%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : TOP001-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /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 09:52:56 AM UTC 2026
% Result : Unsatisfiable 0.11s 5.53s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 15 unt; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 68 ( 36 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 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 : 52 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(lemma_1a_1,axiom,
basis(cx,f),
file('theBenchmark.p',lemma_1a_1) ).
cnf(c_1,plain,
basis(cx,f),
inference(clausify,[status(thm)],[lemma_1a_1]) ).
fof(basis_for_topology_28,axiom,
! [VAR_0,VAR_1] :
( equal_sets(union_of_members(VAR_1),VAR_0)
| ~ basis(VAR_0,VAR_1) ),
file('theBenchmark.p',basis_for_topology_28) ).
cnf(c_2,plain,
( equal_sets(union_of_members(B),A)
| ~ basis(A,B) ),
inference(clausify,[status(thm)],[basis_for_topology_28]) ).
fof(set_theory_3,axiom,
! [VAR_0,VAR_1] :
( subset_sets(VAR_0,VAR_1)
| ~ equal_sets(VAR_0,VAR_1) ),
file('theBenchmark.p',set_theory_3) ).
cnf(c_3,plain,
( subset_sets(A,B)
| ~ equal_sets(A,B) ),
inference(clausify,[status(thm)],[set_theory_3]) ).
cnf(c_4,plain,
equal_sets(union_of_members(f),cx),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(set_theory_2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( element_of_set(VAR_2,VAR_1)
| ~ element_of_set(VAR_2,VAR_0)
| ~ subset_sets(VAR_0,VAR_1) ),
file('theBenchmark.p',set_theory_2) ).
cnf(c_5,plain,
( element_of_set(C,B)
| ~ element_of_set(C,A)
| ~ subset_sets(A,B) ),
inference(clausify,[status(thm)],[set_theory_2]) ).
cnf(c_7,plain,
subset_sets(union_of_members(f),cx),
inference(resolve,[status(thm)],[c_3,c_4]) ).
fof(set_theory_4,axiom,
! [VAR_0,VAR_1] :
( element_of_set(in_1st_set(VAR_0,VAR_1),VAR_0)
| subset_sets(VAR_0,VAR_1) ),
file('theBenchmark.p',set_theory_4) ).
cnf(c_8,plain,
( element_of_set(in_1st_set(A,B),A)
| subset_sets(A,B) ),
inference(clausify,[status(thm)],[set_theory_4]) ).
fof(set_theory_5,axiom,
! [VAR_0,VAR_1] :
( ~ element_of_set(in_1st_set(VAR_0,VAR_1),VAR_1)
| subset_sets(VAR_0,VAR_1) ),
file('theBenchmark.p',set_theory_5) ).
cnf(c_9,plain,
( ~ element_of_set(in_1st_set(A,B),B)
| subset_sets(A,B) ),
inference(clausify,[status(thm)],[set_theory_5]) ).
fof(lemma_1a_2,axiom,
~ subset_sets(union_of_members(top_of_basis(f)),cx),
file('theBenchmark.p',lemma_1a_2) ).
cnf(c_10,plain,
~ subset_sets(union_of_members(top_of_basis(f)),cx),
inference(clausify,[status(thm)],[lemma_1a_2]) ).
cnf(c_11,plain,
element_of_set(in_1st_set(union_of_members(top_of_basis(f)),cx),union_of_members(top_of_basis(f))),
inference(resolve,[status(thm)],[c_10,c_8]) ).
cnf(c_12,plain,
~ element_of_set(in_1st_set(union_of_members(top_of_basis(f)),cx),cx),
inference(resolve,[status(thm)],[c_10,c_9]) ).
cnf(c_15,plain,
( element_of_set(A,cx)
| ~ element_of_set(A,union_of_members(f)) ),
inference(resolve,[status(thm)],[c_5,c_7]) ).
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_16,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_17,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_3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ element_of_collection(VAR_2,VAR_1)
| ~ element_of_set(VAR_0,VAR_2)
| element_of_set(VAR_0,union_of_members(VAR_1)) ),
file('theBenchmark.p',union_of_members_3) ).
cnf(c_18,plain,
( ~ element_of_collection(C,B)
| ~ element_of_set(A,C)
| element_of_set(A,union_of_members(B)) ),
inference(clausify,[status(thm)],[union_of_members_3]) ).
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_19,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_20,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_23,plain,
~ element_of_set(in_1st_set(union_of_members(top_of_basis(f)),cx),union_of_members(f)),
inference(resolve,[status(thm)],[c_15,c_12]) ).
cnf(c_24,plain,
element_of_collection(f1(top_of_basis(f),in_1st_set(union_of_members(top_of_basis(f)),cx)),top_of_basis(f)),
inference(resolve,[status(thm)],[c_19,c_11]) ).
cnf(c_25,plain,
element_of_set(in_1st_set(union_of_members(top_of_basis(f)),cx),f1(top_of_basis(f),in_1st_set(union_of_members(top_of_basis(f)),cx))),
inference(resolve,[status(thm)],[c_20,c_11]) ).
cnf(c_29,plain,
( element_of_set(A,f10(f,f1(top_of_basis(f),in_1st_set(union_of_members(top_of_basis(f)),cx)),A))
| ~ element_of_set(A,f1(top_of_basis(f),in_1st_set(union_of_members(top_of_basis(f)),cx))) ),
inference(resolve,[status(thm)],[c_24,c_17]) ).
cnf(c_30,plain,
( element_of_collection(f10(f,f1(top_of_basis(f),in_1st_set(union_of_members(top_of_basis(f)),cx)),A),f)
| ~ element_of_set(A,f1(top_of_basis(f),in_1st_set(union_of_members(top_of_basis(f)),cx))) ),
inference(resolve,[status(thm)],[c_24,c_16]) ).
cnf(c_45,plain,
element_of_set(in_1st_set(union_of_members(top_of_basis(f)),cx),f10(f,f1(top_of_basis(f),in_1st_set(union_of_members(top_of_basis(f)),cx)),in_1st_set(union_of_members(top_of_basis(f)),cx))),
inference(resolve,[status(thm)],[c_29,c_25]) ).
cnf(c_58,plain,
element_of_collection(f10(f,f1(top_of_basis(f),in_1st_set(union_of_members(top_of_basis(f)),cx)),in_1st_set(union_of_members(top_of_basis(f)),cx)),f),
inference(resolve,[status(thm)],[c_30,c_25]) ).
cnf(c_75,plain,
( ~ element_of_collection(A,f)
| ~ element_of_set(in_1st_set(union_of_members(top_of_basis(f)),cx),A) ),
inference(resolve,[status(thm)],[c_18,c_23]) ).
cnf(c_76,plain,
~ element_of_set(in_1st_set(union_of_members(top_of_basis(f)),cx),f10(f,f1(top_of_basis(f),in_1st_set(union_of_members(top_of_basis(f)),cx)),in_1st_set(union_of_members(top_of_basis(f)),cx))),
inference(resolve,[status(thm)],[c_75,c_58]) ).
cnf(c_74,plain,
$false,
inference(resolve,[status(thm)],[c_45,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP001-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.51 % Computer : n006.cluster.edu
% 0.11/5.51 % Model : x86_64 x86_64
% 0.11/5.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.51 % Memory : 8046.5625MB
% 0.11/5.51 % OS : Linux 6.8.0-71-generic
% 0.11/5.51 % CPULimit : 300
% 0.11/5.51 % WCLimit : 300
% 0.11/5.51 % DateTime : Sat Sep 26 20:29:33 UTC 2026
% 0.11/5.51 % CPUTime :
% 0.11/5.52 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.52 % Process 2053933 was started by sandbox on n006,
% 0.11/5.52 % Sat Sep 26 20:29:33 2026
% 0.11/5.52 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.52
% 0.11/5.52 % From the command line: assign(max_seconds, 300).
% 0.11/5.53
% 0.11/5.53 % SZS status Unsatisfiable for theBenchmark
% 0.11/5.53
% 0.11/5.53 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/5.53 % Length of proof is 25.
% 0.11/5.53 % Level of proof is 5.
% 0.11/5.53 % Maximum clause weight is 23.000.
% 0.11/5.53 % Given clauses 33.
% 0.11/5.53
% 0.11/5.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------