%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO005-1 : 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 : n016.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 20.10s 2.90s
% Output : CNFRefutation 20.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of clauses : 53 ( 27 unt; 0 nHn; 30 RR)
% Number of literals : 101 ( 13 equ; 50 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 125 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_equations,negated_conjecture,
~ sum(x,'multiplicative$uidentity','multiplicative$uidentity') ).
cnf(closure_of_addition,axiom,
sum(X0,X1,add(X0,X1)) ).
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(commutativity_of_multiplication,axiom,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ) ).
cnf(additive_identity1,axiom,
sum('additive$uidentity',X0,X0) ).
cnf(additive_identity2,axiom,
sum(X0,'additive$uidentity',X0) ).
cnf(multiplicative_identity1,axiom,
product('multiplicative$uidentity',X0,X0) ).
cnf(distributivity3,axiom,
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity5,axiom,
( product(X2,X4,X6)
| ~ sum(X0,X5,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ) ).
cnf(additive_inverse1,axiom,
sum(inverse(X0),X0,'multiplicative$uidentity') ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X0),X0,'additive$uidentity') ).
cnf(addition_is_well_defined,axiom,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ) ).
cnf(multiplication_is_well_defined,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
~ sum(x,'multiplicative$uidentity','multiplicative$uidentity'),
inference(clausification,[status(esa)],[prove_equations]) ).
cnf(c1,plain,
sum(X0,X1,add(X0,X1)),
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c2,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c3,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c4,plain,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_multiplication]) ).
cnf(c5,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c6,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c7,plain,
product('multiplicative$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(c13,plain,
( ~ sum(X0,X6,X4)
| ~ product(X5,X1,X6)
| ~ sum(X0,X5,X3)
| product(X3,X2,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity5]) ).
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(c22,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[multiplication_is_well_defined]) ).
cnf(d0,plain,
( ~ product('multiplicative$uidentity',X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c22,c7]) ).
cnf(d1,plain,
sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[c3,c1]) ).
cnf(d2,plain,
( ~ sum(X1,'additive$uidentity',X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c21,c6]) ).
cnf(d3,plain,
'multiplicative$uidentity' = inverse('additive$uidentity'),
inference(resolution,[status(thm)],[d2,c17]) ).
cnf(d4,plain,
product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[c4,c2]) ).
cnf(d5,plain,
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[status(thm)],[c22,c2]) ).
cnf(d6,plain,
multiply(X0,X1) = multiply(X1,X0),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( ~ sum('additive$uidentity',X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c21,c5]) ).
cnf(d8,plain,
( ~ product(X3,X2,X0)
| ~ product(X4,X2,X1)
| ~ sum(inverse(X2),X3,X4)
| sum('additive$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[c19,c11]) ).
cnf(d9,plain,
( ~ product('additive$uidentity',X2,X0)
| ~ product(inverse(X2),X2,X1)
| sum('additive$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[d8,c6]) ).
cnf(d10,plain,
( ~ product('additive$uidentity',X1,X0)
| sum('additive$uidentity',X0,'additive$uidentity') ),
inference(resolution,[status(thm)],[d9,c19]) ).
cnf(d11,plain,
sum('additive$uidentity',multiply(X0,'additive$uidentity'),'additive$uidentity'),
inference(resolution,[status(thm)],[d10,d4]) ).
cnf(d12,plain,
'additive$uidentity' = multiply(X0,'additive$uidentity'),
inference(resolution,[status(thm)],[d11,d7]) ).
cnf(d13,plain,
multiply('additive$uidentity',X0) = 'additive$uidentity',
inference(superposition,[status(thm)],[d12,d6]) ).
cnf(d14,plain,
( product(X5,X2,X4)
| ~ sum(X0,X3,X5)
| ~ sum(X0,multiply(X3,X1),X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c13,c2]) ).
cnf(d15,plain,
( product(X2,X3,'multiplicative$uidentity')
| ~ sum(inverse(multiply(X0,X1)),X1,X3)
| ~ sum(inverse(multiply(X0,X1)),X0,X2) ),
inference(resolution,[status(thm)],[d14,c17]) ).
cnf(d16,plain,
( product(inverse(multiply('additive$uidentity',X0)),X1,'multiplicative$uidentity')
| ~ sum(inverse(multiply('additive$uidentity',X0)),X0,X1) ),
inference(resolution,[status(thm)],[d15,c6]) ).
cnf(d17,plain,
( product(inverse(multiply('additive$uidentity',X0)),X1,'multiplicative$uidentity')
| ~ sum(inverse('additive$uidentity'),X0,X1) ),
inference(demodulation,[status(thm)],[d16,d13]) ).
cnf(d18,plain,
( product(inverse(multiply('additive$uidentity',X0)),X1,'multiplicative$uidentity')
| ~ sum('multiplicative$uidentity',X0,X1) ),
inference(demodulation,[status(thm)],[d17,d3]) ).
cnf(d19,plain,
( product(inverse('additive$uidentity'),X1,'multiplicative$uidentity')
| ~ sum('multiplicative$uidentity',X0,X1) ),
inference(demodulation,[status(thm)],[d18,d13]) ).
cnf(d20,plain,
( product('multiplicative$uidentity',X1,'multiplicative$uidentity')
| ~ sum('multiplicative$uidentity',X0,X1) ),
inference(demodulation,[status(thm)],[d19,d3]) ).
cnf(d21,plain,
product('multiplicative$uidentity',add(X0,'multiplicative$uidentity'),'multiplicative$uidentity'),
inference(resolution,[status(thm)],[d20,d1]) ).
cnf(d22,plain,
add(X0,'multiplicative$uidentity') = 'multiplicative$uidentity',
inference(resolution,[status(thm)],[d21,d0]) ).
cnf(d23,plain,
sum(X0,'multiplicative$uidentity','multiplicative$uidentity'),
inference(superposition,[status(thm)],[d22,c1]) ).
cnf(d24,plain,
$false,
inference(resolution,[status(thm)],[d23,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO005-1 : 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 : n016.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
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 22:39:00 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.10/2.90 % SZS status Unsatisfiable for theBenchmark.p
% 20.10/2.90 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------