%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP509-1 : 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 : n020.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 28.62s 7.70s
% Output : CNFRefutation 28.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 5 RR)
% Number of literals : 33 ( 32 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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 : 74 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(multiply(multiply(X0,X1),X2),inverse(multiply(X0,X2))) = X1 ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ).
cnf(c0,plain,
multiply(multiply(multiply(X0,X1),X2),inverse(multiply(X0,X2))) = X1,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(clausification,[status(esa)],[prove_these_axioms_1]) ).
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(multiply(X1,X3),inverse(multiply(multiply(multiply(X0,X1),X2),X3))) = inverse(multiply(X0,X2)),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d4,plain,
inverse(multiply(X2,multiply(X0,X1))) = inverse(multiply(multiply(X2,X0),X1)),
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
multiply(X1,inverse(multiply(multiply(X0,X1),inverse(multiply(X0,X2))))) = X2,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d6,plain,
multiply(X3,inverse(multiply(X0,inverse(multiply(multiply(X2,multiply(X0,X1)),inverse(multiply(X2,X3))))))) = X1,
inference(superposition,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
multiply(X3,inverse(multiply(X1,inverse(multiply(X0,multiply(multiply(X1,X2),inverse(multiply(X0,X3)))))))) = X2,
inference(demodulation,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
inverse(multiply(X1,inverse(multiply(X1,X2)))) = X2,
inference(demodulation,[status(thm)],[d5,d2]) ).
cnf(d9,plain,
multiply(X2,multiply(multiply(X0,X1),inverse(multiply(X0,X2)))) = X1,
inference(superposition,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
multiply(X0,inverse(multiply(X0,inverse(X1)))) = X1,
inference(superposition,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
multiply(X1,inverse(X0)) = inverse(multiply(X0,inverse(X1))),
inference(superposition,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
multiply(X1,X2) = inverse(multiply(X0,inverse(multiply(multiply(X0,X1),X2)))),
inference(superposition,[status(thm)],[d8,d2]) ).
cnf(d13,plain,
multiply(X1,X2) = inverse(multiply(X0,inverse(multiply(X0,multiply(X1,X2))))),
inference(demodulation,[status(thm)],[d12,d4]) ).
cnf(d14,plain,
multiply(X1,X2) = multiply(X1,X2),
inference(demodulation,[status(thm)],[d13,d8]) ).
cnf(d15,plain,
X1 = multiply(X0,inverse(multiply(X0,inverse(X1)))),
inference(superposition,[status(thm)],[d10,d14]) ).
cnf(d16,plain,
X1 = multiply(X0,multiply(X1,inverse(X0))),
inference(demodulation,[status(thm)],[d15,d11]) ).
cnf(d17,plain,
multiply(multiply(multiply(X0,X2),inverse(multiply(X0,X1))),X1) = X2,
inference(superposition,[status(thm)],[d8,c0]) ).
cnf(d18,plain,
X1 = inverse(multiply(X0,inverse(multiply(X0,X1)))),
inference(superposition,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
X1 = multiply(multiply(X0,X1),inverse(X0)),
inference(demodulation,[status(thm)],[d18,d11]) ).
cnf(d20,plain,
multiply(X0,inverse(multiply(X0,X1))) = inverse(X1),
inference(superposition,[status(thm)],[d19,d11]) ).
cnf(d21,plain,
X0 = multiply(multiply(X0,X1),inverse(X1)),
inference(superposition,[status(thm)],[d20,d16]) ).
cnf(d22,plain,
multiply(X1,X0) = multiply(X0,X1),
inference(superposition,[status(thm)],[d21,d9]) ).
cnf(d23,plain,
multiply(b1,inverse(b1)) != multiply(inverse(a1),a1),
inference(demodulation,[status(thm)],[c1,d22]) ).
cnf(d24,plain,
multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)),
inference(demodulation,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
multiply(X1,inverse(multiply(X0,inverse(X0)))) = X1,
inference(superposition,[status(thm)],[d19,c0]) ).
cnf(d26,plain,
multiply(X1,multiply(X0,inverse(X0))) = X1,
inference(demodulation,[status(thm)],[d25,d11]) ).
cnf(d27,plain,
multiply(X1,inverse(X1)) = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[d26,d19]) ).
cnf(d28,plain,
$false,
inference(resolution,[status(thm)],[d27,d24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP509-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n020.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 14:58:35 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.62/7.70 % SZS status Unsatisfiable for theBenchmark.p
% 28.62/7.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------