%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP060-1 : 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 : n011.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 07:22:14 AM UTC 2026
% Result : Unsatisfiable 149.95s 38.88s
% Output : CNFRefutation 149.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 2
% Syntax : Number of clauses : 90 ( 86 unt; 0 nHn; 6 RR)
% Number of literals : 96 ( 95 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 11 ( 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 : 255 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X0,inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(X3,X1))),X0))))) = X3 ).
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(X1,multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(X3,X1))),X0))))) = X3,
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(X4,inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(X3,X1))),inverse(X0))),multiply(X0,multiply(X3,X4))))) = X1,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d1,plain,
multiply(X5,inverse(multiply(multiply(X4,multiply(X2,inverse(X0))),multiply(X0,multiply(X3,X5))))) = multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),inverse(X4))),
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
X3 = multiply(X5,multiply(multiply(inverse(X5),inverse(multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X2))),inverse(X1))),
inference(superposition,[status(thm)],[d0,d1]) ).
cnf(d3,plain,
X3 = multiply(X4,inverse(multiply(multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),inverse(X5))),multiply(X5,multiply(X2,X4))))),
inference(superposition,[status(thm)],[d1,d2]) ).
cnf(d4,plain,
multiply(X5,inverse(multiply(multiply(X6,multiply(multiply(inverse(X6),inverse(X3)),inverse(X7))),multiply(X7,multiply(X0,X5))))) = inverse(multiply(multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),inverse(X4))),multiply(X4,multiply(X2,X0)))),
inference(superposition,[status(thm)],[d0,d0]) ).
cnf(d5,plain,
X2 = multiply(X4,multiply(X5,inverse(multiply(multiply(X6,multiply(multiply(inverse(X6),inverse(X2)),inverse(X7))),multiply(X7,multiply(X4,X5)))))),
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
X2 = multiply(X4,multiply(X5,multiply(multiply(inverse(X5),inverse(multiply(multiply(inverse(X1),inverse(X2)),X4))),inverse(X1)))),
inference(superposition,[status(thm)],[d1,d5]) ).
cnf(d7,plain,
multiply(X5,multiply(multiply(inverse(X5),inverse(multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X2))),inverse(X1))) = X3,
inference(superposition,[status(thm)],[d1,d0]) ).
cnf(d8,plain,
multiply(inverse(X3),inverse(multiply(X2,multiply(X4,inverse(multiply(multiply(X3,multiply(X1,inverse(X5))),multiply(X5,multiply(X2,X4)))))))) = X1,
inference(superposition,[status(thm)],[d1,c0]) ).
cnf(d9,plain,
multiply(inverse(X1),inverse(multiply(multiply(inverse(X3),inverse(multiply(X4,multiply(X1,multiply(X2,inverse(X3)))))),X4))) = X2,
inference(superposition,[status(thm)],[c0,d8]) ).
cnf(d10,plain,
multiply(X4,inverse(multiply(X2,multiply(X0,multiply(X3,X4))))) = multiply(inverse(X1),inverse(multiply(X2,multiply(X0,multiply(X3,inverse(X1)))))),
inference(superposition,[status(thm)],[d9,c0]) ).
cnf(d11,plain,
multiply(inverse(X2),inverse(multiply(multiply(X4,inverse(multiply(X1,multiply(X2,multiply(X3,X4))))),X1))) = X3,
inference(superposition,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
multiply(X4,multiply(multiply(inverse(X4),inverse(multiply(X3,multiply(X1,inverse(multiply(X2,multiply(X0,multiply(X3,X1)))))))),inverse(X0))) = X2,
inference(superposition,[status(thm)],[d11,d7]) ).
cnf(d13,plain,
X2 = multiply(multiply(X3,inverse(multiply(X4,multiply(X1,multiply(multiply(inverse(X1),inverse(X2)),X3))))),X4),
inference(superposition,[status(thm)],[d12,d6]) ).
cnf(d14,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(X3)),inverse(X0))),multiply(X0,X3)))) = X1,
inference(superposition,[status(thm)],[d13,c0]) ).
cnf(d15,plain,
multiply(X4,inverse(multiply(X3,multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X2))))) = X4,
inference(superposition,[status(thm)],[d7,d14]) ).
cnf(d16,plain,
multiply(X4,inverse(multiply(multiply(X2,inverse(multiply(X3,multiply(X1,multiply(inverse(X1),X2))))),X3))) = X4,
inference(superposition,[status(thm)],[d12,d15]) ).
cnf(d17,plain,
multiply(X0,multiply(inverse(X0),inverse(X1))) = multiply(X3,multiply(inverse(X3),inverse(X1))),
inference(superposition,[status(thm)],[d16,d7]) ).
cnf(d18,plain,
multiply(X0,X3) = multiply(X4,multiply(inverse(X4),inverse(multiply(multiply(X1,inverse(multiply(X2,multiply(X0,multiply(X3,X1))))),X2)))),
inference(superposition,[status(thm)],[d11,d17]) ).
cnf(d19,plain,
multiply(X3,inverse(X3)) = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[d16,d18]) ).
cnf(d20,plain,
multiply(X3,inverse(X3)) = multiply(multiply(X0,inverse(multiply(X1,multiply(X2,multiply(inverse(X2),X0))))),X1),
inference(superposition,[status(thm)],[d19,d16]) ).
cnf(d21,plain,
multiply(X4,inverse(multiply(X3,inverse(X3)))) = X4,
inference(superposition,[status(thm)],[d20,d16]) ).
cnf(d22,plain,
multiply(X2,inverse(multiply(inverse(X1),multiply(X0,multiply(inverse(X0),X2))))) = X1,
inference(superposition,[status(thm)],[d21,c0]) ).
cnf(d23,plain,
multiply(X2,inverse(multiply(inverse(X1),multiply(X0,multiply(inverse(X0),X1))))) = X2,
inference(superposition,[status(thm)],[d21,d15]) ).
cnf(d24,plain,
X2 = multiply(X4,inverse(multiply(X3,multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X4))))),
inference(superposition,[status(thm)],[d2,d3]) ).
cnf(d25,plain,
X1 = multiply(X1,inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(X3)),inverse(X0))),multiply(X0,X3)))),
inference(superposition,[status(thm)],[d13,d24]) ).
cnf(d26,plain,
X4 = multiply(X4,inverse(multiply(X3,multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X2))))),
inference(superposition,[status(thm)],[d7,d25]) ).
cnf(d27,plain,
X4 = multiply(X4,inverse(multiply(multiply(X2,inverse(multiply(X3,multiply(X1,multiply(inverse(X1),X2))))),X3))),
inference(superposition,[status(thm)],[d12,d26]) ).
cnf(d28,plain,
X4 = multiply(X4,inverse(multiply(X3,inverse(X3)))),
inference(superposition,[status(thm)],[d20,d27]) ).
cnf(d29,plain,
multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X2) = multiply(multiply(inverse(X1),inverse(multiply(X4,X3))),X4),
inference(superposition,[status(thm)],[d7,d13]) ).
cnf(d30,plain,
multiply(multiply(inverse(X0),inverse(multiply(X2,inverse(X1)))),X2) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d21,d29]) ).
cnf(d31,plain,
multiply(multiply(inverse(X2),inverse(X0)),X0) = multiply(inverse(X2),multiply(X1,inverse(X1))),
inference(superposition,[status(thm)],[d21,d30]) ).
cnf(d32,plain,
multiply(multiply(inverse(X0),inverse(X3)),X3) = multiply(multiply(inverse(X0),inverse(X2)),X2),
inference(superposition,[status(thm)],[d31,d31]) ).
cnf(d33,plain,
multiply(multiply(X1,inverse(X1)),inverse(X0)) = multiply(multiply(inverse(X0),inverse(X2)),X2),
inference(superposition,[status(thm)],[d19,d32]) ).
cnf(d34,plain,
X2 = multiply(X2,inverse(multiply(multiply(inverse(multiply(X0,inverse(X0))),inverse(X1)),X1))),
inference(superposition,[status(thm)],[d33,d28]) ).
cnf(d35,plain,
X2 = multiply(X2,multiply(X0,multiply(inverse(X0),inverse(multiply(X1,inverse(X1)))))),
inference(superposition,[status(thm)],[d34,d6]) ).
cnf(d36,plain,
X2 = multiply(X2,multiply(X0,inverse(X0))),
inference(demodulation,[status(thm)],[d35,d21]) ).
cnf(d37,plain,
multiply(X1,inverse(multiply(inverse(inverse(inverse(X0))),X0))) = X1,
inference(superposition,[status(thm)],[d36,d23]) ).
cnf(d38,plain,
X0 = inverse(inverse(multiply(X1,multiply(inverse(X1),X0)))),
inference(superposition,[status(thm)],[d37,d22]) ).
cnf(d39,plain,
multiply(X2,multiply(inverse(X2),inverse(inverse(X0)))) = multiply(X0,multiply(X1,inverse(X1))),
inference(superposition,[status(thm)],[d19,d17]) ).
cnf(d40,plain,
multiply(X2,multiply(inverse(X2),inverse(inverse(X0)))) = X0,
inference(demodulation,[status(thm)],[d39,d36]) ).
cnf(d41,plain,
multiply(X0,multiply(X1,inverse(X1))) = X0,
inference(superposition,[status(thm)],[d19,d40]) ).
cnf(d42,plain,
multiply(X1,multiply(inverse(inverse(inverse(X0))),X0)) = X1,
inference(superposition,[status(thm)],[d37,d41]) ).
cnf(d43,plain,
X0 = inverse(inverse(inverse(inverse(X0)))),
inference(superposition,[status(thm)],[d42,d38]) ).
cnf(d44,plain,
X3 = inverse(multiply(multiply(X5,multiply(multiply(inverse(X5),inverse(multiply(X6,multiply(X2,X3)))),inverse(X7))),multiply(X7,multiply(X6,X2)))),
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d45,plain,
X3 = inverse(multiply(X4,multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(multiply(X2,X3),X4))),X2)))),
inference(superposition,[status(thm)],[d7,d44]) ).
cnf(d46,plain,
X2 = inverse(multiply(inverse(multiply(X1,X2)),multiply(X0,multiply(inverse(X0),X1)))),
inference(superposition,[status(thm)],[d21,d45]) ).
cnf(d47,plain,
X1 = inverse(multiply(inverse(multiply(inverse(inverse(X0)),X1)),X0)),
inference(superposition,[status(thm)],[d36,d46]) ).
cnf(d48,plain,
multiply(multiply(X1,inverse(X1)),inverse(X0)) = multiply(inverse(X0),multiply(X2,inverse(X2))),
inference(superposition,[status(thm)],[d19,d31]) ).
cnf(d49,plain,
multiply(multiply(X2,inverse(X2)),inverse(X0)) = inverse(X0),
inference(demodulation,[status(thm)],[d48,d36]) ).
cnf(d50,plain,
multiply(inverse(multiply(X0,inverse(X0))),inverse(X1)) = inverse(X1),
inference(superposition,[status(thm)],[d49,d49]) ).
cnf(d51,plain,
inverse(inverse(inverse(inverse(X0)))) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d50,d47]) ).
cnf(d52,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d51,d43]) ).
cnf(d53,plain,
X1 = multiply(X2,inverse(multiply(inverse(X1),multiply(X0,multiply(inverse(X0),X2))))),
inference(superposition,[status(thm)],[d21,d24]) ).
cnf(d54,plain,
X1 = multiply(inverse(inverse(X0)),inverse(multiply(inverse(X1),X0))),
inference(superposition,[status(thm)],[d36,d53]) ).
cnf(d55,plain,
X1 = multiply(X0,inverse(multiply(inverse(X1),X0))),
inference(demodulation,[status(thm)],[d54,d52]) ).
cnf(d56,plain,
X2 = inverse(multiply(multiply(X3,inverse(multiply(X4,multiply(X1,multiply(multiply(inverse(X1),X2),X3))))),X4)),
inference(superposition,[status(thm)],[d12,d45]) ).
cnf(d57,plain,
multiply(X2,multiply(inverse(X2),X3)) = multiply(X4,multiply(inverse(X4),X3)),
inference(superposition,[status(thm)],[d56,d18]) ).
cnf(d58,plain,
inverse(inverse(X0)) = multiply(X1,multiply(inverse(X1),X0)),
inference(superposition,[status(thm)],[d42,d57]) ).
cnf(d59,plain,
X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(demodulation,[status(thm)],[d58,d52]) ).
cnf(d60,plain,
inverse(inverse(multiply(X1,multiply(inverse(X1),X0)))) = X0,
inference(superposition,[status(thm)],[d37,d53]) ).
cnf(d61,plain,
inverse(inverse(inverse(inverse(X0)))) = X0,
inference(superposition,[status(thm)],[d42,d60]) ).
cnf(d62,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d61,d52]) ).
cnf(d63,plain,
X1 = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[d62,d59]) ).
cnf(d64,plain,
X0 = multiply(multiply(X0,X1),inverse(X1)),
inference(superposition,[status(thm)],[d63,d55]) ).
cnf(d65,plain,
X1 = multiply(multiply(X1,inverse(X0)),X0),
inference(superposition,[status(thm)],[d62,d64]) ).
cnf(d66,plain,
multiply(inverse(inverse(X0)),inverse(multiply(inverse(X1),X0))) = X1,
inference(superposition,[status(thm)],[d36,d22]) ).
cnf(d67,plain,
multiply(X0,inverse(multiply(inverse(X1),X0))) = X1,
inference(demodulation,[status(thm)],[d66,d52]) ).
cnf(d68,plain,
multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(superposition,[status(thm)],[d63,d67]) ).
cnf(d69,plain,
multiply(multiply(X1,inverse(X0)),X0) = X1,
inference(superposition,[status(thm)],[d62,d68]) ).
cnf(d70,plain,
X2 = multiply(X2,inverse(multiply(inverse(X1),multiply(X0,multiply(inverse(X0),X1))))),
inference(superposition,[status(thm)],[d21,d26]) ).
cnf(d71,plain,
multiply(X2,inverse(X2)) = multiply(inverse(X0),multiply(X1,multiply(inverse(X1),X0))),
inference(superposition,[status(thm)],[d70,d19]) ).
cnf(d72,plain,
multiply(X1,inverse(X1)) = multiply(inverse(inverse(inverse(X0))),X0),
inference(superposition,[status(thm)],[d36,d71]) ).
cnf(d73,plain,
multiply(X1,inverse(X1)) = multiply(inverse(X0),X0),
inference(demodulation,[status(thm)],[d72,d52]) ).
cnf(d74,plain,
multiply(multiply(inverse(X1),X1),X0) = X0,
inference(superposition,[status(thm)],[d73,d69]) ).
cnf(d75,plain,
multiply(X2,inverse(multiply(X1,multiply(inverse(multiply(X0,X1)),X2)))) = X0,
inference(superposition,[status(thm)],[d74,c0]) ).
cnf(d76,plain,
X0 = multiply(X2,multiply(X1,multiply(inverse(multiply(X2,X1)),X0))),
inference(superposition,[status(thm)],[d75,d65]) ).
cnf(d77,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[d63,d76]) ).
cnf(d78,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(resolution,[status(thm)],[d74,c1]) ).
cnf(d79,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)) ),
inference(demodulation,[status(thm)],[d78,d77]) ).
cnf(d80,plain,
multiply(inverse(X1),inverse(multiply(X4,multiply(X5,multiply(multiply(inverse(X5),inverse(multiply(X2,X4))),inverse(X1)))))) = X2,
inference(superposition,[status(thm)],[d1,d8]) ).
cnf(d81,plain,
X3 = X3,
inference(demodulation,[status(thm)],[d80,c0]) ).
cnf(d82,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(resolution,[status(thm)],[d81,d79]) ).
cnf(d83,plain,
multiply(X1,multiply(inverse(X0),X0)) = X1,
inference(demodulation,[status(thm)],[d42,d52]) ).
cnf(d84,plain,
multiply(inverse(X1),X1) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[d83,d63]) ).
cnf(d85,plain,
$false,
inference(resolution,[status(thm)],[d84,d82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP060-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 14:20:28 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 149.95/38.88 % SZS status Unsatisfiable for theBenchmark.p
% 149.95/38.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------