%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : TOP004-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n002.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 09:52:26 AM UTC 2026
% Result : Unsatisfiable 3.86s 2.42s
% Output : Refutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 21
% Syntax : Number of formulae : 43 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 119 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 512 ( 76 ~; 76 |; 0 &; 360 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 13 usr; 3 con; 0-5 aty)
% Number of variables : 118 ( 0 ^; 118 !; 0 ?; 118 :)
% Comments :
%------------------------------------------------------------------------------
thf(basis_decl,type,
basis: $i > $i > $o ).
thf(cx_decl,type,
cx: $i ).
thf(f_decl,type,
f: $i ).
thf(element_of_collection_decl,type,
element_of_collection: $i > $i > $o ).
thf(top_of_basis_decl,type,
top_of_basis: $i > $i ).
thf(intersection_of_sets_decl,type,
intersection_of_sets: $i > $i > $i ).
thf(subset_sets_decl,type,
subset_sets: $i > $i > $o ).
thf(equal_sets_decl,type,
equal_sets: $i > $i > $o ).
thf(element_of_set_decl,type,
element_of_set: $i > $i > $o ).
thf(f6_decl,type,
f6: $i > $i > $i > $i > $i > $i ).
thf(f10_decl,type,
f10: $i > $i > $i > $i ).
thf(union_of_members_decl,type,
union_of_members: $i > $i ).
thf(f11_decl,type,
f11: $i > $i > $i ).
thf(8,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ f6 ) ) ) ) @ element_of_collection ) )
| ~ ( E @ ( D @ intersection_of_sets ) @ ( C @ element_of_set ) )
| ~ ( B @ ( E @ element_of_collection ) )
| ~ ( B @ ( D @ element_of_collection ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ basis ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_30) ).
thf(33,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ f6 ) ) ) ) @ element_of_collection ) )
| ~ ( E @ ( D @ intersection_of_sets ) @ ( C @ element_of_set ) )
| ~ ( B @ ( E @ element_of_collection ) )
| ~ ( B @ ( D @ element_of_collection ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ basis ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ element_of_set ) )
| ~ ( C @ ( B @ intersection_of_sets ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_13) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ element_of_set ) )
| ~ ( C @ ( B @ intersection_of_sets ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ element_of_collection ) )
| ~ ( C @ ( A @ element_of_set ) )
| ( B @ union_of_members @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_members_3) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ element_of_collection ) )
| ~ ( C @ ( A @ element_of_set ) )
| ( B @ union_of_members @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ intersection_of_sets ) @ ( C @ ( A @ intersection_of_sets ) @ subset_sets ) )
| ~ ( D @ ( C @ subset_sets ) )
| ~ ( B @ ( A @ subset_sets ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_16) ).
thf(45,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ intersection_of_sets ) @ ( C @ ( A @ intersection_of_sets ) @ subset_sets ) )
| ~ ( D @ ( C @ subset_sets ) )
| ~ ( B @ ( A @ subset_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ f10 ) ) @ ( C @ element_of_set ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_37) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ f10 ) ) @ ( C @ element_of_set ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ element_of_set ) )
| ~ ( C @ ( B @ intersection_of_sets ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_14) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ element_of_set ) )
| ~ ( C @ ( B @ intersection_of_sets ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ f10 ) ) @ subset_sets ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_39) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ f10 ) ) @ subset_sets ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ intersection_of_sets ) @ ( E @ ( D @ ( C @ ( B @ ( A @ f6 ) ) ) ) @ subset_sets ) )
| ~ ( E @ ( D @ intersection_of_sets ) @ ( C @ element_of_set ) )
| ~ ( B @ ( E @ element_of_collection ) )
| ~ ( B @ ( D @ element_of_collection ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ basis ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_31) ).
thf(31,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ intersection_of_sets ) @ ( E @ ( D @ ( C @ ( B @ ( A @ f6 ) ) ) ) @ subset_sets ) )
| ~ ( E @ ( D @ intersection_of_sets ) @ ( C @ element_of_set ) )
| ~ ( B @ ( E @ element_of_collection ) )
| ~ ( B @ ( D @ element_of_collection ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ basis ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( B @ f10 ) ) @ element_of_collection ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_38) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( B @ f10 ) ) @ element_of_collection ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ subset_sets ) )
| ~ ( B @ ( C @ element_of_collection ) )
| ~ ( C @ ( A @ ( B @ f11 ) @ element_of_set ) )
| ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_41) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ subset_sets ) )
| ~ ( B @ ( C @ element_of_collection ) )
| ~ ( C @ ( A @ ( B @ f11 ) @ element_of_set ) )
| ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ f11 ) @ element_of_set ) )
| ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_40) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ f11 ) @ element_of_set ) )
| ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ f6 ) ) ) ) @ ( C @ element_of_set ) )
| ~ ( E @ ( D @ intersection_of_sets ) @ ( C @ element_of_set ) )
| ~ ( B @ ( E @ element_of_collection ) )
| ~ ( B @ ( D @ element_of_collection ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ basis ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_29) ).
thf(47,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ f6 ) ) ) ) @ ( C @ element_of_set ) )
| ~ ( E @ ( D @ intersection_of_sets ) @ ( C @ element_of_set ) )
| ~ ( B @ ( E @ element_of_collection ) )
| ~ ( B @ ( D @ element_of_collection ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ basis ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,negated_conjecture,
! [A: $i] : ( f @ top_of_basis @ ( A @ element_of_collection ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1d_3) ).
thf(24,plain,
! [A: $i] : ( f @ top_of_basis @ ( A @ element_of_collection ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ element_of_set ) )
| ~ ( B @ ( A @ element_of_set ) )
| ( C @ ( B @ intersection_of_sets ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_15) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ element_of_set ) )
| ~ ( B @ ( A @ element_of_set ) )
| ( C @ ( B @ intersection_of_sets ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,negated_conjecture,
! [B: $i,A: $i] :
~ ( f @ top_of_basis @ ( B @ ( A @ intersection_of_sets ) @ element_of_collection ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1d_4) ).
thf(25,plain,
! [B: $i,A: $i] :
~ ( f @ top_of_basis @ ( B @ ( A @ intersection_of_sets ) @ element_of_collection ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,axiom,
! [B: $i,A: $i] : ( A @ ( B @ intersection_of_sets ) @ ( B @ ( A @ intersection_of_sets ) @ equal_sets ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_18) ).
thf(57,plain,
! [B: $i,A: $i] : ( A @ ( B @ intersection_of_sets ) @ ( B @ ( A @ intersection_of_sets ) @ equal_sets ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ element_of_set ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_17) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ element_of_set ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
f @ ( cx @ basis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1d_1) ).
thf(22,plain,
f @ ( cx @ basis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ subset_sets ) )
| ~ ( C @ ( B @ subset_sets ) )
| ~ ( B @ ( A @ subset_sets ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_12) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ subset_sets ) )
| ~ ( C @ ( B @ subset_sets ) )
| ~ ( B @ ( A @ subset_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ union_of_members @ equal_sets ) )
| ~ ( B @ ( A @ basis ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_28) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ union_of_members @ equal_sets ) )
| ~ ( B @ ( A @ basis ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(2,negated_conjecture,
! [A: $i] : ( f @ top_of_basis @ ( A @ element_of_collection ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1d_2) ).
thf(23,plain,
! [A: $i] : ( f @ top_of_basis @ ( A @ element_of_collection ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(60,plain,
$false,
inference(e,[status(thm)],[33,53,41,45,49,39,35,31,43,58,51,47,24,37,25,57,29,22,27,55,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.40 % Computer : n002.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sat Sep 26 20:32:39 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.17 % [INFO] Parsing done (196ms).
% 1.24/1.19 % [INFO] Running in sequential loop mode.
% 1.87/1.59 % [INFO] eprover registered as external prover.
% 2.05/1.60 % [INFO] Scanning for conjecture ...
% 2.05/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 17 axioms. Running axiom selection ...
% 2.23/1.77 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 2.42/1.81 % [INFO] Problem is propositional (TPTP CNF).
% 2.42/1.81 % [INFO] Type checking passed.
% 2.42/1.81 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.86/2.42 % External prover 'e' found a proof!
% 3.86/2.42 % [INFO] Killing All external provers ...
% 3.86/2.42 % Time passed: 1871ms (effective reasoning time: 1221ms)
% 3.86/2.42 % Axioms used in derivation (17): basis_for_topology_28, topology_generated_37, union_of_members_3, basis_for_topology_29, set_theory_18, topology_generated_40, topology_generated_39, set_theory_16, set_theory_13, set_theory_17, set_theory_15, topology_generated_38, topology_generated_41, basis_for_topology_31, set_theory_12, basis_for_topology_30, set_theory_14
% 3.86/2.42 % No. of inferences in proof: 43
% 3.86/2.42 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1871 ms resp. 1221 ms w/o parsing
% 3.86/2.48 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.86/2.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------