%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP515-1 : 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 : n018.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 32.10s 8.37s
% Output : CNFRefutation 32.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of clauses : 62 ( 62 unt; 0 nHn; 6 RR)
% Number of literals : 62 ( 61 equ; 5 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 156 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X0,multiply(multiply(X1,X2),inverse(multiply(X0,X2)))) = X1 ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ).
cnf(c0,plain,
multiply(X0,multiply(multiply(X1,X2),inverse(multiply(X0,X2)))) = X1,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausification,[status(esa)],[prove_these_axioms_3]) ).
cnf(d0,plain,
multiply(X3,multiply(X1,inverse(multiply(X3,multiply(multiply(X1,X2),inverse(multiply(X0,X2))))))) = X0,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d1,plain,
multiply(X0,multiply(X1,inverse(X1))) = X0,
inference(superposition,[status(thm)],[c0,d0]) ).
cnf(d2,plain,
multiply(X0,multiply(X1,inverse(X0))) = X1,
inference(superposition,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
multiply(multiply(X0,X1),multiply(X2,inverse(multiply(X2,X1)))) = X0,
inference(superposition,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
multiply(multiply(X0,X1),multiply(X2,inverse(X0))) = multiply(X2,X1),
inference(superposition,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
multiply(X2,multiply(X1,inverse(multiply(X2,multiply(X1,inverse(X0)))))) = X0,
inference(superposition,[status(thm)],[d2,c0]) ).
cnf(d6,plain,
multiply(X0,multiply(multiply(X1,X2),inverse(X1))) = multiply(X0,X2),
inference(superposition,[status(thm)],[c0,d5]) ).
cnf(d7,plain,
multiply(multiply(X0,X1),X2) = multiply(multiply(X0,X2),X1),
inference(superposition,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
multiply(X0,multiply(multiply(X3,multiply(multiply(X1,X2),inverse(multiply(X0,X2)))),inverse(X1))) = X3,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d9,plain,
multiply(X3,multiply(multiply(X0,inverse(X1)),multiply(multiply(X1,X2),inverse(multiply(X3,X2))))) = X0,
inference(demodulation,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
multiply(multiply(X0,inverse(X1)),X1) = X0,
inference(superposition,[status(thm)],[c0,d9]) ).
cnf(d11,plain,
multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(demodulation,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
multiply(X1,X0) = multiply(X0,X1),
inference(superposition,[status(thm)],[d11,d2]) ).
cnf(d13,plain,
multiply(X2,multiply(X0,X1)) = multiply(multiply(X0,X2),X1),
inference(superposition,[status(thm)],[d12,d7]) ).
cnf(d14,plain,
multiply(multiply(X1,X0),X2) = multiply(multiply(X0,X2),X1),
inference(superposition,[status(thm)],[d12,d7]) ).
cnf(d15,plain,
multiply(X1,multiply(X0,X2)) = multiply(multiply(X1,X2),X0),
inference(demodulation,[status(thm)],[d14,d13]) ).
cnf(d16,plain,
multiply(multiply(X1,inverse(X1)),X0) = X0,
inference(superposition,[status(thm)],[d3,d9]) ).
cnf(d17,plain,
X0 = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d11,d16]) ).
cnf(d18,plain,
multiply(X0,inverse(inverse(X1))) = multiply(X0,X1),
inference(superposition,[status(thm)],[d11,d11]) ).
cnf(d19,plain,
multiply(X1,X0) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d18,d17]) ).
cnf(d20,plain,
multiply(multiply(X0,X2),X1) = multiply(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[d7,d19]) ).
cnf(d21,plain,
multiply(X0,multiply(X2,X1)) = multiply(multiply(X0,X2),X1),
inference(demodulation,[status(thm)],[d20,d15]) ).
cnf(d22,plain,
multiply(X0,multiply(X2,X1)) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[d21,d15]) ).
cnf(d23,plain,
X1 = multiply(multiply(X0,X1),inverse(X0)),
inference(superposition,[status(thm)],[d16,d7]) ).
cnf(d24,plain,
X1 = multiply(inverse(X0),multiply(X0,X1)),
inference(demodulation,[status(thm)],[d23,d12]) ).
cnf(d25,plain,
multiply(X1,inverse(multiply(X1,inverse(X0)))) = X0,
inference(superposition,[status(thm)],[d16,c0]) ).
cnf(d26,plain,
inverse(multiply(X0,inverse(X1))) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d25,d24]) ).
cnf(d27,plain,
multiply(inverse(X0),multiply(X1,X0)) = X1,
inference(superposition,[status(thm)],[d17,d2]) ).
cnf(d28,plain,
multiply(inverse(multiply(X1,X0)),X1) = inverse(X0),
inference(superposition,[status(thm)],[d27,d27]) ).
cnf(d29,plain,
multiply(X0,inverse(multiply(X0,X1))) = inverse(X1),
inference(demodulation,[status(thm)],[d28,d12]) ).
cnf(d30,plain,
multiply(X0,multiply(X3,inverse(multiply(X0,X1)))) = multiply(X3,multiply(X2,inverse(multiply(X2,X1)))),
inference(superposition,[status(thm)],[d3,d4]) ).
cnf(d31,plain,
multiply(X2,multiply(X3,inverse(multiply(X2,X1)))) = multiply(X3,inverse(X1)),
inference(demodulation,[status(thm)],[d30,d29]) ).
cnf(d32,plain,
multiply(X3,multiply(X4,inverse(multiply(X3,multiply(multiply(X4,multiply(multiply(X1,X2),inverse(X1))),inverse(multiply(X0,X2))))))) = X0,
inference(superposition,[status(thm)],[d6,d0]) ).
cnf(d33,plain,
multiply(X1,inverse(multiply(multiply(X1,multiply(multiply(X2,X3),inverse(X2))),inverse(multiply(X4,X3))))) = X4,
inference(demodulation,[status(thm)],[d32,d31]) ).
cnf(d34,plain,
multiply(X0,multiply(inverse(multiply(X0,multiply(multiply(X1,X2),inverse(X1)))),multiply(X3,X2))) = X3,
inference(demodulation,[status(thm)],[d33,d26]) ).
cnf(d35,plain,
multiply(X2,multiply(inverse(multiply(X2,multiply(inverse(X0),multiply(X0,X1)))),multiply(X3,X1))) = X3,
inference(demodulation,[status(thm)],[d34,d12]) ).
cnf(d36,plain,
multiply(X2,multiply(inverse(multiply(X2,X1)),multiply(X3,X1))) = X3,
inference(demodulation,[status(thm)],[d35,d24]) ).
cnf(d37,plain,
multiply(X3,multiply(multiply(multiply(X0,X2),X1),inverse(multiply(X3,X2)))) = multiply(X0,X1),
inference(superposition,[status(thm)],[d7,c0]) ).
cnf(d38,plain,
multiply(multiply(multiply(X1,X2),X3),inverse(X2)) = multiply(X1,X3),
inference(demodulation,[status(thm)],[d37,d31]) ).
cnf(d39,plain,
multiply(inverse(X1),multiply(multiply(X0,X1),X2)) = multiply(X0,X2),
inference(demodulation,[status(thm)],[d38,d12]) ).
cnf(d40,plain,
multiply(X0,multiply(X2,X1)) = multiply(X2,multiply(X0,X1)),
inference(superposition,[status(thm)],[d39,d36]) ).
cnf(d41,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm)],[c1,d12]) ).
cnf(d42,plain,
multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm)],[d41,d40]) ).
cnf(d43,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm)],[d42,d22]) ).
cnf(d44,plain,
inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[d16,d11]) ).
cnf(d45,plain,
X1 = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d44,d24]) ).
cnf(d46,plain,
multiply(X1,multiply(X2,inverse(X0))) = multiply(X2,multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[d2,d4]) ).
cnf(d47,plain,
multiply(X2,multiply(X3,inverse(X0))) = multiply(X3,multiply(X1,inverse(multiply(X0,multiply(X1,inverse(X2)))))),
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d48,plain,
multiply(multiply(X3,multiply(X1,inverse(multiply(X0,multiply(X1,inverse(X2)))))),multiply(X0,inverse(X2))) = X3,
inference(superposition,[status(thm)],[d5,d3]) ).
cnf(d49,plain,
multiply(multiply(X0,multiply(X2,inverse(X3))),multiply(X1,inverse(multiply(X2,multiply(X1,inverse(X3)))))) = X0,
inference(demodulation,[status(thm)],[d48,d7]) ).
cnf(d50,plain,
multiply(X2,multiply(multiply(X0,multiply(X1,inverse(X2))),inverse(X1))) = X0,
inference(demodulation,[status(thm)],[d49,d47]) ).
cnf(d51,plain,
multiply(X2,multiply(multiply(X0,inverse(X1)),multiply(X1,inverse(X2)))) = X0,
inference(demodulation,[status(thm)],[d50,d7]) ).
cnf(d52,plain,
multiply(X2,multiply(X1,multiply(multiply(X0,inverse(X1)),inverse(X2)))) = X0,
inference(demodulation,[status(thm)],[d51,d46]) ).
cnf(d53,plain,
multiply(multiply(X1,inverse(inverse(X0))),inverse(X0)) = X1,
inference(superposition,[status(thm)],[d52,d45]) ).
cnf(d54,plain,
multiply(multiply(X0,inverse(X1)),inverse(inverse(X1))) = X0,
inference(demodulation,[status(thm)],[d53,d7]) ).
cnf(d55,plain,
multiply(inverse(inverse(X1)),multiply(X0,inverse(X1))) = X0,
inference(demodulation,[status(thm)],[d54,d12]) ).
cnf(d56,plain,
X1 = X1,
inference(demodulation,[status(thm)],[d55,d27]) ).
cnf(d57,plain,
$false,
inference(resolution,[status(thm)],[d56,d43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP515-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n018.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 15:00:20 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.10/8.37 % SZS status Unsatisfiable for theBenchmark.p
% 32.10/8.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------