%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO009-2 : 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 : 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 06:54:38 AM UTC 2026
% Result : Unsatisfiable 20.91s 3.07s
% Output : CNFRefutation 20.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 4 RR)
% Number of literals : 35 ( 34 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 : 61 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_operation,negated_conjecture,
multiply(a,add(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(distributivity1,axiom,
add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X1,X2)) ).
cnf(distributivity4,axiom,
multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)) ).
cnf(multiplicative_inverse1,axiom,
multiply(X0,inverse(X0)) = 'additive$uidentity' ).
cnf(additive_id1,axiom,
add(X0,'additive$uidentity') = X0 ).
cnf(additive_id2,axiom,
add('additive$uidentity',X0) = X0 ).
cnf(c0,plain,
multiply(a,add(a,b)) != a,
inference(clausification,[status(esa)],[prove_operation]) ).
cnf(c1,plain,
add(X0,X1) = add(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_add]) ).
cnf(c2,plain,
multiply(X0,X1) = multiply(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_multiply]) ).
cnf(c3,plain,
add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X1,X2)),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c6,plain,
multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(clausification,[status(esa)],[distributivity4]) ).
cnf(c9,plain,
multiply(X0,inverse(X0)) = 'additive$uidentity',
inference(clausification,[status(esa)],[multiplicative_inverse1]) ).
cnf(c13,plain,
add(X0,'additive$uidentity') = X0,
inference(clausification,[status(esa)],[additive_id1]) ).
cnf(c14,plain,
add('additive$uidentity',X0) = X0,
inference(clausification,[status(esa)],[additive_id2]) ).
cnf(d0,plain,
multiply(X0,add(X1,inverse(X0))) = add(multiply(X0,X1),'additive$uidentity'),
inference(superposition,[status(thm)],[c9,c6]) ).
cnf(d1,plain,
multiply(X0,add(X1,inverse(X0))) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d0,c13]) ).
cnf(d2,plain,
X0 = add('additive$uidentity',X0),
inference(superposition,[status(thm)],[c13,c1]) ).
cnf(d3,plain,
multiply(X0,inverse(X0)) = multiply(X0,'additive$uidentity'),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
'additive$uidentity' = multiply(X0,'additive$uidentity'),
inference(demodulation,[status(thm)],[d3,c9]) ).
cnf(d5,plain,
multiply('additive$uidentity',X0) = 'additive$uidentity',
inference(superposition,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
add(multiply('additive$uidentity',X1),X0) = multiply(X0,add(X1,X0)),
inference(superposition,[status(thm)],[c14,c3]) ).
cnf(d7,plain,
add(X1,multiply('additive$uidentity',X0)) = multiply(X1,add(X0,X1)),
inference(superposition,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
add(X1,'additive$uidentity') = multiply(X1,add(X0,X1)),
inference(demodulation,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
X0 = multiply(X0,add(X1,X0)),
inference(demodulation,[status(thm)],[d8,c13]) ).
cnf(d10,plain,
add(multiply(X0,X2),X1) = multiply(add(X1,X0),add(X2,X1)),
inference(superposition,[status(thm)],[c1,c3]) ).
cnf(d11,plain,
add(multiply(X2,multiply('additive$uidentity',X0)),X1) = multiply(add(X1,X2),multiply(X1,add(X0,X1))),
inference(superposition,[status(thm)],[d6,d10]) ).
cnf(d12,plain,
add(multiply(X1,'additive$uidentity'),X2) = multiply(add(X2,X1),multiply(X2,add(X0,X2))),
inference(demodulation,[status(thm)],[d11,d5]) ).
cnf(d13,plain,
add('additive$uidentity',X1) = multiply(add(X1,X0),multiply(X1,add(X2,X1))),
inference(demodulation,[status(thm)],[d12,d4]) ).
cnf(d14,plain,
X0 = multiply(add(X0,X1),multiply(X0,add(X2,X0))),
inference(demodulation,[status(thm)],[d13,c14]) ).
cnf(d15,plain,
X0 = multiply(add(X0,X2),X0),
inference(demodulation,[status(thm)],[d14,d9]) ).
cnf(d16,plain,
X0 = multiply(X0,add(X0,X1)),
inference(demodulation,[status(thm)],[d15,c2]) ).
cnf(d17,plain,
a != a,
inference(demodulation,[status(thm)],[c0,d16]) ).
cnf(d18,plain,
$false,
inference(equality_resolution,[status(thm)],[d17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO009-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n008.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 22:35:09 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.91/3.07 % SZS status Unsatisfiable for theBenchmark.p
% 20.91/3.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------