%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO009-1 : 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 : n026.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 06:54:38 AM UTC 2026
% Result : Unsatisfiable 34.68s 8.12s
% Output : CNFRefutation 34.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 40 ( 22 unt; 0 nHn; 20 RR)
% Number of literals : 78 ( 6 equ; 40 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 105 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_equations,negated_conjecture,
~ product(x,add(x,y),x) ).
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(distributivity1,axiom,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,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(multiplicative_inverse2,axiom,
product(X0,inverse(X0),'additive$uidentity') ).
cnf(addition_is_well_defined,axiom,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ) ).
cnf(c0,plain,
~ product(x,add(x,y),x),
inference(clausification,[status(esa)],[prove_equations]) ).
cnf(c1,plain,
sum(X0,X1,add(X0,X1)),
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c2,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c3,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c4,plain,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_multiplication]) ).
cnf(c5,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c6,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c9,plain,
( sum(X4,X5,X6)
| ~ product(X3,X2,X6)
| ~ product(X3,X1,X5)
| ~ product(X3,X0,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c13,plain,
( ~ sum(X0,X6,X4)
| ~ product(X5,X1,X6)
| ~ sum(X0,X5,X3)
| product(X3,X2,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity5]) ).
cnf(c20,plain,
product(X0,inverse(X0),'additive$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(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[c3,c1]) ).
cnf(d1,plain,
( ~ sum(X1,X5,X3)
| ~ sum(X1,X4,X2)
| ~ product(X0,X4,X5)
| product(add(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[c13,d0]) ).
cnf(d2,plain,
( ~ sum(X2,X1,X3)
| product(add(X0,X2),X2,X3)
| ~ product(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
( product(add(X0,X1),X1,X1)
| ~ product(X0,'additive$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[c4,c2]) ).
cnf(d5,plain,
( ~ sum('additive$uidentity',X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c21,c5]) ).
cnf(d6,plain,
( sum(X4,X3,X2)
| ~ product(X0,X1,X4)
| ~ product(X0,'additive$uidentity',X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c9,c6]) ).
cnf(d7,plain,
( sum(X2,multiply('additive$uidentity',X0),X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
( sum('additive$uidentity',multiply('additive$uidentity',X0),X1)
| ~ product(X0,inverse(X0),X1) ),
inference(resolution,[status(thm)],[d7,c20]) ).
cnf(d9,plain,
sum('additive$uidentity',multiply('additive$uidentity',X0),'additive$uidentity'),
inference(resolution,[status(thm)],[d8,c20]) ).
cnf(d10,plain,
multiply('additive$uidentity',X0) = 'additive$uidentity',
inference(resolution,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
product(X0,'additive$uidentity','additive$uidentity'),
inference(superposition,[status(thm)],[d10,d4]) ).
cnf(d12,plain,
product(add(X0,X1),X1,X1),
inference(resolution,[status(thm)],[d11,d3]) ).
cnf(d13,plain,
product(X0,add(X1,X0),X0),
inference(resolution,[status(thm)],[d12,c4]) ).
cnf(d14,plain,
( ~ sum(X1,X0,X2)
| add(X0,X1) = X2 ),
inference(resolution,[status(thm)],[c21,d0]) ).
cnf(d15,plain,
add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[d14,c1]) ).
cnf(d16,plain,
product(X1,add(X1,X0),X1),
inference(superposition,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
$false,
inference(resolution,[status(thm)],[d16,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : BOO009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n026.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 22:37:25 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 34.68/8.12 % SZS status Unsatisfiable for theBenchmark.p
% 34.68/8.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------