%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP083-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 07:22:17 AM UTC 2026
% Result : Unsatisfiable 128.45s 41.13s
% Output : CNFRefutation 128.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 3
% Syntax : Number of clauses : 156 ( 149 unt; 0 nHn; 9 RR)
% Number of literals : 165 ( 164 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 547 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'('double$udivide'(X0,inverse('double$udivide'(X1,X2))),'double$udivide'(inverse(X1),inverse('double$udivide'(X3,'double$udivide'(X0,X3))))) = X2 ).
cnf(multiply,axiom,
multiply(X0,X1) = inverse('double$udivide'(X1,X0)) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ) ).
cnf(c0,plain,
'double$udivide'('double$udivide'(X0,inverse('double$udivide'(X1,X2))),'double$udivide'(inverse(X1),inverse('double$udivide'(X3,'double$udivide'(X0,X3))))) = X2,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(X0,X1) = inverse('double$udivide'(X1,X0)),
inference(clausification,[status(esa)],[multiply]) ).
cnf(c2,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(clausification,[status(esa)],[prove_these_axioms]) ).
cnf(d0,plain,
'double$udivide'('double$udivide'(X2,multiply(X1,X0)),'double$udivide'(inverse(X0),inverse('double$udivide'(X3,'double$udivide'(X2,X3))))) = X1,
inference(demodulation,[status(thm)],[c0,c1]) ).
cnf(d1,plain,
'double$udivide'('double$udivide'(X1,multiply(X2,X3)),'double$udivide'(inverse(X3),multiply('double$udivide'(X1,X0),X0))) = X2,
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
'double$udivide'('double$udivide'(X2,multiply(X3,'double$udivide'(X0,X1))),'double$udivide'(multiply(X1,X0),multiply('double$udivide'(X2,X4),X4))) = X3,
inference(superposition,[status(thm)],[c1,d1]) ).
cnf(d3,plain,
multiply('double$udivide'(inverse(X2),multiply('double$udivide'(X0,X3),X3)),'double$udivide'(X0,multiply(X1,X2))) = inverse(X1),
inference(superposition,[status(thm)],[d1,c1]) ).
cnf(d4,plain,
'double$udivide'('double$udivide'(X4,inverse(X3)),'double$udivide'(multiply(multiply(X3,X0),X1),multiply('double$udivide'(X4,X5),X5))) = 'double$udivide'(inverse(X0),multiply('double$udivide'(X1,X2),X2)),
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
'double$udivide'(inverse(X2),multiply('double$udivide'(X3,X5),X5)) = 'double$udivide'(inverse(X2),multiply('double$udivide'(X3,X6),X6)),
inference(superposition,[status(thm)],[d4,d4]) ).
cnf(d6,plain,
'double$udivide'(multiply(X1,X0),multiply('double$udivide'(X2,X3),X3)) = 'double$udivide'(inverse('double$udivide'(X0,X1)),multiply('double$udivide'(X2,X4),X4)),
inference(superposition,[status(thm)],[c1,d5]) ).
cnf(d7,plain,
'double$udivide'(multiply(X1,X0),multiply('double$udivide'(X2,X3),X3)) = 'double$udivide'(multiply(X1,X0),multiply('double$udivide'(X2,X4),X4)),
inference(demodulation,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
'double$udivide'('double$udivide'(inverse(X0),multiply('double$udivide'(X1,X4),X4)),'double$udivide'(multiply(X3,X2),multiply('double$udivide'(inverse(X0),X5),X5))) = 'double$udivide'(X1,'double$udivide'(X2,X3)),
inference(superposition,[status(thm)],[d5,d2]) ).
cnf(d9,plain,
'double$udivide'('double$udivide'(X2,multiply(X1,X0)),'double$udivide'(multiply(multiply('double$udivide'(X0,X1),X3),X4),multiply('double$udivide'(X2,X5),X5))) = 'double$udivide'(inverse(X3),multiply('double$udivide'(X4,X6),X6)),
inference(superposition,[status(thm)],[c1,d4]) ).
cnf(d10,plain,
'double$udivide'(inverse(X3),multiply('double$udivide'(X4,X6),X6)) = 'double$udivide'(X1,'double$udivide'(X4,multiply('double$udivide'(X2,'double$udivide'(X1,X2)),X3))),
inference(superposition,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
'double$udivide'(inverse('double$udivide'('double$udivide'(X0,multiply(X1,X2)),X0)),multiply('double$udivide'(inverse(X2),X3),X3)) = X1,
inference(superposition,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
'double$udivide'(multiply(X0,'double$udivide'(X0,multiply(X1,X2))),multiply('double$udivide'(inverse(X2),X3),X3)) = X1,
inference(demodulation,[status(thm)],[d11,c1]) ).
cnf(d13,plain,
X1 = 'double$udivide'(multiply(X0,'double$udivide'(X0,multiply(X1,X2))),multiply('double$udivide'(inverse(X2),X4),X4)),
inference(superposition,[status(thm)],[d12,d7]) ).
cnf(d14,plain,
multiply('double$udivide'(inverse(X2),multiply('double$udivide'(inverse(X0),X4),X4)),'double$udivide'(inverse(X0),multiply('double$udivide'(X1,X3),X3))) = inverse('double$udivide'(X1,X2)),
inference(superposition,[status(thm)],[d5,d3]) ).
cnf(d15,plain,
multiply('double$udivide'(inverse(X1),multiply('double$udivide'(inverse(X2),X3),X3)),'double$udivide'(inverse(X2),multiply('double$udivide'(X0,X4),X4))) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d14,c1]) ).
cnf(d16,plain,
inverse('double$udivide'(X3,X0)) = multiply(X0,X3),
inference(superposition,[status(thm)],[d3,d15]) ).
cnf(d17,plain,
inverse(X1) = multiply('double$udivide'(multiply(X3,X2),multiply('double$udivide'(X0,X4),X4)),'double$udivide'(X0,multiply(X1,'double$udivide'(X2,X3)))),
inference(superposition,[status(thm)],[d2,d16]) ).
cnf(d18,plain,
inverse(X4) = multiply(X1,'double$udivide'(inverse(X2),multiply(X4,'double$udivide'('double$udivide'(X0,multiply(X1,X2)),X0)))),
inference(superposition,[status(thm)],[d12,d17]) ).
cnf(d19,plain,
X1 = 'double$udivide'(inverse(X1),multiply('double$udivide'(inverse('double$udivide'('double$udivide'(X2,multiply(inverse(X0),X0)),X2)),X3),X3)),
inference(superposition,[status(thm)],[d18,d13]) ).
cnf(d20,plain,
X2 = 'double$udivide'(inverse(X2),multiply('double$udivide'(multiply(X0,'double$udivide'(X0,multiply(inverse(X1),X1))),X3),X3)),
inference(demodulation,[status(thm)],[d19,c1]) ).
cnf(d21,plain,
X3 = 'double$udivide'(inverse(X3),multiply(inverse(X1),multiply('double$udivide'(inverse(X1),X2),X2))),
inference(superposition,[status(thm)],[d12,d20]) ).
cnf(d22,plain,
X2 = 'double$udivide'(inverse(X2),multiply(multiply(X1,X0),multiply('double$udivide'(inverse('double$udivide'(X0,X1)),X3),X3))),
inference(superposition,[status(thm)],[c1,d21]) ).
cnf(d23,plain,
X2 = 'double$udivide'(inverse(X2),multiply(multiply(X1,X0),multiply('double$udivide'(multiply(X1,X0),X3),X3))),
inference(demodulation,[status(thm)],[d22,c1]) ).
cnf(d24,plain,
inverse(X0) = multiply(multiply(inverse(X1),multiply('double$udivide'(inverse(X1),X2),X2)),inverse(X0)),
inference(superposition,[status(thm)],[d21,d16]) ).
cnf(d25,plain,
inverse('double$udivide'(X0,X1)) = multiply(multiply(inverse(X2),multiply('double$udivide'(inverse(X2),X3),X3)),multiply(X1,X0)),
inference(superposition,[status(thm)],[c1,d24]) ).
cnf(d26,plain,
multiply(X1,X0) = multiply(multiply(inverse(X2),multiply('double$udivide'(inverse(X2),X3),X3)),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d25,c1]) ).
cnf(d27,plain,
X3 = 'double$udivide'(inverse(X3),multiply('double$udivide'(multiply(inverse(X0),multiply('double$udivide'(inverse(X0),X1),X1)),X2),X2)),
inference(superposition,[status(thm)],[d26,d23]) ).
cnf(d28,plain,
'double$udivide'('double$udivide'(multiply(inverse(X1),multiply('double$udivide'(inverse(X1),X2),X2)),multiply(X4,X0)),X0) = X4,
inference(superposition,[status(thm)],[d27,d1]) ).
cnf(d29,plain,
'double$udivide'(X0,X1) = 'double$udivide'(multiply(X1,X0),multiply(inverse(X2),multiply('double$udivide'(inverse(X2),X3),X3))),
inference(superposition,[status(thm)],[c1,d21]) ).
cnf(d30,plain,
'double$udivide'('double$udivide'(multiply('double$udivide'(inverse(X0),X1),X1),inverse(X0)),multiply('double$udivide'(inverse(X2),X3),X3)) = inverse(X2),
inference(superposition,[status(thm)],[d29,d28]) ).
cnf(d31,plain,
'double$udivide'('double$udivide'(inverse(X2),multiply(X4,'double$udivide'('double$udivide'(X0,multiply(X1,X2)),X0))),X1) = X4,
inference(superposition,[status(thm)],[d12,d2]) ).
cnf(d32,plain,
'double$udivide'('double$udivide'(multiply(X1,X0),multiply(X2,'double$udivide'('double$udivide'(X3,multiply(X4,'double$udivide'(X0,X1))),X3))),X4) = X2,
inference(superposition,[status(thm)],[c1,d31]) ).
cnf(d33,plain,
'double$udivide'('double$udivide'(inverse('double$udivide'('double$udivide'(X2,multiply(inverse(X0),X0)),X2)),multiply(X3,X1)),X1) = X3,
inference(superposition,[status(thm)],[d31,d31]) ).
cnf(d34,plain,
'double$udivide'('double$udivide'(multiply(X0,'double$udivide'(X0,multiply(inverse(X1),X1))),multiply(X2,X3)),X3) = X2,
inference(demodulation,[status(thm)],[d33,c1]) ).
cnf(d35,plain,
inverse(X2) = multiply(X3,'double$udivide'(multiply(X0,'double$udivide'(X0,multiply(inverse(X1),X1))),multiply(X2,X3))),
inference(superposition,[status(thm)],[d34,d16]) ).
cnf(d36,plain,
inverse(inverse(X2)) = multiply(multiply('double$udivide'(inverse(X2),X3),X3),'double$udivide'('double$udivide'(X0,multiply(inverse(X1),X1)),X0)),
inference(superposition,[status(thm)],[d29,d35]) ).
cnf(d37,plain,
'double$udivide'('double$udivide'(multiply(X4,X3),inverse(inverse(X0))),inverse('double$udivide'(X3,X4))) = multiply('double$udivide'(inverse(X0),X1),X1),
inference(superposition,[status(thm)],[d36,d32]) ).
cnf(d38,plain,
'double$udivide'('double$udivide'(multiply(X1,X0),inverse(inverse(X2))),multiply(X1,X0)) = multiply('double$udivide'(inverse(X2),X3),X3),
inference(demodulation,[status(thm)],[d37,c1]) ).
cnf(d39,plain,
multiply('double$udivide'(inverse(X0),X2),X2) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d38,d30]) ).
cnf(d40,plain,
inverse(X1) = multiply('double$udivide'(inverse(X2),multiply('double$udivide'(X0,X3),X3)),'double$udivide'(X0,multiply(X1,X2))),
inference(superposition,[status(thm)],[d1,d16]) ).
cnf(d41,plain,
inverse(X4) = multiply(X0,'double$udivide'(multiply(inverse(X1),multiply('double$udivide'(inverse(X1),X2),X2)),multiply(X4,X0))),
inference(superposition,[status(thm)],[d27,d40]) ).
cnf(d42,plain,
X2 = 'double$udivide'(inverse(X2),multiply('double$udivide'(inverse(multiply(inverse(X0),multiply('double$udivide'(inverse(X0),X1),X1))),X3),X3)),
inference(superposition,[status(thm)],[d41,d13]) ).
cnf(d43,plain,
X3 = 'double$udivide'(inverse(X3),inverse(inverse(multiply(inverse(X0),multiply('double$udivide'(inverse(X0),X1),X1))))),
inference(demodulation,[status(thm)],[d42,d39]) ).
cnf(d44,plain,
X2 = 'double$udivide'(inverse(X2),inverse(inverse(multiply(inverse(X0),inverse(inverse(X0)))))),
inference(demodulation,[status(thm)],[d43,d39]) ).
cnf(d45,plain,
multiply(multiply('double$udivide'(X1,X2),X2),inverse(X0)) = inverse('double$udivide'(inverse(X0),multiply('double$udivide'(X1,X3),X3))),
inference(superposition,[status(thm)],[d5,c1]) ).
cnf(d46,plain,
multiply(multiply('double$udivide'(X1,X3),X3),inverse(X0)) = multiply(multiply('double$udivide'(X1,X2),X2),inverse(X0)),
inference(demodulation,[status(thm)],[d45,c1]) ).
cnf(d47,plain,
'double$udivide'('double$udivide'(X4,multiply(multiply('double$udivide'(X0,X3),X3),inverse(X2))),'double$udivide'(inverse(inverse(X2)),multiply('double$udivide'(X4,X5),X5))) = multiply('double$udivide'(X0,X1),X1),
inference(superposition,[status(thm)],[d46,d1]) ).
cnf(d48,plain,
multiply('double$udivide'(X1,X2),X2) = multiply('double$udivide'(X1,X5),X5),
inference(demodulation,[status(thm)],[d47,d1]) ).
cnf(d49,plain,
'double$udivide'(inverse(X2),multiply('double$udivide'(inverse(multiply(inverse(X0),multiply('double$udivide'(inverse(X0),X1),X1))),X3),X3)) = X2,
inference(superposition,[status(thm)],[d41,d12]) ).
cnf(d50,plain,
'double$udivide'(inverse(X3),inverse(inverse(multiply(inverse(X0),multiply('double$udivide'(inverse(X0),X1),X1))))) = X3,
inference(demodulation,[status(thm)],[d49,d39]) ).
cnf(d51,plain,
'double$udivide'(inverse(X2),inverse(inverse(multiply(inverse(X0),inverse(inverse(X0)))))) = X2,
inference(demodulation,[status(thm)],[d50,d39]) ).
cnf(d52,plain,
'double$udivide'('double$udivide'(inverse(X3),inverse(inverse(X0))),inverse(X3)) = multiply('double$udivide'(inverse(X0),X1),X1),
inference(superposition,[status(thm)],[d36,d31]) ).
cnf(d53,plain,
multiply('double$udivide'(inverse(X0),X3),X3) = 'double$udivide'('double$udivide'(inverse(X2),inverse(inverse(X0))),inverse(X2)),
inference(superposition,[status(thm)],[d52,d48]) ).
cnf(d54,plain,
inverse(inverse(X0)) = 'double$udivide'('double$udivide'(inverse(X2),inverse(inverse(X0))),inverse(X2)),
inference(demodulation,[status(thm)],[d53,d39]) ).
cnf(d55,plain,
inverse(inverse(multiply(inverse(X1),inverse(inverse(X1))))) = 'double$udivide'(X0,inverse(X0)),
inference(superposition,[status(thm)],[d44,d54]) ).
cnf(d56,plain,
'double$udivide'(inverse(X2),'double$udivide'(X1,inverse(X1))) = X2,
inference(superposition,[status(thm)],[d55,d51]) ).
cnf(d57,plain,
inverse(X0) = multiply('double$udivide'(X1,inverse(X1)),inverse(X0)),
inference(superposition,[status(thm)],[d56,d16]) ).
cnf(d58,plain,
multiply('double$udivide'(X0,X1),X1) = inverse(X0),
inference(superposition,[status(thm)],[d57,d48]) ).
cnf(d59,plain,
'double$udivide'('double$udivide'(X3,multiply(X4,'double$udivide'(X1,'double$udivide'(X0,X1)))),'double$udivide'(multiply('double$udivide'(X0,X2),X2),multiply('double$udivide'(X3,X5),X5))) = X4,
inference(superposition,[status(thm)],[d48,d2]) ).
cnf(d60,plain,
'double$udivide'(X1,'double$udivide'(X2,'double$udivide'(X3,X2))) = 'double$udivide'(X1,'double$udivide'(X4,'double$udivide'(X3,X4))),
inference(superposition,[status(thm)],[d59,d8]) ).
cnf(d61,plain,
inverse('double$udivide'(X0,'double$udivide'(X3,'double$udivide'(X2,X3)))) = multiply('double$udivide'(X1,'double$udivide'(X2,X1)),X0),
inference(superposition,[status(thm)],[d60,d16]) ).
cnf(d62,plain,
multiply('double$udivide'(X1,'double$udivide'(X2,X1)),X0) = multiply('double$udivide'(X3,'double$udivide'(X2,X3)),X0),
inference(demodulation,[status(thm)],[d61,c1]) ).
cnf(d63,plain,
multiply('double$udivide'(X2,'double$udivide'(X1,X2)),'double$udivide'(X1,X0)) = multiply('double$udivide'(X0,X3),X3),
inference(superposition,[status(thm)],[d62,d48]) ).
cnf(d64,plain,
multiply(X0,'double$udivide'(X0,X1)) = multiply('double$udivide'(X1,X2),X2),
inference(superposition,[status(thm)],[d56,d63]) ).
cnf(d65,plain,
multiply(X2,'double$udivide'(X2,X0)) = inverse(X0),
inference(demodulation,[status(thm)],[d64,d58]) ).
cnf(d66,plain,
'double$udivide'(multiply(X2,'double$udivide'(X2,multiply(X3,X0))),inverse(inverse(X0))) = X3,
inference(demodulation,[status(thm)],[d12,d39]) ).
cnf(d67,plain,
'double$udivide'(inverse(multiply(X1,X2)),inverse(inverse(X2))) = X1,
inference(demodulation,[status(thm)],[d66,d65]) ).
cnf(d68,plain,
multiply(X0,multiply(inverse(X1),inverse(inverse(X1)))) = X0,
inference(superposition,[status(thm)],[d67,d44]) ).
cnf(d69,plain,
multiply('double$udivide'(inverse(X0),X3),X3) = multiply(X0,multiply(inverse(X1),multiply('double$udivide'(inverse(X1),X2),X2))),
inference(superposition,[status(thm)],[d21,d48]) ).
cnf(d70,plain,
inverse(inverse(X0)) = multiply(X0,multiply(inverse(X2),multiply('double$udivide'(inverse(X2),X3),X3))),
inference(demodulation,[status(thm)],[d69,d39]) ).
cnf(d71,plain,
inverse(inverse(X2)) = multiply(X2,multiply(inverse(X0),inverse(inverse(X0)))),
inference(demodulation,[status(thm)],[d70,d39]) ).
cnf(d72,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d71,d68]) ).
cnf(d73,plain,
inverse(multiply(X1,X0)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[c1,d72]) ).
cnf(d74,plain,
'double$udivide'(inverse(multiply(X1,X0)),X0) = X1,
inference(demodulation,[status(thm)],[d67,d72]) ).
cnf(d75,plain,
'double$udivide'('double$udivide'(X1,X0),X1) = X0,
inference(demodulation,[status(thm)],[d74,d73]) ).
cnf(d76,plain,
'double$udivide'(X1,'double$udivide'(X0,X1)) = X0,
inference(superposition,[status(thm)],[d75,d75]) ).
cnf(d77,plain,
multiply(X0,multiply(inverse(X1),multiply('double$udivide'(inverse(X1),X2),X2))) = multiply('double$udivide'(inverse(X0),X3),X3),
inference(superposition,[status(thm)],[d21,d48]) ).
cnf(d78,plain,
multiply(X2,multiply(inverse(X0),inverse(inverse(X0)))) = multiply('double$udivide'(inverse(X2),X3),X3),
inference(demodulation,[status(thm)],[d77,d39]) ).
cnf(d79,plain,
multiply(X0,multiply(inverse(X2),inverse(inverse(X2)))) = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d78,d39]) ).
cnf(d80,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d79,d68]) ).
cnf(d81,plain,
'double$udivide'(X0,X1) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[c1,d80]) ).
cnf(d82,plain,
'double$udivide'(X1,inverse(X1)) = 'double$udivide'(X2,inverse(X2)),
inference(superposition,[status(thm)],[d55,d55]) ).
cnf(d83,plain,
multiply(inverse(X0),inverse(inverse(X0))) = 'double$udivide'(X1,inverse(X1)),
inference(superposition,[status(thm)],[d82,d44]) ).
cnf(d84,plain,
multiply(X2,'double$udivide'(X1,inverse(X1))) = X2,
inference(superposition,[status(thm)],[d83,d68]) ).
cnf(d85,plain,
multiply(X1,'double$udivide'(inverse(X0),X0)) = X1,
inference(superposition,[status(thm)],[d80,d84]) ).
cnf(d86,plain,
'double$udivide'('double$udivide'(inverse(X1),X1),X0) = inverse(X0),
inference(superposition,[status(thm)],[d85,d81]) ).
cnf(d87,plain,
'double$udivide'('double$udivide'(inverse(X0),multiply('double$udivide'(X1,X3),X3)),'double$udivide'(inverse(X2),multiply('double$udivide'(inverse(X0),X4),X4))) = 'double$udivide'(X1,X2),
inference(superposition,[status(thm)],[d5,d1]) ).
cnf(d88,plain,
'double$udivide'('double$udivide'(inverse(X4),multiply('double$udivide'(inverse(X0),multiply('double$udivide'(X1,X3),X3)),multiply('double$udivide'(X1,X2),X2))),'double$udivide'(inverse(X5),multiply('double$udivide'(inverse(X4),X6),X6))) = 'double$udivide'(inverse(X0),X5),
inference(superposition,[status(thm)],[d5,d87]) ).
cnf(d89,plain,
'double$udivide'('double$udivide'(inverse(X2),multiply('double$udivide'(inverse(X3),inverse(X0)),multiply('double$udivide'(X0,X4),X4))),'double$udivide'(inverse(X5),multiply('double$udivide'(inverse(X2),X6),X6))) = 'double$udivide'(inverse(X3),X5),
inference(demodulation,[status(thm)],[d88,d58]) ).
cnf(d90,plain,
'double$udivide'('double$udivide'(inverse(X2),multiply('double$udivide'(inverse(X3),inverse(X0)),inverse(X0))),'double$udivide'(inverse(X4),multiply('double$udivide'(inverse(X2),X5),X5))) = 'double$udivide'(inverse(X3),X4),
inference(demodulation,[status(thm)],[d89,d58]) ).
cnf(d91,plain,
'double$udivide'('double$udivide'(inverse(X2),inverse(inverse(X0))),'double$udivide'(inverse(X3),multiply('double$udivide'(inverse(X2),X4),X4))) = 'double$udivide'(inverse(X0),X3),
inference(demodulation,[status(thm)],[d90,d58]) ).
cnf(d92,plain,
'double$udivide'('double$udivide'(inverse(X1),X0),'double$udivide'(inverse(X2),multiply('double$udivide'(inverse(X1),X3),X3))) = 'double$udivide'(inverse(X0),X2),
inference(demodulation,[status(thm)],[d91,d72]) ).
cnf(d93,plain,
'double$udivide'('double$udivide'(inverse(X0),X2),'double$udivide'(inverse(X3),inverse(inverse(X0)))) = 'double$udivide'(inverse(X2),X3),
inference(demodulation,[status(thm)],[d92,d58]) ).
cnf(d94,plain,
'double$udivide'('double$udivide'(inverse(X0),X1),'double$udivide'(inverse(X2),X0)) = 'double$udivide'(inverse(X1),X2),
inference(demodulation,[status(thm)],[d93,d72]) ).
cnf(d95,plain,
'double$udivide'(inverse(X0),X1) = inverse('double$udivide'(inverse(X1),X0)),
inference(superposition,[status(thm)],[d94,d86]) ).
cnf(d96,plain,
'double$udivide'(inverse(X1),X0) = multiply(X1,inverse(X0)),
inference(demodulation,[status(thm)],[d95,c1]) ).
cnf(d97,plain,
X2 = 'double$udivide'(multiply(X3,'double$udivide'(X3,multiply(X2,X0))),inverse(inverse(X0))),
inference(demodulation,[status(thm)],[d13,d39]) ).
cnf(d98,plain,
X1 = 'double$udivide'(inverse(multiply(X1,X2)),inverse(inverse(X2))),
inference(demodulation,[status(thm)],[d97,d65]) ).
cnf(d99,plain,
X1 = 'double$udivide'(inverse(multiply(X1,X0)),X0),
inference(demodulation,[status(thm)],[d98,d72]) ).
cnf(d100,plain,
X0 = 'double$udivide'('double$udivide'(X1,X0),X1),
inference(demodulation,[status(thm)],[d99,d73]) ).
cnf(d101,plain,
X0 = 'double$udivide'(X1,'double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[d100,d100]) ).
cnf(d102,plain,
X1 = multiply(X0,inverse('double$udivide'(X1,inverse(X0)))),
inference(superposition,[status(thm)],[d96,d101]) ).
cnf(d103,plain,
X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(demodulation,[status(thm)],[d102,c1]) ).
cnf(d104,plain,
multiply('double$udivide'(inverse(X4),multiply('double$udivide'(inverse(X0),multiply('double$udivide'(X1,X3),X3)),multiply('double$udivide'(X1,X2),X2))),'double$udivide'(inverse(X0),multiply('double$udivide'(X5,X6),X6))) = multiply(X4,X5),
inference(superposition,[status(thm)],[d5,d15]) ).
cnf(d105,plain,
multiply(multiply(X0,inverse(multiply('double$udivide'(inverse(X1),multiply('double$udivide'(X2,X3),X3)),multiply('double$udivide'(X2,X4),X4)))),'double$udivide'(inverse(X1),multiply('double$udivide'(X5,X6),X6))) = multiply(X0,X5),
inference(demodulation,[status(thm)],[d104,d96]) ).
cnf(d106,plain,
multiply(multiply(X4,'double$udivide'(multiply('double$udivide'(X1,X3),X3),'double$udivide'(inverse(X0),multiply('double$udivide'(X1,X2),X2)))),'double$udivide'(inverse(X0),multiply('double$udivide'(X5,X6),X6))) = multiply(X4,X5),
inference(demodulation,[status(thm)],[d105,d73]) ).
cnf(d107,plain,
multiply(multiply(X2,'double$udivide'(inverse(X0),'double$udivide'(inverse(X3),multiply('double$udivide'(X0,X4),X4)))),'double$udivide'(inverse(X3),multiply('double$udivide'(X5,X6),X6))) = multiply(X2,X5),
inference(demodulation,[status(thm)],[d106,d58]) ).
cnf(d108,plain,
multiply(multiply(X3,multiply(X0,inverse('double$udivide'(inverse(X1),multiply('double$udivide'(X0,X2),X2))))),'double$udivide'(inverse(X1),multiply('double$udivide'(X4,X5),X5))) = multiply(X3,X4),
inference(demodulation,[status(thm)],[d107,d96]) ).
cnf(d109,plain,
multiply(multiply(X3,multiply(X1,multiply(multiply('double$udivide'(X1,X2),X2),inverse(X0)))),'double$udivide'(inverse(X0),multiply('double$udivide'(X4,X5),X5))) = multiply(X3,X4),
inference(demodulation,[status(thm)],[d108,c1]) ).
cnf(d110,plain,
multiply(multiply(X2,multiply(X0,multiply(inverse(X0),inverse(X3)))),'double$udivide'(inverse(X3),multiply('double$udivide'(X4,X5),X5))) = multiply(X2,X4),
inference(demodulation,[status(thm)],[d109,d58]) ).
cnf(d111,plain,
multiply(multiply(X2,inverse(X1)),'double$udivide'(inverse(X1),multiply('double$udivide'(X3,X4),X4))) = multiply(X2,X3),
inference(demodulation,[status(thm)],[d110,d103]) ).
cnf(d112,plain,
multiply(multiply(X3,inverse(X0)),multiply(X0,inverse(multiply('double$udivide'(X1,X2),X2)))) = multiply(X3,X1),
inference(demodulation,[status(thm)],[d111,d96]) ).
cnf(d113,plain,
multiply(multiply(X2,inverse(X3)),multiply(X3,'double$udivide'(X1,'double$udivide'(X0,X1)))) = multiply(X2,X0),
inference(demodulation,[status(thm)],[d112,d73]) ).
cnf(d114,plain,
multiply(multiply(X2,inverse(X3)),multiply(X3,X1)) = multiply(X2,X1),
inference(demodulation,[status(thm)],[d113,d76]) ).
cnf(d115,plain,
'double$udivide'(X0,X1) = multiply(inverse(X0),inverse(X1)),
inference(superposition,[status(thm)],[d80,d96]) ).
cnf(d116,plain,
'double$udivide'(X1,inverse(X0)) = multiply(inverse(X1),X0),
inference(superposition,[status(thm)],[d80,d115]) ).
cnf(d117,plain,
multiply(inverse('double$udivide'(inverse(X0),X1)),X0) = X1,
inference(superposition,[status(thm)],[d116,d75]) ).
cnf(d118,plain,
multiply(multiply(X1,inverse(X0)),X0) = X1,
inference(demodulation,[status(thm)],[d117,c1]) ).
cnf(d119,plain,
multiply(multiply(X1,X0),inverse(X0)) = X1,
inference(superposition,[status(thm)],[d80,d118]) ).
cnf(d120,plain,
multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[d119,d114]) ).
cnf(d121,plain,
inverse('double$udivide'('double$udivide'(X3,inverse(X4)),'double$udivide'(multiply(multiply(X4,X0),X1),multiply('double$udivide'(X3,X5),X5)))) = multiply(multiply('double$udivide'(X1,X2),X2),inverse(X0)),
inference(superposition,[status(thm)],[d4,d16]) ).
cnf(d122,plain,
multiply('double$udivide'(multiply(multiply(X1,X2),X3),multiply('double$udivide'(X0,X4),X4)),'double$udivide'(X0,inverse(X1))) = multiply(multiply('double$udivide'(X3,X5),X5),inverse(X2)),
inference(demodulation,[status(thm)],[d121,c1]) ).
cnf(d123,plain,
multiply('double$udivide'(multiply(multiply(X2,X3),X4),inverse(X0)),'double$udivide'(X0,inverse(X2))) = multiply(multiply('double$udivide'(X4,X5),X5),inverse(X3)),
inference(demodulation,[status(thm)],[d122,d58]) ).
cnf(d124,plain,
multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X3),'double$udivide'(X3,inverse(X0))) = multiply(multiply('double$udivide'(X2,X4),X4),inverse(X1)),
inference(demodulation,[status(thm)],[d123,d116]) ).
cnf(d125,plain,
multiply(multiply('double$udivide'(X2,multiply(X0,X1)),X3),'double$udivide'(X3,inverse(X0))) = multiply(multiply('double$udivide'(X2,X4),X4),inverse(X1)),
inference(demodulation,[status(thm)],[d124,d73]) ).
cnf(d126,plain,
multiply(multiply('double$udivide'(X2,multiply(X1,X3)),X0),multiply(inverse(X0),X1)) = multiply(multiply('double$udivide'(X2,X4),X4),inverse(X3)),
inference(demodulation,[status(thm)],[d125,d116]) ).
cnf(d127,plain,
multiply(multiply('double$udivide'(X0,multiply(X2,X3)),X4),multiply(inverse(X4),X2)) = multiply(inverse(X0),inverse(X3)),
inference(demodulation,[status(thm)],[d126,d58]) ).
cnf(d128,plain,
multiply(multiply('double$udivide'(X0,multiply(X2,X1)),X3),multiply(inverse(X3),X2)) = 'double$udivide'(X0,X1),
inference(demodulation,[status(thm)],[d127,d115]) ).
cnf(d129,plain,
multiply('double$udivide'(multiply(X1,X0),multiply('double$udivide'(X2,X3),X3)),'double$udivide'(X2,multiply(X4,'double$udivide'(X0,X1)))) = inverse(X4),
inference(superposition,[status(thm)],[c1,d3]) ).
cnf(d130,plain,
inverse('double$udivide'(multiply(X0,X1),multiply('double$udivide'(X2,X3),X3))) = multiply('double$udivide'(inverse('double$udivide'(X2,multiply(X4,'double$udivide'(X1,X0)))),multiply('double$udivide'(X5,X6),X6)),'double$udivide'(X5,inverse(X4))),
inference(superposition,[status(thm)],[d129,d40]) ).
cnf(d131,plain,
multiply(multiply('double$udivide'(X2,X3),X3),multiply(X0,X1)) = multiply('double$udivide'(inverse('double$udivide'(X2,multiply(X4,'double$udivide'(X1,X0)))),multiply('double$udivide'(X5,X6),X6)),'double$udivide'(X5,inverse(X4))),
inference(demodulation,[status(thm)],[d130,c1]) ).
cnf(d132,plain,
multiply(inverse(X0),multiply(X2,X3)) = multiply('double$udivide'(inverse('double$udivide'(X0,multiply(X4,'double$udivide'(X3,X2)))),multiply('double$udivide'(X5,X6),X6)),'double$udivide'(X5,inverse(X4))),
inference(demodulation,[status(thm)],[d131,d58]) ).
cnf(d133,plain,
multiply(inverse(X0),multiply(X3,X2)) = multiply(multiply('double$udivide'(X0,multiply(X1,'double$udivide'(X2,X3))),inverse(multiply('double$udivide'(X4,X5),X5))),'double$udivide'(X4,inverse(X1))),
inference(demodulation,[status(thm)],[d132,d96]) ).
cnf(d134,plain,
multiply(inverse(X2),multiply(X3,X4)) = multiply(multiply('double$udivide'(X2,multiply(X5,'double$udivide'(X4,X3))),'double$udivide'(X1,'double$udivide'(X0,X1))),'double$udivide'(X0,inverse(X5))),
inference(demodulation,[status(thm)],[d133,d73]) ).
cnf(d135,plain,
multiply(inverse(X2),multiply(X3,X4)) = multiply(multiply('double$udivide'(X2,multiply(X5,'double$udivide'(X4,X3))),X1),'double$udivide'(X1,inverse(X5))),
inference(demodulation,[status(thm)],[d134,d76]) ).
cnf(d136,plain,
multiply(inverse(X2),multiply(X3,X4)) = multiply(multiply('double$udivide'(X2,multiply(X1,'double$udivide'(X4,X3))),X0),multiply(inverse(X0),X1)),
inference(demodulation,[status(thm)],[d135,d116]) ).
cnf(d137,plain,
multiply(inverse(X0),multiply(X3,X2)) = 'double$udivide'(X0,'double$udivide'(X2,X3)),
inference(demodulation,[status(thm)],[d136,d128]) ).
cnf(d138,plain,
inverse('double$udivide'(X1,inverse(X1))) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[d82,d16]) ).
cnf(d139,plain,
multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(demodulation,[status(thm)],[d138,c1]) ).
cnf(d140,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2 ),
inference(resolution,[status(thm)],[d139,c2]) ).
cnf(d141,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(b2),multiply(b2,a2)) != a2 ),
inference(demodulation,[status(thm)],[d140,d120]) ).
cnf(d142,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| 'double$udivide'(b2,'double$udivide'(a2,b2)) != a2 ),
inference(demodulation,[status(thm)],[d141,d137]) ).
cnf(d143,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(demodulation,[status(thm)],[d142,d76]) ).
cnf(d144,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(demodulation,[status(thm)],[d143,d120]) ).
cnf(d145,plain,
'double$udivide'('double$udivide'(inverse(X0),multiply(X4,X5)),'double$udivide'(inverse(X5),multiply('double$udivide'(inverse(X0),multiply('double$udivide'(X1,X3),X3)),multiply('double$udivide'(X1,X2),X2)))) = X4,
inference(superposition,[status(thm)],[d5,d1]) ).
cnf(d146,plain,
'double$udivide'('double$udivide'(inverse(X1),multiply(X5,X0)),'double$udivide'(inverse(X0),multiply('double$udivide'(inverse(X1),X4),X4))) = X5,
inference(superposition,[status(thm)],[d5,d145]) ).
cnf(d147,plain,
X1 = X1,
inference(demodulation,[status(thm)],[d146,d1]) ).
cnf(d148,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(resolution,[status(thm)],[d147,d144]) ).
cnf(d149,plain,
$false,
inference(equality_resolution,[status(thm)],[d148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP083-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:21:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 128.45/41.13 % SZS status Unsatisfiable for theBenchmark.p
% 128.45/41.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------