%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP436-1 : 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 26.38s 15.56s
% Output : CNFRefutation 26.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 2
% Syntax : Number of clauses : 73 ( 73 unt; 0 nHn; 3 RR)
% Number of literals : 73 ( 72 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 229 ( 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_1,negated_conjecture,
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(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(clausification,[status(esa)],[prove_these_axioms_1]) ).
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,multiply(multiply(inverse(X5),inverse(multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X2))),inverse(X1))) = X3,
inference(superposition,[status(thm)],[d1,d0]) ).
cnf(d5,plain,
X2 = multiply(X4,inverse(multiply(X3,multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X4))))),
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d6,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(d7,plain,
multiply(X4,multiply(X5,inverse(multiply(multiply(X6,multiply(multiply(inverse(X6),inverse(X2)),inverse(X7))),multiply(X7,multiply(X4,X5)))))) = X2,
inference(superposition,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
multiply(X4,multiply(X5,multiply(multiply(inverse(X5),inverse(multiply(multiply(inverse(X1),inverse(X2)),X4))),inverse(X1)))) = X2,
inference(superposition,[status(thm)],[d1,d7]) ).
cnf(d9,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(d10,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,d9]) ).
cnf(d11,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)],[d10,c0]) ).
cnf(d12,plain,
multiply(inverse(X2),inverse(multiply(multiply(X4,inverse(multiply(X1,multiply(X2,multiply(X3,X4))))),X1))) = X3,
inference(superposition,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
X2 = multiply(X4,multiply(multiply(inverse(X4),inverse(multiply(X3,multiply(X1,inverse(multiply(X2,multiply(X0,multiply(X3,X1)))))))),inverse(X0))),
inference(superposition,[status(thm)],[d12,d2]) ).
cnf(d14,plain,
multiply(multiply(X3,inverse(multiply(X4,multiply(X1,multiply(multiply(inverse(X1),inverse(X2)),X3))))),X4) = X2,
inference(superposition,[status(thm)],[d13,d8]) ).
cnf(d15,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(X3)),inverse(X0))),multiply(X0,X3)))) = X1,
inference(superposition,[status(thm)],[d14,c0]) ).
cnf(d16,plain,
multiply(X4,inverse(multiply(X3,multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X2))))) = X4,
inference(superposition,[status(thm)],[d2,d15]) ).
cnf(d17,plain,
multiply(X4,inverse(multiply(multiply(X2,inverse(multiply(X3,multiply(X1,multiply(inverse(X1),X2))))),X3))) = X4,
inference(superposition,[status(thm)],[d13,d16]) ).
cnf(d18,plain,
multiply(X3,multiply(inverse(X3),inverse(X1))) = multiply(X0,multiply(inverse(X0),inverse(X1))),
inference(superposition,[status(thm)],[d17,d2]) ).
cnf(d19,plain,
X1 = multiply(inverse(X4),inverse(multiply(multiply(X2,inverse(multiply(X3,multiply(X4,multiply(X1,X2))))),X3))),
inference(superposition,[status(thm)],[d13,d5]) ).
cnf(d20,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)],[d19,d18]) ).
cnf(d21,plain,
X1 = multiply(X1,inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(X3)),inverse(X0))),multiply(X0,X3)))),
inference(superposition,[status(thm)],[d14,d5]) ).
cnf(d22,plain,
X4 = multiply(X4,inverse(multiply(X3,multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X2))))),
inference(superposition,[status(thm)],[d2,d21]) ).
cnf(d23,plain,
X4 = multiply(X4,inverse(multiply(multiply(X2,inverse(multiply(X3,multiply(X1,multiply(inverse(X1),X2))))),X3))),
inference(superposition,[status(thm)],[d13,d22]) ).
cnf(d24,plain,
multiply(X3,inverse(X3)) = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[d23,d20]) ).
cnf(d25,plain,
multiply(X3,inverse(X3)) = multiply(multiply(X0,inverse(multiply(X1,multiply(X2,multiply(inverse(X2),X0))))),X1),
inference(superposition,[status(thm)],[d24,d17]) ).
cnf(d26,plain,
multiply(X4,inverse(multiply(X3,inverse(X3)))) = X4,
inference(superposition,[status(thm)],[d25,d17]) ).
cnf(d27,plain,
X1 = multiply(X2,inverse(multiply(inverse(X1),multiply(X0,multiply(inverse(X0),X2))))),
inference(superposition,[status(thm)],[d26,d5]) ).
cnf(d28,plain,
X2 = multiply(X2,inverse(multiply(inverse(X1),multiply(X0,multiply(inverse(X0),X1))))),
inference(superposition,[status(thm)],[d26,d22]) ).
cnf(d29,plain,
X4 = multiply(X4,inverse(multiply(X3,inverse(X3)))),
inference(superposition,[status(thm)],[d25,d23]) ).
cnf(d30,plain,
multiply(multiply(inverse(X1),inverse(multiply(X4,X3))),X4) = multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X2),
inference(superposition,[status(thm)],[d2,d14]) ).
cnf(d31,plain,
multiply(multiply(inverse(X0),inverse(multiply(X2,inverse(X1)))),X2) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d26,d30]) ).
cnf(d32,plain,
multiply(multiply(inverse(X2),inverse(X0)),X0) = multiply(inverse(X2),multiply(X1,inverse(X1))),
inference(superposition,[status(thm)],[d26,d31]) ).
cnf(d33,plain,
multiply(multiply(inverse(X0),inverse(X3)),X3) = multiply(multiply(inverse(X0),inverse(X2)),X2),
inference(superposition,[status(thm)],[d32,d32]) ).
cnf(d34,plain,
multiply(multiply(X1,inverse(X1)),inverse(X0)) = multiply(multiply(inverse(X0),inverse(X2)),X2),
inference(superposition,[status(thm)],[d24,d33]) ).
cnf(d35,plain,
X2 = multiply(X2,inverse(multiply(multiply(inverse(multiply(X0,inverse(X0))),inverse(X1)),X1))),
inference(superposition,[status(thm)],[d34,d29]) ).
cnf(d36,plain,
multiply(X2,multiply(X0,multiply(inverse(X0),inverse(multiply(X1,inverse(X1)))))) = X2,
inference(superposition,[status(thm)],[d35,d8]) ).
cnf(d37,plain,
multiply(X2,multiply(X0,inverse(X0))) = X2,
inference(demodulation,[status(thm)],[d36,d26]) ).
cnf(d38,plain,
X1 = multiply(X1,inverse(multiply(inverse(inverse(inverse(X0))),X0))),
inference(superposition,[status(thm)],[d37,d28]) ).
cnf(d39,plain,
inverse(inverse(multiply(X1,multiply(inverse(X1),X0)))) = X0,
inference(superposition,[status(thm)],[d38,d27]) ).
cnf(d40,plain,
multiply(X1,multiply(inverse(inverse(inverse(X0))),X0)) = X1,
inference(superposition,[status(thm)],[d38,d37]) ).
cnf(d41,plain,
inverse(inverse(inverse(inverse(X0)))) = X0,
inference(superposition,[status(thm)],[d40,d39]) ).
cnf(d42,plain,
inverse(multiply(multiply(X5,multiply(multiply(inverse(X5),inverse(multiply(X6,multiply(X2,X3)))),inverse(X7))),multiply(X7,multiply(X6,X2)))) = X3,
inference(superposition,[status(thm)],[d6,d0]) ).
cnf(d43,plain,
inverse(multiply(X4,multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(multiply(X2,X3),X4))),X2)))) = X3,
inference(superposition,[status(thm)],[d4,d42]) ).
cnf(d44,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X0,multiply(inverse(X0),X1)))) = X2,
inference(superposition,[status(thm)],[d26,d43]) ).
cnf(d45,plain,
inverse(multiply(inverse(multiply(inverse(inverse(X0)),X1)),X0)) = X1,
inference(superposition,[status(thm)],[d37,d44]) ).
cnf(d46,plain,
multiply(multiply(X1,inverse(X1)),inverse(X0)) = multiply(inverse(X0),multiply(X2,inverse(X2))),
inference(superposition,[status(thm)],[d24,d32]) ).
cnf(d47,plain,
multiply(multiply(X2,inverse(X2)),inverse(X0)) = inverse(X0),
inference(demodulation,[status(thm)],[d46,d37]) ).
cnf(d48,plain,
multiply(inverse(multiply(X0,inverse(X0))),inverse(X1)) = inverse(X1),
inference(superposition,[status(thm)],[d47,d47]) ).
cnf(d49,plain,
inverse(inverse(X0)) = inverse(inverse(inverse(inverse(X0)))),
inference(superposition,[status(thm)],[d48,d45]) ).
cnf(d50,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d49,d41]) ).
cnf(d51,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)],[d6,d3]) ).
cnf(d52,plain,
X3 = inverse(multiply(X4,multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(multiply(X2,X3),X4))),X2)))),
inference(superposition,[status(thm)],[d2,d51]) ).
cnf(d53,plain,
X2 = inverse(multiply(multiply(X3,inverse(multiply(X4,multiply(X1,multiply(multiply(inverse(X1),X2),X3))))),X4)),
inference(superposition,[status(thm)],[d13,d52]) ).
cnf(d54,plain,
multiply(X2,multiply(inverse(X2),X3)) = multiply(X4,multiply(inverse(X4),X3)),
inference(superposition,[status(thm)],[d53,d20]) ).
cnf(d55,plain,
inverse(inverse(X0)) = multiply(X1,multiply(inverse(X1),X0)),
inference(superposition,[status(thm)],[d40,d54]) ).
cnf(d56,plain,
X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(demodulation,[status(thm)],[d55,d50]) ).
cnf(d57,plain,
multiply(X2,inverse(multiply(inverse(X1),multiply(X0,multiply(inverse(X0),X2))))) = X1,
inference(superposition,[status(thm)],[d26,c0]) ).
cnf(d58,plain,
X0 = inverse(inverse(multiply(X1,multiply(inverse(X1),X0)))),
inference(superposition,[status(thm)],[d38,d57]) ).
cnf(d59,plain,
X0 = inverse(inverse(inverse(inverse(X0)))),
inference(superposition,[status(thm)],[d40,d58]) ).
cnf(d60,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d59,d50]) ).
cnf(d61,plain,
X1 = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[d60,d56]) ).
cnf(d62,plain,
multiply(X0,multiply(X1,inverse(X1))) = multiply(X2,multiply(inverse(X2),inverse(inverse(X0)))),
inference(superposition,[status(thm)],[d24,d18]) ).
cnf(d63,plain,
multiply(X1,multiply(X3,inverse(X3))) = multiply(X1,multiply(X2,inverse(X2))),
inference(superposition,[status(thm)],[d62,d62]) ).
cnf(d64,plain,
X0 = multiply(X0,multiply(X2,inverse(X2))),
inference(demodulation,[status(thm)],[d63,d37]) ).
cnf(d65,plain,
X1 = multiply(X1,multiply(inverse(inverse(inverse(X0))),X0)),
inference(superposition,[status(thm)],[d38,d64]) ).
cnf(d66,plain,
X1 = multiply(X1,multiply(inverse(X0),X0)),
inference(demodulation,[status(thm)],[d65,d50]) ).
cnf(d67,plain,
multiply(inverse(X1),X1) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[d66,d61]) ).
cnf(d68,plain,
$false,
inference(resolution,[status(thm)],[d67,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP436-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 14:55:52 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.38/15.56 % SZS status Unsatisfiable for theBenchmark.p
% 26.38/15.56 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------