%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP432-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 07:23:45 AM UTC 2026
% Result : Unsatisfiable 70.14s 11.12s
% Output : CNFRefutation 70.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 2
% Syntax : Number of clauses : 91 ( 91 unt; 0 nHn; 4 RR)
% Number of literals : 91 ( 90 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 300 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X0,inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),X0)))) = X3 ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ).
cnf(c0,plain,
multiply(X0,inverse(multiply(X1,multiply(multiply(multiply(X2,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)),
inference(clausification,[status(esa)],[prove_these_axioms_3]) ).
cnf(d0,plain,
multiply(X4,inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),multiply(X0,inverse(X0))),multiply(X3,X4)))) = X1,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d1,plain,
multiply(X4,inverse(multiply(multiply(multiply(multiply(X5,inverse(X5)),inverse(X3)),multiply(X6,inverse(X6))),multiply(X0,X4)))) = inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),X0))),
inference(superposition,[status(thm)],[c0,d0]) ).
cnf(d2,plain,
inverse(multiply(X5,multiply(multiply(multiply(X6,inverse(X6)),inverse(multiply(multiply(X2,X3),X5))),X2))) = X3,
inference(superposition,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
multiply(X5,inverse(multiply(multiply(X2,multiply(X0,inverse(X0))),multiply(X3,X5)))) = multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X3))),multiply(X4,inverse(X4))),
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d4,plain,
multiply(multiply(X3,inverse(X3)),inverse(multiply(X2,multiply(X4,inverse(multiply(multiply(X1,multiply(X5,inverse(X5))),multiply(X2,X4))))))) = X1,
inference(superposition,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
multiply(multiply(X5,inverse(X5)),inverse(multiply(X2,X3))) = multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X3))),
inference(superposition,[status(thm)],[d0,d4]) ).
cnf(d6,plain,
multiply(inverse(multiply(X1,X2)),inverse(multiply(inverse(X0),multiply(multiply(X3,inverse(X3)),inverse(multiply(X1,X2)))))) = X0,
inference(superposition,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
multiply(X4,inverse(multiply(inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),X0))),multiply(multiply(multiply(X5,inverse(X5)),inverse(X3)),X4)))) = X0,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d8,plain,
X5 = multiply(X2,multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(multiply(X4,inverse(X4)),X2))),X5)),
inference(superposition,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
multiply(X3,inverse(X3)) = multiply(X2,inverse(X2)),
inference(superposition,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
multiply(X1,inverse(X1)) = multiply(multiply(X2,inverse(X2)),inverse(multiply(X0,inverse(X0)))),
inference(superposition,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(X0))),X1)),multiply(X2,inverse(X2)))) = X1,
inference(superposition,[status(thm)],[d10,d2]) ).
cnf(d12,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(multiply(X3,inverse(X3)),X1))) = X2,
inference(superposition,[status(thm)],[d10,d2]) ).
cnf(d13,plain,
inverse(multiply(inverse(X0),multiply(X2,inverse(X2)))) = multiply(multiply(X1,inverse(X1)),X0),
inference(superposition,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
X1 = multiply(multiply(X3,inverse(X3)),multiply(inverse(multiply(X0,inverse(X0))),X1)),
inference(superposition,[status(thm)],[d11,d13]) ).
cnf(d15,plain,
multiply(X2,inverse(multiply(inverse(X0),multiply(multiply(X1,inverse(X1)),X2)))) = X0,
inference(superposition,[status(thm)],[d9,c0]) ).
cnf(d16,plain,
multiply(multiply(X3,inverse(X3)),multiply(inverse(multiply(X0,inverse(X0))),X1)) = X1,
inference(superposition,[status(thm)],[d13,d11]) ).
cnf(d17,plain,
multiply(multiply(inverse(multiply(X1,inverse(X1))),X2),inverse(multiply(inverse(X3),X2))) = X3,
inference(superposition,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
multiply(X1,inverse(multiply(inverse(X3),inverse(multiply(inverse(X1),multiply(X2,inverse(X2))))))) = X3,
inference(superposition,[status(thm)],[d13,d15]) ).
cnf(d19,plain,
multiply(X2,inverse(X1)) = multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X2)))),
inference(superposition,[status(thm)],[c0,d18]) ).
cnf(d20,plain,
multiply(inverse(multiply(X0,inverse(X0))),inverse(inverse(X1))) = X1,
inference(superposition,[status(thm)],[d19,d17]) ).
cnf(d21,plain,
inverse(inverse(X1)) = multiply(multiply(X2,inverse(X2)),X1),
inference(superposition,[status(thm)],[d20,d14]) ).
cnf(d22,plain,
multiply(multiply(X2,inverse(X2)),X0) = multiply(multiply(X3,inverse(X3)),X0),
inference(superposition,[status(thm)],[d13,d13]) ).
cnf(d23,plain,
multiply(multiply(X3,inverse(X3)),X1) = inverse(multiply(inverse(X1),multiply(X2,inverse(X2)))),
inference(superposition,[status(thm)],[d13,d22]) ).
cnf(d24,plain,
inverse(inverse(X1)) = inverse(multiply(inverse(X1),multiply(X2,inverse(X2)))),
inference(demodulation,[status(thm)],[d23,d21]) ).
cnf(d25,plain,
multiply(X5,inverse(multiply(multiply(X3,multiply(X6,inverse(X6))),multiply(multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X3))),multiply(X4,inverse(X4))),X5)))) = multiply(X2,multiply(X0,inverse(X0))),
inference(superposition,[status(thm)],[d0,d0]) ).
cnf(d26,plain,
multiply(X4,multiply(X6,inverse(X6))) = multiply(X4,multiply(X7,inverse(X7))),
inference(superposition,[status(thm)],[d25,d25]) ).
cnf(d27,plain,
multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X3))),X2))),multiply(X6,inverse(X6))) = X3,
inference(superposition,[status(thm)],[d3,d0]) ).
cnf(d28,plain,
multiply(multiply(multiply(X2,inverse(X2)),inverse(inverse(X1))),multiply(X3,inverse(X3))) = X1,
inference(superposition,[status(thm)],[d27,d27]) ).
cnf(d29,plain,
X1 = multiply(multiply(multiply(X0,inverse(X0)),inverse(inverse(X1))),multiply(X3,inverse(X3))),
inference(superposition,[status(thm)],[d28,d26]) ).
cnf(d30,plain,
X1 = multiply(inverse(inverse(inverse(inverse(X1)))),multiply(X2,inverse(X2))),
inference(demodulation,[status(thm)],[d29,d21]) ).
cnf(d31,plain,
inverse(inverse(inverse(inverse(inverse(X0))))) = inverse(X0),
inference(superposition,[status(thm)],[d30,d24]) ).
cnf(d32,plain,
multiply(X2,multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(multiply(X4,inverse(X4)),X2))),X5)) = X5,
inference(superposition,[status(thm)],[d6,d7]) ).
cnf(d33,plain,
multiply(X2,multiply(inverse(inverse(inverse(multiply(multiply(X1,inverse(X1)),X2)))),X3)) = X3,
inference(demodulation,[status(thm)],[d32,d21]) ).
cnf(d34,plain,
multiply(X1,multiply(inverse(inverse(inverse(inverse(inverse(X1))))),X2)) = X2,
inference(demodulation,[status(thm)],[d33,d21]) ).
cnf(d35,plain,
multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[d34,d31]) ).
cnf(d36,plain,
inverse(inverse(X0)) = inverse(inverse(inverse(inverse(X0)))),
inference(superposition,[status(thm)],[d35,d24]) ).
cnf(d37,plain,
inverse(inverse(inverse(X0))) = inverse(X0),
inference(demodulation,[status(thm)],[d31,d36]) ).
cnf(d38,plain,
X0 = inverse(inverse(inverse(inverse(inverse(inverse(X0)))))),
inference(superposition,[status(thm)],[d35,d30]) ).
cnf(d39,plain,
X0 = inverse(inverse(inverse(inverse(X0)))),
inference(demodulation,[status(thm)],[d38,d37]) ).
cnf(d40,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d39,d37]) ).
cnf(d41,plain,
X2 = multiply(inverse(multiply(X0,inverse(X0))),multiply(multiply(X1,inverse(X1)),X2)),
inference(superposition,[status(thm)],[d9,d8]) ).
cnf(d42,plain,
inverse(multiply(X0,inverse(X0))) = multiply(inverse(multiply(X2,inverse(X2))),multiply(X1,inverse(X1))),
inference(superposition,[status(thm)],[d9,d41]) ).
cnf(d43,plain,
inverse(multiply(X3,inverse(X3))) = inverse(multiply(X2,inverse(X2))),
inference(superposition,[status(thm)],[d42,d42]) ).
cnf(d44,plain,
inverse(multiply(inverse(multiply(X1,inverse(X1))),multiply(multiply(X2,inverse(X2)),X0))) = inverse(X0),
inference(superposition,[status(thm)],[d43,d12]) ).
cnf(d45,plain,
inverse(X2) = inverse(X2),
inference(demodulation,[status(thm)],[d44,d41]) ).
cnf(d46,plain,
inverse(multiply(inverse(multiply(multiply(inverse(multiply(X1,inverse(X1))),X2),X3)),X2)) = X3,
inference(superposition,[status(thm)],[d16,d12]) ).
cnf(d47,plain,
X2 = inverse(multiply(inverse(multiply(multiply(inverse(multiply(X0,inverse(X0))),X1),X2)),X1)),
inference(superposition,[status(thm)],[d46,d45]) ).
cnf(d48,plain,
X2 = inverse(multiply(inverse(multiply(X1,X2)),inverse(inverse(X1)))),
inference(superposition,[status(thm)],[d20,d47]) ).
cnf(d49,plain,
X1 = inverse(multiply(inverse(multiply(X0,X1)),X0)),
inference(demodulation,[status(thm)],[d48,d40]) ).
cnf(d50,plain,
multiply(multiply(X2,inverse(X2)),X1) = inverse(inverse(X1)),
inference(superposition,[status(thm)],[d20,d16]) ).
cnf(d51,plain,
multiply(multiply(X1,inverse(X1)),X0) = X0,
inference(demodulation,[status(thm)],[d50,d40]) ).
cnf(d52,plain,
multiply(multiply(X5,inverse(X5)),inverse(multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(X1,multiply(X2,inverse(X2)))))),X4))) = X1,
inference(superposition,[status(thm)],[c0,d4]) ).
cnf(d53,plain,
inverse(multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,multiply(X4,inverse(X4)))))),X2)) = X3,
inference(demodulation,[status(thm)],[d52,d51]) ).
cnf(d54,plain,
inverse(multiply(inverse(multiply(X1,multiply(X2,multiply(X3,inverse(X3))))),X1)) = X2,
inference(demodulation,[status(thm)],[d53,d51]) ).
cnf(d55,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(demodulation,[status(thm)],[d54,d49]) ).
cnf(d56,plain,
X0 = multiply(X0,multiply(X2,inverse(X2))),
inference(demodulation,[status(thm)],[d26,d55]) ).
cnf(d57,plain,
multiply(X4,inverse(multiply(multiply(X1,multiply(X5,inverse(X5))),multiply(X2,X4)))) = multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X1,X2))),multiply(X6,inverse(X6))),
inference(superposition,[status(thm)],[d5,d3]) ).
cnf(d58,plain,
multiply(X2,inverse(multiply(X0,multiply(X3,X2)))) = multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X0,X3))),multiply(X5,inverse(X5))),
inference(demodulation,[status(thm)],[d57,d56]) ).
cnf(d59,plain,
multiply(X4,inverse(multiply(X1,multiply(X2,X4)))) = multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,X2))),
inference(demodulation,[status(thm)],[d58,d56]) ).
cnf(d60,plain,
multiply(X3,inverse(multiply(X1,multiply(X2,X3)))) = inverse(multiply(X1,X2)),
inference(demodulation,[status(thm)],[d59,d51]) ).
cnf(d61,plain,
inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[d40,d45]) ).
cnf(d62,plain,
multiply(X1,multiply(inverse(X0),X0)) = X1,
inference(superposition,[status(thm)],[d61,d55]) ).
cnf(d63,plain,
multiply(X1,inverse(X0)) = inverse(multiply(X0,inverse(X1))),
inference(superposition,[status(thm)],[d62,d60]) ).
cnf(d64,plain,
multiply(inverse(X0),X1) = inverse(multiply(inverse(X1),X0)),
inference(superposition,[status(thm)],[d35,d49]) ).
cnf(d65,plain,
multiply(X6,inverse(multiply(multiply(multiply(multiply(X5,inverse(X5)),inverse(X3)),multiply(X0,inverse(X0))),multiply(X4,X6)))) = inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),X4))),
inference(superposition,[status(thm)],[d7,c0]) ).
cnf(d66,plain,
inverse(multiply(multiply(multiply(multiply(X1,inverse(X1)),inverse(X2)),multiply(X3,inverse(X3))),X4)) = inverse(multiply(X5,multiply(multiply(multiply(X6,inverse(X6)),inverse(multiply(X2,X5))),X4))),
inference(demodulation,[status(thm)],[d65,d60]) ).
cnf(d67,plain,
inverse(multiply(multiply(multiply(X0,inverse(X0)),inverse(X1)),X3)) = inverse(multiply(X4,multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(X1,X4))),X3))),
inference(demodulation,[status(thm)],[d66,d56]) ).
cnf(d68,plain,
inverse(multiply(inverse(X1),X2)) = inverse(multiply(X3,multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X1,X3))),X2))),
inference(demodulation,[status(thm)],[d67,d51]) ).
cnf(d69,plain,
multiply(inverse(X1),X0) = inverse(multiply(X2,multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X0,X2))),X1))),
inference(demodulation,[status(thm)],[d68,d64]) ).
cnf(d70,plain,
multiply(inverse(X3),X1) = inverse(multiply(X2,multiply(inverse(multiply(X1,X2)),X3))),
inference(demodulation,[status(thm)],[d69,d51]) ).
cnf(d71,plain,
multiply(X6,inverse(multiply(inverse(multiply(X2,X5)),multiply(multiply(multiply(X7,inverse(X7)),inverse(X1)),X6)))) = inverse(multiply(X3,multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X5,X3))),multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,X2)))))),
inference(superposition,[status(thm)],[c0,d7]) ).
cnf(d72,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(multiply(X3,inverse(X3)),inverse(X4)))) = inverse(multiply(X5,multiply(multiply(multiply(X6,inverse(X6)),inverse(multiply(X2,X5))),multiply(multiply(X7,inverse(X7)),inverse(multiply(X4,X1)))))),
inference(demodulation,[status(thm)],[d71,d60]) ).
cnf(d73,plain,
multiply(inverse(multiply(multiply(X2,inverse(X2)),inverse(X3))),multiply(X0,X1)) = inverse(multiply(X4,multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(X1,X4))),multiply(multiply(X6,inverse(X6)),inverse(multiply(X3,X0)))))),
inference(demodulation,[status(thm)],[d72,d64]) ).
cnf(d74,plain,
multiply(multiply(X1,inverse(multiply(X0,inverse(X0)))),multiply(X2,X3)) = inverse(multiply(X4,multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(X3,X4))),multiply(multiply(X6,inverse(X6)),inverse(multiply(X1,X2)))))),
inference(demodulation,[status(thm)],[d73,d63]) ).
cnf(d75,plain,
multiply(multiply(X1,multiply(X0,inverse(X0))),multiply(X2,X3)) = inverse(multiply(X4,multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(X3,X4))),multiply(multiply(X6,inverse(X6)),inverse(multiply(X1,X2)))))),
inference(demodulation,[status(thm)],[d74,d63]) ).
cnf(d76,plain,
multiply(X0,multiply(X2,X3)) = inverse(multiply(X4,multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(X3,X4))),multiply(multiply(X6,inverse(X6)),inverse(multiply(X0,X2)))))),
inference(demodulation,[status(thm)],[d75,d56]) ).
cnf(d77,plain,
multiply(X3,multiply(X4,X1)) = inverse(multiply(X2,multiply(inverse(multiply(X1,X2)),multiply(multiply(X5,inverse(X5)),inverse(multiply(X3,X4)))))),
inference(demodulation,[status(thm)],[d76,d51]) ).
cnf(d78,plain,
multiply(X3,multiply(X4,X1)) = multiply(inverse(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X4)))),X1),
inference(demodulation,[status(thm)],[d77,d70]) ).
cnf(d79,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(multiply(X1,X2),inverse(multiply(X0,inverse(X0)))),X3),
inference(demodulation,[status(thm)],[d78,d63]) ).
cnf(d80,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(multiply(X1,X2),multiply(X0,inverse(X0))),X3),
inference(demodulation,[status(thm)],[d79,d63]) ).
cnf(d81,plain,
multiply(X0,multiply(X1,X3)) = multiply(multiply(X0,X1),X3),
inference(demodulation,[status(thm)],[d80,d56]) ).
cnf(d82,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm)],[c1,d81]) ).
cnf(d83,plain,
multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[d40,d35]) ).
cnf(d84,plain,
multiply(inverse(inverse(X0)),multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[d37,d35]) ).
cnf(d85,plain,
X1 = X1,
inference(demodulation,[status(thm)],[d84,d83]) ).
cnf(d86,plain,
$false,
inference(resolution,[status(thm)],[d85,d82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP432-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:55:37 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 70.14/11.12 % SZS status Unsatisfiable for theBenchmark.p
% 70.14/11.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------