%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP418-1 : 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 : n026.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 07:23:44 AM UTC 2026
% Result : Unsatisfiable 22.33s 10.94s
% Output : CNFRefutation 22.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 3 RR)
% Number of literals : 18 ( 17 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 14 ( 4 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 : 53 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = X1 ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ).
cnf(c0,plain,
inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = X1,
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(inverse(multiply(X3,inverse(multiply(X1,inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4))) = multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2)),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d1,plain,
multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)) = X1,
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
X1 = multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)),
inference(superposition,[status(thm)],[c0,d0]) ).
cnf(d3,plain,
X3 = multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(inverse(X3)),inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))))),X1),
inference(superposition,[status(thm)],[d2,d2]) ).
cnf(d4,plain,
X1 = inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4))),
inference(superposition,[status(thm)],[d0,d2]) ).
cnf(d5,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))))),X1)) = X3,
inference(superposition,[status(thm)],[d1,c0]) ).
cnf(d6,plain,
multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2)))))))) = inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X1))),
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
X3 = multiply(inverse(inverse(multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,X1)))),inverse(multiply(X1,inverse(multiply(inverse(X1),X1))))),
inference(superposition,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,X2)) = multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,X2)),
inference(superposition,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X1)))),inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))) = X3,
inference(superposition,[status(thm)],[d6,d5]) ).
cnf(d10,plain,
multiply(inverse(multiply(X3,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))),multiply(X3,X4)) = multiply(X1,multiply(inverse(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2)))),X4)),
inference(superposition,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
multiply(inverse(multiply(X3,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))),multiply(X3,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[d7,d10]) ).
cnf(d12,plain,
multiply(inverse(X2),X2) = multiply(inverse(X3),X3),
inference(superposition,[status(thm)],[d11,d11]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP418-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:55:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.33/10.94 % SZS status Unsatisfiable for theBenchmark.p
% 22.33/10.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------