%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO003-1 : 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 : n007.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 06:54:35 AM UTC 2026
% Result : Unsatisfiable 8.34s 2.34s
% Output : CNFRefutation 8.34s
% 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,
~ product(x,x,x) ).
cnf(closure_of_multiplication,axiom,
product(X0,X1,multiply(X0,X1)) ).
cnf(commutativity_of_multiplication,axiom,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ) ).
cnf(additive_identity1,axiom,
sum('additive$uidentity',X0,X0) ).
cnf(multiplicative_identity1,axiom,
product('multiplicative$uidentity',X0,X0) ).
cnf(distributivity3,axiom,
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ) ).
cnf(additive_inverse1,axiom,
sum(inverse(X0),X0,'multiplicative$uidentity') ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X0),X0,'additive$uidentity') ).
cnf(addition_is_well_defined,axiom,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ) ).
cnf(c0,plain,
~ product(x,x,x),
inference(clausification,[status(esa)],[prove_both_equalities]) ).
cnf(c2,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c4,plain,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_multiplication]) ).
cnf(c5,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c7,plain,
product('multiplicative$uidentity',X0,X0),
inference(clausification,[status(esa)],[multiplicative_identity1]) ).
cnf(c11,plain,
( ~ sum(X6,X3,X0)
| ~ product(X6,X1,X5)
| sum(X5,X4,X2)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity3]) ).
cnf(c17,plain,
sum(inverse(X0),X0,'multiplicative$uidentity'),
inference(clausification,[status(esa)],[additive_inverse1]) ).
cnf(c19,plain,
product(inverse(X0),X0,'additive$uidentity'),
inference(clausification,[status(esa)],[multiplicative_inverse1]) ).
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('additive$uidentity',X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c21,c5]) ).
cnf(d1,plain,
product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[c4,c2]) ).
cnf(d2,plain,
( sum(X4,X3,X1)
| ~ product(inverse(X2),X0,X4)
| ~ product(X2,X0,X3)
| ~ product('multiplicative$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[c17,c11]) ).
cnf(d3,plain,
( sum('additive$uidentity',X1,X2)
| ~ product('multiplicative$uidentity',X0,X2)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[d2,c19]) ).
cnf(d4,plain,
( sum('additive$uidentity',X1,X0)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[d3,c7]) ).
cnf(d5,plain,
sum('additive$uidentity',multiply(X0,X0),X0),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
X0 = multiply(X0,X0),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
product(X0,X0,X0),
inference(superposition,[status(thm)],[d6,c2]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n007.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sat Sep 26 22:30:55 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.34/2.34 % SZS status Unsatisfiable for theBenchmark.p
% 8.34/2.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------