%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP409-1 : 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 : n003.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 82.45s 10.96s
% Output : CNFRefutation 82.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 3 RR)
% Number of literals : 13 ( 12 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 : 37 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))),inverse(multiply(inverse(X2),X2))) = X1 ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ).
cnf(c0,plain,
multiply(multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))),inverse(multiply(inverse(X2),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,
multiply(multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,inverse(inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d1,plain,
multiply(inverse(multiply(X3,inverse(multiply(multiply(X1,inverse(multiply(inverse(X2),X2))),X2)))),multiply(X3,inverse(X2))) = X1,
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
multiply(inverse(multiply(X3,inverse(multiply(X1,X2)))),multiply(X3,inverse(X2))) = multiply(inverse(multiply(X4,inverse(multiply(X1,X2)))),multiply(X4,inverse(X2))),
inference(superposition,[status(thm)],[d0,d0]) ).
cnf(d3,plain,
multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,inverse(multiply(X0,inverse(X2))))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(X0,inverse(multiply(multiply(X1,inverse(multiply(inverse(X2),X2))),X2)))),multiply(X0,inverse(X2)))))),multiply(X4,inverse(multiply(X0,inverse(X2))))),
inference(superposition,[status(thm)],[d1,d2]) ).
cnf(d4,plain,
multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,inverse(multiply(X0,inverse(X2))))) = multiply(inverse(multiply(X4,inverse(X1))),multiply(X4,inverse(multiply(X0,inverse(X2))))),
inference(demodulation,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
multiply(inverse(multiply(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(X2))))),multiply(X0,inverse(inverse(X2)))),inverse(X3))),X1) = multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(multiply(inverse(inverse(X2)),inverse(X2))))),
inference(superposition,[status(thm)],[c0,d4]) ).
cnf(d6,plain,
multiply(inverse(X1),X1) = multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(X2)),inverse(X2))))),multiply(X3,inverse(multiply(inverse(inverse(X2)),inverse(X2))))),
inference(superposition,[status(thm)],[c0,d5]) ).
cnf(d7,plain,
multiply(inverse(X3),X3) = multiply(inverse(X2),X2),
inference(superposition,[status(thm)],[d6,d6]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP409-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n003.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 14:54:07 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 82.45/10.96 % SZS status Unsatisfiable for theBenchmark.p
% 82.45/10.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------