%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP099-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 07:22:19 AM UTC 2026
% Result : Unsatisfiable 168.12s 43.75s
% Output : CNFRefutation 168.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 5
% Syntax : Number of clauses : 283 ( 275 unt; 0 nHn; 14 RR)
% Number of literals : 301 ( 300 equ; 29 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 705 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2))),'double$udivide'(identity,identity)) = X1 ).
cnf(multiply,axiom,
multiply(X0,X1) = 'double$udivide'('double$udivide'(X1,X0),identity) ).
cnf(inverse,axiom,
inverse(X0) = 'double$udivide'(X0,identity) ).
cnf(identity,axiom,
identity = 'double$udivide'(X0,inverse(X0)) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ) ).
cnf(c0,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2))),'double$udivide'(identity,identity)) = X1,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
'double$udivide'('double$udivide'(X0,X1),identity) = multiply(X1,X0),
inference(clausification,[status(esa)],[multiply]) ).
cnf(c2,plain,
'double$udivide'(X0,identity) = inverse(X0),
inference(clausification,[status(esa)],[inverse]) ).
cnf(c3,plain,
'double$udivide'(X0,inverse(X0)) = identity,
inference(clausification,[status(esa)],[identity]) ).
cnf(c4,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity
| multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3) ),
inference(clausification,[status(esa)],[prove_these_axioms]) ).
cnf(d0,plain,
inverse('double$udivide'(X0,X1)) = multiply(X1,X0),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[c0,c2]) ).
cnf(d2,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2))),'double$udivide'('double$udivide'(X3,X1),'double$udivide'(identity,inverse(identity)))),inverse(identity)) = X3,
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d3,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2))),'double$udivide'('double$udivide'(X3,X1),identity)),inverse(identity)) = X3,
inference(demodulation,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
'double$udivide'('double$udivide'('double$udivide'(X2,'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X3)),'double$udivide'(identity,X3))),inverse('double$udivide'(X0,X1))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
'double$udivide'('double$udivide'('double$udivide'(X2,'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X3)),'double$udivide'(identity,X3))),multiply(X1,X0)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
inverse(identity) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d7,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(inverse(X0),'double$udivide'(X1,X2)),'double$udivide'(identity,X2))),inverse(identity)),inverse(identity)) = X0,
inference(superposition,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
'double$udivide'(inverse(X1),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,inverse(X0)),'double$udivide'(identity,identity))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[c2,d1]) ).
cnf(d10,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,inverse(X0)),inverse(identity))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
inverse(inverse(X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d12,plain,
'double$udivide'('double$udivide'(inverse(X0),'double$udivide'('double$udivide'(X1,multiply(identity,X0)),inverse(identity))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,inverse(identity))),identity)),inverse(identity)) = X1,
inference(superposition,[status(thm)],[c3,d1]) ).
cnf(d14,plain,
'double$udivide'('double$udivide'(X1,inverse('double$udivide'(X0,'double$udivide'(X1,inverse(identity))))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d13,c2]) ).
cnf(d15,plain,
'double$udivide'('double$udivide'(X1,multiply('double$udivide'(X1,inverse(identity)),X0)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d14,d0]) ).
cnf(d16,plain,
'double$udivide'('double$udivide'(identity,multiply(identity,X0)),inverse(identity)) = X0,
inference(superposition,[status(thm)],[c3,d15]) ).
cnf(d17,plain,
'double$udivide'('double$udivide'(inverse(X0),X0),inverse(identity)) = identity,
inference(superposition,[status(thm)],[d16,d12]) ).
cnf(d18,plain,
'double$udivide'(inverse(inverse(identity)),inverse(identity)) = identity,
inference(superposition,[status(thm)],[c2,d17]) ).
cnf(d19,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm)],[d18,d8]) ).
cnf(d20,plain,
'double$udivide'(inverse(X0),identity) = X0,
inference(demodulation,[status(thm)],[d8,d19]) ).
cnf(d21,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d20,c2]) ).
cnf(d22,plain,
X0 = multiply(identity,X0),
inference(demodulation,[status(thm)],[d11,d21]) ).
cnf(d23,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,identity),'double$udivide'(identity,inverse(X0)))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[c3,d1]) ).
cnf(d24,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'(inverse(X0),'double$udivide'(identity,inverse(X1)))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d23,c2]) ).
cnf(d25,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'(multiply(identity,X0),'double$udivide'(identity,inverse(X1)))),inverse(identity)) = inverse(X0),
inference(superposition,[status(thm)],[d11,d24]) ).
cnf(d26,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'(X0,'double$udivide'(identity,inverse(X1)))),inverse(identity)) = inverse(X0),
inference(demodulation,[status(thm)],[d25,d22]) ).
cnf(d27,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(X1,'double$udivide'(identity,inverse(X0)))),identity) = inverse(X1),
inference(demodulation,[status(thm)],[d26,d19]) ).
cnf(d28,plain,
inverse('double$udivide'(X0,'double$udivide'(X1,'double$udivide'(identity,inverse(X0))))) = inverse(X1),
inference(demodulation,[status(thm)],[d27,c2]) ).
cnf(d29,plain,
multiply('double$udivide'(X1,'double$udivide'(identity,inverse(X0))),X0) = inverse(X1),
inference(demodulation,[status(thm)],[d28,d0]) ).
cnf(d30,plain,
'double$udivide'('double$udivide'(X2,'double$udivide'(multiply(X1,X0),'double$udivide'(identity,inverse(X2)))),inverse(identity)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d0,d24]) ).
cnf(d31,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(multiply(X1,X2),'double$udivide'(identity,inverse(X0)))),identity) = 'double$udivide'(X2,X1),
inference(demodulation,[status(thm)],[d30,d19]) ).
cnf(d32,plain,
inverse('double$udivide'(X0,'double$udivide'(multiply(X1,X2),'double$udivide'(identity,inverse(X0))))) = 'double$udivide'(X2,X1),
inference(demodulation,[status(thm)],[d31,c2]) ).
cnf(d33,plain,
multiply('double$udivide'(multiply(X1,X2),'double$udivide'(identity,inverse(X0))),X0) = 'double$udivide'(X2,X1),
inference(demodulation,[status(thm)],[d32,d0]) ).
cnf(d34,plain,
inverse(multiply(X0,X1)) = 'double$udivide'(X1,X0),
inference(demodulation,[status(thm)],[d33,d29]) ).
cnf(d35,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(X0),identity)),inverse(identity)) = X0,
inference(superposition,[status(thm)],[c3,d24]) ).
cnf(d36,plain,
'double$udivide'('double$udivide'(identity,inverse(inverse(X0))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d35,c2]) ).
cnf(d37,plain,
'double$udivide'('double$udivide'(identity,X0),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d36,d21]) ).
cnf(d38,plain,
'double$udivide'('double$udivide'(identity,X0),identity) = X0,
inference(demodulation,[status(thm)],[d37,d19]) ).
cnf(d39,plain,
inverse('double$udivide'(identity,X0)) = X0,
inference(demodulation,[status(thm)],[d38,c2]) ).
cnf(d40,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d39,d0]) ).
cnf(d41,plain,
inverse(X0) = 'double$udivide'(identity,X0),
inference(superposition,[status(thm)],[d40,d34]) ).
cnf(d42,plain,
inverse(X1) = multiply(inverse(identity),'double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2)))),
inference(superposition,[status(thm)],[d1,d0]) ).
cnf(d43,plain,
inverse(X1) = multiply(inverse(identity),'double$udivide'(X0,'double$udivide'('double$udivide'(X1,identity),'double$udivide'(identity,inverse(X0))))),
inference(superposition,[status(thm)],[c3,d42]) ).
cnf(d44,plain,
inverse(X0) = multiply(identity,'double$udivide'(X1,'double$udivide'('double$udivide'(X0,identity),'double$udivide'(identity,inverse(X1))))),
inference(demodulation,[status(thm)],[d43,d19]) ).
cnf(d45,plain,
inverse(X1) = 'double$udivide'(X0,'double$udivide'('double$udivide'(X1,identity),'double$udivide'(identity,inverse(X0)))),
inference(demodulation,[status(thm)],[d44,d22]) ).
cnf(d46,plain,
inverse(X0) = 'double$udivide'(X1,'double$udivide'(inverse(X0),'double$udivide'(identity,inverse(X1)))),
inference(demodulation,[status(thm)],[d45,c2]) ).
cnf(d47,plain,
inverse(X1) = 'double$udivide'(X0,'double$udivide'(inverse(X1),inverse(inverse(X0)))),
inference(demodulation,[status(thm)],[d46,d41]) ).
cnf(d48,plain,
inverse(X1) = 'double$udivide'(X0,'double$udivide'(inverse(X1),X0)),
inference(demodulation,[status(thm)],[d47,d21]) ).
cnf(d49,plain,
inverse(X2) = multiply(inverse(identity),'double$udivide'('double$udivide'(X0,'double$udivide'(inverse(X1),'double$udivide'(identity,inverse(X0)))),'double$udivide'('double$udivide'(X2,X1),'double$udivide'(identity,inverse(identity))))),
inference(superposition,[status(thm)],[d24,d42]) ).
cnf(d50,plain,
inverse(X0) = multiply(identity,'double$udivide'('double$udivide'(X1,'double$udivide'(inverse(X2),'double$udivide'(identity,inverse(X1)))),'double$udivide'('double$udivide'(X0,X2),'double$udivide'(identity,inverse(identity))))),
inference(demodulation,[status(thm)],[d49,d19]) ).
cnf(d51,plain,
inverse(X2) = 'double$udivide'('double$udivide'(X0,'double$udivide'(inverse(X1),'double$udivide'(identity,inverse(X0)))),'double$udivide'('double$udivide'(X2,X1),'double$udivide'(identity,inverse(identity)))),
inference(demodulation,[status(thm)],[d50,d22]) ).
cnf(d52,plain,
inverse(X1) = 'double$udivide'('double$udivide'(X0,'double$udivide'(inverse(X2),inverse(inverse(X0)))),'double$udivide'('double$udivide'(X1,X2),'double$udivide'(identity,inverse(identity)))),
inference(demodulation,[status(thm)],[d51,d41]) ).
cnf(d53,plain,
inverse(X1) = 'double$udivide'('double$udivide'(X0,'double$udivide'(inverse(X2),X0)),'double$udivide'('double$udivide'(X1,X2),'double$udivide'(identity,inverse(identity)))),
inference(demodulation,[status(thm)],[d52,d21]) ).
cnf(d54,plain,
inverse(X2) = 'double$udivide'(inverse(X1),'double$udivide'('double$udivide'(X2,X1),'double$udivide'(identity,inverse(identity)))),
inference(demodulation,[status(thm)],[d53,d48]) ).
cnf(d55,plain,
inverse(X0) = 'double$udivide'(inverse(X1),'double$udivide'('double$udivide'(X0,X1),inverse(inverse(identity)))),
inference(demodulation,[status(thm)],[d54,d41]) ).
cnf(d56,plain,
inverse(X0) = 'double$udivide'(inverse(X1),'double$udivide'('double$udivide'(X0,X1),identity)),
inference(demodulation,[status(thm)],[d55,d21]) ).
cnf(d57,plain,
inverse(X0) = 'double$udivide'(inverse(X1),inverse('double$udivide'(X0,X1))),
inference(demodulation,[status(thm)],[d56,c2]) ).
cnf(d58,plain,
inverse(X0) = 'double$udivide'(inverse(X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d57,d0]) ).
cnf(d59,plain,
inverse(identity) = multiply(multiply(identity,X0),inverse(X0)),
inference(superposition,[status(thm)],[d11,d6]) ).
cnf(d60,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(multiply(identity,X0),'double$udivide'(X1,X2)),'double$udivide'(identity,X2))),inverse(identity)),inverse(identity)) = inverse(X0),
inference(superposition,[status(thm)],[d59,d5]) ).
cnf(d61,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),'double$udivide'(identity,X2))),inverse(identity)),inverse(identity)) = inverse(X0),
inference(demodulation,[status(thm)],[d60,d22]) ).
cnf(d62,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X1,X0)),inverse(X0))),inverse(identity)),inverse(identity)) = inverse(X2),
inference(demodulation,[status(thm)],[d61,d41]) ).
cnf(d63,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),inverse(X2))),identity),inverse(identity)) = inverse(X1),
inference(demodulation,[status(thm)],[d62,d19]) ).
cnf(d64,plain,
'double$udivide'(inverse('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),inverse(X2)))),inverse(identity)) = inverse(X1),
inference(demodulation,[status(thm)],[d63,c2]) ).
cnf(d65,plain,
'double$udivide'(multiply('double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),inverse(X2)),X0),inverse(identity)) = inverse(X1),
inference(demodulation,[status(thm)],[d64,d0]) ).
cnf(d66,plain,
'double$udivide'(multiply('double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),inverse(X2)),X1),identity) = inverse(X0),
inference(demodulation,[status(thm)],[d65,d19]) ).
cnf(d67,plain,
inverse(multiply('double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),inverse(X2)),X1)) = inverse(X0),
inference(demodulation,[status(thm)],[d66,c2]) ).
cnf(d68,plain,
'double$udivide'(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),inverse(X2))) = inverse(X0),
inference(demodulation,[status(thm)],[d67,d34]) ).
cnf(d69,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2))),multiply(X1,X3)),'double$udivide'('double$udivide'(X4,X3),'double$udivide'(identity,inverse(identity)))),multiply(X4,X5)),inverse(identity)) = X5,
inference(superposition,[status(thm)],[d5,d5]) ).
cnf(d70,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2))),multiply(X1,X3)),'double$udivide'('double$udivide'(X4,X3),identity)),multiply(X4,X5)),inverse(identity)) = X5,
inference(demodulation,[status(thm)],[d69,c3]) ).
cnf(d71,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'('double$udivide'(X2,'double$udivide'('double$udivide'(X3,'double$udivide'(X2,X4)),'double$udivide'(identity,X4))),multiply(X3,X1)),inverse('double$udivide'(X0,X1))),multiply(X0,X5)),inverse(identity)) = X5,
inference(demodulation,[status(thm)],[d70,c2]) ).
cnf(d72,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'('double$udivide'(X2,'double$udivide'('double$udivide'(X3,'double$udivide'(X2,X4)),'double$udivide'(identity,X4))),multiply(X3,X1)),multiply(X1,X0)),multiply(X0,X5)),inverse(identity)) = X5,
inference(demodulation,[status(thm)],[d71,d0]) ).
cnf(d73,plain,
inverse(multiply(X1,X0)) = multiply(identity,'double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[d0,d11]) ).
cnf(d74,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'('double$udivide'(X2,'double$udivide'('double$udivide'(X3,'double$udivide'(X2,X4)),'double$udivide'(identity,X4))),multiply(X3,identity)),inverse(multiply(X1,X0))),multiply('double$udivide'(X0,X1),X5)),inverse(identity)) = X5,
inference(superposition,[status(thm)],[d73,d72]) ).
cnf(d75,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X1,X0)),inverse(X0))),multiply(X2,identity)),inverse(multiply(X3,X4))),multiply('double$udivide'(X4,X3),X5)),inverse(identity)) = X5,
inference(demodulation,[status(thm)],[d74,d41]) ).
cnf(d76,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(inverse(X1),multiply(X1,identity)),inverse(multiply(X3,X4))),multiply('double$udivide'(X4,X3),X5)),inverse(identity)) = X5,
inference(demodulation,[status(thm)],[d75,d68]) ).
cnf(d77,plain,
'double$udivide'('double$udivide'('double$udivide'(inverse(identity),inverse(multiply(X1,X2))),multiply('double$udivide'(X2,X1),X3)),inverse(identity)) = X3,
inference(demodulation,[status(thm)],[d76,d58]) ).
cnf(d78,plain,
'double$udivide'('double$udivide'('double$udivide'(identity,inverse(multiply(X0,X1))),multiply('double$udivide'(X1,X0),X2)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d77,d19]) ).
cnf(d79,plain,
'double$udivide'('double$udivide'(inverse(inverse(multiply(X0,X1))),multiply('double$udivide'(X1,X0),X2)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d78,d41]) ).
cnf(d80,plain,
'double$udivide'('double$udivide'(multiply(X0,X1),multiply('double$udivide'(X1,X0),X2)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d79,d21]) ).
cnf(d81,plain,
'double$udivide'('double$udivide'(multiply(X0,X1),multiply('double$udivide'(X1,X0),X2)),identity) = X2,
inference(demodulation,[status(thm)],[d80,d19]) ).
cnf(d82,plain,
inverse('double$udivide'(multiply(X0,X1),multiply('double$udivide'(X1,X0),X2))) = X2,
inference(demodulation,[status(thm)],[d81,c2]) ).
cnf(d83,plain,
multiply(multiply('double$udivide'(X1,X0),X2),multiply(X0,X1)) = X2,
inference(demodulation,[status(thm)],[d82,d0]) ).
cnf(d84,plain,
inverse(multiply(identity,X0)) = multiply(identity,inverse(X0)),
inference(superposition,[status(thm)],[d11,d11]) ).
cnf(d85,plain,
'double$udivide'('double$udivide'(multiply(identity,X0),'double$udivide'(inverse(X1),'double$udivide'(identity,multiply(identity,inverse(X0))))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[d84,d24]) ).
cnf(d86,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(inverse(X1),'double$udivide'(identity,multiply(identity,inverse(X0))))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d85,d22]) ).
cnf(d87,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(inverse(X1),inverse(multiply(identity,inverse(X0))))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d86,d41]) ).
cnf(d88,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(inverse(X1),'double$udivide'(inverse(X0),identity))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d87,d34]) ).
cnf(d89,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(inverse(X1),inverse(inverse(X0)))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d88,c2]) ).
cnf(d90,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(inverse(X1),X0)),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d89,d21]) ).
cnf(d91,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(inverse(X1),X0)),identity) = X1,
inference(demodulation,[status(thm)],[d90,d19]) ).
cnf(d92,plain,
inverse('double$udivide'(X0,'double$udivide'(inverse(X1),X0))) = X1,
inference(demodulation,[status(thm)],[d91,c2]) ).
cnf(d93,plain,
multiply('double$udivide'(inverse(X1),X0),X0) = X1,
inference(demodulation,[status(thm)],[d92,d0]) ).
cnf(d94,plain,
multiply(X0,multiply(X1,inverse(X0))) = X1,
inference(superposition,[status(thm)],[d93,d83]) ).
cnf(d95,plain,
multiply('double$udivide'(X0,X1),X1) = inverse(X0),
inference(superposition,[status(thm)],[d21,d93]) ).
cnf(d96,plain,
multiply(X1,inverse(X0)) = 'double$udivide'(X0,inverse(X1)),
inference(superposition,[status(thm)],[d95,d94]) ).
cnf(d97,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)) = 'double$udivide'(X0,multiply('double$udivide'(X0,inverse(identity)),X1)),
inference(superposition,[status(thm)],[d15,d10]) ).
cnf(d98,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X0,identity)),inverse(identity)) = 'double$udivide'(X1,multiply('double$udivide'(X1,inverse(identity)),X0)),
inference(demodulation,[status(thm)],[d97,d19]) ).
cnf(d99,plain,
'double$udivide'('double$udivide'(identity,inverse(X0)),inverse(identity)) = 'double$udivide'(X1,multiply('double$udivide'(X1,inverse(identity)),X0)),
inference(demodulation,[status(thm)],[d98,c2]) ).
cnf(d100,plain,
'double$udivide'('double$udivide'(identity,inverse(X0)),identity) = 'double$udivide'(X1,multiply('double$udivide'(X1,inverse(identity)),X0)),
inference(demodulation,[status(thm)],[d99,d19]) ).
cnf(d101,plain,
inverse('double$udivide'(identity,inverse(X0))) = 'double$udivide'(X1,multiply('double$udivide'(X1,inverse(identity)),X0)),
inference(demodulation,[status(thm)],[d100,c2]) ).
cnf(d102,plain,
multiply(inverse(X0),identity) = 'double$udivide'(X1,multiply('double$udivide'(X1,inverse(identity)),X0)),
inference(demodulation,[status(thm)],[d101,d0]) ).
cnf(d103,plain,
inverse(X0) = 'double$udivide'(X1,multiply('double$udivide'(X1,inverse(identity)),X0)),
inference(demodulation,[status(thm)],[d102,d40]) ).
cnf(d104,plain,
inverse(X0) = 'double$udivide'(X1,multiply('double$udivide'(X1,identity),X0)),
inference(demodulation,[status(thm)],[d103,d19]) ).
cnf(d105,plain,
inverse(X1) = 'double$udivide'(X0,multiply(inverse(X0),X1)),
inference(demodulation,[status(thm)],[d104,c2]) ).
cnf(d106,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,multiply('double$udivide'(X0,inverse(identity)),X1)),'double$udivide'('double$udivide'(X2,X1),'double$udivide'(identity,inverse(identity)))),inverse(identity)) = X2,
inference(superposition,[status(thm)],[d15,d1]) ).
cnf(d107,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,multiply('double$udivide'(X0,identity),X1)),'double$udivide'('double$udivide'(X2,X1),'double$udivide'(identity,inverse(identity)))),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d106,d19]) ).
cnf(d108,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,multiply(inverse(X0),X1)),'double$udivide'('double$udivide'(X2,X1),'double$udivide'(identity,inverse(identity)))),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d107,c2]) ).
cnf(d109,plain,
'double$udivide'('double$udivide'(inverse(X1),'double$udivide'('double$udivide'(X2,X1),'double$udivide'(identity,inverse(identity)))),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d108,d105]) ).
cnf(d110,plain,
'double$udivide'('double$udivide'(inverse(X0),'double$udivide'('double$udivide'(X1,X0),identity)),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d109,c3]) ).
cnf(d111,plain,
'double$udivide'('double$udivide'(inverse(X1),inverse('double$udivide'(X0,X1))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d110,c2]) ).
cnf(d112,plain,
'double$udivide'('double$udivide'(inverse(X1),multiply(X1,X0)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d111,d0]) ).
cnf(d113,plain,
'double$udivide'('double$udivide'(inverse(X0),multiply(X0,X1)),identity) = X1,
inference(demodulation,[status(thm)],[d112,d19]) ).
cnf(d114,plain,
inverse('double$udivide'(inverse(X0),multiply(X0,X1))) = X1,
inference(demodulation,[status(thm)],[d113,c2]) ).
cnf(d115,plain,
multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(demodulation,[status(thm)],[d114,d0]) ).
cnf(d116,plain,
inverse(X3) = multiply(inverse(identity),'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2))),multiply(X1,X3))),
inference(superposition,[status(thm)],[d5,d0]) ).
cnf(d117,plain,
inverse('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2))),multiply(X1,X3))) = multiply(inverse(identity),'double$udivide'('double$udivide'(X4,'double$udivide'('double$udivide'(inverse(identity),'double$udivide'(X4,X5)),'double$udivide'(identity,X5))),inverse(X3))),
inference(superposition,[status(thm)],[d116,d116]) ).
cnf(d118,plain,
multiply(multiply(X1,X3),'double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2)))) = multiply(inverse(identity),'double$udivide'('double$udivide'(X4,'double$udivide'('double$udivide'(inverse(identity),'double$udivide'(X4,X5)),'double$udivide'(identity,X5))),inverse(X3))),
inference(demodulation,[status(thm)],[d117,d0]) ).
cnf(d119,plain,
multiply(multiply(X1,X2),'double$udivide'(X3,'double$udivide'('double$udivide'(X1,'double$udivide'(X3,X0)),inverse(X0)))) = multiply(inverse(identity),'double$udivide'('double$udivide'(X4,'double$udivide'('double$udivide'(inverse(identity),'double$udivide'(X4,X5)),'double$udivide'(identity,X5))),inverse(X2))),
inference(demodulation,[status(thm)],[d118,d41]) ).
cnf(d120,plain,
multiply(multiply(X1,X3),inverse(X1)) = multiply(inverse(identity),'double$udivide'('double$udivide'(X4,'double$udivide'('double$udivide'(inverse(identity),'double$udivide'(X4,X5)),'double$udivide'(identity,X5))),inverse(X3))),
inference(demodulation,[status(thm)],[d119,d68]) ).
cnf(d121,plain,
X1 = multiply(inverse(identity),'double$udivide'('double$udivide'(X2,'double$udivide'('double$udivide'(inverse(identity),'double$udivide'(X2,X3)),'double$udivide'(identity,X3))),inverse(X1))),
inference(demodulation,[status(thm)],[d120,d115]) ).
cnf(d122,plain,
X0 = multiply(identity,'double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(inverse(identity),'double$udivide'(X1,X2)),'double$udivide'(identity,X2))),inverse(X0))),
inference(demodulation,[status(thm)],[d121,d19]) ).
cnf(d123,plain,
X2 = 'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(inverse(identity),'double$udivide'(X0,X1)),'double$udivide'(identity,X1))),inverse(X2)),
inference(demodulation,[status(thm)],[d122,d22]) ).
cnf(d124,plain,
X0 = 'double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(identity,'double$udivide'(X1,X2)),'double$udivide'(identity,X2))),inverse(X0)),
inference(demodulation,[status(thm)],[d123,d19]) ).
cnf(d125,plain,
X2 = 'double$udivide'('double$udivide'(X0,'double$udivide'(inverse('double$udivide'(X0,X1)),'double$udivide'(identity,X1))),inverse(X2)),
inference(demodulation,[status(thm)],[d124,d41]) ).
cnf(d126,plain,
X2 = 'double$udivide'('double$udivide'(X0,'double$udivide'(multiply(X1,X0),'double$udivide'(identity,X1))),inverse(X2)),
inference(demodulation,[status(thm)],[d125,d0]) ).
cnf(d127,plain,
X1 = 'double$udivide'('double$udivide'(X2,'double$udivide'(multiply(X0,X2),inverse(X0))),inverse(X1)),
inference(demodulation,[status(thm)],[d126,d41]) ).
cnf(d128,plain,
inverse('double$udivide'(X0,X1)) = multiply(inverse(identity),'double$udivide'('double$udivide'(X2,'double$udivide'('double$udivide'(identity,'double$udivide'(X2,X3)),'double$udivide'(identity,X3))),inverse(multiply(X1,X0)))),
inference(superposition,[status(thm)],[d73,d116]) ).
cnf(d129,plain,
multiply(X1,X0) = multiply(inverse(identity),'double$udivide'('double$udivide'(X2,'double$udivide'('double$udivide'(identity,'double$udivide'(X2,X3)),'double$udivide'(identity,X3))),inverse(multiply(X1,X0)))),
inference(demodulation,[status(thm)],[d128,d0]) ).
cnf(d130,plain,
multiply(X0,X1) = multiply(identity,'double$udivide'('double$udivide'(X2,'double$udivide'('double$udivide'(identity,'double$udivide'(X2,X3)),'double$udivide'(identity,X3))),inverse(multiply(X0,X1)))),
inference(demodulation,[status(thm)],[d129,d19]) ).
cnf(d131,plain,
multiply(X2,X3) = 'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(identity,'double$udivide'(X0,X1)),'double$udivide'(identity,X1))),inverse(multiply(X2,X3))),
inference(demodulation,[status(thm)],[d130,d22]) ).
cnf(d132,plain,
multiply(X2,X3) = 'double$udivide'('double$udivide'(X0,'double$udivide'(inverse('double$udivide'(X0,X1)),'double$udivide'(identity,X1))),inverse(multiply(X2,X3))),
inference(demodulation,[status(thm)],[d131,d41]) ).
cnf(d133,plain,
multiply(X2,X3) = 'double$udivide'('double$udivide'(X0,'double$udivide'(multiply(X1,X0),'double$udivide'(identity,X1))),inverse(multiply(X2,X3))),
inference(demodulation,[status(thm)],[d132,d0]) ).
cnf(d134,plain,
multiply(X1,X2) = 'double$udivide'('double$udivide'(X3,'double$udivide'(multiply(X0,X3),inverse(X0))),inverse(multiply(X1,X2))),
inference(demodulation,[status(thm)],[d133,d41]) ).
cnf(d135,plain,
multiply(X2,X3) = multiply(X2,X3),
inference(demodulation,[status(thm)],[d134,d127]) ).
cnf(d136,plain,
X1 = multiply(multiply(X0,X1),inverse(X0)),
inference(superposition,[status(thm)],[d115,d135]) ).
cnf(d137,plain,
multiply(inverse(X1),multiply(X0,X1)) = X0,
inference(superposition,[status(thm)],[d58,d93]) ).
cnf(d138,plain,
multiply(X1,X0) = multiply(X1,inverse(inverse(X0))),
inference(superposition,[status(thm)],[d137,d136]) ).
cnf(d139,plain,
multiply(X0,X1) = 'double$udivide'(inverse(X1),inverse(X0)),
inference(demodulation,[status(thm)],[d138,d96]) ).
cnf(d140,plain,
multiply(multiply(inverse(X0),X1),X0) = X1,
inference(superposition,[status(thm)],[d21,d115]) ).
cnf(d141,plain,
inverse('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2)))) = multiply(inverse(identity),'double$udivide'('double$udivide'(X3,'double$udivide'('double$udivide'(inverse(identity),'double$udivide'(X3,X4)),'double$udivide'(identity,X4))),inverse(X1))),
inference(superposition,[status(thm)],[d42,d116]) ).
cnf(d142,plain,
multiply('double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2)),X0) = multiply(inverse(identity),'double$udivide'('double$udivide'(X3,'double$udivide'('double$udivide'(inverse(identity),'double$udivide'(X3,X4)),'double$udivide'(identity,X4))),inverse(X1))),
inference(demodulation,[status(thm)],[d141,d0]) ).
cnf(d143,plain,
multiply('double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),inverse(X0)),X2) = multiply(inverse(identity),'double$udivide'('double$udivide'(X3,'double$udivide'('double$udivide'(inverse(identity),'double$udivide'(X3,X4)),'double$udivide'(identity,X4))),inverse(X1))),
inference(demodulation,[status(thm)],[d142,d41]) ).
cnf(d144,plain,
multiply('double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),inverse(X2)),X1) = multiply(identity,'double$udivide'('double$udivide'(X3,'double$udivide'('double$udivide'(inverse(identity),'double$udivide'(X3,X4)),'double$udivide'(identity,X4))),inverse(X0))),
inference(demodulation,[status(thm)],[d143,d19]) ).
cnf(d145,plain,
multiply('double$udivide'('double$udivide'(X2,'double$udivide'(X3,X4)),inverse(X4)),X3) = 'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(inverse(identity),'double$udivide'(X0,X1)),'double$udivide'(identity,X1))),inverse(X2)),
inference(demodulation,[status(thm)],[d144,d22]) ).
cnf(d146,plain,
multiply('double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),inverse(X2)),X1) = 'double$udivide'('double$udivide'(X3,'double$udivide'('double$udivide'(identity,'double$udivide'(X3,X4)),'double$udivide'(identity,X4))),inverse(X0)),
inference(demodulation,[status(thm)],[d145,d19]) ).
cnf(d147,plain,
multiply('double$udivide'('double$udivide'(X2,'double$udivide'(X3,X4)),inverse(X4)),X3) = 'double$udivide'('double$udivide'(X0,'double$udivide'(inverse('double$udivide'(X0,X1)),'double$udivide'(identity,X1))),inverse(X2)),
inference(demodulation,[status(thm)],[d146,d41]) ).
cnf(d148,plain,
multiply('double$udivide'('double$udivide'(X2,'double$udivide'(X3,X4)),inverse(X4)),X3) = 'double$udivide'('double$udivide'(X0,'double$udivide'(multiply(X1,X0),'double$udivide'(identity,X1))),inverse(X2)),
inference(demodulation,[status(thm)],[d147,d0]) ).
cnf(d149,plain,
multiply('double$udivide'('double$udivide'(X1,'double$udivide'(X2,X3)),inverse(X3)),X2) = 'double$udivide'('double$udivide'(X4,'double$udivide'(multiply(X0,X4),inverse(X0))),inverse(X1)),
inference(demodulation,[status(thm)],[d148,d41]) ).
cnf(d150,plain,
multiply('double$udivide'('double$udivide'(X2,'double$udivide'(X3,X4)),inverse(X4)),X3) = X2,
inference(demodulation,[status(thm)],[d149,d127]) ).
cnf(d151,plain,
multiply(inverse(X1),multiply(X1,X0)) = X0,
inference(superposition,[status(thm)],[d127,d150]) ).
cnf(d152,plain,
multiply(X1,X0) = multiply(X0,X1),
inference(superposition,[status(thm)],[d151,d140]) ).
cnf(d153,plain,
inverse(X1) = multiply(inverse(identity),'double$udivide'(X0,'double$udivide'('double$udivide'(X1,inverse(X0)),inverse(identity)))),
inference(superposition,[status(thm)],[d10,d0]) ).
cnf(d154,plain,
inverse('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2)))) = multiply(inverse(identity),'double$udivide'(identity,'double$udivide'(X1,inverse(identity)))),
inference(superposition,[status(thm)],[d1,d153]) ).
cnf(d155,plain,
multiply('double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2)),X0) = multiply(inverse(identity),'double$udivide'(identity,'double$udivide'(X1,inverse(identity)))),
inference(demodulation,[status(thm)],[d154,d0]) ).
cnf(d156,plain,
multiply(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),'double$udivide'(identity,X2))) = multiply(inverse(identity),'double$udivide'(identity,'double$udivide'(X0,inverse(identity)))),
inference(demodulation,[status(thm)],[d155,d152]) ).
cnf(d157,plain,
multiply(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X1,X0)),inverse(X0))) = multiply(inverse(identity),'double$udivide'(identity,'double$udivide'(X2,inverse(identity)))),
inference(demodulation,[status(thm)],[d156,d41]) ).
cnf(d158,plain,
multiply(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),inverse(X2))) = multiply(identity,'double$udivide'(identity,'double$udivide'(X1,inverse(identity)))),
inference(demodulation,[status(thm)],[d157,d19]) ).
cnf(d159,plain,
multiply(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),inverse(X2))) = 'double$udivide'(identity,'double$udivide'(X0,inverse(identity))),
inference(demodulation,[status(thm)],[d158,d22]) ).
cnf(d160,plain,
multiply(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),inverse(X2))) = inverse('double$udivide'(X0,inverse(identity))),
inference(demodulation,[status(thm)],[d159,d41]) ).
cnf(d161,plain,
multiply(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),inverse(X2))) = multiply(inverse(identity),X0),
inference(demodulation,[status(thm)],[d160,d0]) ).
cnf(d162,plain,
multiply(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),inverse(X2))) = multiply(identity,X1),
inference(demodulation,[status(thm)],[d161,d19]) ).
cnf(d163,plain,
multiply(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),inverse(X2))) = X0,
inference(demodulation,[status(thm)],[d162,d22]) ).
cnf(d164,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)) = 'double$udivide'(X0,'double$udivide'('double$udivide'(X1,inverse(X0)),inverse(identity))),
inference(superposition,[status(thm)],[d10,d10]) ).
cnf(d165,plain,
inverse(X0) = multiply(inverse(identity),'double$udivide'('double$udivide'(X1,inverse(X0)),'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)),'double$udivide'(identity,inverse(identity))))),
inference(superposition,[status(thm)],[d164,d42]) ).
cnf(d166,plain,
inverse(X0) = multiply(identity,'double$udivide'('double$udivide'(X1,inverse(X0)),'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)),'double$udivide'(identity,inverse(identity))))),
inference(demodulation,[status(thm)],[d165,d19]) ).
cnf(d167,plain,
inverse(X1) = 'double$udivide'('double$udivide'(X0,inverse(X1)),'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X0,inverse(identity))),inverse(identity)),'double$udivide'(identity,inverse(identity)))),
inference(demodulation,[status(thm)],[d166,d22]) ).
cnf(d168,plain,
inverse(X1) = 'double$udivide'('double$udivide'(X0,inverse(X1)),'double$udivide'('double$udivide'(inverse('double$udivide'(X0,inverse(identity))),inverse(identity)),'double$udivide'(identity,inverse(identity)))),
inference(demodulation,[status(thm)],[d167,d41]) ).
cnf(d169,plain,
inverse(X1) = 'double$udivide'('double$udivide'(X0,inverse(X1)),'double$udivide'('double$udivide'(multiply(inverse(identity),X0),inverse(identity)),'double$udivide'(identity,inverse(identity)))),
inference(demodulation,[status(thm)],[d168,d0]) ).
cnf(d170,plain,
inverse(X0) = 'double$udivide'('double$udivide'(X1,inverse(X0)),'double$udivide'('double$udivide'(multiply(identity,X1),inverse(identity)),'double$udivide'(identity,inverse(identity)))),
inference(demodulation,[status(thm)],[d169,d19]) ).
cnf(d171,plain,
inverse(X1) = 'double$udivide'('double$udivide'(X0,inverse(X1)),'double$udivide'('double$udivide'(X0,inverse(identity)),'double$udivide'(identity,inverse(identity)))),
inference(demodulation,[status(thm)],[d170,d22]) ).
cnf(d172,plain,
inverse(X0) = 'double$udivide'('double$udivide'(X1,inverse(X0)),'double$udivide'('double$udivide'(X1,identity),'double$udivide'(identity,inverse(identity)))),
inference(demodulation,[status(thm)],[d171,d19]) ).
cnf(d173,plain,
inverse(X1) = 'double$udivide'('double$udivide'(X0,inverse(X1)),'double$udivide'(inverse(X0),'double$udivide'(identity,inverse(identity)))),
inference(demodulation,[status(thm)],[d172,c2]) ).
cnf(d174,plain,
inverse(X0) = 'double$udivide'('double$udivide'(X1,inverse(X0)),'double$udivide'(inverse(X1),inverse(inverse(identity)))),
inference(demodulation,[status(thm)],[d173,d41]) ).
cnf(d175,plain,
inverse(X0) = 'double$udivide'('double$udivide'(X1,inverse(X0)),'double$udivide'(inverse(X1),identity)),
inference(demodulation,[status(thm)],[d174,d21]) ).
cnf(d176,plain,
inverse(X1) = 'double$udivide'('double$udivide'(X0,inverse(X1)),inverse(inverse(X0))),
inference(demodulation,[status(thm)],[d175,c2]) ).
cnf(d177,plain,
inverse(X1) = 'double$udivide'('double$udivide'(X0,inverse(X1)),X0),
inference(demodulation,[status(thm)],[d176,d21]) ).
cnf(d178,plain,
multiply(X0,'double$udivide'(inverse(X2),inverse(X1))) = 'double$udivide'('double$udivide'(X0,X1),inverse(X2)),
inference(superposition,[status(thm)],[d177,d163]) ).
cnf(d179,plain,
multiply(X2,multiply(X1,X0)) = 'double$udivide'('double$udivide'(X2,X1),inverse(X0)),
inference(demodulation,[status(thm)],[d178,d139]) ).
cnf(d180,plain,
multiply(inverse(X0),X1) = multiply(X1,inverse(X0)),
inference(superposition,[status(thm)],[d94,d151]) ).
cnf(d181,plain,
multiply(inverse(X1),X0) = 'double$udivide'(X1,inverse(X0)),
inference(demodulation,[status(thm)],[d180,d96]) ).
cnf(d182,plain,
inverse(multiply(X0,X1)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d151,d105]) ).
cnf(d183,plain,
'double$udivide'(X0,X1) = 'double$udivide'(X1,X0),
inference(superposition,[status(thm)],[d182,d34]) ).
cnf(d184,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,inverse(X0)),'double$udivide'(identity,identity))),multiply(X1,X2)),inverse(identity)) = X2,
inference(superposition,[status(thm)],[c2,d5]) ).
cnf(d185,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,inverse(X0)),inverse(identity))),multiply(X1,X2)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d184,c2]) ).
cnf(d186,plain,
'double$udivide'(multiply(X1,X0),inverse(identity)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d0,d8]) ).
cnf(d187,plain,
'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X1,X0),inverse(identity))),multiply(multiply(X0,X1),X2)),inverse(identity)) = X2,
inference(superposition,[status(thm)],[d186,d185]) ).
cnf(d188,plain,
'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X0,X1),inverse(identity))),multiply(multiply(X1,X0),X2))) = X2,
inference(demodulation,[status(thm)],[d187,d183]) ).
cnf(d189,plain,
'double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X0,X1),inverse(identity))),multiply(multiply(X1,X0),X2))) = X2,
inference(demodulation,[status(thm)],[d188,d19]) ).
cnf(d190,plain,
inverse('double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X0,X1),inverse(identity))),multiply(multiply(X1,X0),X2))) = X2,
inference(demodulation,[status(thm)],[d189,d41]) ).
cnf(d191,plain,
multiply(multiply(multiply(X1,X0),X2),'double$udivide'(identity,'double$udivide'('double$udivide'(X0,X1),inverse(identity)))) = X2,
inference(demodulation,[status(thm)],[d190,d0]) ).
cnf(d192,plain,
multiply(multiply(multiply(X1,X0),X2),inverse('double$udivide'('double$udivide'(X0,X1),inverse(identity)))) = X2,
inference(demodulation,[status(thm)],[d191,d41]) ).
cnf(d193,plain,
multiply(multiply(multiply(X1,X0),X2),multiply(inverse(identity),'double$udivide'(X0,X1))) = X2,
inference(demodulation,[status(thm)],[d192,d0]) ).
cnf(d194,plain,
multiply(multiply(multiply(X0,X1),X2),multiply(identity,'double$udivide'(X1,X0))) = X2,
inference(demodulation,[status(thm)],[d193,d19]) ).
cnf(d195,plain,
multiply(multiply(identity,'double$udivide'(X1,X0)),multiply(multiply(X0,X1),X2)) = X2,
inference(demodulation,[status(thm)],[d194,d152]) ).
cnf(d196,plain,
multiply('double$udivide'(X0,X1),multiply(multiply(X1,X0),X2)) = X2,
inference(demodulation,[status(thm)],[d195,d22]) ).
cnf(d197,plain,
multiply(inverse('double$udivide'(X0,X1)),X2) = multiply(multiply(X1,X0),X2),
inference(superposition,[status(thm)],[d196,d151]) ).
cnf(d198,plain,
'double$udivide'('double$udivide'(X0,X1),inverse(X2)) = multiply(multiply(X1,X0),X2),
inference(demodulation,[status(thm)],[d197,d181]) ).
cnf(d199,plain,
multiply(X0,multiply(X1,X2)) = multiply(multiply(X1,X0),X2),
inference(demodulation,[status(thm)],[d198,d179]) ).
cnf(d200,plain,
X1 = multiply(multiply(inverse(X0),X1),X0),
inference(superposition,[status(thm)],[d140,d135]) ).
cnf(d201,plain,
X1 = multiply(X0,multiply(inverse(X0),X1)),
inference(demodulation,[status(thm)],[d200,d152]) ).
cnf(d202,plain,
'double$udivide'(inverse(X0),multiply(identity,X0)) = identity,
inference(superposition,[status(thm)],[d11,c3]) ).
cnf(d203,plain,
inverse(X1) = multiply(inverse(identity),'double$udivide'(inverse(X0),'double$udivide'('double$udivide'(X1,identity),'double$udivide'(identity,multiply(identity,X0))))),
inference(superposition,[status(thm)],[d202,d42]) ).
cnf(d204,plain,
inverse(X0) = multiply(identity,'double$udivide'(inverse(X1),'double$udivide'('double$udivide'(X0,identity),'double$udivide'(identity,multiply(identity,X1))))),
inference(demodulation,[status(thm)],[d203,d19]) ).
cnf(d205,plain,
inverse(X1) = 'double$udivide'(inverse(X0),'double$udivide'('double$udivide'(X1,identity),'double$udivide'(identity,multiply(identity,X0)))),
inference(demodulation,[status(thm)],[d204,d22]) ).
cnf(d206,plain,
inverse(X0) = 'double$udivide'(inverse(X1),'double$udivide'(inverse(X0),'double$udivide'(identity,multiply(identity,X1)))),
inference(demodulation,[status(thm)],[d205,c2]) ).
cnf(d207,plain,
inverse(X1) = 'double$udivide'(inverse(X0),'double$udivide'(inverse(X1),inverse(multiply(identity,X0)))),
inference(demodulation,[status(thm)],[d206,d41]) ).
cnf(d208,plain,
inverse(X1) = 'double$udivide'(inverse(X0),'double$udivide'(inverse(X1),'double$udivide'(X0,identity))),
inference(demodulation,[status(thm)],[d207,d34]) ).
cnf(d209,plain,
inverse(X1) = 'double$udivide'(inverse(X0),'double$udivide'(inverse(X1),inverse(X0))),
inference(demodulation,[status(thm)],[d208,c2]) ).
cnf(d210,plain,
inverse(X1) = inverse(X1),
inference(demodulation,[status(thm)],[d209,d48]) ).
cnf(d211,plain,
'double$udivide'(X1,X0) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[d34,d210]) ).
cnf(d212,plain,
'double$udivide'(X1,X0) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[d152,d211]) ).
cnf(d213,plain,
X2 = multiply(multiply(X0,X1),multiply('double$udivide'(X0,X1),X2)),
inference(superposition,[status(thm)],[d212,d201]) ).
cnf(d214,plain,
X2 = multiply(X1,multiply(X0,multiply('double$udivide'(X0,X1),X2))),
inference(demodulation,[status(thm)],[d213,d199]) ).
cnf(d215,plain,
inverse(identity) = multiply(multiply(X1,X0),'double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[d0,d6]) ).
cnf(d216,plain,
inverse(identity) = multiply(inverse(identity),'double$udivide'('double$udivide'(X1,X0),multiply(X0,X1))),
inference(superposition,[status(thm)],[d215,d215]) ).
cnf(d217,plain,
identity = multiply(inverse(identity),'double$udivide'('double$udivide'(X0,X1),multiply(X1,X0))),
inference(demodulation,[status(thm)],[d216,d19]) ).
cnf(d218,plain,
identity = multiply(identity,'double$udivide'('double$udivide'(X0,X1),multiply(X1,X0))),
inference(demodulation,[status(thm)],[d217,d19]) ).
cnf(d219,plain,
identity = 'double$udivide'('double$udivide'(X0,X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d218,d22]) ).
cnf(d220,plain,
multiply(identity,multiply(multiply(multiply(X1,X0),'double$udivide'(X0,X1)),X2)) = X2,
inference(superposition,[status(thm)],[d219,d196]) ).
cnf(d221,plain,
multiply(multiply(multiply(X0,X1),'double$udivide'(X1,X0)),X2) = X2,
inference(demodulation,[status(thm)],[d220,d22]) ).
cnf(d222,plain,
multiply('double$udivide'(X1,X0),multiply(multiply(X0,X1),X2)) = X2,
inference(demodulation,[status(thm)],[d221,d199]) ).
cnf(d223,plain,
multiply('double$udivide'(X1,X0),multiply(X1,multiply(X0,X2))) = X2,
inference(demodulation,[status(thm)],[d222,d199]) ).
cnf(d224,plain,
multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,X2)),
inference(superposition,[status(thm)],[d223,d214]) ).
cnf(d225,plain,
'double$udivide'('double$udivide'(inverse(X0),'double$udivide'('double$udivide'(X1,identity),'double$udivide'(identity,multiply(identity,X0)))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[d202,d1]) ).
cnf(d226,plain,
'double$udivide'('double$udivide'(inverse(X1),'double$udivide'(inverse(X0),'double$udivide'(identity,multiply(identity,X1)))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d225,c2]) ).
cnf(d227,plain,
'double$udivide'('double$udivide'(inverse(X1),'double$udivide'(multiply(identity,X0),'double$udivide'(identity,multiply(identity,X1)))),inverse(identity)) = inverse(X0),
inference(superposition,[status(thm)],[d11,d226]) ).
cnf(d228,plain,
'double$udivide'('double$udivide'(inverse(X1),'double$udivide'(X0,'double$udivide'(identity,multiply(identity,X1)))),inverse(identity)) = inverse(X0),
inference(demodulation,[status(thm)],[d227,d22]) ).
cnf(d229,plain,
'double$udivide'('double$udivide'(inverse(X0),'double$udivide'(X1,inverse(multiply(identity,X0)))),inverse(identity)) = inverse(X1),
inference(demodulation,[status(thm)],[d228,d41]) ).
cnf(d230,plain,
'double$udivide'('double$udivide'(inverse(X0),'double$udivide'(X1,'double$udivide'(X0,identity))),inverse(identity)) = inverse(X1),
inference(demodulation,[status(thm)],[d229,d34]) ).
cnf(d231,plain,
'double$udivide'('double$udivide'(inverse(X0),'double$udivide'(X1,inverse(X0))),inverse(identity)) = inverse(X1),
inference(demodulation,[status(thm)],[d230,c2]) ).
cnf(d232,plain,
'double$udivide'('double$udivide'(inverse(X0),'double$udivide'(X1,inverse(X0))),identity) = inverse(X1),
inference(demodulation,[status(thm)],[d231,d19]) ).
cnf(d233,plain,
inverse('double$udivide'(inverse(X0),'double$udivide'(X1,inverse(X0)))) = inverse(X1),
inference(demodulation,[status(thm)],[d232,c2]) ).
cnf(d234,plain,
multiply('double$udivide'(X1,inverse(X0)),inverse(X0)) = inverse(X1),
inference(demodulation,[status(thm)],[d233,d0]) ).
cnf(d235,plain,
multiply(inverse(X1),'double$udivide'(X0,inverse(X1))) = inverse(X0),
inference(demodulation,[status(thm)],[d234,d152]) ).
cnf(d236,plain,
'double$udivide'(X1,inverse(X0)) = multiply(X0,inverse(X1)),
inference(superposition,[status(thm)],[d235,d201]) ).
cnf(d237,plain,
multiply(X2,multiply(X1,X0)) = multiply(X2,inverse('double$udivide'(X0,X1))),
inference(superposition,[status(thm)],[d94,d83]) ).
cnf(d238,plain,
multiply(X0,multiply(X2,X1)) = 'double$udivide'('double$udivide'(X1,X2),inverse(X0)),
inference(demodulation,[status(thm)],[d237,d236]) ).
cnf(d239,plain,
multiply(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),inverse(X2))) = X0,
inference(demodulation,[status(thm)],[d150,d152]) ).
cnf(d240,plain,
multiply(X1,multiply(X2,multiply('double$udivide'(X1,X2),X0))) = X0,
inference(demodulation,[status(thm)],[d239,d238]) ).
cnf(d241,plain,
multiply('double$udivide'(X1,X0),multiply(X2,multiply(X0,X1))) = X2,
inference(superposition,[status(thm)],[d211,d137]) ).
cnf(d242,plain,
multiply(X0,multiply(X1,X2)) = multiply(X2,multiply(X1,X0)),
inference(superposition,[status(thm)],[d241,d240]) ).
cnf(d243,plain,
( multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3)
| multiply(b4,a4) != multiply(a4,b4)
| inverse(identity) != identity
| multiply(identity,a2) != a2 ),
inference(demodulation,[status(thm)],[c4,d6]) ).
cnf(d244,plain,
( multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3)
| multiply(b4,a4) != multiply(a4,b4)
| multiply(identity,a2) != a2 ),
inference(resolution,[status(thm)],[d19,d243]) ).
cnf(d245,plain,
( multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3)
| multiply(b4,a4) != multiply(a4,b4)
| a2 != a2 ),
inference(demodulation,[status(thm)],[d244,d22]) ).
cnf(d246,plain,
( multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3)
| multiply(b4,a4) != multiply(b4,a4)
| a2 != a2 ),
inference(demodulation,[status(thm)],[d245,d152]) ).
cnf(d247,plain,
( multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(a3,b3))
| multiply(b4,a4) != multiply(b4,a4)
| a2 != a2 ),
inference(demodulation,[status(thm)],[d246,d152]) ).
cnf(d248,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,identity),'double$udivide'(identity,inverse(X0)))),multiply(X1,X2)),inverse(identity)) = X2,
inference(superposition,[status(thm)],[c3,d5]) ).
cnf(d249,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'(inverse(X0),'double$udivide'(identity,inverse(X1)))),multiply(X0,X2)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d248,c2]) ).
cnf(d250,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'(multiply(identity,X0),'double$udivide'(identity,inverse(X1)))),multiply(inverse(X0),X2)),inverse(identity)) = X2,
inference(superposition,[status(thm)],[d11,d249]) ).
cnf(d251,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'(X0,'double$udivide'(identity,inverse(X1)))),multiply(inverse(X0),X2)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d250,d22]) ).
cnf(d252,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'(X1,inverse(inverse(X0)))),multiply(inverse(X1),X2)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d251,d41]) ).
cnf(d253,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'(X1,X0)),multiply(inverse(X1),X2)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d252,d21]) ).
cnf(d254,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'(X1,X0)),multiply(inverse(X1),X2)),identity) = X2,
inference(demodulation,[status(thm)],[d253,d19]) ).
cnf(d255,plain,
inverse('double$udivide'('double$udivide'(X0,'double$udivide'(X1,X0)),multiply(inverse(X1),X2))) = X2,
inference(demodulation,[status(thm)],[d254,c2]) ).
cnf(d256,plain,
multiply(multiply(inverse(X1),X2),'double$udivide'(X0,'double$udivide'(X1,X0))) = X2,
inference(demodulation,[status(thm)],[d255,d0]) ).
cnf(d257,plain,
'double$udivide'('double$udivide'('double$udivide'(inverse(X0),'double$udivide'('double$udivide'(X1,identity),'double$udivide'(identity,multiply(identity,X0)))),multiply(X1,X2)),inverse(identity)) = X2,
inference(superposition,[status(thm)],[d202,d5]) ).
cnf(d258,plain,
'double$udivide'('double$udivide'('double$udivide'(inverse(X1),'double$udivide'(inverse(X0),'double$udivide'(identity,multiply(identity,X1)))),multiply(X0,X2)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d257,c2]) ).
cnf(d259,plain,
'double$udivide'('double$udivide'('double$udivide'(inverse(X1),'double$udivide'(multiply(identity,X0),'double$udivide'(identity,multiply(identity,X1)))),multiply(inverse(X0),X2)),inverse(identity)) = X2,
inference(superposition,[status(thm)],[d11,d258]) ).
cnf(d260,plain,
'double$udivide'('double$udivide'('double$udivide'(inverse(X1),'double$udivide'(X0,'double$udivide'(identity,multiply(identity,X1)))),multiply(inverse(X0),X2)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d259,d22]) ).
cnf(d261,plain,
'double$udivide'('double$udivide'('double$udivide'(inverse(X0),'double$udivide'(X1,inverse(multiply(identity,X0)))),multiply(inverse(X1),X2)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d260,d41]) ).
cnf(d262,plain,
'double$udivide'('double$udivide'('double$udivide'(inverse(X0),'double$udivide'(X1,'double$udivide'(X0,identity))),multiply(inverse(X1),X2)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d261,d34]) ).
cnf(d263,plain,
'double$udivide'('double$udivide'('double$udivide'(inverse(X0),'double$udivide'(X1,inverse(X0))),multiply(inverse(X1),X2)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d262,c2]) ).
cnf(d264,plain,
'double$udivide'('double$udivide'('double$udivide'(inverse(X0),'double$udivide'(X1,inverse(X0))),multiply(inverse(X1),X2)),identity) = X2,
inference(demodulation,[status(thm)],[d263,d19]) ).
cnf(d265,plain,
inverse('double$udivide'('double$udivide'(inverse(X0),'double$udivide'(X1,inverse(X0))),multiply(inverse(X1),X2))) = X2,
inference(demodulation,[status(thm)],[d264,c2]) ).
cnf(d266,plain,
multiply(multiply(inverse(X1),X2),'double$udivide'(inverse(X0),'double$udivide'(X1,inverse(X0)))) = X2,
inference(demodulation,[status(thm)],[d265,d0]) ).
cnf(d267,plain,
X1 = X1,
inference(demodulation,[status(thm)],[d266,d256]) ).
cnf(d268,plain,
( multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(a3,b3))
| multiply(b4,a4) != multiply(b4,a4) ),
inference(resolution,[status(thm)],[d267,d247]) ).
cnf(d269,plain,
multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(a3,b3)),
inference(equality_resolution,[status(thm)],[d268]) ).
cnf(d270,plain,
multiply(a3,multiply(b3,c3)) != multiply(b3,multiply(a3,c3)),
inference(demodulation,[status(thm)],[d269,d242]) ).
cnf(d271,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm)],[d270,d224]) ).
cnf(d272,plain,
$false,
inference(resolution,[status(thm)],[d267,d271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP099-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:24:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 168.12/43.75 % SZS status Unsatisfiable for theBenchmark.p
% 168.12/43.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------