%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP408-1 : 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 : n002.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 07:23:42 AM UTC 2026
% Result : Unsatisfiable 102.03s 17.70s
% Output : CNFRefutation 102.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 2
% Syntax : Number of clauses : 49 ( 49 unt; 0 nHn; 4 RR)
% Number of literals : 49 ( 48 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 3 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 : 188 ( 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_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ).
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)),
inference(clausification,[status(esa)],[prove_these_axioms_3]) ).
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(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(d12,plain,
multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),multiply(inverse(X1),multiply(inverse(X1),X1))) = X2,
inference(superposition,[status(thm)],[d11,d2]) ).
cnf(d13,plain,
multiply(inverse(X2),X2) = multiply(X3,multiply(inverse(multiply(inverse(multiply(X4,X1)),multiply(X4,X3))),multiply(inverse(X1),multiply(inverse(X1),X1)))),
inference(superposition,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
multiply(inverse(X4),X4) = multiply(inverse(X3),X3),
inference(superposition,[status(thm)],[d13,d13]) ).
cnf(d15,plain,
inverse(multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X1),multiply(inverse(X1),X1)))) = X1,
inference(superposition,[status(thm)],[d14,d4]) ).
cnf(d16,plain,
inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,multiply(inverse(X0),X0)))) = X0,
inference(superposition,[status(thm)],[d15,d8]) ).
cnf(d17,plain,
inverse(multiply(inverse(multiply(X2,X0)),multiply(X2,multiply(inverse(X1),X1)))) = X0,
inference(superposition,[status(thm)],[d14,d16]) ).
cnf(d18,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(d19,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,d18]) ).
cnf(d20,plain,
multiply(inverse(X2),X1) = multiply(inverse(multiply(X3,X2)),multiply(X3,X1)),
inference(demodulation,[status(thm)],[d19,d17]) ).
cnf(d21,plain,
inverse(multiply(inverse(multiply(inverse(X1),X2)),multiply(inverse(X1),multiply(inverse(X1),X1)))) = X2,
inference(demodulation,[status(thm)],[d4,d20]) ).
cnf(d22,plain,
inverse(multiply(inverse(X1),multiply(inverse(X0),X0))) = X1,
inference(demodulation,[status(thm)],[d21,d20]) ).
cnf(d23,plain,
inverse(multiply(inverse(X1),X0)) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d20,d22]) ).
cnf(d24,plain,
multiply(inverse(multiply(inverse(X1),X1)),X0) = X0,
inference(demodulation,[status(thm)],[d22,d23]) ).
cnf(d25,plain,
multiply(multiply(inverse(X0),X0),X1) = X1,
inference(demodulation,[status(thm)],[d24,d23]) ).
cnf(d26,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(d27,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)],[d26,d20]) ).
cnf(d28,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)],[d27,d23]) ).
cnf(d29,plain,
multiply(inverse(multiply(X4,X2)),X5) = multiply(multiply(inverse(X2),X3),multiply(inverse(multiply(X4,X3)),X5)),
inference(demodulation,[status(thm)],[d28,d20]) ).
cnf(d30,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(d31,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)],[d30,d23]) ).
cnf(d32,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)],[d31,d23]) ).
cnf(d33,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)],[d32,d23]) ).
cnf(d34,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)],[d33,d25]) ).
cnf(d35,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)],[d34,d23]) ).
cnf(d36,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)],[d35,d23]) ).
cnf(d37,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)],[d36,d29]) ).
cnf(d38,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)],[d37,d23]) ).
cnf(d39,plain,
multiply(X3,multiply(X4,X5)) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(multiply(X0,X1)),X2)),multiply(X3,X4)),X5),
inference(demodulation,[status(thm)],[d38,d23]) ).
cnf(d40,plain,
multiply(X3,multiply(X4,X5)) = multiply(multiply(X3,X4),X5),
inference(demodulation,[status(thm)],[d39,d25]) ).
cnf(d41,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm)],[c1,d40]) ).
cnf(d42,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(d43,plain,
X3 = X3,
inference(demodulation,[status(thm)],[d42,d4]) ).
cnf(d44,plain,
$false,
inference(resolution,[status(thm)],[d43,d41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP408-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 14:55:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 102.03/17.70 % SZS status Unsatisfiable for theBenchmark.p
% 102.03/17.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------