%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP433-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 187.90s 27.59s
% Output : CNFRefutation 187.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 2
% Syntax : Number of clauses : 72 ( 72 unt; 0 nHn; 3 RR)
% Number of literals : 72 ( 71 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 14 ( 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 : 260 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3)))) = X2 ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ).
cnf(c0,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3)))) = X2,
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,
inverse(multiply(multiply(multiply(X2,multiply(inverse(multiply(multiply(X0,X1),X2)),X0)),X1),multiply(X4,inverse(X4)))) = multiply(X3,inverse(X3)),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d1,plain,
multiply(X4,inverse(X4)) = multiply(X5,inverse(X5)),
inference(superposition,[status(thm)],[d0,d0]) ).
cnf(d2,plain,
inverse(multiply(multiply(multiply(inverse(multiply(X2,inverse(X2))),X0),X1),multiply(X3,inverse(X3)))) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
inverse(multiply(multiply(inverse(multiply(multiply(X1,X2),inverse(multiply(X0,inverse(X0))))),X1),X2)) = multiply(X4,inverse(X4)),
inference(superposition,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X1,inverse(X1)),X2)),X0),inverse(X0)),multiply(X3,inverse(X3)))) = X2,
inference(superposition,[status(thm)],[d1,c0]) ).
cnf(d5,plain,
inverse(multiply(X1,inverse(X1))) = inverse(multiply(X0,inverse(X0))),
inference(superposition,[status(thm)],[d2,d4]) ).
cnf(d6,plain,
inverse(multiply(X2,inverse(X2))) = inverse(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X1))))),
inference(superposition,[status(thm)],[d5,d5]) ).
cnf(d7,plain,
inverse(multiply(multiply(inverse(multiply(X2,inverse(X2))),X0),inverse(X0))) = multiply(X3,inverse(X3)),
inference(superposition,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X0,inverse(X0)))),X1),multiply(X3,inverse(X3)))) = inverse(X1),
inference(superposition,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
multiply(X2,inverse(X2)) = multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X1)))),
inference(superposition,[status(thm)],[d5,d1]) ).
cnf(d10,plain,
inverse(multiply(multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X2)))),X3),multiply(X4,inverse(X4)))) = inverse(multiply(inverse(inverse(multiply(X0,inverse(X0)))),X3)),
inference(superposition,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
inverse(X2) = inverse(multiply(inverse(inverse(multiply(X4,inverse(X4)))),X2)),
inference(demodulation,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
inverse(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X0,inverse(X0)))),multiply(X1,inverse(X1)))) = multiply(X3,inverse(X3)),
inference(superposition,[status(thm)],[d7,d3]) ).
cnf(d13,plain,
multiply(X3,inverse(X3)) = inverse(inverse(multiply(X1,inverse(X1)))),
inference(superposition,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
inverse(X2) = inverse(multiply(multiply(X1,inverse(X1)),X2)),
inference(superposition,[status(thm)],[d13,d11]) ).
cnf(d15,plain,
inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,inverse(X3)))),inverse(inverse(inverse(multiply(multiply(X0,inverse(X0)),X1))))),multiply(X4,inverse(X4)))) = X1,
inference(superposition,[status(thm)],[d9,d4]) ).
cnf(d16,plain,
inverse(inverse(inverse(inverse(multiply(multiply(X2,inverse(X2)),X3))))) = X3,
inference(demodulation,[status(thm)],[d15,d8]) ).
cnf(d17,plain,
inverse(inverse(inverse(inverse(X1)))) = X1,
inference(demodulation,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
inverse(multiply(multiply(multiply(X2,inverse(X2)),inverse(inverse(inverse(multiply(multiply(X0,inverse(X0)),X1))))),multiply(X3,inverse(X3)))) = X1,
inference(superposition,[status(thm)],[d1,d4]) ).
cnf(d19,plain,
inverse(inverse(inverse(inverse(multiply(multiply(X1,inverse(X1)),X2))))) = X2,
inference(superposition,[status(thm)],[d8,d18]) ).
cnf(d20,plain,
multiply(multiply(X0,inverse(X0)),X1) = X1,
inference(demodulation,[status(thm)],[d19,d17]) ).
cnf(d21,plain,
inverse(inverse(multiply(X1,inverse(X1)))) = multiply(X3,inverse(X3)),
inference(superposition,[status(thm)],[d8,d12]) ).
cnf(d22,plain,
multiply(inverse(inverse(multiply(X1,inverse(X1)))),X2) = X2,
inference(superposition,[status(thm)],[d21,d20]) ).
cnf(d23,plain,
multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X1)))) = multiply(X2,inverse(X2)),
inference(superposition,[status(thm)],[d5,d1]) ).
cnf(d24,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,inverse(X3))))),X0),X1),multiply(X4,inverse(X4)))) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[d23,c0]) ).
cnf(d25,plain,
inverse(multiply(multiply(multiply(inverse(inverse(multiply(X1,inverse(X1)))),X2),X3),multiply(X4,inverse(X4)))) = inverse(multiply(X2,X3)),
inference(demodulation,[status(thm)],[d24,d20]) ).
cnf(d26,plain,
inverse(multiply(multiply(X1,X2),multiply(X3,inverse(X3)))) = inverse(multiply(X1,X2)),
inference(demodulation,[status(thm)],[d25,d22]) ).
cnf(d27,plain,
multiply(inverse(multiply(X0,inverse(X0))),X1) = X1,
inference(superposition,[status(thm)],[d20,d20]) ).
cnf(d28,plain,
inverse(multiply(multiply(multiply(multiply(X4,inverse(X4)),multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1))),X2),multiply(X5,inverse(X5)))) = multiply(X3,inverse(X3)),
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d29,plain,
inverse(multiply(multiply(multiply(inverse(multiply(X6,inverse(X6))),X7),X8),multiply(multiply(multiply(multiply(multiply(X0,inverse(X0)),multiply(X1,multiply(inverse(multiply(multiply(X2,X3),X1)),X2))),X3),multiply(X4,inverse(X4))),multiply(X5,inverse(X5))))) = inverse(multiply(X7,X8)),
inference(superposition,[status(thm)],[d28,d2]) ).
cnf(d30,plain,
inverse(multiply(multiply(X1,X2),multiply(multiply(multiply(multiply(multiply(X3,inverse(X3)),multiply(X4,multiply(inverse(multiply(multiply(X5,X6),X4)),X5))),X6),multiply(X7,inverse(X7))),multiply(X8,inverse(X8))))) = inverse(multiply(X1,X2)),
inference(demodulation,[status(thm)],[d29,d27]) ).
cnf(d31,plain,
inverse(multiply(multiply(X4,X5),multiply(multiply(multiply(multiply(X1,multiply(inverse(multiply(multiply(X2,X3),X1)),X2)),X3),multiply(X6,inverse(X6))),multiply(X7,inverse(X7))))) = inverse(multiply(X4,X5)),
inference(demodulation,[status(thm)],[d30,d20]) ).
cnf(d32,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X6,inverse(X6)),X7)),X8),inverse(X8)),multiply(multiply(multiply(multiply(multiply(X0,inverse(X0)),multiply(X1,multiply(inverse(multiply(multiply(X2,X3),X1)),X2))),X3),multiply(X4,inverse(X4))),multiply(X5,inverse(X5))))) = X7,
inference(superposition,[status(thm)],[d28,d4]) ).
cnf(d33,plain,
inverse(multiply(multiply(multiply(inverse(X1),X2),inverse(X2)),multiply(multiply(multiply(multiply(multiply(X3,inverse(X3)),multiply(X4,multiply(inverse(multiply(multiply(X5,X6),X4)),X5))),X6),multiply(X7,inverse(X7))),multiply(X8,inverse(X8))))) = X1,
inference(demodulation,[status(thm)],[d32,d20]) ).
cnf(d34,plain,
inverse(multiply(multiply(multiply(inverse(X4),X5),inverse(X5)),multiply(multiply(multiply(multiply(X1,multiply(inverse(multiply(multiply(X2,X3),X1)),X2)),X3),multiply(X6,inverse(X6))),multiply(X7,inverse(X7))))) = X4,
inference(demodulation,[status(thm)],[d33,d20]) ).
cnf(d35,plain,
inverse(multiply(multiply(inverse(X0),X1),inverse(X1))) = X0,
inference(demodulation,[status(thm)],[d34,d31]) ).
cnf(d36,plain,
inverse(inverse(inverse(X0))) = multiply(multiply(inverse(X0),X1),inverse(X1)),
inference(superposition,[status(thm)],[d35,d17]) ).
cnf(d37,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X6,inverse(X6)),X7)),X8),inverse(X8)),inverse(multiply(multiply(multiply(multiply(X1,inverse(X1)),multiply(X2,multiply(inverse(multiply(multiply(X3,X4),X2)),X3))),X4),multiply(X5,inverse(X5)))))) = X7,
inference(superposition,[status(thm)],[d28,d4]) ).
cnf(d38,plain,
inverse(multiply(inverse(inverse(inverse(multiply(multiply(X0,inverse(X0)),X1)))),inverse(multiply(multiply(multiply(multiply(X3,inverse(X3)),multiply(X4,multiply(inverse(multiply(multiply(X5,X6),X4)),X5))),X6),multiply(X7,inverse(X7)))))) = X1,
inference(demodulation,[status(thm)],[d37,d36]) ).
cnf(d39,plain,
inverse(multiply(inverse(inverse(inverse(X1))),inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),multiply(X3,multiply(inverse(multiply(multiply(X4,X5),X3)),X4))),X5),multiply(X6,inverse(X6)))))) = X1,
inference(demodulation,[status(thm)],[d38,d20]) ).
cnf(d40,plain,
inverse(multiply(inverse(inverse(inverse(X5))),inverse(multiply(multiply(multiply(X0,inverse(X0)),multiply(X1,multiply(inverse(multiply(multiply(X2,X3),X1)),X2))),X3)))) = X5,
inference(demodulation,[status(thm)],[d39,d26]) ).
cnf(d41,plain,
inverse(multiply(inverse(inverse(inverse(X4))),inverse(multiply(multiply(X1,multiply(inverse(multiply(multiply(X2,X3),X1)),X2)),X3)))) = X4,
inference(demodulation,[status(thm)],[d40,d20]) ).
cnf(d42,plain,
multiply(X6,inverse(X6)) = multiply(multiply(X7,inverse(X7)),inverse(multiply(multiply(multiply(multiply(multiply(X0,inverse(X0)),multiply(X1,multiply(inverse(multiply(multiply(X2,X3),X1)),X2))),X3),multiply(X4,inverse(X4))),multiply(X5,inverse(X5))))),
inference(superposition,[status(thm)],[d28,d9]) ).
cnf(d43,plain,
multiply(X7,inverse(X7)) = inverse(multiply(multiply(multiply(multiply(multiply(X1,inverse(X1)),multiply(X2,multiply(inverse(multiply(multiply(X3,X4),X2)),X3))),X4),multiply(X5,inverse(X5))),multiply(X6,inverse(X6)))),
inference(demodulation,[status(thm)],[d42,d20]) ).
cnf(d44,plain,
multiply(X6,inverse(X6)) = inverse(multiply(multiply(multiply(multiply(X0,inverse(X0)),multiply(X1,multiply(inverse(multiply(multiply(X2,X3),X1)),X2))),X3),multiply(X4,inverse(X4)))),
inference(demodulation,[status(thm)],[d43,d26]) ).
cnf(d45,plain,
multiply(X5,inverse(X5)) = inverse(multiply(multiply(multiply(X0,inverse(X0)),multiply(X1,multiply(inverse(multiply(multiply(X2,X3),X1)),X2))),X3)),
inference(demodulation,[status(thm)],[d44,d26]) ).
cnf(d46,plain,
multiply(X4,inverse(X4)) = inverse(multiply(multiply(X1,multiply(inverse(multiply(multiply(X2,X3),X1)),X2)),X3)),
inference(demodulation,[status(thm)],[d45,d20]) ).
cnf(d47,plain,
inverse(multiply(inverse(inverse(inverse(X4))),multiply(X3,inverse(X3)))) = X4,
inference(superposition,[status(thm)],[d46,d41]) ).
cnf(d48,plain,
inverse(multiply(X0,multiply(X1,inverse(X1)))) = inverse(X0),
inference(superposition,[status(thm)],[d17,d47]) ).
cnf(d49,plain,
inverse(inverse(inverse(inverse(X0)))) = multiply(X0,multiply(X1,inverse(X1))),
inference(superposition,[status(thm)],[d48,d17]) ).
cnf(d50,plain,
X0 = multiply(X0,multiply(X1,inverse(X1))),
inference(demodulation,[status(thm)],[d49,d17]) ).
cnf(d51,plain,
inverse(multiply(multiply(inverse(X1),inverse(inverse(inverse(X0)))),X0)) = X1,
inference(superposition,[status(thm)],[d17,d35]) ).
cnf(d52,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(multiply(inverse(multiply(multiply(X0,inverse(X0)),X1)),X2),inverse(X2)),multiply(X3,inverse(X3))),X1)),X4),X5),multiply(X6,inverse(X6)))) = inverse(multiply(X4,X5)),
inference(superposition,[status(thm)],[d4,d2]) ).
cnf(d53,plain,
X1 = inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,inverse(X0)),X1)),X2),inverse(X2)),multiply(X3,inverse(X3)))),
inference(superposition,[status(thm)],[c0,d52]) ).
cnf(d54,plain,
multiply(X1,inverse(X1)) = inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),X3),inverse(X3)),multiply(X4,inverse(X4)))),
inference(superposition,[status(thm)],[d12,d53]) ).
cnf(d55,plain,
multiply(X3,inverse(X3)) = inverse(inverse(inverse(multiply(X1,inverse(X1))))),
inference(superposition,[status(thm)],[d8,d54]) ).
cnf(d56,plain,
X2 = multiply(X2,inverse(inverse(inverse(multiply(X1,inverse(X1)))))),
inference(superposition,[status(thm)],[d55,d50]) ).
cnf(d57,plain,
inverse(multiply(inverse(X0),multiply(X1,inverse(X1)))) = X0,
inference(superposition,[status(thm)],[d56,d51]) ).
cnf(d58,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d57,d50]) ).
cnf(d59,plain,
X2 = inverse(inverse(inverse(inverse(multiply(multiply(X1,inverse(X1)),X2))))),
inference(superposition,[status(thm)],[d18,d8]) ).
cnf(d60,plain,
X1 = multiply(multiply(X0,inverse(X0)),X1),
inference(demodulation,[status(thm)],[d59,d17]) ).
cnf(d61,plain,
multiply(X1,inverse(X1)) = multiply(inverse(inverse(inverse(X0))),X0),
inference(superposition,[status(thm)],[d17,d1]) ).
cnf(d62,plain,
X2 = multiply(multiply(inverse(inverse(inverse(X1))),X1),X2),
inference(superposition,[status(thm)],[d61,d60]) ).
cnf(d63,plain,
X1 = multiply(multiply(inverse(X0),X0),X1),
inference(demodulation,[status(thm)],[d62,d58]) ).
cnf(d64,plain,
X2 = multiply(X2,multiply(inverse(inverse(inverse(X1))),X1)),
inference(superposition,[status(thm)],[d61,d50]) ).
cnf(d65,plain,
X1 = multiply(X1,multiply(inverse(X0),X0)),
inference(demodulation,[status(thm)],[d64,d58]) ).
cnf(d66,plain,
multiply(inverse(X1),X1) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[d65,d63]) ).
cnf(d67,plain,
$false,
inference(resolution,[status(thm)],[d66,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP433-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:53:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 187.90/27.59 % SZS status Unsatisfiable for theBenchmark.p
% 187.90/27.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------