%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP082-1 : 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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:22:16 AM UTC 2026
% Result : Unsatisfiable 96.15s 19.27s
% Output : CNFRefutation 96.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 3
% Syntax : Number of clauses : 148 ( 143 unt; 0 nHn; 7 RR)
% Number of literals : 157 ( 156 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 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 : 523 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'(inverse(X0),inverse('double$udivide'(inverse('double$udivide'(X0,'double$udivide'(X1,X2))),'double$udivide'(X3,'double$udivide'(X1,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'(inverse(X0),inverse('double$udivide'(inverse('double$udivide'(X0,'double$udivide'(X1,X2))),'double$udivide'(X3,'double$udivide'(X1,X3))))) = X2,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(X0,X1) = inverse('double$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$udivide'(inverse(X0),multiply('double$udivide'(X3,'double$udivide'(X1,X3)),inverse('double$udivide'(X0,'double$udivide'(X1,X2))))) = X2,
inference(demodulation,[status(thm)],[c0,c1]) ).
cnf(d1,plain,
'double$udivide'(inverse(X0),multiply('double$udivide'(X3,'double$udivide'(X1,X3)),multiply('double$udivide'(X1,X2),X0))) = X2,
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
'double$udivide'(inverse(X4),multiply('double$udivide'(X5,'double$udivide'(inverse(X0),X5)),multiply(X3,X4))) = multiply('double$udivide'(X1,'double$udivide'(X2,X1)),multiply('double$udivide'(X2,X3),X0)),
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d3,plain,
multiply('double$udivide'(X4,'double$udivide'(X5,X4)),multiply('double$udivide'(X5,'double$udivide'(inverse(X2),X3)),X2)) = X3,
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
multiply('double$udivide'(X2,'double$udivide'(X3,X2)),multiply('double$udivide'(X3,'double$udivide'(multiply(X1,X0),X4)),'double$udivide'(X0,X1))) = X4,
inference(superposition,[status(thm)],[c1,d3]) ).
cnf(d5,plain,
X3 = multiply('double$udivide'(X4,'double$udivide'(X5,X4)),multiply('double$udivide'(X5,'double$udivide'(inverse(X2),X3)),X2)),
inference(superposition,[status(thm)],[d1,d2]) ).
cnf(d6,plain,
'double$udivide'(inverse(X3),'double$udivide'(inverse(X4),multiply('double$udivide'(X5,'double$udivide'(inverse(X3),X5)),multiply(X2,X4)))) = X2,
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d7,plain,
multiply('double$udivide'(X2,'double$udivide'(inverse(X0),X2)),multiply(X3,X1)) = multiply('double$udivide'(X4,'double$udivide'(inverse(X0),X4)),multiply(X3,X1)),
inference(superposition,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
multiply('double$udivide'(X4,'double$udivide'(X0,X4)),multiply('double$udivide'(X3,'double$udivide'(inverse(multiply(X1,X2)),X3)),multiply(X1,X2))) = X0,
inference(superposition,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
'double$udivide'(inverse(multiply('double$udivide'(X1,'double$udivide'(inverse(X2),X3)),X2)),multiply('double$udivide'(X4,'double$udivide'(X0,X4)),X3)) = 'double$udivide'(X1,X0),
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d10,plain,
X0 = multiply('double$udivide'(X4,'double$udivide'(X0,X4)),multiply('double$udivide'(X3,'double$udivide'(inverse(multiply(X1,X2)),X3)),multiply(X1,X2))),
inference(superposition,[status(thm)],[d7,d5]) ).
cnf(d11,plain,
'double$udivide'(inverse(X1),'double$udivide'(inverse(multiply(X3,X4)),inverse(X1))) = 'double$udivide'(X2,'double$udivide'(inverse(multiply(X3,X4)),X2)),
inference(superposition,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
'double$udivide'(X3,'double$udivide'(inverse(multiply(X1,X2)),X3)) = 'double$udivide'(X4,'double$udivide'(inverse(multiply(X1,X2)),X4)),
inference(superposition,[status(thm)],[d11,d11]) ).
cnf(d13,plain,
multiply('double$udivide'(inverse(multiply(X1,X2)),X0),X0) = inverse('double$udivide'(X3,'double$udivide'(inverse(multiply(X1,X2)),X3))),
inference(superposition,[status(thm)],[d12,c1]) ).
cnf(d14,plain,
multiply('double$udivide'(inverse(multiply(X1,X2)),X3),X3) = multiply('double$udivide'(inverse(multiply(X1,X2)),X0),X0),
inference(demodulation,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
'double$udivide'(inverse(X2),multiply('double$udivide'(X4,'double$udivide'(inverse(multiply(X0,X1)),X4)),multiply('double$udivide'(inverse(multiply(X0,X1)),X3),X3))) = X2,
inference(superposition,[status(thm)],[d14,d1]) ).
cnf(d16,plain,
'double$udivide'(inverse(X6),'double$udivide'(inverse(X4),multiply('double$udivide'(X5,'double$udivide'(inverse(X3),X5)),multiply(X3,X4)))) = X6,
inference(superposition,[status(thm)],[d2,d15]) ).
cnf(d17,plain,
'double$udivide'(inverse(X5),multiply('double$udivide'(X3,'double$udivide'(X4,X3)),multiply('double$udivide'(X4,X2),X2))) = X5,
inference(superposition,[status(thm)],[d2,d16]) ).
cnf(d18,plain,
multiply('double$udivide'(X0,'double$udivide'(inverse(X1),multiply('double$udivide'(X2,X3),X3))),X1) = 'double$udivide'(X0,X2),
inference(superposition,[status(thm)],[d17,d9]) ).
cnf(d19,plain,
multiply('double$udivide'(X4,'double$udivide'(X5,X4)),'double$udivide'(multiply('double$udivide'(X0,X1),X1),X0)) = X5,
inference(superposition,[status(thm)],[d18,d8]) ).
cnf(d20,plain,
multiply('double$udivide'(X3,'double$udivide'(X0,X3)),multiply(X1,multiply('double$udivide'(X1,X2),X2))) = X0,
inference(superposition,[status(thm)],[d19,d4]) ).
cnf(d21,plain,
'double$udivide'(inverse(multiply('double$udivide'('double$udivide'(X1,X2),X3),X3)),X1) = X2,
inference(superposition,[status(thm)],[d20,d1]) ).
cnf(d22,plain,
'double$udivide'(inverse(multiply('double$udivide'(X1,X2),X3)),multiply('double$udivide'(X6,'double$udivide'(X0,X6)),'double$udivide'(inverse(X4),multiply('double$udivide'(X5,'double$udivide'(inverse(X3),X5)),multiply(X2,X4))))) = 'double$udivide'(X1,X0),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d23,plain,
'double$udivide'(inverse(multiply('double$udivide'(X1,X2),X3)),multiply('double$udivide'(X6,'double$udivide'(inverse(X7),X6)),'double$udivide'(inverse(X4),multiply('double$udivide'(X5,'double$udivide'(inverse(X3),X5)),multiply(X2,X4))))) = multiply('double$udivide'(X8,'double$udivide'(X9,X8)),multiply('double$udivide'(X9,'double$udivide'(X0,'double$udivide'(X1,X0))),X7)),
inference(superposition,[status(thm)],[d2,d2]) ).
cnf(d24,plain,
'double$udivide'(X0,inverse(X4)) = multiply('double$udivide'(X7,'double$udivide'(X8,X7)),multiply('double$udivide'(X8,'double$udivide'(X9,'double$udivide'(X0,X9))),X4)),
inference(demodulation,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
'double$udivide'(inverse(X4),'double$udivide'(X3,inverse('double$udivide'(X2,'double$udivide'(X3,X2))))) = X4,
inference(superposition,[status(thm)],[d24,d17]) ).
cnf(d26,plain,
'double$udivide'(inverse(X2),'double$udivide'(X1,multiply('double$udivide'(X1,X0),X0))) = X2,
inference(demodulation,[status(thm)],[d25,c1]) ).
cnf(d27,plain,
multiply(X0,X1) = 'double$udivide'(inverse(X0),inverse(X1)),
inference(superposition,[status(thm)],[d26,d18]) ).
cnf(d28,plain,
multiply('double$udivide'(X0,X1),X2) = 'double$udivide'(multiply(X1,X0),inverse(X2)),
inference(superposition,[status(thm)],[c1,d27]) ).
cnf(d29,plain,
multiply(X2,'double$udivide'(X0,X1)) = 'double$udivide'(inverse(X2),multiply(X1,X0)),
inference(superposition,[status(thm)],[c1,d27]) ).
cnf(d30,plain,
'double$udivide'(inverse(X3),'double$udivide'(inverse(multiply('double$udivide'(X1,X2),X2)),inverse(X1))) = X3,
inference(superposition,[status(thm)],[d20,d16]) ).
cnf(d31,plain,
X0 = 'double$udivide'(X2,'double$udivide'(inverse(multiply('double$udivide'(X0,X1),X1)),X2)),
inference(superposition,[status(thm)],[d30,d12]) ).
cnf(d32,plain,
'double$udivide'(X2,'double$udivide'(inverse(multiply('double$udivide'(X0,X1),X1)),X2)) = X0,
inference(superposition,[status(thm)],[d30,d12]) ).
cnf(d33,plain,
multiply('double$udivide'(inverse(multiply('double$udivide'(X1,X2),X2)),X0),X0) = inverse(X1),
inference(superposition,[status(thm)],[d32,c1]) ).
cnf(d34,plain,
inverse(multiply('double$udivide'(X0,X1),X1)) = 'double$udivide'(X3,'double$udivide'(inverse(inverse(X0)),X3)),
inference(superposition,[status(thm)],[d33,d31]) ).
cnf(d35,plain,
'double$udivide'('double$udivide'(X3,'double$udivide'(inverse(inverse('double$udivide'(X0,X1))),X3)),X0) = X1,
inference(superposition,[status(thm)],[d34,d21]) ).
cnf(d36,plain,
'double$udivide'('double$udivide'(X2,'double$udivide'(inverse(multiply(X1,X0)),X2)),X0) = X1,
inference(demodulation,[status(thm)],[d35,c1]) ).
cnf(d37,plain,
'double$udivide'('double$udivide'(inverse(X2),multiply(multiply(X0,X1),X2)),X1) = X0,
inference(superposition,[status(thm)],[d27,d36]) ).
cnf(d38,plain,
'double$udivide'(multiply(X0,'double$udivide'(X0,multiply(X1,X2))),X2) = X1,
inference(demodulation,[status(thm)],[d37,d29]) ).
cnf(d39,plain,
multiply('double$udivide'('double$udivide'(X0,multiply(X1,inverse(X2))),X0),X2) = X1,
inference(superposition,[status(thm)],[d38,d28]) ).
cnf(d40,plain,
'double$udivide'(inverse(X1),X0) = multiply(X1,inverse(X0)),
inference(superposition,[status(thm)],[d39,d21]) ).
cnf(d41,plain,
'double$udivide'(inverse(X2),multiply(multiply('double$udivide'(X0,X1),X1),X0)) = X2,
inference(demodulation,[status(thm)],[d30,d27]) ).
cnf(d42,plain,
multiply(X0,'double$udivide'(X1,multiply('double$udivide'(X1,X2),X2))) = X0,
inference(demodulation,[status(thm)],[d41,d29]) ).
cnf(d43,plain,
multiply(X2,multiply(X0,'double$udivide'(X1,'double$udivide'(inverse(X0),X1)))) = X2,
inference(superposition,[status(thm)],[d29,d42]) ).
cnf(d44,plain,
multiply(X2,multiply(X0,'double$udivide'(X1,multiply(X0,inverse(X1))))) = X2,
inference(demodulation,[status(thm)],[d43,d40]) ).
cnf(d45,plain,
multiply(X1,'double$udivide'(X0,inverse(X0))) = X1,
inference(superposition,[status(thm)],[d42,d44]) ).
cnf(d46,plain,
multiply(multiply('double$udivide'('double$udivide'(inverse(X0),X1),X2),X2),X0) = X1,
inference(superposition,[status(thm)],[d27,d21]) ).
cnf(d47,plain,
multiply(X1,X0) = multiply(X1,inverse(inverse(X0))),
inference(superposition,[status(thm)],[d39,d46]) ).
cnf(d48,plain,
multiply(multiply('double$udivide'(X1,'double$udivide'(X2,X1)),multiply('double$udivide'(X2,X3),X0)),inverse(X0)) = inverse(X3),
inference(superposition,[status(thm)],[d1,c1]) ).
cnf(d49,plain,
multiply(X3,inverse(X2)) = inverse('double$udivide'(inverse(X2),X3)),
inference(superposition,[status(thm)],[d3,d48]) ).
cnf(d50,plain,
multiply(X1,inverse(X0)) = multiply(X1,inverse(X0)),
inference(demodulation,[status(thm)],[d49,c1]) ).
cnf(d51,plain,
inverse(X2) = multiply(multiply('double$udivide'(X0,'double$udivide'(X1,X0)),multiply('double$udivide'(X1,X2),X3)),inverse(X3)),
inference(superposition,[status(thm)],[d48,d50]) ).
cnf(d52,plain,
inverse(X2) = multiply(X1,inverse(multiply('double$udivide'('double$udivide'(X1,X2),X3),X3))),
inference(superposition,[status(thm)],[d20,d51]) ).
cnf(d53,plain,
inverse(multiply(X1,inverse(X0))) = multiply(X0,inverse(X1)),
inference(superposition,[status(thm)],[d39,d52]) ).
cnf(d54,plain,
multiply('double$udivide'(X2,X3),X3) = multiply('double$udivide'(X4,'double$udivide'(X0,X4)),'double$udivide'(X0,X2)),
inference(superposition,[status(thm)],[d18,d5]) ).
cnf(d55,plain,
multiply('double$udivide'(X2,X4),X4) = multiply('double$udivide'(X2,X3),X3),
inference(superposition,[status(thm)],[d54,d54]) ).
cnf(d56,plain,
inverse(X0) = multiply('double$udivide'(inverse(multiply('double$udivide'(X0,X1),X1)),X3),X3),
inference(superposition,[status(thm)],[d33,d55]) ).
cnf(d57,plain,
inverse('double$udivide'(X0,X1)) = multiply(X1,X0),
inference(superposition,[status(thm)],[d21,d56]) ).
cnf(d58,plain,
inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(superposition,[status(thm)],[d27,d57]) ).
cnf(d59,plain,
inverse(inverse(multiply(X1,X0))) = multiply(X1,inverse(inverse(X0))),
inference(superposition,[status(thm)],[d58,d53]) ).
cnf(d60,plain,
inverse(inverse(multiply(X0,X1))) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d59,d47]) ).
cnf(d61,plain,
inverse(inverse(X0)) = multiply(X0,'double$udivide'(X1,inverse(X1))),
inference(superposition,[status(thm)],[d45,d60]) ).
cnf(d62,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d61,d45]) ).
cnf(d63,plain,
'double$udivide'(X0,X1) = multiply(inverse(X0),inverse(X1)),
inference(superposition,[status(thm)],[d62,d40]) ).
cnf(d64,plain,
'double$udivide'(multiply(inverse(X0),multiply(X0,'double$udivide'(X2,X1))),X2) = X1,
inference(superposition,[status(thm)],[d29,d38]) ).
cnf(d65,plain,
multiply(X1,'double$udivide'(inverse(X0),X0)) = X1,
inference(superposition,[status(thm)],[d62,d45]) ).
cnf(d66,plain,
multiply(X1,multiply(X0,inverse(X0))) = X1,
inference(demodulation,[status(thm)],[d65,d40]) ).
cnf(d67,plain,
multiply(X1,multiply(inverse(X0),X0)) = X1,
inference(superposition,[status(thm)],[d62,d66]) ).
cnf(d68,plain,
'double$udivide'(inverse(inverse('double$udivide'(X0,X1))),X0) = X1,
inference(superposition,[status(thm)],[d67,d64]) ).
cnf(d69,plain,
multiply(inverse('double$udivide'(X0,X1)),inverse(X0)) = X1,
inference(demodulation,[status(thm)],[d68,d40]) ).
cnf(d70,plain,
'double$udivide'('double$udivide'(X0,X1),X0) = X1,
inference(demodulation,[status(thm)],[d69,d63]) ).
cnf(d71,plain,
'double$udivide'(X1,'double$udivide'(X0,X1)) = X0,
inference(superposition,[status(thm)],[d70,d70]) ).
cnf(d72,plain,
X1 = multiply(X0,inverse('double$udivide'(X1,inverse(X0)))),
inference(superposition,[status(thm)],[d71,d40]) ).
cnf(d73,plain,
X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(demodulation,[status(thm)],[d72,c1]) ).
cnf(d74,plain,
'double$udivide'(inverse(X2),multiply(multiply('double$udivide'(X0,X1),X1),X2)) = X0,
inference(superposition,[status(thm)],[d27,d32]) ).
cnf(d75,plain,
multiply(X0,'double$udivide'(X0,multiply('double$udivide'(X1,X2),X2))) = X1,
inference(demodulation,[status(thm)],[d74,d29]) ).
cnf(d76,plain,
multiply(inverse(X0),multiply(X0,'double$udivide'(X2,'double$udivide'(X1,X2)))) = X1,
inference(superposition,[status(thm)],[d29,d75]) ).
cnf(d77,plain,
multiply(inverse(X2),multiply(X2,X1)) = X1,
inference(demodulation,[status(thm)],[d76,d71]) ).
cnf(d78,plain,
X0 = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d77,d67]) ).
cnf(d79,plain,
'double$udivide'(X0,X1) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[c1,d78]) ).
cnf(d80,plain,
X2 = multiply(multiply(X0,X1),multiply('double$udivide'(X1,X0),X2)),
inference(superposition,[status(thm)],[d79,d73]) ).
cnf(d81,plain,
inverse(multiply(X1,X0)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[c1,d62]) ).
cnf(d82,plain,
inverse(multiply(inverse(X1),X0)) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d47,d58]) ).
cnf(d83,plain,
'double$udivide'(X1,inverse(X0)) = multiply(inverse(X1),X0),
inference(demodulation,[status(thm)],[d82,d81]) ).
cnf(d84,plain,
X1 = multiply(inverse('double$udivide'(inverse(X0),X1)),X0),
inference(superposition,[status(thm)],[d70,d83]) ).
cnf(d85,plain,
X1 = multiply(multiply(X1,inverse(X0)),X0),
inference(demodulation,[status(thm)],[d84,c1]) ).
cnf(d86,plain,
X2 = multiply(multiply(X2,'double$udivide'(X1,X0)),multiply(X0,X1)),
inference(superposition,[status(thm)],[d79,d85]) ).
cnf(d87,plain,
'double$udivide'(inverse(inverse(X3)),multiply('double$udivide'(X4,'double$udivide'(inverse(X5),X4)),inverse(X2))) = multiply('double$udivide'(X6,'double$udivide'(X7,X6)),multiply('double$udivide'(X7,multiply('double$udivide'(X0,'double$udivide'(X1,X0)),multiply('double$udivide'(X1,X2),X3))),X5)),
inference(superposition,[status(thm)],[d51,d2]) ).
cnf(d88,plain,
multiply(inverse(X0),inverse(multiply('double$udivide'(X1,'double$udivide'(inverse(X2),X1)),inverse(X3)))) = multiply('double$udivide'(X4,'double$udivide'(X5,X4)),multiply('double$udivide'(X5,multiply('double$udivide'(X6,'double$udivide'(X7,X6)),multiply('double$udivide'(X7,X3),X0))),X2)),
inference(demodulation,[status(thm)],[d87,d40]) ).
cnf(d89,plain,
'double$udivide'(X0,multiply('double$udivide'(X1,'double$udivide'(inverse(X2),X1)),inverse(X3))) = multiply('double$udivide'(X4,'double$udivide'(X5,X4)),multiply('double$udivide'(X5,multiply('double$udivide'(X6,'double$udivide'(X7,X6)),multiply('double$udivide'(X7,X3),X0))),X2)),
inference(demodulation,[status(thm)],[d88,d63]) ).
cnf(d90,plain,
'double$udivide'(X2,multiply(inverse(X1),inverse(X3))) = multiply('double$udivide'(X4,'double$udivide'(X5,X4)),multiply('double$udivide'(X5,multiply('double$udivide'(X6,'double$udivide'(X7,X6)),multiply('double$udivide'(X7,X3),X2))),X1)),
inference(demodulation,[status(thm)],[d89,d71]) ).
cnf(d91,plain,
'double$udivide'(X2,'double$udivide'(X0,X1)) = multiply('double$udivide'(X3,'double$udivide'(X4,X3)),multiply('double$udivide'(X4,multiply('double$udivide'(X5,'double$udivide'(X6,X5)),multiply('double$udivide'(X6,X1),X2))),X0)),
inference(demodulation,[status(thm)],[d90,d63]) ).
cnf(d92,plain,
'double$udivide'(X2,'double$udivide'(X3,X4)) = multiply(X1,multiply('double$udivide'(X1,multiply('double$udivide'(X5,'double$udivide'(X6,X5)),multiply('double$udivide'(X6,X4),X2))),X3)),
inference(demodulation,[status(thm)],[d91,d71]) ).
cnf(d93,plain,
'double$udivide'(X2,'double$udivide'(X3,X4)) = multiply(X5,multiply('double$udivide'(X5,multiply(X1,multiply('double$udivide'(X1,X4),X2))),X3)),
inference(demodulation,[status(thm)],[d92,d71]) ).
cnf(d94,plain,
'double$udivide'(inverse(X4),multiply('double$udivide'(X5,'double$udivide'(inverse(X6),X5)),multiply('double$udivide'(inverse(X1),multiply('double$udivide'(X2,'double$udivide'(inverse(X0),X2)),multiply(X3,X1))),X4))) = multiply('double$udivide'(X7,'double$udivide'(inverse(X0),X7)),multiply(X3,X6)),
inference(superposition,[status(thm)],[d6,d2]) ).
cnf(d95,plain,
multiply(X0,inverse(multiply('double$udivide'(X1,'double$udivide'(inverse(X2),X1)),multiply('double$udivide'(inverse(X3),multiply('double$udivide'(X4,'double$udivide'(inverse(X5),X4)),multiply(X6,X3))),X0)))) = multiply('double$udivide'(X7,'double$udivide'(inverse(X5),X7)),multiply(X6,X2)),
inference(demodulation,[status(thm)],[d94,d40]) ).
cnf(d96,plain,
multiply(X6,'double$udivide'(multiply('double$udivide'(inverse(X2),multiply('double$udivide'(X3,'double$udivide'(inverse(X4),X3)),multiply(X5,X2))),X6),'double$udivide'(X0,'double$udivide'(inverse(X1),X0)))) = multiply('double$udivide'(X7,'double$udivide'(inverse(X4),X7)),multiply(X5,X1)),
inference(demodulation,[status(thm)],[d95,d81]) ).
cnf(d97,plain,
multiply(X4,'double$udivide'(multiply(multiply(X0,inverse(multiply('double$udivide'(X1,'double$udivide'(inverse(X2),X1)),multiply(X3,X0)))),X4),'double$udivide'(X5,'double$udivide'(inverse(X6),X5)))) = multiply('double$udivide'(X7,'double$udivide'(inverse(X2),X7)),multiply(X3,X6)),
inference(demodulation,[status(thm)],[d96,d40]) ).
cnf(d98,plain,
multiply(X4,'double$udivide'(multiply(multiply(X3,'double$udivide'(multiply(X2,X3),'double$udivide'(X0,'double$udivide'(inverse(X1),X0)))),X4),'double$udivide'(X5,'double$udivide'(inverse(X6),X5)))) = multiply('double$udivide'(X7,'double$udivide'(inverse(X1),X7)),multiply(X2,X6)),
inference(demodulation,[status(thm)],[d97,d81]) ).
cnf(d99,plain,
multiply(X2,'double$udivide'(multiply(multiply(X3,'double$udivide'(multiply(X4,X3),inverse(X1))),X2),'double$udivide'(X5,'double$udivide'(inverse(X6),X5)))) = multiply('double$udivide'(X7,'double$udivide'(inverse(X1),X7)),multiply(X4,X6)),
inference(demodulation,[status(thm)],[d98,d71]) ).
cnf(d100,plain,
multiply(X3,'double$udivide'(multiply(multiply(X1,multiply(inverse(multiply(X0,X1)),X2)),X3),'double$udivide'(X4,'double$udivide'(inverse(X5),X4)))) = multiply('double$udivide'(X6,'double$udivide'(inverse(X2),X6)),multiply(X0,X5)),
inference(demodulation,[status(thm)],[d99,d83]) ).
cnf(d101,plain,
multiply(X2,'double$udivide'(multiply(multiply(X1,multiply('double$udivide'(X1,X0),X3)),X2),'double$udivide'(X4,'double$udivide'(inverse(X5),X4)))) = multiply('double$udivide'(X6,'double$udivide'(inverse(X3),X6)),multiply(X0,X5)),
inference(demodulation,[status(thm)],[d100,d81]) ).
cnf(d102,plain,
multiply(X2,'double$udivide'(multiply(multiply(X3,multiply('double$udivide'(X3,X4),X5)),X2),inverse(X1))) = multiply('double$udivide'(X6,'double$udivide'(inverse(X5),X6)),multiply(X4,X1)),
inference(demodulation,[status(thm)],[d101,d71]) ).
cnf(d103,plain,
multiply(X3,multiply(inverse(multiply(multiply(X0,multiply('double$udivide'(X0,X1),X2)),X3)),X4)) = multiply('double$udivide'(X5,'double$udivide'(inverse(X2),X5)),multiply(X1,X4)),
inference(demodulation,[status(thm)],[d102,d83]) ).
cnf(d104,plain,
multiply(X3,multiply('double$udivide'(X3,multiply(X0,multiply('double$udivide'(X0,X1),X2))),X4)) = multiply('double$udivide'(X5,'double$udivide'(inverse(X2),X5)),multiply(X1,X4)),
inference(demodulation,[status(thm)],[d103,d81]) ).
cnf(d105,plain,
'double$udivide'(X3,'double$udivide'(X4,X2)) = multiply('double$udivide'(X5,'double$udivide'(inverse(X3),X5)),multiply(X2,X4)),
inference(demodulation,[status(thm)],[d104,d93]) ).
cnf(d106,plain,
'double$udivide'(X1,'double$udivide'(X2,X3)) = multiply(inverse(X1),multiply(X3,X2)),
inference(demodulation,[status(thm)],[d105,d71]) ).
cnf(d107,plain,
multiply('double$udivide'(inverse(X4),multiply('double$udivide'(X5,'double$udivide'(inverse(X3),X5)),multiply(X2,X4))),inverse(X3)) = inverse(X2),
inference(superposition,[status(thm)],[d2,d48]) ).
cnf(d108,plain,
'double$udivide'(inverse(X4),multiply('double$udivide'(X5,'double$udivide'(inverse(inverse(X2)),X5)),multiply(multiply('double$udivide'(X1,'double$udivide'(inverse(X2),X1)),multiply(X3,X0)),X4))) = multiply('double$udivide'(X6,'double$udivide'(inverse(X0),X6)),inverse(X3)),
inference(superposition,[status(thm)],[d107,d2]) ).
cnf(d109,plain,
multiply(X0,inverse(multiply('double$udivide'(X1,'double$udivide'(inverse(inverse(X2)),X1)),multiply(multiply('double$udivide'(X3,'double$udivide'(inverse(X2),X3)),multiply(X4,X5)),X0)))) = multiply('double$udivide'(X6,'double$udivide'(inverse(X5),X6)),inverse(X4)),
inference(demodulation,[status(thm)],[d108,d40]) ).
cnf(d110,plain,
multiply(X5,'double$udivide'(multiply(multiply('double$udivide'(X2,'double$udivide'(inverse(X1),X2)),multiply(X3,X4)),X5),'double$udivide'(X0,'double$udivide'(inverse(inverse(X1)),X0)))) = multiply('double$udivide'(X6,'double$udivide'(inverse(X4),X6)),inverse(X3)),
inference(demodulation,[status(thm)],[d109,d81]) ).
cnf(d111,plain,
multiply(X2,'double$udivide'(multiply(multiply(inverse(X1),multiply(X3,X4)),X2),'double$udivide'(X5,'double$udivide'(inverse(inverse(X1)),X5)))) = multiply('double$udivide'(X6,'double$udivide'(inverse(X4),X6)),inverse(X3)),
inference(demodulation,[status(thm)],[d110,d71]) ).
cnf(d112,plain,
multiply(X3,'double$udivide'(multiply('double$udivide'(X0,'double$udivide'(X2,X1)),X3),'double$udivide'(X4,'double$udivide'(inverse(inverse(X0)),X4)))) = multiply('double$udivide'(X5,'double$udivide'(inverse(X2),X5)),inverse(X1)),
inference(demodulation,[status(thm)],[d111,d106]) ).
cnf(d113,plain,
multiply(X2,'double$udivide'(multiply('double$udivide'(X1,'double$udivide'(X3,X4)),X2),inverse(inverse(X1)))) = multiply('double$udivide'(X5,'double$udivide'(inverse(X3),X5)),inverse(X4)),
inference(demodulation,[status(thm)],[d112,d71]) ).
cnf(d114,plain,
multiply(X3,multiply(inverse(multiply('double$udivide'(X0,'double$udivide'(X1,X2)),X3)),inverse(X0))) = multiply('double$udivide'(X4,'double$udivide'(inverse(X1),X4)),inverse(X2)),
inference(demodulation,[status(thm)],[d113,d83]) ).
cnf(d115,plain,
multiply(X3,'double$udivide'(multiply('double$udivide'(X0,'double$udivide'(X1,X2)),X3),X0)) = multiply('double$udivide'(X4,'double$udivide'(inverse(X1),X4)),inverse(X2)),
inference(demodulation,[status(thm)],[d114,d63]) ).
cnf(d116,plain,
multiply(X2,'double$udivide'(multiply('double$udivide'(X3,'double$udivide'(X1,X4)),X2),X3)) = multiply(inverse(X1),inverse(X4)),
inference(demodulation,[status(thm)],[d115,d71]) ).
cnf(d117,plain,
multiply(X2,'double$udivide'(multiply('double$udivide'(X3,'double$udivide'(X0,X1)),X2),X3)) = 'double$udivide'(X0,X1),
inference(demodulation,[status(thm)],[d116,d63]) ).
cnf(d118,plain,
multiply(X2,'double$udivide'(multiply(X1,X2),X0)) = 'double$udivide'(X1,X0),
inference(superposition,[status(thm)],[d71,d117]) ).
cnf(d119,plain,
X0 = multiply('double$udivide'(X1,X2),multiply(X2,multiply(X1,X0))),
inference(superposition,[status(thm)],[d118,d86]) ).
cnf(d120,plain,
multiply(X1,multiply(X0,X2)) = multiply(multiply(X1,X0),X2),
inference(superposition,[status(thm)],[d119,d80]) ).
cnf(d121,plain,
'double$udivide'(multiply(inverse(X0),X0),X1) = inverse(X1),
inference(superposition,[status(thm)],[d45,d64]) ).
cnf(d122,plain,
multiply(X1,inverse(multiply('double$udivide'('double$udivide'(X1,X2),X3),X3))) = inverse(X2),
inference(superposition,[status(thm)],[d20,d48]) ).
cnf(d123,plain,
multiply(X0,inverse(X1)) = inverse(multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[d39,d122]) ).
cnf(d124,plain,
multiply(inverse(X1),inverse(X0)) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[d27,c1]) ).
cnf(d125,plain,
multiply(inverse(X0),X1) = inverse(multiply(inverse(X1),X0)),
inference(superposition,[status(thm)],[d47,d124]) ).
cnf(d126,plain,
multiply(X1,inverse(inverse(X0))) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[status(thm)],[d125,d123]) ).
cnf(d127,plain,
multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(demodulation,[status(thm)],[d126,d47]) ).
cnf(d128,plain,
'double$udivide'(multiply(X0,inverse(X0)),X1) = inverse(X1),
inference(superposition,[status(thm)],[d127,d121]) ).
cnf(d129,plain,
X1 = inverse('double$udivide'(X1,multiply(X0,inverse(X0)))),
inference(superposition,[status(thm)],[d71,d128]) ).
cnf(d130,plain,
X0 = multiply(multiply(X1,inverse(X1)),X0),
inference(demodulation,[status(thm)],[d129,c1]) ).
cnf(d131,plain,
X1 = multiply('double$udivide'(X0,inverse(X0)),X1),
inference(superposition,[status(thm)],[d63,d130]) ).
cnf(d132,plain,
X1 = multiply(multiply(inverse(X0),X0),X1),
inference(demodulation,[status(thm)],[d131,d83]) ).
cnf(d133,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(demodulation,[status(thm)],[c2,d132]) ).
cnf(d134,plain,
( a2 != a2
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(demodulation,[status(thm)],[d133,d120]) ).
cnf(d135,plain,
'double$udivide'(inverse(X4),multiply('double$udivide'(X5,'double$udivide'(inverse(X2),X5)),multiply('double$udivide'(inverse(X2),X3),X4))) = X3,
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d136,plain,
X3 = X3,
inference(demodulation,[status(thm)],[d135,d1]) ).
cnf(d137,plain,
( a2 != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(resolution,[status(thm)],[d136,d134]) ).
cnf(d138,plain,
'double$udivide'(X1,inverse(X1)) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[d121,d71]) ).
cnf(d139,plain,
multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(demodulation,[status(thm)],[d138,d83]) ).
cnf(d140,plain,
a2 != a2,
inference(resolution,[status(thm)],[d139,d137]) ).
cnf(d141,plain,
$false,
inference(equality_resolution,[status(thm)],[d140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP082-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n008.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Fri Sep 25 14:22:09 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 96.15/19.27 % SZS status Unsatisfiable for theBenchmark.p
% 96.15/19.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------