%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO003-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 06:54:36 AM UTC 2026
% Result : Unsatisfiable 13.49s 3.44s
% Output : CNFRefutation 13.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 4 RR)
% Number of literals : 18 ( 17 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_a_times_a_is_a,negated_conjecture,
multiply(a,a) != a ).
cnf(distributivity2,axiom,
multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)) ).
cnf(additive_id1,axiom,
add(X0,'additive$uidentity') = X0 ).
cnf(multiplicative_id1,axiom,
multiply(X0,'multiplicative$uidentity') = X0 ).
cnf(additive_inverse1,axiom,
add(X0,inverse(X0)) = 'multiplicative$uidentity' ).
cnf(multiplicative_inverse1,axiom,
multiply(X0,inverse(X0)) = 'additive$uidentity' ).
cnf(c0,plain,
multiply(a,a) != a,
inference(clausification,[status(esa)],[prove_a_times_a_is_a]) ).
cnf(c4,plain,
multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(clausification,[status(esa)],[distributivity2]) ).
cnf(c5,plain,
add(X0,'additive$uidentity') = X0,
inference(clausification,[status(esa)],[additive_id1]) ).
cnf(c6,plain,
multiply(X0,'multiplicative$uidentity') = X0,
inference(clausification,[status(esa)],[multiplicative_id1]) ).
cnf(c7,plain,
add(X0,inverse(X0)) = 'multiplicative$uidentity',
inference(clausification,[status(esa)],[additive_inverse1]) ).
cnf(c8,plain,
multiply(X0,inverse(X0)) = 'additive$uidentity',
inference(clausification,[status(esa)],[multiplicative_inverse1]) ).
cnf(d0,plain,
multiply(X0,add(X1,inverse(X0))) = add(multiply(X0,X1),'additive$uidentity'),
inference(superposition,[status(thm)],[c8,c4]) ).
cnf(d1,plain,
multiply(X0,add(X1,inverse(X0))) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d0,c5]) ).
cnf(d2,plain,
multiply(X0,'multiplicative$uidentity') = multiply(X0,X0),
inference(superposition,[status(thm)],[c7,d1]) ).
cnf(d3,plain,
X0 = multiply(X0,X0),
inference(demodulation,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
a != a,
inference(demodulation,[status(thm)],[c0,d3]) ).
cnf(d5,plain,
$false,
inference(equality_resolution,[status(thm)],[d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : BOO003-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.45 % Computer : n019.cluster.edu
% 0.16/0.45 % Model : x86_64 x86_64
% 0.16/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.45 % Memory : 8046.5625MB
% 0.16/0.45 % OS : Linux 6.8.0-71-generic
% 0.16/0.45 % CPULimit : 300
% 0.16/0.45 % WCLimit : 300
% 0.16/0.45 % DateTime : Sat Sep 26 22:33:34 UTC 2026
% 0.16/0.46 % CPUTime :
% 0.16/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.49/3.44 % SZS status Unsatisfiable for theBenchmark.p
% 13.49/3.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------