%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP412-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 42.12s 9.82s
% Output : CNFRefutation 42.12s
% 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 : 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 : 55 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X0,inverse(X1))),X2))),X1))) = X2 ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ).
cnf(c0,plain,
multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X0,inverse(X1))),X2))),X1))) = X2,
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(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(X3)),X1))) = inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),inverse(X2))),X3))),X2)),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d1,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(X3)),X2)))) = X3,
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
inverse(multiply(multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),inverse(X3))),multiply(inverse(multiply(X0,inverse(X1))),X2)))),X3)) = X2,
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d3,plain,
multiply(inverse(multiply(X4,inverse(X0))),multiply(X4,X3)) = multiply(inverse(multiply(inverse(multiply(X1,inverse(X2))),inverse(X0))),multiply(inverse(multiply(X1,inverse(X2))),X3)),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
multiply(inverse(multiply(X5,inverse(X2))),multiply(X5,X3)) = multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,X3)),
inference(superposition,[status(thm)],[d3,d3]) ).
cnf(d5,plain,
multiply(inverse(X2),multiply(X0,X3)) = multiply(inverse(multiply(X4,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X0,inverse(X1))),X2))),X1)))),multiply(X4,X3)),
inference(superposition,[status(thm)],[c0,d4]) ).
cnf(d6,plain,
inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,X3)))),X2)) = X3,
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d7,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(X4,X2)),multiply(X4,X3)),
inference(superposition,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
multiply(X2,multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(X1,inverse(X0))),multiply(X1,X2)))),X3)) = multiply(inverse(multiply(X4,X0)),multiply(X4,X3)),
inference(superposition,[status(thm)],[d6,d7]) ).
cnf(d9,plain,
multiply(inverse(multiply(X3,inverse(X0))),multiply(X3,inverse(multiply(X2,X0)))) = multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(multiply(inverse(X0),X0),inverse(X1))),X2))),X1),
inference(superposition,[status(thm)],[c0,d1]) ).
cnf(d10,plain,
multiply(multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(multiply(multiply(inverse(X1),X1),inverse(X3))),multiply(multiply(inverse(X1),X1),inverse(X2))))),X3) = X2,
inference(superposition,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
multiply(inverse(X2),X2) = multiply(inverse(multiply(X3,X0)),multiply(X3,X0)),
inference(superposition,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
multiply(inverse(X3),X3) = multiply(inverse(X2),X2),
inference(superposition,[status(thm)],[d11,d11]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP412-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n006.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Fri Sep 25 14:52:41 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 42.12/9.82 % SZS status Unsatisfiable for theBenchmark.p
% 42.12/9.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------