%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : TOP002-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 03:54:38 PM UTC 2026
% Result : Unsatisfiable 5.92s 1.35s
% Output : Proof 5.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 21 unt; 0 def)
% Number of atoms : 29 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 11 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 23 ( 7 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( element_of_set(f11(Vf,U),U)
| element_of_collection(U,top_of_basis(Vf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_40) ).
fof(f0_nnf,plain,
! [U,Vf] :
( element_of_set(f11(Vf,U),U)
| element_of_collection(U,top_of_basis(Vf)) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [U,Vf] :
( element_of_set(f11(Vf,U),U)
| element_of_collection(U,top_of_basis(Vf)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( element_of_set(f11(X1,X0),X0)
| element_of_collection(X0,top_of_basis(X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t9,plain,
or(element_of_collection(X1,top_of_basis(X2)),element_of_set(f11(X2,X1),X1)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t15,plain,
or(element_of_collection(X1,top_of_basis(X2)),element_of_set(f11(X2,X1),X1)) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(f1,axiom,
~ element_of_set(X,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_6) ).
fof(f1_nnf,plain,
! [X] : ~ element_of_set(X,empty_set),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : ~ element_of_set(X,empty_set),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ element_of_set(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t0,plain,
element_of_set(X1,empty_set) = false,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t21,plain,
element_of_set(X1,empty_set) = false,
inference(orient,[status(thm)],[t0]) ).
cnf(t22,plain,
true = or(element_of_collection(empty_set,top_of_basis(X1)),false),
inference(cp,[status(thm)],[t15,t21]) ).
cnf(t1,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t10,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t28,plain,
true = element_of_collection(empty_set,top_of_basis(X1)),
inference(step,[status(thm)],[t22,t10]) ).
cnf(t24,plain,
element_of_collection(empty_set,top_of_basis(X1)) = true,
inference(orient,[status(thm)],[t28]) ).
cnf(f2,negated_conjecture,
~ element_of_collection(empty_set,top_of_basis(f)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1b_2) ).
fof(f2_nnf,plain,
~ element_of_collection(empty_set,top_of_basis(f)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ element_of_collection(empty_set,top_of_basis(f)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ element_of_collection(empty_set,top_of_basis(f)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c1,c2]) ).
cnf(g0_0,plain,
element_of_collection(empty_set,top_of_basis(f)) != false,
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != false,
inference(rw,[status(thm)],[g0_0,t24]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP002-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 04:10:11 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.92/1.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.92/1.35 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------