%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO013-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 06:54:40 AM UTC 2026
% Result : Unsatisfiable 19.65s 13.10s
% Output : CNFRefutation 19.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 18 RR)
% Number of literals : 32 ( 31 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_and_multiplicative_identity,hypothesis,
add(a,b) = 'multiplicative$uidentity' ).
cnf(c_and_multiplicative_identity,hypothesis,
add(a,c) = 'multiplicative$uidentity' ).
cnf(b_a_additive_identity,hypothesis,
multiply(a,b) = 'additive$uidentity' ).
cnf(c_a_additive_identity,hypothesis,
multiply(a,c) = 'additive$uidentity' ).
cnf(prove_b_is_a,negated_conjecture,
b != c ).
cnf(commutativity_of_add,axiom,
add(X0,X1) = add(X1,X0) ).
cnf(distributivity1,axiom,
add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X1,X2)) ).
cnf(multiplicative_id2,axiom,
multiply('multiplicative$uidentity',X0) = X0 ).
cnf(additive_id1,axiom,
add(X0,'additive$uidentity') = X0 ).
cnf(c0,plain,
add(a,b) = 'multiplicative$uidentity',
inference(clausification,[status(esa)],[b_and_multiplicative_identity]) ).
cnf(c1,plain,
add(a,c) = 'multiplicative$uidentity',
inference(clausification,[status(esa)],[c_and_multiplicative_identity]) ).
cnf(c2,plain,
multiply(a,b) = 'additive$uidentity',
inference(clausification,[status(esa)],[b_a_additive_identity]) ).
cnf(c3,plain,
multiply(a,c) = 'additive$uidentity',
inference(clausification,[status(esa)],[c_a_additive_identity]) ).
cnf(c4,plain,
b != c,
inference(clausification,[status(esa)],[prove_b_is_a]) ).
cnf(c5,plain,
add(X0,X1) = add(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_add]) ).
cnf(c7,plain,
add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X1,X2)),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c16,plain,
multiply('multiplicative$uidentity',X0) = X0,
inference(clausification,[status(esa)],[multiplicative_id2]) ).
cnf(c17,plain,
add(X0,'additive$uidentity') = X0,
inference(clausification,[status(esa)],[additive_id1]) ).
cnf(d0,plain,
add(multiply(a,X0),b) = multiply('multiplicative$uidentity',add(X0,b)),
inference(superposition,[status(thm)],[c0,c7]) ).
cnf(d1,plain,
add(b,multiply(a,X0)) = multiply('multiplicative$uidentity',add(X0,b)),
inference(demodulation,[status(thm)],[d0,c5]) ).
cnf(d2,plain,
add(b,multiply(a,X0)) = add(X0,b),
inference(demodulation,[status(thm)],[d1,c16]) ).
cnf(d3,plain,
add(b,'additive$uidentity') = add(c,b),
inference(superposition,[status(thm)],[c3,d2]) ).
cnf(d4,plain,
b = add(c,b),
inference(demodulation,[status(thm)],[d3,c17]) ).
cnf(d5,plain,
b = add(b,c),
inference(demodulation,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
add(multiply(a,X0),c) = multiply('multiplicative$uidentity',add(X0,c)),
inference(superposition,[status(thm)],[c1,c7]) ).
cnf(d7,plain,
add(c,multiply(a,X0)) = multiply('multiplicative$uidentity',add(X0,c)),
inference(demodulation,[status(thm)],[d6,c5]) ).
cnf(d8,plain,
add(c,multiply(a,X0)) = add(X0,c),
inference(demodulation,[status(thm)],[d7,c16]) ).
cnf(d9,plain,
add(c,'additive$uidentity') = add(b,c),
inference(superposition,[status(thm)],[c2,d8]) ).
cnf(d10,plain,
c = add(b,c),
inference(demodulation,[status(thm)],[d9,c17]) ).
cnf(d11,plain,
c = b,
inference(demodulation,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
b != b,
inference(demodulation,[status(thm)],[c4,d11]) ).
cnf(d13,plain,
$false,
inference(equality_resolution,[status(thm)],[d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO013-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.39 % Computer : n017.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Sat Sep 26 22:31:14 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.65/13.10 % SZS status Unsatisfiable for theBenchmark.p
% 19.65/13.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------