%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP440-1 : 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 : n007.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 07:23:46 AM UTC 2026
% Result : Unsatisfiable 9.65s 8.68s
% Output : CNFRefutation 9.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 6 RR)
% Number of literals : 42 ( 41 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 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 : 133 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X0,X2))))))) = X3 ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2 ).
cnf(c0,plain,
inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X0,X2))))))) = X3,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausification,[status(esa)],[prove_these_axioms_2]) ).
cnf(d0,plain,
inverse(multiply(X1,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X0,X2))))),X3)))) = X0,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d1,plain,
inverse(multiply(X1,multiply(X5,multiply(multiply(inverse(X5),multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),X2),inverse(multiply(X3,multiply(X4,X2))))),X3)),X4)))) = X0,
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
inverse(multiply(X4,multiply(X5,multiply(multiply(inverse(X5),multiply(multiply(inverse(X4),multiply(multiply(X3,X6),inverse(multiply(X7,multiply(X8,X6))))),X7)),X8)))) = multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X0,X2)))))),
inference(superposition,[status(thm)],[c0,d1]) ).
cnf(d3,plain,
multiply(X6,multiply(X7,multiply(multiply(inverse(X7),X8),inverse(multiply(inverse(X2),multiply(X6,X8)))))) = X2,
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
inverse(multiply(X0,multiply(X4,multiply(multiply(inverse(X4),multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(inverse(X3),multiply(X0,X2)))))),inverse(multiply(X5,X3)))))) = X5,
inference(superposition,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
inverse(multiply(inverse(X0),multiply(X0,multiply(X3,inverse(multiply(X4,X3)))))) = X4,
inference(superposition,[status(thm)],[d3,d4]) ).
cnf(d6,plain,
multiply(X3,multiply(X4,multiply(multiply(inverse(X4),X5),inverse(multiply(X2,multiply(X3,X5)))))) = multiply(inverse(X0),multiply(X0,multiply(X1,inverse(multiply(X2,X1))))),
inference(superposition,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
multiply(inverse(X4),multiply(X4,multiply(X5,inverse(multiply(inverse(X3),X5))))) = X3,
inference(superposition,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
multiply(inverse(X3),multiply(X3,multiply(multiply(X0,multiply(X1,inverse(multiply(X2,X1)))),X2))) = X0,
inference(superposition,[status(thm)],[d5,d7]) ).
cnf(d9,plain,
X2 = multiply(X6,multiply(X7,multiply(multiply(inverse(X7),X8),inverse(multiply(inverse(X2),multiply(X6,X8)))))),
inference(superposition,[status(thm)],[d1,d2]) ).
cnf(d10,plain,
X0 = multiply(X0,multiply(X3,multiply(multiply(inverse(X3),multiply(X1,inverse(multiply(X2,X1)))),X2))),
inference(superposition,[status(thm)],[d5,d9]) ).
cnf(d11,plain,
X3 = multiply(X3,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(X0,multiply(X1,inverse(multiply(X2,X1)))),X2)),inverse(X0)))),
inference(superposition,[status(thm)],[d5,d10]) ).
cnf(d12,plain,
X3 = multiply(inverse(X4),multiply(X4,multiply(X5,inverse(multiply(inverse(X3),X5))))),
inference(superposition,[status(thm)],[d6,d9]) ).
cnf(d13,plain,
X4 = multiply(X4,multiply(multiply(X0,multiply(X1,inverse(multiply(multiply(X2,inverse(multiply(inverse(X3),X2))),X1)))),multiply(X3,inverse(X0)))),
inference(superposition,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[d13,d8]) ).
cnf(d15,plain,
multiply(multiply(inverse(X0),X0),a2) != a2,
inference(superposition,[status(thm)],[d14,c1]) ).
cnf(d16,plain,
X4 = multiply(X4,multiply(X5,multiply(multiply(inverse(X5),multiply(multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X0,X2))))),X3)),X0))),
inference(superposition,[status(thm)],[c0,d10]) ).
cnf(d17,plain,
X3 = multiply(X3,multiply(X0,multiply(inverse(X0),inverse(multiply(inverse(X1),X1))))),
inference(superposition,[status(thm)],[d13,d16]) ).
cnf(d18,plain,
X2 = multiply(X2,multiply(inverse(multiply(inverse(X0),X0)),multiply(inverse(X1),X1))),
inference(superposition,[status(thm)],[d14,d17]) ).
cnf(d19,plain,
X2 = multiply(X2,multiply(inverse(X1),X1)),
inference(superposition,[status(thm)],[d14,d18]) ).
cnf(d20,plain,
X2 = multiply(X2,inverse(multiply(inverse(X0),X0))),
inference(superposition,[status(thm)],[d18,d18]) ).
cnf(d21,plain,
inverse(multiply(inverse(X3),multiply(X3,multiply(multiply(X0,multiply(X1,inverse(multiply(X2,X1)))),X2)))) = inverse(X0),
inference(superposition,[status(thm)],[d5,d5]) ).
cnf(d22,plain,
multiply(inverse(X4),multiply(X4,multiply(multiply(X0,multiply(multiply(X1,multiply(X2,inverse(multiply(X3,X2)))),X3)),inverse(X1)))) = X0,
inference(superposition,[status(thm)],[d21,d7]) ).
cnf(d23,plain,
multiply(inverse(X3),multiply(X3,multiply(X0,inverse(multiply(inverse(X1),X1))))) = X0,
inference(superposition,[status(thm)],[d13,d22]) ).
cnf(d24,plain,
multiply(inverse(X2),multiply(X2,X0)) = X0,
inference(demodulation,[status(thm)],[d23,d20]) ).
cnf(d25,plain,
inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[d24,d19]) ).
cnf(d26,plain,
multiply(multiply(X0,inverse(X0)),a2) != a2,
inference(superposition,[status(thm)],[d25,d15]) ).
cnf(d27,plain,
X2 = multiply(X1,inverse(multiply(inverse(X2),X1))),
inference(demodulation,[status(thm)],[d12,d24]) ).
cnf(d28,plain,
X0 = multiply(multiply(X0,X1),inverse(X1)),
inference(superposition,[status(thm)],[d24,d27]) ).
cnf(d29,plain,
X0 = multiply(inverse(X4),multiply(X4,multiply(multiply(X0,multiply(multiply(X1,multiply(X2,inverse(multiply(X3,X2)))),X3)),inverse(X1)))),
inference(superposition,[status(thm)],[d21,d12]) ).
cnf(d30,plain,
X0 = multiply(inverse(X3),multiply(X3,multiply(X0,inverse(multiply(inverse(X1),X1))))),
inference(superposition,[status(thm)],[d13,d29]) ).
cnf(d31,plain,
X0 = multiply(inverse(X2),multiply(X2,X0)),
inference(demodulation,[status(thm)],[d30,d20]) ).
cnf(d32,plain,
X0 = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d19,d31]) ).
cnf(d33,plain,
X1 = multiply(multiply(X1,inverse(X0)),X0),
inference(superposition,[status(thm)],[d32,d28]) ).
cnf(d34,plain,
a2 != a2,
inference(superposition,[status(thm)],[d33,d26]) ).
cnf(d35,plain,
inverse(multiply(X1,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X1),X2),inverse(multiply(inverse(X3),multiply(X0,X2))))),inverse(X3))))) = X0,
inference(superposition,[status(thm)],[d3,c0]) ).
cnf(d36,plain,
X4 = X4,
inference(demodulation,[status(thm)],[d35,d0]) ).
cnf(d37,plain,
$false,
inference(resolution,[status(thm)],[d36,d34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP440-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:52:23 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.65/8.68 % SZS status Unsatisfiable for theBenchmark.p
% 9.65/8.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------