%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO012-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 06:54:39 AM UTC 2026
% Result : Unsatisfiable 3.13s 16.36s
% Output : CNFRefutation 3.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 32 ( 19 unt; 0 nHn; 17 RR)
% Number of literals : 65 ( 7 equ; 36 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 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 : 77 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_inverse_is_an_involution,negated_conjecture,
inverse(inverse(x)) != x ).
cnf(closure_of_addition,axiom,
sum(X0,X1,add(X0,X1)) ).
cnf(additive_identity1,axiom,
sum('additive$uidentity',X0,X0) ).
cnf(additive_identity2,axiom,
sum(X0,'additive$uidentity',X0) ).
cnf(distributivity5,axiom,
( product(X2,X4,X6)
| ~ sum(X0,X5,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ) ).
cnf(distributivity8,axiom,
( sum(X5,X1,X6)
| ~ product(X2,X4,X6)
| ~ product(X0,X3,X5)
| ~ sum(X3,X1,X4)
| ~ sum(X0,X1,X2) ) ).
cnf(additive_inverse2,axiom,
sum(X0,inverse(X0),'multiplicative$uidentity') ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X0),X0,'additive$uidentity') ).
cnf(multiplicative_inverse2,axiom,
product(X0,inverse(X0),'additive$uidentity') ).
cnf(addition_is_well_defined,axiom,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ) ).
cnf(c12,plain,
inverse(inverse(x)) != x,
inference(clausification,[status(esa)],[prove_inverse_is_an_involution]) ).
cnf(c13,plain,
sum(X0,X1,add(X0,X1)),
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c17,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c18,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c25,plain,
( ~ sum(X3,X0,X5)
| ~ sum(X3,X1,X6)
| product(X5,X6,X4)
| ~ sum(X3,X2,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity5]) ).
cnf(c28,plain,
( ~ sum(X5,X4,X0)
| sum(X6,X4,X2)
| ~ product(X5,X3,X6)
| ~ sum(X3,X4,X1)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity8]) ).
cnf(c30,plain,
sum(X0,inverse(X0),'multiplicative$uidentity'),
inference(clausification,[status(esa)],[additive_inverse2]) ).
cnf(c31,plain,
product(inverse(X0),X0,'additive$uidentity'),
inference(clausification,[status(esa)],[multiplicative_inverse1]) ).
cnf(c32,plain,
product(X0,inverse(X0),'additive$uidentity'),
inference(clausification,[status(esa)],[multiplicative_inverse2]) ).
cnf(c33,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(d0,plain,
( ~ sum('additive$uidentity',X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c33,c17]) ).
cnf(d1,plain,
( ~ product(X3,X1,X0)
| ~ product(X4,'multiplicative$uidentity',X2)
| ~ sum(X3,inverse(X1),X4)
| sum(X0,inverse(X1),X2) ),
inference(resolution,[status(thm)],[c30,c28]) ).
cnf(d2,plain,
( ~ product(X3,X1,X0)
| ~ product(add(X3,inverse(X1)),'multiplicative$uidentity',X2)
| sum(X0,inverse(X1),X2) ),
inference(resolution,[status(thm)],[d1,c13]) ).
cnf(d3,plain,
( ~ product(add(X0,inverse(inverse(X0))),'multiplicative$uidentity',X1)
| sum('additive$uidentity',inverse(inverse(X0)),X1) ),
inference(resolution,[status(thm)],[d2,c32]) ).
cnf(d4,plain,
( ~ product(X3,X1,'additive$uidentity')
| product(X4,X2,X0)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c25,c18]) ).
cnf(d5,plain,
( ~ product(X3,X1,'additive$uidentity')
| product(add(X0,X3),X2,X0)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d4,c13]) ).
cnf(d6,plain,
( product(add(X1,X0),'multiplicative$uidentity',X1)
| ~ product(X0,inverse(X1),'additive$uidentity') ),
inference(resolution,[status(thm)],[d5,c30]) ).
cnf(d7,plain,
product(add(X0,inverse(inverse(X0))),'multiplicative$uidentity',X0),
inference(resolution,[status(thm)],[d6,c31]) ).
cnf(d8,plain,
sum('additive$uidentity',inverse(inverse(X0)),X0),
inference(resolution,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
X0 = inverse(inverse(X0)),
inference(resolution,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
x != x,
inference(demodulation,[status(thm)],[c12,d9]) ).
cnf(d11,plain,
$false,
inference(equality_resolution,[status(thm)],[d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO012-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.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
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 22:35:15 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.13/16.36 % SZS status Unsatisfiable for theBenchmark.p
% 3.13/16.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------