%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP100-1 : 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 07:22:19 AM UTC 2026
% Result : Unsatisfiable 65.38s 14.97s
% Output : CNFRefutation 65.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 5
% Syntax : Number of clauses : 140 ( 131 unt; 0 nHn; 12 RR)
% Number of literals : 160 ( 159 equ; 30 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 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 : 322 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(X2,identity))),'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$udivide'(X2,identity))),'double$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$udivide'(X0,X1)) = multiply(X1,X0),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
inverse(identity) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d2,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X1,X0)),inverse(X0))),'double$udivide'(identity,identity)) = X2,
inference(demodulation,[status(thm)],[c0,c2]) ).
cnf(d3,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),inverse(X2))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,inverse(X0)),inverse(identity))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[c2,d3]) ).
cnf(d5,plain,
inverse(inverse(X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d6,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,identity),inverse(inverse(X0)))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[c3,d3]) ).
cnf(d7,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'(inverse(X0),inverse(inverse(X1)))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d6,c2]) ).
cnf(d8,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(inverse(X1),multiply(identity,X0))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
'double$udivide'(inverse(X0),multiply(identity,X0)) = identity,
inference(superposition,[status(thm)],[d5,c3]) ).
cnf(d10,plain,
'double$udivide'('double$udivide'(X0,identity),inverse(identity)) = X0,
inference(superposition,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
'double$udivide'(inverse(X0),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d10,c2]) ).
cnf(d12,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X0,inverse(identity))),inverse(identity)) = inverse(X0),
inference(superposition,[status(thm)],[d11,d4]) ).
cnf(d13,plain,
inverse('double$udivide'(X0,inverse(identity))) = X0,
inference(superposition,[status(thm)],[d12,d4]) ).
cnf(d14,plain,
multiply(inverse(identity),X0) = X0,
inference(demodulation,[status(thm)],[d13,d0]) ).
cnf(d15,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[d14,d1]) ).
cnf(d16,plain,
multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[d14,d15]) ).
cnf(d17,plain,
'double$udivide'('double$udivide'(X2,'double$udivide'('double$udivide'(X3,'double$udivide'(X2,'double$udivide'(X0,X1))),multiply(X1,X0))),inverse(identity)) = X3,
inference(superposition,[status(thm)],[d0,d3]) ).
cnf(d18,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X1,inverse(X0))),multiply(identity,X0))),inverse(identity)) = X2,
inference(superposition,[status(thm)],[c2,d17]) ).
cnf(d19,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X1,inverse(X0))),X0)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d18,d16]) ).
cnf(d20,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,inverse(X2))),X2)),identity) = X1,
inference(demodulation,[status(thm)],[d19,d15]) ).
cnf(d21,plain,
inverse('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,inverse(X2))),X2))) = X1,
inference(demodulation,[status(thm)],[d20,c2]) ).
cnf(d22,plain,
multiply('double$udivide'('double$udivide'(X1,'double$udivide'(X0,inverse(X2))),X2),X0) = X1,
inference(demodulation,[status(thm)],[d21,d0]) ).
cnf(d23,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d5,d16]) ).
cnf(d24,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),inverse(X2))),'double$udivide'('double$udivide'(X3,X1),inverse(inverse(identity)))),inverse(identity)) = X3,
inference(superposition,[status(thm)],[d3,d3]) ).
cnf(d25,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),inverse(X2))),'double$udivide'('double$udivide'(X3,X1),multiply(identity,identity))),inverse(identity)) = X3,
inference(demodulation,[status(thm)],[d24,d5]) ).
cnf(d26,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(identity,'double$udivide'(X1,X2)),inverse(X2))),'double$udivide'(inverse(X0),multiply(identity,identity))),inverse(identity)) = X0,
inference(superposition,[status(thm)],[c2,d25]) ).
cnf(d27,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(identity,'double$udivide'(X0,X1)),inverse(X1))),'double$udivide'(inverse(X2),identity)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d26,d16]) ).
cnf(d28,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(identity,'double$udivide'(X1,X2)),inverse(X2))),inverse(inverse(X0))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d27,c2]) ).
cnf(d29,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(identity,'double$udivide'(X1,X2)),inverse(X2))),X0),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d28,d23]) ).
cnf(d30,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(identity,'double$udivide'(X0,X1)),inverse(X1))),X2),identity) = X2,
inference(demodulation,[status(thm)],[d29,d15]) ).
cnf(d31,plain,
inverse('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(identity,'double$udivide'(X0,X1)),inverse(X1))),X2)) = X2,
inference(demodulation,[status(thm)],[d30,c2]) ).
cnf(d32,plain,
multiply(X2,'double$udivide'(X0,'double$udivide'('double$udivide'(identity,'double$udivide'(X0,X1)),inverse(X1)))) = X2,
inference(demodulation,[status(thm)],[d31,d0]) ).
cnf(d33,plain,
'double$udivide'('double$udivide'('double$udivide'(X3,'double$udivide'('double$udivide'(inverse(identity),'double$udivide'(X3,X4)),inverse(X4))),'double$udivide'(X1,multiply(identity,identity))),inverse(identity)) = 'double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),inverse(X2))),
inference(superposition,[status(thm)],[d3,d25]) ).
cnf(d34,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(identity,'double$udivide'(X0,X1)),inverse(X1))),'double$udivide'(X2,multiply(identity,identity))),inverse(identity)) = 'double$udivide'(X3,'double$udivide'('double$udivide'(X2,'double$udivide'(X3,X4)),inverse(X4))),
inference(demodulation,[status(thm)],[d33,d15]) ).
cnf(d35,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(identity,'double$udivide'(X0,X1)),inverse(X1))),'double$udivide'(X2,identity)),inverse(identity)) = 'double$udivide'(X3,'double$udivide'('double$udivide'(X2,'double$udivide'(X3,X4)),inverse(X4))),
inference(demodulation,[status(thm)],[d34,d16]) ).
cnf(d36,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(identity,'double$udivide'(X1,X2)),inverse(X2))),inverse(X0)),inverse(identity)) = 'double$udivide'(X3,'double$udivide'('double$udivide'(X0,'double$udivide'(X3,X4)),inverse(X4))),
inference(demodulation,[status(thm)],[d35,c2]) ).
cnf(d37,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(identity,'double$udivide'(X0,X1)),inverse(X1))),inverse(X2)),identity) = 'double$udivide'(X3,'double$udivide'('double$udivide'(X2,'double$udivide'(X3,X4)),inverse(X4))),
inference(demodulation,[status(thm)],[d36,d15]) ).
cnf(d38,plain,
inverse('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(identity,'double$udivide'(X0,X1)),inverse(X1))),inverse(X2))) = 'double$udivide'(X3,'double$udivide'('double$udivide'(X2,'double$udivide'(X3,X4)),inverse(X4))),
inference(demodulation,[status(thm)],[d37,c2]) ).
cnf(d39,plain,
multiply(inverse(X2),'double$udivide'(X0,'double$udivide'('double$udivide'(identity,'double$udivide'(X0,X1)),inverse(X1)))) = 'double$udivide'(X3,'double$udivide'('double$udivide'(X2,'double$udivide'(X3,X4)),inverse(X4))),
inference(demodulation,[status(thm)],[d38,d0]) ).
cnf(d40,plain,
inverse(X0) = 'double$udivide'(X3,'double$udivide'('double$udivide'(X0,'double$udivide'(X3,X4)),inverse(X4))),
inference(demodulation,[status(thm)],[d39,d32]) ).
cnf(d41,plain,
'double$udivide'('double$udivide'(X0,X1),multiply(X1,X0)) = identity,
inference(superposition,[status(thm)],[d0,c3]) ).
cnf(d42,plain,
'double$udivide'('double$udivide'('double$udivide'(X2,'double$udivide'('double$udivide'(multiply(X1,X0),'double$udivide'(X2,X3)),inverse(X3))),'double$udivide'(identity,multiply(identity,identity))),inverse(identity)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d41,d25]) ).
cnf(d43,plain,
'double$udivide'('double$udivide'(inverse(multiply(X1,X2)),'double$udivide'(identity,multiply(identity,identity))),inverse(identity)) = 'double$udivide'(X2,X1),
inference(demodulation,[status(thm)],[d42,d40]) ).
cnf(d44,plain,
'double$udivide'('double$udivide'(inverse(multiply(X0,X1)),'double$udivide'(identity,identity)),inverse(identity)) = 'double$udivide'(X1,X0),
inference(demodulation,[status(thm)],[d43,d16]) ).
cnf(d45,plain,
'double$udivide'('double$udivide'(inverse(multiply(X0,X1)),inverse(identity)),inverse(identity)) = 'double$udivide'(X1,X0),
inference(demodulation,[status(thm)],[d44,c2]) ).
cnf(d46,plain,
'double$udivide'('double$udivide'(inverse(multiply(X0,X1)),identity),inverse(identity)) = 'double$udivide'(X1,X0),
inference(demodulation,[status(thm)],[d45,d15]) ).
cnf(d47,plain,
'double$udivide'(inverse(inverse(multiply(X0,X1))),inverse(identity)) = 'double$udivide'(X1,X0),
inference(demodulation,[status(thm)],[d46,c2]) ).
cnf(d48,plain,
'double$udivide'(multiply(X0,X1),inverse(identity)) = 'double$udivide'(X1,X0),
inference(demodulation,[status(thm)],[d47,d23]) ).
cnf(d49,plain,
'double$udivide'(multiply(X0,X1),identity) = 'double$udivide'(X1,X0),
inference(demodulation,[status(thm)],[d48,d15]) ).
cnf(d50,plain,
inverse(multiply(X0,X1)) = 'double$udivide'(X1,X0),
inference(demodulation,[status(thm)],[d49,c2]) ).
cnf(d51,plain,
multiply(X2,inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d32,d40]) ).
cnf(d52,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d51,d15]) ).
cnf(d53,plain,
inverse(X0) = 'double$udivide'(identity,X0),
inference(superposition,[status(thm)],[d52,d50]) ).
cnf(d54,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)) = 'double$udivide'(X0,'double$udivide'(inverse(X1),multiply(identity,X0))),
inference(superposition,[status(thm)],[d8,d4]) ).
cnf(d55,plain,
'double$udivide'(inverse('double$udivide'(X0,inverse(identity))),inverse(identity)) = 'double$udivide'(X1,'double$udivide'(inverse(X0),multiply(identity,X1))),
inference(demodulation,[status(thm)],[d54,d53]) ).
cnf(d56,plain,
'double$udivide'(multiply(inverse(identity),X0),inverse(identity)) = 'double$udivide'(X1,'double$udivide'(inverse(X0),multiply(identity,X1))),
inference(demodulation,[status(thm)],[d55,d0]) ).
cnf(d57,plain,
'double$udivide'(multiply(identity,X0),inverse(identity)) = 'double$udivide'(X1,'double$udivide'(inverse(X0),multiply(identity,X1))),
inference(demodulation,[status(thm)],[d56,d15]) ).
cnf(d58,plain,
'double$udivide'(X0,inverse(identity)) = 'double$udivide'(X1,'double$udivide'(inverse(X0),multiply(identity,X1))),
inference(demodulation,[status(thm)],[d57,d16]) ).
cnf(d59,plain,
'double$udivide'(X0,identity) = 'double$udivide'(X1,'double$udivide'(inverse(X0),multiply(identity,X1))),
inference(demodulation,[status(thm)],[d58,d15]) ).
cnf(d60,plain,
inverse(X0) = 'double$udivide'(X1,'double$udivide'(inverse(X0),multiply(identity,X1))),
inference(demodulation,[status(thm)],[d59,c2]) ).
cnf(d61,plain,
inverse(X1) = 'double$udivide'(X0,'double$udivide'(inverse(X1),X0)),
inference(demodulation,[status(thm)],[d60,d16]) ).
cnf(d62,plain,
inverse(inverse(X0)) = 'double$udivide'(X1,'double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[d23,d61]) ).
cnf(d63,plain,
X0 = 'double$udivide'(X1,'double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[d62,d23]) ).
cnf(d64,plain,
multiply('double$udivide'(X1,X0),X1) = inverse(X0),
inference(superposition,[status(thm)],[d63,d22]) ).
cnf(d65,plain,
multiply(X1,X0) = inverse('double$udivide'(X1,X0)),
inference(superposition,[status(thm)],[d63,d64]) ).
cnf(d66,plain,
multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[status(thm)],[d65,d0]) ).
cnf(d67,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X1,inverse(X0))),multiply(identity,X0))),inverse(identity)) = X2,
inference(superposition,[status(thm)],[d5,d3]) ).
cnf(d68,plain,
'double$udivide'(multiply(X1,X0),inverse(identity)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d0,d11]) ).
cnf(d69,plain,
'double$udivide'('double$udivide'(multiply(X0,X1),'double$udivide'('double$udivide'(X2,'double$udivide'(X1,X0)),multiply(identity,identity))),inverse(identity)) = X2,
inference(superposition,[status(thm)],[d68,d67]) ).
cnf(d70,plain,
'double$udivide'('double$udivide'(multiply(X0,X1),'double$udivide'('double$udivide'(X2,'double$udivide'(X1,X0)),identity)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d69,d16]) ).
cnf(d71,plain,
'double$udivide'('double$udivide'(multiply(X2,X1),inverse('double$udivide'(X0,'double$udivide'(X1,X2)))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d70,c2]) ).
cnf(d72,plain,
'double$udivide'('double$udivide'(multiply(X2,X1),multiply('double$udivide'(X1,X2),X0)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d71,d0]) ).
cnf(d73,plain,
'double$udivide'('double$udivide'(multiply(X0,X1),multiply('double$udivide'(X1,X0),X2)),identity) = X2,
inference(demodulation,[status(thm)],[d72,d15]) ).
cnf(d74,plain,
inverse('double$udivide'(multiply(X0,X1),multiply('double$udivide'(X1,X0),X2))) = X2,
inference(demodulation,[status(thm)],[d73,c2]) ).
cnf(d75,plain,
multiply(multiply('double$udivide'(X1,X0),X2),multiply(X0,X1)) = X2,
inference(demodulation,[status(thm)],[d74,d0]) ).
cnf(d76,plain,
multiply(multiply(X1,X0),multiply('double$udivide'(X0,X1),X2)) = X2,
inference(demodulation,[status(thm)],[d75,d66]) ).
cnf(d77,plain,
inverse(multiply(identity,X0)) = multiply(identity,inverse(X0)),
inference(superposition,[status(thm)],[d5,d5]) ).
cnf(d78,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X1,multiply(identity,X0))),multiply(identity,inverse(X0)))),'double$udivide'('double$udivide'(X3,X2),multiply(identity,identity))),inverse(identity)) = X3,
inference(superposition,[status(thm)],[d77,d25]) ).
cnf(d79,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X1,X0)),multiply(identity,inverse(X0)))),'double$udivide'('double$udivide'(X3,X2),multiply(identity,identity))),inverse(identity)) = X3,
inference(demodulation,[status(thm)],[d78,d16]) ).
cnf(d80,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X1,X0)),inverse(X0))),'double$udivide'('double$udivide'(X3,X2),multiply(identity,identity))),inverse(identity)) = X3,
inference(demodulation,[status(thm)],[d79,d16]) ).
cnf(d81,plain,
'double$udivide'('double$udivide'(inverse(X1),'double$udivide'('double$udivide'(X3,X1),multiply(identity,identity))),inverse(identity)) = X3,
inference(demodulation,[status(thm)],[d80,d40]) ).
cnf(d82,plain,
'double$udivide'('double$udivide'(inverse(X0),'double$udivide'('double$udivide'(X1,X0),identity)),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d81,d16]) ).
cnf(d83,plain,
'double$udivide'('double$udivide'(inverse(X1),inverse('double$udivide'(X0,X1))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d82,c2]) ).
cnf(d84,plain,
'double$udivide'('double$udivide'(inverse(X1),multiply(X1,X0)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d83,d0]) ).
cnf(d85,plain,
'double$udivide'('double$udivide'(inverse(X0),multiply(X0,X1)),identity) = X1,
inference(demodulation,[status(thm)],[d84,d15]) ).
cnf(d86,plain,
inverse('double$udivide'(inverse(X0),multiply(X0,X1))) = X1,
inference(demodulation,[status(thm)],[d85,c2]) ).
cnf(d87,plain,
multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(demodulation,[status(thm)],[d86,d0]) ).
cnf(d88,plain,
multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[d87,d66]) ).
cnf(d89,plain,
multiply(inverse(X0),multiply(X1,X0)) = X1,
inference(superposition,[status(thm)],[d66,d88]) ).
cnf(d90,plain,
multiply(multiply(inverse(X0),X1),X0) = X1,
inference(superposition,[status(thm)],[d23,d87]) ).
cnf(d91,plain,
identity = multiply(inverse(X0),X0),
inference(demodulation,[status(thm)],[d1,d15]) ).
cnf(d92,plain,
identity = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[d23,d91]) ).
cnf(d93,plain,
multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d92,d90]) ).
cnf(d94,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d93,d16]) ).
cnf(d95,plain,
'double$udivide'(X0,X1) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[d65,d94]) ).
cnf(d96,plain,
multiply('double$udivide'(X0,X1),multiply(X2,multiply(X0,X1))) = X2,
inference(superposition,[status(thm)],[d95,d89]) ).
cnf(d97,plain,
multiply(multiply(X1,X0),X2) = multiply(X2,multiply(X0,X1)),
inference(superposition,[status(thm)],[d96,d76]) ).
cnf(d98,plain,
( multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3)
| multiply(b4,a4) != multiply(a4,b4)
| inverse(identity) != identity
| multiply(identity,a2) != a2 ),
inference(demodulation,[status(thm)],[c4,d1]) ).
cnf(d99,plain,
( multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3)
| multiply(b4,a4) != multiply(a4,b4)
| multiply(identity,a2) != a2 ),
inference(resolution,[status(thm)],[d15,d98]) ).
cnf(d100,plain,
( multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3)
| multiply(b4,a4) != multiply(a4,b4)
| a2 != a2 ),
inference(demodulation,[status(thm)],[d99,d16]) ).
cnf(d101,plain,
( multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3)
| multiply(b4,a4) != multiply(b4,a4)
| a2 != a2 ),
inference(demodulation,[status(thm)],[d100,d66]) ).
cnf(d102,plain,
( multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(b3,a3))
| multiply(b4,a4) != multiply(b4,a4)
| a2 != a2 ),
inference(demodulation,[status(thm)],[d101,d97]) ).
cnf(d103,plain,
( multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(a3,b3))
| multiply(b4,a4) != multiply(b4,a4)
| a2 != a2 ),
inference(demodulation,[status(thm)],[d102,d66]) ).
cnf(d104,plain,
'double$udivide'('double$udivide'(inverse(X0),'double$udivide'('double$udivide'(X1,identity),inverse(multiply(identity,X0)))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[d9,d3]) ).
cnf(d105,plain,
'double$udivide'('double$udivide'(inverse(X1),'double$udivide'(inverse(X0),inverse(multiply(identity,X1)))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d104,c2]) ).
cnf(d106,plain,
'double$udivide'('double$udivide'(inverse(X0),'double$udivide'(inverse(X1),multiply(identity,inverse(X0)))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d105,d77]) ).
cnf(d107,plain,
X1 = X1,
inference(demodulation,[status(thm)],[d106,d8]) ).
cnf(d108,plain,
( multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(a3,b3))
| multiply(b4,a4) != multiply(b4,a4) ),
inference(resolution,[status(thm)],[d107,d103]) ).
cnf(d109,plain,
inverse(multiply(X0,X1)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d65,d23]) ).
cnf(d110,plain,
'double$udivide'(X0,X1) = 'double$udivide'(X1,X0),
inference(superposition,[status(thm)],[d109,d50]) ).
cnf(d111,plain,
'double$udivide'('double$udivide'(X2,'double$udivide'('double$udivide'(X3,'double$udivide'(X2,'double$udivide'(X1,X0))),multiply(inverse(identity),multiply(X0,X1)))),inverse(identity)) = X3,
inference(superposition,[status(thm)],[d68,d17]) ).
cnf(d112,plain,
'double$udivide'(inverse(identity),'double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,'double$udivide'(X2,X3))),multiply(inverse(identity),multiply(X3,X2))))) = X1,
inference(demodulation,[status(thm)],[d111,d110]) ).
cnf(d113,plain,
'double$udivide'(identity,'double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,'double$udivide'(X2,X3))),multiply(inverse(identity),multiply(X3,X2))))) = X1,
inference(demodulation,[status(thm)],[d112,d15]) ).
cnf(d114,plain,
inverse('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,'double$udivide'(X2,X3))),multiply(inverse(identity),multiply(X3,X2))))) = X1,
inference(demodulation,[status(thm)],[d113,d53]) ).
cnf(d115,plain,
multiply('double$udivide'('double$udivide'(X1,'double$udivide'(X0,'double$udivide'(X2,X3))),multiply(inverse(identity),multiply(X3,X2))),X0) = X1,
inference(demodulation,[status(thm)],[d114,d0]) ).
cnf(d116,plain,
multiply(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,'double$udivide'(X2,X3))),multiply(inverse(identity),multiply(X3,X2)))) = X0,
inference(demodulation,[status(thm)],[d115,d66]) ).
cnf(d117,plain,
multiply(X1,'double$udivide'(multiply(inverse(identity),multiply(X3,X2)),'double$udivide'(X0,'double$udivide'(X1,'double$udivide'(X2,X3))))) = X0,
inference(demodulation,[status(thm)],[d116,d110]) ).
cnf(d118,plain,
multiply(X0,'double$udivide'(multiply(identity,multiply(X1,X2)),'double$udivide'(X3,'double$udivide'(X0,'double$udivide'(X2,X1))))) = X3,
inference(demodulation,[status(thm)],[d117,d15]) ).
cnf(d119,plain,
multiply(X2,'double$udivide'(multiply(X0,X1),'double$udivide'(X3,'double$udivide'(X2,'double$udivide'(X1,X0))))) = X3,
inference(demodulation,[status(thm)],[d118,d16]) ).
cnf(d120,plain,
multiply(X0,'double$udivide'(multiply(X0,X1),'double$udivide'(X2,X1))) = X2,
inference(superposition,[status(thm)],[d63,d119]) ).
cnf(d121,plain,
multiply(X2,'double$udivide'(multiply(X2,X1),'double$udivide'(X1,X0))) = X0,
inference(superposition,[status(thm)],[d110,d120]) ).
cnf(d122,plain,
multiply(multiply(X1,X0),multiply(X2,'double$udivide'(X0,X1))) = X2,
inference(superposition,[status(thm)],[d66,d76]) ).
cnf(d123,plain,
multiply(multiply('double$udivide'(X2,X1),multiply(X0,X1)),X2) = X0,
inference(superposition,[status(thm)],[d120,d122]) ).
cnf(d124,plain,
multiply(X0,multiply('double$udivide'(X0,X1),multiply(X2,X1))) = X2,
inference(demodulation,[status(thm)],[d123,d66]) ).
cnf(d125,plain,
multiply(X0,X1) = 'double$udivide'('double$udivide'(X0,multiply(X1,X2)),X2),
inference(superposition,[status(thm)],[d124,d124]) ).
cnf(d126,plain,
multiply(X0,X1) = 'double$udivide'(X2,'double$udivide'(X0,multiply(X1,X2))),
inference(demodulation,[status(thm)],[d125,d110]) ).
cnf(d127,plain,
multiply(X0,multiply(X1,X2)) = multiply(X2,multiply(X0,X1)),
inference(superposition,[status(thm)],[d126,d121]) ).
cnf(d128,plain,
multiply(b4,a4) != multiply(b4,a4),
inference(resolution,[status(thm)],[d127,d108]) ).
cnf(d129,plain,
$false,
inference(resolution,[status(thm)],[d107,d128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP100-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n020.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 14:23:19 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 65.38/14.97 % SZS status Unsatisfiable for theBenchmark.p
% 65.38/14.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------