c_1379]) ).
cnf(c_3613,plain,
multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),C))),multiply(inverse(C),C))))),multiply(A,inverse(multiply(inverse(E),E)))) = B,
inference(paramod,[status(thm)],[c_3078,c_3612]) ).
cnf(c_3140,plain,
multiply(inverse(inverse(multiply(multiply(A,inverse(multiply(inverse(B),B))),multiply(inverse(B),B)))),inverse(multiply(inverse(C),C))) = A,
inference(paramod,[status(thm)],[c_3078,c_3613]) ).
cnf(c_3141,plain,
multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))) = inverse(multiply(inverse(B),B)),
inference(paramod,[status(thm)],[c_3078,c_1375]) ).
cnf(c_3614,plain,
multiply(multiply(multiply(inverse(multiply(inverse(B),multiply(C,D))),multiply(inverse(multiply(inverse(multiply(C,E)),B)),multiply(inverse(multiply(F,E)),multiply(F,D)))),inverse(multiply(inverse(V6),V6))),V6) = V6,
inference(paramod,[status(thm)],[c_3078,c_2993]) ).
cnf(c_3615,plain,
multiply(multiply(multiply(inverse(multiply(inverse(B),multiply(C,D))),multiply(inverse(multiply(inverse(multiply(C,E)),B)),multiply(inverse(E),D))),inverse(multiply(inverse(V6),V6))),V6) = V6,
inference(paramod,[status(thm)],[c_3078,c_3614]) ).
cnf(c_3616,plain,
multiply(multiply(multiply(inverse(multiply(inverse(B),multiply(C,D))),multiply(inverse(B),multiply(C,D))),inverse(multiply(inverse(V6),V6))),V6) = V6,
inference(paramod,[status(thm)],[c_3073,c_3615]) ).
cnf(c_3617,plain,
multiply(multiply(multiply(inverse(multiply(C,D)),multiply(C,D)),inverse(multiply(inverse(V6),V6))),V6) = V6,
inference(paramod,[status(thm)],[c_3078,c_3616]) ).
cnf(c_3618,plain,
multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(V6),V6))),V6) = V6,
inference(paramod,[status(thm)],[c_3078,c_3617]) ).
cnf(c_3150,plain,
multiply(inverse(multiply(inverse(A),A)),A) = A,
inference(paramod,[status(thm)],[c_3141,c_3618]) ).
cnf(c_3619,plain,
multiply(inverse(multiply(A,multiply(inverse(B),C))),multiply(A,multiply(inverse(inverse(multiply(inverse(E),E))),F))) = multiply(inverse(multiply(V6,multiply(V7,C))),multiply(V6,multiply(V7,multiply(multiply(inverse(multiply(V8,inverse(multiply(B,E)))),multiply(V8,inverse(E))),F)))),
inference(paramod,[status(thm)],[c_3078,c_1794]) ).
cnf(c_3620,plain,
multiply(inverse(multiply(inverse(B),C)),multiply(inverse(inverse(multiply(inverse(E),E))),F)) = multiply(inverse(multiply(V6,multiply(V7,C))),multiply(V6,multiply(V7,multiply(multiply(inverse(multiply(V8,inverse(multiply(B,E)))),multiply(V8,inverse(E))),F)))),
inference(paramod,[status(thm)],[c_3078,c_3619]) ).
cnf(c_3621,plain,
multiply(inverse(multiply(inverse(B),C)),multiply(inverse(inverse(multiply(inverse(E),E))),F)) = multiply(inverse(multiply(V6,multiply(V7,C))),multiply(V6,multiply(V7,multiply(multiply(inverse(inverse(multiply(B,E))),inverse(E)),F)))),
inference(paramod,[status(thm)],[c_3078,c_3620]) ).
cnf(c_3622,plain,
multiply(inverse(multiply(inverse(B),C)),multiply(inverse(inverse(multiply(inverse(E),E))),F)) = multiply(inverse(multiply(V7,C)),multiply(V7,multiply(multiply(inverse(inverse(multiply(B,E))),inverse(E)),F))),
inference(paramod,[status(thm)],[c_3078,c_3621]) ).
cnf(c_3206,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(inverse(multiply(inverse(C),C))),D)) = multiply(inverse(B),multiply(multiply(inverse(inverse(multiply(A,C))),inverse(C)),D)),
inference(paramod,[status(thm)],[c_3078,c_3622]) ).
cnf(c_3623,plain,
multiply(multiply(inverse(inverse(multiply(A,B))),multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(B),E)))),multiply(C,inverse(multiply(A,E)))),inverse(multiply(A,E)))),inverse(multiply(inverse(F),F))) = inverse(multiply(A,E)),
inference(paramod,[status(thm)],[c_3078,c_2549]) ).
cnf(c_3252,plain,
multiply(multiply(inverse(inverse(multiply(A,B))),multiply(multiply(inverse(inverse(multiply(inverse(B),C))),inverse(multiply(A,C))),inverse(multiply(A,C)))),inverse(multiply(inverse(D),D))) = inverse(multiply(A,C)),
inference(paramod,[status(thm)],[c_3078,c_3623]) ).
cnf(c_3624,plain,
multiply(inverse(inverse(multiply(A,B))),multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(B),E)))),multiply(C,inverse(multiply(A,E)))),F)) = multiply(inverse(multiply(V6,inverse(multiply(inverse(multiply(A,E)),multiply(A,E))))),multiply(V6,F)),
inference(paramod,[status(thm)],[c_3078,c_1783]) ).
cnf(c_3625,plain,
multiply(inverse(inverse(multiply(A,B))),multiply(multiply(inverse(inverse(multiply(inverse(B),E))),inverse(multiply(A,E))),F)) = multiply(inverse(multiply(V6,inverse(multiply(inverse(multiply(A,E)),multiply(A,E))))),multiply(V6,F)),
inference(paramod,[status(thm)],[c_3078,c_3624]) ).
cnf(c_3626,plain,
multiply(inverse(inverse(multiply(A,B))),multiply(multiply(inverse(inverse(multiply(inverse(B),E))),inverse(multiply(A,E))),F)) = multiply(inverse(multiply(V6,inverse(multiply(inverse(E),E)))),multiply(V6,F)),
inference(paramod,[status(thm)],[c_3078,c_3625]) ).
cnf(c_3253,plain,
multiply(inverse(inverse(multiply(A,B))),multiply(multiply(inverse(inverse(multiply(inverse(B),C))),inverse(multiply(A,C))),D)) = multiply(inverse(inverse(multiply(inverse(C),C))),D),
inference(paramod,[status(thm)],[c_3078,c_3626]) ).
cnf(c_3627,plain,
multiply(multiply(multiply(inverse(inverse(B)),inverse(inverse(multiply(inverse(C),C)))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(multiply(D,E)),multiply(D,E)))) = B,
inference(paramod,[status(thm)],[c_3078,c_1518]) ).
cnf(c_3628,plain,
multiply(multiply(inverse(inverse(multiply(B,C))),inverse(C)),inverse(multiply(inverse(multiply(D,E)),multiply(D,E)))) = B,
inference(paramod,[status(thm)],[c_3134,c_3627]) ).
cnf(c_3259,plain,
multiply(multiply(inverse(inverse(multiply(A,B))),inverse(B)),inverse(multiply(inverse(C),C))) = A,
inference(paramod,[status(thm)],[c_3078,c_3628]) ).
cnf(c_3629,plain,
multiply(multiply(inverse(multiply(A,inverse(multiply(inverse(C),D)))),multiply(A,inverse(multiply(E,D)))),inverse(multiply(inverse(multiply(F,D)),multiply(F,D)))) = inverse(multiply(E,C)),
inference(paramod,[status(thm)],[c_3078,c_1149]) ).
cnf(c_3630,plain,
multiply(multiply(inverse(inverse(multiply(inverse(C),D))),inverse(multiply(E,D))),inverse(multiply(inverse(multiply(F,D)),multiply(F,D)))) = inverse(multiply(E,C)),
inference(paramod,[status(thm)],[c_3078,c_3629]) ).
cnf(c_3273,plain,
multiply(multiply(inverse(inverse(multiply(inverse(A),B))),inverse(multiply(C,B))),inverse(multiply(inverse(B),B))) = inverse(multiply(C,A)),
inference(paramod,[status(thm)],[c_3078,c_3630]) ).
cnf(c_3631,plain,
multiply(multiply(inverse(inverse(B)),inverse(multiply(C,inverse(D)))),inverse(multiply(inverse(multiply(E,inverse(D))),multiply(E,inverse(D))))) = inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(inverse(D),D))),D)))),
inference(paramod,[status(thm)],[c_3078,c_574]) ).
cnf(c_3632,plain,
multiply(multiply(inverse(inverse(B)),inverse(multiply(C,inverse(D)))),inverse(multiply(inverse(inverse(D)),inverse(D)))) = inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(inverse(D),D))),D)))),
inference(paramod,[status(thm)],[c_3078,c_3631]) ).
cnf(c_3277,plain,
inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),C))),C)))) = multiply(multiply(inverse(inverse(B)),inverse(multiply(A,inverse(C)))),inverse(multiply(inverse(inverse(C)),inverse(C)))),
inference(copy,[status(thm)],[c_3632]) ).
cnf(c_3633,plain,
multiply(inverse(inverse(multiply(B,C))),inverse(C)) = multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(E),E))),
inference(paramod,[status(thm)],[c_3078,c_1539]) ).
cnf(c_3634,plain,
multiply(inverse(inverse(multiply(B,C))),inverse(C)) = multiply(multiply(inverse(inverse(B)),inverse(inverse(multiply(inverse(C),C)))),inverse(multiply(inverse(E),E))),
inference(paramod,[status(thm)],[c_3078,c_3633]) ).
cnf(c_3289,plain,
multiply(multiply(inverse(inverse(A)),inverse(inverse(multiply(inverse(B),B)))),inverse(multiply(inverse(C),C))) = multiply(inverse(inverse(multiply(A,B))),inverse(B)),
inference(copy,[status(thm)],[c_3634]) ).
cnf(c_3635,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(B))) = multiply(multiply(inverse(C),C),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),
inference(paramod,[status(thm)],[c_3150,c_1536]) ).
cnf(c_3636,plain,
multiply(inverse(inverse(B)),inverse(B)) = multiply(multiply(inverse(C),C),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),
inference(paramod,[status(thm)],[c_3078,c_3635]) ).
cnf(c_3637,plain,
multiply(inverse(inverse(B)),inverse(B)) = inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))),
inference(paramod,[status(thm)],[c_3141,c_3636]) ).
cnf(c_3292,plain,
inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))) = multiply(inverse(inverse(A)),inverse(A)),
inference(copy,[status(thm)],[c_3637]) ).
cnf(c_3638,plain,
multiply(inverse(inverse(multiply(B,C))),inverse(C)) = multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(inverse(multiply(inverse(E),E))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),
inference(paramod,[status(thm)],[c_3078,c_1534]) ).
cnf(c_3639,plain,
multiply(inverse(inverse(multiply(B,C))),inverse(C)) = multiply(multiply(inverse(inverse(B)),inverse(inverse(multiply(inverse(E),E)))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),
inference(paramod,[status(thm)],[c_3078,c_3638]) ).
cnf(c_3640,plain,
multiply(inverse(inverse(multiply(B,C))),inverse(C)) = multiply(multiply(inverse(inverse(B)),inverse(inverse(multiply(inverse(E),E)))),multiply(inverse(inverse(C)),inverse(C))),
inference(paramod,[status(thm)],[c_3292,c_3639]) ).
cnf(c_3293,plain,
multiply(multiply(inverse(inverse(A)),inverse(inverse(multiply(inverse(B),B)))),multiply(inverse(inverse(C)),inverse(C))) = multiply(inverse(inverse(multiply(A,C))),inverse(C)),
inference(copy,[status(thm)],[c_3640]) ).
cnf(c_3641,plain,
multiply(multiply(inverse(A),multiply(multiply(inverse(inverse(multiply(A,C))),inverse(C)),inverse(inverse(multiply(inverse(D),D))))),inverse(multiply(inverse(inverse(multiply(inverse(D),D))),inverse(multiply(inverse(D),D))))) = inverse(inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_3078,c_1524]) ).
cnf(c_3642,plain,
multiply(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(inverse(multiply(inverse(D),D)))),inverse(multiply(inverse(inverse(multiply(inverse(D),D))),inverse(multiply(inverse(D),D))))) = inverse(inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_3125,c_3641]) ).
cnf(c_3643,plain,
multiply(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(inverse(multiply(inverse(D),D)))),multiply(inverse(inverse(D)),inverse(D))) = inverse(inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_3292,c_3642]) ).
cnf(c_3295,plain,
multiply(inverse(inverse(multiply(multiply(inverse(A),A),B))),inverse(B)) = inverse(inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_3293,c_3643]) ).
cnf(c_3296,plain,
multiply(multiply(multiply(inverse(A),inverse(B)),inverse(multiply(inverse(B),B))),B) = multiply(C,inverse(multiply(multiply(multiply(A,multiply(C,inverse(D))),inverse(multiply(inverse(D),D))),D))),
inference(paramod,[status(thm)],[c_3078,c_1181]) ).
cnf(c_3304,plain,
multiply(inverse(multiply(inverse(A),A)),B) = B,
inference(paramod,[status(thm)],[c_3141,c_3031]) ).
cnf(c_3305,plain,
multiply(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(B,A))),inverse(multiply(inverse(C),C))) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_3253,c_3252]) ).
cnf(c_3308,plain,
multiply(multiply(inverse(inverse(multiply(A,multiply(inverse(B),B)))),inverse(multiply(inverse(inverse(C)),inverse(C)))),inverse(multiply(inverse(inverse(C)),inverse(C)))) = A,
inference(paramod,[status(thm)],[c_3277,c_1547]) ).
cnf(c_3644,plain,
multiply(inverse(multiply(A,inverse(multiply(multiply(multiply(B,multiply(A,inverse(C))),inverse(multiply(inverse(C),C))),C)))),multiply(D,E)) = multiply(inverse(inverse(multiply(multiply(multiply(B,multiply(D,inverse(F))),inverse(multiply(inverse(F),F))),F))),E),
inference(paramod,[status(thm)],[c_1175,c_3078]) ).
cnf(c_3645,plain,
multiply(multiply(multiply(inverse(inverse(multiply(B,multiply(A,inverse(C))))),inverse(multiply(A,inverse(C)))),inverse(multiply(inverse(inverse(C)),inverse(C)))),multiply(D,E)) = multiply(inverse(inverse(multiply(multiply(multiply(B,multiply(D,inverse(F))),inverse(multiply(inverse(F),F))),F))),E),
inference(paramod,[status(thm)],[c_3277,c_3644]) ).
cnf(c_3646,plain,
multiply(B,multiply(D,E)) = multiply(inverse(inverse(multiply(multiply(multiply(B,multiply(D,inverse(F))),inverse(multiply(inverse(F),F))),F))),E),
inference(paramod,[status(thm)],[c_3259,c_3645]) ).
cnf(c_3331,plain,
multiply(inverse(inverse(multiply(multiply(multiply(A,multiply(B,inverse(C))),inverse(multiply(inverse(C),C))),C))),D) = multiply(A,multiply(B,D)),
inference(copy,[status(thm)],[c_3646]) ).
cnf(c_3647,plain,
multiply(multiply(multiply(A,multiply(B,inverse(multiply(inverse(C),C)))),inverse(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(D),D)))),multiply(inverse(D),D)) = multiply(multiply(multiply(A,multiply(B,inverse(E))),inverse(multiply(inverse(E),E))),E),
inference(paramod,[status(thm)],[c_1364,c_1182]) ).
cnf(c_3338,plain,
multiply(multiply(multiply(A,multiply(B,inverse(multiply(inverse(C),C)))),inverse(multiply(inverse(D),D))),multiply(inverse(D),D)) = multiply(multiply(multiply(A,multiply(B,inverse(E))),inverse(multiply(inverse(E),E))),E),
inference(paramod,[status(thm)],[c_3078,c_3647]) ).
cnf(c_3648,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(A),A))),B)),multiply(inverse(inverse(multiply(inverse(A),A))),C)) = multiply(inverse(multiply(multiply(inverse(D),D),B)),C),
inference(paramod,[status(thm)],[c_3141,c_3076]) ).
cnf(c_3649,plain,
multiply(inverse(B),C) = multiply(inverse(multiply(multiply(inverse(D),D),B)),C),
inference(paramod,[status(thm)],[c_3078,c_3648]) ).
cnf(c_3352,plain,
multiply(inverse(multiply(multiply(inverse(A),A),B)),C) = multiply(inverse(B),C),
inference(copy,[status(thm)],[c_3649]) ).
cnf(c_3361,plain,
multiply(inverse(A),multiply(multiply(inverse(B),B),C)) = multiply(inverse(A),C),
inference(paramod,[status(thm)],[c_3352,c_3078]) ).
cnf(c_3650,plain,
multiply(inverse(multiply(inverse(A),A)),B) = multiply(multiply(inverse(C),C),B),
inference(paramod,[status(thm)],[c_3361,c_3304]) ).
cnf(c_3651,plain,
B = multiply(multiply(inverse(C),C),B),
inference(paramod,[status(thm)],[c_3304,c_3650]) ).
cnf(c_3364,plain,
multiply(multiply(inverse(A),A),B) = B,
inference(copy,[status(thm)],[c_3651]) ).
cnf(c_3652,plain,
multiply(inverse(inverse(B)),inverse(B)) = inverse(inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_3364,c_3295]) ).
cnf(c_3366,plain,
inverse(inverse(multiply(inverse(A),A))) = multiply(inverse(inverse(A)),inverse(A)),
inference(copy,[status(thm)],[c_3652]) ).
cnf(c_3653,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_3364,c_1525]) ).
cnf(c_3368,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(copy,[status(thm)],[c_3653]) ).
cnf(c_3654,plain,
multiply(multiply(multiply(inverse(inverse(A)),inverse(A)),inverse(multiply(B,A))),inverse(multiply(inverse(C),C))) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_3366,c_3305]) ).
cnf(c_3381,plain,
multiply(inverse(multiply(A,B)),inverse(multiply(inverse(C),C))) = inverse(multiply(A,B)),
inference(paramod,[status(thm)],[c_3364,c_3654]) ).
cnf(c_3387,plain,
multiply(multiply(inverse(inverse(A)),multiply(inverse(inverse(B)),inverse(B))),inverse(multiply(inverse(C),C))) = multiply(inverse(inverse(multiply(A,B))),inverse(B)),
inference(paramod,[status(thm)],[c_3366,c_3289]) ).
cnf(c_3655,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(multiply(inverse(inverse(C)),inverse(C)),D)) = multiply(inverse(B),multiply(multiply(inverse(inverse(multiply(A,C))),inverse(C)),D)),
inference(paramod,[status(thm)],[c_3366,c_3206]) ).
cnf(c_3656,plain,
multiply(inverse(multiply(inverse(A),B)),D) = multiply(inverse(B),multiply(multiply(inverse(inverse(multiply(A,C))),inverse(C)),D)),
inference(paramod,[status(thm)],[c_3364,c_3655]) ).
cnf(c_3393,plain,
multiply(inverse(A),multiply(multiply(inverse(inverse(multiply(B,C))),inverse(C)),D)) = multiply(inverse(multiply(inverse(B),A)),D),
inference(copy,[status(thm)],[c_3656]) ).
cnf(c_3657,plain,
multiply(inverse(multiply(A,inverse(multiply(B,multiply(C,inverse(multiply(multiply(multiply(B,multiply(C,inverse(D))),inverse(multiply(inverse(D),D))),D))))))),multiply(A,E)) = multiply(inverse(inverse(multiply(inverse(F),F))),E),
inference(paramod,[status(thm)],[c_1385,c_3078]) ).
cnf(c_3658,plain,
multiply(inverse(inverse(multiply(B,multiply(C,inverse(multiply(multiply(multiply(B,multiply(C,inverse(D))),inverse(multiply(inverse(D),D))),D)))))),E) = multiply(inverse(inverse(multiply(inverse(F),F))),E),
inference(paramod,[status(thm)],[c_3078,c_3657]) ).
cnf(c_3659,plain,
multiply(inverse(inverse(multiply(B,multiply(C,inverse(multiply(multiply(multiply(B,multiply(C,inverse(D))),inverse(multiply(inverse(D),D))),D)))))),E) = multiply(multiply(inverse(inverse(F)),inverse(F)),E),
inference(paramod,[status(thm)],[c_3366,c_3658]) ).
cnf(c_3408,plain,
multiply(inverse(inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(A,multiply(B,inverse(C))),inverse(multiply(inverse(C),C))),C)))))),D) = D,
inference(paramod,[status(thm)],[c_3364,c_3659]) ).
cnf(c_3660,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(inverse(multiply(C,multiply(D,inverse(multiply(multiply(multiply(C,multiply(D,inverse(E))),inverse(multiply(inverse(E),E))),E)))))),inverse(multiply(inverse(F),F)))) = multiply(inverse(B),A),
inference(paramod,[status(thm)],[c_1385,c_3040]) ).
cnf(c_3661,plain,
multiply(inverse(multiply(inverse(A),B)),inverse(multiply(inverse(F),F))) = multiply(inverse(B),A),
inference(paramod,[status(thm)],[c_3408,c_3660]) ).
cnf(c_3411,plain,
inverse(multiply(inverse(A),B)) = multiply(inverse(B),A),
inference(paramod,[status(thm)],[c_3381,c_3661]) ).
cnf(c_3434,plain,
multiply(inverse(A),multiply(multiply(inverse(inverse(multiply(B,C))),inverse(C)),D)) = multiply(multiply(inverse(A),B),D),
inference(paramod,[status(thm)],[c_3411,c_3393]) ).
cnf(c_3437,plain,
multiply(multiply(inverse(inverse(A)),multiply(inverse(inverse(B)),inverse(B))),multiply(inverse(C),C)) = multiply(inverse(inverse(multiply(A,B))),inverse(B)),
inference(paramod,[status(thm)],[c_3411,c_3387]) ).
cnf(c_3662,plain,
multiply(multiply(multiply(A,multiply(B,multiply(inverse(C),C))),inverse(multiply(inverse(D),D))),multiply(inverse(D),D)) = multiply(multiply(multiply(A,multiply(B,inverse(E))),inverse(multiply(inverse(E),E))),E),
inference(paramod,[status(thm)],[c_3411,c_3338]) ).
cnf(c_3663,plain,
multiply(multiply(multiply(A,multiply(B,multiply(inverse(C),C))),multiply(inverse(D),D)),multiply(inverse(D),D)) = multiply(multiply(multiply(A,multiply(B,inverse(E))),inverse(multiply(inverse(E),E))),E),
inference(paramod,[status(thm)],[c_3411,c_3662]) ).
cnf(c_3664,plain,
multiply(multiply(multiply(A,multiply(B,multiply(inverse(C),C))),multiply(inverse(D),D)),multiply(inverse(D),D)) = multiply(multiply(multiply(A,multiply(B,inverse(E))),multiply(inverse(E),E)),E),
inference(paramod,[status(thm)],[c_3411,c_3663]) ).
cnf(c_3457,plain,
multiply(multiply(multiply(A,multiply(B,inverse(C))),multiply(inverse(C),C)),C) = multiply(multiply(multiply(A,multiply(B,multiply(inverse(D),D))),multiply(inverse(E),E)),multiply(inverse(E),E)),
inference(copy,[status(thm)],[c_3664]) ).
cnf(c_3463,plain,
multiply(inverse(inverse(multiply(multiply(multiply(A,multiply(B,inverse(C))),multiply(inverse(C),C)),C))),D) = multiply(A,multiply(B,D)),
inference(paramod,[status(thm)],[c_3411,c_3331]) ).
cnf(c_3665,plain,
multiply(multiply(inverse(inverse(multiply(A,multiply(inverse(B),B)))),multiply(inverse(inverse(C)),inverse(C))),inverse(multiply(inverse(inverse(C)),inverse(C)))) = A,
inference(paramod,[status(thm)],[c_3411,c_3308]) ).
cnf(c_3666,plain,
multiply(multiply(inverse(inverse(multiply(A,multiply(inverse(B),B)))),multiply(inverse(inverse(C)),inverse(C))),multiply(inverse(inverse(C)),inverse(C))) = A,
inference(paramod,[status(thm)],[c_3411,c_3665]) ).
cnf(c_3478,plain,
multiply(inverse(inverse(multiply(multiply(A,multiply(inverse(B),B)),C))),inverse(C)) = A,
inference(paramod,[status(thm)],[c_3437,c_3666]) ).
cnf(c_3667,plain,
multiply(multiply(multiply(inverse(A),inverse(B)),multiply(inverse(B),B)),B) = multiply(C,inverse(multiply(multiply(multiply(A,multiply(C,inverse(D))),inverse(multiply(inverse(D),D))),D))),
inference(paramod,[status(thm)],[c_3411,c_3296]) ).
cnf(c_3482,plain,
multiply(multiply(multiply(inverse(A),inverse(B)),multiply(inverse(B),B)),B) = multiply(C,inverse(multiply(multiply(multiply(A,multiply(C,inverse(D))),multiply(inverse(D),D)),D))),
inference(paramod,[status(thm)],[c_3411,c_3667]) ).
cnf(c_3668,plain,
multiply(multiply(inverse(multiply(inverse(B),A)),inverse(multiply(C,B))),inverse(multiply(inverse(B),B))) = inverse(multiply(C,A)),
inference(paramod,[status(thm)],[c_3411,c_3273]) ).
cnf(c_3669,plain,
multiply(multiply(multiply(inverse(A),B),inverse(multiply(C,B))),inverse(multiply(inverse(B),B))) = inverse(multiply(C,A)),
inference(paramod,[status(thm)],[c_3411,c_3668]) ).
cnf(c_3486,plain,
multiply(multiply(multiply(inverse(A),B),inverse(multiply(C,B))),multiply(inverse(B),B)) = inverse(multiply(C,A)),
inference(paramod,[status(thm)],[c_3411,c_3669]) ).
cnf(c_3489,plain,
multiply(multiply(inverse(inverse(multiply(A,B))),inverse(B)),multiply(inverse(C),C)) = A,
inference(paramod,[status(thm)],[c_3411,c_3259]) ).
cnf(c_3670,plain,
multiply(inverse(inverse(multiply(multiply(A,multiply(inverse(B),B)),multiply(inverse(B),B)))),inverse(multiply(inverse(C),C))) = A,
inference(paramod,[status(thm)],[c_3411,c_3140]) ).
cnf(c_3503,plain,
multiply(inverse(inverse(multiply(multiply(A,multiply(inverse(B),B)),multiply(inverse(B),B)))),multiply(inverse(C),C)) = A,
inference(paramod,[status(thm)],[c_3411,c_3670]) ).
cnf(c_3671,plain,
multiply(multiply(multiply(inverse(inverse(A)),multiply(inverse(B),B)),inverse(multiply(inverse(C),C))),multiply(inverse(C),C)) = A,
inference(paramod,[status(thm)],[c_3411,c_3136]) ).
cnf(c_3505,plain,
multiply(multiply(multiply(inverse(inverse(A)),multiply(inverse(B),B)),multiply(inverse(C),C)),multiply(inverse(C),C)) = A,
inference(paramod,[status(thm)],[c_3411,c_3671]) ).
cnf(c_3513,plain,
multiply(multiply(inverse(A),B),multiply(inverse(C),C)) = multiply(inverse(A),B),
inference(paramod,[status(thm)],[c_3411,c_3040]) ).
cnf(c_3672,plain,
multiply(multiply(inverse(inverse(A)),multiply(inverse(B),B)),multiply(inverse(C),C)) = A,
inference(paramod,[status(thm)],[c_3513,c_3505]) ).
cnf(c_3523,plain,
multiply(inverse(inverse(A)),multiply(inverse(B),B)) = A,
inference(paramod,[status(thm)],[c_3513,c_3672]) ).
cnf(c_3527,plain,
multiply(inverse(inverse(multiply(A,B))),inverse(B)) = A,
inference(paramod,[status(thm)],[c_3513,c_3489]) ).
cnf(c_3531,plain,
multiply(multiply(inverse(A),inverse(B)),B) = multiply(C,inverse(multiply(multiply(multiply(A,multiply(C,inverse(D))),multiply(inverse(D),D)),D))),
inference(paramod,[status(thm)],[c_3513,c_3482]) ).
cnf(c_3673,plain,
multiply(A,multiply(inverse(C),C)) = multiply(inverse(inverse(multiply(A,B))),inverse(B)),
inference(paramod,[status(thm)],[c_3523,c_3437]) ).
cnf(c_3540,plain,
multiply(A,multiply(inverse(B),B)) = A,
inference(paramod,[status(thm)],[c_3527,c_3673]) ).
cnf(c_3674,plain,
multiply(inverse(inverse(multiply(A,multiply(inverse(B),B)))),multiply(inverse(C),C)) = A,
inference(paramod,[status(thm)],[c_3540,c_3503]) ).
cnf(c_3675,plain,
multiply(inverse(inverse(A)),multiply(inverse(C),C)) = A,
inference(paramod,[status(thm)],[c_3540,c_3674]) ).
cnf(c_3544,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_3540,c_3675]) ).
cnf(c_3676,plain,
multiply(multiply(A,multiply(B,inverse(C))),C) = multiply(multiply(multiply(A,multiply(B,multiply(inverse(D),D))),multiply(inverse(E),E)),multiply(inverse(E),E)),
inference(paramod,[status(thm)],[c_3540,c_3457]) ).
cnf(c_3677,plain,
multiply(multiply(A,multiply(B,inverse(C))),C) = multiply(multiply(multiply(A,B),multiply(inverse(E),E)),multiply(inverse(E),E)),
inference(paramod,[status(thm)],[c_3540,c_3676]) ).
cnf(c_3678,plain,
multiply(multiply(A,multiply(B,inverse(C))),C) = multiply(multiply(A,B),multiply(inverse(E),E)),
inference(paramod,[status(thm)],[c_3540,c_3677]) ).
cnf(c_3549,plain,
multiply(multiply(A,multiply(B,inverse(C))),C) = multiply(A,B),
inference(paramod,[status(thm)],[c_3540,c_3678]) ).
cnf(c_3679,plain,
multiply(inverse(inverse(multiply(A,C))),inverse(C)) = A,
inference(paramod,[status(thm)],[c_3540,c_3478]) ).
cnf(c_3560,plain,
multiply(multiply(A,B),inverse(B)) = A,
inference(paramod,[status(thm)],[c_3544,c_3679]) ).
cnf(c_3680,plain,
multiply(inverse(A),multiply(multiply(multiply(B,C),inverse(C)),D)) = multiply(multiply(inverse(A),B),D),
inference(paramod,[status(thm)],[c_3544,c_3434]) ).
cnf(c_3681,plain,
multiply(inverse(A),multiply(B,D)) = multiply(multiply(inverse(A),B),D),
inference(paramod,[status(thm)],[c_3560,c_3680]) ).
cnf(c_3561,plain,
multiply(multiply(inverse(A),B),C) = multiply(inverse(A),multiply(B,C)),
inference(copy,[status(thm)],[c_3681]) ).
cnf(c_3682,plain,
multiply(inverse(A),multiply(inverse(B),B)) = multiply(C,inverse(multiply(multiply(multiply(A,multiply(C,inverse(D))),multiply(inverse(D),D)),D))),
inference(paramod,[status(thm)],[c_3561,c_3531]) ).
cnf(c_3683,plain,
inverse(A) = multiply(C,inverse(multiply(multiply(multiply(A,multiply(C,inverse(D))),multiply(inverse(D),D)),D))),
inference(paramod,[status(thm)],[c_3540,c_3682]) ).
cnf(c_3684,plain,
inverse(A) = multiply(C,inverse(multiply(multiply(A,multiply(C,inverse(D))),D))),
inference(paramod,[status(thm)],[c_3540,c_3683]) ).
cnf(c_3685,plain,
inverse(A) = multiply(C,inverse(multiply(A,C))),
inference(paramod,[status(thm)],[c_3549,c_3684]) ).
cnf(c_3564,plain,
multiply(A,inverse(multiply(B,A))) = inverse(B),
inference(copy,[status(thm)],[c_3685]) ).
cnf(c_3686,plain,
multiply(multiply(inverse(A),multiply(B,inverse(multiply(C,B)))),multiply(inverse(B),B)) = inverse(multiply(C,A)),
inference(paramod,[status(thm)],[c_3561,c_3486]) ).
cnf(c_3687,plain,
multiply(multiply(inverse(A),inverse(C)),multiply(inverse(B),B)) = inverse(multiply(C,A)),
inference(paramod,[status(thm)],[c_3564,c_3686]) ).
cnf(c_3688,plain,
multiply(inverse(A),inverse(C)) = inverse(multiply(C,A)),
inference(paramod,[status(thm)],[c_3540,c_3687]) ).
cnf(c_3572,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_3688]) ).
cnf(c_3689,plain,
multiply(inverse(inverse(multiply(multiply(A,multiply(B,inverse(C))),C))),D) = multiply(A,multiply(B,D)),
inference(paramod,[status(thm)],[c_3540,c_3463]) ).
cnf(c_3690,plain,
multiply(inverse(inverse(multiply(A,B))),D) = multiply(A,multiply(B,D)),
inference(paramod,[status(thm)],[c_3549,c_3689]) ).
cnf(c_3691,plain,
multiply(inverse(multiply(inverse(B),inverse(A))),D) = multiply(A,multiply(B,D)),
inference(paramod,[status(thm)],[c_3572,c_3690]) ).
cnf(c_3692,plain,
multiply(multiply(inverse(inverse(A)),inverse(inverse(B))),D) = multiply(A,multiply(B,D)),
inference(paramod,[status(thm)],[c_3572,c_3691]) ).
cnf(c_3693,plain,
multiply(multiply(A,inverse(inverse(B))),D) = multiply(A,multiply(B,D)),
inference(paramod,[status(thm)],[c_3544,c_3692]) ).
cnf(c_3573,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_3544,c_3693]) ).
cnf(c_3574,plain,
$false,
inference(resolve,[status(thm)],[c_3573,c_3368]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP051-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:19:47 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3677679 was started by sandbox on n005,
% 0.09/0.35 % Fri Sep 25 14:19:47 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 13.94/2.40
% 13.94/2.40 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 13.94/2.40
% 13.94/2.40 % SZS status Unsatisfiable for theBenchmark
% 13.94/2.40
% 13.94/2.40 % Proof 1 at 1.57 (+ 0.34) seconds.
% 13.94/2.40 % Length of proof is 132.
% 13.94/2.40 % Level of proof is 31.
% 13.94/2.40 % Maximum clause weight is 100.000.
% 13.94/2.40 % Given clauses 84.
% 13.94/2.40
% 13.94/2.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------