%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : TOP005-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 09:52:56 AM UTC 2026
% Result : Unsatisfiable 0.06s 0.68s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 9 unt; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 108 ( 49 ~; 59 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 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 : 74 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(lemma_1e_2,axiom,
subset_collections(g,top_of_basis(f)),
file('theBenchmark.p',lemma_1e_2) ).
cnf(c_1,plain,
subset_collections(g,top_of_basis(f)),
inference(clausify,[status(thm)],[lemma_1e_2]) ).
fof(set_theory_21,axiom,
! [VAR_0,VAR_1,VAR_2] :
( element_of_collection(VAR_2,VAR_1)
| ~ element_of_collection(VAR_2,VAR_0)
| ~ subset_collections(VAR_0,VAR_1) ),
file('theBenchmark.p',set_theory_21) ).
cnf(c_2,plain,
( element_of_collection(C,B)
| ~ element_of_collection(C,A)
| ~ subset_collections(A,B) ),
inference(clausify,[status(thm)],[set_theory_21]) ).
cnf(c_3,plain,
( element_of_collection(A,top_of_basis(f))
| ~ element_of_collection(A,g) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(lemma_1e_3,axiom,
~ element_of_collection(union_of_members(g),top_of_basis(f)),
file('theBenchmark.p',lemma_1e_3) ).
cnf(c_4,plain,
~ element_of_collection(union_of_members(g),top_of_basis(f)),
inference(clausify,[status(thm)],[lemma_1e_3]) ).
fof(set_theory_20,axiom,
! [VAR_0,VAR_1,VAR_2] :
( subset_sets(VAR_0,union_of_members(VAR_2))
| ~ element_of_collection(VAR_1,VAR_2)
| ~ subset_sets(VAR_0,VAR_1) ),
file('theBenchmark.p',set_theory_20) ).
cnf(c_5,plain,
( subset_sets(A,union_of_members(C))
| ~ element_of_collection(B,C)
| ~ subset_sets(A,B) ),
inference(clausify,[status(thm)],[set_theory_20]) ).
fof(topology_generated_41,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ subset_sets(VAR_2,VAR_0)
| ~ element_of_collection(VAR_2,VAR_1)
| ~ element_of_set(f11(VAR_1,VAR_0),VAR_2)
| element_of_collection(VAR_0,top_of_basis(VAR_1)) ),
file('theBenchmark.p',topology_generated_41) ).
cnf(c_7,plain,
( ~ subset_sets(C,A)
| ~ element_of_collection(C,B)
| ~ element_of_set(f11(B,A),C)
| element_of_collection(A,top_of_basis(B)) ),
inference(clausify,[status(thm)],[topology_generated_41]) ).
fof(topology_generated_40,axiom,
! [VAR_0,VAR_1] :
( element_of_set(f11(VAR_1,VAR_0),VAR_0)
| element_of_collection(VAR_0,top_of_basis(VAR_1)) ),
file('theBenchmark.p',topology_generated_40) ).
cnf(c_8,plain,
( element_of_set(f11(B,A),A)
| element_of_collection(A,top_of_basis(B)) ),
inference(clausify,[status(thm)],[topology_generated_40]) ).
fof(topology_generated_39,axiom,
! [VAR_0,VAR_1,VAR_2] :
( subset_sets(f10(VAR_1,VAR_0,VAR_2),VAR_0)
| ~ element_of_set(VAR_2,VAR_0)
| ~ element_of_collection(VAR_0,top_of_basis(VAR_1)) ),
file('theBenchmark.p',topology_generated_39) ).
cnf(c_9,plain,
( subset_sets(f10(B,A,C),A)
| ~ element_of_set(C,A)
| ~ element_of_collection(A,top_of_basis(B)) ),
inference(clausify,[status(thm)],[topology_generated_39]) ).
fof(topology_generated_38,axiom,
! [VAR_0,VAR_1,VAR_2] :
( element_of_collection(f10(VAR_1,VAR_0,VAR_2),VAR_1)
| ~ element_of_set(VAR_2,VAR_0)
| ~ element_of_collection(VAR_0,top_of_basis(VAR_1)) ),
file('theBenchmark.p',topology_generated_38) ).
cnf(c_10,plain,
( element_of_collection(f10(B,A,C),B)
| ~ element_of_set(C,A)
| ~ element_of_collection(A,top_of_basis(B)) ),
inference(clausify,[status(thm)],[topology_generated_38]) ).
fof(topology_generated_37,axiom,
! [VAR_0,VAR_1,VAR_2] :
( element_of_set(VAR_2,f10(VAR_1,VAR_0,VAR_2))
| ~ element_of_set(VAR_2,VAR_0)
| ~ element_of_collection(VAR_0,top_of_basis(VAR_1)) ),
file('theBenchmark.p',topology_generated_37) ).
cnf(c_11,plain,
( element_of_set(C,f10(B,A,C))
| ~ element_of_set(C,A)
| ~ element_of_collection(A,top_of_basis(B)) ),
inference(clausify,[status(thm)],[topology_generated_37]) ).
fof(union_of_members_2,axiom,
! [VAR_0,VAR_1] :
( element_of_collection(f1(VAR_1,VAR_0),VAR_1)
| ~ element_of_set(VAR_0,union_of_members(VAR_1)) ),
file('theBenchmark.p',union_of_members_2) ).
cnf(c_12,plain,
( element_of_collection(f1(B,A),B)
| ~ element_of_set(A,union_of_members(B)) ),
inference(clausify,[status(thm)],[union_of_members_2]) ).
fof(union_of_members_1,axiom,
! [VAR_0,VAR_1] :
( element_of_set(VAR_0,f1(VAR_1,VAR_0))
| ~ element_of_set(VAR_0,union_of_members(VAR_1)) ),
file('theBenchmark.p',union_of_members_1) ).
cnf(c_13,plain,
( element_of_set(A,f1(B,A))
| ~ element_of_set(A,union_of_members(B)) ),
inference(clausify,[status(thm)],[union_of_members_1]) ).
cnf(c_20,plain,
( element_of_collection(union_of_members(A),top_of_basis(B))
| element_of_collection(f1(A,f11(B,union_of_members(A))),A) ),
inference(resolve,[status(thm)],[c_12,c_8]) ).
cnf(c_21,plain,
( element_of_collection(union_of_members(B),top_of_basis(A))
| element_of_set(f11(A,union_of_members(B)),f1(B,f11(A,union_of_members(B)))) ),
inference(resolve,[status(thm)],[c_13,c_8]) ).
cnf(c_34,plain,
( subset_sets(C,union_of_members(A))
| ~ subset_sets(C,f1(A,f11(B,union_of_members(A))))
| element_of_collection(union_of_members(A),top_of_basis(B)) ),
inference(resolve,[status(thm)],[c_20,c_5]) ).
cnf(c_35,plain,
( element_of_collection(f1(g,f11(A,union_of_members(g))),top_of_basis(f))
| element_of_collection(union_of_members(g),top_of_basis(A)) ),
inference(resolve,[status(thm)],[c_20,c_3]) ).
cnf(c_39,plain,
( element_of_set(f11(B,union_of_members(A)),f10(C,f1(A,f11(B,union_of_members(A))),f11(B,union_of_members(A))))
| ~ element_of_collection(f1(A,f11(B,union_of_members(A))),top_of_basis(C))
| element_of_collection(union_of_members(A),top_of_basis(B)) ),
inference(resolve,[status(thm)],[c_21,c_11]) ).
cnf(c_40,plain,
( element_of_collection(f10(C,f1(A,f11(B,union_of_members(A))),f11(B,union_of_members(A))),C)
| ~ element_of_collection(f1(A,f11(B,union_of_members(A))),top_of_basis(C))
| element_of_collection(union_of_members(A),top_of_basis(B)) ),
inference(resolve,[status(thm)],[c_21,c_10]) ).
cnf(c_41,plain,
( subset_sets(f10(C,f1(A,f11(B,union_of_members(A))),f11(B,union_of_members(A))),f1(A,f11(B,union_of_members(A))))
| ~ element_of_collection(f1(A,f11(B,union_of_members(A))),top_of_basis(C))
| element_of_collection(union_of_members(A),top_of_basis(B)) ),
inference(resolve,[status(thm)],[c_21,c_9]) ).
cnf(c_137,plain,
( element_of_collection(union_of_members(g),top_of_basis(A))
| element_of_set(f11(A,union_of_members(g)),f10(f,f1(g,f11(A,union_of_members(g))),f11(A,union_of_members(g))))
| element_of_collection(union_of_members(g),top_of_basis(A)) ),
inference(resolve,[status(thm)],[c_39,c_35]) ).
cnf(c_97,plain,
( element_of_set(f11(A,union_of_members(g)),f10(f,f1(g,f11(A,union_of_members(g))),f11(A,union_of_members(g))))
| element_of_collection(union_of_members(g),top_of_basis(A)) ),
inference(copy,[status(thm)],[c_137]) ).
cnf(c_138,plain,
( element_of_collection(union_of_members(g),top_of_basis(A))
| element_of_collection(f10(f,f1(g,f11(A,union_of_members(g))),f11(A,union_of_members(g))),f)
| element_of_collection(union_of_members(g),top_of_basis(A)) ),
inference(resolve,[status(thm)],[c_40,c_35]) ).
cnf(c_98,plain,
( element_of_collection(f10(f,f1(g,f11(A,union_of_members(g))),f11(A,union_of_members(g))),f)
| element_of_collection(union_of_members(g),top_of_basis(A)) ),
inference(copy,[status(thm)],[c_138]) ).
cnf(c_104,plain,
( ~ subset_sets(f10(f,f1(g,f11(A,union_of_members(g))),f11(A,union_of_members(g))),B)
| ~ element_of_set(f11(f,B),f10(f,f1(g,f11(A,union_of_members(g))),f11(A,union_of_members(g))))
| element_of_collection(B,top_of_basis(f))
| element_of_collection(union_of_members(g),top_of_basis(A)) ),
inference(resolve,[status(thm)],[c_98,c_7]) ).
cnf(c_139,plain,
( ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
| ~ element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))))
| element_of_collection(union_of_members(g),top_of_basis(f)) ),
inference(factor,[status(thm)],[c_104]) ).
cnf(c_108,plain,
( ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
| ~ element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g)))) ),
inference(resolve,[status(thm)],[c_4,c_139]) ).
cnf(c_140,plain,
( element_of_collection(union_of_members(g),top_of_basis(f))
| ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g)) ),
inference(resolve,[status(thm)],[c_108,c_97]) ).
cnf(c_130,plain,
~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g)),
inference(resolve,[status(thm)],[c_4,c_140]) ).
cnf(c_141,plain,
( subset_sets(A,union_of_members(g))
| ~ subset_sets(A,f1(g,f11(f,union_of_members(g)))) ),
inference(resolve,[status(thm)],[c_34,c_4]) ).
cnf(c_133,plain,
~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f1(g,f11(f,union_of_members(g)))),
inference(resolve,[status(thm)],[c_141,c_130]) ).
cnf(c_142,plain,
( subset_sets(f10(A,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(A)) ),
inference(resolve,[status(thm)],[c_41,c_4]) ).
cnf(c_135,plain,
~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f)),
inference(resolve,[status(thm)],[c_142,c_133]) ).
cnf(c_143,plain,
element_of_collection(union_of_members(g),top_of_basis(f)),
inference(resolve,[status(thm)],[c_135,c_35]) ).
cnf(c_136,plain,
$false,
inference(resolve,[status(thm)],[c_4,c_143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : TOP005-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.64 % Computer : n011.cluster.edu
% 0.06/0.64 % Model : x86_64 x86_64
% 0.06/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.64 % Memory : 8046.5625MB
% 0.06/0.64 % OS : Linux 6.8.0-71-generic
% 0.06/0.64 % CPULimit : 300
% 0.06/0.64 % WCLimit : 300
% 0.06/0.64 % DateTime : Sat Sep 26 20:30:45 UTC 2026
% 0.06/0.64 % CPUTime :
% 0.06/0.65 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/0.65 % Process 1482966 was started by sandbox2 on n011,
% 0.06/0.65 % Sat Sep 26 20:30:45 2026
% 0.06/0.65 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.06/0.65
% 0.06/0.65 % From the command line: assign(max_seconds, 300).
% 0.06/0.68
% 0.06/0.68 % SZS status Unsatisfiable for theBenchmark
% 0.06/0.68
% 0.06/0.68 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.06/0.68 % Length of proof is 27.
% 0.06/0.68 % Level of proof is 9.
% 0.06/0.68 % Maximum clause weight is 64.000.
% 0.06/0.68 % Given clauses 63.
% 0.06/0.68
% 0.06/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------