%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG005-2 : 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 : n019.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 08:25:33 AM UTC 2026
% Result : Unsatisfiable 31.09s 16.17s
% Output : CNFRefutation 31.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 20 ( 13 unt; 0 nHn; 16 RR)
% Number of literals : 36 ( 0 equ; 18 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 32 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_inverse,axiom,
sum(X0,'additive$uinverse'(X0),'additive$uidentity') ).
cnf(commutativity_of_addition,axiom,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ) ).
cnf(distributivity3,axiom,
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ) ).
cnf(multiplicative_identity1,axiom,
product('additive$uidentity',X0,'additive$uidentity') ).
cnf(a_times_b,hypothesis,
product(a,b,d) ).
cnf(a_inverse_times_b,hypothesis,
product('additive$uinverse'(a),b,c) ).
cnf(prove_sum_is_additive_identity,negated_conjecture,
~ sum(c,d,'additive$uidentity') ).
cnf(c14,plain,
sum(X0,'additive$uinverse'(X0),'additive$uidentity'),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c17,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c22,plain,
( sum(X4,X6,X5)
| ~ product(X1,X3,X6)
| ~ product(X2,X3,X5)
| ~ product(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity3]) ).
cnf(c26,plain,
product('additive$uidentity',X0,'additive$uidentity'),
inference(clausification,[status(esa)],[multiplicative_identity1]) ).
cnf(c28,plain,
product(a,b,d),
inference(clausification,[status(esa)],[a_times_b]) ).
cnf(c29,plain,
product('additive$uinverse'(a),b,c),
inference(clausification,[status(esa)],[a_inverse_times_b]) ).
cnf(c30,plain,
~ sum(c,d,'additive$uidentity'),
inference(clausification,[status(esa)],[prove_sum_is_additive_identity]) ).
cnf(d0,plain,
( ~ product(X4,X3,X0)
| ~ product('additive$uinverse'(X4),X3,X1)
| ~ product('additive$uidentity',X3,X2)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c22,c14]) ).
cnf(d1,plain,
( ~ product('additive$uidentity',b,X1)
| ~ product('additive$uinverse'(a),b,X0)
| sum(d,X0,X1) ),
inference(resolution,[status(thm)],[d0,c28]) ).
cnf(d2,plain,
( ~ product('additive$uidentity',b,X0)
| sum(d,c,X0) ),
inference(resolution,[status(thm)],[d1,c29]) ).
cnf(d3,plain,
sum(d,c,'additive$uidentity'),
inference(resolution,[status(thm)],[d2,c26]) ).
cnf(d4,plain,
sum(c,d,'additive$uidentity'),
inference(resolution,[status(thm)],[d3,c17]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c30,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG005-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 05:44:19 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.09/16.17 % SZS status Unsatisfiable for theBenchmark.p
% 31.09/16.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------