%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP582-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 07:24:05 AM UTC 2026
% Result : Unsatisfiable 28.84s 9.96s
% Output : CNFRefutation 28.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 5
% Syntax : Number of clauses : 129 ( 129 unt; 0 nHn; 19 RR)
% Number of literals : 129 ( 128 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 : 153 ( 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$udivide'(X0,inverse(X0)) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(identity,a2) != a2 ).
cnf(c0,plain,
'double$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(identity,a2) != a2,
inference(clausification,[status(esa)],[prove_these_axioms_2]) ).
cnf(d0,plain,
multiply(X1,X0) = inverse('double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
identity = 'double$udivide'('double$udivide'(X0,X1),multiply(X1,X0)),
inference(superposition,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d3,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,identity),X2)),'double$udivide'(identity,identity)) = 'double$udivide'(X0,'double$udivide'('double$udivide'(identity,X1),'double$udivide'(X2,'double$udivide'(X1,X0)))),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d4,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X0)),'double$udivide'(identity,identity)) = 'double$udivide'(X1,'double$udivide'('double$udivide'(identity,X2),'double$udivide'(X0,'double$udivide'(X2,X1)))),
inference(demodulation,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X0)),inverse(identity)) = 'double$udivide'(X1,'double$udivide'('double$udivide'(identity,X2),'double$udivide'(X0,'double$udivide'(X2,X1)))),
inference(demodulation,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X0)),inverse(identity)) = 'double$udivide'(X1,'double$udivide'(inverse(identity),'double$udivide'(X0,'double$udivide'(identity,X1)))),
inference(superposition,[status(thm)],[c2,d5]) ).
cnf(d7,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X0)),inverse(identity)) = 'double$udivide'(identity,'double$udivide'(inverse(identity),'double$udivide'(X0,inverse(identity)))),
inference(superposition,[status(thm)],[c2,d6]) ).
cnf(d8,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(identity,X1),'double$udivide'(X2,'double$udivide'(X1,X0)))),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[c0,c2]) ).
cnf(d9,plain,
'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X2)),inverse(identity)),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),'double$udivide'(X0,inverse(identity)))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
'double$udivide'(identity,'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(X0,inverse(identity)),inverse(identity)))) = X0,
inference(demodulation,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
'double$udivide'(identity,'double$udivide'(inverse(identity),'double$udivide'(identity,inverse(identity)))) = identity,
inference(superposition,[status(thm)],[c3,d11]) ).
cnf(d13,plain,
'double$udivide'(identity,'double$udivide'(inverse(identity),identity)) = identity,
inference(demodulation,[status(thm)],[d12,c3]) ).
cnf(d14,plain,
'double$udivide'(identity,inverse(inverse(identity))) = identity,
inference(demodulation,[status(thm)],[d13,c2]) ).
cnf(d15,plain,
'double$udivide'(identity,multiply(identity,identity)) = identity,
inference(demodulation,[status(thm)],[d14,d2]) ).
cnf(d16,plain,
multiply(multiply(identity,identity),identity) = inverse(identity),
inference(superposition,[status(thm)],[d15,d0]) ).
cnf(d17,plain,
multiply(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X0)),inverse(identity))) = inverse(X0),
inference(superposition,[status(thm)],[d9,d0]) ).
cnf(d18,plain,
multiply(inverse(identity),'double$udivide'(identity,'double$udivide'(inverse(identity),'double$udivide'(X0,inverse(identity))))) = inverse(X0),
inference(demodulation,[status(thm)],[d17,d7]) ).
cnf(d19,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X1)),inverse(identity)) = 'double$udivide'(inverse(X0),'double$udivide'('double$udivide'(identity,X0),'double$udivide'(X1,identity))),
inference(superposition,[status(thm)],[c3,d5]) ).
cnf(d20,plain,
'double$udivide'(identity,'double$udivide'(inverse(identity),'double$udivide'(X0,inverse(identity)))) = 'double$udivide'(inverse(X1),'double$udivide'('double$udivide'(identity,X1),'double$udivide'(X0,identity))),
inference(demodulation,[status(thm)],[d19,d7]) ).
cnf(d21,plain,
'double$udivide'(identity,'double$udivide'(inverse(identity),'double$udivide'(X0,inverse(identity)))) = 'double$udivide'(inverse(X1),'double$udivide'('double$udivide'(identity,X1),inverse(X0))),
inference(demodulation,[status(thm)],[d20,c2]) ).
cnf(d22,plain,
'double$udivide'(identity,'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,X0),inverse(identity)))) = 'double$udivide'(inverse(X0),identity),
inference(superposition,[status(thm)],[c3,d21]) ).
cnf(d23,plain,
'double$udivide'(identity,'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,X0),inverse(identity)))) = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d22,c2]) ).
cnf(d24,plain,
'double$udivide'(identity,'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,X0),inverse(identity)))) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d23,d2]) ).
cnf(d25,plain,
multiply(inverse(identity),multiply(identity,X0)) = inverse('double$udivide'(identity,X0)),
inference(superposition,[status(thm)],[d24,d18]) ).
cnf(d26,plain,
multiply(inverse(identity),multiply(identity,X0)) = multiply(X0,identity),
inference(demodulation,[status(thm)],[d25,d0]) ).
cnf(d27,plain,
multiply(inverse(X0),X0) = inverse(identity),
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d28,plain,
multiply(identity,inverse(X0)) = inverse(multiply(identity,X0)),
inference(superposition,[status(thm)],[d2,d2]) ).
cnf(d29,plain,
multiply(multiply(identity,inverse(X0)),multiply(identity,X0)) = inverse(identity),
inference(superposition,[status(thm)],[d28,d27]) ).
cnf(d30,plain,
multiply(identity,inverse(identity)) = identity,
inference(superposition,[status(thm)],[d24,d11]) ).
cnf(d31,plain,
multiply(identity,multiply(identity,identity)) = inverse(identity),
inference(superposition,[status(thm)],[d30,d29]) ).
cnf(d32,plain,
multiply(inverse(identity),inverse(identity)) = multiply(multiply(identity,identity),identity),
inference(superposition,[status(thm)],[d31,d26]) ).
cnf(d33,plain,
multiply(inverse(identity),inverse(identity)) = inverse(identity),
inference(demodulation,[status(thm)],[d32,d16]) ).
cnf(d34,plain,
identity = 'double$udivide'('double$udivide'(inverse(identity),inverse(identity)),inverse(identity)),
inference(superposition,[status(thm)],[d33,d1]) ).
cnf(d35,plain,
identity = 'double$udivide'(inverse(X0),multiply(identity,X0)),
inference(superposition,[status(thm)],[d2,c3]) ).
cnf(d36,plain,
'double$udivide'('double$udivide'('double$udivide'(identity,identity),inverse(identity)),inverse(identity)) = multiply(identity,identity),
inference(superposition,[status(thm)],[d35,d9]) ).
cnf(d37,plain,
'double$udivide'('double$udivide'(inverse(identity),inverse(identity)),inverse(identity)) = multiply(identity,identity),
inference(demodulation,[status(thm)],[d36,c2]) ).
cnf(d38,plain,
identity = multiply(identity,identity),
inference(demodulation,[status(thm)],[d37,d34]) ).
cnf(d39,plain,
multiply(identity,identity) = inverse(identity),
inference(demodulation,[status(thm)],[d31,d38]) ).
cnf(d40,plain,
identity = inverse(identity),
inference(demodulation,[status(thm)],[d39,d38]) ).
cnf(d41,plain,
'double$udivide'('double$udivide'('double$udivide'(identity,identity),'double$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'(identity,identity)) = X3,
inference(superposition,[status(thm)],[c0,c0]) ).
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))),'double$udivide'(identity,identity)) = X3,
inference(demodulation,[status(thm)],[d41,c2]) ).
cnf(d43,plain,
'double$udivide'('double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X2)),inverse(identity))),'double$udivide'(X3,X2))),'double$udivide'(identity,identity)) = X3,
inference(demodulation,[status(thm)],[d42,d5]) ).
cnf(d44,plain,
'double$udivide'('double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X0)),inverse(identity))),'double$udivide'(X1,X0))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d43,c2]) ).
cnf(d45,plain,
'double$udivide'('double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,identity),inverse(identity))),'double$udivide'(X0,multiply(identity,identity)))),inverse(identity)) = X0,
inference(superposition,[status(thm)],[d35,d44]) ).
cnf(d46,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,identity),inverse(identity))),'double$udivide'(X0,multiply(identity,identity)))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d45,d40]) ).
cnf(d47,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),inverse(identity))),'double$udivide'(X0,multiply(identity,identity)))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d46,c2]) ).
cnf(d48,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse(identity))),'double$udivide'(X0,multiply(identity,identity)))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d47,d40]) ).
cnf(d49,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,identity),'double$udivide'(X0,multiply(identity,identity)))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d48,c3]) ).
cnf(d50,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),'double$udivide'(X0,multiply(identity,identity)))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d49,c2]) ).
cnf(d51,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,'double$udivide'(X0,multiply(identity,identity)))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d50,d40]) ).
cnf(d52,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,'double$udivide'(X0,identity))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d51,d38]) ).
cnf(d53,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse(X0))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d52,c2]) ).
cnf(d54,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse(X0))),identity) = X0,
inference(demodulation,[status(thm)],[d53,d40]) ).
cnf(d55,plain,
inverse('double$udivide'(identity,'double$udivide'(identity,inverse(X0)))) = X0,
inference(demodulation,[status(thm)],[d54,c2]) ).
cnf(d56,plain,
multiply('double$udivide'(identity,inverse(X0)),identity) = X0,
inference(demodulation,[status(thm)],[d55,d0]) ).
cnf(d57,plain,
'double$udivide'('double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),inverse(X0))),inverse(identity))),identity)),inverse(identity)) = X0,
inference(superposition,[status(thm)],[c3,d44]) ).
cnf(d58,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),inverse(X0))),inverse(identity))),identity)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d57,d40]) ).
cnf(d59,plain,
'double$udivide'('double$udivide'(identity,inverse('double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),inverse(X0))),inverse(identity))))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d58,c2]) ).
cnf(d60,plain,
'double$udivide'('double$udivide'(identity,multiply('double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),inverse(X0))),inverse(identity)),identity)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d59,d0]) ).
cnf(d61,plain,
'double$udivide'('double$udivide'(identity,multiply('double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse(X0))),inverse(identity)),identity)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d60,d40]) ).
cnf(d62,plain,
'double$udivide'('double$udivide'(identity,multiply('double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse(X0))),identity),identity)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d61,d40]) ).
cnf(d63,plain,
'double$udivide'('double$udivide'(identity,multiply(inverse('double$udivide'(identity,'double$udivide'(identity,inverse(X0)))),identity)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d62,c2]) ).
cnf(d64,plain,
'double$udivide'('double$udivide'(identity,multiply(multiply('double$udivide'(identity,inverse(X0)),identity),identity)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d63,d0]) ).
cnf(d65,plain,
'double$udivide'('double$udivide'(identity,multiply(X0,identity)),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d64,d56]) ).
cnf(d66,plain,
'double$udivide'('double$udivide'(identity,multiply(X0,identity)),identity) = X0,
inference(demodulation,[status(thm)],[d65,d40]) ).
cnf(d67,plain,
inverse('double$udivide'(identity,multiply(X0,identity))) = X0,
inference(demodulation,[status(thm)],[d66,c2]) ).
cnf(d68,plain,
multiply(multiply(X0,identity),identity) = X0,
inference(demodulation,[status(thm)],[d67,d0]) ).
cnf(d69,plain,
multiply(X0,identity) = 'double$udivide'(identity,inverse(X0)),
inference(superposition,[status(thm)],[d56,d68]) ).
cnf(d70,plain,
multiply(inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[d27,d40]) ).
cnf(d71,plain,
multiply('double$udivide'(identity,multiply(identity,X0)),identity) = inverse(X0),
inference(superposition,[status(thm)],[d2,d56]) ).
cnf(d72,plain,
multiply(inverse(X0),identity) = 'double$udivide'(identity,multiply(identity,X0)),
inference(superposition,[status(thm)],[d71,d68]) ).
cnf(d73,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X0)),inverse(identity)) = 'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),inverse(identity))),'double$udivide'(X0,multiply(identity,identity)))),
inference(superposition,[status(thm)],[d37,d5]) ).
cnf(d74,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,X0)),inverse(identity)) = 'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),inverse(identity))),'double$udivide'(X0,multiply(identity,identity)))),
inference(demodulation,[status(thm)],[d73,d40]) ).
cnf(d75,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,X0)),identity) = 'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),inverse(identity))),'double$udivide'(X0,multiply(identity,identity)))),
inference(demodulation,[status(thm)],[d74,d40]) ).
cnf(d76,plain,
inverse('double$udivide'(identity,'double$udivide'(identity,X0))) = 'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),inverse(identity))),'double$udivide'(X0,multiply(identity,identity)))),
inference(demodulation,[status(thm)],[d75,c2]) ).
cnf(d77,plain,
multiply('double$udivide'(identity,X0),identity) = 'double$udivide'(inverse(identity),'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),inverse(identity))),'double$udivide'(X0,multiply(identity,identity)))),
inference(demodulation,[status(thm)],[d76,d0]) ).
cnf(d78,plain,
multiply('double$udivide'(identity,X0),identity) = 'double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),inverse(identity))),'double$udivide'(X0,multiply(identity,identity)))),
inference(demodulation,[status(thm)],[d77,d40]) ).
cnf(d79,plain,
multiply('double$udivide'(identity,X0),identity) = 'double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse(identity))),'double$udivide'(X0,multiply(identity,identity)))),
inference(demodulation,[status(thm)],[d78,d40]) ).
cnf(d80,plain,
multiply('double$udivide'(identity,X0),identity) = 'double$udivide'(identity,'double$udivide'('double$udivide'(identity,multiply(identity,identity)),'double$udivide'(X0,multiply(identity,identity)))),
inference(demodulation,[status(thm)],[d79,d69]) ).
cnf(d81,plain,
multiply('double$udivide'(identity,X0),identity) = 'double$udivide'(identity,'double$udivide'(multiply(inverse(identity),identity),'double$udivide'(X0,multiply(identity,identity)))),
inference(demodulation,[status(thm)],[d80,d72]) ).
cnf(d82,plain,
multiply('double$udivide'(identity,X0),identity) = 'double$udivide'(identity,'double$udivide'(identity,'double$udivide'(X0,multiply(identity,identity)))),
inference(demodulation,[status(thm)],[d81,d70]) ).
cnf(d83,plain,
multiply('double$udivide'(identity,X0),identity) = 'double$udivide'(identity,'double$udivide'(identity,'double$udivide'(X0,identity))),
inference(demodulation,[status(thm)],[d82,d38]) ).
cnf(d84,plain,
multiply('double$udivide'(identity,X0),identity) = 'double$udivide'(identity,'double$udivide'(identity,inverse(X0))),
inference(demodulation,[status(thm)],[d83,c2]) ).
cnf(d85,plain,
multiply('double$udivide'(identity,X0),identity) = 'double$udivide'(identity,multiply(X0,identity)),
inference(demodulation,[status(thm)],[d84,d69]) ).
cnf(d86,plain,
'double$udivide'(identity,'double$udivide'(identity,'double$udivide'('double$udivide'(X0,inverse(identity)),inverse(identity)))) = X0,
inference(demodulation,[status(thm)],[d11,d40]) ).
cnf(d87,plain,
'double$udivide'(identity,'double$udivide'(identity,'double$udivide'('double$udivide'(X0,identity),inverse(identity)))) = X0,
inference(demodulation,[status(thm)],[d86,d40]) ).
cnf(d88,plain,
'double$udivide'(identity,'double$udivide'(identity,'double$udivide'('double$udivide'(X0,identity),identity))) = X0,
inference(demodulation,[status(thm)],[d87,d40]) ).
cnf(d89,plain,
'double$udivide'(identity,'double$udivide'(identity,inverse('double$udivide'(X0,identity)))) = X0,
inference(demodulation,[status(thm)],[d88,c2]) ).
cnf(d90,plain,
'double$udivide'(identity,'double$udivide'(identity,multiply(identity,X0))) = X0,
inference(demodulation,[status(thm)],[d89,d0]) ).
cnf(d91,plain,
'double$udivide'(identity,multiply(inverse(X0),identity)) = X0,
inference(demodulation,[status(thm)],[d90,d72]) ).
cnf(d92,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X0)),inverse(identity)) = 'double$udivide'('double$udivide'(X2,'double$udivide'(X1,X0)),'double$udivide'('double$udivide'(identity,'double$udivide'(identity,X1)),'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X2)),inverse(identity)))),
inference(superposition,[status(thm)],[d5,d5]) ).
cnf(d93,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),multiply(identity,X0))),inverse(identity)) = 'double$udivide'('double$udivide'(X1,identity),'double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse(X0))),'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X1)),inverse(identity)))),
inference(superposition,[status(thm)],[d35,d92]) ).
cnf(d94,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,multiply(identity,X0))),inverse(identity)) = 'double$udivide'('double$udivide'(X1,identity),'double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse(X0))),'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X1)),inverse(identity)))),
inference(demodulation,[status(thm)],[d93,d40]) ).
cnf(d95,plain,
'double$udivide'('double$udivide'(identity,multiply(inverse(X0),identity)),inverse(identity)) = 'double$udivide'('double$udivide'(X1,identity),'double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse(X0))),'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X1)),inverse(identity)))),
inference(demodulation,[status(thm)],[d94,d72]) ).
cnf(d96,plain,
'double$udivide'(X0,inverse(identity)) = 'double$udivide'('double$udivide'(X1,identity),'double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse(X0))),'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X1)),inverse(identity)))),
inference(demodulation,[status(thm)],[d95,d91]) ).
cnf(d97,plain,
'double$udivide'(X0,identity) = 'double$udivide'('double$udivide'(X1,identity),'double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse(X0))),'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X1)),inverse(identity)))),
inference(demodulation,[status(thm)],[d96,d40]) ).
cnf(d98,plain,
inverse(X0) = 'double$udivide'('double$udivide'(X1,identity),'double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse(X0))),'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X1)),inverse(identity)))),
inference(demodulation,[status(thm)],[d97,c2]) ).
cnf(d99,plain,
inverse(X1) = 'double$udivide'(inverse(X0),'double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse(X1))),'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X0)),inverse(identity)))),
inference(demodulation,[status(thm)],[d98,c2]) ).
cnf(d100,plain,
inverse(X0) = 'double$udivide'(inverse(X1),'double$udivide'('double$udivide'(identity,multiply(X0,identity)),'double$udivide'('double$udivide'(identity,'double$udivide'(inverse(identity),X1)),inverse(identity)))),
inference(demodulation,[status(thm)],[d99,d69]) ).
cnf(d101,plain,
inverse(X0) = 'double$udivide'(inverse(X1),'double$udivide'('double$udivide'(identity,multiply(X0,identity)),'double$udivide'('double$udivide'(identity,'double$udivide'(identity,X1)),inverse(identity)))),
inference(demodulation,[status(thm)],[d100,d40]) ).
cnf(d102,plain,
inverse(X0) = 'double$udivide'(inverse(X1),'double$udivide'('double$udivide'(identity,multiply(X0,identity)),'double$udivide'('double$udivide'(identity,'double$udivide'(identity,X1)),identity))),
inference(demodulation,[status(thm)],[d101,d40]) ).
cnf(d103,plain,
inverse(X1) = 'double$udivide'(inverse(X0),'double$udivide'('double$udivide'(identity,multiply(X1,identity)),inverse('double$udivide'(identity,'double$udivide'(identity,X0))))),
inference(demodulation,[status(thm)],[d102,c2]) ).
cnf(d104,plain,
inverse(X1) = 'double$udivide'(inverse(X0),'double$udivide'('double$udivide'(identity,multiply(X1,identity)),multiply('double$udivide'(identity,X0),identity))),
inference(demodulation,[status(thm)],[d103,d0]) ).
cnf(d105,plain,
inverse(X1) = 'double$udivide'(inverse(X0),'double$udivide'('double$udivide'(identity,multiply(X1,identity)),'double$udivide'(identity,multiply(X0,identity)))),
inference(demodulation,[status(thm)],[d104,d85]) ).
cnf(d106,plain,
identity = 'double$udivide'('double$udivide'(identity,multiply(X0,identity)),X0),
inference(superposition,[status(thm)],[d68,d1]) ).
cnf(d107,plain,
inverse('double$udivide'(identity,multiply(X0,identity))) = 'double$udivide'(inverse(X0),identity),
inference(superposition,[status(thm)],[d106,d105]) ).
cnf(d108,plain,
multiply(multiply(X0,identity),identity) = 'double$udivide'(inverse(X0),identity),
inference(demodulation,[status(thm)],[d107,d0]) ).
cnf(d109,plain,
X0 = 'double$udivide'(inverse(X0),identity),
inference(demodulation,[status(thm)],[d108,d68]) ).
cnf(d110,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d109,c2]) ).
cnf(d111,plain,
multiply(inverse(X0),identity) = inverse(multiply(X0,identity)),
inference(superposition,[status(thm)],[d69,d0]) ).
cnf(d112,plain,
multiply(inverse(multiply(X0,identity)),identity) = inverse(X0),
inference(superposition,[status(thm)],[d68,d111]) ).
cnf(d113,plain,
multiply(multiply(inverse(X0),identity),identity) = inverse(X0),
inference(demodulation,[status(thm)],[d112,d111]) ).
cnf(d114,plain,
inverse(X0) = inverse(X0),
inference(demodulation,[status(thm)],[d113,d68]) ).
cnf(d115,plain,
inverse(inverse(X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[d2,d114]) ).
cnf(d116,plain,
X0 = multiply(identity,X0),
inference(demodulation,[status(thm)],[d115,d110]) ).
cnf(d117,plain,
a2 != a2,
inference(demodulation,[status(thm)],[c4,d116]) ).
cnf(d118,plain,
$false,
inference(equality_resolution,[status(thm)],[d117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP582-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n013.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Fri Sep 25 15:00:15 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.84/9.96 % SZS status Unsatisfiable for theBenchmark.p
% 28.84/9.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------