%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : TOP001-2 : 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 : n026.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 09:52:36 AM UTC 2026
% Result : Unsatisfiable 9.70s 6.66s
% Output : CNFRefutation 9.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 35 ( 6 unt; 5 nHn; 31 RR)
% Number of literals : 82 ( 0 equ; 45 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 72 ( 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(union_of_members_3,axiom,
( ~ 'element$uof$ucollection'(X2,X1)
| ~ 'element$uof$uset'(X0,X2)
| 'element$uof$uset'(X0,'union$uof$umembers'(X1)) ) ).
cnf(basis_for_topology_28,axiom,
( 'equal$usets'('union$uof$umembers'(X1),X0)
| ~ basis(X0,X1) ) ).
cnf(topology_generated_37,axiom,
( 'element$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$ubasis'(X1)) ) ).
cnf(set_theory_2,axiom,
( 'element$uof$uset'(X2,X1)
| ~ 'element$uof$uset'(X2,X0)
| ~ 'subset$usets'(X0,X1) ) ).
cnf(set_theory_3,axiom,
( 'subset$usets'(X0,X1)
| ~ 'equal$usets'(X0,X1) ) ).
cnf(set_theory_4,axiom,
( 'element$uof$uset'('in$u1st$uset'(X0,X1),X0)
| 'subset$usets'(X0,X1) ) ).
cnf(set_theory_5,axiom,
( ~ 'element$uof$uset'('in$u1st$uset'(X0,X1),X1)
| 'subset$usets'(X0,X1) ) ).
cnf(lemma_1a_1,negated_conjecture,
basis(cx,f) ).
cnf(lemma_1a_2,negated_conjecture,
~ 'subset$usets'('union$uof$umembers'('top$uof$ubasis'(f)),cx) ).
cnf(c0,plain,
( 'element$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$ucollection'(X2,X1)
| ~ 'element$uof$uset'(X0,X2)
| 'element$uof$uset'(X0,'union$uof$umembers'(X1)) ),
inference(clausification,[status(esa)],[union_of_members_3]) ).
cnf(c3,plain,
( 'equal$usets'('union$uof$umembers'(X1),X0)
| ~ basis(X0,X1) ),
inference(clausification,[status(esa)],[basis_for_topology_28]) ).
cnf(c4,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(c5,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(c7,plain,
( 'element$uof$uset'(X2,X1)
| ~ 'element$uof$uset'(X2,X0)
| ~ 'subset$usets'(X0,X1) ),
inference(clausification,[status(esa)],[set_theory_2]) ).
cnf(c8,plain,
( 'subset$usets'(X0,X1)
| ~ 'equal$usets'(X0,X1) ),
inference(clausification,[status(esa)],[set_theory_3]) ).
cnf(c9,plain,
( 'element$uof$uset'('in$u1st$uset'(X0,X1),X0)
| 'subset$usets'(X0,X1) ),
inference(clausification,[status(esa)],[set_theory_4]) ).
cnf(c10,plain,
( ~ 'element$uof$uset'('in$u1st$uset'(X0,X1),X1)
| 'subset$usets'(X0,X1) ),
inference(clausification,[status(esa)],[set_theory_5]) ).
cnf(c11,plain,
basis(cx,f),
inference(clausification,[status(esa)],[lemma_1a_1]) ).
cnf(c12,plain,
~ 'subset$usets'('union$uof$umembers'('top$uof$ubasis'(f)),cx),
inference(clausification,[status(esa)],[lemma_1a_2]) ).
cnf(d0,plain,
( 'subset$usets'('union$uof$umembers'(X1),X0)
| ~ basis(X0,X1) ),
inference(resolution,[status(thm)],[c3,c8]) ).
cnf(d1,plain,
( ~ basis(X1,X2)
| ~ 'element$uof$uset'(X0,'union$uof$umembers'(X2))
| 'element$uof$uset'(X0,X1) ),
inference(resolution,[status(thm)],[c7,d0]) ).
cnf(d2,plain,
( 'element$uof$uset'(X3,'union$uof$umembers'(X2))
| ~ 'element$uof$uset'(X3,f10(X2,X1,X0))
| ~ 'element$uof$ucollection'(X1,'top$uof$ubasis'(X2))
| ~ 'element$uof$uset'(X0,X1) ),
inference(resolution,[status(thm)],[c5,c2]) ).
cnf(d3,plain,
( ~ 'element$uof$ucollection'(X2,'top$uof$ubasis'(X1))
| ~ 'element$uof$uset'(X0,X2)
| ~ 'element$uof$ucollection'(X2,'top$uof$ubasis'(X1))
| ~ 'element$uof$uset'(X0,X2)
| 'element$uof$uset'(X0,'union$uof$umembers'(X1)) ),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
( ~ 'element$uof$uset'(X2,'union$uof$umembers'('top$uof$ubasis'(X1)))
| 'element$uof$uset'(X0,'union$uof$umembers'(X1))
| ~ 'element$uof$uset'(X0,f1('top$uof$ubasis'(X1),X2)) ),
inference(resolution,[status(thm)],[d3,c1]) ).
cnf(d5,plain,
( ~ 'element$uof$uset'(X0,'union$uof$umembers'('top$uof$ubasis'(X1)))
| 'element$uof$uset'(X0,'union$uof$umembers'(X1))
| ~ 'element$uof$uset'(X0,'union$uof$umembers'('top$uof$ubasis'(X1))) ),
inference(resolution,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
( 'subset$usets'('union$uof$umembers'('top$uof$ubasis'(X0)),X1)
| 'element$uof$uset'('in$u1st$uset'('union$uof$umembers'('top$uof$ubasis'(X0)),X1),'union$uof$umembers'(X0)) ),
inference(resolution,[status(thm)],[d5,c9]) ).
cnf(d7,plain,
( ~ basis(X2,X0)
| 'element$uof$uset'('in$u1st$uset'('union$uof$umembers'('top$uof$ubasis'(X0)),X1),X2)
| 'subset$usets'('union$uof$umembers'('top$uof$ubasis'(X0)),X1) ),
inference(resolution,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
( 'subset$usets'('union$uof$umembers'('top$uof$ubasis'(X1)),X0)
| 'subset$usets'('union$uof$umembers'('top$uof$ubasis'(X1)),X0)
| ~ basis(X0,X1) ),
inference(resolution,[status(thm)],[d7,c10]) ).
cnf(d9,plain,
~ basis(cx,f),
inference(resolution,[status(thm)],[d8,c12]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c11,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP001-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n026.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 20:32:32 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.70/6.66 % SZS status Unsatisfiable for theBenchmark.p
% 9.70/6.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------