%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP053-1 : 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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:26:36 AM UTC 2026
% Result : Unsatisfiable 3.88s 0.97s
% Output : CNFRefutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 81
% Number of leaves : 2
% Syntax : Number of formulae : 241 ( 226 unt; 0 def)
% Number of atoms : 260 ( 259 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 35 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 21 ( 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 : 870 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : inverse(multiply(VAR_0,inverse(multiply(inverse(multiply(inverse(multiply(VAR_1,VAR_0)),multiply(VAR_1,inverse(VAR_2)))),inverse(multiply(inverse(VAR_0),VAR_0)))))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(C)))),inverse(multiply(inverse(A),A)))))) = C,
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,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),inverse(multiply(inverse(B),B)))),inverse(multiply(inverse(multiply(C,multiply(B,inverse(D)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),inverse(multiply(inverse(B),B)))))))))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,C))),inverse(multiply(inverse(A),A)))))) = multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(E,D)),multiply(E,inverse(C)))),inverse(multiply(inverse(D),D))))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_9,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),inverse(multiply(inverse(B),B)))),inverse(multiply(inverse(multiply(C,multiply(B,D))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),inverse(multiply(inverse(B),B)))))))))) = multiply(E,inverse(multiply(inverse(multiply(inverse(multiply(F,E)),multiply(F,inverse(D)))),inverse(multiply(inverse(E),E))))),
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_12,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(inverse(C))))),inverse(multiply(inverse(A),A))))) = C,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_15,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,C))),inverse(multiply(inverse(A),A))))))) = C,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_25,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),C)),inverse(multiply(inverse(A),A)))))) = multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,inverse(inverse(C))))),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_12,c_1]) ).
cnf(c_49,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,inverse(C))))))),inverse(multiply(inverse(B),B))) = C,
inference(paramod,[status(thm)],[c_25,c_1]) ).
cnf(c_2502,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(C)))),inverse(multiply(inverse(A),A)))))) = multiply(D,inverse(inverse(multiply(E,inverse(multiply(inverse(multiply(inverse(multiply(D,E)),C)),inverse(multiply(inverse(E),E)))))))),
inference(paramod,[status(thm)],[c_25,c_5]) ).
cnf(c_2503,plain,
C = multiply(D,inverse(inverse(multiply(E,inverse(multiply(inverse(multiply(inverse(multiply(D,E)),C)),inverse(multiply(inverse(E),E)))))))),
inference(paramod,[status(thm)],[c_1,c_2502]) ).
cnf(c_72,plain,
multiply(A,inverse(inverse(multiply(B,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(inverse(B),B)))))))) = C,
inference(copy,[status(thm)],[c_2503]) ).
cnf(c_83,plain,
inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,C)))))),inverse(multiply(inverse(B),B)))) = C,
inference(paramod,[status(thm)],[c_25,c_15]) ).
cnf(c_97,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),C)),inverse(multiply(inverse(A),A)))))) = inverse(multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(B,D)),C)),inverse(multiply(inverse(D),D)))))),
inference(paramod,[status(thm)],[c_25,c_25]) ).
cnf(c_105,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(inverse(multiply(C,inverse(D))))))),A)),D)),inverse(multiply(inverse(A),A)))))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_49,c_1]) ).
cnf(c_2504,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(C,inverse(multiply(inverse(multiply(inverse(multiply(D,C)),multiply(D,inverse(E)))),inverse(multiply(inverse(C),C))))))))),inverse(multiply(inverse(B),B))) = multiply(inverse(multiply(inverse(multiply(F,B)),multiply(F,E))),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_5,c_49]) ).
cnf(c_116,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(inverse(B),B))) = multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,C))),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_1,c_2504]) ).
cnf(c_2505,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(multiply(C,inverse(multiply(inverse(multiply(inverse(multiply(D,C)),E)),inverse(multiply(inverse(C),C))))))))),inverse(multiply(inverse(A),A)))))) = multiply(F,inverse(multiply(inverse(multiply(inverse(multiply(D,F)),E)),inverse(multiply(inverse(F),F))))),
inference(paramod,[status(thm)],[c_72,c_5]) ).
cnf(c_144,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),C)),inverse(multiply(inverse(A),A))))) = multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(B,D)),C)),inverse(multiply(inverse(D),D))))),
inference(paramod,[status(thm)],[c_1,c_2505]) ).
cnf(c_2506,plain,
multiply(A,inverse(inverse(multiply(B,inverse(multiply(inverse(C),inverse(multiply(inverse(B),B)))))))) = inverse(inverse(multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),D)),C)),inverse(multiply(inverse(D),D))))))),
inference(paramod,[status(thm)],[c_72,c_72]) ).
cnf(c_167,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),A)),D)),inverse(multiply(inverse(A),A))))))) = multiply(B,inverse(inverse(multiply(C,inverse(multiply(inverse(D),inverse(multiply(inverse(C),C)))))))),
inference(copy,[status(thm)],[c_2506]) ).
cnf(c_205,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,C)))))),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(multiply(C,D)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))) = D,
inference(paramod,[status(thm)],[c_83,c_72]) ).
cnf(c_2507,plain,
inverse(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,C))),inverse(multiply(inverse(A),A)))),multiply(inverse(multiply(inverse(multiply(D,A)),multiply(D,C))),E))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))))) = E,
inference(paramod,[status(thm)],[c_116,c_15]) ).
cnf(c_221,plain,
multiply(inverse(multiply(A,B)),inverse(inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,C))),E)),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))) = E,
inference(paramod,[status(thm)],[c_167,c_2507]) ).
cnf(c_2508,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(B,C)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))) = multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(E,A)),multiply(E,inverse(inverse(multiply(A,B)))))),D)),C)),inverse(multiply(inverse(D),D))))),
inference(paramod,[status(thm)],[c_83,c_144]) ).
cnf(c_278,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(inverse(multiply(C,D)))))),A)),E)),inverse(multiply(inverse(A),A))))) = multiply(inverse(multiply(inverse(C),C)),inverse(multiply(inverse(multiply(D,E)),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))))),
inference(copy,[status(thm)],[c_2508]) ).
cnf(c_287,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))) = multiply(inverse(A),A),
inference(paramod,[status(thm)],[c_278,c_105]) ).
cnf(c_300,plain,
inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))),inverse(multiply(inverse(multiply(multiply(inverse(B),B),multiply(inverse(multiply(inverse(B),B)),C))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))))),inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))))))))))) = C,
inference(paramod,[status(thm)],[c_287,c_15]) ).
cnf(c_309,plain,
multiply(inverse(multiply(multiply(inverse(A),A),multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))),inverse(C))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))))) = C,
inference(paramod,[status(thm)],[c_287,c_49]) ).
cnf(c_377,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))),inverse(multiply(inverse(multiply(multiply(inverse(B),B),C)),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))))),inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))))) = inverse(multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),D)),C)),inverse(multiply(inverse(D),D)))))),
inference(paramod,[status(thm)],[c_287,c_97]) ).
cnf(c_2509,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),A)),D)),inverse(multiply(inverse(A),A))))))) = inverse(inverse(multiply(multiply(B,E),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(F,C)),multiply(F,E))),D)),inverse(multiply(inverse(multiply(B,E)),multiply(B,E)))))))),
inference(paramod,[status(thm)],[c_221,c_15]) ).
cnf(c_2510,plain,
multiply(B,inverse(inverse(multiply(C,inverse(multiply(inverse(D),inverse(multiply(inverse(C),C)))))))) = inverse(inverse(multiply(multiply(B,E),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(F,C)),multiply(F,E))),D)),inverse(multiply(inverse(multiply(B,E)),multiply(B,E)))))))),
inference(paramod,[status(thm)],[c_167,c_2509]) ).
cnf(c_404,plain,
inverse(inverse(multiply(multiply(A,B),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(C,D)),multiply(C,B))),E)),inverse(multiply(inverse(multiply(A,B)),multiply(A,B)))))))) = multiply(A,inverse(inverse(multiply(D,inverse(multiply(inverse(E),inverse(multiply(inverse(D),D)))))))),
inference(copy,[status(thm)],[c_2510]) ).
cnf(c_2511,plain,
multiply(inverse(multiply(A,B)),inverse(inverse(multiply(C,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),inverse(multiply(inverse(C),C)))))))) = D,
inference(paramod,[status(thm)],[c_144,c_221]) ).
cnf(c_452,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,inverse(multiply(inverse(C),inverse(multiply(inverse(B),B))))))))) = C,
inference(paramod,[status(thm)],[c_167,c_2511]) ).
cnf(c_2512,plain,
multiply(multiply(inverse(A),A),inverse(inverse(multiply(multiply(inverse(multiply(inverse(A),A)),B),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(multiply(inverse(multiply(inverse(D),D)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))),multiply(C,B))),E)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),B)),multiply(inverse(multiply(inverse(A),A)),B))))))))) = E,
inference(paramod,[status(thm)],[c_287,c_221]) ).
cnf(c_453,plain,
multiply(multiply(inverse(A),A),multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))),inverse(multiply(inverse(C),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))))))))))) = C,
inference(paramod,[status(thm)],[c_404,c_2512]) ).
cnf(c_472,plain,
multiply(inverse(multiply(A,multiply(B,inverse(multiply(inverse(multiply(inverse(multiply(C,B)),multiply(C,D))),inverse(multiply(inverse(B),B))))))),multiply(A,inverse(inverse(multiply(multiply(B,inverse(multiply(inverse(multiply(inverse(multiply(C,B)),multiply(C,D))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(E),inverse(multiply(multiply(F,inverse(multiply(inverse(multiply(inverse(multiply(V6,F)),multiply(V6,inverse(D)))),inverse(multiply(inverse(F),F))))),multiply(B,inverse(multiply(inverse(multiply(inverse(multiply(C,B)),multiply(C,D))),inverse(multiply(inverse(B),B)))))))))))))) = E,
inference(paramod,[status(thm)],[c_5,c_452]) ).
cnf(c_2513,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(C,inverse(multiply(inverse(multiply(inverse(multiply(D,C)),multiply(D,inverse(E)))),inverse(multiply(inverse(C),C)))))))) = multiply(inverse(multiply(F,B)),multiply(F,E)),
inference(paramod,[status(thm)],[c_5,c_452]) ).
cnf(c_473,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(paramod,[status(thm)],[c_1,c_2513]) ).
cnf(c_2514,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(B),B))))))))) = multiply(inverse(multiply(inverse(multiply(D,E)),multiply(D,inverse(inverse(multiply(E,C)))))),inverse(multiply(inverse(E),E))),
inference(paramod,[status(thm)],[c_83,c_452]) ).
cnf(c_481,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,C)))))),inverse(multiply(inverse(B),B))) = multiply(inverse(multiply(D,E)),multiply(D,inverse(inverse(multiply(E,inverse(multiply(C,inverse(multiply(inverse(E),E))))))))),
inference(copy,[status(thm)],[c_2514]) ).
cnf(c_486,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(multiply(inverse(B),B)))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_287,c_452]) ).
cnf(c_551,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(multiply(inverse(B),B)))),a2) != a2
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ),
inference(paramod,[status(thm)],[c_486,c_3]) ).
cnf(c_2515,plain,
multiply(inverse(A),multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(inverse(multiply(C,inverse(A))))))),inverse(multiply(inverse(C),C)))) = multiply(inverse(D),D),
inference(paramod,[status(thm)],[c_49,c_486]) ).
cnf(c_604,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(paramod,[status(thm)],[c_49,c_2515]) ).
cnf(c_670,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(multiply(inverse(B),B)))),a2) != a2 ),
inference(resolve,[status(thm)],[c_604,c_551]) ).
cnf(c_2516,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(E,D)),multiply(E,inverse(F)))),inverse(multiply(inverse(D),D))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))) = inverse(multiply(inverse(multiply(C,multiply(B,F))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),inverse(multiply(inverse(B),B)))))))),
inference(paramod,[status(thm)],[c_9,c_72]) ).
cnf(c_680,plain,
inverse(multiply(inverse(multiply(A,multiply(B,C))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,inverse(A)))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,inverse(A)))),inverse(multiply(inverse(B),B)))))))) = multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,inverse(A)))),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(multiply(E,inverse(multiply(inverse(multiply(inverse(multiply(F,E)),multiply(F,inverse(C)))),inverse(multiply(inverse(E),E))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))),
inference(copy,[status(thm)],[c_2516]) ).
cnf(c_2517,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(A),multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(inverse(multiply(C,inverse(A))))))),inverse(multiply(inverse(C),C)))),a2) != a2 ),
inference(paramod,[status(thm)],[c_49,c_670]) ).
cnf(c_698,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(A),A),a2) != a2 ),
inference(paramod,[status(thm)],[c_49,c_2517]) ).
cnf(c_738,plain,
inverse(multiply(inverse(A),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(A)),inverse(A))))))) = A,
inference(paramod,[status(thm)],[c_604,c_1]) ).
cnf(c_756,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(A),A))))))) = A,
inference(paramod,[status(thm)],[c_604,c_15]) ).
cnf(c_763,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),C)),inverse(multiply(inverse(A),A)))))) = multiply(inverse(multiply(inverse(multiply(inverse(inverse(inverse(C))),B)),multiply(inverse(D),D))),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_604,c_25]) ).
cnf(c_778,plain,
multiply(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(C),C))),inverse(multiply(inverse(B),B))) = multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,A))),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_604,c_116]) ).
cnf(c_801,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(paramod,[status(thm)],[c_604,c_473]) ).
cnf(c_802,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(C),C)) = multiply(inverse(multiply(D,B)),multiply(D,A)),
inference(paramod,[status(thm)],[c_604,c_473]) ).
cnf(c_810,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(C),C))))))) = A,
inference(paramod,[status(thm)],[c_604,c_756]) ).
cnf(c_825,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),B)),a2) != a2 ),
inference(paramod,[status(thm)],[c_801,c_698]) ).
cnf(c_826,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),B)) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_801,c_604]) ).
cnf(c_894,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(multiply(inverse(A),A)),multiply(inverse(multiply(inverse(B),B)),multiply(inverse(C),C))),a2) != a2 ),
inference(paramod,[status(thm)],[c_801,c_825]) ).
cnf(c_916,plain,
multiply(inverse(multiply(inverse(multiply(inverse(A),A)),B)),multiply(inverse(C),C)) = multiply(inverse(multiply(D,B)),multiply(D,multiply(inverse(E),E))),
inference(paramod,[status(thm)],[c_826,c_473]) ).
cnf(c_953,plain,
multiply(inverse(multiply(inverse(A),multiply(inverse(B),B))),multiply(inverse(C),C)) = multiply(inverse(multiply(inverse(D),D)),multiply(inverse(multiply(inverse(E),E)),A)),
inference(paramod,[status(thm)],[c_826,c_802]) ).
cnf(c_966,plain,
inverse(multiply(inverse(A),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(C),C)))))) = A,
inference(paramod,[status(thm)],[c_604,c_738]) ).
cnf(c_2518,plain,
multiply(inverse(multiply(inverse(A),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(C)),inverse(C))))))),multiply(inverse(D),D)) = multiply(C,multiply(inverse(C),A)),
inference(paramod,[status(thm)],[c_738,c_802]) ).
cnf(c_993,plain,
multiply(A,multiply(inverse(B),B)) = multiply(C,multiply(inverse(C),A)),
inference(paramod,[status(thm)],[c_966,c_2518]) ).
cnf(c_2519,plain,
multiply(multiply(inverse(A),A),multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))),inverse(multiply(inverse(C),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))))))))) = C,
inference(paramod,[status(thm)],[c_966,c_453]) ).
cnf(c_997,plain,
multiply(multiply(inverse(A),A),multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))),C))))) = C,
inference(paramod,[status(thm)],[c_966,c_2519]) ).
cnf(c_2520,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))),inverse(multiply(inverse(multiply(multiply(inverse(B),B),C)),inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))) = inverse(multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),D)),C)),inverse(multiply(inverse(D),D)))))),
inference(paramod,[status(thm)],[c_966,c_377]) ).
cnf(c_998,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))),multiply(multiply(inverse(B),B),C))) = inverse(multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),D)),C)),inverse(multiply(inverse(D),D)))))),
inference(paramod,[status(thm)],[c_966,c_2520]) ).
cnf(c_2521,plain,
multiply(inverse(inverse(C)),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))))) = C,
inference(paramod,[status(thm)],[c_997,c_309]) ).
cnf(c_1002,plain,
multiply(inverse(inverse(A)),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))))) = A,
inference(paramod,[status(thm)],[c_966,c_2521]) ).
cnf(c_2522,plain,
inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))),inverse(multiply(inverse(multiply(multiply(inverse(B),B),multiply(inverse(multiply(inverse(B),B)),C))),inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))))))))) = C,
inference(paramod,[status(thm)],[c_1002,c_300]) ).
cnf(c_1004,plain,
inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))),multiply(multiply(inverse(B),B),multiply(inverse(multiply(inverse(B),B)),C))))) = C,
inference(paramod,[status(thm)],[c_966,c_2522]) ).
cnf(c_2523,plain,
multiply(A,multiply(inverse(A),inverse(multiply(inverse(B),B)))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_993,c_604]) ).
cnf(c_1017,plain,
multiply(inverse(A),A) = multiply(B,multiply(inverse(B),inverse(multiply(inverse(C),C)))),
inference(copy,[status(thm)],[c_2523]) ).
cnf(c_2524,plain,
multiply(A,multiply(inverse(B),B)) = multiply(A,multiply(inverse(multiply(inverse(C),C)),multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_826,c_993]) ).
cnf(c_1052,plain,
multiply(A,multiply(inverse(multiply(inverse(B),B)),multiply(inverse(C),C))) = multiply(A,multiply(inverse(D),D)),
inference(copy,[status(thm)],[c_2524]) ).
cnf(c_1063,plain,
multiply(A,multiply(inverse(A),B)) = multiply(C,multiply(inverse(C),B)),
inference(paramod,[status(thm)],[c_993,c_993]) ).
cnf(c_1228,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(D),D))))) = multiply(inverse(multiply(C,B)),multiply(inverse(E),E)),
inference(paramod,[status(thm)],[c_1017,c_801]) ).
cnf(c_1232,plain,
multiply(inverse(multiply(inverse(A),multiply(inverse(B),inverse(multiply(inverse(C),C))))),multiply(inverse(D),D)) = multiply(inverse(multiply(inverse(E),E)),multiply(B,A)),
inference(paramod,[status(thm)],[c_1017,c_802]) ).
cnf(c_2525,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(multiply(inverse(C),C)),inverse(multiply(inverse(D),D))))))))) = A,
inference(paramod,[status(thm)],[c_966,c_810]) ).
cnf(c_1249,plain,
inverse(inverse(multiply(A,multiply(inverse(B),B)))) = A,
inference(paramod,[status(thm)],[c_966,c_2525]) ).
cnf(c_1267,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(multiply(A,multiply(inverse(A),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(C),C))))))),multiply(inverse(multiply(inverse(D),D)),multiply(inverse(E),E))),a2) != a2 ),
inference(paramod,[status(thm)],[c_966,c_894]) ).
cnf(c_2526,plain,
inverse(multiply(inverse(A),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(multiply(inverse(C),C)),inverse(multiply(inverse(D),D)))))))) = A,
inference(paramod,[status(thm)],[c_966,c_966]) ).
cnf(c_1301,plain,
inverse(multiply(inverse(A),multiply(inverse(B),B))) = A,
inference(paramod,[status(thm)],[c_966,c_2526]) ).
cnf(c_2527,plain,
multiply(A,multiply(inverse(C),C)) = multiply(inverse(multiply(inverse(D),D)),multiply(inverse(multiply(inverse(E),E)),A)),
inference(paramod,[status(thm)],[c_1301,c_953]) ).
cnf(c_1340,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(multiply(inverse(B),B)),C)) = multiply(C,multiply(inverse(D),D)),
inference(copy,[status(thm)],[c_2527]) ).
cnf(c_2528,plain,
multiply(multiply(inverse(A),B),inverse(multiply(inverse(B),B))) = multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,A))),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_1301,c_778]) ).
cnf(c_1362,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(inverse(B),B))) = multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B))),
inference(copy,[status(thm)],[c_2528]) ).
cnf(c_1365,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),C)),inverse(multiply(inverse(A),A)))))) = multiply(multiply(inverse(inverse(inverse(C))),B),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_1301,c_763]) ).
cnf(c_2529,plain,
inverse(multiply(inverse(multiply(A,multiply(B,C))),inverse(multiply(inverse(inverse(multiply(multiply(inverse(inverse(A)),B),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,inverse(A)))),inverse(multiply(inverse(B),B)))))))) = multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,inverse(A)))),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(multiply(E,inverse(multiply(inverse(multiply(inverse(multiply(F,E)),multiply(F,inverse(C)))),inverse(multiply(inverse(E),E))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))),
inference(paramod,[status(thm)],[c_1362,c_680]) ).
cnf(c_2530,plain,
inverse(multiply(inverse(multiply(A,multiply(B,C))),inverse(multiply(inverse(inverse(multiply(multiply(inverse(inverse(A)),B),inverse(multiply(inverse(B),B))))),inverse(multiply(multiply(inverse(inverse(A)),B),inverse(multiply(inverse(B),B)))))))) = multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,inverse(A)))),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(multiply(E,inverse(multiply(inverse(multiply(inverse(multiply(F,E)),multiply(F,inverse(C)))),inverse(multiply(inverse(E),E))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))),
inference(paramod,[status(thm)],[c_1362,c_2529]) ).
cnf(c_1486,plain,
inverse(multiply(inverse(multiply(A,multiply(B,C))),inverse(multiply(inverse(inverse(multiply(multiply(inverse(inverse(A)),B),inverse(multiply(inverse(B),B))))),inverse(multiply(multiply(inverse(inverse(A)),B),inverse(multiply(inverse(B),B)))))))) = multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,inverse(A)))),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(multiply(E,inverse(multiply(multiply(inverse(inverse(C)),E),inverse(multiply(inverse(E),E))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))),
inference(paramod,[status(thm)],[c_1362,c_2530]) ).
cnf(c_2531,plain,
multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(inverse(D),B),inverse(multiply(inverse(B),B))))))),multiply(A,inverse(inverse(multiply(multiply(B,inverse(multiply(inverse(multiply(inverse(multiply(C,B)),multiply(C,D))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(E),inverse(multiply(multiply(F,inverse(multiply(inverse(multiply(inverse(multiply(V6,F)),multiply(V6,inverse(D)))),inverse(multiply(inverse(F),F))))),multiply(B,inverse(multiply(inverse(multiply(inverse(multiply(C,B)),multiply(C,D))),inverse(multiply(inverse(B),B)))))))))))))) = E,
inference(paramod,[status(thm)],[c_1362,c_472]) ).
cnf(c_2532,plain,
multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(inverse(D),B),inverse(multiply(inverse(B),B))))))),multiply(A,inverse(inverse(multiply(multiply(B,inverse(multiply(multiply(inverse(D),B),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(E),inverse(multiply(multiply(F,inverse(multiply(inverse(multiply(inverse(multiply(V6,F)),multiply(V6,inverse(D)))),inverse(multiply(inverse(F),F))))),multiply(B,inverse(multiply(inverse(multiply(inverse(multiply(C,B)),multiply(C,D))),inverse(multiply(inverse(B),B)))))))))))))) = E,
inference(paramod,[status(thm)],[c_1362,c_2531]) ).
cnf(c_2533,plain,
multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(inverse(D),B),inverse(multiply(inverse(B),B))))))),multiply(A,inverse(inverse(multiply(multiply(B,inverse(multiply(multiply(inverse(D),B),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(E),inverse(multiply(multiply(F,inverse(multiply(multiply(inverse(inverse(D)),F),inverse(multiply(inverse(F),F))))),multiply(B,inverse(multiply(inverse(multiply(inverse(multiply(C,B)),multiply(C,D))),inverse(multiply(inverse(B),B)))))))))))))) = E,
inference(paramod,[status(thm)],[c_1362,c_2532]) ).
cnf(c_1507,plain,
multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B))))))),multiply(A,inverse(inverse(multiply(multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(D),inverse(multiply(multiply(E,inverse(multiply(multiply(inverse(inverse(C)),E),inverse(multiply(inverse(E),E))))),multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B)))))))))))))) = D,
inference(paramod,[status(thm)],[c_1362,c_2533]) ).
cnf(c_2534,plain,
multiply(multiply(inverse(inverse(inverse(multiply(B,C)))),B),inverse(multiply(inverse(B),B))) = multiply(inverse(multiply(D,E)),multiply(D,inverse(inverse(multiply(E,inverse(multiply(C,inverse(multiply(inverse(E),E))))))))),
inference(paramod,[status(thm)],[c_1362,c_481]) ).
cnf(c_1649,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(B),B))))))))) = multiply(multiply(inverse(inverse(inverse(multiply(D,C)))),D),inverse(multiply(inverse(D),D))),
inference(copy,[status(thm)],[c_2534]) ).
cnf(c_1693,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))),multiply(multiply(inverse(B),B),C))) = multiply(multiply(inverse(inverse(inverse(C))),inverse(multiply(inverse(B),B))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),
inference(paramod,[status(thm)],[c_1365,c_998]) ).
cnf(c_1725,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,B))),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(C),C)),inverse(multiply(inverse(D),D)))),E)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))) = E,
inference(paramod,[status(thm)],[c_810,c_205]) ).
cnf(c_1742,plain,
multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(inverse(multiply(inverse(C),C)))))),inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))),inverse(multiply(inverse(multiply(multiply(inverse(D),D),E)),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))))) = E,
inference(paramod,[status(thm)],[c_826,c_205]) ).
cnf(c_1871,plain,
inverse(inverse(multiply(A,multiply(inverse(A),B)))) = B,
inference(paramod,[status(thm)],[c_993,c_1249]) ).
cnf(c_1915,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = multiply(inverse(C),B),
inference(paramod,[status(thm)],[c_473,c_1301]) ).
cnf(c_1922,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(multiply(inverse(B),B)),C)) = multiply(D,multiply(inverse(D),C)),
inference(paramod,[status(thm)],[c_1301,c_801]) ).
cnf(c_1924,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),C))) = multiply(inverse(C),B),
inference(paramod,[status(thm)],[c_801,c_1301]) ).
cnf(c_1940,plain,
inverse(multiply(A,multiply(inverse(A),inverse(B)))) = B,
inference(paramod,[status(thm)],[c_993,c_1301]) ).
cnf(c_2001,plain,
multiply(multiply(inverse(inverse(inverse(multiply(inverse(A),A)))),inverse(multiply(inverse(B),B))),inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))),inverse(multiply(inverse(multiply(multiply(inverse(C),C),D)),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))))) = D,
inference(paramod,[status(thm)],[c_1915,c_1742]) ).
cnf(c_2006,plain,
multiply(multiply(inverse(A),A),inverse(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(C),C)))),D)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))))) = D,
inference(paramod,[status(thm)],[c_1915,c_1725]) ).
cnf(c_2064,plain,
inverse(multiply(inverse(multiply(A,multiply(B,C))),inverse(multiply(inverse(inverse(multiply(multiply(inverse(inverse(A)),B),inverse(multiply(inverse(B),B))))),inverse(multiply(multiply(inverse(inverse(A)),B),inverse(multiply(inverse(B),B)))))))) = multiply(multiply(inverse(inverse(A)),B),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(multiply(D,inverse(multiply(multiply(inverse(inverse(C)),D),inverse(multiply(inverse(D),D))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))),
inference(paramod,[status(thm)],[c_1915,c_1486]) ).
cnf(c_2137,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(B),B))),multiply(inverse(multiply(inverse(C),C)),multiply(inverse(D),D))),a2) != a2 ),
inference(paramod,[status(thm)],[c_1940,c_1267]) ).
cnf(c_2535,plain,
inverse(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,C)))) = C,
inference(paramod,[status(thm)],[c_801,c_1871]) ).
cnf(c_2153,plain,
inverse(multiply(inverse(A),inverse(multiply(inverse(B),B)))) = A,
inference(paramod,[status(thm)],[c_1915,c_2535]) ).
cnf(c_2181,plain,
inverse(inverse(multiply(A,multiply(B,multiply(inverse(B),C))))) = multiply(inverse(inverse(A)),C),
inference(paramod,[status(thm)],[c_1063,c_1871]) ).
cnf(c_2536,plain,
inverse(inverse(multiply(A,multiply(B,multiply(inverse(B),inverse(multiply(inverse(C),C))))))) = A,
inference(paramod,[status(thm)],[c_1017,c_1871]) ).
cnf(c_2185,plain,
multiply(inverse(inverse(A)),inverse(multiply(inverse(B),B))) = A,
inference(paramod,[status(thm)],[c_2181,c_2536]) ).
cnf(c_2537,plain,
multiply(A,multiply(B,C)) = multiply(multiply(inverse(inverse(A)),B),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(multiply(D,inverse(multiply(multiply(inverse(inverse(C)),D),inverse(multiply(inverse(D),D))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))),
inference(paramod,[status(thm)],[c_2153,c_2064]) ).
cnf(c_2538,plain,
multiply(A,multiply(B,C)) = multiply(multiply(inverse(inverse(A)),B),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(multiply(D,inverse(multiply(multiply(inverse(inverse(C)),D),inverse(multiply(inverse(D),D))))),inverse(multiply(inverse(B),B)))))))),
inference(paramod,[status(thm)],[c_2185,c_2537]) ).
cnf(c_2224,plain,
multiply(multiply(inverse(inverse(A)),B),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(multiply(C,inverse(multiply(multiply(inverse(inverse(D)),C),inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(B),B)))))))) = multiply(A,multiply(B,D)),
inference(copy,[status(thm)],[c_2538]) ).
cnf(c_2539,plain,
multiply(multiply(inverse(A),A),inverse(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(multiply(inverse(B),B),D)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))))) = D,
inference(paramod,[status(thm)],[c_2153,c_2006]) ).
cnf(c_2540,plain,
multiply(multiply(inverse(A),A),inverse(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(multiply(inverse(B),B),D)),inverse(multiply(inverse(A),A)))))))) = D,
inference(paramod,[status(thm)],[c_2185,c_2539]) ).
cnf(c_2244,plain,
multiply(multiply(inverse(A),A),inverse(inverse(multiply(inverse(multiply(inverse(A),A)),multiply(multiply(inverse(B),B),C))))) = C,
inference(paramod,[status(thm)],[c_2153,c_2540]) ).
cnf(c_2541,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))),inverse(multiply(inverse(multiply(multiply(inverse(C),C),D)),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))))) = D,
inference(paramod,[status(thm)],[c_2185,c_2001]) ).
cnf(c_2542,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(multiply(multiply(inverse(C),C),D)),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))))) = D,
inference(paramod,[status(thm)],[c_2185,c_2541]) ).
cnf(c_2543,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(multiply(multiply(inverse(C),C),D)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))))) = D,
inference(paramod,[status(thm)],[c_2185,c_2542]) ).
cnf(c_2544,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(multiply(multiply(inverse(C),C),D)),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))) = D,
inference(paramod,[status(thm)],[c_2185,c_2543]) ).
cnf(c_2545,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(multiply(multiply(inverse(C),C),D)),inverse(multiply(inverse(B),B)))))))) = D,
inference(paramod,[status(thm)],[c_2185,c_2544]) ).
cnf(c_2247,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(multiply(inverse(B),B)),multiply(multiply(inverse(C),C),D))))) = D,
inference(paramod,[status(thm)],[c_2153,c_2545]) ).
cnf(c_2546,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(B),B)))),multiply(multiply(inverse(B),B),C))) = multiply(multiply(inverse(inverse(inverse(C))),inverse(multiply(inverse(B),B))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),
inference(paramod,[status(thm)],[c_2185,c_1693]) ).
cnf(c_2547,plain,
inverse(multiply(multiply(inverse(A),A),multiply(multiply(inverse(B),B),C))) = multiply(multiply(inverse(inverse(inverse(C))),inverse(multiply(inverse(B),B))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),
inference(paramod,[status(thm)],[c_2153,c_2546]) ).
cnf(c_2548,plain,
inverse(multiply(multiply(inverse(A),A),multiply(multiply(inverse(B),B),C))) = multiply(inverse(C),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),
inference(paramod,[status(thm)],[c_2185,c_2547]) ).
cnf(c_2269,plain,
inverse(multiply(multiply(inverse(A),A),multiply(multiply(inverse(B),B),C))) = multiply(inverse(C),inverse(multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_2185,c_2548]) ).
cnf(c_2549,plain,
inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(B),B)))),multiply(multiply(inverse(B),B),multiply(inverse(multiply(inverse(B),B)),C))))) = C,
inference(paramod,[status(thm)],[c_2185,c_1004]) ).
cnf(c_2550,plain,
inverse(inverse(multiply(multiply(inverse(A),A),multiply(multiply(inverse(B),B),multiply(inverse(multiply(inverse(B),B)),C))))) = C,
inference(paramod,[status(thm)],[c_2153,c_2549]) ).
cnf(c_2551,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),C)),inverse(multiply(inverse(B),B)))) = C,
inference(paramod,[status(thm)],[c_2269,c_2550]) ).
cnf(c_2351,plain,
multiply(inverse(multiply(inverse(A),A)),B) = B,
inference(paramod,[status(thm)],[c_2153,c_2551]) ).
cnf(c_2384,plain,
multiply(multiply(inverse(inverse(A)),B),inverse(inverse(inverse(multiply(multiply(C,inverse(multiply(multiply(inverse(inverse(D)),C),inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(B),B))))))) = multiply(A,multiply(B,D)),
inference(paramod,[status(thm)],[c_2351,c_2224]) ).
cnf(c_2552,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(multiply(inverse(C),C),D)))) = D,
inference(paramod,[status(thm)],[c_2351,c_2247]) ).
cnf(c_2407,plain,
inverse(inverse(multiply(multiply(inverse(A),A),B))) = B,
inference(paramod,[status(thm)],[c_2351,c_2552]) ).
cnf(c_2553,plain,
multiply(multiply(inverse(A),A),inverse(inverse(multiply(multiply(inverse(B),B),C)))) = C,
inference(paramod,[status(thm)],[c_2351,c_2244]) ).
cnf(c_2410,plain,
multiply(multiply(inverse(A),A),B) = B,
inference(paramod,[status(thm)],[c_2407,c_2553]) ).
cnf(c_2554,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(multiply(inverse(C),C)),multiply(inverse(D),D))),a2) != a2 ),
inference(paramod,[status(thm)],[c_2351,c_2137]) ).
cnf(c_2555,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(D),D)),a2) != a2 ),
inference(paramod,[status(thm)],[c_2351,c_2554]) ).
cnf(c_2556,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(D),D),a2) != a2 ),
inference(paramod,[status(thm)],[c_2351,c_2555]) ).
cnf(c_2557,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_2410,c_2556]) ).
cnf(c_2428,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(copy,[status(thm)],[c_2557]) ).
cnf(c_2436,plain,
inverse(multiply(inverse(A),B)) = multiply(inverse(B),A),
inference(paramod,[status(thm)],[c_2351,c_1924]) ).
cnf(c_2558,plain,
multiply(multiply(inverse(A),A),multiply(inverse(multiply(inverse(B),B)),C)) = multiply(D,multiply(inverse(D),C)),
inference(paramod,[status(thm)],[c_2436,c_1922]) ).
cnf(c_2559,plain,
multiply(multiply(inverse(A),A),multiply(multiply(inverse(B),B),C)) = multiply(D,multiply(inverse(D),C)),
inference(paramod,[status(thm)],[c_2436,c_2558]) ).
cnf(c_2560,plain,
multiply(multiply(inverse(A),A),C) = multiply(D,multiply(inverse(D),C)),
inference(paramod,[status(thm)],[c_2410,c_2559]) ).
cnf(c_2561,plain,
C = multiply(D,multiply(inverse(D),C)),
inference(paramod,[status(thm)],[c_2410,c_2560]) ).
cnf(c_2437,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(copy,[status(thm)],[c_2561]) ).
cnf(c_2562,plain,
multiply(multiply(inverse(A),A),multiply(inverse(multiply(inverse(B),B)),C)) = multiply(C,multiply(inverse(D),D)),
inference(paramod,[status(thm)],[c_2436,c_1340]) ).
cnf(c_2563,plain,
multiply(multiply(inverse(A),A),multiply(multiply(inverse(B),B),C)) = multiply(C,multiply(inverse(D),D)),
inference(paramod,[status(thm)],[c_2436,c_2562]) ).
cnf(c_2564,plain,
multiply(multiply(inverse(A),A),C) = multiply(C,multiply(inverse(D),D)),
inference(paramod,[status(thm)],[c_2410,c_2563]) ).
cnf(c_2565,plain,
C = multiply(C,multiply(inverse(D),D)),
inference(paramod,[status(thm)],[c_2410,c_2564]) ).
cnf(c_2447,plain,
multiply(A,multiply(inverse(B),B)) = A,
inference(copy,[status(thm)],[c_2565]) ).
cnf(c_2566,plain,
multiply(inverse(multiply(inverse(A),multiply(inverse(B),multiply(inverse(C),C)))),multiply(inverse(D),D)) = multiply(inverse(multiply(inverse(E),E)),multiply(B,A)),
inference(paramod,[status(thm)],[c_2436,c_1232]) ).
cnf(c_2567,plain,
multiply(inverse(multiply(inverse(A),inverse(B))),multiply(inverse(D),D)) = multiply(inverse(multiply(inverse(E),E)),multiply(B,A)),
inference(paramod,[status(thm)],[c_2447,c_2566]) ).
cnf(c_2568,plain,
multiply(multiply(inverse(inverse(B)),A),multiply(inverse(D),D)) = multiply(inverse(multiply(inverse(E),E)),multiply(B,A)),
inference(paramod,[status(thm)],[c_2436,c_2567]) ).
cnf(c_2569,plain,
multiply(inverse(inverse(B)),A) = multiply(inverse(multiply(inverse(E),E)),multiply(B,A)),
inference(paramod,[status(thm)],[c_2447,c_2568]) ).
cnf(c_2570,plain,
multiply(inverse(inverse(B)),A) = multiply(multiply(inverse(E),E),multiply(B,A)),
inference(paramod,[status(thm)],[c_2436,c_2569]) ).
cnf(c_2448,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_2410,c_2570]) ).
cnf(c_2571,plain,
multiply(multiply(inverse(A),A),multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(D),D))))) = multiply(inverse(multiply(C,B)),multiply(inverse(E),E)),
inference(paramod,[status(thm)],[c_2436,c_1228]) ).
cnf(c_2572,plain,
multiply(multiply(inverse(A),A),multiply(inverse(B),multiply(inverse(C),multiply(inverse(D),D)))) = multiply(inverse(multiply(C,B)),multiply(inverse(E),E)),
inference(paramod,[status(thm)],[c_2436,c_2571]) ).
cnf(c_2573,plain,
multiply(multiply(inverse(A),A),multiply(inverse(B),inverse(C))) = multiply(inverse(multiply(C,B)),multiply(inverse(E),E)),
inference(paramod,[status(thm)],[c_2447,c_2572]) ).
cnf(c_2574,plain,
multiply(inverse(B),inverse(C)) = multiply(inverse(multiply(C,B)),multiply(inverse(E),E)),
inference(paramod,[status(thm)],[c_2410,c_2573]) ).
cnf(c_2575,plain,
multiply(inverse(B),inverse(C)) = inverse(multiply(C,B)),
inference(paramod,[status(thm)],[c_2447,c_2574]) ).
cnf(c_2449,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_2575]) ).
cnf(c_2576,plain,
multiply(A,multiply(multiply(inverse(B),inverse(inverse(B))),multiply(inverse(C),C))) = multiply(A,multiply(inverse(D),D)),
inference(paramod,[status(thm)],[c_2449,c_1052]) ).
cnf(c_2577,plain,
multiply(A,multiply(inverse(B),inverse(inverse(B)))) = multiply(A,multiply(inverse(D),D)),
inference(paramod,[status(thm)],[c_2447,c_2576]) ).
cnf(c_2458,plain,
multiply(A,multiply(inverse(B),inverse(inverse(B)))) = A,
inference(paramod,[status(thm)],[c_2447,c_2577]) ).
cnf(c_2578,plain,
multiply(inverse(multiply(multiply(inverse(A),inverse(inverse(A))),B)),multiply(inverse(C),C)) = multiply(inverse(multiply(D,B)),multiply(D,multiply(inverse(E),E))),
inference(paramod,[status(thm)],[c_2449,c_916]) ).
cnf(c_2579,plain,
multiply(multiply(inverse(B),inverse(multiply(inverse(A),inverse(inverse(A))))),multiply(inverse(C),C)) = multiply(inverse(multiply(D,B)),multiply(D,multiply(inverse(E),E))),
inference(paramod,[status(thm)],[c_2449,c_2578]) ).
cnf(c_2580,plain,
multiply(multiply(inverse(B),multiply(inverse(inverse(inverse(A))),inverse(inverse(A)))),multiply(inverse(C),C)) = multiply(inverse(multiply(D,B)),multiply(D,multiply(inverse(E),E))),
inference(paramod,[status(thm)],[c_2449,c_2579]) ).
cnf(c_2581,plain,
multiply(multiply(inverse(B),multiply(inverse(A),inverse(inverse(A)))),multiply(inverse(C),C)) = multiply(inverse(multiply(D,B)),multiply(D,multiply(inverse(E),E))),
inference(paramod,[status(thm)],[c_2448,c_2580]) ).
cnf(c_2582,plain,
multiply(inverse(B),multiply(inverse(C),C)) = multiply(inverse(multiply(D,B)),multiply(D,multiply(inverse(E),E))),
inference(paramod,[status(thm)],[c_2458,c_2581]) ).
cnf(c_2583,plain,
inverse(B) = multiply(inverse(multiply(D,B)),multiply(D,multiply(inverse(E),E))),
inference(paramod,[status(thm)],[c_2447,c_2582]) ).
cnf(c_2584,plain,
inverse(B) = multiply(multiply(inverse(B),inverse(D)),multiply(D,multiply(inverse(E),E))),
inference(paramod,[status(thm)],[c_2449,c_2583]) ).
cnf(c_2585,plain,
inverse(B) = multiply(multiply(inverse(B),inverse(D)),D),
inference(paramod,[status(thm)],[c_2447,c_2584]) ).
cnf(c_2472,plain,
multiply(multiply(inverse(A),inverse(B)),B) = inverse(A),
inference(copy,[status(thm)],[c_2585]) ).
cnf(c_2586,plain,
multiply(multiply(inverse(B),inverse(A)),multiply(A,inverse(inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(B),B))))))))) = multiply(multiply(inverse(inverse(inverse(multiply(D,C)))),D),inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_2449,c_1649]) ).
cnf(c_2587,plain,
multiply(multiply(inverse(B),inverse(A)),multiply(A,inverse(inverse(multiply(B,inverse(multiply(C,multiply(inverse(B),inverse(inverse(B)))))))))) = multiply(multiply(inverse(inverse(inverse(multiply(D,C)))),D),inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_2449,c_2586]) ).
cnf(c_2588,plain,
multiply(multiply(inverse(B),inverse(A)),multiply(A,inverse(inverse(multiply(B,inverse(C)))))) = multiply(multiply(inverse(inverse(inverse(multiply(D,C)))),D),inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_2458,c_2587]) ).
cnf(c_2589,plain,
multiply(multiply(inverse(B),inverse(A)),multiply(A,inverse(multiply(inverse(inverse(C)),inverse(B))))) = multiply(multiply(inverse(inverse(inverse(multiply(D,C)))),D),inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_2449,c_2588]) ).
cnf(c_2590,plain,
multiply(multiply(inverse(B),inverse(A)),multiply(A,inverse(multiply(C,inverse(B))))) = multiply(multiply(inverse(inverse(inverse(multiply(D,C)))),D),inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_2448,c_2589]) ).
cnf(c_2591,plain,
multiply(multiply(inverse(B),inverse(A)),multiply(A,multiply(inverse(inverse(B)),inverse(C)))) = multiply(multiply(inverse(inverse(inverse(multiply(D,C)))),D),inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_2449,c_2590]) ).
cnf(c_2592,plain,
multiply(multiply(inverse(B),inverse(A)),multiply(A,multiply(B,inverse(C)))) = multiply(multiply(inverse(inverse(inverse(multiply(D,C)))),D),inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_2448,c_2591]) ).
cnf(c_2593,plain,
multiply(multiply(inverse(B),inverse(A)),multiply(A,multiply(B,inverse(C)))) = multiply(multiply(inverse(inverse(multiply(inverse(C),inverse(D)))),D),inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_2449,c_2592]) ).
cnf(c_2594,plain,
multiply(multiply(inverse(B),inverse(A)),multiply(A,multiply(B,inverse(C)))) = multiply(multiply(inverse(multiply(inverse(inverse(D)),inverse(inverse(C)))),D),inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_2449,c_2593]) ).
cnf(c_2595,plain,
multiply(multiply(inverse(B),inverse(A)),multiply(A,multiply(B,inverse(C)))) = multiply(multiply(inverse(multiply(D,inverse(inverse(C)))),D),inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_2448,c_2594]) ).
cnf(c_2596,plain,
multiply(multiply(inverse(B),inverse(A)),multiply(A,multiply(B,inverse(C)))) = multiply(multiply(multiply(inverse(inverse(inverse(C))),inverse(D)),D),inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_2449,c_2595]) ).
cnf(c_2597,plain,
multiply(multiply(inverse(B),inverse(A)),multiply(A,multiply(B,inverse(C)))) = multiply(multiply(multiply(inverse(C),inverse(D)),D),inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_2448,c_2596]) ).
cnf(c_2598,plain,
multiply(multiply(inverse(B),inverse(A)),multiply(A,multiply(B,inverse(C)))) = multiply(inverse(C),inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_2472,c_2597]) ).
cnf(c_2599,plain,
multiply(multiply(inverse(B),inverse(A)),multiply(A,multiply(B,inverse(C)))) = multiply(inverse(C),multiply(inverse(D),inverse(inverse(D)))),
inference(paramod,[status(thm)],[c_2449,c_2598]) ).
cnf(c_2486,plain,
multiply(multiply(inverse(A),inverse(B)),multiply(B,multiply(A,inverse(C)))) = inverse(C),
inference(paramod,[status(thm)],[c_2458,c_2599]) ).
cnf(c_2600,plain,
multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(inverse(C),B),multiply(inverse(B),inverse(inverse(B)))))))),multiply(A,inverse(inverse(multiply(multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(D),inverse(multiply(multiply(E,inverse(multiply(multiply(inverse(inverse(C)),E),inverse(multiply(inverse(E),E))))),multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B)))))))))))))) = D,
inference(paramod,[status(thm)],[c_2449,c_1507]) ).
cnf(c_2601,plain,
multiply(inverse(multiply(A,multiply(B,inverse(multiply(inverse(C),B))))),multiply(A,inverse(inverse(multiply(multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(D),inverse(multiply(multiply(E,inverse(multiply(multiply(inverse(inverse(C)),E),inverse(multiply(inverse(E),E))))),multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B)))))))))))))) = D,
inference(paramod,[status(thm)],[c_2458,c_2600]) ).
cnf(c_2602,plain,
multiply(inverse(multiply(A,multiply(B,multiply(inverse(B),inverse(inverse(C)))))),multiply(A,inverse(inverse(multiply(multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(D),inverse(multiply(multiply(E,inverse(multiply(multiply(inverse(inverse(C)),E),inverse(multiply(inverse(E),E))))),multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B)))))))))))))) = D,
inference(paramod,[status(thm)],[c_2449,c_2601]) ).
cnf(c_2603,plain,
multiply(inverse(multiply(A,inverse(inverse(C)))),multiply(A,inverse(inverse(multiply(multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(D),inverse(multiply(multiply(E,inverse(multiply(multiply(inverse(inverse(C)),E),inverse(multiply(inverse(E),E))))),multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B)))))))))))))) = D,
inference(paramod,[status(thm)],[c_2437,c_2602]) ).
cnf(c_2604,plain,
multiply(multiply(inverse(inverse(inverse(C))),inverse(A)),multiply(A,inverse(inverse(multiply(multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(D),inverse(multiply(multiply(E,inverse(multiply(multiply(inverse(inverse(C)),E),inverse(multiply(inverse(E),E))))),multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B)))))))))))))) = D,
inference(paramod,[status(thm)],[c_2449,c_2603]) ).
cnf(c_2605,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(inverse(multiply(multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(D),inverse(multiply(multiply(E,inverse(multiply(multiply(inverse(inverse(C)),E),inverse(multiply(inverse(E),E))))),multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B)))))))))))))) = D,
inference(paramod,[status(thm)],[c_2448,c_2604]) ).
cnf(c_2606,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(inverse(multiply(multiply(B,inverse(multiply(multiply(inverse(C),B),multiply(inverse(B),inverse(inverse(B)))))),inverse(multiply(inverse(D),inverse(multiply(multiply(E,inverse(multiply(multiply(inverse(inverse(C)),E),inverse(multiply(inverse(E),E))))),multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B)))))))))))))) = D,
inference(paramod,[status(thm)],[c_2449,c_2605]) ).
cnf(c_2607,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(inverse(multiply(multiply(B,inverse(multiply(inverse(C),B))),inverse(multiply(inverse(D),inverse(multiply(multiply(E,inverse(multiply(multiply(inverse(inverse(C)),E),inverse(multiply(inverse(E),E))))),multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B)))))))))))))) = D,
inference(paramod,[status(thm)],[c_2458,c_2606]) ).
cnf(c_2608,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(inverse(multiply(multiply(B,multiply(inverse(B),inverse(inverse(C)))),inverse(multiply(inverse(D),inverse(multiply(multiply(E,inverse(multiply(multiply(inverse(inverse(C)),E),inverse(multiply(inverse(E),E))))),multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B)))))))))))))) = D,
inference(paramod,[status(thm)],[c_2449,c_2607]) ).
cnf(c_2609,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(inverse(multiply(inverse(inverse(C)),inverse(multiply(inverse(D),inverse(multiply(multiply(E,inverse(multiply(multiply(inverse(inverse(C)),E),inverse(multiply(inverse(E),E))))),multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B)))))))))))))) = D,
inference(paramod,[status(thm)],[c_2437,c_2608]) ).
cnf(c_2610,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(inverse(multiply(inverse(inverse(C)),inverse(multiply(inverse(D),inverse(multiply(multiply(E,inverse(multiply(multiply(C,E),inverse(multiply(inverse(E),E))))),multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B)))))))))))))) = D,
inference(paramod,[status(thm)],[c_2448,c_2609]) ).
cnf(c_2611,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(inverse(multiply(inverse(inverse(C)),inverse(multiply(inverse(D),inverse(multiply(multiply(E,inverse(multiply(multiply(C,E),multiply(inverse(E),inverse(inverse(E)))))),multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B)))))))))))))) = D,
inference(paramod,[status(thm)],[c_2449,c_2610]) ).
cnf(c_2612,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(inverse(multiply(inverse(inverse(C)),inverse(multiply(inverse(D),inverse(multiply(multiply(E,inverse(multiply(C,E))),multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B)))))))))))))) = D,
inference(paramod,[status(thm)],[c_2458,c_2611]) ).
cnf(c_2613,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(inverse(multiply(inverse(inverse(C)),inverse(multiply(inverse(D),inverse(multiply(multiply(E,multiply(inverse(E),inverse(C))),multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B)))))))))))))) = D,
inference(paramod,[status(thm)],[c_2449,c_2612]) ).
cnf(c_2614,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(inverse(multiply(inverse(inverse(C)),inverse(multiply(inverse(D),inverse(multiply(inverse(C),multiply(B,inverse(multiply(multiply(inverse(C),B),inverse(multiply(inverse(B),B)))))))))))))) = D,
inference(paramod,[status(thm)],[c_2437,c_2613]) ).
cnf(c_2615,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(inverse(multiply(inverse(inverse(C)),inverse(multiply(inverse(D),inverse(multiply(inverse(C),multiply(B,inverse(multiply(multiply(inverse(C),B),multiply(inverse(B),inverse(inverse(B))))))))))))))) = D,
inference(paramod,[status(thm)],[c_2449,c_2614]) ).
cnf(c_2616,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(inverse(multiply(inverse(inverse(C)),inverse(multiply(inverse(D),inverse(multiply(inverse(C),multiply(B,inverse(multiply(inverse(C),B)))))))))))) = D,
inference(paramod,[status(thm)],[c_2458,c_2615]) ).
cnf(c_2617,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(inverse(multiply(inverse(inverse(C)),inverse(multiply(inverse(D),inverse(multiply(inverse(C),multiply(B,multiply(inverse(B),inverse(inverse(C))))))))))))) = D,
inference(paramod,[status(thm)],[c_2449,c_2616]) ).
cnf(c_2618,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(inverse(multiply(inverse(inverse(C)),inverse(multiply(inverse(D),inverse(multiply(inverse(C),inverse(inverse(C))))))))))) = D,
inference(paramod,[status(thm)],[c_2437,c_2617]) ).
cnf(c_2619,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(inverse(multiply(inverse(inverse(C)),inverse(multiply(inverse(D),multiply(inverse(inverse(inverse(C))),inverse(inverse(C)))))))))) = D,
inference(paramod,[status(thm)],[c_2449,c_2618]) ).
cnf(c_2620,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(inverse(multiply(inverse(inverse(C)),inverse(multiply(inverse(D),multiply(inverse(C),inverse(inverse(C)))))))))) = D,
inference(paramod,[status(thm)],[c_2448,c_2619]) ).
cnf(c_2621,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(inverse(multiply(inverse(inverse(C)),inverse(inverse(D))))))) = D,
inference(paramod,[status(thm)],[c_2458,c_2620]) ).
cnf(c_2622,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(inverse(multiply(C,inverse(inverse(D))))))) = D,
inference(paramod,[status(thm)],[c_2448,c_2621]) ).
cnf(c_2623,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(multiply(inverse(inverse(inverse(D))),inverse(C))))) = D,
inference(paramod,[status(thm)],[c_2449,c_2622]) ).
cnf(c_2624,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,inverse(multiply(inverse(D),inverse(C))))) = D,
inference(paramod,[status(thm)],[c_2448,c_2623]) ).
cnf(c_2625,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,multiply(inverse(inverse(C)),inverse(inverse(D))))) = D,
inference(paramod,[status(thm)],[c_2449,c_2624]) ).
cnf(c_2626,plain,
multiply(multiply(inverse(C),inverse(A)),multiply(A,multiply(C,inverse(inverse(D))))) = D,
inference(paramod,[status(thm)],[c_2448,c_2625]) ).
cnf(c_2488,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_2486,c_2626]) ).
cnf(c_2627,plain,
multiply(multiply(A,B),inverse(inverse(inverse(multiply(multiply(C,inverse(multiply(multiply(inverse(inverse(D)),C),inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(B),B))))))) = multiply(A,multiply(B,D)),
inference(paramod,[status(thm)],[c_2488,c_2384]) ).
cnf(c_2628,plain,
multiply(multiply(A,B),inverse(inverse(inverse(multiply(multiply(C,inverse(multiply(multiply(D,C),inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(B),B))))))) = multiply(A,multiply(B,D)),
inference(paramod,[status(thm)],[c_2488,c_2627]) ).
cnf(c_2629,plain,
multiply(multiply(A,B),inverse(inverse(inverse(multiply(multiply(C,inverse(multiply(multiply(D,C),multiply(inverse(C),inverse(inverse(C)))))),inverse(multiply(inverse(B),B))))))) = multiply(A,multiply(B,D)),
inference(paramod,[status(thm)],[c_2449,c_2628]) ).
cnf(c_2630,plain,
multiply(multiply(A,B),inverse(inverse(inverse(multiply(multiply(C,inverse(multiply(multiply(D,C),multiply(inverse(C),C)))),inverse(multiply(inverse(B),B))))))) = multiply(A,multiply(B,D)),
inference(paramod,[status(thm)],[c_2488,c_2629]) ).
cnf(c_2631,plain,
multiply(multiply(A,B),inverse(inverse(inverse(multiply(multiply(C,inverse(multiply(D,C))),inverse(multiply(inverse(B),B))))))) = multiply(A,multiply(B,D)),
inference(paramod,[status(thm)],[c_2447,c_2630]) ).
cnf(c_2632,plain,
multiply(multiply(A,B),inverse(inverse(inverse(multiply(multiply(C,multiply(inverse(C),inverse(D))),inverse(multiply(inverse(B),B))))))) = multiply(A,multiply(B,D)),
inference(paramod,[status(thm)],[c_2449,c_2631]) ).
cnf(c_2633,plain,
multiply(multiply(A,B),inverse(inverse(inverse(multiply(inverse(D),inverse(multiply(inverse(B),B))))))) = multiply(A,multiply(B,D)),
inference(paramod,[status(thm)],[c_2437,c_2632]) ).
cnf(c_2634,plain,
multiply(multiply(A,B),inverse(inverse(inverse(multiply(inverse(D),multiply(inverse(B),inverse(inverse(B)))))))) = multiply(A,multiply(B,D)),
inference(paramod,[status(thm)],[c_2449,c_2633]) ).
cnf(c_2635,plain,
multiply(multiply(A,B),inverse(inverse(inverse(multiply(inverse(D),multiply(inverse(B),B)))))) = multiply(A,multiply(B,D)),
inference(paramod,[status(thm)],[c_2488,c_2634]) ).
cnf(c_2636,plain,
multiply(multiply(A,B),inverse(inverse(inverse(inverse(D))))) = multiply(A,multiply(B,D)),
inference(paramod,[status(thm)],[c_2447,c_2635]) ).
cnf(c_2637,plain,
multiply(multiply(A,B),inverse(inverse(D))) = multiply(A,multiply(B,D)),
inference(paramod,[status(thm)],[c_2488,c_2636]) ).
cnf(c_2500,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_2488,c_2637]) ).
cnf(c_2501,plain,
$false,
inference(resolve,[status(thm)],[c_2500,c_2428]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP053-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:23:12 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1560184 was started by sandbox on n015,
% 0.08/0.36 % Fri Sep 25 14:23:12 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 3.88/0.97
% 3.88/0.97 % SZS status Unsatisfiable for theBenchmark
% 3.88/0.97
% 3.88/0.97 % Proof 1 at 0.52 (+ 0.07) seconds.
% 3.88/0.97 % Length of proof is 103.
% 3.88/0.97 % Level of proof is 27.
% 3.88/0.97 % Maximum clause weight is 99.000.
% 3.88/0.97 % Given clauses 57.
% 3.88/0.97
% 3.88/0.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------