%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG039-2 : 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 : n018.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 19.47s 4.80s
% Output : CNFRefutation 19.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 38 ( 22 unt; 0 nHn; 17 RR)
% Number of literals : 62 ( 0 equ; 26 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 84 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sum_substitution1,axiom,
( sum(X1,X2,X3)
| ~ sum(X0,X2,X3)
| ~ equalish(X0,X1) ) ).
cnf(product_substitution3,axiom,
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ) ).
cnf(additive_identity1,axiom,
sum('additive$uidentity',X0,X0) ).
cnf(closure_of_multiplication,axiom,
product(X0,X1,multiply(X0,X1)) ).
cnf(commutativity_of_addition,axiom,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ) ).
cnf(multiplicative_identity1,axiom,
product('additive$uidentity',X0,'additive$uidentity') ).
cnf(addition_is_well_defined,axiom,
( equalish(X2,X3)
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ) ).
cnf(multiplication_is_well_defined,axiom,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(absorbtion1,axiom,
sum(X0,add(X0,X1),X1) ).
cnf(clause35,axiom,
equalish(multiply(X0,X0),X0) ).
cnf(clause44,axiom,
product(a,multiply(b,X0),multiply(X1,X0)) ).
cnf(prove_c_equals_d,negated_conjecture,
~ equalish(c,d) ).
cnf(c2,plain,
( sum(X1,X2,X3)
| ~ sum(X0,X2,X3)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[sum_substitution1]) ).
cnf(c9,plain,
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[product_substitution3]) ).
cnf(c12,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c14,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c18,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c25,plain,
product('additive$uidentity',X0,'additive$uidentity'),
inference(clausification,[status(esa)],[multiplicative_identity1]) ).
cnf(c27,plain,
( equalish(X2,X3)
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(c28,plain,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[multiplication_is_well_defined]) ).
cnf(c31,plain,
sum(X0,add(X0,X1),X1),
inference(clausification,[status(esa)],[absorbtion1]) ).
cnf(c36,plain,
equalish(multiply(X0,X0),X0),
inference(clausification,[status(esa)],[clause35]) ).
cnf(c45,plain,
product(a,multiply(b,X0),multiply(X1,X0)),
inference(clausification,[status(esa)],[clause44]) ).
cnf(c73,plain,
~ equalish(c,d),
inference(clausification,[status(esa)],[prove_c_equals_d]) ).
cnf(d0,plain,
sum(add(X0,X1),X0,X1),
inference(resolution,[status(thm)],[c31,c18]) ).
cnf(d1,plain,
( ~ sum(add(X2,X0),X2,X1)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[d0,c27]) ).
cnf(d2,plain,
( sum(X0,X1,X1)
| ~ equalish('additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c2,c12]) ).
cnf(d3,plain,
( ~ product('additive$uidentity',X1,X0)
| equalish('additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c28,c25]) ).
cnf(d4,plain,
( product(X0,X1,X2)
| ~ equalish(multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[c14,c9]) ).
cnf(d5,plain,
( ~ product(a,multiply(b,X1),X2)
| equalish(multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[c45,c28]) ).
cnf(d6,plain,
( product(a,multiply(b,X1),X2)
| ~ equalish(multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[c45,c9]) ).
cnf(d7,plain,
product(a,multiply(b,X0),X0),
inference(resolution,[status(thm)],[d6,c36]) ).
cnf(d8,plain,
equalish(multiply(X0,X1),X1),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
product(X0,X1,X1),
inference(resolution,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
equalish('additive$uidentity',X0),
inference(resolution,[status(thm)],[d9,d3]) ).
cnf(d11,plain,
sum(X0,X1,X1),
inference(resolution,[status(thm)],[d10,d2]) ).
cnf(d12,plain,
equalish(X0,X1),
inference(resolution,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,c73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG039-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n018.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 05:53:38 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.47/4.80 % SZS status Unsatisfiable for theBenchmark.p
% 19.47/4.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------