%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP061-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 07:22:14 AM UTC 2026
% Result : Unsatisfiable 15.60s 50.39s
% Output : CNFRefutation 15.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 2
% Syntax : Number of clauses : 50 ( 44 unt; 0 nHn; 8 RR)
% Number of literals : 58 ( 57 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 159 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X0,X2))))))) = X3 ).
cnf(prove_these_axioms,negated_conjecture,
( 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,
inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X0,X2))))))) = X3,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
( 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,
inverse(multiply(X1,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X0,X2))))),X3)))) = X0,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d1,plain,
inverse(multiply(X1,multiply(X5,multiply(multiply(inverse(X5),multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),X2),inverse(multiply(X3,multiply(X4,X2))))),X3)),X4)))) = X0,
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
inverse(multiply(X4,multiply(X5,multiply(multiply(inverse(X5),multiply(multiply(inverse(X4),multiply(multiply(X3,X6),inverse(multiply(X7,multiply(X8,X6))))),X7)),X8)))) = multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X0,X2)))))),
inference(superposition,[status(thm)],[c0,d1]) ).
cnf(d3,plain,
multiply(X6,multiply(X7,multiply(multiply(inverse(X7),X8),inverse(multiply(inverse(X2),multiply(X6,X8)))))) = X2,
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
inverse(multiply(X0,multiply(X4,multiply(multiply(inverse(X4),multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(inverse(X3),multiply(X0,X2)))))),inverse(multiply(X5,X3)))))) = X5,
inference(superposition,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
X2 = multiply(X6,multiply(X7,multiply(multiply(inverse(X7),X8),inverse(multiply(inverse(X2),multiply(X6,X8)))))),
inference(superposition,[status(thm)],[d1,d2]) ).
cnf(d6,plain,
inverse(multiply(inverse(X0),multiply(X0,multiply(X3,inverse(multiply(X4,X3)))))) = X4,
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
multiply(X0,multiply(X3,multiply(multiply(inverse(X3),multiply(X1,inverse(multiply(X2,X1)))),X2))) = X0,
inference(superposition,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
multiply(X3,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(X0,multiply(X1,inverse(multiply(X2,X1)))),X2)),inverse(X0)))) = X3,
inference(superposition,[status(thm)],[d6,d7]) ).
cnf(d9,plain,
multiply(X3,multiply(X4,multiply(multiply(inverse(X4),X5),inverse(multiply(X2,multiply(X3,X5)))))) = multiply(inverse(X0),multiply(X0,multiply(X1,inverse(multiply(X2,X1))))),
inference(superposition,[status(thm)],[d6,d3]) ).
cnf(d10,plain,
X3 = multiply(inverse(X4),multiply(X4,multiply(X5,inverse(multiply(inverse(X3),X5))))),
inference(superposition,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
multiply(X4,multiply(multiply(X0,multiply(X1,inverse(multiply(multiply(X2,inverse(multiply(inverse(X3),X2))),X1)))),multiply(X3,inverse(X0)))) = X4,
inference(superposition,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
multiply(X3,multiply(X0,multiply(inverse(X0),inverse(multiply(inverse(X1),X1))))) = X3,
inference(superposition,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
X3 = inverse(multiply(X4,multiply(X5,multiply(multiply(inverse(X5),multiply(multiply(inverse(X4),multiply(multiply(inverse(X3),X6),inverse(multiply(X7,multiply(X8,X6))))),X7)),X8)))),
inference(superposition,[status(thm)],[d2,d5]) ).
cnf(d14,plain,
inverse(multiply(X6,multiply(X7,multiply(multiply(inverse(X7),multiply(multiply(inverse(X6),multiply(multiply(X2,X8),inverse(multiply(X9,multiply(X10,X8))))),X9)),X10)))) = multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X5,X3))))),X4)),X5))),
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d15,plain,
X2 = inverse(inverse(multiply(X6,multiply(X7,multiply(multiply(inverse(X7),multiply(multiply(inverse(X6),multiply(multiply(X2,X8),inverse(multiply(X9,multiply(X10,X8))))),X9)),X10))))),
inference(superposition,[status(thm)],[d14,d13]) ).
cnf(d16,plain,
X2 = inverse(multiply(X6,multiply(X7,multiply(multiply(inverse(X7),X8),inverse(multiply(X2,multiply(X6,X8))))))),
inference(superposition,[status(thm)],[d2,d15]) ).
cnf(d17,plain,
X3 = inverse(multiply(inverse(X4),multiply(X4,multiply(X5,inverse(multiply(X3,X5)))))),
inference(superposition,[status(thm)],[d9,d16]) ).
cnf(d18,plain,
X0 = multiply(inverse(X3),multiply(X3,multiply(multiply(X0,multiply(X1,inverse(multiply(X2,X1)))),X2))),
inference(superposition,[status(thm)],[d17,d10]) ).
cnf(d19,plain,
multiply(inverse(X1),X1) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[d11,d18]) ).
cnf(d20,plain,
multiply(X2,multiply(inverse(multiply(inverse(X0),X0)),multiply(inverse(X1),X1))) = X2,
inference(superposition,[status(thm)],[d19,d12]) ).
cnf(d21,plain,
multiply(X2,inverse(multiply(inverse(X0),X0))) = X2,
inference(superposition,[status(thm)],[d20,d20]) ).
cnf(d22,plain,
multiply(inverse(X4),multiply(X4,multiply(X5,inverse(multiply(inverse(X3),X5))))) = X3,
inference(superposition,[status(thm)],[d9,d3]) ).
cnf(d23,plain,
inverse(multiply(inverse(X3),multiply(X3,multiply(multiply(X0,multiply(X1,inverse(multiply(X2,X1)))),X2)))) = inverse(X0),
inference(superposition,[status(thm)],[d6,d6]) ).
cnf(d24,plain,
multiply(inverse(X4),multiply(X4,multiply(multiply(X0,multiply(multiply(X1,multiply(X2,inverse(multiply(X3,X2)))),X3)),inverse(X1)))) = X0,
inference(superposition,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
multiply(inverse(X3),multiply(X3,multiply(X0,inverse(multiply(inverse(X1),X1))))) = X0,
inference(superposition,[status(thm)],[d11,d24]) ).
cnf(d26,plain,
multiply(inverse(X2),multiply(X2,X0)) = X0,
inference(demodulation,[status(thm)],[d25,d21]) ).
cnf(d27,plain,
multiply(X1,inverse(multiply(inverse(X2),X1))) = X2,
inference(demodulation,[status(thm)],[d22,d26]) ).
cnf(d28,plain,
multiply(inverse(X0),X1) = inverse(multiply(inverse(X1),X0)),
inference(superposition,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(superposition,[status(thm)],[d26,d27]) ).
cnf(d30,plain,
multiply(X2,multiply(inverse(X1),X1)) = X2,
inference(superposition,[status(thm)],[d19,d20]) ).
cnf(d31,plain,
X0 = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d26,d30]) ).
cnf(d32,plain,
multiply(multiply(X1,inverse(X0)),X0) = X1,
inference(superposition,[status(thm)],[d31,d29]) ).
cnf(d33,plain,
multiply(inverse(X1),X1) = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[d31,d19]) ).
cnf(d34,plain,
multiply(multiply(inverse(X1),X1),X0) = X0,
inference(superposition,[status(thm)],[d33,d32]) ).
cnf(d35,plain,
multiply(X2,multiply(X0,inverse(multiply(inverse(X1),multiply(X2,X0))))) = X1,
inference(superposition,[status(thm)],[d34,d3]) ).
cnf(d36,plain,
multiply(X1,multiply(X2,multiply(inverse(multiply(X1,X2)),X0))) = X0,
inference(demodulation,[status(thm)],[d35,d28]) ).
cnf(d37,plain,
multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[d26,d36]) ).
cnf(d38,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2 ),
inference(resolution,[status(thm)],[d19,c1]) ).
cnf(d39,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(b2),multiply(b2,a2)) != a2 ),
inference(demodulation,[status(thm)],[d38,d37]) ).
cnf(d40,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(demodulation,[status(thm)],[d39,d26]) ).
cnf(d41,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(demodulation,[status(thm)],[d40,d37]) ).
cnf(d42,plain,
inverse(multiply(X1,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X1),X2),inverse(multiply(inverse(X3),multiply(X0,X2))))),inverse(X3))))) = X0,
inference(superposition,[status(thm)],[d3,c0]) ).
cnf(d43,plain,
X4 = X4,
inference(demodulation,[status(thm)],[d42,d0]) ).
cnf(d44,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(resolution,[status(thm)],[d43,d41]) ).
cnf(d45,plain,
$false,
inference(equality_resolution,[status(thm)],[d44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP061-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.46 % Computer : n017.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Fri Sep 25 14:15:47 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.60/50.39 % SZS status Unsatisfiable for theBenchmark.p
% 15.60/50.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------