%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV420^1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n005.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 : Wed Sep 30 08:37:16 AM UTC 2026
% Result : Theorem 4.38s 2.52s
% Output : Refutation 4.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 37 ( 31 unt; 0 typ; 23 def)
% Number of atoms : 280 ( 118 equ; 0 cnn)
% Maximal formula atoms : 57 ( 7 avg)
% Number of connectives : 821 ( 48 ~; 68 |; 120 &; 464 @)
% ( 0 <=>; 121 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 85 ( 85 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 5 con; 0-3 aty)
% Number of variables : 229 ( 43 ^; 137 !; 35 ?; 229 :)
% ( 0 !>; 0 ?*; 0 @-; 14 @+)
% Comments :
%------------------------------------------------------------------------------
thf(emptyset_decl,type,
emptyset: $i > $o ).
thf(union_decl,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(intersection_decl,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(is_function_decl,type,
is_function: ( $i > $o ) > ( $i > $i ) > ( $i > $o ) > $o ).
thf(injection_decl,type,
injection: ( $i > $o ) > ( $i > $i ) > ( $i > $o ) > $o ).
thf(surjection_decl,type,
surjection: ( $i > $o ) > ( $i > $i ) > ( $i > $o ) > $o ).
thf(bijection_decl,type,
bijection: ( $i > $o ) > ( $i > $i ) > ( $i > $o ) > $o ).
thf(equinumerous_decl,type,
equinumerous: ( $i > $o ) > ( $i > $o ) > $o ).
thf(embedding_decl,type,
embedding: ( $i > $o ) > ( $i > $o ) > $o ).
thf(sk1_decl,type,
sk1: $i > $o ).
thf(sk2_decl,type,
sk2: $i > $o ).
thf(sk3_decl,type,
sk3: $i > $o ).
thf(sk4_decl,type,
sk4: $i > $o ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk12_decl,type,
sk12: $i > $i ).
thf(sk13_decl,type,
sk13: ( $i > $i ) > $i ).
thf(sk14_decl,type,
sk14: ( $i > $i ) > $i ).
thf(emptyset_def,definition,
( emptyset
= ( ^ [A: $i] : $false ) ) ).
thf(union_def,definition,
( union
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(intersection_def,definition,
( intersection
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(is_function_def,definition,
( is_function
= ( ^ [A: $i > $o,B: $i > $i,C: $i > $o] :
! [D: $i] :
( ( A @ D )
=> ( C @ ( B @ D ) ) ) ) ) ).
thf(injection_def,definition,
( injection
= ( ^ [A: $i > $o,B: $i > $i,C: $i > $o] :
( ( is_function @ A @ B @ C )
=> ! [D: $i,E: $i] :
( ( ( A @ D )
& ( A @ E )
& ( ( B @ D )
= ( B @ E ) ) )
=> ( D = E ) ) ) ) ) ).
thf(surjection_def,definition,
( surjection
= ( ^ [A: $i > $o,B: $i > $i,C: $i > $o] :
( ( is_function @ A @ B @ C )
=> ! [D: $i] :
( ( C @ D )
=> ? [E: $i] :
( ( A @ E )
& ( ( B @ E )
= D ) ) ) ) ) ) ).
thf(bijection_def,definition,
( bijection
= ( ^ [A: $i > $o,B: $i > $i,C: $i > $o] :
( ( injection @ A @ B @ C )
& ( surjection @ A @ B @ C ) ) ) ) ).
thf(equinumerous_def,definition,
( equinumerous
= ( ^ [A: $i > $o,B: $i > $o] :
? [C: $i > $i] : ( bijection @ A @ C @ B ) ) ) ).
thf(embedding_def,definition,
( embedding
= ( ^ [A: $i > $o,B: $i > $o] :
? [C: $i > $i] : ( injection @ A @ C @ B ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $o] :
~ ! [B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ? [E: $i > $i] :
( ( ! [F: $i] :
( ( A @ F )
=> ( B @ ( E @ F ) ) )
=> ! [F: $i,G: $i] :
( ( ( A @ F )
& ( A @ G )
& ( ( E @ F )
= ( E @ G ) ) )
=> ( F = G ) ) )
& ( ! [F: $i] :
( ( A @ F )
=> ( B @ ( E @ F ) ) )
=> ! [F: $i] :
( ( B @ F )
=> ? [G: $i] :
( ( A @ G )
& ( ( E @ G )
= F ) ) ) ) )
& ? [E: $i > $i] :
( ( ! [F: $i] :
( ( C @ F )
=> ( D @ ( E @ F ) ) )
=> ! [F: $i,G: $i] :
( ( ( C @ F )
& ( C @ G )
& ( ( E @ F )
= ( E @ G ) ) )
=> ( F = G ) ) )
& ( ! [F: $i] :
( ( C @ F )
=> ( D @ ( E @ F ) ) )
=> ! [F: $i] :
( ( D @ F )
=> ? [G: $i] :
( ( C @ G )
& ( ( E @ G )
= F ) ) ) ) )
& ( ( ^ [E: $i] :
( ( B @ E )
& ( D @ E ) ) )
= ( ^ [E: $i] : $false ) ) )
=> ( ! [E: $i > $i,F: $i] :
( ( ( A @ F )
| ( C @ F ) )
=> ( ( B @ ( E @ F ) )
| ( D @ ( E @ F ) ) ) )
=> ? [E: $i > $i] :
! [F: $i,G: $i] :
( ( ( ( A @ F )
| ( C @ F ) )
& ( ( A @ G )
| ( C @ G ) )
& ( ( E @ F )
= ( E @ G ) ) )
=> ( F = G ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $o] :
~ ! [B: $i > $o,C: $i > $o] :
( ( ? [D: $i > $i] :
( ( ! [E: $i] :
( ( sk1 @ E )
=> ( A @ ( D @ E ) ) )
=> ! [E: $i,F: $i] :
( ( ( sk1 @ E )
& ( sk1 @ F )
& ( ( D @ E )
= ( D @ F ) ) )
=> ( E = F ) ) )
& ( ! [E: $i] :
( ( sk1 @ E )
=> ( A @ ( D @ E ) ) )
=> ! [E: $i] :
( ( A @ E )
=> ? [F: $i] :
( ( sk1 @ F )
& ( ( D @ F )
= E ) ) ) ) )
& ? [D: $i > $i] :
( ( ! [E: $i] :
( ( B @ E )
=> ( C @ ( D @ E ) ) )
=> ! [E: $i,F: $i] :
( ( ( B @ E )
& ( B @ F )
& ( ( D @ E )
= ( D @ F ) ) )
=> ( E = F ) ) )
& ( ! [E: $i] :
( ( B @ E )
=> ( C @ ( D @ E ) ) )
=> ! [E: $i] :
( ( C @ E )
=> ? [F: $i] :
( ( B @ F )
& ( ( D @ F )
= E ) ) ) ) )
& ( ( ^ [D: $i] :
( ( A @ D )
& ( C @ D ) ) )
= ( ^ [D: $i] : $false ) ) )
=> ( ! [D: $i > $i,E: $i] :
( ( ( sk1 @ E )
| ( B @ E ) )
=> ( ( A @ ( D @ E ) )
| ( C @ ( D @ E ) ) ) )
=> ? [D: $i > $i] :
! [E: $i,F: $i] :
( ( ( ( sk1 @ E )
| ( B @ E ) )
& ( ( sk1 @ F )
| ( B @ F ) )
& ( ( D @ E )
= ( D @ F ) ) )
=> ( E = F ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $o] :
~ ! [B: $i > $o] :
( ( ? [C: $i > $i] :
( ( ! [D: $i] :
( ( sk1 @ D )
=> ( sk2 @ ( C @ D ) ) )
=> ! [D: $i,E: $i] :
( ( ( sk1 @ D )
& ( sk1 @ E )
& ( ( C @ D )
= ( C @ E ) ) )
=> ( D = E ) ) )
& ( ! [D: $i] :
( ( sk1 @ D )
=> ( sk2 @ ( C @ D ) ) )
=> ! [D: $i] :
( ( sk2 @ D )
=> ? [E: $i] :
( ( sk1 @ E )
& ( ( C @ E )
= D ) ) ) ) )
& ? [C: $i > $i] :
( ( ! [D: $i] :
( ( A @ D )
=> ( B @ ( C @ D ) ) )
=> ! [D: $i,E: $i] :
( ( ( A @ D )
& ( A @ E )
& ( ( C @ D )
= ( C @ E ) ) )
=> ( D = E ) ) )
& ( ! [D: $i] :
( ( A @ D )
=> ( B @ ( C @ D ) ) )
=> ! [D: $i] :
( ( B @ D )
=> ? [E: $i] :
( ( A @ E )
& ( ( C @ E )
= D ) ) ) ) )
& ( ( ^ [C: $i] :
( ( sk2 @ C )
& ( B @ C ) ) )
= ( ^ [C: $i] : $false ) ) )
=> ( ! [C: $i > $i,D: $i] :
( ( ( sk1 @ D )
| ( A @ D ) )
=> ( ( sk2 @ ( C @ D ) )
| ( B @ ( C @ D ) ) ) )
=> ? [C: $i > $i] :
! [D: $i,E: $i] :
( ( ( ( sk1 @ D )
| ( A @ D ) )
& ( ( sk1 @ E )
| ( A @ E ) )
& ( ( C @ D )
= ( C @ E ) ) )
=> ( D = E ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i > $o] :
~ ( ( ? [B: $i > $i] :
( ( ! [C: $i] :
( ( sk1 @ C )
=> ( sk2 @ ( B @ C ) ) )
=> ! [C: $i,D: $i] :
( ( ( sk1 @ C )
& ( sk1 @ D )
& ( ( B @ C )
= ( B @ D ) ) )
=> ( C = D ) ) )
& ( ! [C: $i] :
( ( sk1 @ C )
=> ( sk2 @ ( B @ C ) ) )
=> ! [C: $i] :
( ( sk2 @ C )
=> ? [D: $i] :
( ( sk1 @ D )
& ( ( B @ D )
= C ) ) ) ) )
& ? [B: $i > $i] :
( ( ! [C: $i] :
( ( sk3 @ C )
=> ( A @ ( B @ C ) ) )
=> ! [C: $i,D: $i] :
( ( ( sk3 @ C )
& ( sk3 @ D )
& ( ( B @ C )
= ( B @ D ) ) )
=> ( C = D ) ) )
& ( ! [C: $i] :
( ( sk3 @ C )
=> ( A @ ( B @ C ) ) )
=> ! [C: $i] :
( ( A @ C )
=> ? [D: $i] :
( ( sk3 @ D )
& ( ( B @ D )
= C ) ) ) ) )
& ( ( ^ [B: $i] :
( ( sk2 @ B )
& ( A @ B ) ) )
= ( ^ [B: $i] : $false ) ) )
=> ( ! [B: $i > $i,C: $i] :
( ( ( sk1 @ C )
| ( sk3 @ C ) )
=> ( ( sk2 @ ( B @ C ) )
| ( A @ ( B @ C ) ) ) )
=> ? [B: $i > $i] :
! [C: $i,D: $i] :
( ( ( ( sk1 @ C )
| ( sk3 @ C ) )
& ( ( sk1 @ D )
| ( sk3 @ D ) )
& ( ( B @ C )
= ( B @ D ) ) )
=> ( C = D ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i > $i] :
( ( ! [B: $i] :
( ( sk1 @ B )
=> ( sk2 @ ( A @ B ) ) )
=> ! [B: $i,C: $i] :
( ( ( sk1 @ B )
& ( sk1 @ C )
& ( ( A @ B )
= ( A @ C ) ) )
=> ( B = C ) ) )
& ( ! [B: $i] :
( ( sk1 @ B )
=> ( sk2 @ ( A @ B ) ) )
=> ! [B: $i] :
( ( sk2 @ B )
=> ? [C: $i] :
( ( sk1 @ C )
& ( ( A @ C )
= B ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ( sk1 @ A )
=> ( sk2 @ ( sk5 @ A ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( ( sk1 @ A )
=> ( sk2 @ ( sk5 @ A ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[B: $i] :
( ( sk1 @ B )
& ( ( sk5 @ B )
= A ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i > $i] :
( ( ! [B: $i] :
( ( sk3 @ B )
=> ( sk4 @ ( A @ B ) ) )
=> ! [B: $i,C: $i] :
( ( ( sk3 @ B )
& ( sk3 @ C )
& ( ( A @ B )
= ( A @ C ) ) )
=> ( B = C ) ) )
& ( ! [B: $i] :
( ( sk3 @ B )
=> ( sk4 @ ( A @ B ) ) )
=> ! [B: $i] :
( ( sk4 @ B )
=> ? [C: $i] :
( ( sk3 @ C )
& ( ( A @ C )
= B ) ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
~ ( ( sk3 @ A )
=> ( sk4 @ ( sk9 @ A ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
~ ( ( sk3 @ A )
=> ( sk4 @ ( sk9 @ A ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i] :
@+[B: $i] :
( ( sk3 @ B )
& ( ( sk9 @ B )
= A ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i > $i] :
@+[B: $i] :
~ ! [C: $i] :
( ( ( ( sk1 @ B )
| ( sk3 @ B ) )
& ( ( sk1 @ C )
| ( sk3 @ C ) )
& ( ( A @ B )
= ( A @ C ) ) )
=> ( B = C ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i > $i] :
@+[B: $i] :
~ ( ( ( ( sk1 @ ( sk13 @ A ) )
| ( sk3 @ ( sk13 @ A ) ) )
& ( ( sk1 @ B )
| ( sk3 @ B ) )
& ( ( A @ ( sk13 @ A ) )
= ( A @ B ) ) )
=> ( ( sk13 @ A )
= B ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $o,B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( equinumerous @ A @ B )
& ( equinumerous @ C @ D )
& ( ( intersection @ B @ D )
= emptyset ) )
=> ( embedding @ ( union @ A @ C ) @ ( union @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o,B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( equinumerous @ A @ B )
& ( equinumerous @ C @ D )
& ( ( intersection @ B @ D )
= emptyset ) )
=> ( embedding @ ( union @ A @ C ) @ ( union @ B @ D ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $o,B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ? [E: $i > $i] :
( ( ! [F: $i] :
( ( A @ F )
=> ( B @ ( E @ F ) ) )
=> ! [F: $i,G: $i] :
( ( ( A @ F )
& ( A @ G )
& ( ( E @ F )
= ( E @ G ) ) )
=> ( F = G ) ) )
& ( ! [F: $i] :
( ( A @ F )
=> ( B @ ( E @ F ) ) )
=> ! [F: $i] :
( ( B @ F )
=> ? [G: $i] :
( ( A @ G )
& ( ( E @ G )
= F ) ) ) ) )
& ? [E: $i > $i] :
( ( ! [F: $i] :
( ( C @ F )
=> ( D @ ( E @ F ) ) )
=> ! [F: $i,G: $i] :
( ( ( C @ F )
& ( C @ G )
& ( ( E @ F )
= ( E @ G ) ) )
=> ( F = G ) ) )
& ( ! [F: $i] :
( ( C @ F )
=> ( D @ ( E @ F ) ) )
=> ! [F: $i] :
( ( D @ F )
=> ? [G: $i] :
( ( C @ G )
& ( ( E @ G )
= F ) ) ) ) )
& ( ( ^ [E: $i] :
( ( B @ E )
& ( D @ E ) ) )
= ( ^ [E: $i] : $false ) ) )
=> ? [E: $i > $i] :
( ! [F: $i] :
( ( ( A @ F )
| ( C @ F ) )
=> ( ( B @ ( E @ F ) )
| ( D @ ( E @ F ) ) ) )
=> ! [F: $i,G: $i] :
( ( ( ( A @ F )
| ( C @ F ) )
& ( ( A @ G )
| ( C @ G ) )
& ( ( E @ F )
= ( E @ G ) ) )
=> ( F = G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ! [A: $i > $o,B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ? [E: $i > $i] :
( ( ! [F: $i] :
( ( A @ F )
=> ( B @ ( E @ F ) ) )
=> ! [F: $i,G: $i] :
( ( ( A @ F )
& ( A @ G )
& ( ( E @ F )
= ( E @ G ) ) )
=> ( F = G ) ) )
& ( ! [F: $i] :
( ( A @ F )
=> ( B @ ( E @ F ) ) )
=> ! [F: $i] :
( ( B @ F )
=> ? [G: $i] :
( ( A @ G )
& ( ( E @ G )
= F ) ) ) ) )
& ? [E: $i > $i] :
( ( ! [F: $i] :
( ( C @ F )
=> ( D @ ( E @ F ) ) )
=> ! [F: $i,G: $i] :
( ( ( C @ F )
& ( C @ G )
& ( ( E @ F )
= ( E @ G ) ) )
=> ( F = G ) ) )
& ( ! [F: $i] :
( ( C @ F )
=> ( D @ ( E @ F ) ) )
=> ! [F: $i] :
( ( D @ F )
=> ? [G: $i] :
( ( C @ G )
& ( ( E @ G )
= F ) ) ) ) )
& ( ( ^ [E: $i] :
( ( B @ E )
& ( D @ E ) ) )
= ( ^ [E: $i] : $false ) ) )
=> ( ! [E: $i > $i,F: $i] :
( ( ( A @ F )
| ( C @ F ) )
=> ( ( B @ ( E @ F ) )
| ( D @ ( E @ F ) ) ) )
=> ? [E: $i > $i] :
! [F: $i,G: $i] :
( ( ( ( A @ F )
| ( C @ F ) )
& ( ( A @ G )
| ( C @ G ) )
& ( ( E @ F )
= ( E @ G ) ) )
=> ( F = G ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [I: $i > $i,H: $i,G: $i > $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ sk6 )
| ~ ( sk1 @ A )
| ~ ( sk1 @ B )
| ( ( sk5 @ A )
!= ( sk5 @ B ) )
| ( A = B ) )
& ( ~ ( sk2 @ ( sk5 @ sk6 ) )
| ~ ( sk1 @ A )
| ~ ( sk1 @ B )
| ( ( sk5 @ A )
!= ( sk5 @ B ) )
| ( A = B ) )
& ( ( sk1 @ sk7 )
| ~ ( sk2 @ C )
| ( sk1 @ ( sk8 @ C ) ) )
& ( ( sk1 @ sk7 )
| ~ ( sk2 @ C )
| ( ( sk5 @ ( sk8 @ C ) )
= C ) )
& ( ~ ( sk2 @ ( sk5 @ sk7 ) )
| ~ ( sk2 @ C )
| ( sk1 @ ( sk8 @ C ) ) )
& ( ~ ( sk2 @ ( sk5 @ sk7 ) )
| ~ ( sk2 @ C )
| ( ( sk5 @ ( sk8 @ C ) )
= C ) )
& ( ( sk3 @ sk10 )
| ~ ( sk3 @ D )
| ~ ( sk3 @ E )
| ( ( sk9 @ D )
!= ( sk9 @ E ) )
| ( D = E ) )
& ( ~ ( sk4 @ ( sk9 @ sk10 ) )
| ~ ( sk3 @ D )
| ~ ( sk3 @ E )
| ( ( sk9 @ D )
!= ( sk9 @ E ) )
| ( D = E ) )
& ( ( sk3 @ sk11 )
| ~ ( sk4 @ F )
| ( sk3 @ ( sk12 @ F ) ) )
& ( ( sk3 @ sk11 )
| ~ ( sk4 @ F )
| ( ( sk9 @ ( sk12 @ F ) )
= F ) )
& ( ~ ( sk4 @ ( sk9 @ sk11 ) )
| ~ ( sk4 @ F )
| ( sk3 @ ( sk12 @ F ) ) )
& ( ~ ( sk4 @ ( sk9 @ sk11 ) )
| ~ ( sk4 @ F )
| ( ( sk9 @ ( sk12 @ F ) )
= F ) )
& ( ( ^ [J: $i] :
( ( sk2 @ J )
& ( sk4 @ J ) ) )
= ( ^ [J: $i] : $false ) )
& ( ~ ( sk1 @ H )
| ( sk2 @ ( G @ H ) )
| ( sk4 @ ( G @ H ) ) )
& ( ~ ( sk3 @ H )
| ( sk2 @ ( G @ H ) )
| ( sk4 @ ( G @ H ) ) )
& ( ( sk1 @ ( sk13 @ I ) )
| ( sk3 @ ( sk13 @ I ) ) )
& ( ( sk1 @ ( sk14 @ I ) )
| ( sk3 @ ( sk14 @ I ) ) )
& ( ( I @ ( sk13 @ I ) )
= ( I @ ( sk14 @ I ) ) )
& ( ( sk13 @ I )
!= ( sk14 @ I ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(8,plain,
! [A: $i > $i] :
( ( A @ ( sk13 @ A ) )
= ( A @ ( sk14 @ A ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(47,plain,
! [A: $i > $i] :
( ( A @ ( sk14 @ A ) )
= ( A @ ( sk13 @ A ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(48,plain,
! [A: $i > $i] :
( ( A @ ( sk14 @ A ) )
= ( A @ ( sk13 @ A ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(15,plain,
! [A: $i > $i] :
( ( sk13 @ A )
!= ( sk14 @ A ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(50,plain,
! [A: $i > $i] :
( ( sk14 @ A )
!= ( sk13 @ A ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(51,plain,
! [A: $i > $i] :
( ( sk14 @ A )
!= ( sk13 @ A ) ),
inference(simp,[status(thm)],[50]) ).
thf(55,plain,
! [B: $i > $i,A: $i > $i] :
( ( ( A @ ( sk13 @ A ) )
!= ( sk13 @ B ) )
| ( ( A @ ( sk14 @ A ) )
!= ( sk14 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[48,51]) ).
thf(59,plain,
( ( sk13
@ ^ [A: $i] : A )
!= ( sk13
@ ^ [A: $i] : A ) ),
inference(pre_uni,[status(thm)],[55:[bind(A,$thf( ^ [C: $i] : C )),bind(B,$thf( ^ [C: $i] : C ))]]) ).
thf(60,plain,
$false,
inference(pattern_uni,[status(thm)],[59:[]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV420^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % 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
% 0.10/0.22 % Computer : n005.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 15:45:31 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 0.97/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.14/1.02 % [INFO] Parsing done (211ms).
% 1.14/1.03 % [INFO] Running in sequential loop mode.
% 2.06/1.42 % [INFO] eprover registered as external prover.
% 2.06/1.43 % [INFO] Scanning for conjecture ...
% 2.22/1.57 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.41/1.61 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.41/1.61 % [INFO] Problem is higher-order (TPTP THF).
% 2.41/1.61 % [INFO] Type checking passed.
% 2.41/1.62 % [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 ...
% 4.38/2.51 % [INFO] Killing All external provers ...
% 4.38/2.52 % Time passed: 2148ms (effective reasoning time: 1476ms)
% 4.38/2.52 % 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)>
% 4.38/2.52 % Axioms used in derivation (0):
% 4.38/2.52 % No. of inferences in proof: 14
% 4.38/2.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2148 ms resp. 1476 ms w/o parsing
% 4.73/2.67 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.73/2.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------