%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP085-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 07:22:17 AM UTC 2026
% Result : Unsatisfiable 60.74s 13.88s
% Output : CNFRefutation 60.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 2
% Syntax : Number of clauses : 82 ( 72 unt; 0 nHn; 12 RR)
% Number of literals : 103 ( 102 equ; 32 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 203 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(multiply(multiply(X0,X1),X2),inverse(multiply(X0,X2))) = X1 ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| 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(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(clausification,[status(esa)],[prove_these_axioms]) ).
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,
inverse(inverse(X1)) = X1,
inference(demodulation,[status(thm)],[d4,d7]) ).
cnf(d9,plain,
multiply(multiply(X1,X3),inverse(multiply(multiply(multiply(X0,X1),X2),X3))) = inverse(multiply(X0,X2)),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d10,plain,
multiply(X1,X0) = inverse(inverse(multiply(X0,X1))),
inference(superposition,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
multiply(X1,X0) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
multiply(inverse(X1),inverse(X0)) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[d7,d1]) ).
cnf(d13,plain,
multiply(inverse(X1),X0) = inverse(multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d8,d12]) ).
cnf(d14,plain,
inverse(multiply(X1,X0)) = multiply(inverse(X1),inverse(X0)),
inference(superposition,[status(thm)],[d12,d11]) ).
cnf(d15,plain,
inverse(multiply(X0,X1)) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
multiply(multiply(multiply(X3,X4),inverse(multiply(multiply(multiply(multiply(X0,X1),X2),X3),inverse(X1)))),inverse(inverse(multiply(X0,X2)))) = X4,
inference(superposition,[status(thm)],[d0,d0]) ).
cnf(d17,plain,
multiply(inverse(inverse(multiply(X2,X4))),multiply(multiply(X0,X1),inverse(multiply(multiply(multiply(multiply(X2,X3),X4),X0),inverse(X3))))) = X1,
inference(demodulation,[status(thm)],[d16,d11]) ).
cnf(d18,plain,
multiply(multiply(X0,X1),multiply(multiply(X2,X3),inverse(multiply(multiply(multiply(multiply(X0,X4),X1),X2),inverse(X4))))) = X3,
inference(demodulation,[status(thm)],[d17,d8]) ).
cnf(d19,plain,
multiply(multiply(X0,X2),multiply(multiply(X3,X4),inverse(multiply(inverse(X1),multiply(multiply(multiply(X0,X1),X2),X3))))) = X4,
inference(demodulation,[status(thm)],[d18,d15]) ).
cnf(d20,plain,
multiply(multiply(X1,X2),multiply(multiply(X3,X4),multiply(inverse(multiply(multiply(multiply(X1,X0),X2),X3)),X0))) = X4,
inference(demodulation,[status(thm)],[d19,d13]) ).
cnf(d21,plain,
multiply(multiply(X0,X2),multiply(multiply(X3,X4),multiply(X1,inverse(multiply(multiply(multiply(X0,X1),X2),X3))))) = X4,
inference(demodulation,[status(thm)],[d20,d11]) ).
cnf(d22,plain,
multiply(multiply(multiply(X0,X2),inverse(multiply(X0,X1))),X1) = X2,
inference(superposition,[status(thm)],[d4,c0]) ).
cnf(d23,plain,
X1 = inverse(multiply(X0,inverse(multiply(X0,X1)))),
inference(superposition,[status(thm)],[d22,d1]) ).
cnf(d24,plain,
X1 = inverse(inverse(X1)),
inference(demodulation,[status(thm)],[d23,d7]) ).
cnf(d25,plain,
inverse(multiply(multiply(inverse(X0),X1),X0)) = inverse(X1),
inference(superposition,[status(thm)],[d12,d7]) ).
cnf(d26,plain,
inverse(multiply(X0,multiply(inverse(X0),X1))) = inverse(X1),
inference(demodulation,[status(thm)],[d25,d11]) ).
cnf(d27,plain,
multiply(X0,multiply(inverse(X0),X1)) = inverse(inverse(X1)),
inference(superposition,[status(thm)],[d26,d24]) ).
cnf(d28,plain,
multiply(X1,multiply(inverse(X1),X0)) = X0,
inference(demodulation,[status(thm)],[d27,d8]) ).
cnf(d29,plain,
multiply(X0,multiply(X1,inverse(X0))) = X1,
inference(superposition,[status(thm)],[d11,d28]) ).
cnf(d30,plain,
multiply(multiply(X0,X2),X1) = multiply(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[d29,d21]) ).
cnf(d31,plain,
multiply(multiply(X0,X2),X1) = multiply(X2,multiply(X0,X1)),
inference(superposition,[status(thm)],[d30,d11]) ).
cnf(d32,plain,
multiply(multiply(X1,X0),X2) = multiply(multiply(X0,X2),X1),
inference(superposition,[status(thm)],[d11,d30]) ).
cnf(d33,plain,
multiply(X1,multiply(X0,X2)) = multiply(multiply(X1,X2),X0),
inference(demodulation,[status(thm)],[d32,d31]) ).
cnf(d34,plain,
multiply(X0,multiply(X2,X1)) = multiply(X2,multiply(X0,X1)),
inference(superposition,[status(thm)],[d33,d11]) ).
cnf(d35,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2 ),
inference(resolution,[status(thm)],[d11,c1]) ).
cnf(d36,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(b2,multiply(inverse(b2),a2)) != a2 ),
inference(demodulation,[status(thm)],[d35,d31]) ).
cnf(d37,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(demodulation,[status(thm)],[d36,d28]) ).
cnf(d38,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(demodulation,[status(thm)],[d37,d31]) ).
cnf(d39,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(demodulation,[status(thm)],[d38,d34]) ).
cnf(d40,plain,
( multiply(a1,inverse(a1)) != multiply(inverse(b1),b1)
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(demodulation,[status(thm)],[d39,d11]) ).
cnf(d41,plain,
( multiply(a1,inverse(a1)) != multiply(b1,inverse(b1))
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(demodulation,[status(thm)],[d40,d11]) ).
cnf(d42,plain,
multiply(X0,inverse(X1)) = inverse(multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[d8,d12]) ).
cnf(d43,plain,
multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(superposition,[status(thm)],[d28,d28]) ).
cnf(d44,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d43,d8]) ).
cnf(d45,plain,
inverse(X1) = multiply(X0,inverse(multiply(X0,X1))),
inference(superposition,[status(thm)],[d7,d44]) ).
cnf(d46,plain,
multiply(inverse(multiply(X1,X2)),inverse(X0)) = inverse(multiply(multiply(X1,X0),X2)),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d47,plain,
inverse(multiply(X2,multiply(X0,X1))) = inverse(multiply(multiply(X0,X2),X1)),
inference(demodulation,[status(thm)],[d46,d12]) ).
cnf(d48,plain,
multiply(multiply(multiply(X0,X3),inverse(multiply(multiply(X1,X0),inverse(multiply(X1,X2))))),inverse(X2)) = X3,
inference(superposition,[status(thm)],[d3,c0]) ).
cnf(d49,plain,
multiply(inverse(X3),multiply(multiply(X0,X1),inverse(multiply(multiply(X2,X0),inverse(multiply(X2,X3)))))) = X1,
inference(demodulation,[status(thm)],[d48,d11]) ).
cnf(d50,plain,
multiply(inverse(X2),multiply(multiply(X1,X3),multiply(multiply(X0,X2),inverse(multiply(X0,X1))))) = X3,
inference(demodulation,[status(thm)],[d49,d42]) ).
cnf(d51,plain,
multiply(inverse(X1),multiply(X0,X1)) = X0,
inference(superposition,[status(thm)],[d29,d50]) ).
cnf(d52,plain,
inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(superposition,[status(thm)],[d14,d11]) ).
cnf(d53,plain,
multiply(inverse(inverse(X1)),inverse(multiply(X1,X0))) = inverse(X0),
inference(superposition,[status(thm)],[d52,d51]) ).
cnf(d54,plain,
inverse(multiply(multiply(X0,X1),inverse(X0))) = inverse(X1),
inference(demodulation,[status(thm)],[d53,d12]) ).
cnf(d55,plain,
inverse(multiply(X1,multiply(X0,inverse(X0)))) = inverse(X1),
inference(demodulation,[status(thm)],[d54,d47]) ).
cnf(d56,plain,
inverse(multiply(X1,inverse(X1))) = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[d55,d45]) ).
cnf(d57,plain,
multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(demodulation,[status(thm)],[d56,d42]) ).
cnf(d58,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(resolution,[status(thm)],[d57,d41]) ).
cnf(d59,plain,
multiply(X0,multiply(X1,inverse(X1))) = X0,
inference(superposition,[status(thm)],[d57,d29]) ).
cnf(d60,plain,
X1 = multiply(inverse(X0),multiply(X1,X0)),
inference(superposition,[status(thm)],[d51,d44]) ).
cnf(d61,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(d62,plain,
multiply(X2,multiply(X0,X1)) = inverse(multiply(X3,inverse(multiply(multiply(X0,multiply(X3,X2)),X1)))),
inference(demodulation,[status(thm)],[d61,d8]) ).
cnf(d63,plain,
multiply(X2,multiply(X1,X3)) = multiply(multiply(multiply(X1,multiply(X0,X2)),X3),inverse(X0)),
inference(demodulation,[status(thm)],[d62,d42]) ).
cnf(d64,plain,
multiply(X2,multiply(X0,X3)) = multiply(inverse(X1),multiply(multiply(X0,multiply(X1,X2)),X3)),
inference(demodulation,[status(thm)],[d63,d11]) ).
cnf(d65,plain,
multiply(X1,multiply(X0,X2)) = multiply(X2,multiply(X1,X0)),
inference(superposition,[status(thm)],[d64,d60]) ).
cnf(d66,plain,
multiply(X1,multiply(X0,X2)) = multiply(X2,multiply(X0,X1)),
inference(superposition,[status(thm)],[d31,d11]) ).
cnf(d67,plain,
multiply(X2,multiply(X1,X0)) = multiply(X2,multiply(X0,X1)),
inference(superposition,[status(thm)],[d66,d65]) ).
cnf(d68,plain,
multiply(multiply(multiply(multiply(inverse(multiply(X1,X2)),X3),X4),inverse(multiply(X0,X3))),inverse(inverse(multiply(multiply(X1,X0),X2)))) = X4,
inference(superposition,[status(thm)],[d2,d0]) ).
cnf(d69,plain,
multiply(inverse(inverse(multiply(multiply(X0,X4),X1))),multiply(multiply(multiply(inverse(multiply(X0,X1)),X2),X3),inverse(multiply(X4,X2)))) = X3,
inference(demodulation,[status(thm)],[d68,d11]) ).
cnf(d70,plain,
multiply(multiply(multiply(X0,X1),X2),multiply(multiply(multiply(inverse(multiply(X0,X2)),X3),X4),inverse(multiply(X1,X3)))) = X4,
inference(demodulation,[status(thm)],[d69,d8]) ).
cnf(d71,plain,
X2 = multiply(multiply(X0,multiply(inverse(multiply(X0,X1)),X2)),X1),
inference(superposition,[status(thm)],[d70,d59]) ).
cnf(d72,plain,
X2 = multiply(multiply(inverse(multiply(X0,X1)),X2),multiply(X0,X1)),
inference(demodulation,[status(thm)],[d71,d31]) ).
cnf(d73,plain,
X2 = multiply(X2,multiply(inverse(multiply(X0,X1)),multiply(X0,X1))),
inference(demodulation,[status(thm)],[d72,d31]) ).
cnf(d74,plain,
X0 = multiply(X0,multiply(multiply(X1,X2),inverse(multiply(X1,X2)))),
inference(demodulation,[status(thm)],[d73,d67]) ).
cnf(d75,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d74,d59]) ).
cnf(d76,plain,
a2 != a2,
inference(resolution,[status(thm)],[d75,d58]) ).
cnf(d77,plain,
$false,
inference(equality_resolution,[status(thm)],[d76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP085-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n006.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 14:21:25 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 60.74/13.88 % SZS status Unsatisfiable for theBenchmark.p
% 60.74/13.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------