%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET764+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 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 : n016.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 08:30:51 AM UTC 2026
% Result : Theorem 11.58s 5.06s
% Output : Refutation 12.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 29
% Syntax : Number of formulae : 60 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 402 ( 18 equ; 0 cnn)
% Maximal formula atoms : 26 ( 6 avg)
% Number of connectives : 1408 ( 7 ~; 6 |; 185 &;1059 @)
% ( 30 <=>; 121 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 30 usr; 2 con; 0-6 aty)
% Number of variables : 316 ( 0 ^; 287 !; 29 ?; 316 :)
% Comments :
%------------------------------------------------------------------------------
thf(maps_decl,type,
maps: $i > $i > $i > $o ).
thf(equal_set_decl,type,
equal_set: $i > $i > $o ).
thf(inverse_image2_decl,type,
inverse_image2: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(equal_maps_decl,type,
equal_maps: $i > $i > $i > $i > $o ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(apply_decl,type,
apply: $i > $i > $i > $o ).
thf(compose_function_decl,type,
compose_function: $i > $i > $i > $i > $i > $i ).
thf(increasing_decl,type,
increasing: $i > $i > $i > $i > $i > $o ).
thf(intersection_decl,type,
intersection: $i > $i > $i ).
thf(inverse_predicate_decl,type,
inverse_predicate: $i > $i > $i > $i > $o ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(inverse_function_decl,type,
inverse_function: $i > $i > $i > $i ).
thf(power_set_decl,type,
power_set: $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(one_to_one_decl,type,
one_to_one: $i > $i > $i > $o ).
thf(injective_decl,type,
injective: $i > $i > $i > $o ).
thf(surjective_decl,type,
surjective: $i > $i > $i > $o ).
thf(product_decl,type,
product: $i > $i ).
thf(compose_predicate_decl,type,
compose_predicate: $i > $i > $i > $i > $i > $i > $o ).
thf(decreasing_decl,type,
decreasing: $i > $i > $i > $i > $i > $o ).
thf(image2_decl,type,
image2: $i > $i > $i ).
thf(inverse_image3_decl,type,
inverse_image3: $i > $i > $i > $i ).
thf(difference_decl,type,
difference: $i > $i > $i ).
thf(identity_decl,type,
identity: $i > $i > $o ).
thf(union_decl,type,
union: $i > $i > $i ).
thf(sum_decl,type,
sum: $i > $i ).
thf(image3_decl,type,
image3: $i > $i > $i > $i ).
thf(isomorphism_decl,type,
isomorphism: $i > $i > $i > $i > $i > $o ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( E @ member ) )
& ( B @ ( D @ member ) ) )
=> ( ( E @ ( D @ ( A @ apply ) ) )
<=> ( D @ ( E @ ( C @ ( B @ ( A @ inverse_function ) ) @ apply ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_function) ).
thf(115,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( E @ member ) )
& ( B @ ( D @ member ) ) )
=> ( ( ( D @ ( E @ ( C @ ( B @ ( A @ inverse_function ) ) @ apply ) ) )
=> ( E @ ( D @ ( A @ apply ) ) ) )
& ( ( E @ ( D @ ( A @ apply ) ) )
=> ( D @ ( E @ ( C @ ( B @ ( A @ inverse_function ) ) @ apply ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ member ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(125,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( B @ singleton @ ( A @ member ) ) )
& ( ( B @ singleton @ ( A @ member ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ one_to_one ) ) )
<=> ( ( C @ ( B @ ( A @ surjective ) ) )
& ( C @ ( B @ ( A @ injective ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one) ).
thf(133,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ ( A @ surjective ) ) )
& ( C @ ( B @ ( A @ injective ) ) ) )
=> ( C @ ( B @ ( A @ one_to_one ) ) ) )
& ( ( C @ ( B @ ( A @ one_to_one ) ) )
=> ( ( C @ ( B @ ( A @ surjective ) ) )
& ( C @ ( B @ ( A @ injective ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ inverse_image2 ) @ ( C @ member ) )
<=> ? [D: $i] :
( ( D @ ( C @ ( A @ apply ) ) )
& ( B @ ( D @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_image2) ).
thf(334,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ ( C @ ( A @ apply ) ) )
& ( B @ ( D @ member ) ) )
=> ( B @ ( A @ inverse_image2 ) @ ( C @ member ) ) )
& ( ( B @ ( A @ inverse_image2 ) @ ( C @ member ) )
=> ? [D: $i] :
( ( D @ ( C @ ( A @ apply ) ) )
& ( B @ ( D @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ union ) @ ( A @ member ) )
<=> ( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
thf(256,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) ) )
=> ( C @ ( B @ union ) @ ( A @ member ) ) )
& ( ( C @ ( B @ union ) @ ( A @ member ) )
=> ( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( E @ ( G @ member ) )
& ( C @ ( F @ member ) ) )
=> ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ compose_function ) ) ) ) @ apply ) ) )
<=> ? [H: $i] :
( ( G @ ( H @ ( A @ apply ) ) )
& ( H @ ( F @ ( B @ apply ) ) )
& ( D @ ( H @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_function) ).
thf(54,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( E @ ( G @ member ) )
& ( C @ ( F @ member ) ) )
=> ( ( ? [H: $i] :
( ( G @ ( H @ ( A @ apply ) ) )
& ( H @ ( F @ ( B @ apply ) ) )
& ( D @ ( H @ member ) ) )
=> ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ compose_function ) ) ) ) @ apply ) ) ) )
& ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ compose_function ) ) ) ) @ apply ) ) )
=> ? [H: $i] :
( ( G @ ( H @ ( A @ apply ) ) )
& ( H @ ( F @ ( B @ apply ) ) )
& ( D @ ( H @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ image3 ) ) @ ( D @ member ) )
<=> ( ? [E: $i] :
( ( D @ ( E @ ( A @ apply ) ) )
& ( B @ ( E @ member ) ) )
& ( C @ ( D @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image3) ).
thf(271,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ? [E: $i] :
( ( D @ ( E @ ( A @ apply ) ) )
& ( B @ ( E @ member ) ) )
& ( C @ ( D @ member ) ) )
=> ( C @ ( B @ ( A @ image3 ) ) @ ( D @ member ) ) )
& ( ( C @ ( B @ ( A @ image3 ) ) @ ( D @ member ) )
=> ( ? [E: $i] :
( ( D @ ( E @ ( A @ apply ) ) )
& ( B @ ( E @ member ) ) )
& ( C @ ( D @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ product @ ( A @ member ) )
<=> ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product) ).
thf(140,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( A @ member ) ) )
=> ( B @ product @ ( A @ member ) ) )
& ( ( B @ product @ ( A @ member ) )
=> ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( A @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ surjective ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ member ) )
=> ? [E: $i] :
( ( D @ ( E @ ( A @ apply ) ) )
& ( B @ ( E @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjective) ).
thf(171,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( C @ ( D @ member ) )
=> ? [E: $i] :
( ( D @ ( E @ ( A @ apply ) ) )
& ( B @ ( E @ member ) ) ) )
=> ( C @ ( B @ ( A @ surjective ) ) ) )
& ( ( C @ ( B @ ( A @ surjective ) ) )
=> ! [D: $i] :
( ( C @ ( D @ member ) )
=> ? [E: $i] :
( ( D @ ( E @ ( A @ apply ) ) )
& ( B @ ( E @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ equal_maps ) ) ) )
<=> ! [E: $i,F: $i,G: $i] :
( ( ( D @ ( G @ member ) )
& ( D @ ( F @ member ) )
& ( C @ ( E @ member ) ) )
=> ( ( ( G @ ( E @ ( B @ apply ) ) )
& ( F @ ( E @ ( A @ apply ) ) ) )
=> ( F = G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_maps) ).
thf(36,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i,F: $i,G: $i] :
( ( ( D @ ( G @ member ) )
& ( D @ ( F @ member ) )
& ( C @ ( E @ member ) ) )
=> ( ( ( G @ ( E @ ( B @ apply ) ) )
& ( F @ ( E @ ( A @ apply ) ) ) )
=> ( F = G ) ) )
=> ( D @ ( C @ ( B @ ( A @ equal_maps ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ equal_maps ) ) ) )
=> ! [E: $i,F: $i,G: $i] :
( ( ( D @ ( G @ member ) )
& ( D @ ( F @ member ) )
& ( C @ ( E @ member ) ) )
=> ( ( ( G @ ( E @ ( B @ apply ) ) )
& ( F @ ( E @ ( A @ apply ) ) ) )
=> ( F = G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equal_set ) )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
thf(341,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( A @ equal_set ) ) )
& ( ( B @ ( A @ equal_set ) )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ image2 ) @ ( C @ member ) )
<=> ? [D: $i] :
( ( C @ ( D @ ( A @ apply ) ) )
& ( B @ ( D @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image2) ).
thf(200,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( C @ ( D @ ( A @ apply ) ) )
& ( B @ ( D @ member ) ) )
=> ( B @ ( A @ image2 ) @ ( C @ member ) ) )
& ( ( B @ ( A @ image2 ) @ ( C @ member ) )
=> ? [D: $i] :
( ( C @ ( D @ ( A @ apply ) ) )
& ( B @ ( D @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ inverse_image3 ) ) @ ( D @ member ) )
<=> ( ? [E: $i] :
( ( E @ ( D @ ( A @ apply ) ) )
& ( B @ ( E @ member ) ) )
& ( C @ ( D @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_image3) ).
thf(215,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ? [E: $i] :
( ( E @ ( D @ ( A @ apply ) ) )
& ( B @ ( E @ member ) ) )
& ( C @ ( D @ member ) ) )
=> ( C @ ( B @ ( A @ inverse_image3 ) ) @ ( D @ member ) ) )
& ( ( C @ ( B @ ( A @ inverse_image3 ) ) @ ( D @ member ) )
=> ( ? [E: $i] :
( ( E @ ( D @ ( A @ apply ) ) )
& ( B @ ( E @ member ) ) )
& ( C @ ( D @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ identity ) )
<=> ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( C @ ( A @ apply ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
thf(248,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( C @ ( A @ apply ) ) ) )
=> ( B @ ( A @ identity ) ) )
& ( ( B @ ( A @ identity ) )
=> ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( C @ ( A @ apply ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ increasing ) ) ) ) )
<=> ! [F: $i,G: $i,H: $i,I: $i] :
( ( ( I @ ( H @ ( A @ apply ) ) )
& ( G @ ( F @ ( A @ apply ) ) )
& ( H @ ( F @ ( C @ apply ) ) )
& ( D @ ( I @ member ) )
& ( B @ ( H @ member ) )
& ( D @ ( G @ member ) )
& ( B @ ( F @ member ) ) )
=> ( I @ ( G @ ( E @ apply ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',increasing_function) ).
thf(60,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i,G: $i,H: $i,I: $i] :
( ( ( I @ ( H @ ( A @ apply ) ) )
& ( G @ ( F @ ( A @ apply ) ) )
& ( H @ ( F @ ( C @ apply ) ) )
& ( D @ ( I @ member ) )
& ( B @ ( H @ member ) )
& ( D @ ( G @ member ) )
& ( B @ ( F @ member ) ) )
=> ( I @ ( G @ ( E @ apply ) ) ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ increasing ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ increasing ) ) ) ) )
=> ! [F: $i,G: $i,H: $i,I: $i] :
( ( ( I @ ( H @ ( A @ apply ) ) )
& ( G @ ( F @ ( A @ apply ) ) )
& ( H @ ( F @ ( C @ apply ) ) )
& ( D @ ( I @ member ) )
& ( B @ ( H @ member ) )
& ( D @ ( G @ member ) )
& ( B @ ( F @ member ) ) )
=> ( I @ ( G @ ( E @ apply ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ compose_predicate ) ) ) ) ) )
<=> ! [G: $i,H: $i] :
( ( ( F @ ( H @ member ) )
& ( D @ ( G @ member ) ) )
=> ( ( H @ ( G @ ( A @ apply ) ) )
<=> ? [I: $i] :
( ( H @ ( I @ ( B @ apply ) ) )
& ( I @ ( G @ ( C @ apply ) ) )
& ( E @ ( I @ member ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_predicate) ).
thf(148,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i,H: $i] :
( ( ( F @ ( H @ member ) )
& ( D @ ( G @ member ) ) )
=> ( ( ? [I: $i] :
( ( H @ ( I @ ( B @ apply ) ) )
& ( I @ ( G @ ( C @ apply ) ) )
& ( E @ ( I @ member ) ) )
=> ( H @ ( G @ ( A @ apply ) ) ) )
& ( ( H @ ( G @ ( A @ apply ) ) )
=> ? [I: $i] :
( ( H @ ( I @ ( B @ apply ) ) )
& ( I @ ( G @ ( C @ apply ) ) )
& ( E @ ( I @ member ) ) ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ compose_predicate ) ) ) ) ) ) )
& ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ compose_predicate ) ) ) ) ) )
=> ! [G: $i,H: $i] :
( ( ( F @ ( H @ member ) )
& ( D @ ( G @ member ) ) )
=> ( ( ? [I: $i] :
( ( H @ ( I @ ( B @ apply ) ) )
& ( I @ ( G @ ( C @ apply ) ) )
& ( E @ ( I @ member ) ) )
=> ( H @ ( G @ ( A @ apply ) ) ) )
& ( ( H @ ( G @ ( A @ apply ) ) )
=> ? [I: $i] :
( ( H @ ( I @ ( B @ apply ) ) )
& ( I @ ( G @ ( C @ apply ) ) )
& ( E @ ( I @ member ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ sum @ ( A @ member ) )
<=> ? [C: $i] :
( ( C @ ( A @ member ) )
& ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum) ).
thf(264,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ ( A @ member ) )
& ( B @ ( C @ member ) ) )
=> ( B @ sum @ ( A @ member ) ) )
& ( ( B @ sum @ ( A @ member ) )
=> ? [C: $i] :
( ( C @ ( A @ member ) )
& ( B @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ isomorphism ) ) ) ) )
<=> ( ! [F: $i,G: $i,H: $i,I: $i] :
( ( ( I @ ( H @ ( A @ apply ) ) )
& ( G @ ( F @ ( A @ apply ) ) )
& ( D @ ( I @ member ) )
& ( B @ ( H @ member ) )
& ( D @ ( G @ member ) )
& ( B @ ( F @ member ) ) )
=> ( ( H @ ( F @ ( C @ apply ) ) )
<=> ( I @ ( G @ ( E @ apply ) ) ) ) )
& ( D @ ( B @ ( A @ one_to_one ) ) )
& ( D @ ( B @ ( A @ maps ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isomorphism) ).
thf(279,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ! [F: $i,G: $i,H: $i,I: $i] :
( ( ( I @ ( H @ ( A @ apply ) ) )
& ( G @ ( F @ ( A @ apply ) ) )
& ( D @ ( I @ member ) )
& ( B @ ( H @ member ) )
& ( D @ ( G @ member ) )
& ( B @ ( F @ member ) ) )
=> ( ( ( I @ ( G @ ( E @ apply ) ) )
=> ( H @ ( F @ ( C @ apply ) ) ) )
& ( ( H @ ( F @ ( C @ apply ) ) )
=> ( I @ ( G @ ( E @ apply ) ) ) ) ) )
& ( D @ ( B @ ( A @ one_to_one ) ) )
& ( D @ ( B @ ( A @ maps ) ) ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ isomorphism ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ isomorphism ) ) ) ) )
=> ( ! [F: $i,G: $i,H: $i,I: $i] :
( ( ( I @ ( H @ ( A @ apply ) ) )
& ( G @ ( F @ ( A @ apply ) ) )
& ( D @ ( I @ member ) )
& ( B @ ( H @ member ) )
& ( D @ ( G @ member ) )
& ( B @ ( F @ member ) ) )
=> ( ( ( I @ ( G @ ( E @ apply ) ) )
=> ( H @ ( F @ ( C @ apply ) ) ) )
& ( ( H @ ( F @ ( C @ apply ) ) )
=> ( I @ ( G @ ( E @ apply ) ) ) ) ) )
& ( D @ ( B @ ( A @ one_to_one ) ) )
& ( D @ ( B @ ( A @ maps ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ decreasing ) ) ) ) )
<=> ! [F: $i,G: $i,H: $i,I: $i] :
( ( ( I @ ( H @ ( A @ apply ) ) )
& ( G @ ( F @ ( A @ apply ) ) )
& ( H @ ( F @ ( C @ apply ) ) )
& ( D @ ( I @ member ) )
& ( B @ ( H @ member ) )
& ( D @ ( G @ member ) )
& ( B @ ( F @ member ) ) )
=> ( G @ ( I @ ( E @ apply ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',decreasing_function) ).
thf(180,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i,G: $i,H: $i,I: $i] :
( ( ( I @ ( H @ ( A @ apply ) ) )
& ( G @ ( F @ ( A @ apply ) ) )
& ( H @ ( F @ ( C @ apply ) ) )
& ( D @ ( I @ member ) )
& ( B @ ( H @ member ) )
& ( D @ ( G @ member ) )
& ( B @ ( F @ member ) ) )
=> ( G @ ( I @ ( E @ apply ) ) ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ decreasing ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ decreasing ) ) ) ) )
=> ! [F: $i,G: $i,H: $i,I: $i] :
( ( ( I @ ( H @ ( A @ apply ) ) )
& ( G @ ( F @ ( A @ apply ) ) )
& ( H @ ( F @ ( C @ apply ) ) )
& ( D @ ( I @ member ) )
& ( B @ ( H @ member ) )
& ( D @ ( G @ member ) )
& ( B @ ( F @ member ) ) )
=> ( G @ ( I @ ( E @ apply ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ injective ) ) )
<=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( F @ member ) )
& ( B @ ( E @ member ) )
& ( B @ ( D @ member ) ) )
=> ( ( ( F @ ( E @ ( A @ apply ) ) )
& ( F @ ( D @ ( A @ apply ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injective) ).
thf(223,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( F @ member ) )
& ( B @ ( E @ member ) )
& ( B @ ( D @ member ) ) )
=> ( ( ( F @ ( E @ ( A @ apply ) ) )
& ( F @ ( D @ ( A @ apply ) ) ) )
=> ( D = E ) ) )
=> ( C @ ( B @ ( A @ injective ) ) ) )
& ( ( C @ ( B @ ( A @ injective ) ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( F @ member ) )
& ( B @ ( E @ member ) )
& ( B @ ( D @ member ) ) )
=> ( ( ( F @ ( E @ ( A @ apply ) ) )
& ( F @ ( D @ ( A @ apply ) ) ) )
=> ( D = E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ maps ) ) )
<=> ( ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( F @ member ) )
& ( C @ ( E @ member ) )
& ( B @ ( D @ member ) ) )
=> ( ( ( F @ ( D @ ( A @ apply ) ) )
& ( E @ ( D @ ( A @ apply ) ) ) )
=> ( E = F ) ) )
& ! [D: $i] :
( ( B @ ( D @ member ) )
=> ? [E: $i] :
( ( E @ ( D @ ( A @ apply ) ) )
& ( C @ ( E @ member ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps) ).
thf(306,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( F @ member ) )
& ( C @ ( E @ member ) )
& ( B @ ( D @ member ) ) )
=> ( ( ( F @ ( D @ ( A @ apply ) ) )
& ( E @ ( D @ ( A @ apply ) ) ) )
=> ( E = F ) ) )
& ! [D: $i] :
( ( B @ ( D @ member ) )
=> ? [E: $i] :
( ( E @ ( D @ ( A @ apply ) ) )
& ( C @ ( E @ member ) ) ) ) )
=> ( C @ ( B @ ( A @ maps ) ) ) )
& ( ( C @ ( B @ ( A @ maps ) ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( F @ member ) )
& ( C @ ( E @ member ) )
& ( B @ ( D @ member ) ) )
=> ( ( ( F @ ( D @ ( A @ apply ) ) )
& ( E @ ( D @ ( A @ apply ) ) ) )
=> ( E = F ) ) )
& ! [D: $i] :
( ( B @ ( D @ member ) )
=> ? [E: $i] :
( ( E @ ( D @ ( A @ apply ) ) )
& ( C @ ( E @ member ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ difference ) @ ( A @ member ) )
<=> ( ~ ( B @ ( A @ member ) )
& ( C @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).
thf(241,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( B @ ( A @ member ) )
& ( C @ ( A @ member ) ) )
=> ( B @ ( C @ difference ) @ ( A @ member ) ) )
& ( ( B @ ( C @ difference ) @ ( A @ member ) )
=> ( ~ ( B @ ( A @ member ) )
& ( C @ ( A @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ intersection ) @ ( A @ member ) )
<=> ( ( C @ ( A @ member ) )
& ( B @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
thf(80,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ member ) )
& ( B @ ( A @ member ) ) )
=> ( C @ ( B @ intersection ) @ ( A @ member ) ) )
& ( ( C @ ( B @ intersection ) @ ( A @ member ) )
=> ( ( C @ ( A @ member ) )
& ( B @ ( A @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(28,axiom,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
thf(331,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ maps ) ) )
=> ( empty_set @ ( empty_set @ ( A @ inverse_image2 ) @ equal_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa14) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ maps ) ) )
=> ( empty_set @ ( empty_set @ ( A @ inverse_image2 ) @ equal_set ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(31,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ maps ) ) )
=> ( empty_set @ ( empty_set @ ( A @ inverse_image2 ) @ equal_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ inverse_predicate ) ) ) )
<=> ! [E: $i,F: $i] :
( ( ( D @ ( F @ member ) )
& ( C @ ( E @ member ) ) )
=> ( ( F @ ( E @ ( B @ apply ) ) )
<=> ( E @ ( F @ ( A @ apply ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_predicate) ).
thf(87,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i,F: $i] :
( ( ( D @ ( F @ member ) )
& ( C @ ( E @ member ) ) )
=> ( ( ( E @ ( F @ ( A @ apply ) ) )
=> ( F @ ( E @ ( B @ apply ) ) ) )
& ( ( F @ ( E @ ( B @ apply ) ) )
=> ( E @ ( F @ ( A @ apply ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ inverse_predicate ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ inverse_predicate ) ) ) )
=> ! [E: $i,F: $i] :
( ( ( D @ ( F @ member ) )
& ( C @ ( E @ member ) ) )
=> ( ( ( E @ ( F @ ( A @ apply ) ) )
=> ( F @ ( E @ ( B @ apply ) ) ) )
& ( ( F @ ( E @ ( B @ apply ) ) )
=> ( E @ ( F @ ( A @ apply ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
<=> ( ( A = C )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
thf(104,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A = C )
| ( A = B ) )
=> ( C @ ( B @ unordered_pair ) @ ( A @ member ) ) )
& ( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
=> ( ( A = C )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ power_set @ ( A @ member ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_set) ).
thf(119,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( B @ power_set @ ( A @ member ) ) )
& ( ( B @ power_set @ ( A @ member ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
thf(207,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(352,plain,
$false,
inference(e,[status(thm)],[115,125,133,334,256,54,271,140,171,36,341,200,215,248,60,148,264,279,180,223,306,241,80,331,31,87,104,119,207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET764+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 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
% 0.14/0.40 % Computer : n016.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 08:18:30 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.16/0.41 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
% 1.34/1.26 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.87/1.59 % [INFO] Parsing done (323ms).
% 2.25/1.61 % [INFO] Running in sequential loop mode.
% 3.38/2.21 % [INFO] eprover registered as external prover.
% 3.38/2.22 % [INFO] Scanning for conjecture ...
% 3.58/2.37 % [INFO] Found a conjecture (or negated_conjecture) and 28 axioms. Running axiom selection ...
% 3.78/2.49 % [INFO] Axiom selection finished. Selected 28 axioms (removed 0 axioms).
% 4.28/2.63 % [INFO] Problem is first-order (TPTP FOF).
% 4.28/2.65 % [INFO] Type checking passed.
% 4.28/2.66 % [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 ...
% 10.89/5.05 % External prover 'e' found a proof!
% 10.89/5.05 % [INFO] Killing All external provers ...
% 10.89/5.05 % Time passed: 4429ms (effective reasoning time: 3430ms)
% 10.89/5.05 % 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)>
% 11.58/5.06 % Axioms used in derivation (28): power_set, unordered_pair, inverse_image3, union, intersection, one_to_one, surjective, injective, increasing_function, image2, identity, difference, sum, product, empty_set, inverse_predicate, isomorphism, decreasing_function, image3, subset, equal_maps, inverse_function, equal_set, compose_function, inverse_image2, singleton, maps, compose_predicate
% 11.58/5.06 % No. of inferences in proof: 60
% 11.58/5.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4429 ms resp. 3430 ms w/o parsing
% 12.13/5.21 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.13/5.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------