%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG001-4 : 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 : n009.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 08:25:32 AM UTC 2026
% Result : Unsatisfiable 24.83s 15.62s
% Output : CNFRefutation 24.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 20 ( 12 unt; 0 nHn; 10 RR)
% Number of literals : 39 ( 4 equ; 21 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cancellation2,axiom,
( X0 = X3
| ~ sum(X3,X1,X2)
| ~ sum(X0,X1,X2) ) ).
cnf(prove_a_times_additive_id_is_additive_id,negated_conjecture,
~ product(a,'additive$uidentity','additive$uidentity') ).
cnf(additive_identity1,axiom,
sum('additive$uidentity',X0,X0) ).
cnf(additive_identity2,axiom,
sum(X0,'additive$uidentity',X0) ).
cnf(closure_of_multiplication,axiom,
product(X0,X1,multiply(X0,X1)) ).
cnf(distributivity1,axiom,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(c1,plain,
( X0 = X3
| ~ sum(X3,X1,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[cancellation2]) ).
cnf(c2,plain,
~ product(a,'additive$uidentity','additive$uidentity'),
inference(clausification,[status(esa)],[prove_a_times_additive_id_is_additive_id]) ).
cnf(c3,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c4,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c5,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c14,plain,
( ~ product(X0,X5,X3)
| ~ product(X0,X6,X4)
| ~ sum(X5,X1,X6)
| sum(X3,X2,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(d0,plain,
( ~ sum(X0,X1,X1)
| X0 = 'additive$uidentity' ),
inference(resolution,[status(thm)],[c1,c3]) ).
cnf(d1,plain,
( ~ product(X3,'additive$uidentity',X1)
| ~ product(X3,X4,X0)
| ~ product(X3,X4,X2)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c14,c4]) ).
cnf(d2,plain,
( ~ product(X2,'additive$uidentity',X1)
| ~ product(X2,X3,X0)
| sum(X0,X1,multiply(X2,X3)) ),
inference(resolution,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
( ~ product(X0,'additive$uidentity',X2)
| sum(multiply(X0,X1),X2,multiply(X0,X1)) ),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
sum(multiply(X0,X1),multiply(X0,'additive$uidentity'),multiply(X0,X1)),
inference(resolution,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
multiply(X0,'additive$uidentity') = 'additive$uidentity',
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
product(X0,'additive$uidentity','additive$uidentity'),
inference(superposition,[status(thm)],[d5,c5]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG001-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.41 % Computer : n009.cluster.edu
% 0.06/0.41 % Model : x86_64 x86_64
% 0.06/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.41 % Memory : 8046.5625MB
% 0.06/0.41 % OS : Linux 6.8.0-71-generic
% 0.06/0.41 % CPULimit : 300
% 0.06/0.41 % WCLimit : 300
% 0.06/0.41 % DateTime : Sat Sep 26 05:43:14 UTC 2026
% 0.06/0.41 % CPUTime :
% 0.06/0.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.83/15.62 % SZS status Unsatisfiable for theBenchmark.p
% 24.83/15.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------