%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO016-1 : 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 : n019.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 06:54:41 AM UTC 2026
% Result : Unsatisfiable 28.15s 10.61s
% Output : CNFRefutation 28.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 46 ( 24 unt; 0 nHn; 27 RR)
% Number of literals : 97 ( 6 equ; 54 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 122 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(x_times_y,hypothesis,
product(x,y,z) ).
cnf(prove_sum,negated_conjecture,
~ sum(x,z,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(additive_identity1,axiom,
sum('additive$uidentity',X0,X0) ).
cnf(additive_identity2,axiom,
sum(X0,'additive$uidentity',X0) ).
cnf(multiplicative_identity2,axiom,
product(X0,'multiplicative$uidentity',X0) ).
cnf(distributivity1,axiom,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity2,axiom,
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity5,axiom,
( product(X2,X4,X6)
| ~ sum(X0,X5,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ) ).
cnf(multiplicative_inverse2,axiom,
product(X0,inverse(X0),'additive$uidentity') ).
cnf(multiplication_is_well_defined,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
product(x,y,z),
inference(clausification,[status(esa)],[x_times_y]) ).
cnf(c1,plain,
~ sum(x,z,x),
inference(clausification,[status(esa)],[prove_sum]) ).
cnf(c2,plain,
sum(X0,X1,add(X0,X1)),
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c3,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c4,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c6,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c7,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c9,plain,
product(X0,'multiplicative$uidentity',X0),
inference(clausification,[status(esa)],[multiplicative_identity2]) ).
cnf(c10,plain,
( sum(X4,X5,X6)
| ~ product(X3,X2,X6)
| ~ product(X3,X1,X5)
| ~ product(X3,X0,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c11,plain,
( ~ sum(X5,X3,X1)
| ~ sum(X6,X4,X2)
| ~ product(X0,X5,X6)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity2]) ).
cnf(c14,plain,
( ~ sum(X0,X6,X4)
| ~ product(X5,X1,X6)
| ~ sum(X0,X5,X3)
| product(X3,X2,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity5]) ).
cnf(c21,plain,
product(X0,inverse(X0),'additive$uidentity'),
inference(clausification,[status(esa)],[multiplicative_inverse2]) ).
cnf(c23,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[multiplication_is_well_defined]) ).
cnf(d0,plain,
( ~ sum(X3,X1,'multiplicative$uidentity')
| sum(X4,X2,X0)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c10,c9]) ).
cnf(d1,plain,
( ~ sum('multiplicative$uidentity',X1,'multiplicative$uidentity')
| sum(X0,X2,X0)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d0,c9]) ).
cnf(d2,plain,
( ~ sum('multiplicative$uidentity',y,'multiplicative$uidentity')
| sum(x,z,x) ),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
~ sum('multiplicative$uidentity',y,'multiplicative$uidentity'),
inference(resolution,[status(thm)],[c1,d2]) ).
cnf(d4,plain,
sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[c4,c2]) ).
cnf(d5,plain,
( ~ product(X0,'multiplicative$uidentity',X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c23,c9]) ).
cnf(d6,plain,
( ~ product(X1,inverse(X1),X0)
| 'additive$uidentity' = X0 ),
inference(resolution,[status(thm)],[c23,c21]) ).
cnf(d7,plain,
( ~ sum(X3,X5,X1)
| ~ sum(X4,multiply(X0,X5),X2)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c11,c3]) ).
cnf(d8,plain,
( ~ sum(inverse(X0),X3,X1)
| ~ sum('additive$uidentity',multiply(X0,X3),X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d7,c21]) ).
cnf(d9,plain,
( ~ sum(inverse(X0),X2,X1)
| product(X0,X1,multiply(X0,X2)) ),
inference(resolution,[status(thm)],[d8,c6]) ).
cnf(d10,plain,
product(X0,inverse(X0),multiply(X0,'additive$uidentity')),
inference(resolution,[status(thm)],[d9,c7]) ).
cnf(d11,plain,
'additive$uidentity' = multiply(X0,'additive$uidentity'),
inference(resolution,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
( ~ sum(X3,X5,X0)
| ~ sum(X3,multiply(X5,X4),X2)
| ~ sum(X3,X4,X1)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c14,c3]) ).
cnf(d13,plain,
( ~ sum(X1,multiply(X0,X4),X3)
| ~ sum(X1,X4,X2)
| product(add(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[d12,d4]) ).
cnf(d14,plain,
( ~ sum(X1,multiply(X0,'additive$uidentity'),X2)
| product(add(X0,X1),X1,X2) ),
inference(resolution,[status(thm)],[d13,c7]) ).
cnf(d15,plain,
( ~ sum(X1,'additive$uidentity',X2)
| product(add(X0,X1),X1,X2) ),
inference(demodulation,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
product(add(X0,X1),X1,X1),
inference(resolution,[status(thm)],[d15,c7]) ).
cnf(d17,plain,
add(X0,'multiplicative$uidentity') = 'multiplicative$uidentity',
inference(resolution,[status(thm)],[d16,d5]) ).
cnf(d18,plain,
sum('multiplicative$uidentity',X0,'multiplicative$uidentity'),
inference(superposition,[status(thm)],[d17,d4]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[d18,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.58 % Computer : n019.cluster.edu
% 0.11/5.58 % Model : x86_64 x86_64
% 0.11/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.58 % Memory : 8046.5625MB
% 0.11/5.58 % OS : Linux 6.8.0-71-generic
% 0.11/5.58 % CPULimit : 300
% 0.11/5.58 % WCLimit : 300
% 0.11/5.59 % DateTime : Sat Sep 26 22:36:41 UTC 2026
% 0.11/5.59 % CPUTime :
% 0.11/5.59 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.15/10.61 % SZS status Unsatisfiable for theBenchmark.p
% 28.15/10.61 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------