%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP568-1 : 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 : n020.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 07:24:02 AM UTC 2026
% Result : Unsatisfiable 19.79s 4.91s
% Output : CNFRefutation 19.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 5
% Syntax : Number of clauses : 165 ( 165 unt; 0 nHn; 5 RR)
% Number of literals : 165 ( 164 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 442 ( 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$udivide'(X0,inverse(X0)) ).
cnf(prove_these_axioms_4,negated_conjecture,
multiply(a,b) != multiply(b,a) ).
cnf(c0,plain,
'double$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,
multiply(X0,X1) = 'double$udivide'('double$udivide'(X1,X0),identity),
inference(clausification,[status(esa)],[multiply]) ).
cnf(c2,plain,
inverse(X0) = 'double$udivide'(X0,identity),
inference(clausification,[status(esa)],[inverse]) ).
cnf(c3,plain,
identity = 'double$udivide'(X0,inverse(X0)),
inference(clausification,[status(esa)],[identity]) ).
cnf(c4,plain,
multiply(a,b) != multiply(b,a),
inference(clausification,[status(esa)],[prove_these_axioms_4]) ).
cnf(d0,plain,
multiply(X1,X0) = inverse('double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
'double$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$udivide'(X0,'double$udivide'('double$udivide'(X1,inverse(X0)),'double$udivide'(identity,identity))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[c2,d1]) ).
cnf(d3,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,inverse(X0)),inverse(identity))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(identity,inverse(identity))),inverse(identity)) = X0,
inference(superposition,[status(thm)],[c3,d3]) ).
cnf(d5,plain,
'double$udivide'('double$udivide'(X0,identity),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
'double$udivide'(inverse(X0),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d8,plain,
'double$udivide'('double$udivide'(inverse(X0),'double$udivide'('double$udivide'(X1,multiply(identity,X0)),inverse(identity))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,inverse(identity))),identity)),inverse(identity)) = X1,
inference(superposition,[status(thm)],[c3,d1]) ).
cnf(d10,plain,
'double$udivide'('double$udivide'(X1,inverse('double$udivide'(X0,'double$udivide'(X1,inverse(identity))))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
'double$udivide'('double$udivide'(X1,multiply('double$udivide'(X1,inverse(identity)),X0)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
'double$udivide'('double$udivide'(identity,multiply(identity,X0)),inverse(identity)) = X0,
inference(superposition,[status(thm)],[c3,d11]) ).
cnf(d13,plain,
'double$udivide'('double$udivide'(inverse(X0),X0),inverse(identity)) = identity,
inference(superposition,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
'double$udivide'(inverse(inverse(identity)),inverse(identity)) = identity,
inference(superposition,[status(thm)],[c2,d13]) ).
cnf(d15,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm)],[d14,d6]) ).
cnf(d16,plain,
'double$udivide'(inverse(X0),identity) = X0,
inference(demodulation,[status(thm)],[d6,d15]) ).
cnf(d17,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d16,c2]) ).
cnf(d18,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,identity),'double$udivide'(identity,inverse(X0)))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[c3,d1]) ).
cnf(d19,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'(inverse(X0),'double$udivide'(identity,inverse(X1)))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d18,c2]) ).
cnf(d20,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(X0),identity)),inverse(identity)) = X0,
inference(superposition,[status(thm)],[c3,d19]) ).
cnf(d21,plain,
'double$udivide'('double$udivide'(identity,inverse(inverse(X0))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d20,c2]) ).
cnf(d22,plain,
'double$udivide'('double$udivide'(identity,X0),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d21,d17]) ).
cnf(d23,plain,
'double$udivide'('double$udivide'(identity,X0),identity) = X0,
inference(demodulation,[status(thm)],[d22,d15]) ).
cnf(d24,plain,
inverse('double$udivide'(identity,X0)) = X0,
inference(demodulation,[status(thm)],[d23,c2]) ).
cnf(d25,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d24,d0]) ).
cnf(d26,plain,
'double$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)],[d11,d3]) ).
cnf(d27,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X0,identity)),inverse(identity)) = 'double$udivide'(X1,multiply('double$udivide'(X1,inverse(identity)),X0)),
inference(demodulation,[status(thm)],[d26,d15]) ).
cnf(d28,plain,
'double$udivide'('double$udivide'(identity,inverse(X0)),inverse(identity)) = 'double$udivide'(X1,multiply('double$udivide'(X1,inverse(identity)),X0)),
inference(demodulation,[status(thm)],[d27,c2]) ).
cnf(d29,plain,
'double$udivide'('double$udivide'(identity,inverse(X0)),identity) = 'double$udivide'(X1,multiply('double$udivide'(X1,inverse(identity)),X0)),
inference(demodulation,[status(thm)],[d28,d15]) ).
cnf(d30,plain,
inverse('double$udivide'(identity,inverse(X0))) = 'double$udivide'(X1,multiply('double$udivide'(X1,inverse(identity)),X0)),
inference(demodulation,[status(thm)],[d29,c2]) ).
cnf(d31,plain,
multiply(inverse(X0),identity) = 'double$udivide'(X1,multiply('double$udivide'(X1,inverse(identity)),X0)),
inference(demodulation,[status(thm)],[d30,d0]) ).
cnf(d32,plain,
inverse(X0) = 'double$udivide'(X1,multiply('double$udivide'(X1,inverse(identity)),X0)),
inference(demodulation,[status(thm)],[d31,d25]) ).
cnf(d33,plain,
inverse(X0) = 'double$udivide'(X1,multiply('double$udivide'(X1,identity),X0)),
inference(demodulation,[status(thm)],[d32,d15]) ).
cnf(d34,plain,
inverse(X1) = 'double$udivide'(X0,multiply(inverse(X0),X1)),
inference(demodulation,[status(thm)],[d33,c2]) ).
cnf(d35,plain,
'double$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)],[d11,d1]) ).
cnf(d36,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,multiply('double$udivide'(X0,identity),X1)),'double$udivide'('double$udivide'(X2,X1),'double$udivide'(identity,inverse(identity)))),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d35,d15]) ).
cnf(d37,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,multiply(inverse(X0),X1)),'double$udivide'('double$udivide'(X2,X1),'double$udivide'(identity,inverse(identity)))),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d36,c2]) ).
cnf(d38,plain,
'double$udivide'('double$udivide'(inverse(X1),'double$udivide'('double$udivide'(X2,X1),'double$udivide'(identity,inverse(identity)))),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d37,d34]) ).
cnf(d39,plain,
'double$udivide'('double$udivide'(inverse(X0),'double$udivide'('double$udivide'(X1,X0),identity)),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d38,c3]) ).
cnf(d40,plain,
'double$udivide'('double$udivide'(inverse(X1),inverse('double$udivide'(X0,X1))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d39,c2]) ).
cnf(d41,plain,
'double$udivide'('double$udivide'(inverse(X1),multiply(X1,X0)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d40,d0]) ).
cnf(d42,plain,
'double$udivide'('double$udivide'(inverse(X0),multiply(X0,X1)),identity) = X1,
inference(demodulation,[status(thm)],[d41,d15]) ).
cnf(d43,plain,
inverse('double$udivide'(inverse(X0),multiply(X0,X1))) = X1,
inference(demodulation,[status(thm)],[d42,c2]) ).
cnf(d44,plain,
multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(demodulation,[status(thm)],[d43,d0]) ).
cnf(d45,plain,
multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[d7,d17]) ).
cnf(d46,plain,
multiply(inverse(identity),'double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2)))) = inverse(X1),
inference(superposition,[status(thm)],[d1,d0]) ).
cnf(d47,plain,
multiply(inverse(identity),'double$udivide'(X0,'double$udivide'('double$udivide'(X1,identity),'double$udivide'(identity,inverse(X0))))) = inverse(X1),
inference(superposition,[status(thm)],[c3,d46]) ).
cnf(d48,plain,
multiply(identity,'double$udivide'(X0,'double$udivide'('double$udivide'(X1,identity),'double$udivide'(identity,inverse(X0))))) = inverse(X1),
inference(demodulation,[status(thm)],[d47,d15]) ).
cnf(d49,plain,
'double$udivide'(X0,'double$udivide'('double$udivide'(X1,identity),'double$udivide'(identity,inverse(X0)))) = inverse(X1),
inference(demodulation,[status(thm)],[d48,d45]) ).
cnf(d50,plain,
'double$udivide'(X1,'double$udivide'(inverse(X0),'double$udivide'(identity,inverse(X1)))) = inverse(X0),
inference(demodulation,[status(thm)],[d49,c2]) ).
cnf(d51,plain,
multiply(inverse(identity),'double$udivide'('double$udivide'(X0,'double$udivide'(inverse(X1),'double$udivide'(identity,inverse(X0)))),'double$udivide'('double$udivide'(X2,X1),'double$udivide'(identity,inverse(identity))))) = inverse(X2),
inference(superposition,[status(thm)],[d19,d46]) ).
cnf(d52,plain,
multiply(identity,'double$udivide'('double$udivide'(X0,'double$udivide'(inverse(X1),'double$udivide'(identity,inverse(X0)))),'double$udivide'('double$udivide'(X2,X1),'double$udivide'(identity,inverse(identity))))) = inverse(X2),
inference(demodulation,[status(thm)],[d51,d15]) ).
cnf(d53,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(inverse(X1),'double$udivide'(identity,inverse(X0)))),'double$udivide'('double$udivide'(X2,X1),'double$udivide'(identity,inverse(identity)))) = inverse(X2),
inference(demodulation,[status(thm)],[d52,d45]) ).
cnf(d54,plain,
'double$udivide'(inverse(X1),'double$udivide'('double$udivide'(X2,X1),'double$udivide'(identity,inverse(identity)))) = inverse(X2),
inference(demodulation,[status(thm)],[d53,d50]) ).
cnf(d55,plain,
'double$udivide'(inverse(X0),'double$udivide'('double$udivide'(X1,X0),identity)) = inverse(X1),
inference(demodulation,[status(thm)],[d54,c3]) ).
cnf(d56,plain,
'double$udivide'(inverse(X1),inverse('double$udivide'(X0,X1))) = inverse(X0),
inference(demodulation,[status(thm)],[d55,c2]) ).
cnf(d57,plain,
'double$udivide'(inverse(X1),multiply(X1,X0)) = inverse(X0),
inference(demodulation,[status(thm)],[d56,d0]) ).
cnf(d58,plain,
multiply(inverse(identity),'double$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(X3),
inference(superposition,[status(thm)],[d1,d46]) ).
cnf(d59,plain,
multiply(identity,'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$udivide'(identity,inverse(identity))))) = inverse(X3),
inference(demodulation,[status(thm)],[d58,d15]) ).
cnf(d60,plain,
'double$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(X3),
inference(demodulation,[status(thm)],[d59,d45]) ).
cnf(d61,plain,
'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(X3),
inference(demodulation,[status(thm)],[d60,c3]) ).
cnf(d62,plain,
'double$udivide'('double$udivide'(X2,'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X3)),'double$udivide'(identity,X3))),inverse('double$udivide'(X0,X1))) = inverse(X0),
inference(demodulation,[status(thm)],[d61,c2]) ).
cnf(d63,plain,
'double$udivide'('double$udivide'(X2,'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X3)),'double$udivide'(identity,X3))),multiply(X1,X0)) = inverse(X0),
inference(demodulation,[status(thm)],[d62,d0]) ).
cnf(d64,plain,
'double$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$udivide'(identity,inverse(identity)))),inverse(identity)) = X3,
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d65,plain,
'double$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)],[d64,c3]) ).
cnf(d66,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)],[d65,c2]) ).
cnf(d67,plain,
'double$udivide'('double$udivide'('double$udivide'(X2,'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X3)),'double$udivide'(identity,X3))),multiply(X1,X0)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d66,d0]) ).
cnf(d68,plain,
'double$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$udivide'(identity,inverse(identity)))),multiply(X4,X5)),inverse(identity)) = X5,
inference(superposition,[status(thm)],[d67,d67]) ).
cnf(d69,plain,
'double$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),identity)),multiply(X4,X5)),inverse(identity)) = X5,
inference(demodulation,[status(thm)],[d68,c3]) ).
cnf(d70,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)],[d69,c2]) ).
cnf(d71,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'('double$udivide'(X2,'double$udivide'('double$udivide'(X3,'double$udivide'(X2,X4)),'double$udivide'(identity,X4))),multiply(X3,X1)),multiply(X1,X0)),multiply(X0,X5)),inverse(identity)) = X5,
inference(demodulation,[status(thm)],[d70,d0]) ).
cnf(d72,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'('double$udivide'(X3,'double$udivide'('double$udivide'(X4,'double$udivide'(X3,X5)),'double$udivide'(identity,X5))),multiply(X4,X6)),multiply(X6,inverse(identity))),inverse(X1)),inverse(identity)) = 'double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2))),
inference(superposition,[status(thm)],[d46,d71]) ).
cnf(d73,plain,
'double$udivide'('double$udivide'('double$udivide'(inverse(X3),multiply(X3,inverse(identity))),inverse(X4)),inverse(identity)) = 'double$udivide'(X5,'double$udivide'('double$udivide'(X4,'double$udivide'(X5,X6)),'double$udivide'(identity,X6))),
inference(demodulation,[status(thm)],[d72,d63]) ).
cnf(d74,plain,
'double$udivide'('double$udivide'(inverse(inverse(identity)),inverse(X1)),inverse(identity)) = 'double$udivide'(X2,'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X3)),'double$udivide'(identity,X3))),
inference(demodulation,[status(thm)],[d73,d57]) ).
cnf(d75,plain,
'double$udivide'('double$udivide'(identity,inverse(X0)),inverse(identity)) = 'double$udivide'(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),'double$udivide'(identity,X2))),
inference(demodulation,[status(thm)],[d74,d17]) ).
cnf(d76,plain,
'double$udivide'('double$udivide'(identity,inverse(X0)),identity) = 'double$udivide'(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),'double$udivide'(identity,X2))),
inference(demodulation,[status(thm)],[d75,d15]) ).
cnf(d77,plain,
inverse('double$udivide'(identity,inverse(X0))) = 'double$udivide'(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),'double$udivide'(identity,X2))),
inference(demodulation,[status(thm)],[d76,c2]) ).
cnf(d78,plain,
multiply(inverse(X0),identity) = 'double$udivide'(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),'double$udivide'(identity,X2))),
inference(demodulation,[status(thm)],[d77,d0]) ).
cnf(d79,plain,
inverse(X0) = 'double$udivide'(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),'double$udivide'(identity,X2))),
inference(demodulation,[status(thm)],[d78,d25]) ).
cnf(d80,plain,
multiply(inverse(identity),'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2))),multiply(X1,X3))) = inverse(X3),
inference(superposition,[status(thm)],[d67,d0]) ).
cnf(d81,plain,
multiply(inverse(identity),'double$udivide'('double$udivide'(X4,'double$udivide'('double$udivide'(inverse(identity),'double$udivide'(X4,X5)),'double$udivide'(identity,X5))),inverse(X3))) = inverse('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)],[d80,d80]) ).
cnf(d82,plain,
multiply(identity,'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(inverse(identity),'double$udivide'(X0,X1)),'double$udivide'(identity,X1))),inverse(X2))) = inverse('double$udivide'('double$udivide'(X3,'double$udivide'('double$udivide'(X4,'double$udivide'(X3,X5)),'double$udivide'(identity,X5))),multiply(X4,X2))),
inference(demodulation,[status(thm)],[d81,d15]) ).
cnf(d83,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(inverse(identity),'double$udivide'(X0,X1)),'double$udivide'(identity,X1))),inverse(X2)) = inverse('double$udivide'('double$udivide'(X3,'double$udivide'('double$udivide'(X4,'double$udivide'(X3,X5)),'double$udivide'(identity,X5))),multiply(X4,X2))),
inference(demodulation,[status(thm)],[d82,d45]) ).
cnf(d84,plain,
'double$udivide'(inverse(inverse(identity)),inverse(X2)) = inverse('double$udivide'('double$udivide'(X3,'double$udivide'('double$udivide'(X4,'double$udivide'(X3,X5)),'double$udivide'(identity,X5))),multiply(X4,X2))),
inference(demodulation,[status(thm)],[d83,d79]) ).
cnf(d85,plain,
'double$udivide'(identity,inverse(X0)) = inverse('double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X1,X3)),'double$udivide'(identity,X3))),multiply(X2,X0))),
inference(demodulation,[status(thm)],[d84,d17]) ).
cnf(d86,plain,
'double$udivide'(identity,inverse(X3)) = multiply(multiply(X1,X3),'double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2)))),
inference(demodulation,[status(thm)],[d85,d0]) ).
cnf(d87,plain,
'double$udivide'(identity,inverse(X3)) = multiply(multiply(X1,X3),inverse(X1)),
inference(demodulation,[status(thm)],[d86,d79]) ).
cnf(d88,plain,
'double$udivide'(identity,inverse(X1)) = X1,
inference(demodulation,[status(thm)],[d87,d44]) ).
cnf(d89,plain,
multiply(inverse(identity),inverse(X0)) = inverse(X0),
inference(superposition,[status(thm)],[d6,d0]) ).
cnf(d90,plain,
multiply(identity,inverse(X0)) = inverse(X0),
inference(demodulation,[status(thm)],[d89,d15]) ).
cnf(d91,plain,
inverse(X0) = inverse(X0),
inference(demodulation,[status(thm)],[d90,d45]) ).
cnf(d92,plain,
X0 = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d17,d91]) ).
cnf(d93,plain,
'double$udivide'(identity,X0) = inverse(X0),
inference(superposition,[status(thm)],[d92,d88]) ).
cnf(d94,plain,
inverse(multiply(X1,X0)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d0,d17]) ).
cnf(d95,plain,
'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$udivide'(identity,inverse(identity)))),inverse(identity)) = X4,
inference(superposition,[status(thm)],[d67,d1]) ).
cnf(d96,plain,
'double$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$udivide'(X4,X3),identity)),inverse(identity)) = X4,
inference(demodulation,[status(thm)],[d95,c3]) ).
cnf(d97,plain,
'double$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))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d96,c2]) ).
cnf(d98,plain,
'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)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d97,d0]) ).
cnf(d99,plain,
multiply(inverse(X0),X0) = inverse(identity),
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d100,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X1,X3)),'double$udivide'(identity,X3))),multiply(X2,inverse(X0))),inverse(identity)),inverse(identity)) = X0,
inference(superposition,[status(thm)],[d99,d98]) ).
cnf(d101,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X1,X0)),inverse(X0))),multiply(X2,inverse(X3))),inverse(identity)),inverse(identity)) = X3,
inference(demodulation,[status(thm)],[d100,d93]) ).
cnf(d102,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),inverse(X2))),multiply(X1,inverse(X3))),identity),inverse(identity)) = X3,
inference(demodulation,[status(thm)],[d101,d15]) ).
cnf(d103,plain,
'double$udivide'(inverse('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),inverse(X2))),multiply(X1,inverse(X3)))),inverse(identity)) = X3,
inference(demodulation,[status(thm)],[d102,c2]) ).
cnf(d104,plain,
'double$udivide'(multiply(multiply(X1,inverse(X3)),'double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),inverse(X2)))),inverse(identity)) = X3,
inference(demodulation,[status(thm)],[d103,d0]) ).
cnf(d105,plain,
'double$udivide'(multiply(multiply(X0,inverse(X1)),'double$udivide'(X2,'double$udivide'('double$udivide'(X0,'double$udivide'(X2,X3)),inverse(X3)))),identity) = X1,
inference(demodulation,[status(thm)],[d104,d15]) ).
cnf(d106,plain,
inverse(multiply(multiply(X0,inverse(X1)),'double$udivide'(X2,'double$udivide'('double$udivide'(X0,'double$udivide'(X2,X3)),inverse(X3))))) = X1,
inference(demodulation,[status(thm)],[d105,c2]) ).
cnf(d107,plain,
'double$udivide'('double$udivide'(X2,'double$udivide'('double$udivide'(X0,'double$udivide'(X2,X3)),inverse(X3))),multiply(X0,inverse(X1))) = X1,
inference(demodulation,[status(thm)],[d106,d94]) ).
cnf(d108,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(X3,'double$udivide'('double$udivide'(X4,'double$udivide'(X3,X5)),'double$udivide'(identity,X5))),multiply(X4,inverse(identity))),inverse(X1)),inverse(identity)) = 'double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2))),
inference(superposition,[status(thm)],[d46,d98]) ).
cnf(d109,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X1,X0)),inverse(X0))),multiply(X2,inverse(identity))),inverse(X3)),inverse(identity)) = 'double$udivide'(X4,'double$udivide'('double$udivide'(X3,'double$udivide'(X4,X5)),'double$udivide'(identity,X5))),
inference(demodulation,[status(thm)],[d108,d93]) ).
cnf(d110,plain,
'double$udivide'('double$udivide'(identity,inverse(X3)),inverse(identity)) = 'double$udivide'(X4,'double$udivide'('double$udivide'(X3,'double$udivide'(X4,X5)),'double$udivide'(identity,X5))),
inference(demodulation,[status(thm)],[d109,d107]) ).
cnf(d111,plain,
'double$udivide'(inverse(inverse(X0)),inverse(identity)) = 'double$udivide'(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),'double$udivide'(identity,X2))),
inference(demodulation,[status(thm)],[d110,d93]) ).
cnf(d112,plain,
'double$udivide'(X0,inverse(identity)) = 'double$udivide'(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),'double$udivide'(identity,X2))),
inference(demodulation,[status(thm)],[d111,d17]) ).
cnf(d113,plain,
'double$udivide'(X0,identity) = 'double$udivide'(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),'double$udivide'(identity,X2))),
inference(demodulation,[status(thm)],[d112,d15]) ).
cnf(d114,plain,
inverse(X0) = 'double$udivide'(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),'double$udivide'(identity,X2))),
inference(demodulation,[status(thm)],[d113,c2]) ).
cnf(d115,plain,
inverse(X1) = 'double$udivide'(X2,'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),inverse(X0))),
inference(demodulation,[status(thm)],[d114,d93]) ).
cnf(d116,plain,
multiply(identity,'double$udivide'(X0,X1)) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[d0,d7]) ).
cnf(d117,plain,
'double$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$udivide'(X0,X1),X5)),inverse(identity)) = X5,
inference(superposition,[status(thm)],[d116,d71]) ).
cnf(d118,plain,
'double$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)],[d117,d93]) ).
cnf(d119,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(inverse(X1),multiply(X1,identity)),inverse(multiply(X3,X4))),multiply('double$udivide'(X4,X3),X5)),inverse(identity)) = X5,
inference(demodulation,[status(thm)],[d118,d115]) ).
cnf(d120,plain,
'double$udivide'('double$udivide'('double$udivide'(inverse(identity),inverse(multiply(X1,X2))),multiply('double$udivide'(X2,X1),X3)),inverse(identity)) = X3,
inference(demodulation,[status(thm)],[d119,d57]) ).
cnf(d121,plain,
'double$udivide'('double$udivide'('double$udivide'(identity,inverse(multiply(X0,X1))),multiply('double$udivide'(X1,X0),X2)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d120,d15]) ).
cnf(d122,plain,
'double$udivide'('double$udivide'(inverse(inverse(multiply(X0,X1))),multiply('double$udivide'(X1,X0),X2)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d121,d93]) ).
cnf(d123,plain,
'double$udivide'('double$udivide'(multiply(X0,X1),multiply('double$udivide'(X1,X0),X2)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d122,d17]) ).
cnf(d124,plain,
'double$udivide'('double$udivide'(multiply(X0,X1),multiply('double$udivide'(X1,X0),X2)),identity) = X2,
inference(demodulation,[status(thm)],[d123,d15]) ).
cnf(d125,plain,
inverse('double$udivide'(multiply(X0,X1),multiply('double$udivide'(X1,X0),X2))) = X2,
inference(demodulation,[status(thm)],[d124,c2]) ).
cnf(d126,plain,
multiply(multiply('double$udivide'(X1,X0),X2),multiply(X0,X1)) = X2,
inference(demodulation,[status(thm)],[d125,d0]) ).
cnf(d127,plain,
multiply(multiply(identity,X0),inverse(X0)) = inverse(identity),
inference(superposition,[status(thm)],[d7,d99]) ).
cnf(d128,plain,
multiply(inverse(identity),'double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(multiply(identity,X0),'double$udivide'(X1,X2)),'double$udivide'(identity,X2))),inverse(identity))) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d127,d80]) ).
cnf(d129,plain,
multiply(identity,'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(multiply(identity,X1),'double$udivide'(X0,X2)),'double$udivide'(identity,X2))),inverse(identity))) = inverse(inverse(X1)),
inference(demodulation,[status(thm)],[d128,d15]) ).
cnf(d130,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(multiply(identity,X1),'double$udivide'(X0,X2)),'double$udivide'(identity,X2))),inverse(identity)) = inverse(inverse(X1)),
inference(demodulation,[status(thm)],[d129,d45]) ).
cnf(d131,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),'double$udivide'(identity,X2))),inverse(identity)) = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d130,d45]) ).
cnf(d132,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X1,X0)),inverse(X0))),inverse(identity)) = inverse(inverse(X2)),
inference(demodulation,[status(thm)],[d131,d93]) ).
cnf(d133,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),inverse(X2))),identity) = inverse(inverse(X1)),
inference(demodulation,[status(thm)],[d132,d15]) ).
cnf(d134,plain,
inverse('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),inverse(X2)))) = inverse(inverse(X1)),
inference(demodulation,[status(thm)],[d133,c2]) ).
cnf(d135,plain,
multiply('double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),inverse(X2)),X0) = inverse(inverse(X1)),
inference(demodulation,[status(thm)],[d134,d0]) ).
cnf(d136,plain,
multiply('double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),inverse(X2)),X1) = X0,
inference(demodulation,[status(thm)],[d135,d17]) ).
cnf(d137,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,identity),'double$udivide'(identity,inverse(X0)))),multiply(X1,X2)),inverse(identity)) = X2,
inference(superposition,[status(thm)],[c3,d67]) ).
cnf(d138,plain,
'double$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)],[d137,c2]) ).
cnf(d139,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'(inverse(inverse(X0)),'double$udivide'(identity,inverse(X1)))),inverse(identity)),inverse(identity)) = X0,
inference(superposition,[status(thm)],[d99,d138]) ).
cnf(d140,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'(X0,'double$udivide'(identity,inverse(X1)))),inverse(identity)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d139,d17]) ).
cnf(d141,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'(X1,inverse(inverse(X0)))),inverse(identity)),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d140,d93]) ).
cnf(d142,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'(X1,X0)),inverse(identity)),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d141,d17]) ).
cnf(d143,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'(X1,X0)),identity),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d142,d15]) ).
cnf(d144,plain,
'double$udivide'(inverse('double$udivide'(X0,'double$udivide'(X1,X0))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d143,c2]) ).
cnf(d145,plain,
'double$udivide'(multiply('double$udivide'(X1,X0),X0),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d144,d0]) ).
cnf(d146,plain,
'double$udivide'(multiply('double$udivide'(X0,X1),X1),identity) = X0,
inference(demodulation,[status(thm)],[d145,d15]) ).
cnf(d147,plain,
inverse(multiply('double$udivide'(X0,X1),X1)) = X0,
inference(demodulation,[status(thm)],[d146,c2]) ).
cnf(d148,plain,
'double$udivide'(X1,'double$udivide'(X0,X1)) = X0,
inference(demodulation,[status(thm)],[d147,d94]) ).
cnf(d149,plain,
multiply('double$udivide'(X1,inverse(X0)),X1) = X0,
inference(superposition,[status(thm)],[d148,d136]) ).
cnf(d150,plain,
multiply(X1,multiply(inverse(X1),X0)) = X0,
inference(superposition,[status(thm)],[d149,d126]) ).
cnf(d151,plain,
multiply('double$udivide'(X1,X0),X0) = inverse(X1),
inference(superposition,[status(thm)],[d148,d0]) ).
cnf(d152,plain,
multiply(inverse(X0),multiply(X1,X0)) = X1,
inference(superposition,[status(thm)],[d151,d126]) ).
cnf(d153,plain,
multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[status(thm)],[d152,d150]) ).
cnf(d154,plain,
$false,
inference(resolution,[status(thm)],[d153,c4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP568-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n020.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 15:01:03 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.79/4.91 % SZS status Unsatisfiable for theBenchmark.p
% 19.79/4.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------