%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP103-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 07:22:20 AM UTC 2026
% Result : Unsatisfiable 230.17s 33.47s
% Output : CNFRefutation 230.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 62
% Number of leaves : 5
% Syntax : Number of clauses : 203 ( 192 unt; 0 nHn; 16 RR)
% Number of literals : 231 ( 230 equ; 40 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 12 ( 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 : 380 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(identity,X1),'double$udivide'(X2,'double$udivide'(X1,X0)))),'double$udivide'(identity,identity)) = X2 ).
cnf(multiply,axiom,
multiply(X0,X1) = 'double$udivide'('double$udivide'(X1,X0),identity) ).
cnf(inverse,axiom,
inverse(X0) = 'double$udivide'(X0,identity) ).
cnf(identity,axiom,
identity = 'double$udivide'(X0,inverse(X0)) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ) ).
cnf(c0,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(identity,X1),'double$udivide'(X2,'double$udivide'(X1,X0)))),'double$udivide'(identity,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(a4,b4) != multiply(b4,a4)
| 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$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(identity,X1),'double$udivide'(X2,'double$udivide'(X1,X0)))),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[c0,c2]) ).
cnf(d2,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,X0),'double$udivide'(X1,inverse(X0)))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[c2,d1]) ).
cnf(d3,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,X0),identity)),inverse(identity)) = X0,
inference(superposition,[status(thm)],[c3,d2]) ).
cnf(d4,plain,
'double$udivide'('double$udivide'(identity,inverse('double$udivide'(identity,X0))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
'double$udivide'('double$udivide'(identity,multiply(X0,identity)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
multiply(inverse(X0),X0) = inverse(identity),
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d7,plain,
'double$udivide'('double$udivide'(identity,inverse(identity)),inverse(identity)) = inverse(identity),
inference(superposition,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
'double$udivide'(identity,inverse(identity)) = inverse(identity),
inference(demodulation,[status(thm)],[d7,c3]) ).
cnf(d9,plain,
identity = inverse(identity),
inference(demodulation,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
'double$udivide'('double$udivide'(identity,multiply(X0,identity)),identity) = X0,
inference(demodulation,[status(thm)],[d5,d9]) ).
cnf(d11,plain,
inverse('double$udivide'(identity,multiply(X0,identity))) = X0,
inference(demodulation,[status(thm)],[d10,c2]) ).
cnf(d12,plain,
multiply(multiply(X0,identity),identity) = X0,
inference(demodulation,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
'double$udivide'('double$udivide'(inverse(X0),'double$udivide'('double$udivide'(identity,X0),'double$udivide'(X1,identity))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[c3,d1]) ).
cnf(d14,plain,
'double$udivide'('double$udivide'(inverse(X1),'double$udivide'('double$udivide'(identity,X1),inverse(X0))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d13,c2]) ).
cnf(d15,plain,
'double$udivide'('double$udivide'(inverse(X0),'double$udivide'('double$udivide'(identity,X0),inverse(X1))),identity) = X1,
inference(demodulation,[status(thm)],[d14,d9]) ).
cnf(d16,plain,
inverse('double$udivide'(inverse(X0),'double$udivide'('double$udivide'(identity,X0),inverse(X1)))) = X1,
inference(demodulation,[status(thm)],[d15,c2]) ).
cnf(d17,plain,
multiply('double$udivide'('double$udivide'(identity,X0),inverse(X1)),inverse(X0)) = X1,
inference(demodulation,[status(thm)],[d16,d0]) ).
cnf(d18,plain,
multiply(identity,inverse(X0)) = 'double$udivide'(identity,X0),
inference(superposition,[status(thm)],[c3,d17]) ).
cnf(d19,plain,
multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d20,plain,
multiply(identity,inverse(X0)) = inverse(multiply(identity,X0)),
inference(superposition,[status(thm)],[d19,d19]) ).
cnf(d21,plain,
'double$udivide'(identity,X0) = inverse(multiply(identity,X0)),
inference(demodulation,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
'double$udivide'(identity,inverse(X0)) = inverse('double$udivide'(identity,X0)),
inference(superposition,[status(thm)],[d18,d21]) ).
cnf(d23,plain,
'double$udivide'(identity,inverse(X0)) = multiply(X0,identity),
inference(demodulation,[status(thm)],[d22,d0]) ).
cnf(d24,plain,
multiply(inverse(X0),identity) = inverse(multiply(X0,identity)),
inference(superposition,[status(thm)],[d23,d0]) ).
cnf(d25,plain,
multiply(inverse(multiply(X0,identity)),identity) = inverse(X0),
inference(superposition,[status(thm)],[d12,d24]) ).
cnf(d26,plain,
multiply(multiply(inverse(X0),identity),identity) = inverse(X0),
inference(demodulation,[status(thm)],[d25,d24]) ).
cnf(d27,plain,
inverse(X0) = inverse(X0),
inference(demodulation,[status(thm)],[d26,d12]) ).
cnf(d28,plain,
inverse('double$udivide'(X0,X1)) = multiply(X1,X0),
inference(superposition,[status(thm)],[d0,d27]) ).
cnf(d29,plain,
multiply(identity,multiply(X1,X0)) = 'double$udivide'(identity,'double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[d0,d18]) ).
cnf(d30,plain,
multiply(identity,'double$udivide'(X0,X1)) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[d0,d19]) ).
cnf(d31,plain,
multiply(identity,inverse('double$udivide'(X0,X1))) = inverse(inverse(multiply(X1,X0))),
inference(superposition,[status(thm)],[d30,d20]) ).
cnf(d32,plain,
multiply(identity,multiply(X1,X0)) = inverse(inverse(multiply(X1,X0))),
inference(demodulation,[status(thm)],[d31,d0]) ).
cnf(d33,plain,
multiply(identity,multiply(X0,X1)) = multiply(identity,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d32,d19]) ).
cnf(d34,plain,
multiply(identity,inverse(multiply(X1,X0))) = multiply(identity,multiply(identity,'double$udivide'(X0,X1))),
inference(superposition,[status(thm)],[d30,d33]) ).
cnf(d35,plain,
'double$udivide'(identity,multiply(X0,X1)) = multiply(identity,multiply(identity,'double$udivide'(X1,X0))),
inference(demodulation,[status(thm)],[d34,d18]) ).
cnf(d36,plain,
'double$udivide'(identity,multiply(X1,X0)) = 'double$udivide'(identity,'double$udivide'('double$udivide'(X0,X1),identity)),
inference(demodulation,[status(thm)],[d35,d29]) ).
cnf(d37,plain,
'double$udivide'(identity,multiply(X1,X0)) = 'double$udivide'(identity,inverse('double$udivide'(X0,X1))),
inference(demodulation,[status(thm)],[d36,c2]) ).
cnf(d38,plain,
'double$udivide'(identity,multiply(X1,X0)) = multiply('double$udivide'(X0,X1),identity),
inference(demodulation,[status(thm)],[d37,d23]) ).
cnf(d39,plain,
multiply(identity,X2) = inverse(multiply(inverse(identity),'double$udivide'(X0,'double$udivide'('double$udivide'(identity,X1),'double$udivide'(X2,'double$udivide'(X1,X0)))))),
inference(superposition,[status(thm)],[d1,d30]) ).
cnf(d40,plain,
multiply(identity,X0) = inverse(multiply(identity,'double$udivide'(X1,'double$udivide'('double$udivide'(identity,X2),'double$udivide'(X0,'double$udivide'(X2,X1)))))),
inference(demodulation,[status(thm)],[d39,d9]) ).
cnf(d41,plain,
multiply(identity,X2) = 'double$udivide'(identity,'double$udivide'(X0,'double$udivide'('double$udivide'(identity,X1),'double$udivide'(X2,'double$udivide'(X1,X0))))),
inference(demodulation,[status(thm)],[d40,d21]) ).
cnf(d42,plain,
'double$udivide'('double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'(X0,'double$udivide'('double$udivide'(identity,X1),'double$udivide'(X2,'double$udivide'(X1,X0))))),'double$udivide'(X3,X2))),inverse(identity)) = X3,
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d43,plain,
multiply(identity,X3) = inverse(multiply(inverse(identity),'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'(X0,'double$udivide'('double$udivide'(identity,X1),'double$udivide'(X2,'double$udivide'(X1,X0))))),'double$udivide'(X3,X2))))),
inference(superposition,[status(thm)],[d42,d30]) ).
cnf(d44,plain,
multiply(identity,X0) = inverse(multiply(identity,'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'(X1,'double$udivide'('double$udivide'(identity,X2),'double$udivide'(X3,'double$udivide'(X2,X1))))),'double$udivide'(X0,X3))))),
inference(demodulation,[status(thm)],[d43,d9]) ).
cnf(d45,plain,
multiply(identity,X3) = 'double$udivide'(identity,'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'(X0,'double$udivide'('double$udivide'(identity,X1),'double$udivide'(X2,'double$udivide'(X1,X0))))),'double$udivide'(X3,X2)))),
inference(demodulation,[status(thm)],[d44,d21]) ).
cnf(d46,plain,
multiply(identity,X0) = 'double$udivide'(identity,'double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(X1,'double$udivide'('double$udivide'(identity,X2),'double$udivide'(X3,'double$udivide'(X2,X1))))),'double$udivide'(X0,X3)))),
inference(demodulation,[status(thm)],[d45,d9]) ).
cnf(d47,plain,
multiply(identity,X3) = 'double$udivide'(identity,'double$udivide'(identity,'double$udivide'(multiply(identity,X2),'double$udivide'(X3,X2)))),
inference(demodulation,[status(thm)],[d46,d41]) ).
cnf(d48,plain,
'double$udivide'('double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'(X0,'double$udivide'('double$udivide'(identity,X1),'double$udivide'(X2,'double$udivide'(X1,X0))))),'double$udivide'(X3,X2)))),'double$udivide'(X4,X3))),inverse(identity)) = X4,
inference(superposition,[status(thm)],[d42,d1]) ).
cnf(d49,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'(X0,'double$udivide'('double$udivide'(identity,X1),'double$udivide'(X2,'double$udivide'(X1,X0))))),'double$udivide'(X3,X2)))),'double$udivide'(X4,X3))),inverse(identity)) = X4,
inference(demodulation,[status(thm)],[d48,d9]) ).
cnf(d50,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(X0,'double$udivide'('double$udivide'(identity,X1),'double$udivide'(X2,'double$udivide'(X1,X0))))),'double$udivide'(X3,X2)))),'double$udivide'(X4,X3))),inverse(identity)) = X4,
inference(demodulation,[status(thm)],[d49,d9]) ).
cnf(d51,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(identity,'double$udivide'(multiply(identity,X2),'double$udivide'(X3,X2)))),'double$udivide'(X4,X3))),inverse(identity)) = X4,
inference(demodulation,[status(thm)],[d50,d41]) ).
cnf(d52,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(identity,'double$udivide'(multiply(identity,X0),'double$udivide'(X1,X0)))),'double$udivide'(X2,X1))),identity) = X2,
inference(demodulation,[status(thm)],[d51,d9]) ).
cnf(d53,plain,
inverse('double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(identity,'double$udivide'(multiply(identity,X0),'double$udivide'(X1,X0)))),'double$udivide'(X2,X1)))) = X2,
inference(demodulation,[status(thm)],[d52,c2]) ).
cnf(d54,plain,
multiply('double$udivide'('double$udivide'(identity,'double$udivide'(identity,'double$udivide'(multiply(identity,X0),'double$udivide'(X1,X0)))),'double$udivide'(X2,X1)),identity) = X2,
inference(demodulation,[status(thm)],[d53,d0]) ).
cnf(d55,plain,
multiply('double$udivide'(multiply(identity,X1),'double$udivide'(X2,X1)),identity) = X2,
inference(demodulation,[status(thm)],[d54,d47]) ).
cnf(d56,plain,
'double$udivide'(identity,multiply('double$udivide'(X1,X0),multiply(identity,X0))) = X1,
inference(demodulation,[status(thm)],[d55,d38]) ).
cnf(d57,plain,
identity = 'double$udivide'('double$udivide'(X0,X1),multiply(X1,X0)),
inference(superposition,[status(thm)],[d0,c3]) ).
cnf(d58,plain,
'double$udivide'('double$udivide'(multiply(X1,X0),'double$udivide'('double$udivide'(identity,'double$udivide'(X0,X1)),'double$udivide'(X2,identity))),inverse(identity)) = X2,
inference(superposition,[status(thm)],[d57,d1]) ).
cnf(d59,plain,
'double$udivide'('double$udivide'(multiply(X1,X2),'double$udivide'('double$udivide'(identity,'double$udivide'(X2,X1)),inverse(X0))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d58,c2]) ).
cnf(d60,plain,
'double$udivide'('double$udivide'(multiply(X0,X1),'double$udivide'('double$udivide'(identity,'double$udivide'(X1,X0)),inverse(X2))),identity) = X2,
inference(demodulation,[status(thm)],[d59,d9]) ).
cnf(d61,plain,
inverse('double$udivide'(multiply(X0,X1),'double$udivide'('double$udivide'(identity,'double$udivide'(X1,X0)),inverse(X2)))) = X2,
inference(demodulation,[status(thm)],[d60,c2]) ).
cnf(d62,plain,
multiply('double$udivide'('double$udivide'(identity,'double$udivide'(X1,X0)),inverse(X2)),multiply(X0,X1)) = X2,
inference(demodulation,[status(thm)],[d61,d0]) ).
cnf(d63,plain,
'double$udivide'(identity,X0) = 'double$udivide'(identity,'double$udivide'(inverse(X0),identity)),
inference(superposition,[status(thm)],[d62,d56]) ).
cnf(d64,plain,
'double$udivide'(identity,X0) = 'double$udivide'(identity,inverse(inverse(X0))),
inference(demodulation,[status(thm)],[d63,c2]) ).
cnf(d65,plain,
'double$udivide'(identity,X0) = multiply(inverse(X0),identity),
inference(demodulation,[status(thm)],[d64,d23]) ).
cnf(d66,plain,
identity = 'double$udivide'('double$udivide'(identity,multiply(X0,identity)),X0),
inference(superposition,[status(thm)],[d12,d57]) ).
cnf(d67,plain,
multiply(identity,inverse(multiply(inverse(X0),identity))) = X0,
inference(superposition,[status(thm)],[d66,d17]) ).
cnf(d68,plain,
'double$udivide'(identity,multiply(inverse(X0),identity)) = X0,
inference(demodulation,[status(thm)],[d67,d18]) ).
cnf(d69,plain,
'double$udivide'(identity,'double$udivide'(identity,X0)) = X0,
inference(demodulation,[status(thm)],[d68,d65]) ).
cnf(d70,plain,
multiply(identity,multiply(X0,identity)) = inverse(multiply(inverse(X0),identity)),
inference(superposition,[status(thm)],[d23,d30]) ).
cnf(d71,plain,
'double$udivide'(identity,'double$udivide'(identity,X0)) = inverse(multiply(inverse(X0),identity)),
inference(demodulation,[status(thm)],[d70,d29]) ).
cnf(d72,plain,
'double$udivide'(identity,'double$udivide'(identity,X0)) = multiply(inverse(inverse(X0)),identity),
inference(demodulation,[status(thm)],[d71,d24]) ).
cnf(d73,plain,
'double$udivide'(identity,'double$udivide'(identity,X0)) = multiply(multiply(identity,X0),identity),
inference(demodulation,[status(thm)],[d72,d19]) ).
cnf(d74,plain,
multiply(identity,multiply(identity,X0)) = inverse(multiply(identity,inverse(X0))),
inference(superposition,[status(thm)],[d20,d19]) ).
cnf(d75,plain,
multiply(identity,multiply(identity,X0)) = multiply(identity,inverse(inverse(X0))),
inference(demodulation,[status(thm)],[d74,d20]) ).
cnf(d76,plain,
multiply(identity,multiply(identity,X0)) = multiply(identity,multiply(identity,X0)),
inference(demodulation,[status(thm)],[d75,d19]) ).
cnf(d77,plain,
multiply(identity,multiply(identity,'double$udivide'(X0,X1))) = multiply(identity,inverse(multiply(X1,X0))),
inference(superposition,[status(thm)],[d30,d76]) ).
cnf(d78,plain,
multiply(identity,inverse(multiply(X1,X0))) = multiply(identity,inverse(multiply(X1,X0))),
inference(demodulation,[status(thm)],[d77,d30]) ).
cnf(d79,plain,
'double$udivide'(identity,multiply(X0,X1)) = multiply(identity,inverse(multiply(X0,X1))),
inference(demodulation,[status(thm)],[d78,d18]) ).
cnf(d80,plain,
'double$udivide'(identity,multiply(X0,X1)) = 'double$udivide'(identity,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d79,d18]) ).
cnf(d81,plain,
X0 = 'double$udivide'(identity,multiply(inverse(X0),identity)),
inference(superposition,[status(thm)],[d68,d80]) ).
cnf(d82,plain,
inverse(inverse(X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[d19,d27]) ).
cnf(d83,plain,
inverse(X0) = 'double$udivide'(identity,multiply(multiply(identity,X0),identity)),
inference(superposition,[status(thm)],[d82,d81]) ).
cnf(d84,plain,
inverse(X0) = 'double$udivide'(identity,'double$udivide'(identity,'double$udivide'(identity,X0))),
inference(demodulation,[status(thm)],[d83,d73]) ).
cnf(d85,plain,
inverse(X0) = 'double$udivide'(identity,X0),
inference(demodulation,[status(thm)],[d84,d69]) ).
cnf(d86,plain,
inverse('double$udivide'(identity,X0)) = X0,
inference(demodulation,[status(thm)],[d69,d85]) ).
cnf(d87,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d86,d85]) ).
cnf(d88,plain,
inverse(multiply(X1,X0)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d0,d87]) ).
cnf(d89,plain,
X0 = multiply(identity,X0),
inference(demodulation,[status(thm)],[d82,d87]) ).
cnf(d90,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(inverse(identity),'double$udivide'(X1,'double$udivide'(identity,X0)))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[c2,d1]) ).
cnf(d91,plain,
multiply(identity,X1) = inverse(multiply(inverse(identity),'double$udivide'(X0,'double$udivide'(inverse(identity),'double$udivide'(X1,'double$udivide'(identity,X0)))))),
inference(superposition,[status(thm)],[d90,d30]) ).
cnf(d92,plain,
X0 = inverse(multiply(inverse(identity),'double$udivide'(X1,'double$udivide'(inverse(identity),'double$udivide'(X0,'double$udivide'(identity,X1)))))),
inference(demodulation,[status(thm)],[d91,d89]) ).
cnf(d93,plain,
X0 = inverse(multiply(identity,'double$udivide'(X1,'double$udivide'(inverse(identity),'double$udivide'(X0,'double$udivide'(identity,X1)))))),
inference(demodulation,[status(thm)],[d92,d9]) ).
cnf(d94,plain,
X1 = inverse('double$udivide'(X0,'double$udivide'(inverse(identity),'double$udivide'(X1,'double$udivide'(identity,X0))))),
inference(demodulation,[status(thm)],[d93,d89]) ).
cnf(d95,plain,
X1 = multiply('double$udivide'(inverse(identity),'double$udivide'(X1,'double$udivide'(identity,X0))),X0),
inference(demodulation,[status(thm)],[d94,d0]) ).
cnf(d96,plain,
X0 = multiply('double$udivide'(identity,'double$udivide'(X0,'double$udivide'(identity,X1))),X1),
inference(demodulation,[status(thm)],[d95,d9]) ).
cnf(d97,plain,
X0 = multiply(inverse('double$udivide'(X0,'double$udivide'(identity,X1))),X1),
inference(demodulation,[status(thm)],[d96,d85]) ).
cnf(d98,plain,
X0 = multiply(multiply('double$udivide'(identity,X1),X0),X1),
inference(demodulation,[status(thm)],[d97,d0]) ).
cnf(d99,plain,
X1 = multiply(multiply(inverse(X0),X1),X0),
inference(demodulation,[status(thm)],[d98,d85]) ).
cnf(d100,plain,
'double$udivide'('double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'(X0,'double$udivide'(inverse(identity),'double$udivide'(X1,'double$udivide'(identity,X0))))),'double$udivide'(X2,X1))),inverse(identity)) = X2,
inference(superposition,[status(thm)],[d90,d1]) ).
cnf(d101,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(X0,'double$udivide'(inverse(identity),'double$udivide'(X1,'double$udivide'(identity,X0))))),'double$udivide'(X2,X1))),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d100,d9]) ).
cnf(d102,plain,
'double$udivide'(inverse('double$udivide'('double$udivide'(identity,'double$udivide'(X0,'double$udivide'(inverse(identity),'double$udivide'(X1,'double$udivide'(identity,X0))))),'double$udivide'(X2,X1))),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d101,d85]) ).
cnf(d103,plain,
'double$udivide'(multiply('double$udivide'(X2,X1),'double$udivide'(identity,'double$udivide'(X0,'double$udivide'(inverse(identity),'double$udivide'(X1,'double$udivide'(identity,X0)))))),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d102,d0]) ).
cnf(d104,plain,
'double$udivide'(multiply('double$udivide'(X2,X1),inverse('double$udivide'(X0,'double$udivide'(inverse(identity),'double$udivide'(X1,'double$udivide'(identity,X0)))))),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d103,d85]) ).
cnf(d105,plain,
'double$udivide'(multiply('double$udivide'(X2,X1),multiply('double$udivide'(inverse(identity),'double$udivide'(X1,'double$udivide'(identity,X0))),X0)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d104,d0]) ).
cnf(d106,plain,
'double$udivide'(multiply('double$udivide'(X0,X1),multiply('double$udivide'(identity,'double$udivide'(X1,'double$udivide'(identity,X2))),X2)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d105,d9]) ).
cnf(d107,plain,
'double$udivide'(multiply('double$udivide'(X2,X0),multiply(inverse('double$udivide'(X0,'double$udivide'(identity,X1))),X1)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d106,d85]) ).
cnf(d108,plain,
'double$udivide'(multiply('double$udivide'(X2,X0),multiply(multiply('double$udivide'(identity,X1),X0),X1)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d107,d0]) ).
cnf(d109,plain,
'double$udivide'(multiply('double$udivide'(X1,X2),multiply(multiply(inverse(X0),X2),X0)),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d108,d85]) ).
cnf(d110,plain,
'double$udivide'(multiply('double$udivide'(X0,X1),multiply(multiply(inverse(X2),X1),X2)),identity) = X0,
inference(demodulation,[status(thm)],[d109,d9]) ).
cnf(d111,plain,
inverse(multiply('double$udivide'(X0,X1),multiply(multiply(inverse(X2),X1),X2))) = X0,
inference(demodulation,[status(thm)],[d110,c2]) ).
cnf(d112,plain,
inverse(multiply('double$udivide'(X2,X1),X1)) = X2,
inference(demodulation,[status(thm)],[d111,d99]) ).
cnf(d113,plain,
'double$udivide'(X1,'double$udivide'(X0,X1)) = X0,
inference(demodulation,[status(thm)],[d112,d88]) ).
cnf(d114,plain,
inverse(X1) = multiply('double$udivide'(X1,X0),X0),
inference(superposition,[status(thm)],[d113,d28]) ).
cnf(d115,plain,
'double$udivide'('double$udivide'(X1,X0),X1) = X0,
inference(superposition,[status(thm)],[d113,d113]) ).
cnf(d116,plain,
identity = 'double$udivide'(inverse(X0),multiply(identity,X0)),
inference(superposition,[status(thm)],[d19,c3]) ).
cnf(d117,plain,
identity = 'double$udivide'(multiply(identity,X0),multiply(identity,inverse(X0))),
inference(superposition,[status(thm)],[d19,d116]) ).
cnf(d118,plain,
identity = 'double$udivide'(multiply(identity,multiply(identity,X0)),multiply(identity,multiply(identity,inverse(X0)))),
inference(superposition,[status(thm)],[d20,d117]) ).
cnf(d119,plain,
'double$udivide'('double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'(X1,'double$udivide'('double$udivide'(identity,X2),'double$udivide'(multiply(identity,multiply(identity,inverse(X0))),'double$udivide'(X2,X1))))),identity)),inverse(identity)) = multiply(identity,multiply(identity,X0)),
inference(superposition,[status(thm)],[d118,d42]) ).
cnf(d120,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X0,'double$udivide'('double$udivide'(identity,X1),'double$udivide'(multiply(identity,multiply(identity,inverse(X2))),'double$udivide'(X1,X0))))),identity) = multiply(identity,multiply(identity,X2)),
inference(demodulation,[status(thm)],[d119,d115]) ).
cnf(d121,plain,
'double$udivide'(X0,'double$udivide'('double$udivide'(identity,X1),'double$udivide'(multiply(identity,multiply(identity,inverse(X2))),'double$udivide'(X1,X0)))) = multiply(identity,multiply(identity,X2)),
inference(demodulation,[status(thm)],[d120,d115]) ).
cnf(d122,plain,
'double$udivide'(X1,'double$udivide'(inverse(X0),'double$udivide'(multiply(identity,multiply(identity,inverse(X2))),'double$udivide'(X0,X1)))) = multiply(identity,multiply(identity,X2)),
inference(demodulation,[status(thm)],[d121,d85]) ).
cnf(d123,plain,
'double$udivide'(X1,'double$udivide'(inverse(X2),'double$udivide'(multiply(identity,inverse(X0)),'double$udivide'(X2,X1)))) = multiply(identity,multiply(identity,X0)),
inference(demodulation,[status(thm)],[d122,d89]) ).
cnf(d124,plain,
'double$udivide'(X1,'double$udivide'(inverse(X2),'double$udivide'(inverse(X0),'double$udivide'(X2,X1)))) = multiply(identity,multiply(identity,X0)),
inference(demodulation,[status(thm)],[d123,d89]) ).
cnf(d125,plain,
'double$udivide'(X1,'double$udivide'(inverse(X2),'double$udivide'(inverse(X0),'double$udivide'(X2,X1)))) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d124,d89]) ).
cnf(d126,plain,
'double$udivide'(X1,'double$udivide'(inverse(X2),'double$udivide'(inverse(X0),'double$udivide'(X2,X1)))) = X0,
inference(demodulation,[status(thm)],[d125,d89]) ).
cnf(d127,plain,
'double$udivide'('double$udivide'(X1,inverse(inverse(X0))),X0) = X1,
inference(superposition,[status(thm)],[d126,d126]) ).
cnf(d128,plain,
'double$udivide'('double$udivide'(X1,X0),X0) = X1,
inference(demodulation,[status(thm)],[d127,d87]) ).
cnf(d129,plain,
inverse('double$udivide'(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[d128,d114]) ).
cnf(d130,plain,
multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[status(thm)],[d129,d28]) ).
cnf(d131,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(identity,'double$udivide'(X1,'double$udivide'(inverse(identity),X0)))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[c3,d1]) ).
cnf(d132,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(identity,'double$udivide'(X1,'double$udivide'(identity,X0)))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d131,d9]) ).
cnf(d133,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(identity,'double$udivide'(X1,'double$udivide'(identity,X0)))),identity) = X1,
inference(demodulation,[status(thm)],[d132,d9]) ).
cnf(d134,plain,
inverse('double$udivide'(X0,'double$udivide'(identity,'double$udivide'(X1,'double$udivide'(identity,X0))))) = X1,
inference(demodulation,[status(thm)],[d133,c2]) ).
cnf(d135,plain,
multiply('double$udivide'(identity,'double$udivide'(X1,'double$udivide'(identity,X0))),X0) = X1,
inference(demodulation,[status(thm)],[d134,d0]) ).
cnf(d136,plain,
multiply(inverse('double$udivide'(X0,'double$udivide'(identity,X1))),X1) = X0,
inference(demodulation,[status(thm)],[d135,d85]) ).
cnf(d137,plain,
multiply(inverse('double$udivide'(X1,inverse(X0))),X0) = X1,
inference(demodulation,[status(thm)],[d136,d85]) ).
cnf(d138,plain,
multiply(multiply(inverse(X1),X0),X1) = X0,
inference(demodulation,[status(thm)],[d137,d0]) ).
cnf(d139,plain,
X0 = 'double$udivide'(identity,'double$udivide'(identity,X0)),
inference(demodulation,[status(thm)],[d81,d65]) ).
cnf(d140,plain,
X0 = inverse('double$udivide'(identity,X0)),
inference(demodulation,[status(thm)],[d139,d85]) ).
cnf(d141,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d140,d0]) ).
cnf(d142,plain,
inverse(multiply(identity,X0)) = 'double$udivide'(identity,X0),
inference(superposition,[status(thm)],[d21,d27]) ).
cnf(d143,plain,
inverse('double$udivide'(identity,X0)) = 'double$udivide'(identity,inverse(X0)),
inference(superposition,[status(thm)],[d18,d142]) ).
cnf(d144,plain,
multiply(X0,identity) = 'double$udivide'(identity,inverse(X0)),
inference(demodulation,[status(thm)],[d143,d0]) ).
cnf(d145,plain,
multiply(X0,identity) = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d144,d85]) ).
cnf(d146,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d145,d141]) ).
cnf(d147,plain,
multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(superposition,[status(thm)],[d146,d138]) ).
cnf(d148,plain,
multiply(multiply('double$udivide'(X0,X1),X2),multiply(X0,X1)) = X2,
inference(superposition,[status(thm)],[d129,d147]) ).
cnf(d149,plain,
multiply(multiply(X0,X1),multiply('double$udivide'(X0,X1),X2)) = X2,
inference(demodulation,[status(thm)],[d148,d130]) ).
cnf(d150,plain,
X2 = multiply(multiply(multiply(X1,X0),X2),'double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[d0,d99]) ).
cnf(d151,plain,
X2 = multiply('double$udivide'(X1,X0),multiply(multiply(X0,X1),X2)),
inference(demodulation,[status(thm)],[d150,d130]) ).
cnf(d152,plain,
X2 = multiply('double$udivide'(X1,X0),multiply(X2,multiply(X0,X1))),
inference(superposition,[status(thm)],[d130,d151]) ).
cnf(d153,plain,
multiply(multiply(X0,X1),X2) = multiply(X2,multiply(X1,X0)),
inference(superposition,[status(thm)],[d152,d149]) ).
cnf(d154,plain,
multiply(X2,multiply(X0,X1)) = multiply(X2,multiply(X1,X0)),
inference(superposition,[status(thm)],[d153,d130]) ).
cnf(d155,plain,
multiply(inverse(identity),'double$udivide'(X0,'double$udivide'(inverse(identity),'double$udivide'(X1,'double$udivide'(identity,X0))))) = inverse(X1),
inference(superposition,[status(thm)],[d90,d0]) ).
cnf(d156,plain,
multiply(identity,'double$udivide'(X0,'double$udivide'(inverse(identity),'double$udivide'(X1,'double$udivide'(identity,X0))))) = inverse(X1),
inference(demodulation,[status(thm)],[d155,d9]) ).
cnf(d157,plain,
'double$udivide'(X0,'double$udivide'(inverse(identity),'double$udivide'(X1,'double$udivide'(identity,X0)))) = inverse(X1),
inference(demodulation,[status(thm)],[d156,d89]) ).
cnf(d158,plain,
'double$udivide'(X0,'double$udivide'(identity,'double$udivide'(X1,'double$udivide'(identity,X0)))) = inverse(X1),
inference(demodulation,[status(thm)],[d157,d9]) ).
cnf(d159,plain,
'double$udivide'(X1,inverse('double$udivide'(X0,'double$udivide'(identity,X1)))) = inverse(X0),
inference(demodulation,[status(thm)],[d158,d85]) ).
cnf(d160,plain,
'double$udivide'(X1,multiply('double$udivide'(identity,X1),X0)) = inverse(X0),
inference(demodulation,[status(thm)],[d159,d0]) ).
cnf(d161,plain,
'double$udivide'(X0,multiply(inverse(X0),X1)) = inverse(X1),
inference(demodulation,[status(thm)],[d160,d85]) ).
cnf(d162,plain,
'double$udivide'(inverse(X1),X0) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d161,d115]) ).
cnf(d163,plain,
'double$udivide'(inverse(X2),'double$udivide'(X0,X1)) = multiply(multiply(X1,X0),X2),
inference(superposition,[status(thm)],[d0,d162]) ).
cnf(d164,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(identity,X1),'double$udivide'(X2,'double$udivide'(X1,X0)))),identity) = X2,
inference(demodulation,[status(thm)],[d1,d9]) ).
cnf(d165,plain,
inverse('double$udivide'(X0,'double$udivide'('double$udivide'(identity,X1),'double$udivide'(X2,'double$udivide'(X1,X0))))) = X2,
inference(demodulation,[status(thm)],[d164,c2]) ).
cnf(d166,plain,
multiply('double$udivide'('double$udivide'(identity,X1),'double$udivide'(X2,'double$udivide'(X1,X0))),X0) = X2,
inference(demodulation,[status(thm)],[d165,d0]) ).
cnf(d167,plain,
multiply(X2,'double$udivide'('double$udivide'(identity,X0),'double$udivide'(X1,'double$udivide'(X0,X2)))) = X1,
inference(demodulation,[status(thm)],[d166,d130]) ).
cnf(d168,plain,
multiply(X1,'double$udivide'(inverse(X0),'double$udivide'(X2,'double$udivide'(X0,X1)))) = X2,
inference(demodulation,[status(thm)],[d167,d85]) ).
cnf(d169,plain,
multiply(X2,multiply(multiply('double$udivide'(X0,X2),X1),X0)) = X1,
inference(demodulation,[status(thm)],[d168,d163]) ).
cnf(d170,plain,
multiply(X0,multiply(X1,multiply('double$udivide'(X1,X0),X2))) = X2,
inference(demodulation,[status(thm)],[d169,d154]) ).
cnf(d171,plain,
multiply(X1,multiply(X0,X2)) = multiply(X2,multiply(X1,X0)),
inference(superposition,[status(thm)],[d152,d170]) ).
cnf(d172,plain,
( multiply(a4,b4) != multiply(b4,a4)
| inverse(identity) != identity
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2 ),
inference(demodulation,[status(thm)],[c4,d6]) ).
cnf(d173,plain,
( multiply(a4,b4) != multiply(b4,a4)
| identity != identity
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2 ),
inference(demodulation,[status(thm)],[d172,d9]) ).
cnf(d174,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2
| identity != identity ),
inference(demodulation,[status(thm)],[d173,d89]) ).
cnf(d175,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| a2 != a2
| identity != identity ),
inference(demodulation,[status(thm)],[d174,d130]) ).
cnf(d176,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| a2 != a2
| identity != identity ),
inference(demodulation,[status(thm)],[d175,d130]) ).
cnf(d177,plain,
identity = 'double$udivide'(multiply(identity,X0),'double$udivide'(identity,X0)),
inference(demodulation,[status(thm)],[d117,d18]) ).
cnf(d178,plain,
multiply('double$udivide'(identity,identity),X0) = multiply(identity,X0),
inference(superposition,[status(thm)],[d177,d135]) ).
cnf(d179,plain,
multiply(inverse(identity),X0) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d178,c2]) ).
cnf(d180,plain,
multiply(identity,X0) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d179,d9]) ).
cnf(d181,plain,
'double$udivide'(identity,X0) = multiply(identity,inverse(X0)),
inference(superposition,[status(thm)],[d18,d180]) ).
cnf(d182,plain,
'double$udivide'(identity,inverse(X0)) = inverse('double$udivide'(identity,X0)),
inference(superposition,[status(thm)],[d181,d21]) ).
cnf(d183,plain,
multiply(X0,identity) = inverse('double$udivide'(identity,X0)),
inference(demodulation,[status(thm)],[d182,d23]) ).
cnf(d184,plain,
multiply(X0,identity) = multiply(X0,identity),
inference(demodulation,[status(thm)],[d183,d0]) ).
cnf(d185,plain,
X0 = multiply('double$udivide'(identity,'double$udivide'(X0,'double$udivide'(identity,identity))),identity),
inference(superposition,[status(thm)],[d135,d184]) ).
cnf(d186,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d185,d135]) ).
cnf(d187,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(resolution,[status(thm)],[d186,d176]) ).
cnf(d188,plain,
( a2 != a2
| multiply(b3,multiply(c3,a3)) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(a4,b4) ),
inference(demodulation,[status(thm)],[d187,d171]) ).
cnf(d189,plain,
( a2 != a2
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(a4,b4) ),
inference(demodulation,[status(thm)],[d188,d171]) ).
cnf(d190,plain,
( a2 != a2
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)) ),
inference(resolution,[status(thm)],[d186,d189]) ).
cnf(d191,plain,
a2 != a2,
inference(equality_resolution,[status(thm)],[d190]) ).
cnf(d192,plain,
$false,
inference(resolution,[status(thm)],[d186,d191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP103-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:22:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 230.17/33.47 % SZS status Unsatisfiable for theBenchmark.p
% 230.17/33.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------