%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD029-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 07:10:49 AM UTC 2026
% Result : Unsatisfiable 2.23s 15.36s
% Output : CNFRefutation 2.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 18
% Syntax : Number of clauses : 70 ( 24 unt; 10 nHn; 70 RR)
% Number of literals : 160 ( 0 equ; 83 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 107 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(b_is_defined,hypothesis,
defined(b) ).
cnf(u_is_defined,hypothesis,
defined(u) ).
cnf(v_is_defined,hypothesis,
defined(v) ).
cnf(not_sum_5,negated_conjecture,
~ sum('additive$uidentity',b,'additive$uidentity') ).
cnf(product_6,negated_conjecture,
product(a,u,b) ).
cnf(product_7,negated_conjecture,
product(a,v,b) ).
cnf(not_product_8,negated_conjecture,
~ product('multiplicative$uidentity',u,v) ).
cnf(associativity_addition_1,axiom,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ) ).
cnf(commutativity_addition,axiom,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ) ).
cnf(associativity_multiplication_1,axiom,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ) ).
cnf(associativity_multiplication_2,axiom,
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ) ).
cnf(existence_of_inverse_multiplication,axiom,
( ~ defined(X0)
| sum('additive$uidentity',X0,'additive$uidentity')
| product('multiplicative$uinverse'(X0),X0,'multiplicative$uidentity') ) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ) ).
cnf(distributivity_1,axiom,
( ~ product(X4,X6,X1)
| ~ product(X3,X6,X0)
| ~ product(X5,X6,X2)
| ~ sum(X3,X4,X5)
| sum(X0,X1,X2) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
defined(b),
inference(clausification,[status(esa)],[b_is_defined]) ).
cnf(c2,plain,
defined(u),
inference(clausification,[status(esa)],[u_is_defined]) ).
cnf(c3,plain,
defined(v),
inference(clausification,[status(esa)],[v_is_defined]) ).
cnf(c4,plain,
~ sum('additive$uidentity',b,'additive$uidentity'),
inference(clausification,[status(esa)],[not_sum_5]) ).
cnf(c5,plain,
product(a,u,b),
inference(clausification,[status(esa)],[product_6]) ).
cnf(c6,plain,
product(a,v,b),
inference(clausification,[status(esa)],[product_7]) ).
cnf(c7,plain,
~ product('multiplicative$uidentity',u,v),
inference(clausification,[status(esa)],[not_product_8]) ).
cnf(c8,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_addition_1]) ).
cnf(c10,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c11,plain,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(c12,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(c13,plain,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_multiplication_1]) ).
cnf(c14,plain,
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_multiplication_2]) ).
cnf(c15,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_multiplication]) ).
cnf(c16,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,'additive$uidentity')
| product('multiplicative$uinverse'(X0),X0,'multiplicative$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_multiplication]) ).
cnf(c17,plain,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_multiplication]) ).
cnf(c18,plain,
( ~ sum(X3,X5,X6)
| ~ product(X6,X4,X2)
| ~ product(X5,X4,X1)
| ~ product(X3,X4,X0)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity_1]) ).
cnf(d0,plain,
( ~ defined(X0)
| sum(X0,'additive$uinverse'(X0),'additive$uidentity') ),
inference(resolution,[status(thm)],[c12,c11]) ).
cnf(d1,plain,
( ~ sum(X3,X0,X1)
| sum(X3,'additive$uidentity',X2)
| ~ sum(X1,'additive$uinverse'(X0),X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d0,c8]) ).
cnf(d2,plain,
( ~ defined(X0)
| sum(X1,'additive$uidentity','additive$uidentity')
| ~ sum(X1,X0,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ product(X2,u,X0)
| ~ product(X3,u,X1)
| ~ sum(a,X2,X3)
| sum(b,X0,X1) ),
inference(resolution,[status(thm)],[c18,c5]) ).
cnf(d4,plain,
( ~ product(X0,u,X1)
| sum(b,b,X1)
| ~ sum(a,a,X0) ),
inference(resolution,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
( sum(b,b,b)
| ~ sum(a,a,a) ),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
( ~ defined(X1)
| ~ sum(X3,'additive$uidentity',X0)
| sum(X3,X1,X2)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c8,c10]) ).
cnf(d7,plain,
( ~ defined(X0)
| ~ sum(X1,'additive$uidentity','additive$uidentity')
| sum(X1,X0,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d6,c10]) ).
cnf(d8,plain,
( ~ defined(X0)
| product(X0,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[c17,c15]) ).
cnf(d9,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X3,X2)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c13,c15]) ).
cnf(d10,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X1,X0)
| ~ product(X0,'multiplicative$uidentity',X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
( product(X0,'multiplicative$uinverse'(X0),'multiplicative$uidentity')
| sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c16,c17]) ).
cnf(d12,plain,
product(v,a,b),
inference(resolution,[status(thm)],[c17,c6]) ).
cnf(d13,plain,
( product(v,X2,X1)
| ~ product(a,X0,X2)
| ~ product(b,X0,X1) ),
inference(resolution,[status(thm)],[c13,d12]) ).
cnf(d14,plain,
product(u,a,b),
inference(resolution,[status(thm)],[c17,c5]) ).
cnf(d15,plain,
( ~ product(u,X2,X1)
| ~ product(a,X0,X2)
| product(b,X0,X1) ),
inference(resolution,[status(thm)],[c14,d14]) ).
cnf(d16,plain,
( ~ defined(u)
| product(b,X0,u)
| ~ product(a,X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d15,d8]) ).
cnf(d17,plain,
( product(b,X0,u)
| ~ product(a,X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c2,d16]) ).
cnf(d18,plain,
( sum('additive$uidentity',a,'additive$uidentity')
| ~ defined(a)
| product(b,'multiplicative$uinverse'(a),u) ),
inference(resolution,[status(thm)],[d17,d11]) ).
cnf(d19,plain,
( product(b,'multiplicative$uinverse'(a),u)
| sum('additive$uidentity',a,'additive$uidentity') ),
inference(resolution,[status(thm)],[c0,d18]) ).
cnf(d20,plain,
( product(v,X0,u)
| ~ product(a,'multiplicative$uinverse'(a),X0)
| sum('additive$uidentity',a,'additive$uidentity') ),
inference(resolution,[status(thm)],[d19,d13]) ).
cnf(d21,plain,
( sum('additive$uidentity',a,'additive$uidentity')
| ~ defined(a)
| product(v,'multiplicative$uidentity',u)
| sum('additive$uidentity',a,'additive$uidentity') ),
inference(resolution,[status(thm)],[d20,d11]) ).
cnf(d22,plain,
( product(v,'multiplicative$uidentity',u)
| sum('additive$uidentity',a,'additive$uidentity') ),
inference(resolution,[status(thm)],[c0,d21]) ).
cnf(d23,plain,
( product('multiplicative$uidentity',u,v)
| ~ defined(v)
| sum('additive$uidentity',a,'additive$uidentity') ),
inference(resolution,[status(thm)],[d22,d10]) ).
cnf(d24,plain,
( product('multiplicative$uidentity',u,v)
| sum('additive$uidentity',a,'additive$uidentity') ),
inference(resolution,[status(thm)],[c3,d23]) ).
cnf(d25,plain,
sum('additive$uidentity',a,'additive$uidentity'),
inference(resolution,[status(thm)],[c7,d24]) ).
cnf(d26,plain,
sum(a,'additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[d25,c12]) ).
cnf(d27,plain,
( sum(a,X0,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d26,d7]) ).
cnf(d28,plain,
( sum(b,b,b)
| ~ defined(a) ),
inference(resolution,[status(thm)],[d27,d5]) ).
cnf(d29,plain,
sum(b,b,b),
inference(resolution,[status(thm)],[c0,d28]) ).
cnf(d30,plain,
( sum(b,'additive$uidentity','additive$uidentity')
| ~ defined(b) ),
inference(resolution,[status(thm)],[d29,d2]) ).
cnf(d31,plain,
sum(b,'additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[c1,d30]) ).
cnf(d32,plain,
sum('additive$uidentity',b,'additive$uidentity'),
inference(resolution,[status(thm)],[d31,c12]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[c4,d32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD029-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.41 % Computer : n016.cluster.edu
% 0.07/0.41 % Model : x86_64 x86_64
% 0.07/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.41 % Memory : 8046.5625MB
% 0.07/0.41 % OS : Linux 6.8.0-71-generic
% 0.07/0.41 % CPULimit : 300
% 0.07/0.41 % WCLimit : 300
% 0.07/0.41 % DateTime : Sun Sep 27 02:29:46 UTC 2026
% 0.07/0.42 % CPUTime :
% 0.07/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.23/15.36 % SZS status Unsatisfiable for theBenchmark.p
% 2.23/15.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------