%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO004-1 : 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 : n015.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 06:54:36 AM UTC 2026
% Result : Unsatisfiable 16.29s 3.93s
% Output : CNFRefutation 16.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 27 ( 17 unt; 0 nHn; 13 RR)
% Number of literals : 48 ( 4 equ; 23 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_both_equalities,negated_conjecture,
~ sum(x,x,x) ).
cnf(closure_of_addition,axiom,
sum(X0,X1,add(X0,X1)) ).
cnf(commutativity_of_addition,axiom,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ) ).
cnf(additive_identity2,axiom,
sum(X0,'additive$uidentity',X0) ).
cnf(multiplicative_identity2,axiom,
product(X0,'multiplicative$uidentity',X0) ).
cnf(distributivity6,axiom,
( sum(X0,X5,X6)
| ~ product(X2,X4,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ) ).
cnf(additive_inverse2,axiom,
sum(X0,inverse(X0),'multiplicative$uidentity') ).
cnf(multiplicative_inverse2,axiom,
product(X0,inverse(X0),'additive$uidentity') ).
cnf(addition_is_well_defined,axiom,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ) ).
cnf(c0,plain,
~ sum(x,x,x),
inference(clausification,[status(esa)],[prove_both_equalities]) ).
cnf(c1,plain,
sum(X0,X1,add(X0,X1)),
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c3,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c6,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c8,plain,
product(X0,'multiplicative$uidentity',X0),
inference(clausification,[status(esa)],[multiplicative_identity2]) ).
cnf(c14,plain,
( ~ sum(X0,X3,X5)
| sum(X0,X4,X6)
| ~ product(X2,X5,X6)
| ~ product(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity6]) ).
cnf(c18,plain,
sum(X0,inverse(X0),'multiplicative$uidentity'),
inference(clausification,[status(esa)],[additive_inverse2]) ).
cnf(c20,plain,
product(X0,inverse(X0),'additive$uidentity'),
inference(clausification,[status(esa)],[multiplicative_inverse2]) ).
cnf(c21,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(d0,plain,
( ~ sum(X1,'additive$uidentity',X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c21,c6]) ).
cnf(d1,plain,
sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[c3,c1]) ).
cnf(d2,plain,
( ~ product(X4,X3,X1)
| ~ sum(X0,X4,X2)
| ~ sum(X0,X3,'multiplicative$uidentity')
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c14,c8]) ).
cnf(d3,plain,
( sum(X0,'additive$uidentity',X2)
| ~ sum(X0,inverse(X1),'multiplicative$uidentity')
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d2,c20]) ).
cnf(d4,plain,
( sum(X0,'additive$uidentity',X1)
| ~ sum(X0,X0,X1) ),
inference(resolution,[status(thm)],[d3,c18]) ).
cnf(d5,plain,
sum(X0,'additive$uidentity',add(X0,X0)),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
add(X0,X0) = X0,
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
sum(X0,X0,X0),
inference(superposition,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 22:37:44 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.29/3.93 % SZS status Unsatisfiable for theBenchmark.p
% 16.29/3.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------