%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP511-1 : 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 8.68s 7.78s
% Output : CNFRefutation 8.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 2
% Syntax : Number of clauses : 41 ( 41 unt; 0 nHn; 6 RR)
% Number of literals : 41 ( 40 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 92 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(multiply(multiply(X0,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(multiply(multiply(X0,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(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,
inverse(multiply(X1,inverse(multiply(X1,X2)))) = X2,
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
multiply(X1,X2) = inverse(multiply(X0,inverse(multiply(multiply(X0,X1),X2)))),
inference(superposition,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
multiply(X0,X1) = inverse(inverse(multiply(X0,X1))),
inference(superposition,[status(thm)],[d2,d5]) ).
cnf(d7,plain,
multiply(X0,inverse(multiply(X0,X1))) = inverse(X1),
inference(superposition,[status(thm)],[d4,d6]) ).
cnf(d8,plain,
multiply(inverse(X1),inverse(X0)) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
inverse(inverse(X1)) = X1,
inference(demodulation,[status(thm)],[d4,d7]) ).
cnf(d10,plain,
multiply(inverse(X1),X0) = inverse(multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
multiply(multiply(multiply(X0,X2),inverse(multiply(X0,X1))),X1) = X2,
inference(superposition,[status(thm)],[d4,c0]) ).
cnf(d12,plain,
X1 = inverse(multiply(X0,inverse(multiply(X0,X1)))),
inference(superposition,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
X1 = inverse(inverse(X1)),
inference(demodulation,[status(thm)],[d12,d7]) ).
cnf(d14,plain,
multiply(multiply(X1,X3),inverse(multiply(multiply(multiply(X0,X1),X2),X3))) = inverse(multiply(X0,X2)),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d15,plain,
multiply(X1,X0) = inverse(inverse(multiply(X0,X1))),
inference(superposition,[status(thm)],[d14,d5]) ).
cnf(d16,plain,
multiply(X1,X0) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(superposition,[status(thm)],[d16,d7]) ).
cnf(d18,plain,
inverse(multiply(multiply(X1,inverse(X0)),X0)) = inverse(X1),
inference(superposition,[status(thm)],[d8,d17]) ).
cnf(d19,plain,
inverse(multiply(X1,multiply(X0,inverse(X1)))) = inverse(X0),
inference(demodulation,[status(thm)],[d18,d16]) ).
cnf(d20,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(d21,plain,
inverse(multiply(multiply(X2,inverse(multiply(X1,X3))),multiply(multiply(X0,X1),inverse(multiply(X0,X2))))) = X3,
inference(demodulation,[status(thm)],[d20,d8]) ).
cnf(d22,plain,
X1 = inverse(multiply(inverse(multiply(X0,X1)),X0)),
inference(superposition,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
X1 = multiply(inverse(X0),multiply(X0,X1)),
inference(demodulation,[status(thm)],[d22,d10]) ).
cnf(d24,plain,
X1 = multiply(inverse(X0),multiply(X1,X0)),
inference(superposition,[status(thm)],[d16,d23]) ).
cnf(d25,plain,
multiply(X0,inverse(X1)) = inverse(multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[d9,d8]) ).
cnf(d26,plain,
multiply(X1,inverse(inverse(multiply(X2,X3)))) = inverse(multiply(X0,inverse(multiply(multiply(X2,multiply(X0,X1)),X3)))),
inference(superposition,[status(thm)],[d2,d2]) ).
cnf(d27,plain,
multiply(X2,multiply(X0,X1)) = inverse(multiply(X3,inverse(multiply(multiply(X0,multiply(X3,X2)),X1)))),
inference(demodulation,[status(thm)],[d26,d13]) ).
cnf(d28,plain,
multiply(X2,multiply(X1,X3)) = multiply(multiply(multiply(X1,multiply(X0,X2)),X3),inverse(X0)),
inference(demodulation,[status(thm)],[d27,d25]) ).
cnf(d29,plain,
multiply(X2,multiply(X0,X3)) = multiply(inverse(X1),multiply(multiply(X0,multiply(X1,X2)),X3)),
inference(demodulation,[status(thm)],[d28,d16]) ).
cnf(d30,plain,
multiply(X1,multiply(X0,X2)) = multiply(X2,multiply(X1,X0)),
inference(superposition,[status(thm)],[d29,d24]) ).
cnf(d31,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm)],[c1,d16]) ).
cnf(d32,plain,
multiply(b3,multiply(c3,a3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm)],[d31,d30]) ).
cnf(d33,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm)],[d32,d30]) ).
cnf(d34,plain,
multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(superposition,[status(thm)],[d23,d23]) ).
cnf(d35,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d34,d13]) ).
cnf(d36,plain,
$false,
inference(resolution,[status(thm)],[d35,d33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP511-1 : 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 : n018.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
% 0.09/0.37 % DateTime : Fri Sep 25 14:59:52 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.68/7.78 % SZS status Unsatisfiable for theBenchmark.p
% 8.68/7.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------