%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP014-1 : 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 : n003.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 07:26:10 AM UTC 2026
% Result : Unsatisfiable 2.53s 0.79s
% Output : CNFRefutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 107
% Number of leaves : 2
% Syntax : Number of formulae : 272 ( 272 unt; 0 def)
% Number of atoms : 272 ( 271 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 972 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(group_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : multiply(VAR_0,inverse(multiply(multiply(inverse(multiply(inverse(VAR_1),multiply(inverse(VAR_0),VAR_2))),VAR_3),inverse(multiply(VAR_1,VAR_3))))) = VAR_2,
file('theBenchmark.p',group_axiom) ).
cnf(c_1,plain,
multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(inverse(A),C))),D),inverse(multiply(B,D))))) = C,
inference(clausify,[status(thm)],[group_axiom]) ).
fof(prove_associativity,axiom,
multiply(a,multiply(b,c)) != multiply(multiply(a,b),c),
file('theBenchmark.p',prove_associativity) ).
cnf(c_2,plain,
multiply(a,multiply(b,c)) != multiply(multiply(a,b),c),
inference(clausify,[status(thm)],[prove_associativity]) ).
cnf(c_3,plain,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
inference(copy,[status(thm)],[c_2]) ).
cnf(c_4,plain,
multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),C)),D),inverse(multiply(B,D))))) = inverse(multiply(multiply(inverse(multiply(inverse(E),multiply(inverse(inverse(A)),C))),F),inverse(multiply(E,F)))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
inverse(multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(inverse(B)),multiply(inverse(B),C)))),D),inverse(multiply(A,D)))) = C,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_6,plain,
multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),C)),D),inverse(multiply(B,D)))))) = C,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_9,plain,
multiply(A,inverse(multiply(multiply(inverse(B),C),inverse(multiply(inverse(A),C))))) = inverse(multiply(multiply(inverse(multiply(inverse(D),B)),E),inverse(multiply(D,E)))),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_1784,plain,
multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(inverse(A),inverse(multiply(multiply(inverse(multiply(inverse(C),D)),E),inverse(multiply(C,E))))))),F),inverse(multiply(B,F))))) = inverse(multiply(multiply(inverse(multiply(inverse(V6),D)),V7),inverse(multiply(V6,V7)))),
inference(paramod,[status(thm)],[c_6,c_4]) ).
cnf(c_11,plain,
inverse(multiply(multiply(inverse(multiply(inverse(A),B)),C),inverse(multiply(A,C)))) = inverse(multiply(multiply(inverse(multiply(inverse(D),B)),E),inverse(multiply(D,E)))),
inference(paramod,[status(thm)],[c_1,c_1784]) ).
cnf(c_13,plain,
multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(B),C),inverse(multiply(D,C)))))) = multiply(D,inverse(multiply(multiply(inverse(multiply(inverse(E),B)),F),inverse(multiply(E,F))))),
inference(paramod,[status(thm)],[c_6,c_6]) ).
cnf(c_14,plain,
multiply(A,multiply(B,inverse(multiply(multiply(inverse(multiply(inverse(A),C)),D),inverse(multiply(inverse(B),D)))))) = C,
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_18,plain,
multiply(inverse(A),multiply(A,multiply(B,inverse(multiply(multiply(inverse(C),D),inverse(multiply(inverse(B),D))))))) = C,
inference(paramod,[status(thm)],[c_9,c_6]) ).
cnf(c_1785,plain,
multiply(inverse(A),multiply(A,B)) = multiply(inverse(inverse(C)),multiply(inverse(C),B)),
inference(paramod,[status(thm)],[c_1,c_18]) ).
cnf(c_26,plain,
multiply(inverse(inverse(A)),multiply(inverse(A),B)) = multiply(inverse(C),multiply(C,B)),
inference(copy,[status(thm)],[c_1785]) ).
cnf(c_1786,plain,
multiply(inverse(A),multiply(A,multiply(B,inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(C),D)),E),inverse(multiply(C,E)))),F),inverse(multiply(inverse(B),F))))))) = multiply(multiply(inverse(multiply(inverse(V6),D)),V7),inverse(multiply(V6,V7))),
inference(paramod,[status(thm)],[c_11,c_18]) ).
cnf(c_30,plain,
multiply(multiply(inverse(multiply(inverse(A),B)),C),inverse(multiply(A,C))) = multiply(multiply(inverse(multiply(inverse(D),B)),E),inverse(multiply(D,E))),
inference(paramod,[status(thm)],[c_18,c_1786]) ).
cnf(c_1787,plain,
inverse(multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(B),multiply(inverse(multiply(multiply(inverse(multiply(inverse(C),multiply(inverse(inverse(D)),multiply(inverse(D),B)))),E),inverse(multiply(C,E)))),F)))),V6),inverse(multiply(A,V6)))) = F,
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_40,plain,
inverse(multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(B),multiply(B,C)))),D),inverse(multiply(A,D)))) = C,
inference(paramod,[status(thm)],[c_5,c_1787]) ).
cnf(c_41,plain,
multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(B,C))),D),inverse(multiply(inverse(A),D))))) = C,
inference(paramod,[status(thm)],[c_26,c_1]) ).
cnf(c_84,plain,
multiply(inverse(A),multiply(A,B)) = multiply(inverse(C),multiply(C,B)),
inference(paramod,[status(thm)],[c_26,c_26]) ).
cnf(c_235,plain,
inverse(multiply(multiply(inverse(A),B),inverse(multiply(inverse(C),B)))) = inverse(multiply(multiply(inverse(A),D),inverse(multiply(inverse(C),D)))),
inference(paramod,[status(thm)],[c_18,c_40]) ).
cnf(c_1788,plain,
multiply(inverse(A),multiply(A,multiply(B,inverse(multiply(multiply(inverse(multiply(multiply(inverse(C),D),inverse(multiply(inverse(E),D)))),F),inverse(multiply(inverse(B),F))))))) = multiply(multiply(inverse(C),V6),inverse(multiply(inverse(E),V6))),
inference(paramod,[status(thm)],[c_235,c_18]) ).
cnf(c_301,plain,
multiply(multiply(inverse(A),B),inverse(multiply(inverse(C),B))) = multiply(multiply(inverse(A),D),inverse(multiply(inverse(C),D))),
inference(paramod,[status(thm)],[c_18,c_1788]) ).
cnf(c_1789,plain,
inverse(multiply(multiply(inverse(A),B),inverse(multiply(C,B)))) = inverse(multiply(multiply(inverse(A),D),inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(E),multiply(inverse(F),multiply(F,C)))),V6),inverse(multiply(E,V6)))),D)))),
inference(paramod,[status(thm)],[c_40,c_235]) ).
cnf(c_318,plain,
inverse(multiply(multiply(inverse(A),B),inverse(multiply(C,B)))) = inverse(multiply(multiply(inverse(A),D),inverse(multiply(C,D)))),
inference(paramod,[status(thm)],[c_40,c_1789]) ).
cnf(c_1790,plain,
multiply(multiply(inverse(A),B),inverse(multiply(C,B))) = multiply(multiply(inverse(A),D),inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(E),multiply(inverse(F),multiply(F,C)))),V6),inverse(multiply(E,V6)))),D))),
inference(paramod,[status(thm)],[c_40,c_301]) ).
cnf(c_350,plain,
multiply(multiply(inverse(A),B),inverse(multiply(C,B))) = multiply(multiply(inverse(A),D),inverse(multiply(C,D))),
inference(paramod,[status(thm)],[c_40,c_1790]) ).
cnf(c_374,plain,
multiply(multiply(multiply(A,inverse(multiply(multiply(inverse(B),C),inverse(multiply(inverse(A),C))))),D),inverse(multiply(E,D))) = multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(F),B)),V6),inverse(multiply(F,V6)))),V7),inverse(multiply(E,V7))),
inference(paramod,[status(thm)],[c_9,c_350]) ).
cnf(c_383,plain,
multiply(multiply(inverse(A),multiply(A,B)),inverse(multiply(C,multiply(D,B)))) = multiply(multiply(inverse(D),E),inverse(multiply(C,E))),
inference(paramod,[status(thm)],[c_84,c_350]) ).
cnf(c_1791,plain,
multiply(multiply(A,B),inverse(multiply(C,B))) = multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(D),multiply(inverse(E),multiply(E,A)))),F),inverse(multiply(D,F)))),V6),inverse(multiply(C,V6))),
inference(paramod,[status(thm)],[c_40,c_350]) ).
cnf(c_398,plain,
multiply(multiply(A,B),inverse(multiply(C,B))) = multiply(multiply(A,D),inverse(multiply(C,D))),
inference(paramod,[status(thm)],[c_40,c_1791]) ).
cnf(c_422,plain,
multiply(inverse(multiply(A,B)),multiply(multiply(A,C),inverse(multiply(D,C)))) = multiply(inverse(E),multiply(E,inverse(multiply(D,B)))),
inference(paramod,[status(thm)],[c_398,c_84]) ).
cnf(c_1792,plain,
multiply(multiply(A,inverse(multiply(B,C))),D) = multiply(multiply(A,E),inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(inverse(F),multiply(F,D)))),C),E))),
inference(paramod,[status(thm)],[c_40,c_398]) ).
cnf(c_440,plain,
multiply(multiply(A,B),inverse(multiply(multiply(inverse(multiply(inverse(C),multiply(inverse(D),multiply(D,E)))),F),B))) = multiply(multiply(A,inverse(multiply(C,F))),E),
inference(copy,[status(thm)],[c_1792]) ).
cnf(c_1793,plain,
inverse(multiply(multiply(A,B),inverse(multiply(C,B)))) = inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(D),multiply(inverse(E),multiply(E,A)))),F),inverse(multiply(D,F)))),V6),inverse(multiply(C,V6)))),
inference(paramod,[status(thm)],[c_40,c_318]) ).
cnf(c_469,plain,
inverse(multiply(multiply(A,B),inverse(multiply(C,B)))) = inverse(multiply(multiply(A,D),inverse(multiply(C,D)))),
inference(paramod,[status(thm)],[c_40,c_1793]) ).
cnf(c_1794,plain,
multiply(multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),C)),D),inverse(multiply(B,D)))))),inverse(C)) = multiply(multiply(inverse(E),F),inverse(multiply(inverse(E),F))),
inference(paramod,[status(thm)],[c_6,c_383]) ).
cnf(c_1795,plain,
multiply(C,inverse(C)) = multiply(multiply(inverse(E),F),inverse(multiply(inverse(E),F))),
inference(paramod,[status(thm)],[c_6,c_1794]) ).
cnf(c_624,plain,
multiply(multiply(inverse(A),B),inverse(multiply(inverse(A),B))) = multiply(C,inverse(C)),
inference(copy,[status(thm)],[c_1795]) ).
cnf(c_1796,plain,
multiply(A,inverse(multiply(inverse(B),inverse(multiply(multiply(inverse(multiply(inverse(C),multiply(inverse(inverse(B)),A))),D),inverse(multiply(C,D))))))) = multiply(E,inverse(E)),
inference(paramod,[status(thm)],[c_1,c_624]) ).
cnf(c_726,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(paramod,[status(thm)],[c_1,c_1796]) ).
cnf(c_842,plain,
multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(inverse(A),C))),inverse(B)),inverse(multiply(D,inverse(D)))))) = C,
inference(paramod,[status(thm)],[c_726,c_1]) ).
cnf(c_869,plain,
multiply(inverse(A),multiply(B,inverse(B))) = multiply(inverse(C),multiply(C,inverse(A))),
inference(paramod,[status(thm)],[c_726,c_84]) ).
cnf(c_894,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(C)))) = multiply(multiply(C,D),inverse(multiply(B,D))),
inference(paramod,[status(thm)],[c_726,c_398]) ).
cnf(c_895,plain,
multiply(multiply(A,inverse(B)),inverse(multiply(C,inverse(C)))) = multiply(multiply(A,D),inverse(multiply(B,D))),
inference(paramod,[status(thm)],[c_726,c_398]) ).
cnf(c_896,plain,
inverse(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(C))))) = inverse(multiply(multiply(C,D),inverse(multiply(B,D)))),
inference(paramod,[status(thm)],[c_726,c_469]) ).
cnf(c_1797,plain,
inverse(multiply(A,inverse(A))) = inverse(multiply(multiply(B,C),inverse(multiply(B,C)))),
inference(paramod,[status(thm)],[c_726,c_469]) ).
cnf(c_898,plain,
inverse(multiply(multiply(A,B),inverse(multiply(A,B)))) = inverse(multiply(C,inverse(C))),
inference(copy,[status(thm)],[c_1797]) ).
cnf(c_1798,plain,
multiply(A,multiply(B,inverse(B))) = multiply(inverse(C),multiply(C,inverse(multiply(multiply(inverse(multiply(inverse(D),multiply(inverse(E),multiply(E,A)))),F),inverse(multiply(D,F)))))),
inference(paramod,[status(thm)],[c_40,c_869]) ).
cnf(c_1799,plain,
multiply(A,multiply(B,inverse(B))) = multiply(inverse(C),multiply(C,A)),
inference(paramod,[status(thm)],[c_40,c_1798]) ).
cnf(c_997,plain,
multiply(inverse(A),multiply(A,B)) = multiply(B,multiply(C,inverse(C))),
inference(copy,[status(thm)],[c_1799]) ).
cnf(c_1054,plain,
multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(B,multiply(C,inverse(C)))),D),inverse(multiply(E,D)))))) = multiply(E,B),
inference(paramod,[status(thm)],[c_997,c_6]) ).
cnf(c_1060,plain,
multiply(A,inverse(multiply(multiply(inverse(multiply(B,C)),D),inverse(multiply(inverse(A),D))))) = inverse(multiply(multiply(inverse(multiply(C,multiply(E,inverse(E)))),F),inverse(multiply(B,F)))),
inference(paramod,[status(thm)],[c_997,c_9]) ).
cnf(c_1063,plain,
multiply(A,inverse(multiply(multiply(inverse(B),C),inverse(multiply(inverse(A),C))))) = inverse(multiply(multiply(inverse(multiply(inverse(D),B)),multiply(E,inverse(E))),inverse(multiply(inverse(F),multiply(F,D))))),
inference(paramod,[status(thm)],[c_997,c_9]) ).
cnf(c_1109,plain,
inverse(multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(B),multiply(B,C)))),multiply(D,inverse(D))),inverse(multiply(inverse(E),multiply(E,A))))) = C,
inference(paramod,[status(thm)],[c_997,c_40]) ).
cnf(c_1122,plain,
multiply(multiply(A,multiply(B,C)),inverse(multiply(C,multiply(D,inverse(D))))) = multiply(multiply(A,E),inverse(multiply(inverse(B),E))),
inference(paramod,[status(thm)],[c_997,c_398]) ).
cnf(c_1131,plain,
multiply(inverse(multiply(A,multiply(B,inverse(B)))),multiply(multiply(inverse(C),D),inverse(multiply(E,D)))) = multiply(inverse(F),multiply(F,inverse(multiply(E,multiply(C,A))))),
inference(paramod,[status(thm)],[c_997,c_422]) ).
cnf(c_1800,plain,
multiply(inverse(inverse(A)),multiply(B,multiply(C,inverse(C)))) = multiply(multiply(A,B),multiply(D,inverse(D))),
inference(paramod,[status(thm)],[c_997,c_997]) ).
cnf(c_1158,plain,
multiply(multiply(A,B),multiply(C,inverse(C))) = multiply(inverse(inverse(A)),multiply(B,multiply(D,inverse(D)))),
inference(copy,[status(thm)],[c_1800]) ).
cnf(c_1159,plain,
multiply(A,multiply(B,inverse(B))) = multiply(A,multiply(C,inverse(C))),
inference(paramod,[status(thm)],[c_997,c_997]) ).
cnf(c_1161,plain,
multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(inverse(A),C))),multiply(D,inverse(D))),inverse(multiply(B,multiply(E,inverse(E))))))) = C,
inference(paramod,[status(thm)],[c_1159,c_1]) ).
cnf(c_1164,plain,
multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),C)),multiply(D,inverse(D))),inverse(multiply(B,multiply(E,inverse(E)))))))) = C,
inference(paramod,[status(thm)],[c_1159,c_6]) ).
cnf(c_1186,plain,
multiply(multiply(A,multiply(B,inverse(B))),inverse(multiply(C,multiply(D,inverse(D))))) = multiply(multiply(A,E),inverse(multiply(C,E))),
inference(paramod,[status(thm)],[c_1159,c_398]) ).
cnf(c_1801,plain,
multiply(multiply(inverse(A),multiply(A,B)),inverse(multiply(C,multiply(D,B)))) = multiply(multiply(inverse(D),multiply(E,inverse(E))),inverse(multiply(C,multiply(F,inverse(F))))),
inference(paramod,[status(thm)],[c_1159,c_383]) ).
cnf(c_1192,plain,
multiply(multiply(inverse(A),multiply(B,inverse(B))),inverse(multiply(C,multiply(D,inverse(D))))) = multiply(multiply(inverse(E),multiply(E,F)),inverse(multiply(C,multiply(A,F)))),
inference(copy,[status(thm)],[c_1801]) ).
cnf(c_1802,plain,
inverse(multiply(A,inverse(multiply(B,inverse(multiply(multiply(inverse(multiply(inverse(C),multiply(inverse(B),A))),D),inverse(multiply(C,D)))))))) = inverse(multiply(E,inverse(E))),
inference(paramod,[status(thm)],[c_1,c_898]) ).
cnf(c_1200,plain,
inverse(multiply(A,inverse(A))) = inverse(multiply(B,inverse(B))),
inference(paramod,[status(thm)],[c_1,c_1802]) ).
cnf(c_1324,plain,
multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(B),C),inverse(multiply(D,C)))))) = multiply(D,inverse(multiply(multiply(inverse(multiply(inverse(E),B)),inverse(E)),inverse(multiply(F,inverse(F)))))),
inference(paramod,[status(thm)],[c_726,c_13]) ).
cnf(c_1350,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(multiply(inverse(B),C),inverse(multiply(inverse(multiply(D,inverse(D))),C))))) = inverse(multiply(multiply(inverse(multiply(inverse(E),B)),F),inverse(multiply(E,F)))),
inference(paramod,[status(thm)],[c_1200,c_9]) ).
cnf(c_1365,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(B,C))),D),inverse(multiply(inverse(multiply(E,inverse(E))),D))))) = C,
inference(paramod,[status(thm)],[c_1200,c_41]) ).
cnf(c_1366,plain,
inverse(multiply(multiply(inverse(multiply(inverse(multiply(A,inverse(A))),multiply(inverse(B),multiply(B,C)))),D),inverse(multiply(multiply(E,inverse(E)),D)))) = C,
inference(paramod,[status(thm)],[c_1200,c_40]) ).
cnf(c_1376,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))) = multiply(C,inverse(C)),
inference(paramod,[status(thm)],[c_1200,c_726]) ).
cnf(c_1416,plain,
multiply(A,multiply(B,inverse(B))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_1376,c_14]) ).
cnf(c_1431,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))),inverse(multiply(C,inverse(inverse(multiply(inverse(C),D)))))) = multiply(multiply(inverse(multiply(inverse(E),D)),F),inverse(multiply(E,F))),
inference(paramod,[status(thm)],[c_1376,c_30]) ).
cnf(c_1475,plain,
multiply(inverse(multiply(multiply(A,inverse(A)),B)),multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(multiply(E,inverse(E))))))) = multiply(inverse(F),multiply(F,inverse(multiply(D,B)))),
inference(paramod,[status(thm)],[c_1376,c_422]) ).
cnf(c_1493,plain,
multiply(multiply(inverse(A),multiply(A,B)),inverse(multiply(C,multiply(D,B)))) = multiply(multiply(inverse(D),inverse(C)),inverse(multiply(multiply(E,inverse(E)),inverse(multiply(F,inverse(F)))))),
inference(paramod,[status(thm)],[c_1376,c_383]) ).
cnf(c_1803,plain,
multiply(inverse(A),multiply(A,B)) = multiply(B,multiply(C,inverse(C))),
inference(paramod,[status(thm)],[c_1376,c_997]) ).
cnf(c_1502,plain,
multiply(inverse(A),multiply(A,B)) = inverse(inverse(B)),
inference(paramod,[status(thm)],[c_1416,c_1803]) ).
cnf(c_1804,plain,
multiply(inverse(inverse(inverse(A))),inverse(multiply(C,multiply(D,inverse(D))))) = multiply(multiply(inverse(E),multiply(E,F)),inverse(multiply(C,multiply(A,F)))),
inference(paramod,[status(thm)],[c_1416,c_1192]) ).
cnf(c_1805,plain,
multiply(inverse(inverse(inverse(A))),inverse(inverse(inverse(C)))) = multiply(multiply(inverse(E),multiply(E,F)),inverse(multiply(C,multiply(A,F)))),
inference(paramod,[status(thm)],[c_1416,c_1804]) ).
cnf(c_1806,plain,
multiply(inverse(inverse(inverse(A))),inverse(inverse(inverse(C)))) = multiply(inverse(inverse(F)),inverse(multiply(C,multiply(A,F)))),
inference(paramod,[status(thm)],[c_1502,c_1805]) ).
cnf(c_1530,plain,
multiply(inverse(inverse(A)),inverse(multiply(B,multiply(C,A)))) = multiply(inverse(inverse(inverse(C))),inverse(inverse(inverse(B)))),
inference(copy,[status(thm)],[c_1806]) ).
cnf(c_1807,plain,
multiply(inverse(inverse(A)),inverse(multiply(C,multiply(D,inverse(D))))) = multiply(multiply(A,E),inverse(multiply(C,E))),
inference(paramod,[status(thm)],[c_1416,c_1186]) ).
cnf(c_1808,plain,
multiply(inverse(inverse(A)),inverse(inverse(inverse(C)))) = multiply(multiply(A,E),inverse(multiply(C,E))),
inference(paramod,[status(thm)],[c_1416,c_1807]) ).
cnf(c_1535,plain,
multiply(multiply(A,B),inverse(multiply(C,B))) = multiply(inverse(inverse(A)),inverse(inverse(inverse(C)))),
inference(copy,[status(thm)],[c_1808]) ).
cnf(c_1809,plain,
multiply(inverse(A),multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(inverse(B),C)))),inverse(multiply(B,multiply(E,inverse(E)))))))) = C,
inference(paramod,[status(thm)],[c_1416,c_1164]) ).
cnf(c_1810,plain,
multiply(inverse(A),multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(inverse(B),C)))),inverse(inverse(inverse(B))))))) = C,
inference(paramod,[status(thm)],[c_1416,c_1809]) ).
cnf(c_1549,plain,
inverse(inverse(inverse(multiply(inverse(inverse(inverse(multiply(inverse(A),B)))),inverse(inverse(inverse(A))))))) = B,
inference(paramod,[status(thm)],[c_1502,c_1810]) ).
cnf(c_1811,plain,
multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(inverse(B),multiply(inverse(A),C))))),inverse(multiply(B,multiply(E,inverse(E))))))) = C,
inference(paramod,[status(thm)],[c_1416,c_1161]) ).
cnf(c_1550,plain,
multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(inverse(B),multiply(inverse(A),C))))),inverse(inverse(inverse(B)))))) = C,
inference(paramod,[status(thm)],[c_1416,c_1811]) ).
cnf(c_1812,plain,
inverse(inverse(multiply(A,B))) = multiply(inverse(inverse(A)),multiply(B,multiply(D,inverse(D)))),
inference(paramod,[status(thm)],[c_1416,c_1158]) ).
cnf(c_1551,plain,
inverse(inverse(multiply(A,B))) = multiply(inverse(inverse(A)),inverse(inverse(B))),
inference(paramod,[status(thm)],[c_1416,c_1812]) ).
cnf(c_1813,plain,
multiply(inverse(inverse(inverse(A))),multiply(multiply(inverse(C),D),inverse(multiply(E,D)))) = multiply(inverse(F),multiply(F,inverse(multiply(E,multiply(C,A))))),
inference(paramod,[status(thm)],[c_1416,c_1131]) ).
cnf(c_1814,plain,
multiply(inverse(inverse(inverse(A))),multiply(inverse(inverse(inverse(C))),inverse(inverse(inverse(E))))) = multiply(inverse(F),multiply(F,inverse(multiply(E,multiply(C,A))))),
inference(paramod,[status(thm)],[c_1535,c_1813]) ).
cnf(c_1815,plain,
multiply(inverse(inverse(inverse(A))),multiply(inverse(inverse(inverse(C))),inverse(inverse(inverse(E))))) = inverse(inverse(inverse(multiply(E,multiply(C,A))))),
inference(paramod,[status(thm)],[c_1502,c_1814]) ).
cnf(c_1816,plain,
multiply(inverse(inverse(inverse(A))),multiply(inverse(inverse(inverse(C))),inverse(inverse(inverse(E))))) = inverse(multiply(inverse(inverse(E)),inverse(inverse(multiply(C,A))))),
inference(paramod,[status(thm)],[c_1551,c_1815]) ).
cnf(c_1817,plain,
multiply(inverse(inverse(inverse(A))),multiply(inverse(inverse(inverse(C))),inverse(inverse(inverse(E))))) = inverse(multiply(inverse(inverse(E)),multiply(inverse(inverse(C)),inverse(inverse(A))))),
inference(paramod,[status(thm)],[c_1551,c_1816]) ).
cnf(c_1556,plain,
inverse(multiply(inverse(inverse(A)),multiply(inverse(inverse(B)),inverse(inverse(C))))) = multiply(inverse(inverse(inverse(C))),multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(A))))),
inference(copy,[status(thm)],[c_1817]) ).
cnf(c_1818,plain,
multiply(multiply(A,multiply(B,C)),inverse(inverse(inverse(C)))) = multiply(multiply(A,E),inverse(multiply(inverse(B),E))),
inference(paramod,[status(thm)],[c_1416,c_1122]) ).
cnf(c_1558,plain,
multiply(multiply(A,multiply(B,C)),inverse(inverse(inverse(C)))) = multiply(inverse(inverse(A)),inverse(inverse(inverse(inverse(B))))),
inference(paramod,[status(thm)],[c_1535,c_1818]) ).
cnf(c_1819,plain,
inverse(multiply(multiply(inverse(multiply(inverse(A),inverse(inverse(C)))),multiply(D,inverse(D))),inverse(multiply(inverse(E),multiply(E,A))))) = C,
inference(paramod,[status(thm)],[c_1502,c_1109]) ).
cnf(c_1820,plain,
inverse(multiply(inverse(inverse(inverse(multiply(inverse(A),inverse(inverse(C)))))),inverse(multiply(inverse(E),multiply(E,A))))) = C,
inference(paramod,[status(thm)],[c_1416,c_1819]) ).
cnf(c_1821,plain,
inverse(multiply(inverse(multiply(inverse(inverse(inverse(A))),inverse(inverse(inverse(inverse(C)))))),inverse(multiply(inverse(E),multiply(E,A))))) = C,
inference(paramod,[status(thm)],[c_1551,c_1820]) ).
cnf(c_1560,plain,
inverse(multiply(inverse(multiply(inverse(inverse(inverse(A))),inverse(inverse(inverse(inverse(B)))))),inverse(inverse(inverse(A))))) = B,
inference(paramod,[status(thm)],[c_1502,c_1821]) ).
cnf(c_1822,plain,
multiply(A,inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(inverse(A))))))) = inverse(multiply(multiply(inverse(multiply(inverse(D),B)),multiply(E,inverse(E))),inverse(multiply(inverse(F),multiply(F,D))))),
inference(paramod,[status(thm)],[c_1535,c_1063]) ).
cnf(c_1823,plain,
multiply(A,inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(inverse(A))))))) = inverse(multiply(inverse(inverse(inverse(multiply(inverse(D),B)))),inverse(multiply(inverse(F),multiply(F,D))))),
inference(paramod,[status(thm)],[c_1416,c_1822]) ).
cnf(c_1824,plain,
multiply(A,inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(inverse(A))))))) = inverse(multiply(inverse(multiply(inverse(inverse(inverse(D))),inverse(inverse(B)))),inverse(multiply(inverse(F),multiply(F,D))))),
inference(paramod,[status(thm)],[c_1551,c_1823]) ).
cnf(c_1566,plain,
multiply(A,inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(inverse(A))))))) = inverse(multiply(inverse(multiply(inverse(inverse(inverse(C))),inverse(inverse(B)))),inverse(inverse(inverse(C))))),
inference(paramod,[status(thm)],[c_1502,c_1824]) ).
cnf(c_1825,plain,
multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(B,C)))),inverse(inverse(inverse(inverse(A))))))) = inverse(multiply(multiply(inverse(multiply(C,multiply(E,inverse(E)))),F),inverse(multiply(B,F)))),
inference(paramod,[status(thm)],[c_1535,c_1060]) ).
cnf(c_1826,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(inverse(B)),inverse(inverse(C)))),inverse(inverse(inverse(inverse(A))))))) = inverse(multiply(multiply(inverse(multiply(C,multiply(E,inverse(E)))),F),inverse(multiply(B,F)))),
inference(paramod,[status(thm)],[c_1551,c_1825]) ).
cnf(c_1827,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(inverse(B)),inverse(inverse(C)))),inverse(inverse(inverse(inverse(A))))))) = inverse(multiply(multiply(inverse(inverse(inverse(C))),F),inverse(multiply(B,F)))),
inference(paramod,[status(thm)],[c_1416,c_1826]) ).
cnf(c_1567,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(inverse(B)),inverse(inverse(C)))),inverse(inverse(inverse(inverse(A))))))) = inverse(multiply(inverse(inverse(inverse(inverse(inverse(C))))),inverse(inverse(inverse(B))))),
inference(paramod,[status(thm)],[c_1535,c_1827]) ).
cnf(c_1828,plain,
multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(inverse(inverse(B))),D),inverse(multiply(E,D)))))) = multiply(E,B),
inference(paramod,[status(thm)],[c_1416,c_1054]) ).
cnf(c_1829,plain,
multiply(inverse(A),multiply(A,inverse(multiply(inverse(inverse(inverse(inverse(inverse(B))))),inverse(inverse(inverse(E))))))) = multiply(E,B),
inference(paramod,[status(thm)],[c_1535,c_1828]) ).
cnf(c_1830,plain,
inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(B))))),inverse(inverse(inverse(E))))))) = multiply(E,B),
inference(paramod,[status(thm)],[c_1502,c_1829]) ).
cnf(c_1568,plain,
inverse(multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(A))))))),inverse(inverse(inverse(inverse(inverse(B))))))) = multiply(B,A),
inference(paramod,[status(thm)],[c_1551,c_1830]) ).
cnf(c_1831,plain,
multiply(inverse(multiply(multiply(A,inverse(A)),B)),multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(multiply(E,inverse(E))))))) = inverse(inverse(inverse(multiply(D,B)))),
inference(paramod,[status(thm)],[c_1502,c_1475]) ).
cnf(c_1574,plain,
multiply(inverse(multiply(multiply(A,inverse(A)),B)),multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(multiply(E,inverse(E))))))) = inverse(multiply(inverse(inverse(D)),inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_1551,c_1831]) ).
cnf(c_1832,plain,
multiply(inverse(A),multiply(A,inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(D))))))) = multiply(D,inverse(multiply(multiply(inverse(multiply(inverse(E),B)),inverse(E)),inverse(multiply(F,inverse(F)))))),
inference(paramod,[status(thm)],[c_1535,c_1324]) ).
cnf(c_1833,plain,
inverse(inverse(inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(D))))))) = multiply(D,inverse(multiply(multiply(inverse(multiply(inverse(E),B)),inverse(E)),inverse(multiply(F,inverse(F)))))),
inference(paramod,[status(thm)],[c_1502,c_1832]) ).
cnf(c_1834,plain,
inverse(multiply(inverse(inverse(inverse(inverse(inverse(B))))),inverse(inverse(inverse(inverse(inverse(D))))))) = multiply(D,inverse(multiply(multiply(inverse(multiply(inverse(E),B)),inverse(E)),inverse(multiply(F,inverse(F)))))),
inference(paramod,[status(thm)],[c_1551,c_1833]) ).
cnf(c_1577,plain,
multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),C)),inverse(B)),inverse(multiply(D,inverse(D)))))) = inverse(multiply(inverse(inverse(inverse(inverse(inverse(C))))),inverse(inverse(inverse(inverse(inverse(A))))))),
inference(copy,[status(thm)],[c_1834]) ).
cnf(c_1835,plain,
multiply(inverse(inverse(B)),inverse(multiply(C,multiply(D,B)))) = multiply(multiply(inverse(D),inverse(C)),inverse(multiply(multiply(E,inverse(E)),inverse(multiply(F,inverse(F)))))),
inference(paramod,[status(thm)],[c_1502,c_1493]) ).
cnf(c_1836,plain,
multiply(inverse(inverse(inverse(D))),inverse(inverse(inverse(C)))) = multiply(multiply(inverse(D),inverse(C)),inverse(multiply(multiply(E,inverse(E)),inverse(multiply(F,inverse(F)))))),
inference(paramod,[status(thm)],[c_1530,c_1835]) ).
cnf(c_1608,plain,
multiply(multiply(inverse(A),inverse(B)),inverse(multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(D)))))) = multiply(inverse(inverse(inverse(A))),inverse(inverse(inverse(B)))),
inference(copy,[status(thm)],[c_1836]) ).
cnf(c_1837,plain,
inverse(multiply(multiply(inverse(multiply(inverse(multiply(A,inverse(A))),inverse(inverse(C)))),D),inverse(multiply(multiply(E,inverse(E)),D)))) = C,
inference(paramod,[status(thm)],[c_1502,c_1366]) ).
cnf(c_1838,plain,
inverse(multiply(inverse(inverse(inverse(multiply(inverse(multiply(A,inverse(A))),inverse(inverse(C)))))),inverse(inverse(inverse(multiply(E,inverse(E))))))) = C,
inference(paramod,[status(thm)],[c_1535,c_1837]) ).
cnf(c_1839,plain,
inverse(multiply(inverse(multiply(inverse(inverse(inverse(multiply(A,inverse(A))))),inverse(inverse(inverse(inverse(C)))))),inverse(inverse(inverse(multiply(E,inverse(E))))))) = C,
inference(paramod,[status(thm)],[c_1551,c_1838]) ).
cnf(c_1840,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(A)),inverse(inverse(inverse(A))))),inverse(inverse(inverse(inverse(C)))))),inverse(inverse(inverse(multiply(E,inverse(E))))))) = C,
inference(paramod,[status(thm)],[c_1551,c_1839]) ).
cnf(c_1618,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(A)),inverse(inverse(inverse(A))))),inverse(inverse(inverse(inverse(B)))))),inverse(multiply(inverse(inverse(C)),inverse(inverse(inverse(C))))))) = B,
inference(paramod,[status(thm)],[c_1551,c_1840]) ).
cnf(c_1841,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(multiply(inverse(inverse(inverse(C))),D),inverse(multiply(inverse(multiply(E,inverse(E))),D))))) = C,
inference(paramod,[status(thm)],[c_1502,c_1365]) ).
cnf(c_1842,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(inverse(inverse(inverse(inverse(C))))),inverse(inverse(inverse(inverse(multiply(E,inverse(E))))))))) = C,
inference(paramod,[status(thm)],[c_1535,c_1841]) ).
cnf(c_1843,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(inverse(inverse(inverse(inverse(C))))),inverse(inverse(multiply(inverse(inverse(E)),inverse(inverse(inverse(E))))))))) = C,
inference(paramod,[status(thm)],[c_1551,c_1842]) ).
cnf(c_1844,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(inverse(inverse(inverse(inverse(C))))),multiply(inverse(inverse(inverse(inverse(E)))),inverse(inverse(inverse(inverse(inverse(E))))))))) = C,
inference(paramod,[status(thm)],[c_1551,c_1843]) ).
cnf(c_1619,plain,
multiply(multiply(A,inverse(A)),inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(B))))))))) = B,
inference(paramod,[status(thm)],[c_1416,c_1844]) ).
cnf(c_1845,plain,
multiply(multiply(A,B),inverse(multiply(multiply(inverse(multiply(inverse(C),inverse(inverse(E)))),F),B))) = multiply(multiply(A,inverse(multiply(C,F))),E),
inference(paramod,[status(thm)],[c_1502,c_440]) ).
cnf(c_1846,plain,
multiply(inverse(inverse(A)),inverse(inverse(inverse(multiply(inverse(multiply(inverse(C),inverse(inverse(E)))),F))))) = multiply(multiply(A,inverse(multiply(C,F))),E),
inference(paramod,[status(thm)],[c_1535,c_1845]) ).
cnf(c_1847,plain,
multiply(inverse(inverse(A)),inverse(multiply(inverse(inverse(inverse(multiply(inverse(C),inverse(inverse(E)))))),inverse(inverse(F))))) = multiply(multiply(A,inverse(multiply(C,F))),E),
inference(paramod,[status(thm)],[c_1551,c_1846]) ).
cnf(c_1848,plain,
multiply(inverse(inverse(A)),inverse(multiply(inverse(multiply(inverse(inverse(inverse(C))),inverse(inverse(inverse(inverse(E)))))),inverse(inverse(F))))) = multiply(multiply(A,inverse(multiply(C,F))),E),
inference(paramod,[status(thm)],[c_1551,c_1847]) ).
cnf(c_1639,plain,
multiply(multiply(A,inverse(multiply(B,C))),D) = multiply(inverse(inverse(A)),inverse(multiply(inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(inverse(D)))))),inverse(inverse(C))))),
inference(copy,[status(thm)],[c_1848]) ).
cnf(c_1849,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(inverse(multiply(D,inverse(D))))))))) = inverse(multiply(multiply(inverse(multiply(inverse(E),B)),F),inverse(multiply(E,F)))),
inference(paramod,[status(thm)],[c_1535,c_1350]) ).
cnf(c_1850,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(multiply(inverse(inverse(D)),inverse(inverse(inverse(D))))))))) = inverse(multiply(multiply(inverse(multiply(inverse(E),B)),F),inverse(multiply(E,F)))),
inference(paramod,[status(thm)],[c_1551,c_1849]) ).
cnf(c_1851,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(inverse(inverse(B))),multiply(inverse(inverse(inverse(inverse(D)))),inverse(inverse(inverse(inverse(inverse(D))))))))) = inverse(multiply(multiply(inverse(multiply(inverse(E),B)),F),inverse(multiply(E,F)))),
inference(paramod,[status(thm)],[c_1551,c_1850]) ).
cnf(c_1852,plain,
multiply(multiply(A,inverse(A)),inverse(inverse(inverse(inverse(inverse(inverse(B))))))) = inverse(multiply(multiply(inverse(multiply(inverse(E),B)),F),inverse(multiply(E,F)))),
inference(paramod,[status(thm)],[c_1416,c_1851]) ).
cnf(c_1853,plain,
multiply(multiply(A,inverse(A)),inverse(inverse(inverse(inverse(inverse(inverse(B))))))) = inverse(multiply(inverse(inverse(inverse(multiply(inverse(E),B)))),inverse(inverse(inverse(E))))),
inference(paramod,[status(thm)],[c_1535,c_1852]) ).
cnf(c_1652,plain,
multiply(multiply(A,inverse(A)),inverse(inverse(inverse(inverse(inverse(inverse(B))))))) = inverse(multiply(inverse(multiply(inverse(inverse(inverse(C))),inverse(inverse(B)))),inverse(inverse(inverse(C))))),
inference(paramod,[status(thm)],[c_1551,c_1853]) ).
cnf(c_1654,plain,
inverse(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(C))))) = inverse(multiply(inverse(inverse(C)),inverse(inverse(inverse(B))))),
inference(paramod,[status(thm)],[c_1535,c_896]) ).
cnf(c_1854,plain,
multiply(multiply(multiply(A,inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(inverse(A))))))),D),inverse(multiply(E,D))) = multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(F),B)),V6),inverse(multiply(F,V6)))),V7),inverse(multiply(E,V7))),
inference(paramod,[status(thm)],[c_1535,c_374]) ).
cnf(c_1855,plain,
multiply(multiply(inverse(inverse(A)),inverse(multiply(inverse(multiply(inverse(inverse(inverse(inverse(inverse(inverse(B)))))),inverse(inverse(inverse(inverse(D)))))),inverse(inverse(inverse(inverse(inverse(inverse(A))))))))),inverse(multiply(E,D))) = multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(F),B)),V6),inverse(multiply(F,V6)))),V7),inverse(multiply(E,V7))),
inference(paramod,[status(thm)],[c_1639,c_1854]) ).
cnf(c_1856,plain,
multiply(inverse(multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(D))))))),inverse(inverse(inverse(inverse(inverse(inverse(inverse(B))))))))),inverse(multiply(E,D))) = multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(F),B)),V6),inverse(multiply(F,V6)))),V7),inverse(multiply(E,V7))),
inference(paramod,[status(thm)],[c_1567,c_1855]) ).
cnf(c_1857,plain,
multiply(multiply(inverse(inverse(B)),D),inverse(multiply(E,D))) = multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(F),B)),V6),inverse(multiply(F,V6)))),V7),inverse(multiply(E,V7))),
inference(paramod,[status(thm)],[c_1568,c_1856]) ).
cnf(c_1858,plain,
multiply(inverse(inverse(inverse(inverse(B)))),inverse(inverse(inverse(E)))) = multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(F),B)),V6),inverse(multiply(F,V6)))),V7),inverse(multiply(E,V7))),
inference(paramod,[status(thm)],[c_1535,c_1857]) ).
cnf(c_1859,plain,
multiply(inverse(inverse(inverse(inverse(B)))),inverse(inverse(inverse(E)))) = multiply(multiply(inverse(multiply(inverse(inverse(inverse(multiply(inverse(F),B)))),inverse(inverse(inverse(F))))),V7),inverse(multiply(E,V7))),
inference(paramod,[status(thm)],[c_1535,c_1858]) ).
cnf(c_1860,plain,
multiply(inverse(inverse(inverse(inverse(B)))),inverse(inverse(inverse(E)))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(inverse(inverse(F))),inverse(inverse(B)))),inverse(inverse(inverse(F))))),V7),inverse(multiply(E,V7))),
inference(paramod,[status(thm)],[c_1551,c_1859]) ).
cnf(c_1861,plain,
multiply(inverse(inverse(inverse(inverse(B)))),inverse(inverse(inverse(E)))) = multiply(inverse(inverse(inverse(multiply(inverse(multiply(inverse(inverse(inverse(F))),inverse(inverse(B)))),inverse(inverse(inverse(F))))))),inverse(inverse(inverse(E)))),
inference(paramod,[status(thm)],[c_1535,c_1860]) ).
cnf(c_1862,plain,
multiply(inverse(inverse(inverse(inverse(B)))),inverse(inverse(inverse(E)))) = multiply(inverse(multiply(inverse(inverse(inverse(multiply(inverse(inverse(inverse(F))),inverse(inverse(B)))))),inverse(inverse(inverse(inverse(inverse(F))))))),inverse(inverse(inverse(E)))),
inference(paramod,[status(thm)],[c_1551,c_1861]) ).
cnf(c_1863,plain,
multiply(inverse(inverse(inverse(inverse(B)))),inverse(inverse(inverse(E)))) = multiply(inverse(multiply(inverse(multiply(inverse(inverse(inverse(inverse(inverse(F))))),inverse(inverse(inverse(inverse(B)))))),inverse(inverse(inverse(inverse(inverse(F))))))),inverse(inverse(inverse(E)))),
inference(paramod,[status(thm)],[c_1551,c_1862]) ).
cnf(c_1667,plain,
multiply(inverse(inverse(inverse(inverse(A)))),inverse(inverse(inverse(B)))) = multiply(A,inverse(inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_1560,c_1863]) ).
cnf(c_1864,plain,
multiply(A,multiply(B,inverse(multiply(inverse(inverse(inverse(multiply(inverse(A),C)))),inverse(inverse(inverse(inverse(B)))))))) = C,
inference(paramod,[status(thm)],[c_1535,c_14]) ).
cnf(c_1865,plain,
multiply(A,multiply(B,inverse(multiply(inverse(multiply(inverse(inverse(inverse(A))),inverse(inverse(C)))),inverse(inverse(inverse(inverse(B)))))))) = C,
inference(paramod,[status(thm)],[c_1551,c_1864]) ).
cnf(c_1866,plain,
multiply(A,inverse(multiply(inverse(inverse(inverse(inverse(inverse(C))))),inverse(inverse(inverse(inverse(A))))))) = C,
inference(paramod,[status(thm)],[c_1567,c_1865]) ).
cnf(c_1671,plain,
multiply(A,inverse(multiply(inverse(B),inverse(inverse(inverse(inverse(A))))))) = B,
inference(paramod,[status(thm)],[c_1667,c_1866]) ).
cnf(c_1867,plain,
multiply(A,inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(inverse(A))))))) = inverse(multiply(multiply(inverse(multiply(inverse(D),B)),E),inverse(multiply(D,E)))),
inference(paramod,[status(thm)],[c_1535,c_9]) ).
cnf(c_1868,plain,
inverse(inverse(B)) = inverse(multiply(multiply(inverse(multiply(inverse(D),B)),E),inverse(multiply(D,E)))),
inference(paramod,[status(thm)],[c_1671,c_1867]) ).
cnf(c_1869,plain,
inverse(inverse(B)) = inverse(multiply(inverse(inverse(inverse(multiply(inverse(D),B)))),inverse(inverse(inverse(D))))),
inference(paramod,[status(thm)],[c_1535,c_1868]) ).
cnf(c_1870,plain,
inverse(inverse(B)) = inverse(multiply(inverse(multiply(inverse(inverse(inverse(D))),inverse(inverse(B)))),inverse(inverse(inverse(D))))),
inference(paramod,[status(thm)],[c_1551,c_1869]) ).
cnf(c_1672,plain,
inverse(multiply(inverse(multiply(inverse(inverse(inverse(A))),inverse(inverse(B)))),inverse(inverse(inverse(A))))) = inverse(inverse(B)),
inference(copy,[status(thm)],[c_1870]) ).
cnf(c_1871,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))),inverse(multiply(C,multiply(inverse(inverse(inverse(C))),inverse(inverse(D)))))) = multiply(multiply(inverse(multiply(inverse(E),D)),F),inverse(multiply(E,F))),
inference(paramod,[status(thm)],[c_1551,c_1431]) ).
cnf(c_1872,plain,
multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(multiply(inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(inverse(inverse(multiply(C,multiply(inverse(inverse(inverse(C))),inverse(inverse(D))))))))))),inverse(inverse(inverse(B)))))) = multiply(multiply(inverse(multiply(inverse(E),D)),F),inverse(multiply(E,F))),
inference(paramod,[status(thm)],[c_1639,c_1871]) ).
cnf(c_1873,plain,
multiply(multiply(inverse(inverse(A)),inverse(inverse(inverse(A)))),inverse(multiply(inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(inverse(inverse(multiply(C,multiply(inverse(inverse(inverse(C))),inverse(inverse(D))))))))))),inverse(inverse(inverse(B)))))) = multiply(multiply(inverse(multiply(inverse(E),D)),F),inverse(multiply(E,F))),
inference(paramod,[status(thm)],[c_1551,c_1872]) ).
cnf(c_1874,plain,
multiply(multiply(inverse(inverse(A)),inverse(inverse(inverse(A)))),inverse(multiply(inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(multiply(inverse(inverse(C)),inverse(inverse(multiply(inverse(inverse(inverse(C))),inverse(inverse(D))))))))))),inverse(inverse(inverse(B)))))) = multiply(multiply(inverse(multiply(inverse(E),D)),F),inverse(multiply(E,F))),
inference(paramod,[status(thm)],[c_1551,c_1873]) ).
cnf(c_1875,plain,
multiply(multiply(inverse(inverse(A)),inverse(inverse(inverse(A)))),inverse(multiply(inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(multiply(inverse(inverse(C)),multiply(inverse(inverse(inverse(inverse(inverse(C))))),inverse(inverse(inverse(inverse(D))))))))))),inverse(inverse(inverse(B)))))) = multiply(multiply(inverse(multiply(inverse(E),D)),F),inverse(multiply(E,F))),
inference(paramod,[status(thm)],[c_1551,c_1874]) ).
cnf(c_1876,plain,
multiply(multiply(inverse(inverse(A)),inverse(inverse(inverse(A)))),inverse(multiply(inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(multiply(inverse(inverse(C)),multiply(inverse(C),inverse(inverse(inverse(inverse(D))))))))))),inverse(inverse(inverse(B)))))) = multiply(multiply(inverse(multiply(inverse(E),D)),F),inverse(multiply(E,F))),
inference(paramod,[status(thm)],[c_1667,c_1875]) ).
cnf(c_1877,plain,
multiply(multiply(inverse(inverse(A)),inverse(inverse(inverse(A)))),inverse(multiply(inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(D))))))))))),inverse(inverse(inverse(B)))))) = multiply(multiply(inverse(multiply(inverse(E),D)),F),inverse(multiply(E,F))),
inference(paramod,[status(thm)],[c_1502,c_1876]) ).
cnf(c_1878,plain,
multiply(multiply(inverse(inverse(A)),inverse(inverse(inverse(A)))),inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(D)))))))))) = multiply(multiply(inverse(multiply(inverse(E),D)),F),inverse(multiply(E,F))),
inference(paramod,[status(thm)],[c_1672,c_1877]) ).
cnf(c_1879,plain,
inverse(D) = multiply(multiply(inverse(multiply(inverse(E),D)),F),inverse(multiply(E,F))),
inference(paramod,[status(thm)],[c_1619,c_1878]) ).
cnf(c_1880,plain,
inverse(D) = multiply(inverse(inverse(inverse(multiply(inverse(E),D)))),inverse(inverse(inverse(E)))),
inference(paramod,[status(thm)],[c_1535,c_1879]) ).
cnf(c_1881,plain,
inverse(D) = multiply(inverse(multiply(inverse(inverse(inverse(E))),inverse(inverse(D)))),inverse(inverse(inverse(E)))),
inference(paramod,[status(thm)],[c_1551,c_1880]) ).
cnf(c_1676,plain,
multiply(inverse(multiply(inverse(inverse(inverse(A))),inverse(inverse(B)))),inverse(inverse(inverse(A)))) = inverse(B),
inference(copy,[status(thm)],[c_1881]) ).
cnf(c_1679,plain,
multiply(multiply(A,inverse(B)),inverse(multiply(C,inverse(C)))) = multiply(inverse(inverse(A)),inverse(inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_1535,c_895]) ).
cnf(c_1680,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(C)))) = multiply(inverse(inverse(C)),inverse(inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_1535,c_894]) ).
cnf(c_1882,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(multiply(inverse(A),C))))),inverse(inverse(inverse(B)))))) = C,
inference(paramod,[status(thm)],[c_1551,c_1550]) ).
cnf(c_1883,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(inverse(inverse(B))),multiply(inverse(inverse(inverse(A))),inverse(inverse(C))))),inverse(inverse(inverse(B)))))) = C,
inference(paramod,[status(thm)],[c_1551,c_1882]) ).
cnf(c_1884,plain,
multiply(A,inverse(multiply(multiply(inverse(inverse(inverse(C))),multiply(inverse(inverse(inverse(inverse(A)))),inverse(inverse(inverse(inverse(B)))))),inverse(inverse(inverse(B)))))) = C,
inference(paramod,[status(thm)],[c_1556,c_1883]) ).
cnf(c_1687,plain,
multiply(A,inverse(multiply(multiply(inverse(inverse(inverse(B))),multiply(A,inverse(inverse(inverse(inverse(C)))))),inverse(inverse(inverse(C)))))) = B,
inference(paramod,[status(thm)],[c_1667,c_1884]) ).
cnf(c_1885,plain,
inverse(inverse(inverse(multiply(inverse(multiply(inverse(inverse(inverse(A))),inverse(inverse(B)))),inverse(inverse(inverse(A))))))) = B,
inference(paramod,[status(thm)],[c_1551,c_1549]) ).
cnf(c_1688,plain,
inverse(inverse(inverse(inverse(A)))) = A,
inference(paramod,[status(thm)],[c_1676,c_1885]) ).
cnf(c_1886,plain,
multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(inverse(B),multiply(inverse(A),C))))),inverse(inverse(inverse(B)))))) = C,
inference(paramod,[status(thm)],[c_1679,c_842]) ).
cnf(c_1887,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(multiply(inverse(A),C))))),inverse(inverse(inverse(B)))))) = C,
inference(paramod,[status(thm)],[c_1551,c_1886]) ).
cnf(c_1888,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(inverse(inverse(B))),multiply(inverse(inverse(inverse(A))),inverse(inverse(C))))),inverse(inverse(inverse(B)))))) = C,
inference(paramod,[status(thm)],[c_1551,c_1887]) ).
cnf(c_1889,plain,
multiply(A,inverse(multiply(multiply(inverse(inverse(inverse(C))),multiply(inverse(inverse(inverse(inverse(A)))),inverse(inverse(inverse(inverse(B)))))),inverse(inverse(inverse(B)))))) = C,
inference(paramod,[status(thm)],[c_1556,c_1888]) ).
cnf(c_1890,plain,
multiply(A,inverse(multiply(multiply(inverse(inverse(inverse(C))),multiply(A,inverse(inverse(inverse(inverse(B)))))),inverse(inverse(inverse(B)))))) = C,
inference(paramod,[status(thm)],[c_1688,c_1889]) ).
cnf(c_1891,plain,
multiply(A,inverse(multiply(multiply(inverse(inverse(inverse(C))),multiply(A,B)),inverse(inverse(inverse(B)))))) = C,
inference(paramod,[status(thm)],[c_1688,c_1890]) ).
cnf(c_1892,plain,
multiply(A,inverse(multiply(inverse(inverse(inverse(inverse(inverse(C))))),inverse(inverse(inverse(inverse(A))))))) = C,
inference(paramod,[status(thm)],[c_1558,c_1891]) ).
cnf(c_1893,plain,
multiply(A,inverse(multiply(inverse(C),inverse(inverse(inverse(inverse(A))))))) = C,
inference(paramod,[status(thm)],[c_1688,c_1892]) ).
cnf(c_1700,plain,
multiply(A,inverse(multiply(inverse(B),A))) = B,
inference(paramod,[status(thm)],[c_1688,c_1893]) ).
cnf(c_1894,plain,
multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(inverse(B),C)))),inverse(inverse(inverse(B)))))) = inverse(multiply(inverse(inverse(inverse(inverse(inverse(C))))),inverse(inverse(inverse(inverse(inverse(A))))))),
inference(paramod,[status(thm)],[c_1679,c_1577]) ).
cnf(c_1895,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(C)))),inverse(inverse(inverse(B)))))) = inverse(multiply(inverse(inverse(inverse(inverse(inverse(C))))),inverse(inverse(inverse(inverse(inverse(A))))))),
inference(paramod,[status(thm)],[c_1551,c_1894]) ).
cnf(c_1896,plain,
multiply(A,inverse(inverse(C))) = inverse(multiply(inverse(inverse(inverse(inverse(inverse(C))))),inverse(inverse(inverse(inverse(inverse(A))))))),
inference(paramod,[status(thm)],[c_1676,c_1895]) ).
cnf(c_1897,plain,
multiply(A,inverse(inverse(C))) = inverse(multiply(inverse(C),inverse(inverse(inverse(inverse(inverse(A))))))),
inference(paramod,[status(thm)],[c_1688,c_1896]) ).
cnf(c_1898,plain,
multiply(A,inverse(inverse(C))) = inverse(multiply(inverse(C),inverse(A))),
inference(paramod,[status(thm)],[c_1688,c_1897]) ).
cnf(c_1705,plain,
inverse(multiply(inverse(A),inverse(B))) = multiply(B,inverse(inverse(A))),
inference(copy,[status(thm)],[c_1898]) ).
cnf(c_1899,plain,
multiply(multiply(inverse(A),inverse(B)),inverse(multiply(inverse(inverse(D)),inverse(inverse(inverse(D)))))) = multiply(inverse(inverse(inverse(A))),inverse(inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_1680,c_1608]) ).
cnf(c_1900,plain,
multiply(multiply(inverse(A),inverse(B)),multiply(inverse(inverse(D)),inverse(inverse(inverse(D))))) = multiply(inverse(inverse(inverse(A))),inverse(inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_1705,c_1899]) ).
cnf(c_1901,plain,
inverse(inverse(multiply(inverse(A),inverse(B)))) = multiply(inverse(inverse(inverse(A))),inverse(inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_1416,c_1900]) ).
cnf(c_1715,plain,
inverse(multiply(A,inverse(inverse(B)))) = multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(A)))),
inference(paramod,[status(thm)],[c_1705,c_1901]) ).
cnf(c_1902,plain,
inverse(multiply(inverse(multiply(multiply(inverse(inverse(inverse(inverse(A)))),inverse(inverse(inverse(inverse(inverse(A)))))),inverse(inverse(inverse(inverse(B)))))),inverse(multiply(inverse(inverse(C)),inverse(inverse(inverse(C))))))) = B,
inference(paramod,[status(thm)],[c_1715,c_1618]) ).
cnf(c_1903,plain,
inverse(multiply(inverse(multiply(multiply(A,inverse(inverse(inverse(inverse(inverse(A)))))),inverse(inverse(inverse(inverse(B)))))),inverse(multiply(inverse(inverse(C)),inverse(inverse(inverse(C))))))) = B,
inference(paramod,[status(thm)],[c_1688,c_1902]) ).
cnf(c_1904,plain,
inverse(multiply(inverse(multiply(multiply(A,inverse(A)),inverse(inverse(inverse(inverse(B)))))),inverse(multiply(inverse(inverse(C)),inverse(inverse(inverse(C))))))) = B,
inference(paramod,[status(thm)],[c_1688,c_1903]) ).
cnf(c_1905,plain,
inverse(multiply(inverse(multiply(multiply(A,inverse(A)),B)),inverse(multiply(inverse(inverse(C)),inverse(inverse(inverse(C))))))) = B,
inference(paramod,[status(thm)],[c_1688,c_1904]) ).
cnf(c_1906,plain,
inverse(multiply(inverse(multiply(multiply(A,inverse(A)),B)),multiply(inverse(inverse(inverse(inverse(C)))),inverse(inverse(inverse(inverse(inverse(C)))))))) = B,
inference(paramod,[status(thm)],[c_1715,c_1905]) ).
cnf(c_1907,plain,
inverse(multiply(inverse(multiply(multiply(A,inverse(A)),B)),multiply(C,inverse(inverse(inverse(inverse(inverse(C)))))))) = B,
inference(paramod,[status(thm)],[c_1688,c_1906]) ).
cnf(c_1908,plain,
inverse(multiply(inverse(multiply(multiply(A,inverse(A)),B)),multiply(C,inverse(C)))) = B,
inference(paramod,[status(thm)],[c_1688,c_1907]) ).
cnf(c_1909,plain,
inverse(inverse(inverse(inverse(multiply(multiply(A,inverse(A)),B))))) = B,
inference(paramod,[status(thm)],[c_1416,c_1908]) ).
cnf(c_1910,plain,
inverse(inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(inverse(B))))) = B,
inference(paramod,[status(thm)],[c_1551,c_1909]) ).
cnf(c_1911,plain,
inverse(inverse(multiply(multiply(inverse(inverse(A)),inverse(inverse(inverse(A)))),inverse(inverse(B))))) = B,
inference(paramod,[status(thm)],[c_1551,c_1910]) ).
cnf(c_1912,plain,
inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(inverse(multiply(inverse(inverse(A)),inverse(inverse(inverse(A))))))))) = B,
inference(paramod,[status(thm)],[c_1715,c_1911]) ).
cnf(c_1913,plain,
inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(multiply(inverse(inverse(inverse(inverse(A)))),inverse(inverse(inverse(inverse(inverse(A)))))))))) = B,
inference(paramod,[status(thm)],[c_1715,c_1912]) ).
cnf(c_1914,plain,
inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(multiply(A,inverse(inverse(inverse(inverse(inverse(A)))))))))) = B,
inference(paramod,[status(thm)],[c_1688,c_1913]) ).
cnf(c_1915,plain,
inverse(multiply(inverse(inverse(inverse(B))),inverse(inverse(multiply(A,inverse(A)))))) = B,
inference(paramod,[status(thm)],[c_1688,c_1914]) ).
cnf(c_1916,plain,
inverse(multiply(inverse(inverse(inverse(B))),multiply(inverse(inverse(A)),inverse(inverse(inverse(A)))))) = B,
inference(paramod,[status(thm)],[c_1551,c_1915]) ).
cnf(c_1917,plain,
inverse(inverse(inverse(inverse(inverse(inverse(B)))))) = B,
inference(paramod,[status(thm)],[c_1416,c_1916]) ).
cnf(c_1718,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_1688,c_1917]) ).
cnf(c_1918,plain,
multiply(A,inverse(multiply(inverse(B),inverse(inverse(inverse(inverse(A))))))) = inverse(multiply(inverse(multiply(inverse(inverse(inverse(C))),inverse(inverse(B)))),inverse(inverse(inverse(C))))),
inference(paramod,[status(thm)],[c_1718,c_1566]) ).
cnf(c_1919,plain,
multiply(A,inverse(multiply(inverse(B),inverse(inverse(A))))) = inverse(multiply(inverse(multiply(inverse(inverse(inverse(C))),inverse(inverse(B)))),inverse(inverse(inverse(C))))),
inference(paramod,[status(thm)],[c_1718,c_1918]) ).
cnf(c_1920,plain,
multiply(A,inverse(multiply(inverse(B),A))) = inverse(multiply(inverse(multiply(inverse(inverse(inverse(C))),inverse(inverse(B)))),inverse(inverse(inverse(C))))),
inference(paramod,[status(thm)],[c_1718,c_1919]) ).
cnf(c_1921,plain,
B = inverse(multiply(inverse(multiply(inverse(inverse(inverse(C))),inverse(inverse(B)))),inverse(inverse(inverse(C))))),
inference(paramod,[status(thm)],[c_1700,c_1920]) ).
cnf(c_1922,plain,
B = inverse(multiply(inverse(multiply(inverse(C),inverse(inverse(B)))),inverse(inverse(inverse(C))))),
inference(paramod,[status(thm)],[c_1718,c_1921]) ).
cnf(c_1923,plain,
B = inverse(multiply(inverse(multiply(inverse(C),B)),inverse(inverse(inverse(C))))),
inference(paramod,[status(thm)],[c_1718,c_1922]) ).
cnf(c_1924,plain,
B = inverse(multiply(inverse(multiply(inverse(C),B)),inverse(C))),
inference(paramod,[status(thm)],[c_1718,c_1923]) ).
cnf(c_1925,plain,
B = multiply(C,inverse(inverse(multiply(inverse(C),B)))),
inference(paramod,[status(thm)],[c_1705,c_1924]) ).
cnf(c_1926,plain,
B = multiply(C,multiply(inverse(C),B)),
inference(paramod,[status(thm)],[c_1718,c_1925]) ).
cnf(c_1728,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(copy,[status(thm)],[c_1926]) ).
cnf(c_1927,plain,
multiply(multiply(A,inverse(A)),inverse(inverse(inverse(inverse(B))))) = inverse(multiply(inverse(multiply(inverse(inverse(inverse(C))),inverse(inverse(B)))),inverse(inverse(inverse(C))))),
inference(paramod,[status(thm)],[c_1718,c_1652]) ).
cnf(c_1928,plain,
multiply(multiply(A,inverse(A)),inverse(inverse(B))) = inverse(multiply(inverse(multiply(inverse(inverse(inverse(C))),inverse(inverse(B)))),inverse(inverse(inverse(C))))),
inference(paramod,[status(thm)],[c_1718,c_1927]) ).
cnf(c_1929,plain,
multiply(multiply(A,inverse(A)),B) = inverse(multiply(inverse(multiply(inverse(inverse(inverse(C))),inverse(inverse(B)))),inverse(inverse(inverse(C))))),
inference(paramod,[status(thm)],[c_1718,c_1928]) ).
cnf(c_1930,plain,
multiply(multiply(A,inverse(A)),B) = inverse(multiply(inverse(multiply(inverse(C),inverse(inverse(B)))),inverse(inverse(inverse(C))))),
inference(paramod,[status(thm)],[c_1718,c_1929]) ).
cnf(c_1931,plain,
multiply(multiply(A,inverse(A)),B) = inverse(multiply(inverse(multiply(inverse(C),B)),inverse(inverse(inverse(C))))),
inference(paramod,[status(thm)],[c_1718,c_1930]) ).
cnf(c_1932,plain,
multiply(multiply(A,inverse(A)),B) = inverse(multiply(inverse(multiply(inverse(C),B)),inverse(C))),
inference(paramod,[status(thm)],[c_1718,c_1931]) ).
cnf(c_1933,plain,
multiply(multiply(A,inverse(A)),B) = multiply(C,inverse(inverse(multiply(inverse(C),B)))),
inference(paramod,[status(thm)],[c_1705,c_1932]) ).
cnf(c_1934,plain,
multiply(multiply(A,inverse(A)),B) = multiply(C,multiply(inverse(C),B)),
inference(paramod,[status(thm)],[c_1718,c_1933]) ).
cnf(c_1731,plain,
multiply(multiply(A,inverse(A)),B) = B,
inference(paramod,[status(thm)],[c_1728,c_1934]) ).
cnf(c_1935,plain,
inverse(inverse(multiply(B,inverse(C)))) = inverse(multiply(inverse(inverse(C)),inverse(inverse(inverse(B))))),
inference(paramod,[status(thm)],[c_1731,c_1654]) ).
cnf(c_1936,plain,
multiply(B,inverse(C)) = inverse(multiply(inverse(inverse(C)),inverse(inverse(inverse(B))))),
inference(paramod,[status(thm)],[c_1718,c_1935]) ).
cnf(c_1937,plain,
multiply(B,inverse(C)) = inverse(multiply(C,inverse(inverse(inverse(B))))),
inference(paramod,[status(thm)],[c_1718,c_1936]) ).
cnf(c_1938,plain,
multiply(B,inverse(C)) = inverse(multiply(C,inverse(B))),
inference(paramod,[status(thm)],[c_1718,c_1937]) ).
cnf(c_1740,plain,
inverse(multiply(A,inverse(B))) = multiply(B,inverse(A)),
inference(copy,[status(thm)],[c_1938]) ).
cnf(c_1939,plain,
multiply(inverse(B),multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(multiply(E,inverse(E))))))) = inverse(multiply(inverse(inverse(D)),inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_1731,c_1574]) ).
cnf(c_1940,plain,
multiply(inverse(B),multiply(multiply(C,inverse(C)),inverse(multiply(D,multiply(E,inverse(E)))))) = inverse(multiply(inverse(inverse(D)),inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_1740,c_1939]) ).
cnf(c_1941,plain,
multiply(inverse(B),multiply(multiply(C,inverse(C)),inverse(inverse(inverse(D))))) = inverse(multiply(inverse(inverse(D)),inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_1416,c_1940]) ).
cnf(c_1942,plain,
multiply(inverse(B),multiply(multiply(C,inverse(C)),inverse(D))) = inverse(multiply(inverse(inverse(D)),inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_1718,c_1941]) ).
cnf(c_1943,plain,
multiply(inverse(B),inverse(D)) = inverse(multiply(inverse(inverse(D)),inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_1731,c_1942]) ).
cnf(c_1944,plain,
multiply(inverse(B),inverse(D)) = inverse(multiply(D,inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_1718,c_1943]) ).
cnf(c_1945,plain,
multiply(inverse(B),inverse(D)) = inverse(multiply(D,B)),
inference(paramod,[status(thm)],[c_1718,c_1944]) ).
cnf(c_1741,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_1945]) ).
cnf(c_1946,plain,
multiply(A,inverse(multiply(multiply(inverse(B),multiply(A,inverse(inverse(inverse(inverse(C)))))),inverse(inverse(inverse(C)))))) = B,
inference(paramod,[status(thm)],[c_1718,c_1687]) ).
cnf(c_1947,plain,
multiply(A,inverse(multiply(multiply(inverse(B),multiply(A,inverse(inverse(C)))),inverse(inverse(inverse(C)))))) = B,
inference(paramod,[status(thm)],[c_1718,c_1946]) ).
cnf(c_1948,plain,
multiply(A,inverse(multiply(multiply(inverse(B),multiply(A,C)),inverse(inverse(inverse(C)))))) = B,
inference(paramod,[status(thm)],[c_1718,c_1947]) ).
cnf(c_1949,plain,
multiply(A,inverse(multiply(multiply(inverse(B),multiply(A,C)),inverse(C)))) = B,
inference(paramod,[status(thm)],[c_1718,c_1948]) ).
cnf(c_1950,plain,
multiply(A,multiply(inverse(inverse(C)),inverse(multiply(inverse(B),multiply(A,C))))) = B,
inference(paramod,[status(thm)],[c_1741,c_1949]) ).
cnf(c_1951,plain,
multiply(A,multiply(C,inverse(multiply(inverse(B),multiply(A,C))))) = B,
inference(paramod,[status(thm)],[c_1718,c_1950]) ).
cnf(c_1952,plain,
multiply(A,multiply(C,multiply(inverse(multiply(A,C)),inverse(inverse(B))))) = B,
inference(paramod,[status(thm)],[c_1741,c_1951]) ).
cnf(c_1953,plain,
multiply(A,multiply(C,multiply(multiply(inverse(C),inverse(A)),inverse(inverse(B))))) = B,
inference(paramod,[status(thm)],[c_1741,c_1952]) ).
cnf(c_1744,plain,
multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(A)),C))) = C,
inference(paramod,[status(thm)],[c_1718,c_1953]) ).
cnf(c_1954,plain,
multiply(A,multiply(B,C)) = multiply(inverse(multiply(inverse(B),inverse(A))),C),
inference(paramod,[status(thm)],[c_1728,c_1744]) ).
cnf(c_1955,plain,
multiply(A,multiply(B,C)) = multiply(multiply(inverse(inverse(A)),inverse(inverse(B))),C),
inference(paramod,[status(thm)],[c_1741,c_1954]) ).
cnf(c_1956,plain,
multiply(A,multiply(B,C)) = multiply(multiply(A,inverse(inverse(B))),C),
inference(paramod,[status(thm)],[c_1718,c_1955]) ).
cnf(c_1957,plain,
multiply(A,multiply(B,C)) = multiply(multiply(A,B),C),
inference(paramod,[status(thm)],[c_1718,c_1956]) ).
cnf(c_1782,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(copy,[status(thm)],[c_1957]) ).
cnf(c_1783,plain,
$false,
inference(resolve,[status(thm)],[c_1782,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 14:18:08 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 353321 was started by sandbox on n003,
% 0.11/0.37 % Fri Sep 25 14:18:08 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 2.53/0.79
% 2.53/0.79 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 2.53/0.79
% 2.53/0.79 % SZS status Unsatisfiable for theBenchmark
% 2.53/0.79
% 2.53/0.79 % Proof 1 at 0.31 (+ 0.09) seconds.
% 2.53/0.79 % Length of proof is 96.
% 2.53/0.79 % Level of proof is 31.
% 2.53/0.79 % Maximum clause weight is 97.000.
% 2.53/0.79 % Given clauses 52.
% 2.53/0.79
% 2.53/0.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------