%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP510-1 : 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 : n017.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 07:23:55 AM UTC 2026
% Result : Unsatisfiable 8.36s 3.29s
% Output : CNFRefutation 8.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 3 RR)
% Number of literals : 28 ( 27 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 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 : 67 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(multiply(multiply(X0,X1),X2),inverse(multiply(X0,X2))) = X1 ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2 ).
cnf(c0,plain,
multiply(multiply(multiply(X0,X1),X2),inverse(multiply(X0,X2))) = X1,
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,
multiply(multiply(multiply(multiply(multiply(X0,X1),X2),X3),inverse(multiply(X0,X2))),inverse(X1)) = X3,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d1,plain,
multiply(multiply(X1,inverse(multiply(X0,X2))),inverse(X1)) = inverse(multiply(X0,X2)),
inference(superposition,[status(thm)],[c0,d0]) ).
cnf(d2,plain,
multiply(X1,inverse(multiply(multiply(X0,X1),X2))) = inverse(multiply(X0,X2)),
inference(superposition,[status(thm)],[c0,d1]) ).
cnf(d3,plain,
multiply(X1,inverse(multiply(multiply(X0,X1),inverse(multiply(X0,X2))))) = X2,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d4,plain,
multiply(X3,inverse(multiply(multiply(X0,X3),inverse(X2)))) = inverse(multiply(multiply(X1,X0),inverse(multiply(X1,X2)))),
inference(superposition,[status(thm)],[d3,d3]) ).
cnf(d5,plain,
inverse(multiply(X1,inverse(X2))) = inverse(multiply(multiply(X3,X1),inverse(multiply(X3,X2)))),
inference(demodulation,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
multiply(inverse(multiply(multiply(X1,X0),inverse(multiply(X1,X2)))),inverse(multiply(X2,inverse(multiply(X0,X3))))) = X3,
inference(superposition,[status(thm)],[d3,d3]) ).
cnf(d7,plain,
multiply(inverse(multiply(X1,inverse(X2))),inverse(multiply(X2,inverse(multiply(X1,X3))))) = X3,
inference(demodulation,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
inverse(multiply(X1,inverse(multiply(X1,X2)))) = X2,
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d9,plain,
multiply(inverse(multiply(X0,inverse(X0))),X1) = X1,
inference(superposition,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
X1 = inverse(multiply(X0,inverse(multiply(X0,X1)))),
inference(superposition,[status(thm)],[d7,d9]) ).
cnf(d11,plain,
multiply(X3,inverse(multiply(X0,inverse(multiply(multiply(X2,multiply(X0,X1)),inverse(multiply(X2,X3))))))) = X1,
inference(superposition,[status(thm)],[d3,c0]) ).
cnf(d12,plain,
multiply(X3,inverse(multiply(X1,inverse(multiply(multiply(X1,X2),inverse(X3)))))) = X2,
inference(demodulation,[status(thm)],[d11,d5]) ).
cnf(d13,plain,
inverse(multiply(multiply(X0,X1),inverse(X0))) = inverse(X1),
inference(superposition,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
multiply(multiply(X2,X3),inverse(multiply(X0,X3))) = inverse(multiply(multiply(X1,X0),inverse(multiply(X1,X2)))),
inference(superposition,[status(thm)],[d3,c0]) ).
cnf(d15,plain,
multiply(multiply(X2,X3),inverse(multiply(X1,X3))) = inverse(multiply(X1,inverse(X2))),
inference(demodulation,[status(thm)],[d14,d5]) ).
cnf(d16,plain,
inverse(inverse(multiply(multiply(X0,X1),inverse(X0)))) = X1,
inference(superposition,[status(thm)],[d15,d8]) ).
cnf(d17,plain,
inverse(inverse(X1)) = X1,
inference(demodulation,[status(thm)],[d16,d13]) ).
cnf(d18,plain,
multiply(inverse(inverse(multiply(X0,inverse(X0)))),X2) = X2,
inference(superposition,[status(thm)],[d15,d9]) ).
cnf(d19,plain,
multiply(multiply(X0,inverse(X0)),X1) = X1,
inference(demodulation,[status(thm)],[d18,d17]) ).
cnf(d20,plain,
X1 = inverse(inverse(multiply(multiply(X0,X1),inverse(X0)))),
inference(superposition,[status(thm)],[d15,d10]) ).
cnf(d21,plain,
X1 = inverse(inverse(X1)),
inference(demodulation,[status(thm)],[d20,d13]) ).
cnf(d22,plain,
multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
$false,
inference(resolution,[status(thm)],[d22,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP510-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n017.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Fri Sep 25 14:53:03 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.36/3.29 % SZS status Unsatisfiable for theBenchmark.p
% 8.36/3.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------