%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP416-1 : 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 : n009.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 07:23:43 AM UTC 2026
% Result : Unsatisfiable 83.17s 14.31s
% Output : CNFRefutation 83.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of clauses : 58 ( 58 unt; 0 nHn; 8 RR)
% Number of literals : 58 ( 57 equ; 7 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 16 ( 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 : 143 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0)))))) = X2 ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2 ).
cnf(c0,plain,
inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0)))))) = X2,
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(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X2))),inverse(multiply(inverse(X3),X3)))))) = multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0))))),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d1,plain,
multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,inverse(inverse(X2))))),inverse(multiply(inverse(X3),X3))))) = X2,
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X0,X3)),X2)),inverse(multiply(inverse(X3),X3)))))) = multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(inverse(X2))))),inverse(multiply(inverse(X0),X0))),
inference(superposition,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
multiply(X1,inverse(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X1,X3)),X2)),inverse(multiply(inverse(X3),X3)))))))) = X2,
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
multiply(X0,inverse(inverse(multiply(X1,inverse(multiply(inverse(X3),inverse(multiply(inverse(X1),X1)))))))) = inverse(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),X3)),inverse(multiply(inverse(X2),X2))))))),
inference(superposition,[status(thm)],[d3,d3]) ).
cnf(d5,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2))))))))) = X3,
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
inverse(X2) = multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,inverse(inverse(inverse(X2)))))),inverse(multiply(inverse(X3),X3))))),
inference(superposition,[status(thm)],[d1,d0]) ).
cnf(d7,plain,
inverse(X2) = inverse(X2),
inference(demodulation,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
X2 = multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,inverse(inverse(X2))))),inverse(multiply(inverse(X3),X3))))),
inference(superposition,[status(thm)],[c0,d0]) ).
cnf(d9,plain,
X2 = inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,inverse(X2)))),inverse(multiply(inverse(X3),X3)))))),
inference(superposition,[status(thm)],[d0,d8]) ).
cnf(d10,plain,
X2 = multiply(inverse(multiply(inverse(multiply(X3,X1)),multiply(X3,inverse(inverse(multiply(X1,inverse(X2))))))),inverse(multiply(inverse(X1),X1))),
inference(superposition,[status(thm)],[d2,d9]) ).
cnf(d11,plain,
inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(inverse(multiply(X1,inverse(X2))))))),X3)),X2)),inverse(multiply(inverse(X3),X3)))))) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
X2 = inverse(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X2))),inverse(multiply(inverse(X3),X3))))))),
inference(superposition,[status(thm)],[d0,d9]) ).
cnf(d13,plain,
X2 = inverse(multiply(inverse(multiply(inverse(multiply(X3,X1)),multiply(X3,inverse(inverse(multiply(X1,X2)))))),inverse(multiply(inverse(X1),X1)))),
inference(superposition,[status(thm)],[d2,d12]) ).
cnf(d14,plain,
inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1)))))))) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[d13,d11]) ).
cnf(d15,plain,
multiply(inverse(X0),X0) = inverse(multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(inverse(multiply(inverse(X0),X0))),inverse(multiply(inverse(X0),X0)))))))),
inference(superposition,[status(thm)],[d14,d7]) ).
cnf(d16,plain,
multiply(inverse(multiply(X2,inverse(multiply(inverse(X0),X0)))),multiply(X2,inverse(multiply(inverse(X0),X0)))) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[d15,d5]) ).
cnf(d17,plain,
multiply(inverse(X2),X2) = multiply(inverse(X3),X3),
inference(superposition,[status(thm)],[d16,d16]) ).
cnf(d18,plain,
inverse(multiply(inverse(X1),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(inverse(X1)),inverse(X1))))))) = X1,
inference(superposition,[status(thm)],[d17,c0]) ).
cnf(d19,plain,
inverse(multiply(inverse(X0),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X1),X1)))))) = X0,
inference(superposition,[status(thm)],[d17,d18]) ).
cnf(d20,plain,
inverse(multiply(inverse(X2),X2)) = inverse(multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(inverse(X1),X1)))),
inference(superposition,[status(thm)],[d17,d19]) ).
cnf(d21,plain,
inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2)))) = X3,
inference(superposition,[status(thm)],[d20,d19]) ).
cnf(d22,plain,
inverse(multiply(inverse(X2),multiply(inverse(X0),X0))) = X2,
inference(demodulation,[status(thm)],[d19,d21]) ).
cnf(d23,plain,
multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(inverse(multiply(X1,X0))))) = X0,
inference(demodulation,[status(thm)],[d5,d21]) ).
cnf(d24,plain,
inverse(X1) = multiply(inverse(inverse(inverse(multiply(X0,X1)))),X0),
inference(superposition,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
inverse(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X2))),inverse(multiply(inverse(X3),X3))))))) = X2,
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d26,plain,
inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0)))),inverse(multiply(inverse(multiply(X2,multiply(X0,X3))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0))))),inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0))))))))))) = X3,
inference(superposition,[status(thm)],[d9,d25]) ).
cnf(d27,plain,
inverse(inverse(multiply(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2))),inverse(multiply(inverse(multiply(X2,multiply(X1,X3))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X1),X1))))),inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X1),X1))))))))))) = X3,
inference(demodulation,[status(thm)],[d26,d21]) ).
cnf(d28,plain,
inverse(inverse(multiply(multiply(inverse(multiply(X3,X1)),multiply(X3,inverse(X0))),multiply(X0,multiply(X1,X2))))) = X2,
inference(demodulation,[status(thm)],[d27,d21]) ).
cnf(d29,plain,
multiply(inverse(inverse(X1)),inverse(multiply(inverse(X2),X2))) = X1,
inference(superposition,[status(thm)],[d20,d1]) ).
cnf(d30,plain,
multiply(inverse(inverse(X1)),multiply(inverse(X0),X0)) = X1,
inference(superposition,[status(thm)],[d22,d29]) ).
cnf(d31,plain,
inverse(X1) = inverse(multiply(multiply(inverse(X0),X0),X1)),
inference(superposition,[status(thm)],[d24,d30]) ).
cnf(d32,plain,
inverse(inverse(multiply(X1,multiply(inverse(X1),X2)))) = X2,
inference(superposition,[status(thm)],[d31,d28]) ).
cnf(d33,plain,
inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[status(thm)],[d32,d24]) ).
cnf(d34,plain,
X1 = inverse(multiply(inverse(X1),inverse(multiply(inverse(X2),X2)))),
inference(superposition,[status(thm)],[d20,d9]) ).
cnf(d35,plain,
inverse(multiply(inverse(X2),X2)) = multiply(inverse(X0),X0),
inference(demodulation,[status(thm)],[d20,d21]) ).
cnf(d36,plain,
inverse(inverse(multiply(inverse(X1),X1))) = multiply(inverse(X2),X2),
inference(superposition,[status(thm)],[d35,d35]) ).
cnf(d37,plain,
X2 = inverse(multiply(inverse(X2),inverse(inverse(inverse(multiply(inverse(X1),X1)))))),
inference(superposition,[status(thm)],[d36,d34]) ).
cnf(d38,plain,
X0 = multiply(inverse(inverse(inverse(inverse(multiply(inverse(X1),X1))))),X0),
inference(demodulation,[status(thm)],[d37,d33]) ).
cnf(d39,plain,
X1 = multiply(inverse(inverse(inverse(multiply(inverse(X0),X0)))),X1),
inference(demodulation,[status(thm)],[d38,d33]) ).
cnf(d40,plain,
X1 = multiply(inverse(inverse(multiply(inverse(X0),X0))),X1),
inference(demodulation,[status(thm)],[d39,d33]) ).
cnf(d41,plain,
X1 = multiply(inverse(multiply(inverse(X0),X0)),X1),
inference(demodulation,[status(thm)],[d40,d33]) ).
cnf(d42,plain,
X1 = multiply(multiply(inverse(X0),X0),X1),
inference(demodulation,[status(thm)],[d41,d33]) ).
cnf(d43,plain,
multiply(multiply(inverse(X0),X0),a2) != a2,
inference(superposition,[status(thm)],[d17,c1]) ).
cnf(d44,plain,
multiply(inverse(multiply(X3,X0)),multiply(X3,X2)) = multiply(inverse(multiply(X1,X0)),multiply(X1,X2)),
inference(superposition,[status(thm)],[d25,d5]) ).
cnf(d45,plain,
multiply(inverse(multiply(inverse(X0),X2)),multiply(inverse(X1),X1)) = multiply(inverse(multiply(X3,X2)),multiply(X3,X0)),
inference(superposition,[status(thm)],[d17,d44]) ).
cnf(d46,plain,
multiply(multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X2),X2)),a2) != a2,
inference(superposition,[status(thm)],[d45,d43]) ).
cnf(d47,plain,
multiply(multiply(multiply(inverse(X0),X0),multiply(inverse(X1),X1)),a2) != a2,
inference(superposition,[status(thm)],[d22,d46]) ).
cnf(d48,plain,
multiply(multiply(inverse(X1),X1),a2) != a2,
inference(demodulation,[status(thm)],[d47,d42]) ).
cnf(d49,plain,
a2 != a2,
inference(demodulation,[status(thm)],[d48,d42]) ).
cnf(d50,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0)))),inverse(multiply(inverse(multiply(X2,multiply(X0,inverse(X3)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0))))),inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0)))))))))) = X3,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d51,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(inverse(X2))))),inverse(multiply(inverse(X0),X0)))),inverse(multiply(inverse(multiply(inverse(X2),multiply(X0,inverse(X3)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(inverse(X2))))),inverse(multiply(inverse(X0),X0))))),inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(inverse(X2))))),inverse(multiply(inverse(X0),X0)))))))))) = X3,
inference(superposition,[status(thm)],[d1,c0]) ).
cnf(d52,plain,
X3 = X3,
inference(demodulation,[status(thm)],[d51,d50]) ).
cnf(d53,plain,
$false,
inference(resolution,[status(thm)],[d52,d49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP416-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:52:44 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 83.17/14.31 % SZS status Unsatisfiable for theBenchmark.p
% 83.17/14.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------