%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG038-2 : 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 : n026.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 08:25:40 AM UTC 2026
% Result : Unsatisfiable 11.42s 2.04s
% Output : CNFRefutation 11.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 23 ( 10 unt; 0 nHn; 13 RR)
% Number of literals : 42 ( 0 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sum_substitution3,axiom,
( sum(X2,X3,X1)
| ~ sum(X2,X3,X0)
| ~ equalish(X0,X1) ) ).
cnf(additive_identity2,axiom,
sum(X0,'additive$uidentity',X0) ).
cnf(addition_is_well_defined,axiom,
( equalish(X2,X3)
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ) ).
cnf(multiplication_is_well_defined,axiom,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(multiplicative_identity1,axiom,
product('additive$uidentity',X0,'additive$uidentity') ).
cnf(some_property,hypothesis,
( product(X0,h(X0,X1),X1)
| ~ equalish(X0,'additive$uidentity') ) ).
cnf(a_not_additive_identity,negated_conjecture,
~ equalish(a,'additive$uidentity') ).
cnf(c4,plain,
( sum(X2,X3,X1)
| ~ sum(X2,X3,X0)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[sum_substitution3]) ).
cnf(c9,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c22,plain,
( equalish(X2,X3)
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(c23,plain,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[multiplication_is_well_defined]) ).
cnf(c24,plain,
product('additive$uidentity',X0,'additive$uidentity'),
inference(clausification,[status(esa)],[multiplicative_identity1]) ).
cnf(c26,plain,
( product(X0,h(X0,X1),X1)
| ~ equalish(X0,'additive$uidentity') ),
inference(clausification,[status(esa)],[some_property]) ).
cnf(c28,plain,
~ equalish(a,'additive$uidentity'),
inference(clausification,[status(esa)],[a_not_additive_identity]) ).
cnf(d0,plain,
( sum(X0,'additive$uidentity',X1)
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[c4,c9]) ).
cnf(d1,plain,
( ~ sum(X1,'additive$uidentity',X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c22,c9]) ).
cnf(d2,plain,
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ product('additive$uidentity',X1,X0)
| equalish('additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c23,c24]) ).
cnf(d4,plain,
( ~ equalish('additive$uidentity','additive$uidentity')
| equalish('additive$uidentity',X0) ),
inference(resolution,[status(thm)],[d3,c26]) ).
cnf(d5,plain,
equalish(X0,X0),
inference(resolution,[status(thm)],[d1,c9]) ).
cnf(d6,plain,
equalish('additive$uidentity',X0),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
equalish(X0,'additive$uidentity'),
inference(resolution,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,c28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG038-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 05:53:56 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.42/2.04 % SZS status Unsatisfiable for theBenchmark.p
% 11.42/2.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------