%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP407-1 : 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 : n011.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 90.58s 18.70s
% Output : CNFRefutation 144.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 4 RR)
% Number of literals : 32 ( 31 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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 : 91 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(X1),multiply(inverse(X1),X1))))) = X2 ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2 ).
cnf(c0,plain,
multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(X1),multiply(inverse(X1),X1))))) = X2,
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(X0,inverse(multiply(inverse(X3),multiply(inverse(X1),multiply(inverse(X1),X1))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),X3)),multiply(inverse(X2),multiply(inverse(X2),X2)))),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d1,plain,
multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(X3),multiply(inverse(X1),multiply(inverse(X1),X1)))))) = X3,
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X3)),multiply(inverse(multiply(X0,X1)),X2))),multiply(inverse(X3),multiply(inverse(X3),X3)))) = X2,
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d3,plain,
multiply(inverse(multiply(X4,X2)),multiply(X4,X3)) = multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(multiply(X0,X1)),X3)),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
multiply(inverse(multiply(X5,X2)),multiply(X5,X3)) = multiply(inverse(multiply(X4,X2)),multiply(X4,X3)),
inference(superposition,[status(thm)],[d3,d3]) ).
cnf(d5,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X4,X2)),multiply(X4,X3))),multiply(inverse(X2),multiply(inverse(X2),X2)))) = X3,
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d6,plain,
multiply(X2,multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))),X3)) = multiply(inverse(multiply(X4,multiply(inverse(X1),multiply(inverse(X1),X1)))),multiply(X4,X3)),
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
multiply(X5,multiply(inverse(multiply(inverse(multiply(X6,X1)),multiply(X6,X5))),X2)) = multiply(X3,multiply(inverse(multiply(inverse(multiply(X4,X1)),multiply(X4,X3))),X2)),
inference(superposition,[status(thm)],[d6,d6]) ).
cnf(d8,plain,
multiply(inverse(multiply(X0,X1)),inverse(multiply(X2,multiply(inverse(multiply(X0,X2)),multiply(inverse(multiply(X0,X2)),multiply(X0,X2)))))) = multiply(inverse(X1),multiply(inverse(X1),X1)),
inference(superposition,[status(thm)],[d5,c0]) ).
cnf(d9,plain,
multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),multiply(inverse(X1),multiply(inverse(X1),X1))) = X2,
inference(superposition,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
multiply(inverse(X2),X2) = multiply(X3,multiply(inverse(multiply(inverse(multiply(X4,X1)),multiply(X4,X3))),multiply(inverse(X1),multiply(inverse(X1),X1)))),
inference(superposition,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
multiply(inverse(X4),X4) = multiply(inverse(X3),X3),
inference(superposition,[status(thm)],[d10,d10]) ).
cnf(d12,plain,
multiply(multiply(inverse(X0),X0),a2) != a2,
inference(superposition,[status(thm)],[d11,c1]) ).
cnf(d13,plain,
multiply(inverse(multiply(X3,X0)),multiply(X3,inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,multiply(inverse(X0),X0)))))) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d4,d1]) ).
cnf(d14,plain,
inverse(multiply(inverse(multiply(inverse(X1),X3)),multiply(inverse(X1),multiply(inverse(X1),X1)))) = inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,multiply(inverse(X1),X1)))),
inference(superposition,[status(thm)],[d13,d5]) ).
cnf(d15,plain,
inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,multiply(inverse(X0),X0)))) = inverse(multiply(inverse(multiply(X3,X1)),multiply(X3,multiply(inverse(X0),X0)))),
inference(superposition,[status(thm)],[d14,d14]) ).
cnf(d16,plain,
inverse(multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X1),multiply(inverse(X1),X1)))) = X1,
inference(superposition,[status(thm)],[d11,d5]) ).
cnf(d17,plain,
inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,multiply(inverse(X0),X0)))) = X0,
inference(superposition,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
inverse(multiply(inverse(multiply(X2,X0)),multiply(X2,multiply(inverse(X1),X1)))) = X0,
inference(superposition,[status(thm)],[d11,d17]) ).
cnf(d19,plain,
X2 = multiply(inverse(multiply(X3,X1)),multiply(X3,inverse(multiply(inverse(X2),multiply(inverse(X1),multiply(inverse(X1),X1)))))),
inference(superposition,[status(thm)],[d1,d4]) ).
cnf(d20,plain,
multiply(inverse(X0),X1) = multiply(inverse(multiply(X3,X0)),multiply(X3,inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,multiply(inverse(X0),X0)))))),
inference(superposition,[status(thm)],[d4,d19]) ).
cnf(d21,plain,
multiply(inverse(X2),X1) = multiply(inverse(multiply(X3,X2)),multiply(X3,X1)),
inference(demodulation,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
inverse(multiply(inverse(multiply(inverse(X1),X2)),multiply(inverse(X1),multiply(inverse(X1),X1)))) = X2,
inference(demodulation,[status(thm)],[d5,d21]) ).
cnf(d23,plain,
inverse(multiply(inverse(X1),multiply(inverse(X0),X0))) = X1,
inference(demodulation,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
inverse(multiply(inverse(X1),X0)) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d21,d23]) ).
cnf(d25,plain,
multiply(inverse(multiply(inverse(X1),X1)),X0) = X0,
inference(demodulation,[status(thm)],[d23,d24]) ).
cnf(d26,plain,
multiply(multiply(inverse(X0),X0),X1) = X1,
inference(demodulation,[status(thm)],[d25,d24]) ).
cnf(d27,plain,
$false,
inference(resolution,[status(thm)],[d26,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP407-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:52:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 90.58/18.70 % SZS status Unsatisfiable for theBenchmark.p
% 90.58/18.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------