%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD035-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 07:10:51 AM UTC 2026
% Result : Unsatisfiable 46.34s 9.25s
% Output : CNFRefutation 46.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of clauses : 60 ( 25 unt; 7 nHn; 60 RR)
% Number of literals : 123 ( 0 equ; 60 neg)
% Maximal clause size : 4 ( 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; 0-2 aty)
% Number of variables : 65 ( 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(u_is_defined,hypothesis,
defined(u) ).
cnf(product_5,negated_conjecture,
product(a,c,u) ).
cnf(product_6,negated_conjecture,
product(b,c,u) ).
cnf(not_sum_7,negated_conjecture,
~ sum('additive$uidentity',c,'additive$uidentity') ).
cnf(not_product_8,negated_conjecture,
~ product('multiplicative$uidentity',a,b) ).
cnf(associativity_multiplication_1,axiom,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ) ).
cnf(associativity_multiplication_2,axiom,
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X0)
| product('multiplicative$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(well_definedness_of_multiplicative_identity,axiom,
defined('multiplicative$uidentity') ).
cnf(totality_of_multiplication,axiom,
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
defined(b),
inference(clausification,[status(esa)],[b_is_defined]) ).
cnf(c2,plain,
defined(c),
inference(clausification,[status(esa)],[c_is_defined]) ).
cnf(c3,plain,
defined(u),
inference(clausification,[status(esa)],[u_is_defined]) ).
cnf(c4,plain,
product(a,c,u),
inference(clausification,[status(esa)],[product_5]) ).
cnf(c5,plain,
product(b,c,u),
inference(clausification,[status(esa)],[product_6]) ).
cnf(c6,plain,
~ sum('additive$uidentity',c,'additive$uidentity'),
inference(clausification,[status(esa)],[not_sum_7]) ).
cnf(c7,plain,
~ product('multiplicative$uidentity',a,b),
inference(clausification,[status(esa)],[not_product_8]) ).
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$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_multiplication]) ).
cnf(c17,plain,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_multiplication]) ).
cnf(c24,plain,
defined('multiplicative$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_multiplicative_identity]) ).
cnf(c27,plain,
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ),
inference(clausification,[status(esa)],[totality_of_multiplication]) ).
cnf(d0,plain,
( ~ defined(X0)
| product(X0,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[c17,c15]) ).
cnf(d1,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X3,X2)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c13,c15]) ).
cnf(d2,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X1,X0)
| ~ product(X0,'multiplicative$uidentity',X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( product(X0,'multiplicative$uinverse'(X0),'multiplicative$uidentity')
| sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c16,c17]) ).
cnf(d4,plain,
( product(b,X2,X1)
| ~ product(c,X0,X2)
| ~ product(u,X0,X1) ),
inference(resolution,[status(thm)],[c13,c5]) ).
cnf(d5,plain,
( product(X0,X1,multiply(X1,X0))
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c27,c17]) ).
cnf(d6,plain,
( ~ defined(X0)
| ~ defined('multiplicative$uidentity')
| product('multiplicative$uidentity',multiply('multiplicative$uidentity',X0),X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d2,d5]) ).
cnf(d7,plain,
( product('multiplicative$uidentity',multiply('multiplicative$uidentity',X0),X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c24,d6]) ).
cnf(d8,plain,
( product(multiply('multiplicative$uidentity',X0),'multiplicative$uidentity',X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d7,c17]) ).
cnf(d9,plain,
product(c,a,u),
inference(resolution,[status(thm)],[c17,c4]) ).
cnf(d10,plain,
( product(c,X2,X1)
| ~ product(a,X0,X2)
| ~ product(u,X0,X1) ),
inference(resolution,[status(thm)],[c13,d9]) ).
cnf(d11,plain,
( ~ defined(u)
| product(c,X0,u)
| ~ product(a,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
( product(c,X0,u)
| ~ product(a,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[c3,d11]) ).
cnf(d13,plain,
( ~ defined(a)
| ~ defined('multiplicative$uidentity')
| product(c,multiply('multiplicative$uidentity',a),u) ),
inference(resolution,[status(thm)],[d12,d5]) ).
cnf(d14,plain,
( product(c,multiply('multiplicative$uidentity',a),u)
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c0,d13]) ).
cnf(d15,plain,
product(c,multiply('multiplicative$uidentity',a),u),
inference(resolution,[status(thm)],[c24,d14]) ).
cnf(d16,plain,
product(multiply('multiplicative$uidentity',a),c,u),
inference(resolution,[status(thm)],[d15,c17]) ).
cnf(d17,plain,
( ~ product(multiply('multiplicative$uidentity',a),X2,X1)
| ~ product(c,X0,X2)
| product(u,X0,X1) ),
inference(resolution,[status(thm)],[c14,d16]) ).
cnf(d18,plain,
( ~ defined(a)
| product(u,X0,a)
| ~ product(c,X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d17,d8]) ).
cnf(d19,plain,
( product(u,X0,a)
| ~ product(c,X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c0,d18]) ).
cnf(d20,plain,
( sum('additive$uidentity',c,'additive$uidentity')
| ~ defined(c)
| product(u,'multiplicative$uinverse'(c),a) ),
inference(resolution,[status(thm)],[d19,d3]) ).
cnf(d21,plain,
( sum('additive$uidentity',c,'additive$uidentity')
| product(u,'multiplicative$uinverse'(c),a) ),
inference(resolution,[status(thm)],[c2,d20]) ).
cnf(d22,plain,
product(u,'multiplicative$uinverse'(c),a),
inference(resolution,[status(thm)],[c6,d21]) ).
cnf(d23,plain,
( ~ product(c,'multiplicative$uinverse'(c),X0)
| product(b,X0,a) ),
inference(resolution,[status(thm)],[d22,d4]) ).
cnf(d24,plain,
( sum('additive$uidentity',c,'additive$uidentity')
| ~ defined(c)
| product(b,'multiplicative$uidentity',a) ),
inference(resolution,[status(thm)],[d23,d3]) ).
cnf(d25,plain,
( sum('additive$uidentity',c,'additive$uidentity')
| product(b,'multiplicative$uidentity',a) ),
inference(resolution,[status(thm)],[c2,d24]) ).
cnf(d26,plain,
product(b,'multiplicative$uidentity',a),
inference(resolution,[status(thm)],[c6,d25]) ).
cnf(d27,plain,
( product('multiplicative$uidentity',a,b)
| ~ defined(b) ),
inference(resolution,[status(thm)],[d26,d2]) ).
cnf(d28,plain,
product('multiplicative$uidentity',a,b),
inference(resolution,[status(thm)],[c1,d27]) ).
cnf(d29,plain,
$false,
inference(resolution,[status(thm)],[c7,d28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD035-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n004.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 27 02:25:52 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 46.34/9.25 % SZS status Unsatisfiable for theBenchmark.p
% 46.34/9.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------