%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO070-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 06:54:46 AM UTC 2026
% Result : Unsatisfiable 20.02s 18.05s
% Output : CNFRefutation 20.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 2
% Syntax : Number of clauses : 38 ( 38 unt; 0 nHn; 3 RR)
% Number of literals : 38 ( 37 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 168 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,X4),X5,multiply(X2,X3,X6))),multiply(X3,multiply(X6,X5,X4),X2)) = X1 ).
cnf(prove_tba_axioms_4,negated_conjecture,
multiply(a,a,b) != a ).
cnf(c0,plain,
multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,X4),X5,multiply(X2,X3,X6))),multiply(X3,multiply(X6,X5,X4),X2)) = X1,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(a,a,b) != a,
inference(clausification,[status(esa)],[prove_tba_axioms_4]) ).
cnf(d0,plain,
multiply(multiply(X0,X1,X3),inverse(multiply(multiply(X4,X5,X6),X7,multiply(X4,X5,X8))),multiply(X5,multiply(X8,X7,X6),X4)) = multiply(X1,multiply(X3,inverse(multiply(X0,X1,X2)),X2),X0),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d1,plain,
X1 = multiply(inverse(X0),multiply(X1,inverse(multiply(X0,inverse(X0),X7)),X7),X0),
inference(superposition,[status(thm)],[c0,d0]) ).
cnf(d2,plain,
X1 = multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X3,X4,X5),X6,multiply(X3,X4,X7))),multiply(X4,multiply(X7,X6,X5),X3)),
inference(superposition,[status(thm)],[d0,d1]) ).
cnf(d3,plain,
X3 = multiply(multiply(X4,inverse(X4),X3),inverse(multiply(multiply(X0,inverse(X0),X2),inverse(multiply(X0,inverse(X0),X2)),multiply(X0,inverse(X0),X1))),X1),
inference(superposition,[status(thm)],[d1,d2]) ).
cnf(d4,plain,
X3 = multiply(multiply(X4,inverse(X4),X3),inverse(multiply(X0,inverse(X0),multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X0,inverse(X0),X1)),X2))),X2),
inference(superposition,[status(thm)],[d3,d3]) ).
cnf(d5,plain,
multiply(inverse(X0),multiply(X1,inverse(multiply(X0,inverse(X0),X7)),X7),X0) = X1,
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d6,plain,
multiply(multiply(X7,inverse(X7),X8),inverse(multiply(multiply(X9,X10,multiply(X3,multiply(X6,X5,X4),X2)),inverse(multiply(multiply(X2,X3,X4),X5,multiply(X2,X3,X6))),multiply(X9,X10,multiply(X0,inverse(X0),X1)))),multiply(X10,X1,X9)) = X8,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d7,plain,
multiply(multiply(X3,inverse(X3),X4),inverse(multiply(multiply(X0,inverse(X0),X2),inverse(multiply(X0,inverse(X0),X2)),multiply(X0,inverse(X0),X1))),X1) = X4,
inference(superposition,[status(thm)],[d5,c0]) ).
cnf(d8,plain,
multiply(multiply(X5,inverse(X5),X6),inverse(multiply(inverse(X1),multiply(multiply(X0,inverse(X0),multiply(X2,inverse(X2),X3)),inverse(multiply(X1,inverse(X1),X4)),X4),X1)),multiply(inverse(X0),X3,X0)) = X6,
inference(superposition,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
multiply(multiply(X5,inverse(X5),X6),inverse(multiply(X1,inverse(X1),multiply(X2,inverse(X2),X3))),multiply(inverse(X1),X3,X1)) = X6,
inference(demodulation,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
X3 = multiply(multiply(X4,inverse(X4),X3),inverse(multiply(X0,inverse(X0),multiply(X1,inverse(X1),X2))),multiply(inverse(X0),X2,X0)),
inference(superposition,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
multiply(multiply(X1,inverse(X1),X2),inverse(multiply(X3,inverse(X3),multiply(X4,inverse(X4),X5))),multiply(inverse(X3),X5,X3)) = multiply(inverse(X0),X2,X0),
inference(superposition,[status(thm)],[d9,d9]) ).
cnf(d12,plain,
X1 = multiply(inverse(X5),X1,X5),
inference(demodulation,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
X1 = multiply(X1,inverse(multiply(X0,inverse(X0),X2)),X2),
inference(demodulation,[status(thm)],[d1,d12]) ).
cnf(d14,plain,
inverse(multiply(X1,inverse(X1),X0)) = inverse(X0),
inference(superposition,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
X2 = multiply(X2,inverse(X1),X1),
inference(demodulation,[status(thm)],[d13,d14]) ).
cnf(d16,plain,
X3 = multiply(multiply(X4,inverse(X4),X3),inverse(multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X0,inverse(X0),X1)),X2)),X2),
inference(demodulation,[status(thm)],[d4,d14]) ).
cnf(d17,plain,
X3 = multiply(multiply(X4,inverse(X4),X3),inverse(X2),X2),
inference(demodulation,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
X1 = multiply(X0,inverse(X0),X1),
inference(demodulation,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
multiply(multiply(X9,inverse(X9),X10),inverse(multiply(multiply(multiply(X0,X1,X2),inverse(multiply(multiply(X3,X4,X5),X6,multiply(X3,X4,X7))),X11),X12,multiply(X1,multiply(X2,inverse(multiply(X0,X1,X8)),X8),X0))),multiply(inverse(multiply(multiply(X3,X4,X5),X6,multiply(X3,X4,X7))),multiply(multiply(X4,multiply(X7,X6,X5),X3),X12,X11),multiply(X0,X1,X2))) = X10,
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d20,plain,
multiply(X1,inverse(multiply(multiply(multiply(X2,X3,X4),inverse(multiply(multiply(X5,X6,X7),X8,multiply(X5,X6,X9))),X10),X11,multiply(X3,multiply(X4,inverse(multiply(X2,X3,X12)),X12),X2))),multiply(inverse(multiply(multiply(X5,X6,X7),X8,multiply(X5,X6,X9))),multiply(multiply(X6,multiply(X9,X8,X7),X5),X11,X10),multiply(X2,X3,X4))) = X1,
inference(demodulation,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
multiply(multiply(X9,X10,X11),inverse(multiply(multiply(multiply(X0,X1,X2),inverse(multiply(multiply(X3,X4,X5),X6,multiply(X3,X4,X7))),X12),X13,multiply(X1,multiply(X2,inverse(multiply(X0,X1,X8)),X8),X0))),multiply(inverse(multiply(multiply(X3,X4,X5),X6,multiply(X3,X4,X7))),multiply(multiply(X4,multiply(X7,X6,X5),X3),X13,X12),multiply(X0,X1,X2))) = multiply(X10,multiply(X11,inverse(multiply(X9,X10,X14)),X14),X9),
inference(superposition,[status(thm)],[d0,d0]) ).
cnf(d22,plain,
multiply(X0,X1,X2) = multiply(X1,multiply(X2,inverse(multiply(X0,X1,X14)),X14),X0),
inference(demodulation,[status(thm)],[d21,d20]) ).
cnf(d23,plain,
multiply(X0,X1,multiply(X0,X1,X2)) = multiply(X1,X2,X0),
inference(superposition,[status(thm)],[d18,d22]) ).
cnf(d24,plain,
multiply(X1,inverse(multiply(X0,inverse(X0),X2)),X2) = X1,
inference(demodulation,[status(thm)],[d5,d12]) ).
cnf(d25,plain,
multiply(X2,inverse(X1),X1) = X2,
inference(demodulation,[status(thm)],[d24,d14]) ).
cnf(d26,plain,
inverse(inverse(inverse(X0))) = inverse(X0),
inference(superposition,[status(thm)],[d12,d14]) ).
cnf(d27,plain,
X1 = multiply(X1,inverse(X0),inverse(inverse(X0))),
inference(superposition,[status(thm)],[d26,d15]) ).
cnf(d28,plain,
X0 = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d18,d27]) ).
cnf(d29,plain,
multiply(X1,X0,inverse(X0)) = X1,
inference(superposition,[status(thm)],[d28,d25]) ).
cnf(d30,plain,
multiply(X0,X1,X0) = multiply(X1,inverse(X1),X0),
inference(superposition,[status(thm)],[d29,d23]) ).
cnf(d31,plain,
multiply(X1,X0,X1) = X1,
inference(demodulation,[status(thm)],[d30,d18]) ).
cnf(d32,plain,
multiply(X0,X0,X1) = X0,
inference(superposition,[status(thm)],[d31,d22]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[d32,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : BOO070-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/15.54 % Computer : n012.cluster.edu
% 0.03/15.54 % Model : x86_64 x86_64
% 0.03/15.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/15.54 % Memory : 8046.5625MB
% 0.03/15.54 % OS : Linux 6.8.0-71-generic
% 0.03/15.54 % CPULimit : 300
% 0.03/15.54 % WCLimit : 300
% 0.03/15.54 % DateTime : Sat Sep 26 22:42:52 UTC 2026
% 0.03/15.54 % CPUTime :
% 0.03/15.54 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.02/18.05 % SZS status Unsatisfiable for theBenchmark.p
% 20.02/18.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------