%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP489-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 07:23:52 AM UTC 2026
% Result : Unsatisfiable 40.15s 9.38s
% Output : CNFRefutation 40.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 70
% Number of leaves : 5
% Syntax : Number of clauses : 170 ( 170 unt; 0 nHn; 7 RR)
% Number of literals : 170 ( 169 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 347 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'(X0,'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X0,identity),'double$udivide'(X1,X2))),X1),identity)) = X2 ).
cnf(multiply,axiom,
multiply(X0,X1) = 'double$udivide'('double$udivide'(X1,X0),identity) ).
cnf(inverse,axiom,
inverse(X0) = 'double$udivide'(X0,identity) ).
cnf(identity,axiom,
identity = 'double$udivide'(X0,inverse(X0)) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ).
cnf(c0,plain,
'double$udivide'(X0,'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X0,identity),'double$udivide'(X1,X2))),X1),identity)) = X2,
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(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausification,[status(esa)],[prove_these_axioms_3]) ).
cnf(d0,plain,
multiply(X1,X0) = inverse('double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d2,plain,
identity = 'double$udivide'(inverse(X0),multiply(identity,X0)),
inference(superposition,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
'double$udivide'(X0,inverse('double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X0,identity),'double$udivide'(X1,X2))),X1))) = X2,
inference(demodulation,[status(thm)],[c0,c2]) ).
cnf(d4,plain,
'double$udivide'(X0,inverse('double$udivide'('double$udivide'(identity,'double$udivide'(inverse(X0),'double$udivide'(X1,X2))),X1))) = X2,
inference(demodulation,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
'double$udivide'(X1,inverse('double$udivide'('double$udivide'(identity,'double$udivide'(inverse(X1),identity)),X0))) = inverse(X0),
inference(superposition,[status(thm)],[c3,d4]) ).
cnf(d6,plain,
'double$udivide'(X0,multiply(X1,'double$udivide'(identity,'double$udivide'(inverse(X0),identity)))) = inverse(X1),
inference(demodulation,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
'double$udivide'(X0,multiply(X1,'double$udivide'(identity,inverse(inverse(X0))))) = inverse(X1),
inference(demodulation,[status(thm)],[d6,c2]) ).
cnf(d8,plain,
'double$udivide'(X0,multiply(X1,'double$udivide'(identity,multiply(identity,X0)))) = inverse(X1),
inference(demodulation,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
multiply(identity,inverse(X0)) = inverse(multiply(identity,X0)),
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d10,plain,
multiply(identity,'double$udivide'(X0,X1)) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[d0,d1]) ).
cnf(d11,plain,
'double$udivide'(X0,inverse(inverse('double$udivide'(identity,'double$udivide'(inverse(X0),'double$udivide'(identity,X1)))))) = X1,
inference(superposition,[status(thm)],[c2,d4]) ).
cnf(d12,plain,
'double$udivide'(X0,multiply(identity,'double$udivide'(identity,'double$udivide'(inverse(X0),'double$udivide'(identity,X1))))) = X1,
inference(demodulation,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
'double$udivide'(X0,inverse(multiply('double$udivide'(inverse(X0),'double$udivide'(identity,X1)),identity))) = X1,
inference(demodulation,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
'double$udivide'(X0,inverse(multiply('double$udivide'(inverse(X0),inverse(identity)),identity))) = identity,
inference(superposition,[status(thm)],[c2,d13]) ).
cnf(d15,plain,
'double$udivide'(X1,inverse('double$udivide'('double$udivide'(identity,'double$udivide'(inverse(X1),inverse(X0))),X0))) = identity,
inference(superposition,[status(thm)],[c2,d4]) ).
cnf(d16,plain,
'double$udivide'(X0,multiply(X1,'double$udivide'(identity,'double$udivide'(inverse(X0),inverse(X1))))) = identity,
inference(demodulation,[status(thm)],[d15,d0]) ).
cnf(d17,plain,
'double$udivide'(X0,multiply(inverse(X0),'double$udivide'(identity,identity))) = identity,
inference(superposition,[status(thm)],[c3,d16]) ).
cnf(d18,plain,
'double$udivide'(X0,multiply(inverse(X0),inverse(identity))) = identity,
inference(demodulation,[status(thm)],[d17,c2]) ).
cnf(d19,plain,
multiply(inverse(X0),X0) = inverse(identity),
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d20,plain,
'double$udivide'(inverse(identity),inverse(identity)) = identity,
inference(superposition,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
'double$udivide'(identity,inverse(multiply(identity,identity))) = identity,
inference(superposition,[status(thm)],[d20,d14]) ).
cnf(d22,plain,
'double$udivide'(identity,multiply(identity,inverse(identity))) = identity,
inference(demodulation,[status(thm)],[d21,d9]) ).
cnf(d23,plain,
'double$udivide'(inverse(identity),multiply(X0,identity)) = inverse(X0),
inference(superposition,[status(thm)],[d22,d8]) ).
cnf(d24,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[d23,d2]) ).
cnf(d25,plain,
'double$udivide'(identity,multiply(X0,identity)) = inverse(X0),
inference(demodulation,[status(thm)],[d23,d24]) ).
cnf(d26,plain,
multiply(multiply(X0,identity),identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d25,d0]) ).
cnf(d27,plain,
multiply(multiply(X0,identity),identity) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d26,d1]) ).
cnf(d28,plain,
'double$udivide'(identity,multiply(identity,X0)) = inverse(multiply(X0,identity)),
inference(superposition,[status(thm)],[d27,d25]) ).
cnf(d29,plain,
'double$udivide'(X0,multiply(X1,inverse(multiply(X0,identity)))) = inverse(X1),
inference(demodulation,[status(thm)],[d8,d28]) ).
cnf(d30,plain,
'double$udivide'(X3,inverse('double$udivide'('double$udivide'(identity,'double$udivide'(inverse(X3),X2)),X0))) = inverse('double$udivide'('double$udivide'(identity,'double$udivide'(inverse(X0),'double$udivide'(X1,X2))),X1)),
inference(superposition,[status(thm)],[d4,d4]) ).
cnf(d31,plain,
'double$udivide'(X0,multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X0),X1)))) = inverse('double$udivide'('double$udivide'(identity,'double$udivide'(inverse(X2),'double$udivide'(X3,X1))),X3)),
inference(demodulation,[status(thm)],[d30,d0]) ).
cnf(d32,plain,
'double$udivide'(X3,multiply(X0,'double$udivide'(identity,'double$udivide'(inverse(X3),X2)))) = multiply(X1,'double$udivide'(identity,'double$udivide'(inverse(X0),'double$udivide'(X1,X2)))),
inference(demodulation,[status(thm)],[d31,d0]) ).
cnf(d33,plain,
'double$udivide'(X0,multiply(X1,'double$udivide'(identity,inverse(inverse(X0))))) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X2,identity)))),
inference(superposition,[status(thm)],[c2,d32]) ).
cnf(d34,plain,
'double$udivide'(X0,multiply(X1,'double$udivide'(identity,multiply(identity,X0)))) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X2,identity)))),
inference(demodulation,[status(thm)],[d33,d1]) ).
cnf(d35,plain,
'double$udivide'(X0,multiply(X1,inverse(multiply(X0,identity)))) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X2,identity)))),
inference(demodulation,[status(thm)],[d34,d28]) ).
cnf(d36,plain,
inverse(X1) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X2,identity)))),
inference(demodulation,[status(thm)],[d35,d29]) ).
cnf(d37,plain,
inverse(X1) = multiply(X0,'double$udivide'(identity,'double$udivide'(inverse(X1),inverse(X0)))),
inference(demodulation,[status(thm)],[d36,c2]) ).
cnf(d38,plain,
inverse(X0) = multiply(inverse(X0),'double$udivide'(identity,identity)),
inference(superposition,[status(thm)],[c3,d37]) ).
cnf(d39,plain,
inverse(X0) = multiply(inverse(X0),inverse(identity)),
inference(demodulation,[status(thm)],[d38,c2]) ).
cnf(d40,plain,
inverse(X0) = multiply(inverse(X0),identity),
inference(demodulation,[status(thm)],[d39,d24]) ).
cnf(d41,plain,
multiply(inverse(X0),identity) = multiply(identity,inverse(X0)),
inference(superposition,[status(thm)],[d40,d27]) ).
cnf(d42,plain,
inverse(X0) = multiply(identity,inverse(X0)),
inference(demodulation,[status(thm)],[d41,d40]) ).
cnf(d43,plain,
multiply(identity,multiply(identity,X0)) = inverse(multiply(identity,inverse(X0))),
inference(superposition,[status(thm)],[d9,d1]) ).
cnf(d44,plain,
multiply(identity,multiply(identity,X0)) = multiply(identity,inverse(inverse(X0))),
inference(demodulation,[status(thm)],[d43,d9]) ).
cnf(d45,plain,
multiply(identity,multiply(identity,X0)) = multiply(identity,multiply(identity,X0)),
inference(demodulation,[status(thm)],[d44,d1]) ).
cnf(d46,plain,
multiply(identity,inverse(multiply(X1,X0))) = multiply(identity,multiply(identity,'double$udivide'(X0,X1))),
inference(superposition,[status(thm)],[d10,d45]) ).
cnf(d47,plain,
multiply(identity,inverse(multiply(X1,X0))) = multiply(identity,inverse(multiply(X1,X0))),
inference(demodulation,[status(thm)],[d46,d10]) ).
cnf(d48,plain,
multiply(multiply(identity,X0),identity) = multiply(identity,multiply(X0,identity)),
inference(superposition,[status(thm)],[d27,d27]) ).
cnf(d49,plain,
multiply(multiply(X1,X0),'double$udivide'(X0,X1)) = inverse(identity),
inference(superposition,[status(thm)],[d0,d19]) ).
cnf(d50,plain,
multiply(multiply(X0,X1),'double$udivide'(X1,X0)) = identity,
inference(demodulation,[status(thm)],[d49,d24]) ).
cnf(d51,plain,
'double$udivide'(X0,identity) = inverse(multiply(multiply(identity,X0),identity)),
inference(superposition,[status(thm)],[d50,d8]) ).
cnf(d52,plain,
inverse(X0) = inverse(multiply(multiply(identity,X0),identity)),
inference(demodulation,[status(thm)],[d51,c2]) ).
cnf(d53,plain,
inverse(X0) = inverse(multiply(identity,multiply(X0,identity))),
inference(demodulation,[status(thm)],[d52,d48]) ).
cnf(d54,plain,
inverse(X0) = multiply(identity,inverse(multiply(X0,identity))),
inference(demodulation,[status(thm)],[d53,d9]) ).
cnf(d55,plain,
multiply(identity,inverse(multiply(X0,identity))) = inverse(X0),
inference(superposition,[status(thm)],[d54,d47]) ).
cnf(d56,plain,
inverse(multiply(X0,identity)) = inverse(X0),
inference(demodulation,[status(thm)],[d55,d42]) ).
cnf(d57,plain,
'double$udivide'(inverse(X0),inverse(multiply('double$udivide'(multiply(identity,X0),'double$udivide'(identity,X1)),identity))) = X1,
inference(superposition,[status(thm)],[d1,d13]) ).
cnf(d58,plain,
'double$udivide'(inverse(X0),inverse('double$udivide'(multiply(identity,X0),'double$udivide'(identity,X1)))) = X1,
inference(demodulation,[status(thm)],[d57,d56]) ).
cnf(d59,plain,
'double$udivide'(inverse(X0),multiply('double$udivide'(identity,X1),multiply(identity,X0))) = X1,
inference(demodulation,[status(thm)],[d58,d0]) ).
cnf(d60,plain,
'double$udivide'(identity,inverse(X0)) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d40,d25]) ).
cnf(d61,plain,
'double$udivide'(identity,inverse(X0)) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d60,d1]) ).
cnf(d62,plain,
'double$udivide'(X2,multiply(X0,'double$udivide'(identity,'double$udivide'(inverse(X2),X1)))) = inverse(multiply('double$udivide'(inverse(X0),'double$udivide'(identity,X1)),identity)),
inference(superposition,[status(thm)],[d10,d32]) ).
cnf(d63,plain,
'double$udivide'(X2,multiply(X0,'double$udivide'(identity,'double$udivide'(inverse(X2),X1)))) = inverse('double$udivide'(inverse(X0),'double$udivide'(identity,X1))),
inference(demodulation,[status(thm)],[d62,d56]) ).
cnf(d64,plain,
'double$udivide'(X2,multiply(X0,'double$udivide'(identity,'double$udivide'(inverse(X2),X1)))) = multiply('double$udivide'(identity,X1),inverse(X0)),
inference(demodulation,[status(thm)],[d63,d0]) ).
cnf(d65,plain,
'double$udivide'(X1,multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X1),inverse(X0))))) = multiply(X0,'double$udivide'(identity,'double$udivide'(inverse(X2),identity))),
inference(superposition,[status(thm)],[c3,d32]) ).
cnf(d66,plain,
multiply('double$udivide'(identity,inverse(X2)),inverse(X1)) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X1),identity))),
inference(demodulation,[status(thm)],[d65,d64]) ).
cnf(d67,plain,
multiply(multiply(identity,X0),inverse(X1)) = multiply(X0,'double$udivide'(identity,'double$udivide'(inverse(X1),identity))),
inference(demodulation,[status(thm)],[d66,d61]) ).
cnf(d68,plain,
multiply(multiply(identity,X1),inverse(X0)) = multiply(X1,'double$udivide'(identity,inverse(inverse(X0)))),
inference(demodulation,[status(thm)],[d67,c2]) ).
cnf(d69,plain,
multiply(multiply(identity,X1),inverse(X0)) = multiply(X1,multiply(identity,inverse(X0))),
inference(demodulation,[status(thm)],[d68,d61]) ).
cnf(d70,plain,
multiply(multiply(identity,X1),inverse(X0)) = multiply(X1,inverse(X0)),
inference(demodulation,[status(thm)],[d69,d42]) ).
cnf(d71,plain,
identity = 'double$udivide'('double$udivide'(X0,X1),multiply(X1,X0)),
inference(superposition,[status(thm)],[d0,c3]) ).
cnf(d72,plain,
multiply(inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[d19,d24]) ).
cnf(d73,plain,
identity = 'double$udivide'('double$udivide'(X0,inverse(X0)),identity),
inference(superposition,[status(thm)],[d72,d71]) ).
cnf(d74,plain,
identity = inverse('double$udivide'(X0,inverse(X0))),
inference(demodulation,[status(thm)],[d73,c2]) ).
cnf(d75,plain,
identity = multiply(inverse(X0),X0),
inference(demodulation,[status(thm)],[d74,d0]) ).
cnf(d76,plain,
identity = multiply(multiply(identity,X0),inverse(X0)),
inference(superposition,[status(thm)],[d1,d75]) ).
cnf(d77,plain,
identity = multiply(X0,inverse(X0)),
inference(demodulation,[status(thm)],[d76,d70]) ).
cnf(d78,plain,
identity = multiply('double$udivide'(X0,X1),multiply(X1,X0)),
inference(superposition,[status(thm)],[d0,d77]) ).
cnf(d79,plain,
inverse('double$udivide'(X0,X1)) = multiply(multiply(X1,X0),identity),
inference(superposition,[status(thm)],[d0,d40]) ).
cnf(d80,plain,
multiply(X1,X0) = multiply(multiply(X1,X0),identity),
inference(demodulation,[status(thm)],[d79,d0]) ).
cnf(d81,plain,
multiply(X0,identity) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d27,d80]) ).
cnf(d82,plain,
identity = multiply('double$udivide'(identity,X0),multiply(identity,X0)),
inference(superposition,[status(thm)],[d81,d78]) ).
cnf(d83,plain,
'double$udivide'(inverse(X0),identity) = X0,
inference(superposition,[status(thm)],[d82,d59]) ).
cnf(d84,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d83,c2]) ).
cnf(d85,plain,
multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[d1,d84]) ).
cnf(d86,plain,
multiply(X0,X1) = multiply(identity,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d80,d81]) ).
cnf(d87,plain,
multiply(identity,inverse('double$udivide'(X0,X1))) = inverse(inverse(multiply(X1,X0))),
inference(superposition,[status(thm)],[d10,d9]) ).
cnf(d88,plain,
multiply(identity,multiply(X1,X0)) = inverse(inverse(multiply(X1,X0))),
inference(demodulation,[status(thm)],[d87,d0]) ).
cnf(d89,plain,
multiply(identity,multiply(X0,X1)) = multiply(identity,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d88,d1]) ).
cnf(d90,plain,
multiply(identity,multiply(identity,'double$udivide'(X0,X1))) = multiply(identity,inverse(multiply(X1,X0))),
inference(superposition,[status(thm)],[d10,d89]) ).
cnf(d91,plain,
multiply(identity,'double$udivide'(X0,X1)) = multiply(identity,inverse(multiply(X1,X0))),
inference(demodulation,[status(thm)],[d90,d86]) ).
cnf(d92,plain,
inverse(multiply(X1,X0)) = multiply(identity,inverse(multiply(X1,X0))),
inference(demodulation,[status(thm)],[d91,d10]) ).
cnf(d93,plain,
inverse(multiply(X0,X1)) = inverse(multiply(X0,X1)),
inference(demodulation,[status(thm)],[d92,d42]) ).
cnf(d94,plain,
inverse(multiply(identity,X0)) = inverse(X0),
inference(superposition,[status(thm)],[d85,d93]) ).
cnf(d95,plain,
inverse(X0) = inverse(X0),
inference(demodulation,[status(thm)],[d94,d85]) ).
cnf(d96,plain,
inverse('double$udivide'(X0,X1)) = multiply(X1,X0),
inference(superposition,[status(thm)],[d0,d95]) ).
cnf(d97,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d81,d85]) ).
cnf(d98,plain,
'double$udivide'(identity,multiply(identity,X0)) = inverse(X0),
inference(demodulation,[status(thm)],[d28,d56]) ).
cnf(d99,plain,
'double$udivide'(identity,X0) = inverse(X0),
inference(demodulation,[status(thm)],[d98,d85]) ).
cnf(d100,plain,
'double$udivide'(X0,multiply(X1,'double$udivide'(identity,identity))) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X2,inverse(multiply('double$udivide'(inverse(inverse(X0)),inverse(identity)),identity)))))),
inference(superposition,[status(thm)],[d14,d32]) ).
cnf(d101,plain,
'double$udivide'(X0,multiply(X1,inverse(identity))) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X2,inverse(multiply('double$udivide'(inverse(inverse(X0)),inverse(identity)),identity)))))),
inference(demodulation,[status(thm)],[d100,d99]) ).
cnf(d102,plain,
'double$udivide'(X0,multiply(X1,identity)) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X2,inverse(multiply('double$udivide'(inverse(inverse(X0)),inverse(identity)),identity)))))),
inference(demodulation,[status(thm)],[d101,d24]) ).
cnf(d103,plain,
'double$udivide'(X1,X0) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X0),'double$udivide'(X2,inverse(multiply('double$udivide'(inverse(inverse(X1)),inverse(identity)),identity)))))),
inference(demodulation,[status(thm)],[d102,d97]) ).
cnf(d104,plain,
'double$udivide'(X2,X0) = multiply(X1,inverse('double$udivide'(inverse(X0),'double$udivide'(X1,inverse(multiply('double$udivide'(inverse(inverse(X2)),inverse(identity)),identity)))))),
inference(demodulation,[status(thm)],[d103,d99]) ).
cnf(d105,plain,
'double$udivide'(X2,X0) = multiply(X1,multiply('double$udivide'(X1,inverse(multiply('double$udivide'(inverse(inverse(X2)),inverse(identity)),identity))),inverse(X0))),
inference(demodulation,[status(thm)],[d104,d0]) ).
cnf(d106,plain,
'double$udivide'(X0,X1) = multiply(X2,multiply('double$udivide'(X2,inverse('double$udivide'(inverse(inverse(X0)),inverse(identity)))),inverse(X1))),
inference(demodulation,[status(thm)],[d105,d97]) ).
cnf(d107,plain,
'double$udivide'(X0,X1) = multiply(X2,multiply('double$udivide'(X2,multiply(inverse(identity),inverse(inverse(X0)))),inverse(X1))),
inference(demodulation,[status(thm)],[d106,d0]) ).
cnf(d108,plain,
'double$udivide'(X0,X1) = multiply(X2,multiply('double$udivide'(X2,multiply(identity,inverse(inverse(X0)))),inverse(X1))),
inference(demodulation,[status(thm)],[d107,d24]) ).
cnf(d109,plain,
'double$udivide'(X0,X1) = multiply(X2,multiply('double$udivide'(X2,inverse(inverse(X0))),inverse(X1))),
inference(demodulation,[status(thm)],[d108,d85]) ).
cnf(d110,plain,
'double$udivide'(X0,X1) = multiply(X2,multiply('double$udivide'(X2,X0),inverse(X1))),
inference(demodulation,[status(thm)],[d109,d84]) ).
cnf(d111,plain,
'double$udivide'(X1,'double$udivide'(X0,X1)) = multiply(X0,identity),
inference(superposition,[status(thm)],[d77,d110]) ).
cnf(d112,plain,
'double$udivide'(X1,'double$udivide'(X0,X1)) = X0,
inference(demodulation,[status(thm)],[d111,d97]) ).
cnf(d113,plain,
'double$udivide'('double$udivide'(X1,X0),X1) = X0,
inference(superposition,[status(thm)],[d112,d112]) ).
cnf(d114,plain,
'double$udivide'(X0,multiply(X1,inverse(X0))) = inverse(X1),
inference(demodulation,[status(thm)],[d29,d56]) ).
cnf(d115,plain,
'double$udivide'(inverse(X0),multiply(X1,X0)) = inverse(X1),
inference(superposition,[status(thm)],[d84,d114]) ).
cnf(d116,plain,
'double$udivide'(inverse(X1),inverse(X0)) = multiply(X1,X0),
inference(superposition,[status(thm)],[d115,d113]) ).
cnf(d117,plain,
'double$udivide'(inverse(X1),X0) = multiply(X1,inverse(X0)),
inference(superposition,[status(thm)],[d114,d113]) ).
cnf(d118,plain,
inverse(multiply(X1,X0)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d0,d84]) ).
cnf(d119,plain,
'double$udivide'(X0,inverse(multiply('double$udivide'(inverse(X0),identity),identity))) = inverse(identity),
inference(superposition,[status(thm)],[c3,d13]) ).
cnf(d120,plain,
'double$udivide'(X0,inverse(multiply(inverse(inverse(X0)),identity))) = inverse(identity),
inference(demodulation,[status(thm)],[d119,c2]) ).
cnf(d121,plain,
'double$udivide'(X0,inverse(multiply(multiply(identity,X0),identity))) = inverse(identity),
inference(demodulation,[status(thm)],[d120,d1]) ).
cnf(d122,plain,
'double$udivide'(X0,multiply(X1,'double$udivide'(identity,inverse(identity)))) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X2,inverse(multiply(multiply(identity,inverse(X0)),identity)))))),
inference(superposition,[status(thm)],[d121,d32]) ).
cnf(d123,plain,
'double$udivide'(X0,multiply(X1,inverse(inverse(identity)))) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X2,inverse(multiply(multiply(identity,inverse(X0)),identity)))))),
inference(demodulation,[status(thm)],[d122,d99]) ).
cnf(d124,plain,
'double$udivide'(X0,multiply(X1,identity)) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X2,inverse(multiply(multiply(identity,inverse(X0)),identity)))))),
inference(demodulation,[status(thm)],[d123,d84]) ).
cnf(d125,plain,
'double$udivide'(X1,X0) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X0),'double$udivide'(X2,inverse(multiply(multiply(identity,inverse(X1)),identity)))))),
inference(demodulation,[status(thm)],[d124,d97]) ).
cnf(d126,plain,
'double$udivide'(X2,X0) = multiply(X1,inverse('double$udivide'(inverse(X0),'double$udivide'(X1,inverse(multiply(multiply(identity,inverse(X2)),identity)))))),
inference(demodulation,[status(thm)],[d125,d99]) ).
cnf(d127,plain,
'double$udivide'(X2,X0) = multiply(X1,multiply('double$udivide'(X1,inverse(multiply(multiply(identity,inverse(X2)),identity))),inverse(X0))),
inference(demodulation,[status(thm)],[d126,d0]) ).
cnf(d128,plain,
'double$udivide'(X1,X2) = 'double$udivide'(inverse(multiply(multiply(identity,inverse(X1)),identity)),X2),
inference(demodulation,[status(thm)],[d127,d110]) ).
cnf(d129,plain,
'double$udivide'(X0,X1) = 'double$udivide'('double$udivide'(identity,multiply(identity,inverse(X0))),X1),
inference(demodulation,[status(thm)],[d128,d118]) ).
cnf(d130,plain,
'double$udivide'(X0,X1) = 'double$udivide'(inverse(multiply(identity,inverse(X0))),X1),
inference(demodulation,[status(thm)],[d129,d99]) ).
cnf(d131,plain,
'double$udivide'(X0,X1) = 'double$udivide'('double$udivide'(inverse(X0),identity),X1),
inference(demodulation,[status(thm)],[d130,d118]) ).
cnf(d132,plain,
'double$udivide'(X0,X1) = 'double$udivide'(inverse(inverse(X0)),X1),
inference(demodulation,[status(thm)],[d131,c2]) ).
cnf(d133,plain,
'double$udivide'(X0,X1) = 'double$udivide'(X0,X1),
inference(demodulation,[status(thm)],[d132,d84]) ).
cnf(d134,plain,
X1 = 'double$udivide'(X0,'double$udivide'(X1,X0)),
inference(superposition,[status(thm)],[d112,d133]) ).
cnf(d135,plain,
'double$udivide'(X0,multiply(X2,'double$udivide'(identity,identity))) = multiply(X3,'double$udivide'(identity,'double$udivide'(inverse(X2),'double$udivide'(X3,multiply(X1,'double$udivide'(identity,'double$udivide'(inverse(inverse(X0)),inverse(X1)))))))),
inference(superposition,[status(thm)],[d16,d32]) ).
cnf(d136,plain,
'double$udivide'(X0,multiply(X1,inverse(identity))) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X2,multiply(X3,'double$udivide'(identity,'double$udivide'(inverse(inverse(X0)),inverse(X3)))))))),
inference(demodulation,[status(thm)],[d135,d99]) ).
cnf(d137,plain,
'double$udivide'(X1,'double$udivide'(inverse(X0),identity)) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X0),'double$udivide'(X2,multiply(X3,'double$udivide'(identity,'double$udivide'(inverse(inverse(X1)),inverse(X3)))))))),
inference(demodulation,[status(thm)],[d136,d117]) ).
cnf(d138,plain,
'double$udivide'(X1,inverse(inverse(X0))) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X0),'double$udivide'(X2,multiply(X3,'double$udivide'(identity,'double$udivide'(inverse(inverse(X1)),inverse(X3)))))))),
inference(demodulation,[status(thm)],[d137,c2]) ).
cnf(d139,plain,
'double$udivide'(X1,X0) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X0),'double$udivide'(X2,multiply(X3,'double$udivide'(identity,'double$udivide'(inverse(inverse(X1)),inverse(X3)))))))),
inference(demodulation,[status(thm)],[d138,d84]) ).
cnf(d140,plain,
'double$udivide'(X3,X0) = multiply(X1,inverse('double$udivide'(inverse(X0),'double$udivide'(X1,multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(inverse(X3)),inverse(X2)))))))),
inference(demodulation,[status(thm)],[d139,d99]) ).
cnf(d141,plain,
'double$udivide'(X3,X1) = 'double$udivide'(inverse(X0),'double$udivide'(inverse(X1),'double$udivide'(X0,multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(inverse(X3)),inverse(X2))))))),
inference(demodulation,[status(thm)],[d140,d117]) ).
cnf(d142,plain,
'double$udivide'(X0,X2) = 'double$udivide'(inverse(X3),'double$udivide'(inverse(X2),'double$udivide'(X3,multiply(X1,inverse('double$udivide'(inverse(inverse(X0)),inverse(X1))))))),
inference(demodulation,[status(thm)],[d141,d99]) ).
cnf(d143,plain,
'double$udivide'(X1,X2) = 'double$udivide'(inverse(X3),'double$udivide'(inverse(X2),'double$udivide'(X3,'double$udivide'(inverse(X0),'double$udivide'(inverse(inverse(X1)),inverse(X0)))))),
inference(demodulation,[status(thm)],[d142,d117]) ).
cnf(d144,plain,
'double$udivide'(X1,X2) = 'double$udivide'(inverse(X3),'double$udivide'(inverse(X2),'double$udivide'(X3,inverse(inverse(X1))))),
inference(demodulation,[status(thm)],[d143,d134]) ).
cnf(d145,plain,
'double$udivide'(X0,X1) = 'double$udivide'(inverse(X2),'double$udivide'(inverse(X1),'double$udivide'(X2,X0))),
inference(demodulation,[status(thm)],[d144,d84]) ).
cnf(d146,plain,
'double$udivide'(X0,multiply(X2,'double$udivide'(identity,inverse(X1)))) = multiply(X3,'double$udivide'(identity,'double$udivide'(inverse(X2),'double$udivide'(X3,multiply(X1,'double$udivide'(identity,multiply(identity,inverse(X0)))))))),
inference(superposition,[status(thm)],[d8,d32]) ).
cnf(d147,plain,
'double$udivide'(X1,multiply(X2,inverse(inverse(X0)))) = multiply(X3,'double$udivide'(identity,'double$udivide'(inverse(X2),'double$udivide'(X3,multiply(X0,'double$udivide'(identity,multiply(identity,inverse(X1)))))))),
inference(demodulation,[status(thm)],[d146,d99]) ).
cnf(d148,plain,
'double$udivide'(X2,'double$udivide'(inverse(X0),inverse(X1))) = multiply(X3,'double$udivide'(identity,'double$udivide'(inverse(X0),'double$udivide'(X3,multiply(X1,'double$udivide'(identity,multiply(identity,inverse(X2)))))))),
inference(demodulation,[status(thm)],[d147,d117]) ).
cnf(d149,plain,
'double$udivide'(X2,multiply(X0,X1)) = multiply(X3,'double$udivide'(identity,'double$udivide'(inverse(X0),'double$udivide'(X3,multiply(X1,'double$udivide'(identity,multiply(identity,inverse(X2)))))))),
inference(demodulation,[status(thm)],[d148,d116]) ).
cnf(d150,plain,
'double$udivide'(X3,multiply(X0,X2)) = multiply(X1,inverse('double$udivide'(inverse(X0),'double$udivide'(X1,multiply(X2,'double$udivide'(identity,multiply(identity,inverse(X3)))))))),
inference(demodulation,[status(thm)],[d149,d99]) ).
cnf(d151,plain,
'double$udivide'(X3,multiply(X1,X2)) = 'double$udivide'(inverse(X0),'double$udivide'(inverse(X1),'double$udivide'(X0,multiply(X2,'double$udivide'(identity,multiply(identity,inverse(X3))))))),
inference(demodulation,[status(thm)],[d150,d117]) ).
cnf(d152,plain,
'double$udivide'(X3,multiply(X1,X2)) = 'double$udivide'(multiply(X2,'double$udivide'(identity,multiply(identity,inverse(X3)))),X1),
inference(demodulation,[status(thm)],[d151,d145]) ).
cnf(d153,plain,
'double$udivide'(X0,multiply(X1,X2)) = 'double$udivide'(multiply(X2,inverse(multiply(identity,inverse(X0)))),X1),
inference(demodulation,[status(thm)],[d152,d99]) ).
cnf(d154,plain,
'double$udivide'(X1,multiply(X2,X0)) = 'double$udivide'('double$udivide'(inverse(X0),multiply(identity,inverse(X1))),X2),
inference(demodulation,[status(thm)],[d153,d117]) ).
cnf(d155,plain,
'double$udivide'(X0,multiply(X1,X2)) = 'double$udivide'('double$udivide'(inverse(X2),inverse(X0)),X1),
inference(demodulation,[status(thm)],[d154,d85]) ).
cnf(d156,plain,
'double$udivide'(X1,multiply(X2,X0)) = 'double$udivide'(multiply(X0,X1),X2),
inference(demodulation,[status(thm)],[d155,d116]) ).
cnf(d157,plain,
inverse('double$udivide'(X1,multiply(X2,X0))) = multiply(X2,multiply(X0,X1)),
inference(superposition,[status(thm)],[d156,d96]) ).
cnf(d158,plain,
multiply(multiply(X1,X2),X0) = multiply(X1,multiply(X2,X0)),
inference(demodulation,[status(thm)],[d157,d0]) ).
cnf(d159,plain,
$false,
inference(resolution,[status(thm)],[d158,c4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP489-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n018.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 14:58:36 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 40.15/9.38 % SZS status Unsatisfiable for theBenchmark.p
% 40.15/9.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------