%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG040-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 08:25:41 AM UTC 2026
% Result : Unsatisfiable 34.62s 9.61s
% Output : CNFRefutation 34.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 26 ( 17 unt; 0 nHn; 26 RR)
% Number of literals : 44 ( 0 equ; 20 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 32 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_of_addition,axiom,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ) ).
cnf(distributivity1,axiom,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(product_symmetry,hypothesis,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ) ).
cnf(b_plus_c,negated_conjecture,
sum(b,c,d) ).
cnf(d_plus_a,negated_conjecture,
product(d,a,'additive$uidentity') ).
cnf(b_plus_a,negated_conjecture,
product(b,a,l) ).
cnf(c_plus_a,negated_conjecture,
product(c,a,n) ).
cnf(prove_equation,negated_conjecture,
~ sum(l,n,'additive$uidentity') ).
cnf(c8,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c11,plain,
( ~ product(X0,X3,X5)
| ~ product(X0,X4,X6)
| sum(X5,X2,X6)
| ~ sum(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c19,plain,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_symmetry]) ).
cnf(c20,plain,
sum(b,c,d),
inference(clausification,[status(esa)],[b_plus_c]) ).
cnf(c21,plain,
product(d,a,'additive$uidentity'),
inference(clausification,[status(esa)],[d_plus_a]) ).
cnf(c22,plain,
product(b,a,l),
inference(clausification,[status(esa)],[b_plus_a]) ).
cnf(c23,plain,
product(c,a,n),
inference(clausification,[status(esa)],[c_plus_a]) ).
cnf(c24,plain,
~ sum(l,n,'additive$uidentity'),
inference(clausification,[status(esa)],[prove_equation]) ).
cnf(d0,plain,
product(a,d,'additive$uidentity'),
inference(resolution,[status(thm)],[c19,c21]) ).
cnf(d1,plain,
product(a,c,n),
inference(resolution,[status(thm)],[c19,c23]) ).
cnf(d2,plain,
product(a,b,l),
inference(resolution,[status(thm)],[c19,c22]) ).
cnf(d3,plain,
( ~ product(a,X2,X0)
| ~ product(a,X3,X1)
| ~ sum(X2,b,X3)
| sum(X0,l,X1) ),
inference(resolution,[status(thm)],[c11,d2]) ).
cnf(d4,plain,
( ~ product(a,X0,X1)
| sum(n,l,X1)
| ~ sum(c,b,X0) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( sum(n,l,'additive$uidentity')
| ~ sum(c,b,d) ),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
sum(c,b,d),
inference(resolution,[status(thm)],[c8,c20]) ).
cnf(d7,plain,
sum(n,l,'additive$uidentity'),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
sum(l,n,'additive$uidentity'),
inference(resolution,[status(thm)],[d7,c8]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[c24,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG040-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n002.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 05:54:08 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 34.62/9.61 % SZS status Unsatisfiable for theBenchmark.p
% 34.62/9.61 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------