%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG245-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 06:48:13 AM UTC 2026
% Result : Unsatisfiable 55.27s 44.66s
% Output : CNFRefutation 55.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 3 RR)
% Number of literals : 39 ( 38 equ; 2 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; 4 con; 0-2 aty)
% Number of variables : 122 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c01,axiom,
mult(X0,mult(X1,X2)) = mult(mult(X0,X1),mult(X0,X2)) ).
cnf(c02,axiom,
mult(mult(X0,X1),X2) = mult(mult(X0,X2),mult(X1,X2)) ).
cnf(c03,axiom,
mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3)))) = mult(mult(X0,X2),mult(X1,X3)) ).
cnf(c04,axiom,
mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))),mult(mult(X0,X2),mult(X1,X3))) = mult(mult(X0,X1),mult(X2,X3)) ).
cnf(c05,axiom,
mult(X0,X0) = X0 ).
cnf(goals,negated_conjecture,
mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))) != mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))) ).
cnf(c_0,plain,
mult(X0,mult(X1,X2)) = mult(mult(X0,X1),mult(X0,X2)),
inference(clausification,[status(esa)],[c01]) ).
cnf(c_1,plain,
mult(mult(X0,X1),X2) = mult(mult(X0,X2),mult(X1,X2)),
inference(clausification,[status(esa)],[c02]) ).
cnf(c_2,plain,
mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3)))) = mult(mult(X0,X2),mult(X1,X3)),
inference(clausification,[status(esa)],[c03]) ).
cnf(c_3,plain,
mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))),mult(mult(X0,X2),mult(X1,X3))) = mult(mult(X0,X1),mult(X2,X3)),
inference(clausification,[status(esa)],[c04]) ).
cnf(c_4,plain,
mult(X0,X0) = X0,
inference(clausification,[status(esa)],[c05]) ).
cnf(c_5,plain,
mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))) != mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),
inference(clausification,[status(esa)],[goals]) ).
cnf(d0,plain,
mult(mult(X3,mult(X0,X1)),mult(X2,X1)) = mult(mult(X3,mult(X2,X1)),mult(mult(X0,X2),X1)),
inference(superposition,[status(thm)],[c_1,c_1]) ).
cnf(d1,plain,
mult(mult(X0,X1),mult(mult(X1,X2),X2)) = mult(mult(mult(X0,X1),mult(X0,X2)),mult(X1,X2)),
inference(superposition,[status(thm)],[d0,c_0]) ).
cnf(d2,plain,
mult(mult(X0,X1),mult(mult(X1,X2),X2)) = mult(mult(X0,mult(X1,X2)),mult(X1,X2)),
inference(demodulation,[status(thm)],[d1,c_0]) ).
cnf(d3,plain,
mult(X0,mult(X1,X1)) = mult(X0,X1),
inference(superposition,[status(thm)],[c_0,c_4]) ).
cnf(d4,plain,
mult(X1,X0) = mult(X1,X0),
inference(demodulation,[status(thm)],[d3,c_4]) ).
cnf(d5,plain,
mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))),mult(mult(X0,X2),mult(X1,X3))) = mult(mult(X0,X1),mult(X2,X3)),
inference(superposition,[status(thm)],[c_3,d4]) ).
cnf(d6,plain,
mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(X0,X2)),mult(mult(mult(X0,X2),mult(X1,X3)),mult(X1,X3))) = mult(mult(X0,X1),mult(X2,X3)),
inference(demodulation,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
mult(mult(mult(mult(X0,X2),mult(X1,X3)),mult(X0,X1)),mult(mult(mult(X0,X1),X2),mult(mult(X2,X3),X3))) = mult(mult(X0,X2),mult(X1,X3)),
inference(demodulation,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
mult(mult(mult(X0,X1),mult(X2,X3)),mult(X4,mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))))) = mult(mult(mult(mult(X0,X1),mult(X2,X3)),X4),mult(mult(X0,X2),mult(X1,X3))),
inference(superposition,[status(thm)],[c_2,c_0]) ).
cnf(d9,plain,
mult(mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))),X4),mult(mult(X0,X2),mult(X1,X3))) = mult(mult(mult(X0,X1),mult(X2,X3)),mult(X4,mult(mult(X0,X2),mult(X1,X3)))),
inference(superposition,[status(thm)],[c_3,c_1]) ).
cnf(d10,plain,
mult(X0,mult(X1,X0)) = mult(mult(X0,X1),X0),
inference(superposition,[status(thm)],[c_4,c_0]) ).
cnf(d11,plain,
mult(mult(X0,X1),X0) = mult(X0,mult(X1,X0)),
inference(superposition,[status(thm)],[d10,d4]) ).
cnf(d12,plain,
mult(mult(mult(X0,X1),X0),X1) = mult(mult(X0,X1),mult(X1,mult(X0,X1))),
inference(superposition,[status(thm)],[c_1,d11]) ).
cnf(d13,plain,
mult(mult(X0,mult(X1,X0)),X1) = mult(mult(X0,X1),mult(X1,mult(X0,X1))),
inference(demodulation,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))),mult(mult(X0,X1),mult(X2,X3)))),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3)))) = mult(mult(mult(X0,X2),mult(X1,X3)),mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3)))))),
inference(superposition,[status(thm)],[c_2,d13]) ).
cnf(d15,plain,
mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))),mult(mult(X0,X1),mult(X2,X3))),mult(mult(X0,X2),mult(X1,X3)))) = mult(mult(mult(X0,X2),mult(X1,X3)),mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3)))))),
inference(demodulation,[status(thm)],[d14,c_0]) ).
cnf(d16,plain,
mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))))) = mult(mult(mult(X0,X2),mult(X1,X3)),mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3)))))),
inference(demodulation,[status(thm)],[d15,d9]) ).
cnf(d17,plain,
mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X1),mult(X2,X3))),mult(mult(X0,X2),mult(X1,X3))) = mult(mult(mult(X0,X2),mult(X1,X3)),mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3)))))),
inference(demodulation,[status(thm)],[d16,d8]) ).
cnf(d18,plain,
mult(mult(mult(X0,X1),mult(mult(X2,X3),mult(X2,X3))),mult(mult(X0,X2),mult(X1,X3))) = mult(mult(mult(X0,X2),mult(X1,X3)),mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3)))))),
inference(demodulation,[status(thm)],[d17,c_0]) ).
cnf(d19,plain,
mult(mult(mult(X2,X3),mult(X0,mult(X1,X1))),mult(mult(X2,X0),mult(X3,X1))) = mult(mult(mult(X2,X0),mult(X3,X1)),mult(mult(mult(mult(X2,X3),mult(X0,X1)),mult(mult(X2,X0),mult(X3,X1))),mult(mult(mult(X2,X3),mult(X0,X1)),mult(mult(mult(X2,X3),mult(X0,X1)),mult(mult(X2,X0),mult(X3,X1)))))),
inference(demodulation,[status(thm)],[d18,c_0]) ).
cnf(d20,plain,
mult(mult(mult(X1,X2),mult(X3,X0)),mult(mult(X1,X3),mult(X2,X0))) = mult(mult(mult(X1,X3),mult(X2,X0)),mult(mult(mult(mult(X1,X2),mult(X3,X0)),mult(mult(X1,X3),mult(X2,X0))),mult(mult(mult(X1,X2),mult(X3,X0)),mult(mult(mult(X1,X2),mult(X3,X0)),mult(mult(X1,X3),mult(X2,X0)))))),
inference(demodulation,[status(thm)],[d19,c_4]) ).
cnf(d21,plain,
mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))) = mult(mult(mult(X0,X2),mult(X1,X3)),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(X0,X2),mult(X1,X3)),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3)))))),
inference(demodulation,[status(thm)],[d20,c_0]) ).
cnf(d22,plain,
mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))) = mult(mult(mult(X0,X2),mult(X1,X3)),mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))),mult(mult(X0,X2),mult(X1,X3)))),
inference(demodulation,[status(thm)],[d21,d8]) ).
cnf(d23,plain,
mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))) = mult(mult(mult(X0,X2),mult(X1,X3)),mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(X0,X2)),mult(mult(mult(X0,X2),mult(X1,X3)),mult(X1,X3)))),
inference(demodulation,[status(thm)],[d22,d2]) ).
cnf(d24,plain,
mult(mult(mult(X0,X2),mult(X1,X3)),mult(mult(X0,X1),mult(X2,X3))) = mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(mult(X0,X2),mult(X1,X3)),mult(X0,X1)),mult(mult(mult(X0,X1),X2),mult(mult(X2,X3),X3)))),
inference(demodulation,[status(thm)],[d23,d2]) ).
cnf(d25,plain,
mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))) = mult(mult(mult(X0,X2),mult(X1,X3)),mult(mult(X0,X1),mult(X2,X3))),
inference(demodulation,[status(thm)],[d24,d7]) ).
cnf(d26,plain,
$false,
inference(resolution,[status(thm)],[d25,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG245-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n008.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 21:45:09 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 55.27/44.66 % SZS status Unsatisfiable for theBenchmark.p
% 55.27/44.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------