%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU364+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 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 08:38:35 AM UTC 2026
% Result : Theorem 8.66s 8.64s
% Output : Refutation 8.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 36 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 170 ( 20 equ; 0 cnn)
% Maximal formula atoms : 31 ( 4 avg)
% Number of connectives : 455 ( 37 ~; 0 |; 98 &; 284 @)
% ( 3 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 1 con; 0-3 aty)
% Number of variables : 100 ( 0 ^; 52 !; 48 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_carrier_decl,type,
empty_carrier: $i > $o ).
thf(transitive_relstr_decl,type,
transitive_relstr: $i > $o ).
thf(rel_str_decl,type,
rel_str: $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(finite_decl,type,
finite: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(relstr_set_smaller_decl,type,
relstr_set_smaller: $i > $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(7,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(52,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(78,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(70,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(41,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(64,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(54,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(48,plain,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(72,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ powerset @ ( C @ element ) )
& ( C @ finite )
& ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ transitive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ? [H: $i] :
( ( H @ ( G @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( H @ in ) )
& ( A @ the_carrier @ ( H @ element ) ) )
& ( G = F ) )
& ( D = F )
& ? [G: $i] :
( ? [H: $i] :
( ( H @ ( G @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( H @ in ) )
& ( A @ the_carrier @ ( H @ element ) ) )
& ( G = E ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( H @ ( G @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( H @ in ) )
& ( A @ the_carrier @ ( H @ element ) ) )
& ( G = E ) )
& ( F = E )
& ( C @ powerset @ ( F @ in ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e11_2_1__waybel_0__1) ).
thf(87,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ powerset @ ( C @ element ) )
& ( C @ finite )
& ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ transitive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ? [H: $i] :
( ( H @ ( G @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( H @ in ) )
& ( A @ the_carrier @ ( H @ element ) ) )
& ( G = F ) )
& ( D = F )
& ? [G: $i] :
( ? [H: $i] :
( ( H @ ( G @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( H @ in ) )
& ( A @ the_carrier @ ( H @ element ) ) )
& ( G = E ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( H @ ( G @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( H @ in ) )
& ( A @ the_carrier @ ( H @ element ) ) )
& ( G = E ) )
& ( F = E )
& ( C @ powerset @ ( F @ in ) ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( H @ ( G @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( H @ in ) )
& ( A @ the_carrier @ ( H @ element ) ) )
& ( G = E ) )
& ( F = E )
& ( C @ powerset @ ( F @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( B @ powerset @ ( C @ element ) )
& ( C @ finite )
& ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ transitive_relstr )
& ~ ( A @ empty_carrier ) )
=> ? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ( ? [F: $i] :
( ? [G: $i] :
( ( G @ ( F @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( G @ in ) )
& ( A @ the_carrier @ ( G @ element ) ) )
& ( F = E ) )
& ( C @ powerset @ ( E @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e11_2_1__waybel_0__1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( B @ powerset @ ( C @ element ) )
& ( C @ finite )
& ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ transitive_relstr )
& ~ ( A @ empty_carrier ) )
=> ? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ( ? [F: $i] :
( ? [G: $i] :
( ( G @ ( F @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( G @ in ) )
& ( A @ the_carrier @ ( G @ element ) ) )
& ( F = E ) )
& ( C @ powerset @ ( E @ in ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( B @ powerset @ ( C @ element ) )
& ( C @ finite )
& ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ transitive_relstr )
& ~ ( A @ empty_carrier ) )
=> ? [D: $i] :
! [E: $i] :
( ( ( ? [F: $i] :
( ? [G: $i] :
( ( G @ ( F @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( G @ in ) )
& ( A @ the_carrier @ ( G @ element ) ) )
& ( F = E ) )
& ( C @ powerset @ ( E @ in ) ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ( ? [F: $i] :
( ? [G: $i] :
( ( G @ ( F @ ( A @ relstr_set_smaller ) ) )
& ( B @ ( G @ in ) )
& ( A @ the_carrier @ ( G @ element ) ) )
& ( F = E ) )
& ( C @ powerset @ ( E @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(68,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(83,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(44,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(59,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(81,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(76,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(39,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(465,plain,
$false,
inference(e,[status(thm)],[52,78,70,41,64,54,48,72,87,19,68,83,44,59,81,76,39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU364+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.23/5.48 % Computer : n006.cluster.edu
% 0.23/5.48 % Model : x86_64 x86_64
% 0.23/5.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/5.48 % Memory : 8046.5625MB
% 0.23/5.48 % OS : Linux 6.8.0-71-generic
% 0.23/5.48 % CPULimit : 300
% 0.23/5.48 % WCLimit : 300
% 0.23/5.48 % DateTime : Sat Sep 26 09:19:18 UTC 2026
% 0.23/5.48 % CPUTime :
% 0.23/5.48 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.03/6.07 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/6.26 % [INFO] Parsing done (189ms).
% 1.31/6.27 % [INFO] Running in sequential loop mode.
% 1.99/6.67 % [INFO] eprover registered as external prover.
% 1.99/6.68 % [INFO] Scanning for conjecture ...
% 2.21/6.80 % [INFO] Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ...
% 2.37/6.88 % [INFO] Axiom selection finished. Selected 16 axioms (removed 4 axioms).
% 2.57/6.91 % [INFO] Problem is first-order (TPTP FOF).
% 2.57/6.92 % [INFO] Type checking passed.
% 2.57/6.92 % [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 ...
% 8.66/8.63 % External prover 'e' found a proof!
% 8.66/8.64 % [INFO] Killing All external provers ...
% 8.66/8.64 % Time passed: 3011ms (effective reasoning time: 2356ms)
% 8.66/8.64 % Solved by 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)>
% 8.66/8.64 % Axioms used in derivation (16): cc2_finset_1, rc4_finset_1, rc2_subset_1, rc1_subset_1, s1_tarski__e11_2_1__waybel_0__1, dt_l1_orders_2, fc1_struct_0, rc3_finset_1, rc5_struct_0, rc2_xboole_0, antisymmetry_r2_hidden, rc3_struct_0, fc1_subset_1, rc1_finset_1, cc1_finset_1, rc1_xboole_0
% 8.66/8.64 % No. of inferences in proof: 36
% 8.66/8.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3011 ms resp. 2356 ms w/o parsing
% 8.66/8.69 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.66/8.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------