%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP053-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 07:22:13 AM UTC 2026
% Result : Unsatisfiable 148.59s 19.39s
% Output : CNFRefutation 148.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 2
% Syntax : Number of clauses : 121 ( 116 unt; 0 nHn; 7 RR)
% Number of literals : 128 ( 127 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 418 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0)))))) = X2 ).
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,
inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0)))))) = X2,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,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,
inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X2))),inverse(multiply(inverse(X3),X3)))))) = multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0))))),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d1,plain,
X2 = multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,inverse(inverse(X2))))),inverse(multiply(inverse(X3),X3))))),
inference(superposition,[status(thm)],[c0,d0]) ).
cnf(d2,plain,
X2 = inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,inverse(X2)))),inverse(multiply(inverse(X3),X3)))))),
inference(superposition,[status(thm)],[d0,d1]) ).
cnf(d3,plain,
multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,inverse(inverse(X2))))),inverse(multiply(inverse(X3),X3))))) = X2,
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d4,plain,
inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X0,X3)),X2)),inverse(multiply(inverse(X3),X3)))))) = multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(inverse(X2))))),inverse(multiply(inverse(X0),X0))),
inference(superposition,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
multiply(X1,inverse(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X1,X3)),X2)),inverse(multiply(inverse(X3),X3)))))))) = X2,
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
X2 = multiply(X1,inverse(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X1,X3)),X2)),inverse(multiply(inverse(X3),X3)))))))),
inference(superposition,[status(thm)],[d4,d1]) ).
cnf(d7,plain,
inverse(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),X3)),inverse(multiply(inverse(X2),X2))))))) = multiply(X0,inverse(inverse(multiply(X1,inverse(multiply(inverse(X3),inverse(multiply(inverse(X1),X1)))))))),
inference(superposition,[status(thm)],[d6,d6]) ).
cnf(d8,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2))))))))) = X3,
inference(superposition,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
inverse(X2) = multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,inverse(inverse(inverse(X2)))))),inverse(multiply(inverse(X3),X3))))),
inference(superposition,[status(thm)],[d3,d0]) ).
cnf(d10,plain,
inverse(X2) = inverse(X2),
inference(demodulation,[status(thm)],[d9,d3]) ).
cnf(d11,plain,
X2 = multiply(inverse(multiply(inverse(multiply(X3,X1)),multiply(X3,inverse(inverse(multiply(X1,inverse(X2))))))),inverse(multiply(inverse(X1),X1))),
inference(superposition,[status(thm)],[d4,d2]) ).
cnf(d12,plain,
multiply(inverse(X1),X1) = inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(inverse(multiply(X1,inverse(X2))))))),X3)),X2)),inverse(multiply(inverse(X3),X3)))))),
inference(superposition,[status(thm)],[d11,d2]) ).
cnf(d13,plain,
inverse(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X2))),inverse(multiply(inverse(X3),X3))))))) = X2,
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d14,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X3,X1)),multiply(X3,inverse(inverse(multiply(X1,X2)))))),inverse(multiply(inverse(X1),X1)))) = X2,
inference(superposition,[status(thm)],[d4,d13]) ).
cnf(d15,plain,
multiply(inverse(X1),X1) = inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1)))))))),
inference(superposition,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
inverse(multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(inverse(multiply(inverse(X0),X0))),inverse(multiply(inverse(X0),X0)))))))) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[d15,d10]) ).
cnf(d17,plain,
multiply(inverse(multiply(X2,inverse(multiply(inverse(X0),X0)))),multiply(X2,inverse(multiply(inverse(X0),X0)))) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[d16,d8]) ).
cnf(d18,plain,
multiply(inverse(X2),X2) = multiply(inverse(X3),X3),
inference(superposition,[status(thm)],[d17,d17]) ).
cnf(d19,plain,
X1 = inverse(multiply(inverse(X1),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(inverse(X1)),inverse(X1))))))),
inference(superposition,[status(thm)],[d18,d2]) ).
cnf(d20,plain,
X0 = inverse(multiply(inverse(X0),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X1),X1)))))),
inference(superposition,[status(thm)],[d18,d19]) ).
cnf(d21,plain,
inverse(multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(inverse(X1),X1)))) = inverse(multiply(inverse(X2),X2)),
inference(superposition,[status(thm)],[d18,d20]) ).
cnf(d22,plain,
X1 = inverse(multiply(inverse(X1),inverse(multiply(inverse(X2),X2)))),
inference(superposition,[status(thm)],[d21,d2]) ).
cnf(d23,plain,
X2 = inverse(multiply(inverse(X2),multiply(inverse(X0),X0))),
inference(demodulation,[status(thm)],[d20,d22]) ).
cnf(d24,plain,
multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(inverse(multiply(X1,X2))))) = X2,
inference(demodulation,[status(thm)],[d14,d22]) ).
cnf(d25,plain,
multiply(inverse(inverse(inverse(multiply(X0,X1)))),X0) = inverse(X1),
inference(superposition,[status(thm)],[d24,d23]) ).
cnf(d26,plain,
inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0)))),inverse(multiply(inverse(multiply(X2,multiply(X0,X3))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0))))),inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0))))))))))) = X3,
inference(superposition,[status(thm)],[d2,d13]) ).
cnf(d27,plain,
inverse(inverse(multiply(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2))),inverse(multiply(inverse(multiply(X2,multiply(X1,X3))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X1),X1))))),inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X1),X1))))))))))) = X3,
inference(demodulation,[status(thm)],[d26,d22]) ).
cnf(d28,plain,
inverse(inverse(multiply(multiply(inverse(multiply(X3,X1)),multiply(X3,inverse(X0))),multiply(X0,multiply(X1,X2))))) = X2,
inference(demodulation,[status(thm)],[d27,d22]) ).
cnf(d29,plain,
multiply(inverse(inverse(X1)),inverse(multiply(inverse(X2),X2))) = X1,
inference(superposition,[status(thm)],[d21,d3]) ).
cnf(d30,plain,
multiply(inverse(inverse(X1)),multiply(inverse(X0),X0)) = X1,
inference(superposition,[status(thm)],[d23,d29]) ).
cnf(d31,plain,
inverse(X1) = inverse(multiply(multiply(inverse(X0),X0),X1)),
inference(superposition,[status(thm)],[d25,d30]) ).
cnf(d32,plain,
inverse(inverse(multiply(X1,multiply(inverse(X1),X2)))) = X2,
inference(superposition,[status(thm)],[d31,d28]) ).
cnf(d33,plain,
multiply(inverse(X1),X0) = inverse(multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d32,d25]) ).
cnf(d34,plain,
multiply(inverse(X0),X0) = inverse(multiply(inverse(X2),X2)),
inference(demodulation,[status(thm)],[d21,d22]) ).
cnf(d35,plain,
X2 = inverse(multiply(inverse(X2),inverse(inverse(multiply(inverse(X1),X1))))),
inference(superposition,[status(thm)],[d34,d22]) ).
cnf(d36,plain,
X0 = multiply(inverse(inverse(inverse(multiply(inverse(X1),X1)))),X0),
inference(demodulation,[status(thm)],[d35,d33]) ).
cnf(d37,plain,
X1 = multiply(inverse(inverse(multiply(inverse(X0),X0))),X1),
inference(demodulation,[status(thm)],[d36,d33]) ).
cnf(d38,plain,
X1 = multiply(inverse(multiply(inverse(X0),X0)),X1),
inference(demodulation,[status(thm)],[d37,d33]) ).
cnf(d39,plain,
X1 = multiply(multiply(inverse(X0),X0),X1),
inference(demodulation,[status(thm)],[d38,d33]) ).
cnf(d40,plain,
X1 = multiply(inverse(inverse(X1)),inverse(multiply(inverse(X2),X2))),
inference(superposition,[status(thm)],[d21,d1]) ).
cnf(d41,plain,
inverse(multiply(inverse(multiply(inverse(X0),X0)),X1)) = inverse(X1),
inference(superposition,[status(thm)],[d25,d40]) ).
cnf(d42,plain,
multiply(inverse(X1),multiply(inverse(X0),X0)) = inverse(X1),
inference(demodulation,[status(thm)],[d41,d33]) ).
cnf(d43,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d30,d42]) ).
cnf(d44,plain,
multiply(inverse(X1),inverse(X0)) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[d43,d33]) ).
cnf(d45,plain,
X4 = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),X2)),inverse(multiply(inverse(X0),X0)))),inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(X3,X1)),multiply(X3,inverse(inverse(X2))))),inverse(multiply(inverse(X1),X1))),multiply(X0,inverse(inverse(X4))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),X2)),inverse(multiply(inverse(X0),X0))))),inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),X2)),inverse(multiply(inverse(X0),X0))))))))),
inference(superposition,[status(thm)],[d4,d1]) ).
cnf(d46,plain,
X4 = inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(X3,X0)),multiply(X3,inverse(inverse(X2))))),inverse(multiply(inverse(X0),X0))),multiply(X1,inverse(inverse(X4))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),inverse(multiply(inverse(X1),X1))))),inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),inverse(multiply(inverse(X1),X1))))))),multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),inverse(multiply(inverse(X1),X1))))),
inference(demodulation,[status(thm)],[d45,d44]) ).
cnf(d47,plain,
X4 = inverse(multiply(inverse(multiply(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X3)),X2)),inverse(multiply(inverse(X3),X3))))),inverse(multiply(inverse(multiply(inverse(multiply(X1,X3)),X2)),inverse(multiply(inverse(X3),X3))))),multiply(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(inverse(X2))))),inverse(multiply(inverse(X1),X1))),multiply(X3,inverse(inverse(X4)))))),multiply(inverse(multiply(inverse(multiply(X1,X3)),X2)),inverse(multiply(inverse(X3),X3))))),
inference(demodulation,[status(thm)],[d46,d44]) ).
cnf(d48,plain,
X4 = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),inverse(multiply(inverse(X1),X1)))),multiply(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),inverse(multiply(inverse(X1),X1))))),inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),inverse(multiply(inverse(X1),X1))))),multiply(multiply(inverse(multiply(inverse(multiply(X3,X0)),multiply(X3,inverse(inverse(X2))))),inverse(multiply(inverse(X0),X0))),multiply(X1,inverse(inverse(X4)))))),
inference(demodulation,[status(thm)],[d47,d33]) ).
cnf(d49,plain,
X3 = multiply(multiply(inverse(inverse(multiply(inverse(X1),X1))),multiply(inverse(multiply(X0,X1)),X2)),multiply(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),inverse(multiply(inverse(X1),X1))))),inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),inverse(multiply(inverse(X1),X1))))),multiply(multiply(inverse(multiply(inverse(multiply(X4,X0)),multiply(X4,inverse(inverse(X2))))),inverse(multiply(inverse(X0),X0))),multiply(X1,inverse(inverse(X3)))))),
inference(demodulation,[status(thm)],[d48,d33]) ).
cnf(d50,plain,
X1 = multiply(multiply(multiply(inverse(X0),X0),multiply(inverse(multiply(X2,X0)),X3)),multiply(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X2,X0)),X3)),inverse(multiply(inverse(X0),X0))))),inverse(multiply(inverse(multiply(inverse(multiply(X2,X0)),X3)),inverse(multiply(inverse(X0),X0))))),multiply(multiply(inverse(multiply(inverse(multiply(X4,X2)),multiply(X4,inverse(inverse(X3))))),inverse(multiply(inverse(X2),X2))),multiply(X0,inverse(inverse(X1)))))),
inference(demodulation,[status(thm)],[d49,d43]) ).
cnf(d51,plain,
X3 = multiply(multiply(inverse(multiply(X1,X0)),X2),multiply(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),X2)),inverse(multiply(inverse(X0),X0))))),inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),X2)),inverse(multiply(inverse(X0),X0))))),multiply(multiply(inverse(multiply(inverse(multiply(X4,X1)),multiply(X4,inverse(inverse(X2))))),inverse(multiply(inverse(X1),X1))),multiply(X0,inverse(inverse(X3)))))),
inference(demodulation,[status(thm)],[d50,d39]) ).
cnf(d52,plain,
X4 = multiply(multiply(inverse(multiply(X0,X1)),X2),multiply(multiply(inverse(multiply(inverse(multiply(X3,X0)),multiply(X3,inverse(inverse(X2))))),inverse(multiply(inverse(X0),X0))),multiply(X1,inverse(inverse(X4))))),
inference(demodulation,[status(thm)],[d51,d39]) ).
cnf(d53,plain,
X3 = multiply(multiply(inverse(multiply(X1,X4)),X2),multiply(inverse(multiply(multiply(inverse(X1),X1),multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(inverse(X2)))))),multiply(X4,inverse(inverse(X3))))),
inference(demodulation,[status(thm)],[d52,d44]) ).
cnf(d54,plain,
X3 = multiply(multiply(inverse(multiply(X0,X4)),X2),multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(inverse(X2))))),multiply(X4,inverse(inverse(X3))))),
inference(demodulation,[status(thm)],[d53,d39]) ).
cnf(d55,plain,
X3 = multiply(multiply(inverse(multiply(X1,X4)),X2),multiply(multiply(inverse(multiply(X0,inverse(inverse(X2)))),multiply(X0,X1)),multiply(X4,inverse(inverse(X3))))),
inference(demodulation,[status(thm)],[d54,d33]) ).
cnf(d56,plain,
X1 = multiply(multiply(inverse(multiply(X2,X3)),X0),multiply(multiply(inverse(multiply(X4,X0)),multiply(X4,X2)),multiply(X3,inverse(inverse(X1))))),
inference(demodulation,[status(thm)],[d55,d43]) ).
cnf(d57,plain,
X0 = multiply(multiply(inverse(multiply(X1,X2)),X3),multiply(multiply(inverse(multiply(X4,X3)),multiply(X4,X1)),multiply(X2,X0))),
inference(demodulation,[status(thm)],[d56,d43]) ).
cnf(d58,plain,
X3 = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0)))),inverse(multiply(inverse(multiply(X2,multiply(X0,inverse(inverse(X3))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0))))),inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0))))))))),
inference(superposition,[status(thm)],[c0,d1]) ).
cnf(d59,plain,
X3 = multiply(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2))),inverse(multiply(inverse(multiply(X2,multiply(X1,inverse(inverse(X3))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X1),X1))))),inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X1),X1))))))))),
inference(demodulation,[status(thm)],[d58,d22]) ).
cnf(d60,plain,
X2 = multiply(multiply(inverse(multiply(X3,X1)),multiply(X3,inverse(X0))),multiply(X0,multiply(X1,inverse(inverse(X2))))),
inference(demodulation,[status(thm)],[d59,d22]) ).
cnf(d61,plain,
X2 = multiply(X1,multiply(inverse(X1),inverse(inverse(X2)))),
inference(superposition,[status(thm)],[d39,d60]) ).
cnf(d62,plain,
X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(demodulation,[status(thm)],[d61,d43]) ).
cnf(d63,plain,
multiply(inverse(inverse(X2)),inverse(inverse(multiply(inverse(X1),X1)))) = X2,
inference(superposition,[status(thm)],[d34,d29]) ).
cnf(d64,plain,
multiply(inverse(multiply(inverse(inverse(X0)),inverse(X1))),X0) = X1,
inference(superposition,[status(thm)],[d63,d24]) ).
cnf(d65,plain,
multiply(multiply(inverse(inverse(X1)),inverse(X0)),X0) = X1,
inference(demodulation,[status(thm)],[d64,d33]) ).
cnf(d66,plain,
multiply(multiply(X0,inverse(X1)),X1) = X0,
inference(demodulation,[status(thm)],[d65,d43]) ).
cnf(d67,plain,
X2 = multiply(inverse(inverse(X2)),multiply(inverse(X1),X1)),
inference(superposition,[status(thm)],[d34,d40]) ).
cnf(d68,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d67,d42]) ).
cnf(d69,plain,
multiply(multiply(X1,X0),inverse(X0)) = X1,
inference(superposition,[status(thm)],[d68,d66]) ).
cnf(d70,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0)))),inverse(multiply(inverse(multiply(X2,multiply(X0,inverse(inverse(X3))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0))))),inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0))))))))) = X3,
inference(superposition,[status(thm)],[d2,d3]) ).
cnf(d71,plain,
multiply(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2))),inverse(multiply(inverse(multiply(X2,multiply(X1,inverse(inverse(X3))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X1),X1))))),inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X1),X1))))))))) = X3,
inference(demodulation,[status(thm)],[d70,d22]) ).
cnf(d72,plain,
multiply(multiply(inverse(multiply(X3,X1)),multiply(X3,inverse(X0))),multiply(X0,multiply(X1,inverse(inverse(X2))))) = X2,
inference(demodulation,[status(thm)],[d71,d22]) ).
cnf(d73,plain,
multiply(X1,multiply(inverse(X1),inverse(inverse(X2)))) = X2,
inference(superposition,[status(thm)],[d39,d72]) ).
cnf(d74,plain,
multiply(X1,multiply(inverse(X1),X0)) = X0,
inference(demodulation,[status(thm)],[d73,d43]) ).
cnf(d75,plain,
multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[d68,d74]) ).
cnf(d76,plain,
multiply(X1,inverse(multiply(X0,X1))) = inverse(X0),
inference(superposition,[status(thm)],[d75,d69]) ).
cnf(d77,plain,
inverse(multiply(X1,inverse(X0))) = multiply(X0,inverse(X1)),
inference(superposition,[status(thm)],[d76,d62]) ).
cnf(d78,plain,
inverse(multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X6))),inverse(multiply(inverse(X4),X4)))))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),X2)),inverse(multiply(inverse(X0),X0)))),inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(X3,X1)),multiply(X3,inverse(inverse(X2))))),inverse(multiply(inverse(X1),X1))),multiply(X0,inverse(X6)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),X2)),inverse(multiply(inverse(X0),X0))))),inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),X2)),inverse(multiply(inverse(X0),X0))))))))),
inference(superposition,[status(thm)],[d4,d0]) ).
cnf(d79,plain,
multiply(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,X2))),inverse(multiply(inverse(X0),X0))),inverse(X0)) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X5)),inverse(multiply(inverse(X4),X4)))),inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(X6,X3)),multiply(X6,inverse(inverse(X5))))),inverse(multiply(inverse(X3),X3))),multiply(X4,inverse(X2)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X5)),inverse(multiply(inverse(X4),X4))))),inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X5)),inverse(multiply(inverse(X4),X4))))))))),
inference(demodulation,[status(thm)],[d78,d77]) ).
cnf(d80,plain,
multiply(inverse(multiply(multiply(inverse(X1),X1),multiply(inverse(multiply(X0,X1)),multiply(X0,X2)))),inverse(X1)) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X5)),inverse(multiply(inverse(X4),X4)))),inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(X6,X3)),multiply(X6,inverse(inverse(X5))))),inverse(multiply(inverse(X3),X3))),multiply(X4,inverse(X2)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X5)),inverse(multiply(inverse(X4),X4))))),inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X5)),inverse(multiply(inverse(X4),X4))))))))),
inference(demodulation,[status(thm)],[d79,d44]) ).
cnf(d81,plain,
inverse(multiply(X0,multiply(multiply(inverse(X0),X0),multiply(inverse(multiply(X1,X0)),multiply(X1,X2))))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X5)),inverse(multiply(inverse(X4),X4)))),inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(X6,X3)),multiply(X6,inverse(inverse(X5))))),inverse(multiply(inverse(X3),X3))),multiply(X4,inverse(X2)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X5)),inverse(multiply(inverse(X4),X4))))),inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X5)),inverse(multiply(inverse(X4),X4))))))))),
inference(demodulation,[status(thm)],[d80,d44]) ).
cnf(d82,plain,
inverse(multiply(X0,multiply(inverse(multiply(X1,X0)),multiply(X1,X2)))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X5)),inverse(multiply(inverse(X4),X4)))),inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(X6,X3)),multiply(X6,inverse(inverse(X5))))),inverse(multiply(inverse(X3),X3))),multiply(X4,inverse(X2)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X5)),inverse(multiply(inverse(X4),X4))))),inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X5)),inverse(multiply(inverse(X4),X4))))))))),
inference(demodulation,[status(thm)],[d81,d39]) ).
cnf(d83,plain,
inverse(multiply(X5,multiply(inverse(multiply(X6,X5)),multiply(X6,X4)))) = inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(X3,X0)),multiply(X3,inverse(inverse(X2))))),inverse(multiply(inverse(X0),X0))),multiply(X1,inverse(X4)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),inverse(multiply(inverse(X1),X1))))),inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),inverse(multiply(inverse(X1),X1))))))),multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),inverse(multiply(inverse(X1),X1))))),
inference(demodulation,[status(thm)],[d82,d44]) ).
cnf(d84,plain,
inverse(multiply(X5,multiply(inverse(multiply(X6,X5)),multiply(X6,X4)))) = inverse(multiply(inverse(multiply(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X3)),X2)),inverse(multiply(inverse(X3),X3))))),inverse(multiply(inverse(multiply(inverse(multiply(X1,X3)),X2)),inverse(multiply(inverse(X3),X3))))),multiply(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(inverse(X2))))),inverse(multiply(inverse(X1),X1))),multiply(X3,inverse(X4))))),multiply(inverse(multiply(inverse(multiply(X1,X3)),X2)),inverse(multiply(inverse(X3),X3))))),
inference(demodulation,[status(thm)],[d83,d44]) ).
cnf(d85,plain,
inverse(multiply(X5,multiply(inverse(multiply(X6,X5)),multiply(X6,X4)))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),inverse(multiply(inverse(X1),X1)))),multiply(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),inverse(multiply(inverse(X1),X1))))),inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),inverse(multiply(inverse(X1),X1))))),multiply(multiply(inverse(multiply(inverse(multiply(X3,X0)),multiply(X3,inverse(inverse(X2))))),inverse(multiply(inverse(X0),X0))),multiply(X1,inverse(X4))))),
inference(demodulation,[status(thm)],[d84,d33]) ).
cnf(d86,plain,
inverse(multiply(X3,multiply(inverse(multiply(X4,X3)),multiply(X4,X5)))) = multiply(multiply(inverse(inverse(multiply(inverse(X1),X1))),multiply(inverse(multiply(X0,X1)),X2)),multiply(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),inverse(multiply(inverse(X1),X1))))),inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),inverse(multiply(inverse(X1),X1))))),multiply(multiply(inverse(multiply(inverse(multiply(X6,X0)),multiply(X6,inverse(inverse(X2))))),inverse(multiply(inverse(X0),X0))),multiply(X1,inverse(X5))))),
inference(demodulation,[status(thm)],[d85,d33]) ).
cnf(d87,plain,
inverse(multiply(X1,multiply(inverse(multiply(X2,X1)),multiply(X2,X3)))) = multiply(multiply(multiply(inverse(X0),X0),multiply(inverse(multiply(X4,X0)),X5)),multiply(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X4,X0)),X5)),inverse(multiply(inverse(X0),X0))))),inverse(multiply(inverse(multiply(inverse(multiply(X4,X0)),X5)),inverse(multiply(inverse(X0),X0))))),multiply(multiply(inverse(multiply(inverse(multiply(X6,X4)),multiply(X6,inverse(inverse(X5))))),inverse(multiply(inverse(X4),X4))),multiply(X0,inverse(X3))))),
inference(demodulation,[status(thm)],[d86,d43]) ).
cnf(d88,plain,
inverse(multiply(X3,multiply(inverse(multiply(X4,X3)),multiply(X4,X5)))) = multiply(multiply(inverse(multiply(X1,X0)),X2),multiply(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),X2)),inverse(multiply(inverse(X0),X0))))),inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),X2)),inverse(multiply(inverse(X0),X0))))),multiply(multiply(inverse(multiply(inverse(multiply(X6,X1)),multiply(X6,inverse(inverse(X2))))),inverse(multiply(inverse(X1),X1))),multiply(X0,inverse(X5))))),
inference(demodulation,[status(thm)],[d87,d39]) ).
cnf(d89,plain,
inverse(multiply(X5,multiply(inverse(multiply(X6,X5)),multiply(X6,X4)))) = multiply(multiply(inverse(multiply(X0,X1)),X2),multiply(multiply(inverse(multiply(inverse(multiply(X3,X0)),multiply(X3,inverse(inverse(X2))))),inverse(multiply(inverse(X0),X0))),multiply(X1,inverse(X4)))),
inference(demodulation,[status(thm)],[d88,d39]) ).
cnf(d90,plain,
inverse(multiply(X3,multiply(inverse(multiply(X4,X3)),multiply(X4,X5)))) = multiply(multiply(inverse(multiply(X1,X6)),X2),multiply(inverse(multiply(multiply(inverse(X1),X1),multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(inverse(X2)))))),multiply(X6,inverse(X5)))),
inference(demodulation,[status(thm)],[d89,d44]) ).
cnf(d91,plain,
inverse(multiply(X3,multiply(inverse(multiply(X4,X3)),multiply(X4,X5)))) = multiply(multiply(inverse(multiply(X0,X6)),X2),multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(inverse(X2))))),multiply(X6,inverse(X5)))),
inference(demodulation,[status(thm)],[d90,d39]) ).
cnf(d92,plain,
inverse(multiply(X3,multiply(inverse(multiply(X4,X3)),multiply(X4,X5)))) = multiply(multiply(inverse(multiply(X1,X6)),X2),multiply(multiply(inverse(multiply(X0,inverse(inverse(X2)))),multiply(X0,X1)),multiply(X6,inverse(X5)))),
inference(demodulation,[status(thm)],[d91,d33]) ).
cnf(d93,plain,
inverse(multiply(X2,multiply(inverse(multiply(X3,X2)),multiply(X3,X4)))) = multiply(multiply(inverse(multiply(X5,X6)),X1),multiply(multiply(multiply(inverse(X1),inverse(X0)),multiply(X0,X5)),multiply(X6,inverse(X4)))),
inference(demodulation,[status(thm)],[d92,d77]) ).
cnf(d94,plain,
inverse(multiply(X2,multiply(inverse(multiply(X3,X2)),multiply(X3,X4)))) = multiply(multiply(inverse(multiply(X5,X6)),X0),multiply(multiply(inverse(multiply(X1,X0)),multiply(X1,X5)),multiply(X6,inverse(X4)))),
inference(demodulation,[status(thm)],[d93,d44]) ).
cnf(d95,plain,
inverse(multiply(X5,multiply(inverse(multiply(X6,X5)),multiply(X6,X4)))) = inverse(X4),
inference(demodulation,[status(thm)],[d94,d57]) ).
cnf(d96,plain,
inverse(multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,inverse(X2)))),inverse(multiply(inverse(X4),X4)))))) = multiply(X1,inverse(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X1,X3)),X2)),inverse(multiply(inverse(X3),X3)))))))),
inference(superposition,[status(thm)],[d4,d0]) ).
cnf(d97,plain,
multiply(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0))),inverse(X0)) = multiply(X3,inverse(inverse(multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X2)),inverse(multiply(inverse(X4),X4)))))))),
inference(demodulation,[status(thm)],[d96,d77]) ).
cnf(d98,plain,
multiply(inverse(multiply(multiply(inverse(X1),X1),multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2))))),inverse(X1)) = multiply(X3,inverse(inverse(multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X2)),inverse(multiply(inverse(X4),X4)))))))),
inference(demodulation,[status(thm)],[d97,d44]) ).
cnf(d99,plain,
inverse(multiply(X0,multiply(multiply(inverse(X0),X0),multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))))) = multiply(X3,inverse(inverse(multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X2)),inverse(multiply(inverse(X4),X4)))))))),
inference(demodulation,[status(thm)],[d98,d44]) ).
cnf(d100,plain,
inverse(multiply(X0,multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2))))) = multiply(X3,inverse(inverse(multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X2)),inverse(multiply(inverse(X4),X4)))))))),
inference(demodulation,[status(thm)],[d99,d39]) ).
cnf(d101,plain,
inverse(inverse(X2)) = multiply(X3,inverse(inverse(multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X2)),inverse(multiply(inverse(X4),X4)))))))),
inference(demodulation,[status(thm)],[d100,d95]) ).
cnf(d102,plain,
X0 = multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X0)),inverse(multiply(inverse(X2),X2)))))))),
inference(demodulation,[status(thm)],[d101,d43]) ).
cnf(d103,plain,
X2 = multiply(X1,multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),X2)),inverse(multiply(inverse(X0),X0)))))),
inference(demodulation,[status(thm)],[d102,d43]) ).
cnf(d104,plain,
X2 = multiply(X0,multiply(X1,multiply(inverse(inverse(multiply(inverse(X1),X1))),multiply(inverse(multiply(X0,X1)),X2)))),
inference(demodulation,[status(thm)],[d103,d33]) ).
cnf(d105,plain,
X1 = multiply(X2,multiply(X0,multiply(multiply(inverse(X0),X0),multiply(inverse(multiply(X2,X0)),X1)))),
inference(demodulation,[status(thm)],[d104,d43]) ).
cnf(d106,plain,
X2 = multiply(X1,multiply(X0,multiply(inverse(multiply(X1,X0)),X2))),
inference(demodulation,[status(thm)],[d105,d39]) ).
cnf(d107,plain,
X1 = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[d68,d62]) ).
cnf(d108,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[d107,d106]) ).
cnf(d109,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2 ),
inference(resolution,[status(thm)],[d18,c1]) ).
cnf(d110,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(demodulation,[status(thm)],[d109,d39]) ).
cnf(d111,plain,
( a2 != a2
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)) ),
inference(demodulation,[status(thm)],[d110,d108]) ).
cnf(d112,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0)))),inverse(multiply(inverse(multiply(X2,multiply(X0,inverse(X3)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0))))),inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0)))))))))) = X3,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d113,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(inverse(X2))))),inverse(multiply(inverse(X0),X0)))),inverse(multiply(inverse(multiply(inverse(X2),multiply(X0,inverse(X3)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(inverse(X2))))),inverse(multiply(inverse(X0),X0))))),inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(inverse(X2))))),inverse(multiply(inverse(X0),X0)))))))))) = X3,
inference(superposition,[status(thm)],[d3,c0]) ).
cnf(d114,plain,
X3 = X3,
inference(demodulation,[status(thm)],[d113,d112]) ).
cnf(d115,plain,
a2 != a2,
inference(resolution,[status(thm)],[d114,d111]) ).
cnf(d116,plain,
$false,
inference(equality_resolution,[status(thm)],[d115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP053-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.54 % Computer : n008.cluster.edu
% 0.10/0.54 % Model : x86_64 x86_64
% 0.10/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.54 % Memory : 8046.5625MB
% 0.10/0.54 % OS : Linux 6.8.0-71-generic
% 0.10/0.54 % CPULimit : 300
% 0.10/0.54 % WCLimit : 300
% 0.10/0.54 % DateTime : Fri Sep 25 14:20:40 UTC 2026
% 0.10/0.54 % CPUTime :
% 0.10/0.54 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 148.59/19.39 % SZS status Unsatisfiable for theBenchmark.p
% 148.59/19.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------