%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP050-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 56.78s 20.98s
% Output : CNFRefutation 56.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 2
% Syntax : Number of clauses : 92 ( 86 unt; 0 nHn; 8 RR)
% Number of literals : 100 ( 99 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 15 ( 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 : 336 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(X1),multiply(inverse(X1),X1))))) = 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,
multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(X1),multiply(inverse(X1),X1))))) = 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,
multiply(X0,inverse(multiply(inverse(X3),multiply(inverse(X1),multiply(inverse(X1),X1))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),X3)),multiply(inverse(X2),multiply(inverse(X2),X2)))),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d1,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X3)),multiply(inverse(multiply(X0,X1)),X2))),multiply(inverse(X3),multiply(inverse(X3),X3)))) = X2,
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(X3),multiply(inverse(X1),multiply(inverse(X1),X1)))))) = X3,
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d3,plain,
multiply(inverse(multiply(X4,X2)),multiply(X4,X3)) = multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(multiply(X0,X1)),X3)),
inference(superposition,[status(thm)],[d1,d2]) ).
cnf(d4,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X4,X2)),multiply(X4,X3))),multiply(inverse(X2),multiply(inverse(X2),X2)))) = X3,
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
multiply(inverse(multiply(X5,X2)),multiply(X5,X3)) = multiply(inverse(multiply(X4,X2)),multiply(X4,X3)),
inference(superposition,[status(thm)],[d3,d3]) ).
cnf(d6,plain,
multiply(inverse(multiply(X3,X0)),multiply(X3,inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,multiply(inverse(X0),X0)))))) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
inverse(multiply(inverse(multiply(inverse(X1),X3)),multiply(inverse(X1),multiply(inverse(X1),X1)))) = inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,multiply(inverse(X1),X1)))),
inference(superposition,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,multiply(inverse(X0),X0)))) = inverse(multiply(inverse(multiply(X3,X1)),multiply(X3,multiply(inverse(X0),X0)))),
inference(superposition,[status(thm)],[d7,d7]) ).
cnf(d9,plain,
multiply(X2,multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))),X3)) = multiply(inverse(multiply(X4,multiply(inverse(X1),multiply(inverse(X1),X1)))),multiply(X4,X3)),
inference(superposition,[status(thm)],[d4,d5]) ).
cnf(d10,plain,
multiply(X5,multiply(inverse(multiply(inverse(multiply(X6,X1)),multiply(X6,X5))),X2)) = multiply(X3,multiply(inverse(multiply(inverse(multiply(X4,X1)),multiply(X4,X3))),X2)),
inference(superposition,[status(thm)],[d9,d9]) ).
cnf(d11,plain,
multiply(inverse(multiply(X3,multiply(X0,X1))),multiply(X3,inverse(multiply(inverse(X4),multiply(inverse(multiply(X0,X1)),multiply(inverse(multiply(X2,X1)),multiply(X2,X1))))))) = X4,
inference(superposition,[status(thm)],[d5,d2]) ).
cnf(d12,plain,
multiply(inverse(multiply(X0,X1)),inverse(multiply(X2,multiply(inverse(multiply(X0,X2)),multiply(inverse(multiply(X0,X2)),multiply(X0,X2)))))) = multiply(inverse(X1),multiply(inverse(X1),X1)),
inference(superposition,[status(thm)],[d4,c0]) ).
cnf(d13,plain,
multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),multiply(inverse(X1),multiply(inverse(X1),X1))) = X2,
inference(superposition,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
multiply(X3,multiply(inverse(multiply(inverse(multiply(X4,X1)),multiply(X4,X3))),multiply(inverse(X1),multiply(inverse(X1),X1)))) = multiply(inverse(X2),X2),
inference(superposition,[status(thm)],[d13,d10]) ).
cnf(d15,plain,
multiply(inverse(X3),X3) = multiply(inverse(X4),X4),
inference(superposition,[status(thm)],[d14,d14]) ).
cnf(d16,plain,
inverse(multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X1),multiply(inverse(X1),X1)))) = X1,
inference(superposition,[status(thm)],[d15,d4]) ).
cnf(d17,plain,
X0 = inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,multiply(inverse(X0),X0)))),
inference(superposition,[status(thm)],[d16,d8]) ).
cnf(d18,plain,
X0 = inverse(multiply(inverse(multiply(X2,X0)),multiply(X2,multiply(inverse(X1),X1)))),
inference(superposition,[status(thm)],[d15,d17]) ).
cnf(d19,plain,
X2 = multiply(inverse(multiply(X3,X1)),multiply(X3,inverse(multiply(inverse(X2),multiply(inverse(X1),multiply(inverse(X1),X1)))))),
inference(superposition,[status(thm)],[d2,d5]) ).
cnf(d20,plain,
multiply(inverse(X0),X1) = multiply(inverse(multiply(X3,X0)),multiply(X3,inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,multiply(inverse(X0),X0)))))),
inference(superposition,[status(thm)],[d5,d19]) ).
cnf(d21,plain,
multiply(inverse(X2),X1) = multiply(inverse(multiply(X3,X2)),multiply(X3,X1)),
inference(demodulation,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X3,multiply(X0,X1))),multiply(X3,X4))),multiply(inverse(multiply(X0,X1)),multiply(inverse(multiply(X2,X1)),multiply(X2,X1))))) = X4,
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d23,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(multiply(X1,X2)),multiply(inverse(multiply(X4,X2)),multiply(X4,X2))))) = X3,
inference(demodulation,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
inverse(multiply(inverse(X2),multiply(inverse(multiply(X3,X1)),multiply(X3,X1)))) = X2,
inference(demodulation,[status(thm)],[d23,d21]) ).
cnf(d25,plain,
inverse(multiply(inverse(X2),multiply(inverse(X1),X1))) = X2,
inference(demodulation,[status(thm)],[d24,d21]) ).
cnf(d26,plain,
inverse(multiply(inverse(X1),X0)) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d21,d25]) ).
cnf(d27,plain,
multiply(inverse(multiply(inverse(X1),X1)),X0) = X0,
inference(demodulation,[status(thm)],[d25,d26]) ).
cnf(d28,plain,
multiply(multiply(inverse(X0),X0),X1) = X1,
inference(demodulation,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
multiply(inverse(multiply(X5,multiply(X0,X2))),multiply(X5,X6)) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X1)),multiply(inverse(multiply(X3,X4)),X2))),multiply(inverse(multiply(X0,X1)),X6)),
inference(superposition,[status(thm)],[d3,d3]) ).
cnf(d30,plain,
multiply(inverse(multiply(X1,X2)),X3) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X5)),X6)),multiply(inverse(multiply(X4,X5)),X2))),multiply(inverse(multiply(X1,X6)),X3)),
inference(demodulation,[status(thm)],[d29,d21]) ).
cnf(d31,plain,
multiply(inverse(multiply(X4,X3)),X5) = multiply(multiply(inverse(multiply(inverse(multiply(X0,X1)),X3)),multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(multiply(X4,X2)),X5)),
inference(demodulation,[status(thm)],[d30,d26]) ).
cnf(d32,plain,
multiply(inverse(multiply(X4,X2)),X5) = multiply(multiply(inverse(X2),X3),multiply(inverse(multiply(X4,X3)),X5)),
inference(demodulation,[status(thm)],[d31,d21]) ).
cnf(d33,plain,
multiply(X4,inverse(multiply(inverse(X5),multiply(inverse(multiply(X0,X1)),multiply(inverse(multiply(inverse(multiply(X2,X3)),X1)),multiply(inverse(multiply(X2,X3)),X1)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,multiply(X0,X1))),X6)),X5)),multiply(inverse(X6),multiply(inverse(X6),X6)))),
inference(superposition,[status(thm)],[d3,d0]) ).
cnf(d34,plain,
multiply(X5,multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(inverse(multiply(inverse(multiply(X3,X4)),X2)),multiply(inverse(multiply(X3,X4)),X2)))),X0)) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X5,multiply(X1,X2))),X6)),X0)),multiply(inverse(X6),multiply(inverse(X6),X6)))),
inference(demodulation,[status(thm)],[d33,d26]) ).
cnf(d35,plain,
multiply(X4,multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X3)),X1)),multiply(inverse(multiply(X2,X3)),X1))),multiply(X0,X1)),X5)) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,multiply(X0,X1))),X6)),X5)),multiply(inverse(X6),multiply(inverse(X6),X6)))),
inference(demodulation,[status(thm)],[d34,d26]) ).
cnf(d36,plain,
multiply(X3,multiply(multiply(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(multiply(X0,X1)),X2)),multiply(X4,X2)),X5)) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,multiply(X4,X2))),X6)),X5)),multiply(inverse(X6),multiply(inverse(X6),X6)))),
inference(demodulation,[status(thm)],[d35,d26]) ).
cnf(d37,plain,
multiply(X4,multiply(multiply(X3,X2),X5)) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,multiply(X3,X2))),X6)),X5)),multiply(inverse(X6),multiply(inverse(X6),X6)))),
inference(demodulation,[status(thm)],[d36,d28]) ).
cnf(d38,plain,
multiply(X0,multiply(multiply(X1,X2),X4)) = multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(multiply(inverse(multiply(X0,multiply(X1,X2))),X3)),X4)),
inference(demodulation,[status(thm)],[d37,d26]) ).
cnf(d39,plain,
multiply(X1,multiply(multiply(X2,X3),X4)) = multiply(multiply(inverse(multiply(inverse(X0),X0)),X0),multiply(inverse(multiply(inverse(multiply(X1,multiply(X2,X3))),X0)),X4)),
inference(demodulation,[status(thm)],[d38,d26]) ).
cnf(d40,plain,
multiply(X1,multiply(multiply(X2,X3),X4)) = multiply(inverse(multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(inverse(X0),X0))),X4),
inference(demodulation,[status(thm)],[d39,d32]) ).
cnf(d41,plain,
multiply(X0,multiply(multiply(X1,X2),X4)) = multiply(multiply(inverse(multiply(inverse(X3),X3)),multiply(X0,multiply(X1,X2))),X4),
inference(demodulation,[status(thm)],[d40,d26]) ).
cnf(d42,plain,
multiply(X1,multiply(multiply(X2,X3),X4)) = multiply(multiply(multiply(inverse(X0),X0),multiply(X1,multiply(X2,X3))),X4),
inference(demodulation,[status(thm)],[d41,d26]) ).
cnf(d43,plain,
multiply(X1,multiply(multiply(X2,X3),X4)) = multiply(multiply(X1,multiply(X2,X3)),X4),
inference(demodulation,[status(thm)],[d42,d28]) ).
cnf(d44,plain,
multiply(X4,inverse(multiply(inverse(X5),multiply(inverse(X6),multiply(inverse(X6),X6))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X6)),multiply(X0,X1))),X5)),multiply(inverse(multiply(X0,X1)),multiply(inverse(multiply(inverse(multiply(X2,X3)),X1)),multiply(inverse(multiply(X2,X3)),X1))))),
inference(superposition,[status(thm)],[d3,d0]) ).
cnf(d45,plain,
multiply(X2,multiply(inverse(multiply(inverse(X1),multiply(inverse(X1),X1))),X0)) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X3,X4))),X0)),multiply(inverse(multiply(X3,X4)),multiply(inverse(multiply(inverse(multiply(X5,X6)),X4)),multiply(inverse(multiply(X5,X6)),X4))))),
inference(demodulation,[status(thm)],[d44,d26]) ).
cnf(d46,plain,
multiply(X1,multiply(multiply(inverse(multiply(inverse(X0),X0)),X0),X2)) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X3,X4))),X2)),multiply(inverse(multiply(X3,X4)),multiply(inverse(multiply(inverse(multiply(X5,X6)),X4)),multiply(inverse(multiply(X5,X6)),X4))))),
inference(demodulation,[status(thm)],[d45,d26]) ).
cnf(d47,plain,
multiply(X1,multiply(multiply(multiply(inverse(X0),X0),X0),X2)) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X3,X4))),X2)),multiply(inverse(multiply(X3,X4)),multiply(inverse(multiply(inverse(multiply(X5,X6)),X4)),multiply(inverse(multiply(X5,X6)),X4))))),
inference(demodulation,[status(thm)],[d46,d26]) ).
cnf(d48,plain,
multiply(X1,multiply(X0,X2)) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X3,X4))),X2)),multiply(inverse(multiply(X3,X4)),multiply(inverse(multiply(inverse(multiply(X5,X6)),X4)),multiply(inverse(multiply(X5,X6)),X4))))),
inference(demodulation,[status(thm)],[d47,d28]) ).
cnf(d49,plain,
multiply(X0,multiply(X1,X4)) = multiply(inverse(multiply(inverse(multiply(X2,X3)),multiply(inverse(multiply(inverse(multiply(X5,X6)),X3)),multiply(inverse(multiply(X5,X6)),X3)))),multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X2,X3))),X4)),
inference(demodulation,[status(thm)],[d48,d26]) ).
cnf(d50,plain,
multiply(X4,multiply(X5,X6)) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X3)),X1)),multiply(inverse(multiply(X2,X3)),X1))),multiply(X0,X1)),multiply(inverse(multiply(inverse(multiply(X4,X5)),multiply(X0,X1))),X6)),
inference(demodulation,[status(thm)],[d49,d26]) ).
cnf(d51,plain,
multiply(X4,multiply(X5,X6)) = multiply(inverse(multiply(inverse(multiply(X4,X5)),multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(multiply(X0,X1)),X2)))),X6),
inference(demodulation,[status(thm)],[d50,d32]) ).
cnf(d52,plain,
multiply(X0,multiply(X1,X5)) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X3)),X4)),multiply(inverse(multiply(X2,X3)),X4))),multiply(X0,X1)),X5),
inference(demodulation,[status(thm)],[d51,d26]) ).
cnf(d53,plain,
multiply(X3,multiply(X4,X5)) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(multiply(X0,X1)),X2))),multiply(multiply(X3,X4),X5)),
inference(demodulation,[status(thm)],[d52,d43]) ).
cnf(d54,plain,
multiply(X3,multiply(X4,X5)) = multiply(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(multiply(X0,X1)),X2)),multiply(multiply(X3,X4),X5)),
inference(demodulation,[status(thm)],[d53,d26]) ).
cnf(d55,plain,
multiply(X3,multiply(X4,X5)) = multiply(multiply(X3,X4),X5),
inference(demodulation,[status(thm)],[d54,d28]) ).
cnf(d56,plain,
X1 = inverse(multiply(inverse(X1),multiply(inverse(X2),X2))),
inference(demodulation,[status(thm)],[d18,d21]) ).
cnf(d57,plain,
multiply(inverse(X0),X1) = inverse(multiply(inverse(X1),X0)),
inference(superposition,[status(thm)],[d21,d56]) ).
cnf(d58,plain,
multiply(inverse(multiply(inverse(X1),inverse(X2))),multiply(inverse(X1),multiply(inverse(X1),X1))) = X2,
inference(demodulation,[status(thm)],[d13,d21]) ).
cnf(d59,plain,
multiply(inverse(inverse(X1)),multiply(inverse(X0),X0)) = X1,
inference(demodulation,[status(thm)],[d58,d21]) ).
cnf(d60,plain,
inverse(multiply(inverse(multiply(inverse(X1),X1)),X0)) = inverse(X0),
inference(superposition,[status(thm)],[d59,d16]) ).
cnf(d61,plain,
multiply(inverse(X1),multiply(inverse(X0),X0)) = inverse(X1),
inference(demodulation,[status(thm)],[d60,d26]) ).
cnf(d62,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d59,d61]) ).
cnf(d63,plain,
multiply(inverse(X1),inverse(X0)) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[d62,d57]) ).
cnf(d64,plain,
multiply(X0,inverse(X1)) = inverse(multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[d62,d63]) ).
cnf(d65,plain,
multiply(X0,multiply(inverse(X1),X1)) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d62,d61]) ).
cnf(d66,plain,
multiply(X0,multiply(inverse(X1),X1)) = X0,
inference(demodulation,[status(thm)],[d65,d62]) ).
cnf(d67,plain,
multiply(inverse(multiply(X4,multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(multiply(X0,X1)),X3))),multiply(inverse(X2),multiply(inverse(X2),X2))))),multiply(X4,inverse(multiply(inverse(X5),multiply(X3,multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(multiply(X0,X1)),X3))),multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(multiply(X0,X1)),X3))),multiply(inverse(X2),multiply(inverse(X2),X2))))))))) = X5,
inference(superposition,[status(thm)],[d1,d2]) ).
cnf(d68,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(multiply(X1,X2)),X4))),multiply(inverse(X3),multiply(inverse(X3),X3)))),inverse(multiply(inverse(X5),multiply(X4,multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(multiply(X1,X2)),X4))),multiply(inverse(X3),multiply(inverse(X3),X3)))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(multiply(X1,X2)),X4))),multiply(inverse(X3),multiply(inverse(X3),X3)))))))) = X5,
inference(demodulation,[status(thm)],[d67,d21]) ).
cnf(d69,plain,
inverse(multiply(multiply(inverse(X4),multiply(X3,multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(multiply(X0,X1)),X3))),multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(multiply(X0,X1)),X3))),multiply(inverse(X2),multiply(inverse(X2),X2)))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(multiply(X0,X1)),X3))),multiply(inverse(X2),multiply(inverse(X2),X2))))) = X4,
inference(demodulation,[status(thm)],[d68,d63]) ).
cnf(d70,plain,
inverse(multiply(multiply(inverse(X4),X0),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(multiply(X1,X2)),X0))),multiply(inverse(X3),multiply(inverse(X3),X3))))) = X4,
inference(demodulation,[status(thm)],[d69,d66]) ).
cnf(d71,plain,
inverse(multiply(multiply(inverse(X4),X3),multiply(multiply(inverse(multiply(inverse(multiply(X0,X1)),X3)),multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(X2),multiply(inverse(X2),X2))))) = X4,
inference(demodulation,[status(thm)],[d70,d26]) ).
cnf(d72,plain,
inverse(multiply(multiply(inverse(X4),X2),multiply(multiply(inverse(X2),X3),multiply(inverse(X3),multiply(inverse(X3),X3))))) = X4,
inference(demodulation,[status(thm)],[d71,d21]) ).
cnf(d73,plain,
inverse(multiply(multiply(inverse(X1),X2),multiply(multiply(inverse(X2),X0),inverse(X0)))) = X1,
inference(demodulation,[status(thm)],[d72,d66]) ).
cnf(d74,plain,
X0 = multiply(inverse(multiply(inverse(X1),X1)),X0),
inference(demodulation,[status(thm)],[d56,d26]) ).
cnf(d75,plain,
X1 = multiply(multiply(inverse(X0),X0),X1),
inference(demodulation,[status(thm)],[d74,d26]) ).
cnf(d76,plain,
inverse(multiply(multiply(inverse(X0),X1),inverse(X1))) = X0,
inference(superposition,[status(thm)],[d75,d73]) ).
cnf(d77,plain,
multiply(X1,inverse(multiply(inverse(X0),X1))) = X0,
inference(demodulation,[status(thm)],[d76,d64]) ).
cnf(d78,plain,
multiply(X1,multiply(inverse(X1),X0)) = X0,
inference(demodulation,[status(thm)],[d77,d26]) ).
cnf(d79,plain,
multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[d62,d78]) ).
cnf(d80,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2 ),
inference(resolution,[status(thm)],[d15,c1]) ).
cnf(d81,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(b2),multiply(b2,a2)) != a2 ),
inference(demodulation,[status(thm)],[d80,d55]) ).
cnf(d82,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(demodulation,[status(thm)],[d81,d79]) ).
cnf(d83,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(demodulation,[status(thm)],[d82,d55]) ).
cnf(d84,plain,
X2 = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X3)),multiply(inverse(multiply(X0,X1)),X2))),multiply(inverse(X3),multiply(inverse(X3),X3)))),
inference(superposition,[status(thm)],[c0,d0]) ).
cnf(d85,plain,
X3 = X3,
inference(demodulation,[status(thm)],[d84,d4]) ).
cnf(d86,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(resolution,[status(thm)],[d85,d83]) ).
cnf(d87,plain,
$false,
inference(equality_resolution,[status(thm)],[d86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP050-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n016.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 14:24:44 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 56.78/20.98 % SZS status Unsatisfiable for theBenchmark.p
% 56.78/20.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------