%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO013-3 : 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 : n013.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 9.47s 15.05s
% Output : CNFRefutation 9.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 37 ( 23 unt; 0 nHn; 30 RR)
% Number of literals : 63 ( 7 equ; 28 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 : 52 ( 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_multiplication,axiom,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ) ).
cnf(additive_identity1,axiom,
sum('additive$uidentity',X0,X0) ).
cnf(multiplicative_identity2,axiom,
product(X0,'multiplicative$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(addition_is_well_defined,axiom,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ) ).
cnf(c1,plain,
sum(x,y,'multiplicative$uidentity'),
inference(clausification,[status(esa)],[sum_to_multiplicative_identity1]) ).
cnf(c2,plain,
sum(x,z,'multiplicative$uidentity'),
inference(clausification,[status(esa)],[sum_to_multiplicative_identity2]) ).
cnf(c3,plain,
product(x,y,'additive$uidentity'),
inference(clausification,[status(esa)],[product_to_additive_identity1]) ).
cnf(c4,plain,
product(x,z,'additive$uidentity'),
inference(clausification,[status(esa)],[product_to_additive_identity2]) ).
cnf(c5,plain,
y != z,
inference(clausification,[status(esa)],[prove_both_inverse_are_equal]) ).
cnf(c7,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c9,plain,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_multiplication]) ).
cnf(c10,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c13,plain,
product(X0,'multiplicative$uidentity',X0),
inference(clausification,[status(esa)],[multiplicative_identity2]) ).
cnf(c14,plain,
( ~ product(X0,X6,X4)
| ~ product(X0,X5,X3)
| ~ sum(X5,X6,X1)
| sum(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c26,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(d0,plain,
( ~ sum('additive$uidentity',X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c26,c10]) ).
cnf(d1,plain,
product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[c9,c7]) ).
cnf(d2,plain,
product(z,x,'additive$uidentity'),
inference(resolution,[status(thm)],[c9,c4]) ).
cnf(d3,plain,
( ~ product(X2,X3,X0)
| ~ product(X2,X4,X1)
| ~ sum(X3,X4,'multiplicative$uidentity')
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c14,c13]) ).
cnf(d4,plain,
( ~ product(z,X0,X1)
| sum('additive$uidentity',X1,z)
| ~ sum(x,X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( sum('additive$uidentity',multiply(z,X0),z)
| ~ sum(x,X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d4,c7]) ).
cnf(d6,plain,
( z = multiply(z,X0)
| ~ sum(x,X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
( ~ sum(x,X0,'multiplicative$uidentity')
| product(X0,z,z) ),
inference(superposition,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
product(y,z,z),
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
product(y,x,'additive$uidentity'),
inference(resolution,[status(thm)],[c9,c3]) ).
cnf(d10,plain,
( ~ product(y,X0,X1)
| sum('additive$uidentity',X1,y)
| ~ sum(x,X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d3,d9]) ).
cnf(d11,plain,
( sum('additive$uidentity',z,y)
| ~ sum(x,z,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
sum('additive$uidentity',z,y),
inference(resolution,[status(thm)],[c2,d11]) ).
cnf(d13,plain,
y = z,
inference(resolution,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[c5,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO013-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/10.61 % Computer : n013.cluster.edu
% 0.08/10.61 % Model : x86_64 x86_64
% 0.08/10.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.61 % Memory : 8046.5625MB
% 0.08/10.61 % OS : Linux 6.8.0-71-generic
% 0.08/10.61 % CPULimit : 300
% 0.08/10.61 % WCLimit : 300
% 0.08/10.61 % DateTime : Sat Sep 26 22:35:21 UTC 2026
% 0.08/10.62 % CPUTime :
% 0.08/10.62 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.47/15.05 % SZS status Unsatisfiable for theBenchmark.p
% 9.47/15.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------