%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP080-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 07:22:16 AM UTC 2026
% Result : Unsatisfiable 42.11s 7.76s
% Output : CNFRefutation 42.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 5
% Syntax : Number of clauses : 147 ( 142 unt; 0 nHn; 18 RR)
% Number of literals : 155 ( 154 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 266 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'('double$udivide'(identity,'double$udivide'(X0,'double$udivide'(X1,identity))),'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),identity)) = X2 ).
cnf(multiply,axiom,
multiply(X0,X1) = 'double$udivide'('double$udivide'(X1,X0),identity) ).
cnf(inverse,axiom,
inverse(X0) = 'double$udivide'(X0,identity) ).
cnf(identity,axiom,
identity = 'double$udivide'(X0,inverse(X0)) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ) ).
cnf(c0,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X0,'double$udivide'(X1,identity))),'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),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))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
inference(clausification,[status(esa)],[prove_these_axioms]) ).
cnf(d0,plain,
multiply(X1,X0) = inverse('double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d2,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(X0))),'double$udivide'('double$udivide'(X0,'double$udivide'(X2,X1)),identity)) = X2,
inference(demodulation,[status(thm)],[c0,c2]) ).
cnf(d3,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X2,inverse(X0))),inverse('double$udivide'(X0,'double$udivide'(X1,X2)))) = X1,
inference(demodulation,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[c3,d3]) ).
cnf(d5,plain,
'double$udivide'('double$udivide'(identity,identity),inverse('double$udivide'(X0,'double$udivide'(X1,X0)))) = X1,
inference(superposition,[status(thm)],[c3,d3]) ).
cnf(d6,plain,
'double$udivide'(inverse(identity),inverse('double$udivide'(X0,'double$udivide'(X1,X0)))) = X1,
inference(demodulation,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
'double$udivide'(identity,inverse('double$udivide'(X0,'double$udivide'(X1,X0)))) = X1,
inference(demodulation,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
'double$udivide'(identity,multiply('double$udivide'(X1,X0),X0)) = X1,
inference(demodulation,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
'double$udivide'(identity,multiply(inverse(X0),identity)) = X0,
inference(superposition,[status(thm)],[c2,d8]) ).
cnf(d10,plain,
'double$udivide'(identity,multiply(multiply(identity,X0),identity)) = inverse(X0),
inference(superposition,[status(thm)],[d1,d9]) ).
cnf(d11,plain,
'double$udivide'(identity,multiply(identity,inverse(X0))) = X0,
inference(superposition,[status(thm)],[c3,d8]) ).
cnf(d12,plain,
multiply(multiply(identity,inverse(X0)),identity) = inverse(X0),
inference(superposition,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
'double$udivide'(identity,inverse(X0)) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
'double$udivide'(identity,inverse(X0)) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse(X1))),inverse('double$udivide'(X1,inverse(X0)))) = X0,
inference(superposition,[status(thm)],[c2,d3]) ).
cnf(d16,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse(X0))),multiply(inverse(X1),X0)) = X1,
inference(demodulation,[status(thm)],[d15,d0]) ).
cnf(d17,plain,
multiply(inverse(X0),X0) = inverse(identity),
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d18,plain,
multiply(inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[d17,d4]) ).
cnf(d19,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse(X0))),identity) = X0,
inference(superposition,[status(thm)],[d18,d16]) ).
cnf(d20,plain,
inverse('double$udivide'(identity,'double$udivide'(identity,inverse(X0)))) = X0,
inference(demodulation,[status(thm)],[d19,c2]) ).
cnf(d21,plain,
multiply('double$udivide'(identity,inverse(X0)),identity) = X0,
inference(demodulation,[status(thm)],[d20,d0]) ).
cnf(d22,plain,
multiply(multiply(identity,X0),identity) = X0,
inference(demodulation,[status(thm)],[d21,d14]) ).
cnf(d23,plain,
'double$udivide'(identity,X0) = inverse(X0),
inference(demodulation,[status(thm)],[d10,d22]) ).
cnf(d24,plain,
multiply(identity,inverse(X0)) = inverse(multiply(identity,X0)),
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d25,plain,
inverse(multiply(identity,inverse(X0))) = X0,
inference(demodulation,[status(thm)],[d11,d23]) ).
cnf(d26,plain,
multiply(identity,inverse(inverse(X0))) = X0,
inference(demodulation,[status(thm)],[d25,d24]) ).
cnf(d27,plain,
multiply(identity,multiply(identity,X0)) = X0,
inference(demodulation,[status(thm)],[d26,d1]) ).
cnf(d28,plain,
multiply(X0,identity) = multiply(identity,X0),
inference(superposition,[status(thm)],[d27,d22]) ).
cnf(d29,plain,
multiply(identity,'double$udivide'(X0,X1)) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[d0,d1]) ).
cnf(d30,plain,
multiply(inverse(multiply(X1,X0)),identity) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d29,d22]) ).
cnf(d31,plain,
multiply(identity,inverse(multiply(X0,X1))) = 'double$udivide'(X1,X0),
inference(demodulation,[status(thm)],[d30,d28]) ).
cnf(d32,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(inverse('double$udivide'(X1,'double$udivide'(X2,X0))),inverse(X3))),inverse('double$udivide'(X3,X2))) = 'double$udivide'(identity,'double$udivide'(X0,inverse(X1))),
inference(superposition,[status(thm)],[d3,d3]) ).
cnf(d33,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(multiply('double$udivide'(X1,X2),X0),inverse(X3))),inverse('double$udivide'(X3,X1))) = 'double$udivide'(identity,'double$udivide'(X2,inverse(X0))),
inference(demodulation,[status(thm)],[d32,d0]) ).
cnf(d34,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(multiply('double$udivide'(X1,X2),X3),inverse(X0))),multiply(X1,X0)) = 'double$udivide'(identity,'double$udivide'(X2,inverse(X3))),
inference(demodulation,[status(thm)],[d33,d0]) ).
cnf(d35,plain,
identity = 'double$udivide'(inverse(X0),multiply(identity,X0)),
inference(superposition,[status(thm)],[d1,c3]) ).
cnf(d36,plain,
multiply(identity,identity) = inverse(identity),
inference(superposition,[status(thm)],[d4,d1]) ).
cnf(d37,plain,
multiply(identity,identity) = identity,
inference(demodulation,[status(thm)],[d36,d4]) ).
cnf(d38,plain,
identity = 'double$udivide'(inverse(identity),identity),
inference(superposition,[status(thm)],[d37,d35]) ).
cnf(d39,plain,
identity = inverse(inverse(identity)),
inference(demodulation,[status(thm)],[d38,c2]) ).
cnf(d40,plain,
identity = multiply(identity,identity),
inference(demodulation,[status(thm)],[d39,d1]) ).
cnf(d41,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(multiply('double$udivide'(identity,X0),X1),inverse(identity))),identity) = 'double$udivide'(identity,'double$udivide'(X0,inverse(X1))),
inference(superposition,[status(thm)],[d40,d34]) ).
cnf(d42,plain,
inverse('double$udivide'(identity,'double$udivide'(multiply('double$udivide'(identity,X0),X1),inverse(identity)))) = 'double$udivide'(identity,'double$udivide'(X0,inverse(X1))),
inference(demodulation,[status(thm)],[d41,c2]) ).
cnf(d43,plain,
multiply('double$udivide'(multiply('double$udivide'(identity,X0),X1),inverse(identity)),identity) = 'double$udivide'(identity,'double$udivide'(X0,inverse(X1))),
inference(demodulation,[status(thm)],[d42,d0]) ).
cnf(d44,plain,
multiply(identity,'double$udivide'(multiply('double$udivide'(identity,X0),X1),inverse(identity))) = 'double$udivide'(identity,'double$udivide'(X0,inverse(X1))),
inference(demodulation,[status(thm)],[d43,d28]) ).
cnf(d45,plain,
inverse(multiply(inverse(identity),multiply('double$udivide'(identity,X0),X1))) = 'double$udivide'(identity,'double$udivide'(X0,inverse(X1))),
inference(demodulation,[status(thm)],[d44,d29]) ).
cnf(d46,plain,
inverse(multiply(identity,multiply('double$udivide'(identity,X0),X1))) = 'double$udivide'(identity,'double$udivide'(X0,inverse(X1))),
inference(demodulation,[status(thm)],[d45,d4]) ).
cnf(d47,plain,
multiply(identity,inverse(multiply('double$udivide'(identity,X0),X1))) = 'double$udivide'(identity,'double$udivide'(X0,inverse(X1))),
inference(demodulation,[status(thm)],[d46,d24]) ).
cnf(d48,plain,
'double$udivide'(X1,'double$udivide'(identity,X0)) = 'double$udivide'(identity,'double$udivide'(X0,inverse(X1))),
inference(demodulation,[status(thm)],[d47,d31]) ).
cnf(d49,plain,
'double$udivide'(X1,inverse(X0)) = 'double$udivide'(identity,'double$udivide'(X0,inverse(X1))),
inference(demodulation,[status(thm)],[d48,d23]) ).
cnf(d50,plain,
'double$udivide'(X1,inverse(X0)) = inverse('double$udivide'(X0,inverse(X1))),
inference(demodulation,[status(thm)],[d49,d23]) ).
cnf(d51,plain,
'double$udivide'(X1,inverse(X0)) = multiply(inverse(X1),X0),
inference(demodulation,[status(thm)],[d50,d0]) ).
cnf(d52,plain,
'double$udivide'('double$udivide'(identity,X2),inverse('double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),'double$udivide'(X3,'double$udivide'(identity,'double$udivide'(X0,inverse(X1))))))) = X3,
inference(superposition,[status(thm)],[d3,d3]) ).
cnf(d53,plain,
'double$udivide'('double$udivide'(identity,X1),multiply('double$udivide'(X3,'double$udivide'(identity,'double$udivide'(X2,inverse(X0)))),'double$udivide'(X0,'double$udivide'(X1,X2)))) = X3,
inference(demodulation,[status(thm)],[d52,d0]) ).
cnf(d54,plain,
'double$udivide'('double$udivide'(identity,X0),multiply('double$udivide'(X1,'double$udivide'(identity,'double$udivide'(X2,identity))),'double$udivide'(identity,'double$udivide'(X0,X2)))) = X1,
inference(superposition,[status(thm)],[d4,d53]) ).
cnf(d55,plain,
'double$udivide'(inverse(X0),multiply('double$udivide'(X1,'double$udivide'(identity,'double$udivide'(X2,identity))),'double$udivide'(identity,'double$udivide'(X0,X2)))) = X1,
inference(demodulation,[status(thm)],[d54,d23]) ).
cnf(d56,plain,
'double$udivide'(inverse(X1),multiply('double$udivide'(X2,inverse('double$udivide'(X0,identity))),'double$udivide'(identity,'double$udivide'(X1,X0)))) = X2,
inference(demodulation,[status(thm)],[d55,d23]) ).
cnf(d57,plain,
'double$udivide'(inverse(X1),multiply('double$udivide'(X2,multiply(identity,X0)),'double$udivide'(identity,'double$udivide'(X1,X0)))) = X2,
inference(demodulation,[status(thm)],[d56,d0]) ).
cnf(d58,plain,
'double$udivide'(inverse(X0),multiply('double$udivide'(X2,multiply(identity,X1)),inverse('double$udivide'(X0,X1)))) = X2,
inference(demodulation,[status(thm)],[d57,d23]) ).
cnf(d59,plain,
'double$udivide'(inverse(X0),multiply('double$udivide'(X2,multiply(identity,X1)),multiply(X1,X0))) = X2,
inference(demodulation,[status(thm)],[d58,d0]) ).
cnf(d60,plain,
multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d23,d0]) ).
cnf(d61,plain,
multiply(identity,X0) = multiply(X0,identity),
inference(superposition,[status(thm)],[d60,d1]) ).
cnf(d62,plain,
multiply(identity,inverse(X0)) = 'double$udivide'(X0,inverse(identity)),
inference(superposition,[status(thm)],[d51,d61]) ).
cnf(d63,plain,
multiply(identity,inverse(X0)) = 'double$udivide'(X0,identity),
inference(demodulation,[status(thm)],[d62,d4]) ).
cnf(d64,plain,
multiply(identity,inverse(X0)) = inverse(X0),
inference(demodulation,[status(thm)],[d63,c2]) ).
cnf(d65,plain,
inverse(multiply('double$udivide'(X0,X1),X1)) = X0,
inference(demodulation,[status(thm)],[d8,d23]) ).
cnf(d66,plain,
identity = 'double$udivide'(multiply('double$udivide'(X0,X1),X1),X0),
inference(superposition,[status(thm)],[d65,c3]) ).
cnf(d67,plain,
inverse(multiply(identity,X0)) = multiply('double$udivide'(X0,X1),X1),
inference(superposition,[status(thm)],[d66,d65]) ).
cnf(d68,plain,
multiply(identity,inverse(X0)) = multiply('double$udivide'(X0,X1),X1),
inference(demodulation,[status(thm)],[d67,d24]) ).
cnf(d69,plain,
inverse(X0) = multiply('double$udivide'(X0,X1),X1),
inference(demodulation,[status(thm)],[d68,d64]) ).
cnf(d70,plain,
'double$udivide'(inverse(identity),inverse(X0)) = X0,
inference(superposition,[status(thm)],[d69,d59]) ).
cnf(d71,plain,
'double$udivide'(identity,inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d70,d4]) ).
cnf(d72,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d71,d23]) ).
cnf(d73,plain,
'double$udivide'(inverse(X0),inverse(X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[d72,d51]) ).
cnf(d74,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(X0),inverse(X1))),inverse('double$udivide'(X1,identity))) = X0,
inference(superposition,[status(thm)],[c3,d3]) ).
cnf(d75,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(X1),inverse(X0))),multiply(identity,X0)) = X1,
inference(demodulation,[status(thm)],[d74,d0]) ).
cnf(d76,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(X2),inverse('double$udivide'(X0,X1)))),inverse(multiply(X1,X0))) = X2,
inference(superposition,[status(thm)],[d29,d75]) ).
cnf(d77,plain,
'double$udivide'(inverse('double$udivide'(inverse(X0),inverse('double$udivide'(X1,X2)))),inverse(multiply(X2,X1))) = X0,
inference(demodulation,[status(thm)],[d76,d23]) ).
cnf(d78,plain,
multiply('double$udivide'(inverse(X0),inverse('double$udivide'(X1,X2))),multiply(X2,X1)) = X0,
inference(demodulation,[status(thm)],[d77,d73]) ).
cnf(d79,plain,
multiply(multiply(X0,'double$udivide'(X1,X2)),multiply(X2,X1)) = X0,
inference(demodulation,[status(thm)],[d78,d73]) ).
cnf(d80,plain,
'double$udivide'('double$udivide'(X0,X1),inverse(X2)) = multiply(multiply(X1,X0),X2),
inference(superposition,[status(thm)],[d0,d51]) ).
cnf(d81,plain,
inverse(inverse(X0)) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d14,d23]) ).
cnf(d82,plain,
X0 = multiply(identity,X0),
inference(demodulation,[status(thm)],[d81,d72]) ).
cnf(d83,plain,
multiply(identity,X0) = 'double$udivide'(X1,'double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[d65,d31]) ).
cnf(d84,plain,
X0 = 'double$udivide'(X1,'double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[d83,d82]) ).
cnf(d85,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d60,d72]) ).
cnf(d86,plain,
multiply(multiply(identity,X0),inverse(X0)) = identity,
inference(superposition,[status(thm)],[d1,d18]) ).
cnf(d87,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(multiply('double$udivide'(multiply(identity,X0),X1),X2),inverse(inverse(X0)))),identity) = 'double$udivide'(identity,'double$udivide'(X1,inverse(X2))),
inference(superposition,[status(thm)],[d86,d34]) ).
cnf(d88,plain,
inverse('double$udivide'(identity,'double$udivide'(multiply('double$udivide'(multiply(identity,X0),X1),X2),inverse(inverse(X0))))) = 'double$udivide'(identity,'double$udivide'(X1,inverse(X2))),
inference(demodulation,[status(thm)],[d87,c2]) ).
cnf(d89,plain,
multiply('double$udivide'(multiply('double$udivide'(multiply(identity,X0),X1),X2),inverse(inverse(X0))),identity) = 'double$udivide'(identity,'double$udivide'(X1,inverse(X2))),
inference(demodulation,[status(thm)],[d88,d0]) ).
cnf(d90,plain,
'double$udivide'(multiply('double$udivide'(multiply(identity,X0),X1),X2),inverse(inverse(X0))) = 'double$udivide'(identity,'double$udivide'(X1,inverse(X2))),
inference(demodulation,[status(thm)],[d89,d85]) ).
cnf(d91,plain,
'double$udivide'(multiply('double$udivide'(X0,X1),X2),inverse(inverse(X0))) = 'double$udivide'(identity,'double$udivide'(X1,inverse(X2))),
inference(demodulation,[status(thm)],[d90,d82]) ).
cnf(d92,plain,
'double$udivide'(multiply('double$udivide'(X0,X1),X2),X0) = 'double$udivide'(identity,'double$udivide'(X1,inverse(X2))),
inference(demodulation,[status(thm)],[d91,d72]) ).
cnf(d93,plain,
'double$udivide'(multiply('double$udivide'(X2,X0),X1),X2) = inverse('double$udivide'(X0,inverse(X1))),
inference(demodulation,[status(thm)],[d92,d23]) ).
cnf(d94,plain,
'double$udivide'(multiply('double$udivide'(X2,X0),X1),X2) = multiply(inverse(X1),X0),
inference(demodulation,[status(thm)],[d93,d0]) ).
cnf(d95,plain,
'double$udivide'(multiply('double$udivide'(X2,X1),X0),X2) = 'double$udivide'(X0,inverse(X1)),
inference(demodulation,[status(thm)],[d94,d51]) ).
cnf(d96,plain,
multiply('double$udivide'(X0,X1),X2) = 'double$udivide'(X0,'double$udivide'(X2,inverse(X1))),
inference(superposition,[status(thm)],[d95,d84]) ).
cnf(d97,plain,
'double$udivide'(multiply(X1,X2),X0) = 'double$udivide'(X2,inverse('double$udivide'(X1,X0))),
inference(superposition,[status(thm)],[d84,d95]) ).
cnf(d98,plain,
'double$udivide'(multiply(X0,X2),X1) = 'double$udivide'(X2,multiply(X1,X0)),
inference(demodulation,[status(thm)],[d97,d0]) ).
cnf(d99,plain,
'double$udivide'(inverse(X2),multiply(X1,X0)) = multiply(X2,'double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[d0,d73]) ).
cnf(d100,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X2,inverse(X0))),multiply('double$udivide'(X1,X2),X0)) = X1,
inference(demodulation,[status(thm)],[d3,d0]) ).
cnf(d101,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X0,identity)),inverse('double$udivide'(identity,'double$udivide'(X1,X0)))) = X1,
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d102,plain,
'double$udivide'('double$udivide'(identity,inverse(X0)),inverse('double$udivide'(identity,'double$udivide'(X1,X0)))) = X1,
inference(demodulation,[status(thm)],[d101,c2]) ).
cnf(d103,plain,
'double$udivide'('double$udivide'(identity,inverse(X1)),multiply('double$udivide'(X0,X1),identity)) = X0,
inference(demodulation,[status(thm)],[d102,d0]) ).
cnf(d104,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(multiply('double$udivide'(X1,X0),identity),inverse(X2))),multiply(X1,X2)) = 'double$udivide'(identity,inverse(X0)),
inference(superposition,[status(thm)],[d103,d100]) ).
cnf(d105,plain,
'double$udivide'(inverse('double$udivide'(multiply('double$udivide'(X0,X1),identity),inverse(X2))),multiply(X0,X2)) = 'double$udivide'(identity,inverse(X1)),
inference(demodulation,[status(thm)],[d104,d23]) ).
cnf(d106,plain,
multiply('double$udivide'(multiply('double$udivide'(X0,X1),identity),inverse(X2)),'double$udivide'(X2,X0)) = 'double$udivide'(identity,inverse(X1)),
inference(demodulation,[status(thm)],[d105,d99]) ).
cnf(d107,plain,
multiply('double$udivide'(identity,multiply(inverse(X2),'double$udivide'(X0,X1))),'double$udivide'(X2,X0)) = 'double$udivide'(identity,inverse(X1)),
inference(demodulation,[status(thm)],[d106,d98]) ).
cnf(d108,plain,
multiply(inverse(multiply(inverse(X0),'double$udivide'(X1,X2))),'double$udivide'(X0,X1)) = 'double$udivide'(identity,inverse(X2)),
inference(demodulation,[status(thm)],[d107,d23]) ).
cnf(d109,plain,
'double$udivide'(multiply(inverse(X0),'double$udivide'(X1,X2)),inverse('double$udivide'(X0,X1))) = 'double$udivide'(identity,inverse(X2)),
inference(demodulation,[status(thm)],[d108,d51]) ).
cnf(d110,plain,
'double$udivide'('double$udivide'(X1,X2),multiply(inverse('double$udivide'(X0,X1)),inverse(X0))) = 'double$udivide'(identity,inverse(X2)),
inference(demodulation,[status(thm)],[d109,d98]) ).
cnf(d111,plain,
'double$udivide'('double$udivide'(X1,X2),'double$udivide'('double$udivide'(X0,X1),inverse(inverse(X0)))) = 'double$udivide'(identity,inverse(X2)),
inference(demodulation,[status(thm)],[d110,d51]) ).
cnf(d112,plain,
multiply('double$udivide'('double$udivide'(X0,X1),inverse(X2)),'double$udivide'(X2,X0)) = 'double$udivide'(identity,inverse(X1)),
inference(demodulation,[status(thm)],[d111,d96]) ).
cnf(d113,plain,
multiply(multiply(multiply(X1,X0),X2),'double$udivide'(X2,X0)) = 'double$udivide'(identity,inverse(X1)),
inference(demodulation,[status(thm)],[d112,d80]) ).
cnf(d114,plain,
multiply(multiply(multiply(X0,X1),X2),'double$udivide'(X2,X1)) = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d113,d23]) ).
cnf(d115,plain,
multiply(multiply(multiply(X0,X1),X2),'double$udivide'(X2,X1)) = X0,
inference(demodulation,[status(thm)],[d114,d72]) ).
cnf(d116,plain,
multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[d115,d79]) ).
cnf(d117,plain,
( identity != identity
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2 ),
inference(demodulation,[status(thm)],[c4,d18]) ).
cnf(d118,plain,
multiply(multiply(X1,X0),'double$udivide'(X0,X1)) = identity,
inference(superposition,[status(thm)],[d0,d18]) ).
cnf(d119,plain,
identity = 'double$udivide'('double$udivide'(X0,X1),multiply(X1,X0)),
inference(superposition,[status(thm)],[d0,c3]) ).
cnf(d120,plain,
identity = 'double$udivide'('double$udivide'(X0,inverse(X0)),identity),
inference(superposition,[status(thm)],[d18,d119]) ).
cnf(d121,plain,
identity = inverse('double$udivide'(X0,inverse(X0))),
inference(demodulation,[status(thm)],[d120,c2]) ).
cnf(d122,plain,
identity = multiply(inverse(X0),X0),
inference(demodulation,[status(thm)],[d121,d0]) ).
cnf(d123,plain,
identity = multiply(multiply(identity,X0),inverse(X0)),
inference(superposition,[status(thm)],[d1,d122]) ).
cnf(d124,plain,
multiply(identity,'double$udivide'(inverse(X0),multiply(identity,X0))) = identity,
inference(superposition,[status(thm)],[d123,d118]) ).
cnf(d125,plain,
inverse(multiply(multiply(identity,X0),inverse(X0))) = identity,
inference(demodulation,[status(thm)],[d124,d29]) ).
cnf(d126,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm)],[d125,d86]) ).
cnf(d127,plain,
multiply('double$udivide'(identity,identity),identity) = identity,
inference(superposition,[status(thm)],[d126,d21]) ).
cnf(d128,plain,
multiply(inverse(identity),identity) = identity,
inference(demodulation,[status(thm)],[d127,c2]) ).
cnf(d129,plain,
identity = identity,
inference(demodulation,[status(thm)],[d128,d18]) ).
cnf(d130,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2 ),
inference(resolution,[status(thm)],[d129,d117]) ).
cnf(d131,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(demodulation,[status(thm)],[d130,d82]) ).
cnf(d132,plain,
'double$udivide'(identity,multiply('double$udivide'(X0,identity),identity)) = X0,
inference(superposition,[status(thm)],[c3,d103]) ).
cnf(d133,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d132,d8]) ).
cnf(d134,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(resolution,[status(thm)],[d133,d131]) ).
cnf(d135,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm)],[d134,d116]) ).
cnf(d136,plain,
$false,
inference(resolution,[status(thm)],[d133,d135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP080-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:16:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 42.11/7.76 % SZS status Unsatisfiable for theBenchmark.p
% 42.11/7.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------