%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : TOP005-2 : 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 : n015.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 09:52:37 AM UTC 2026
% Result : Unsatisfiable 26.37s 3.87s
% Output : CNFRefutation 26.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of clauses : 34 ( 7 unt; 2 nHn; 32 RR)
% Number of literals : 98 ( 0 equ; 65 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 71 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(union_of_members_1,axiom,
( 'element$uof$uset'(X0,f1(X1,X0))
| ~ 'element$uof$uset'(X0,'union$uof$umembers'(X1)) ) ).
cnf(union_of_members_2,axiom,
( 'element$uof$ucollection'(f1(X1,X0),X1)
| ~ 'element$uof$uset'(X0,'union$uof$umembers'(X1)) ) ).
cnf(topology_generated_37,axiom,
( 'element$uof$uset'(X2,f10(X1,X0,X2))
| ~ 'element$uof$uset'(X2,X0)
| ~ 'element$uof$ucollection'(X0,'top$uof$ubasis'(X1)) ) ).
cnf(topology_generated_38,axiom,
( 'element$uof$ucollection'(f10(X1,X0,X2),X1)
| ~ 'element$uof$uset'(X2,X0)
| ~ 'element$uof$ucollection'(X0,'top$uof$ubasis'(X1)) ) ).
cnf(topology_generated_39,axiom,
( 'subset$usets'(f10(X1,X0,X2),X0)
| ~ 'element$uof$uset'(X2,X0)
| ~ 'element$uof$ucollection'(X0,'top$uof$ubasis'(X1)) ) ).
cnf(topology_generated_40,axiom,
( 'element$uof$uset'(f11(X1,X0),X0)
| 'element$uof$ucollection'(X0,'top$uof$ubasis'(X1)) ) ).
cnf(topology_generated_41,axiom,
( ~ 'subset$usets'(X2,X0)
| ~ 'element$uof$ucollection'(X2,X1)
| ~ 'element$uof$uset'(f11(X1,X0),X2)
| 'element$uof$ucollection'(X0,'top$uof$ubasis'(X1)) ) ).
cnf(set_theory_20,axiom,
( 'subset$usets'(X0,'union$uof$umembers'(X2))
| ~ 'element$uof$ucollection'(X1,X2)
| ~ 'subset$usets'(X0,X1) ) ).
cnf(set_theory_21,axiom,
( 'element$uof$ucollection'(X2,X1)
| ~ 'element$uof$ucollection'(X2,X0)
| ~ 'subset$ucollections'(X0,X1) ) ).
cnf(lemma_1e_2,negated_conjecture,
'subset$ucollections'(g,'top$uof$ubasis'(f)) ).
cnf(lemma_1e_3,negated_conjecture,
~ 'element$uof$ucollection'('union$uof$umembers'(g),'top$uof$ubasis'(f)) ).
cnf(c0,plain,
( 'element$uof$uset'(X0,f1(X1,X0))
| ~ 'element$uof$uset'(X0,'union$uof$umembers'(X1)) ),
inference(clausification,[status(esa)],[union_of_members_1]) ).
cnf(c1,plain,
( 'element$uof$ucollection'(f1(X1,X0),X1)
| ~ 'element$uof$uset'(X0,'union$uof$umembers'(X1)) ),
inference(clausification,[status(esa)],[union_of_members_2]) ).
cnf(c2,plain,
( 'element$uof$uset'(X2,f10(X1,X0,X2))
| ~ 'element$uof$uset'(X2,X0)
| ~ 'element$uof$ucollection'(X0,'top$uof$ubasis'(X1)) ),
inference(clausification,[status(esa)],[topology_generated_37]) ).
cnf(c3,plain,
( 'element$uof$ucollection'(f10(X1,X0,X2),X1)
| ~ 'element$uof$uset'(X2,X0)
| ~ 'element$uof$ucollection'(X0,'top$uof$ubasis'(X1)) ),
inference(clausification,[status(esa)],[topology_generated_38]) ).
cnf(c4,plain,
( 'subset$usets'(f10(X1,X0,X2),X0)
| ~ 'element$uof$uset'(X2,X0)
| ~ 'element$uof$ucollection'(X0,'top$uof$ubasis'(X1)) ),
inference(clausification,[status(esa)],[topology_generated_39]) ).
cnf(c5,plain,
( 'element$uof$uset'(f11(X1,X0),X0)
| 'element$uof$ucollection'(X0,'top$uof$ubasis'(X1)) ),
inference(clausification,[status(esa)],[topology_generated_40]) ).
cnf(c6,plain,
( ~ 'subset$usets'(X2,X0)
| ~ 'element$uof$ucollection'(X2,X1)
| ~ 'element$uof$uset'(f11(X1,X0),X2)
| 'element$uof$ucollection'(X0,'top$uof$ubasis'(X1)) ),
inference(clausification,[status(esa)],[topology_generated_41]) ).
cnf(c8,plain,
( 'subset$usets'(X0,'union$uof$umembers'(X2))
| ~ 'element$uof$ucollection'(X1,X2)
| ~ 'subset$usets'(X0,X1) ),
inference(clausification,[status(esa)],[set_theory_20]) ).
cnf(c9,plain,
( 'element$uof$ucollection'(X2,X1)
| ~ 'element$uof$ucollection'(X2,X0)
| ~ 'subset$ucollections'(X0,X1) ),
inference(clausification,[status(esa)],[set_theory_21]) ).
cnf(c10,plain,
'subset$ucollections'(g,'top$uof$ubasis'(f)),
inference(clausification,[status(esa)],[lemma_1e_2]) ).
cnf(c11,plain,
~ 'element$uof$ucollection'('union$uof$umembers'(g),'top$uof$ubasis'(f)),
inference(clausification,[status(esa)],[lemma_1e_3]) ).
cnf(d0,plain,
( ~ 'element$uof$ucollection'(X0,g)
| 'element$uof$ucollection'(X0,'top$uof$ubasis'(f)) ),
inference(resolution,[status(thm)],[c9,c10]) ).
cnf(d1,plain,
( ~ 'element$uof$ucollection'(X1,'top$uof$ubasis'(X0))
| ~ 'element$uof$uset'(f11(X2,X3),X1)
| ~ 'subset$usets'(f10(X0,X1,f11(X2,X3)),X3)
| 'element$uof$ucollection'(X3,'top$uof$ubasis'(X2))
| ~ 'element$uof$ucollection'(f10(X0,X1,f11(X2,X3)),X2) ),
inference(resolution,[status(thm)],[c6,c2]) ).
cnf(d2,plain,
( ~ 'subset$usets'(f10(X3,X2,f11(X0,'union$uof$umembers'(X1))),X4)
| ~ 'element$uof$ucollection'(X4,X1)
| ~ 'element$uof$ucollection'(f10(X3,X2,f11(X0,'union$uof$umembers'(X1))),X0)
| ~ 'element$uof$ucollection'(X2,'top$uof$ubasis'(X3))
| 'element$uof$ucollection'('union$uof$umembers'(X1),'top$uof$ubasis'(X0))
| ~ 'element$uof$uset'(f11(X0,'union$uof$umembers'(X1)),X2) ),
inference(resolution,[status(thm)],[d1,c8]) ).
cnf(d3,plain,
( ~ 'element$uof$ucollection'(X2,'top$uof$ubasis'(X3))
| ~ 'element$uof$uset'(f11(X0,'union$uof$umembers'(X1)),X2)
| ~ 'element$uof$ucollection'(f10(X3,X2,f11(X0,'union$uof$umembers'(X1))),X0)
| 'element$uof$ucollection'('union$uof$umembers'(X1),'top$uof$ubasis'(X0))
| ~ 'element$uof$ucollection'(X2,'top$uof$ubasis'(X3))
| ~ 'element$uof$ucollection'(X2,X1)
| ~ 'element$uof$uset'(f11(X0,'union$uof$umembers'(X1)),X2) ),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
( ~ 'element$uof$ucollection'(X2,'top$uof$ubasis'(X0))
| ~ 'element$uof$uset'(f11(X0,'union$uof$umembers'(X1)),X2)
| 'element$uof$ucollection'('union$uof$umembers'(X1),'top$uof$ubasis'(X0))
| ~ 'element$uof$ucollection'(X2,'top$uof$ubasis'(X0))
| ~ 'element$uof$ucollection'(X2,X1)
| ~ 'element$uof$uset'(f11(X0,'union$uof$umembers'(X1)),X2) ),
inference(resolution,[status(thm)],[d3,c3]) ).
cnf(d5,plain,
( ~ 'element$uof$uset'(f11(X1,'union$uof$umembers'(X2)),'union$uof$umembers'(X0))
| 'element$uof$ucollection'('union$uof$umembers'(X2),'top$uof$ubasis'(X1))
| ~ 'element$uof$ucollection'(f1(X0,f11(X1,'union$uof$umembers'(X2))),'top$uof$ubasis'(X1))
| ~ 'element$uof$ucollection'(f1(X0,f11(X1,'union$uof$umembers'(X2))),X2) ),
inference(resolution,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
( ~ 'element$uof$ucollection'(f1(X1,f11(f,'union$uof$umembers'(X0))),g)
| ~ 'element$uof$ucollection'(f1(X1,f11(f,'union$uof$umembers'(X0))),X0)
| 'element$uof$ucollection'('union$uof$umembers'(X0),'top$uof$ubasis'(f))
| ~ 'element$uof$uset'(f11(f,'union$uof$umembers'(X0)),'union$uof$umembers'(X1)) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
( ~ 'element$uof$uset'(f11(f,'union$uof$umembers'(X0)),'union$uof$umembers'(g))
| ~ 'element$uof$ucollection'(f1(g,f11(f,'union$uof$umembers'(X0))),X0)
| 'element$uof$ucollection'('union$uof$umembers'(X0),'top$uof$ubasis'(f))
| ~ 'element$uof$uset'(f11(f,'union$uof$umembers'(X0)),'union$uof$umembers'(g)) ),
inference(resolution,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
( ~ 'element$uof$uset'(f11(f,'union$uof$umembers'(g)),'union$uof$umembers'(g))
| 'element$uof$ucollection'('union$uof$umembers'(g),'top$uof$ubasis'(f))
| ~ 'element$uof$uset'(f11(f,'union$uof$umembers'(g)),'union$uof$umembers'(g)) ),
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
~ 'element$uof$uset'(f11(f,'union$uof$umembers'(g)),'union$uof$umembers'(g)),
inference(resolution,[status(thm)],[c11,d8]) ).
cnf(d10,plain,
'element$uof$ucollection'('union$uof$umembers'(g),'top$uof$ubasis'(f)),
inference(resolution,[status(thm)],[d9,c5]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[c11,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP005-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 20:34:00 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.37/3.87 % SZS status Unsatisfiable for theBenchmark.p
% 26.37/3.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------