%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO013-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 06:54:40 AM UTC 2026
% Result : Unsatisfiable 5.52s 9.67s
% Output : CNFRefutation 5.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of clauses : 51 ( 30 unt; 0 nHn; 41 RR)
% Number of literals : 94 ( 12 equ; 45 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; 5 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sum_to_multiplicative_identity1,negated_conjecture,
sum(x,y,'multiplicative$uidentity') ).
cnf(sum_to_multiplicative_identity2,negated_conjecture,
sum(x,z,'multiplicative$uidentity') ).
cnf(product_to_additive_identity1,negated_conjecture,
product(x,y,'additive$uidentity') ).
cnf(product_to_additive_identity2,negated_conjecture,
product(x,z,'additive$uidentity') ).
cnf(prove_both_inverse_are_equal,negated_conjecture,
y != z ).
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_identity2,axiom,
product(X0,'multiplicative$uidentity',X0) ).
cnf(distributivity1,axiom,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity2,axiom,
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(addition_is_well_defined,axiom,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ) ).
cnf(multiplication_is_well_defined,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
sum(x,y,'multiplicative$uidentity'),
inference(clausification,[status(esa)],[sum_to_multiplicative_identity1]) ).
cnf(c1,plain,
sum(x,z,'multiplicative$uidentity'),
inference(clausification,[status(esa)],[sum_to_multiplicative_identity2]) ).
cnf(c2,plain,
product(x,y,'additive$uidentity'),
inference(clausification,[status(esa)],[product_to_additive_identity1]) ).
cnf(c3,plain,
product(x,z,'additive$uidentity'),
inference(clausification,[status(esa)],[product_to_additive_identity2]) ).
cnf(c4,plain,
z != y,
inference(clausification,[status(esa)],[prove_both_inverse_are_equal]) ).
cnf(c6,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c7,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c8,plain,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_multiplication]) ).
cnf(c9,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c10,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c12,plain,
product(X0,'multiplicative$uidentity',X0),
inference(clausification,[status(esa)],[multiplicative_identity2]) ).
cnf(c13,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(c14,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(c25,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(c26,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[multiplication_is_well_defined]) ).
cnf(d0,plain,
( ~ product(X0,'multiplicative$uidentity',X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c26,c12]) ).
cnf(d1,plain,
product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[c8,c6]) ).
cnf(d2,plain,
( ~ sum('additive$uidentity',X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c25,c9]) ).
cnf(d3,plain,
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[status(thm)],[c26,c6]) ).
cnf(d4,plain,
multiply(X0,X1) = multiply(X1,X0),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
product(y,x,'additive$uidentity'),
inference(resolution,[status(thm)],[c8,c2]) ).
cnf(d6,plain,
( ~ product(X3,x,X0)
| ~ product(X3,z,X1)
| ~ product(X3,'multiplicative$uidentity',X2)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c13,c1]) ).
cnf(d7,plain,
( ~ product(y,z,X0)
| ~ product(y,'multiplicative$uidentity',X1)
| sum('additive$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( ~ product(y,z,X0)
| sum('additive$uidentity',X0,y) ),
inference(resolution,[status(thm)],[d7,c12]) ).
cnf(d9,plain,
sum('additive$uidentity',multiply(z,y),y),
inference(resolution,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
sum('additive$uidentity',multiply(y,z),y),
inference(demodulation,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
y = multiply(y,z),
inference(resolution,[status(thm)],[d10,d2]) ).
cnf(d12,plain,
product(z,y,y),
inference(superposition,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
product(z,x,'additive$uidentity'),
inference(resolution,[status(thm)],[c8,c3]) ).
cnf(d14,plain,
sum(y,x,'multiplicative$uidentity'),
inference(resolution,[status(thm)],[c7,c0]) ).
cnf(d15,plain,
( ~ product(X3,X0,X4)
| ~ product(X3,X1,'additive$uidentity')
| product(X3,X2,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c14,c10]) ).
cnf(d16,plain,
( ~ product(X0,y,X1)
| ~ product(X0,x,'additive$uidentity')
| product(X0,'multiplicative$uidentity',X1) ),
inference(resolution,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
( product(z,'multiplicative$uidentity',X0)
| ~ product(z,y,X0) ),
inference(resolution,[status(thm)],[d16,d13]) ).
cnf(d18,plain,
product(z,'multiplicative$uidentity',y),
inference(resolution,[status(thm)],[d17,d12]) ).
cnf(d19,plain,
z = y,
inference(resolution,[status(thm)],[d18,d0]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[c4,d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.42 % Computer : n009.cluster.edu
% 0.09/0.42 % Model : x86_64 x86_64
% 0.09/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.42 % Memory : 8046.5625MB
% 0.09/0.42 % OS : Linux 6.8.0-71-generic
% 0.09/0.42 % CPULimit : 300
% 0.09/0.42 % WCLimit : 300
% 0.09/0.42 % DateTime : Sat Sep 26 22:35:46 UTC 2026
% 0.09/0.43 % CPUTime :
% 0.09/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.52/9.67 % SZS status Unsatisfiable for theBenchmark.p
% 5.52/9.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------