%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP574-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:24:03 AM UTC 2026
% Result : Unsatisfiable 44.72s 6.34s
% Output : CNFRefutation 44.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 5
% Syntax : Number of clauses : 143 ( 143 unt; 0 nHn; 17 RR)
% Number of literals : 143 ( 142 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 251 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),'double$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$udivide'(X0,inverse(X0)) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(identity,a2) != a2 ).
cnf(c0,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),'double$udivide'(X2,identity))),'double$udivide'(identity,identity)) = X1,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(X0,X1) = 'double$udivide'('double$udivide'(X1,X0),identity),
inference(clausification,[status(esa)],[multiply]) ).
cnf(c2,plain,
inverse(X0) = 'double$udivide'(X0,identity),
inference(clausification,[status(esa)],[inverse]) ).
cnf(c3,plain,
identity = 'double$udivide'(X0,inverse(X0)),
inference(clausification,[status(esa)],[identity]) ).
cnf(c4,plain,
multiply(identity,a2) != a2,
inference(clausification,[status(esa)],[prove_these_axioms_2]) ).
cnf(d0,plain,
multiply(X1,X0) = inverse('double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d2,plain,
multiply(identity,inverse(X0)) = inverse(multiply(identity,X0)),
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d3,plain,
multiply(identity,'double$udivide'(X0,X1)) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[d0,d1]) ).
cnf(d4,plain,
multiply(identity,inverse('double$udivide'(X0,X1))) = inverse(inverse(multiply(X1,X0))),
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
multiply(identity,multiply(X1,X0)) = inverse(inverse(multiply(X1,X0))),
inference(demodulation,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
multiply(identity,multiply(X0,X1)) = multiply(identity,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X1,'double$udivide'(identity,identity))),'double$udivide'(identity,identity)) = 'double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),'double$udivide'(X2,identity))),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d8,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X0,inverse(identity))),'double$udivide'(identity,identity)) = 'double$udivide'(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X2,X1)),'double$udivide'(X2,identity))),
inference(demodulation,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X0,inverse(identity))),inverse(identity)) = 'double$udivide'(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X2,X1)),'double$udivide'(X2,identity))),
inference(demodulation,[status(thm)],[d8,c2]) ).
cnf(d10,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)) = 'double$udivide'(X2,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),inverse(X0))),
inference(demodulation,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X0,X1)),inverse(X0))),'double$udivide'(identity,identity)) = X2,
inference(demodulation,[status(thm)],[c0,c2]) ).
cnf(d12,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),inverse(X2))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d11,c2]) ).
cnf(d13,plain,
'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
'double$udivide'('double$udivide'('double$udivide'(identity,identity),inverse(identity)),inverse(identity)) = identity,
inference(superposition,[status(thm)],[c3,d13]) ).
cnf(d15,plain,
'double$udivide'('double$udivide'(inverse(identity),inverse(identity)),inverse(identity)) = identity,
inference(demodulation,[status(thm)],[d14,c2]) ).
cnf(d16,plain,
'double$udivide'('double$udivide'('double$udivide'(identity,identity),inverse(identity)),inverse(identity)) = 'double$udivide'(inverse(identity),inverse(identity)),
inference(superposition,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
'double$udivide'('double$udivide'(inverse(identity),inverse(identity)),inverse(identity)) = 'double$udivide'(inverse(identity),inverse(identity)),
inference(demodulation,[status(thm)],[d16,c2]) ).
cnf(d18,plain,
identity = 'double$udivide'(inverse(identity),inverse(identity)),
inference(demodulation,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
'double$udivide'('double$udivide'('double$udivide'(identity,identity),inverse(identity)),inverse(identity)) = inverse(identity),
inference(superposition,[status(thm)],[d18,d13]) ).
cnf(d20,plain,
'double$udivide'('double$udivide'(inverse(identity),inverse(identity)),inverse(identity)) = inverse(identity),
inference(demodulation,[status(thm)],[d19,c2]) ).
cnf(d21,plain,
'double$udivide'(identity,inverse(identity)) = inverse(identity),
inference(demodulation,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
identity = inverse(identity),
inference(demodulation,[status(thm)],[d21,c3]) ).
cnf(d23,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)) = 'double$udivide'(inverse(X0),'double$udivide'('double$udivide'(X1,identity),inverse(X0))),
inference(superposition,[status(thm)],[c3,d10]) ).
cnf(d24,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X0,identity)),inverse(identity)) = 'double$udivide'(inverse(X1),'double$udivide'('double$udivide'(X0,identity),inverse(X1))),
inference(demodulation,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
'double$udivide'('double$udivide'(identity,inverse(X0)),inverse(identity)) = 'double$udivide'(inverse(X1),'double$udivide'('double$udivide'(X0,identity),inverse(X1))),
inference(demodulation,[status(thm)],[d24,c2]) ).
cnf(d26,plain,
'double$udivide'('double$udivide'(identity,inverse(X0)),identity) = 'double$udivide'(inverse(X1),'double$udivide'('double$udivide'(X0,identity),inverse(X1))),
inference(demodulation,[status(thm)],[d25,d22]) ).
cnf(d27,plain,
inverse('double$udivide'(identity,inverse(X0))) = 'double$udivide'(inverse(X1),'double$udivide'('double$udivide'(X0,identity),inverse(X1))),
inference(demodulation,[status(thm)],[d26,c2]) ).
cnf(d28,plain,
multiply(inverse(X0),identity) = 'double$udivide'(inverse(X1),'double$udivide'('double$udivide'(X0,identity),inverse(X1))),
inference(demodulation,[status(thm)],[d27,d0]) ).
cnf(d29,plain,
multiply(inverse(X0),identity) = 'double$udivide'(inverse(X1),'double$udivide'(inverse(X0),inverse(X1))),
inference(demodulation,[status(thm)],[d28,c2]) ).
cnf(d30,plain,
multiply(inverse(X0),identity) = 'double$udivide'(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[c3,d29]) ).
cnf(d31,plain,
multiply(inverse(X0),identity) = inverse(inverse(inverse(X0))),
inference(demodulation,[status(thm)],[d30,c2]) ).
cnf(d32,plain,
multiply(inverse(X0),identity) = multiply(identity,inverse(X0)),
inference(demodulation,[status(thm)],[d31,d1]) ).
cnf(d33,plain,
'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X0,identity)),inverse(identity)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d13,d22]) ).
cnf(d34,plain,
'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X0,identity)),identity),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d33,d22]) ).
cnf(d35,plain,
'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X0,identity)),identity),identity) = X0,
inference(demodulation,[status(thm)],[d34,d22]) ).
cnf(d36,plain,
inverse('double$udivide'('double$udivide'(identity,'double$udivide'(X0,identity)),identity)) = X0,
inference(demodulation,[status(thm)],[d35,c2]) ).
cnf(d37,plain,
multiply(identity,'double$udivide'(identity,'double$udivide'(X0,identity))) = X0,
inference(demodulation,[status(thm)],[d36,d0]) ).
cnf(d38,plain,
inverse(multiply('double$udivide'(X0,identity),identity)) = X0,
inference(demodulation,[status(thm)],[d37,d3]) ).
cnf(d39,plain,
inverse(multiply(inverse(X0),identity)) = X0,
inference(demodulation,[status(thm)],[d38,c2]) ).
cnf(d40,plain,
inverse(multiply(identity,inverse(X0))) = X0,
inference(demodulation,[status(thm)],[d39,d32]) ).
cnf(d41,plain,
multiply(identity,inverse(inverse(X0))) = X0,
inference(demodulation,[status(thm)],[d40,d2]) ).
cnf(d42,plain,
multiply(identity,multiply(identity,X0)) = X0,
inference(demodulation,[status(thm)],[d41,d1]) ).
cnf(d43,plain,
X0 = multiply(identity,multiply(identity,X0)),
inference(superposition,[status(thm)],[d42,d6]) ).
cnf(d44,plain,
multiply(multiply(identity,X0),identity) = multiply(identity,inverse(inverse(X0))),
inference(superposition,[status(thm)],[d1,d32]) ).
cnf(d45,plain,
multiply(multiply(identity,X0),identity) = multiply(identity,multiply(identity,X0)),
inference(demodulation,[status(thm)],[d44,d1]) ).
cnf(d46,plain,
multiply(multiply(identity,X0),identity) = X0,
inference(demodulation,[status(thm)],[d45,d42]) ).
cnf(d47,plain,
multiply(X0,identity) = multiply(identity,X0),
inference(superposition,[status(thm)],[d42,d46]) ).
cnf(d48,plain,
X0 = multiply(identity,multiply(X0,identity)),
inference(superposition,[status(thm)],[d47,d43]) ).
cnf(d49,plain,
multiply(identity,inverse(multiply(X1,X0))) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d3,d42]) ).
cnf(d50,plain,
multiply(identity,inverse(multiply(X0,identity))) = inverse(X0),
inference(superposition,[status(thm)],[d48,d2]) ).
cnf(d51,plain,
'double$udivide'(identity,X0) = inverse(X0),
inference(demodulation,[status(thm)],[d50,d49]) ).
cnf(d52,plain,
identity = 'double$udivide'(inverse(X0),multiply(identity,X0)),
inference(superposition,[status(thm)],[d1,c3]) ).
cnf(d53,plain,
identity = 'double$udivide'(multiply(identity,inverse(X0)),multiply(identity,multiply(identity,X0))),
inference(superposition,[status(thm)],[d2,d52]) ).
cnf(d54,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)) = 'double$udivide'(multiply(identity,multiply(identity,X0)),'double$udivide'('double$udivide'(X1,identity),inverse(multiply(identity,inverse(X0))))),
inference(superposition,[status(thm)],[d53,d10]) ).
cnf(d55,plain,
'double$udivide'(inverse('double$udivide'(X0,inverse(identity))),inverse(identity)) = 'double$udivide'(multiply(identity,multiply(identity,X1)),'double$udivide'('double$udivide'(X0,identity),inverse(multiply(identity,inverse(X1))))),
inference(demodulation,[status(thm)],[d54,d51]) ).
cnf(d56,plain,
'double$udivide'(multiply(inverse(identity),X0),inverse(identity)) = 'double$udivide'(multiply(identity,multiply(identity,X1)),'double$udivide'('double$udivide'(X0,identity),inverse(multiply(identity,inverse(X1))))),
inference(demodulation,[status(thm)],[d55,d0]) ).
cnf(d57,plain,
'double$udivide'(multiply(identity,X0),inverse(identity)) = 'double$udivide'(multiply(identity,multiply(identity,X1)),'double$udivide'('double$udivide'(X0,identity),inverse(multiply(identity,inverse(X1))))),
inference(demodulation,[status(thm)],[d56,d22]) ).
cnf(d58,plain,
'double$udivide'(multiply(identity,X0),identity) = 'double$udivide'(multiply(identity,multiply(identity,X1)),'double$udivide'('double$udivide'(X0,identity),inverse(multiply(identity,inverse(X1))))),
inference(demodulation,[status(thm)],[d57,d22]) ).
cnf(d59,plain,
inverse(multiply(identity,X0)) = 'double$udivide'(multiply(identity,multiply(identity,X1)),'double$udivide'('double$udivide'(X0,identity),inverse(multiply(identity,inverse(X1))))),
inference(demodulation,[status(thm)],[d58,c2]) ).
cnf(d60,plain,
multiply(identity,inverse(X0)) = 'double$udivide'(multiply(identity,multiply(identity,X1)),'double$udivide'('double$udivide'(X0,identity),inverse(multiply(identity,inverse(X1))))),
inference(demodulation,[status(thm)],[d59,d2]) ).
cnf(d61,plain,
multiply(identity,inverse(X1)) = 'double$udivide'(X0,'double$udivide'('double$udivide'(X1,identity),inverse(multiply(identity,inverse(X0))))),
inference(demodulation,[status(thm)],[d60,d42]) ).
cnf(d62,plain,
multiply(identity,inverse(X0)) = 'double$udivide'(X1,'double$udivide'(inverse(X0),inverse(multiply(identity,inverse(X1))))),
inference(demodulation,[status(thm)],[d61,c2]) ).
cnf(d63,plain,
multiply(identity,inverse(X1)) = 'double$udivide'(X0,'double$udivide'(inverse(X1),multiply(identity,inverse(inverse(X0))))),
inference(demodulation,[status(thm)],[d62,d2]) ).
cnf(d64,plain,
multiply(identity,inverse(X1)) = 'double$udivide'(X0,'double$udivide'(inverse(X1),multiply(identity,multiply(identity,X0)))),
inference(demodulation,[status(thm)],[d63,d1]) ).
cnf(d65,plain,
multiply(identity,inverse(X1)) = 'double$udivide'(X0,'double$udivide'(inverse(X1),X0)),
inference(demodulation,[status(thm)],[d64,d42]) ).
cnf(d66,plain,
multiply(inverse(identity),inverse(identity)) = inverse(identity),
inference(superposition,[status(thm)],[d18,d0]) ).
cnf(d67,plain,
multiply(identity,inverse(identity)) = inverse(identity),
inference(demodulation,[status(thm)],[d66,d22]) ).
cnf(d68,plain,
multiply(identity,identity) = inverse(identity),
inference(demodulation,[status(thm)],[d67,d22]) ).
cnf(d69,plain,
multiply(identity,identity) = identity,
inference(demodulation,[status(thm)],[d68,d22]) ).
cnf(d70,plain,
multiply(identity,inverse(X0)) = inverse(multiply(X0,identity)),
inference(superposition,[status(thm)],[d47,d2]) ).
cnf(d71,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)) = 'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(X1,X0),inverse('double$udivide'('double$udivide'(identity,'double$udivide'(X0,inverse(identity))),inverse(identity))))),
inference(superposition,[status(thm)],[d13,d10]) ).
cnf(d72,plain,
'double$udivide'(inverse('double$udivide'(X0,inverse(identity))),inverse(identity)) = 'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(X0,X1),inverse('double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity))))),
inference(demodulation,[status(thm)],[d71,d51]) ).
cnf(d73,plain,
'double$udivide'(multiply(inverse(identity),X0),inverse(identity)) = 'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(X0,X1),inverse('double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity))))),
inference(demodulation,[status(thm)],[d72,d0]) ).
cnf(d74,plain,
'double$udivide'(multiply(identity,X0),inverse(identity)) = 'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(X0,X1),inverse('double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity))))),
inference(demodulation,[status(thm)],[d73,d22]) ).
cnf(d75,plain,
'double$udivide'(multiply(identity,X0),identity) = 'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(X0,X1),inverse('double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity))))),
inference(demodulation,[status(thm)],[d74,d22]) ).
cnf(d76,plain,
inverse(multiply(identity,X0)) = 'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(X0,X1),inverse('double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity))))),
inference(demodulation,[status(thm)],[d75,c2]) ).
cnf(d77,plain,
multiply(identity,inverse(X0)) = 'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(X0,X1),inverse('double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity))))),
inference(demodulation,[status(thm)],[d76,d2]) ).
cnf(d78,plain,
multiply(identity,inverse(X0)) = 'double$udivide'(identity,'double$udivide'('double$udivide'(X0,X1),inverse('double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity))))),
inference(demodulation,[status(thm)],[d77,d22]) ).
cnf(d79,plain,
multiply(identity,inverse(X0)) = inverse('double$udivide'('double$udivide'(X0,X1),inverse('double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity))))),
inference(demodulation,[status(thm)],[d78,d51]) ).
cnf(d80,plain,
multiply(identity,inverse(X0)) = multiply(inverse('double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity))),'double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[d79,d0]) ).
cnf(d81,plain,
multiply(identity,inverse(X1)) = multiply(multiply(inverse(identity),'double$udivide'(identity,'double$udivide'(X0,inverse(identity)))),'double$udivide'(X1,X0)),
inference(demodulation,[status(thm)],[d80,d0]) ).
cnf(d82,plain,
multiply(identity,inverse(X0)) = multiply(multiply(identity,'double$udivide'(identity,'double$udivide'(X1,inverse(identity)))),'double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[d81,d22]) ).
cnf(d83,plain,
multiply(identity,inverse(X1)) = multiply(inverse(multiply('double$udivide'(X0,inverse(identity)),identity)),'double$udivide'(X1,X0)),
inference(demodulation,[status(thm)],[d82,d3]) ).
cnf(d84,plain,
multiply(identity,inverse(X1)) = multiply(multiply(identity,inverse('double$udivide'(X0,inverse(identity)))),'double$udivide'(X1,X0)),
inference(demodulation,[status(thm)],[d83,d70]) ).
cnf(d85,plain,
multiply(identity,inverse(X1)) = multiply(multiply(identity,multiply(inverse(identity),X0)),'double$udivide'(X1,X0)),
inference(demodulation,[status(thm)],[d84,d0]) ).
cnf(d86,plain,
multiply(identity,inverse(X0)) = multiply(multiply(identity,multiply(identity,X1)),'double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[d85,d22]) ).
cnf(d87,plain,
multiply(identity,inverse(X1)) = multiply(X0,'double$udivide'(X1,X0)),
inference(demodulation,[status(thm)],[d86,d42]) ).
cnf(d88,plain,
multiply(identity,inverse(identity)) = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[d51,d87]) ).
cnf(d89,plain,
multiply(identity,identity) = multiply(X0,inverse(X0)),
inference(demodulation,[status(thm)],[d88,d22]) ).
cnf(d90,plain,
identity = multiply(X0,inverse(X0)),
inference(demodulation,[status(thm)],[d89,d69]) ).
cnf(d91,plain,
multiply(identity,inverse(identity)) = 'double$udivide'(inverse(X0),X0),
inference(superposition,[status(thm)],[d90,d49]) ).
cnf(d92,plain,
identity = 'double$udivide'(inverse(X0),X0),
inference(demodulation,[status(thm)],[d91,d90]) ).
cnf(d93,plain,
multiply(identity,inverse(X0)) = 'double$udivide'(X0,identity),
inference(superposition,[status(thm)],[d92,d65]) ).
cnf(d94,plain,
multiply(identity,inverse(X0)) = inverse(X0),
inference(demodulation,[status(thm)],[d93,c2]) ).
cnf(d95,plain,
multiply(identity,inverse(multiply(identity,X0))) = inverse(X0),
inference(superposition,[status(thm)],[d42,d2]) ).
cnf(d96,plain,
multiply(identity,multiply(identity,inverse(X0))) = inverse(X0),
inference(demodulation,[status(thm)],[d95,d2]) ).
cnf(d97,plain,
inverse(X0) = inverse(X0),
inference(demodulation,[status(thm)],[d96,d42]) ).
cnf(d98,plain,
inverse('double$udivide'(X0,X1)) = multiply(X1,X0),
inference(superposition,[status(thm)],[d0,d97]) ).
cnf(d99,plain,
inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[d51,d98]) ).
cnf(d100,plain,
multiply(identity,multiply(X0,identity)) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d99,d94]) ).
cnf(d101,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d100,d48]) ).
cnf(d102,plain,
inverse(inverse(X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[d1,d97]) ).
cnf(d103,plain,
X0 = multiply(identity,X0),
inference(demodulation,[status(thm)],[d102,d101]) ).
cnf(d104,plain,
a2 != a2,
inference(demodulation,[status(thm)],[c4,d103]) ).
cnf(d105,plain,
'double$udivide'('double$udivide'('double$udivide'(identity,identity),'double$udivide'('double$udivide'(X3,X1),'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),'double$udivide'(X2,identity))),identity))),'double$udivide'(identity,identity)) = X3,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d106,plain,
'double$udivide'('double$udivide'(inverse(identity),'double$udivide'('double$udivide'(X0,X1),'double$udivide'('double$udivide'(X2,'double$udivide'('double$udivide'(X1,'double$udivide'(X3,X2)),'double$udivide'(X3,identity))),identity))),'double$udivide'(identity,identity)) = X0,
inference(demodulation,[status(thm)],[d105,c2]) ).
cnf(d107,plain,
'double$udivide'('double$udivide'(inverse(identity),'double$udivide'('double$udivide'(X3,X1),inverse('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),'double$udivide'(X2,identity)))))),'double$udivide'(identity,identity)) = X3,
inference(demodulation,[status(thm)],[d106,c2]) ).
cnf(d108,plain,
'double$udivide'('double$udivide'(inverse(identity),'double$udivide'('double$udivide'(X3,X1),multiply('double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),'double$udivide'(X2,identity)),X0))),'double$udivide'(identity,identity)) = X3,
inference(demodulation,[status(thm)],[d107,d0]) ).
cnf(d109,plain,
'double$udivide'('double$udivide'(inverse(identity),'double$udivide'('double$udivide'(X1,X2),multiply('double$udivide'('double$udivide'(X2,'double$udivide'(X0,X3)),inverse(X0)),X3))),'double$udivide'(identity,identity)) = X1,
inference(demodulation,[status(thm)],[d108,c2]) ).
cnf(d110,plain,
'double$udivide'('double$udivide'(inverse(identity),'double$udivide'('double$udivide'(X0,X1),multiply('double$udivide'('double$udivide'(X1,'double$udivide'(X2,X3)),inverse(X2)),X3))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d109,c2]) ).
cnf(d111,plain,
identity = 'double$udivide'('double$udivide'(X0,X1),multiply(X1,X0)),
inference(superposition,[status(thm)],[d0,c3]) ).
cnf(d112,plain,
'double$udivide'('double$udivide'(inverse(identity),'double$udivide'('double$udivide'(X2,X3),multiply('double$udivide'('double$udivide'(X3,identity),inverse('double$udivide'(X0,X1))),multiply(X1,X0)))),inverse(identity)) = X2,
inference(superposition,[status(thm)],[d111,d110]) ).
cnf(d113,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X0,X1),multiply('double$udivide'('double$udivide'(X1,identity),inverse('double$udivide'(X2,X3))),multiply(X3,X2)))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d112,d22]) ).
cnf(d114,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X1,X0),multiply('double$udivide'(inverse(X0),inverse('double$udivide'(X2,X3))),multiply(X3,X2)))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d113,c2]) ).
cnf(d115,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X2,X3),multiply('double$udivide'(inverse(X3),multiply(X1,X0)),multiply(X1,X0)))),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d114,d0]) ).
cnf(d116,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X0,X1),multiply('double$udivide'(inverse(X1),multiply(X2,X3)),multiply(X2,X3)))),identity) = X0,
inference(demodulation,[status(thm)],[d115,d22]) ).
cnf(d117,plain,
inverse('double$udivide'(identity,'double$udivide'('double$udivide'(X0,X1),multiply('double$udivide'(inverse(X1),multiply(X2,X3)),multiply(X2,X3))))) = X0,
inference(demodulation,[status(thm)],[d116,c2]) ).
cnf(d118,plain,
multiply('double$udivide'('double$udivide'(X0,X1),multiply('double$udivide'(inverse(X1),multiply(X2,X3)),multiply(X2,X3))),identity) = X0,
inference(demodulation,[status(thm)],[d117,d0]) ).
cnf(d119,plain,
multiply(identity,'double$udivide'('double$udivide'(X0,X1),multiply('double$udivide'(inverse(X1),multiply(X2,X3)),multiply(X2,X3)))) = X0,
inference(demodulation,[status(thm)],[d118,d47]) ).
cnf(d120,plain,
inverse(multiply(multiply('double$udivide'(inverse(X1),multiply(X2,X3)),multiply(X2,X3)),'double$udivide'(X0,X1))) = X0,
inference(demodulation,[status(thm)],[d119,d3]) ).
cnf(d121,plain,
identity = 'double$udivide'(multiply(identity,X0),multiply(identity,inverse(X0))),
inference(superposition,[status(thm)],[d1,d52]) ).
cnf(d122,plain,
'double$udivide'('double$udivide'(inverse(identity),'double$udivide'('double$udivide'(X1,X2),multiply('double$udivide'('double$udivide'(X2,identity),inverse(multiply(identity,X0))),multiply(identity,inverse(X0))))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[d121,d110]) ).
cnf(d123,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X0,X1),multiply('double$udivide'('double$udivide'(X1,identity),inverse(multiply(identity,X2))),multiply(identity,inverse(X2))))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d122,d22]) ).
cnf(d124,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X1,X0),multiply('double$udivide'(inverse(X0),inverse(multiply(identity,X2))),multiply(identity,inverse(X2))))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d123,c2]) ).
cnf(d125,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X1,X2),multiply('double$udivide'(inverse(X2),multiply(identity,inverse(X0))),multiply(identity,inverse(X0))))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d124,d2]) ).
cnf(d126,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X0,X1),multiply('double$udivide'(inverse(X1),multiply(identity,inverse(X2))),multiply(identity,inverse(X2))))),identity) = X0,
inference(demodulation,[status(thm)],[d125,d22]) ).
cnf(d127,plain,
inverse('double$udivide'(identity,'double$udivide'('double$udivide'(X0,X1),multiply('double$udivide'(inverse(X1),multiply(identity,inverse(X2))),multiply(identity,inverse(X2)))))) = X0,
inference(demodulation,[status(thm)],[d126,c2]) ).
cnf(d128,plain,
multiply('double$udivide'('double$udivide'(X0,X1),multiply('double$udivide'(inverse(X1),multiply(identity,inverse(X2))),multiply(identity,inverse(X2)))),identity) = X0,
inference(demodulation,[status(thm)],[d127,d0]) ).
cnf(d129,plain,
multiply(identity,'double$udivide'('double$udivide'(X0,X1),multiply('double$udivide'(inverse(X1),multiply(identity,inverse(X2))),multiply(identity,inverse(X2))))) = X0,
inference(demodulation,[status(thm)],[d128,d47]) ).
cnf(d130,plain,
inverse(multiply(multiply('double$udivide'(inverse(X1),multiply(identity,inverse(X2))),multiply(identity,inverse(X2))),'double$udivide'(X0,X1))) = X0,
inference(demodulation,[status(thm)],[d129,d3]) ).
cnf(d131,plain,
X2 = X2,
inference(demodulation,[status(thm)],[d130,d120]) ).
cnf(d132,plain,
$false,
inference(resolution,[status(thm)],[d131,d104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP574-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n010.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 15:01:14 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.72/6.34 % SZS status Unsatisfiable for theBenchmark.p
% 44.72/6.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------