%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO010-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 06:54:38 AM UTC 2026
% Result : Unsatisfiable 28.27s 9.02s
% Output : CNFRefutation 28.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 4 RR)
% Number of literals : 26 ( 25 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 : 40 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_a_plus_ab_is_a,negated_conjecture,
add(a,multiply(a,b)) != a ).
cnf(commutativity_of_add,axiom,
add(X0,X1) = add(X1,X0) ).
cnf(commutativity_of_multiply,axiom,
multiply(X0,X1) = multiply(X1,X0) ).
cnf(distributivity2,axiom,
add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)) ).
cnf(distributivity3,axiom,
multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)) ).
cnf(additive_inverse1,axiom,
add(X0,inverse(X0)) = 'multiplicative$uidentity' ).
cnf(multiplicative_id2,axiom,
multiply('multiplicative$uidentity',X0) = X0 ).
cnf(c0,plain,
add(a,multiply(a,b)) != a,
inference(clausification,[status(esa)],[prove_a_plus_ab_is_a]) ).
cnf(c1,plain,
add(X0,X1) = add(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_add]) ).
cnf(c2,plain,
multiply(X0,X1) = multiply(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_multiply]) ).
cnf(c4,plain,
add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
inference(clausification,[status(esa)],[distributivity2]) ).
cnf(c5,plain,
multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
inference(clausification,[status(esa)],[distributivity3]) ).
cnf(c7,plain,
add(X0,inverse(X0)) = 'multiplicative$uidentity',
inference(clausification,[status(esa)],[additive_inverse1]) ).
cnf(c12,plain,
multiply('multiplicative$uidentity',X0) = X0,
inference(clausification,[status(esa)],[multiplicative_id2]) ).
cnf(d0,plain,
add(X0,multiply(inverse(X0),X1)) = multiply('multiplicative$uidentity',add(X0,X1)),
inference(superposition,[status(thm)],[c7,c4]) ).
cnf(d1,plain,
add(X0,multiply(inverse(X0),X1)) = add(X0,X1),
inference(demodulation,[status(thm)],[d0,c12]) ).
cnf(d2,plain,
X0 = multiply(X0,'multiplicative$uidentity'),
inference(superposition,[status(thm)],[c12,c2]) ).
cnf(d3,plain,
add(X0,inverse(X0)) = add(X0,'multiplicative$uidentity'),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
'multiplicative$uidentity' = add(X0,'multiplicative$uidentity'),
inference(demodulation,[status(thm)],[d3,c7]) ).
cnf(d5,plain,
add('multiplicative$uidentity',X0) = 'multiplicative$uidentity',
inference(superposition,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
multiply(add('multiplicative$uidentity',X1),X0) = add(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[c12,c5]) ).
cnf(d7,plain,
multiply('multiplicative$uidentity',X1) = add(X1,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
X0 = add(X0,multiply(X1,X0)),
inference(demodulation,[status(thm)],[d7,c12]) ).
cnf(d9,plain,
X1 = add(X1,multiply(X1,X0)),
inference(superposition,[status(thm)],[c2,d8]) ).
cnf(d10,plain,
a != a,
inference(demodulation,[status(thm)],[c0,d9]) ).
cnf(d11,plain,
$false,
inference(equality_resolution,[status(thm)],[d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO010-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n010.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 22:35:51 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.27/9.02 % SZS status Unsatisfiable for theBenchmark.p
% 28.27/9.02 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------