%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD050-4 : 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 : n011.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 07:10:54 AM UTC 2026
% Result : Unsatisfiable 80.27s 10.65s
% Output : CNFRefutation 80.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of clauses : 55 ( 29 unt; 7 nHn; 55 RR)
% Number of literals : 99 ( 0 equ; 43 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 53 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(b_is_defined,hypothesis,
defined(b) ).
cnf(c_is_defined,hypothesis,
defined(c) ).
cnf(d_is_defined,hypothesis,
defined(d) ).
cnf(not_sum_7,negated_conjecture,
~ sum('additive$uidentity',b,'additive$uidentity') ).
cnf(not_sum_8,negated_conjecture,
~ sum('additive$uidentity',d,'additive$uidentity') ).
cnf(product_9,negated_conjecture,
product(a,'multiplicative$uinverse'(b),s) ).
cnf(product_10,negated_conjecture,
product(a,d,k) ).
cnf(product_11,negated_conjecture,
product(b,c,k) ).
cnf(not_product_12,negated_conjecture,
~ product(c,'multiplicative$uinverse'(d),s) ).
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$uidentity') ) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
defined(b),
inference(clausification,[status(esa)],[b_is_defined]) ).
cnf(c2,plain,
defined(c),
inference(clausification,[status(esa)],[c_is_defined]) ).
cnf(c3,plain,
defined(d),
inference(clausification,[status(esa)],[d_is_defined]) ).
cnf(c6,plain,
~ sum('additive$uidentity',b,'additive$uidentity'),
inference(clausification,[status(esa)],[not_sum_7]) ).
cnf(c7,plain,
~ sum('additive$uidentity',d,'additive$uidentity'),
inference(clausification,[status(esa)],[not_sum_8]) ).
cnf(c8,plain,
product(a,'multiplicative$uinverse'(b),s),
inference(clausification,[status(esa)],[product_9]) ).
cnf(c9,plain,
product(a,d,k),
inference(clausification,[status(esa)],[product_10]) ).
cnf(c10,plain,
product(b,c,k),
inference(clausification,[status(esa)],[product_11]) ).
cnf(c11,plain,
~ product(c,'multiplicative$uinverse'(d),s),
inference(clausification,[status(esa)],[not_product_12]) ).
cnf(c17,plain,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_multiplication_1]) ).
cnf(c18,plain,
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_multiplication_2]) ).
cnf(c19,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_multiplication]) ).
cnf(c20,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(c21,plain,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_multiplication]) ).
cnf(d0,plain,
( product(X0,'multiplicative$uinverse'(X0),'multiplicative$uidentity')
| sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c20,c21]) ).
cnf(d1,plain,
( ~ defined(X0)
| product(X0,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[c21,c19]) ).
cnf(d2,plain,
product('multiplicative$uinverse'(b),a,s),
inference(resolution,[status(thm)],[c21,c8]) ).
cnf(d3,plain,
( ~ product('multiplicative$uinverse'(b),X2,X1)
| ~ product(a,X0,X2)
| product(s,X0,X1) ),
inference(resolution,[status(thm)],[c18,d2]) ).
cnf(d4,plain,
( product(s,X0,s)
| ~ product(a,X0,a) ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( ~ defined(a)
| product(s,'multiplicative$uidentity',s) ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
product(s,'multiplicative$uidentity',s),
inference(resolution,[status(thm)],[c0,d5]) ).
cnf(d7,plain,
product(d,a,k),
inference(resolution,[status(thm)],[c21,c9]) ).
cnf(d8,plain,
( product(d,X2,X1)
| ~ product(a,X0,X2)
| ~ product(k,X0,X1) ),
inference(resolution,[status(thm)],[c17,d7]) ).
cnf(d9,plain,
product(c,b,k),
inference(resolution,[status(thm)],[c21,c10]) ).
cnf(d10,plain,
( ~ product(c,X2,X1)
| ~ product(b,X0,X2)
| product(k,X0,X1) ),
inference(resolution,[status(thm)],[c18,d9]) ).
cnf(d11,plain,
( ~ defined(c)
| product(k,X0,c)
| ~ product(b,X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
( product(k,X0,c)
| ~ product(b,X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c2,d11]) ).
cnf(d13,plain,
( sum('additive$uidentity',b,'additive$uidentity')
| ~ defined(b)
| product(k,'multiplicative$uinverse'(b),c) ),
inference(resolution,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
( product(k,'multiplicative$uinverse'(b),c)
| sum('additive$uidentity',b,'additive$uidentity') ),
inference(resolution,[status(thm)],[c1,d13]) ).
cnf(d15,plain,
product(k,'multiplicative$uinverse'(b),c),
inference(resolution,[status(thm)],[c6,d14]) ).
cnf(d16,plain,
( product(d,X0,c)
| ~ product(a,'multiplicative$uinverse'(b),X0) ),
inference(resolution,[status(thm)],[d15,d8]) ).
cnf(d17,plain,
product(d,s,c),
inference(resolution,[status(thm)],[d16,c8]) ).
cnf(d18,plain,
product(s,d,c),
inference(resolution,[status(thm)],[d17,c21]) ).
cnf(d19,plain,
( ~ product(s,X2,X1)
| ~ product(d,X0,X2)
| product(c,X0,X1) ),
inference(resolution,[status(thm)],[d18,c18]) ).
cnf(d20,plain,
( ~ product(d,X0,'multiplicative$uidentity')
| product(c,X0,s) ),
inference(resolution,[status(thm)],[d19,d6]) ).
cnf(d21,plain,
( sum('additive$uidentity',d,'additive$uidentity')
| ~ defined(d)
| product(c,'multiplicative$uinverse'(d),s) ),
inference(resolution,[status(thm)],[d20,d0]) ).
cnf(d22,plain,
( product(c,'multiplicative$uinverse'(d),s)
| sum('additive$uidentity',d,'additive$uidentity') ),
inference(resolution,[status(thm)],[c3,d21]) ).
cnf(d23,plain,
product(c,'multiplicative$uinverse'(d),s),
inference(resolution,[status(thm)],[c7,d22]) ).
cnf(d24,plain,
$false,
inference(resolution,[status(thm)],[c11,d23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD050-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n011.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sun Sep 27 02:30:01 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 80.27/10.65 % SZS status Unsatisfiable for theBenchmark.p
% 80.27/10.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------