%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD016-3 : 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 : n006.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 07:10:45 AM UTC 2026
% Result : Unsatisfiable 19.96s 2.95s
% Output : CNFRefutation 19.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of clauses : 64 ( 23 unt; 2 nHn; 64 RR)
% Number of literals : 141 ( 0 equ; 79 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 : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 82 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(u_is_defined,hypothesis,
defined(u) ).
cnf(v_is_defined,hypothesis,
defined(v) ).
cnf(sum_5,negated_conjecture,
sum(a,u,b) ).
cnf(sum_6,negated_conjecture,
sum(a,v,b) ).
cnf(not_sum_7,negated_conjecture,
~ sum('additive$uidentity',u,v) ).
cnf(associativity_addition_1,axiom,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ) ).
cnf(associativity_addition_2,axiom,
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| sum('additive$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(antisymmetry_of_order_relation,axiom,
( ~ 'less$uor$uequal'(X1,X0)
| ~ 'less$uor$uequal'(X0,X1)
| sum('additive$uidentity',X0,X1) ) ).
cnf(totality_of_order_relation,axiom,
( ~ defined(X1)
| ~ defined(X0)
| 'less$uor$uequal'(X1,X0)
| 'less$uor$uequal'(X0,X1) ) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ 'less$uor$uequal'(X2,X3)
| 'less$uor$uequal'(X0,X1) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c2,plain,
defined(u),
inference(clausification,[status(esa)],[u_is_defined]) ).
cnf(c3,plain,
defined(v),
inference(clausification,[status(esa)],[v_is_defined]) ).
cnf(c4,plain,
sum(a,u,b),
inference(clausification,[status(esa)],[sum_5]) ).
cnf(c5,plain,
sum(a,v,b),
inference(clausification,[status(esa)],[sum_6]) ).
cnf(c6,plain,
~ sum('additive$uidentity',u,v),
inference(clausification,[status(esa)],[not_sum_7]) ).
cnf(c7,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(c8,plain,
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_addition_2]) ).
cnf(c9,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c10,plain,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(c11,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(c27,plain,
( ~ 'less$uor$uequal'(X1,X0)
| ~ 'less$uor$uequal'(X0,X1)
| sum('additive$uidentity',X0,X1) ),
inference(clausification,[status(esa)],[antisymmetry_of_order_relation]) ).
cnf(c29,plain,
( ~ defined(X1)
| ~ defined(X0)
| 'less$uor$uequal'(X1,X0)
| 'less$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[totality_of_order_relation]) ).
cnf(c30,plain,
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ 'less$uor$uequal'(X2,X3)
| 'less$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[compatibility_of_order_relation_and_addition]) ).
cnf(d0,plain,
( ~ sum(X2,a,X0)
| sum(X2,b,X1)
| ~ sum(X0,v,X1) ),
inference(resolution,[status(thm)],[c7,c5]) ).
cnf(d1,plain,
( ~ defined(v)
| sum(X0,b,v)
| ~ sum(X0,a,'additive$uidentity') ),
inference(resolution,[status(thm)],[d0,c9]) ).
cnf(d2,plain,
( sum(X0,b,v)
| ~ sum(X0,a,'additive$uidentity') ),
inference(resolution,[status(thm)],[c3,d1]) ).
cnf(d3,plain,
( ~ defined(a)
| sum('additive$uinverse'(a),b,v) ),
inference(resolution,[status(thm)],[d2,c10]) ).
cnf(d4,plain,
sum('additive$uinverse'(a),b,v),
inference(resolution,[status(thm)],[c0,d3]) ).
cnf(d5,plain,
sum(b,'additive$uinverse'(a),v),
inference(resolution,[status(thm)],[d4,c11]) ).
cnf(d6,plain,
( ~ sum(X2,a,X0)
| sum(X2,b,X1)
| ~ sum(X0,u,X1) ),
inference(resolution,[status(thm)],[c7,c4]) ).
cnf(d7,plain,
( ~ defined(u)
| sum(X0,b,u)
| ~ sum(X0,a,'additive$uidentity') ),
inference(resolution,[status(thm)],[d6,c9]) ).
cnf(d8,plain,
( sum(X0,b,u)
| ~ sum(X0,a,'additive$uidentity') ),
inference(resolution,[status(thm)],[c2,d7]) ).
cnf(d9,plain,
( ~ defined(a)
| sum('additive$uinverse'(a),b,u) ),
inference(resolution,[status(thm)],[d8,c10]) ).
cnf(d10,plain,
sum('additive$uinverse'(a),b,u),
inference(resolution,[status(thm)],[c0,d9]) ).
cnf(d11,plain,
sum(b,'additive$uinverse'(a),u),
inference(resolution,[status(thm)],[d10,c11]) ).
cnf(d12,plain,
( ~ 'less$uor$uequal'(b,X0)
| 'less$uor$uequal'(u,X1)
| ~ sum(X0,'additive$uinverse'(a),X1) ),
inference(resolution,[status(thm)],[d11,c30]) ).
cnf(d13,plain,
( 'less$uor$uequal'(u,v)
| ~ 'less$uor$uequal'(b,b) ),
inference(resolution,[status(thm)],[d12,d5]) ).
cnf(d14,plain,
( 'less$uor$uequal'(X0,X0)
| ~ defined(X0)
| ~ defined(X0) ),
inference(factoring,[status(thm)],[c29]) ).
cnf(d15,plain,
( ~ 'less$uor$uequal'(a,X0)
| 'less$uor$uequal'(b,X1)
| ~ sum(X0,u,X1) ),
inference(resolution,[status(thm)],[c30,c4]) ).
cnf(d16,plain,
( 'less$uor$uequal'(b,b)
| ~ 'less$uor$uequal'(a,a) ),
inference(resolution,[status(thm)],[d15,c4]) ).
cnf(d17,plain,
( ~ defined(a)
| 'less$uor$uequal'(b,b) ),
inference(resolution,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
'less$uor$uequal'(b,b),
inference(resolution,[status(thm)],[c0,d17]) ).
cnf(d19,plain,
'less$uor$uequal'(u,v),
inference(resolution,[status(thm)],[d18,d13]) ).
cnf(d20,plain,
( ~ 'less$uor$uequal'(v,u)
| ~ 'less$uor$uequal'(u,v) ),
inference(resolution,[status(thm)],[c27,c6]) ).
cnf(d21,plain,
( ~ defined(X1)
| ~ 'less$uor$uequal'('additive$uidentity',X0)
| 'less$uor$uequal'(X1,X2)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c30,c9]) ).
cnf(d22,plain,
( ~ sum('additive$uinverse'(X0),X3,X2)
| ~ sum(X0,X1,X3)
| sum('additive$uidentity',X1,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c10,c8]) ).
cnf(d23,plain,
( sum('additive$uidentity',X0,u)
| ~ sum(a,X0,b)
| ~ defined(a) ),
inference(resolution,[status(thm)],[d10,d22]) ).
cnf(d24,plain,
( sum('additive$uidentity',X0,u)
| ~ sum(a,X0,b) ),
inference(resolution,[status(thm)],[c0,d23]) ).
cnf(d25,plain,
sum('additive$uidentity',v,u),
inference(resolution,[status(thm)],[d24,c5]) ).
cnf(d26,plain,
( ~ 'less$uor$uequal'('additive$uidentity','additive$uidentity')
| 'less$uor$uequal'(v,u)
| ~ defined(v) ),
inference(resolution,[status(thm)],[d25,d21]) ).
cnf(d27,plain,
( ~ 'less$uor$uequal'('additive$uidentity','additive$uidentity')
| 'less$uor$uequal'(v,u) ),
inference(resolution,[status(thm)],[c3,d26]) ).
cnf(d28,plain,
( ~ defined(X0)
| sum(X0,'additive$uinverse'(X0),'additive$uidentity') ),
inference(resolution,[status(thm)],[c11,c10]) ).
cnf(d29,plain,
( ~ defined(X1)
| ~ 'less$uor$uequal'(X1,X0)
| 'less$uor$uequal'('additive$uidentity',X2)
| ~ sum(X0,'additive$uinverse'(X1),X2) ),
inference(resolution,[status(thm)],[c30,d28]) ).
cnf(d30,plain,
( ~ defined(X0)
| 'less$uor$uequal'('additive$uidentity','additive$uidentity')
| ~ 'less$uor$uequal'(X0,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d29,d28]) ).
cnf(d31,plain,
( ~ defined(X0)
| 'less$uor$uequal'('additive$uidentity','additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d30,d14]) ).
cnf(d32,plain,
'less$uor$uequal'('additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[d31,c0]) ).
cnf(d33,plain,
'less$uor$uequal'(v,u),
inference(resolution,[status(thm)],[d32,d27]) ).
cnf(d34,plain,
~ 'less$uor$uequal'(u,v),
inference(resolution,[status(thm)],[d33,d20]) ).
cnf(d35,plain,
$false,
inference(resolution,[status(thm)],[d34,d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD016-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 02:22:10 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.96/2.95 % SZS status Unsatisfiable for theBenchmark.p
% 19.96/2.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------