%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU359+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n012.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 08:38:33 AM UTC 2026
% Result : Theorem 58.71s 32.93s
% Output : Refutation 58.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 64
% Number of leaves : 12
% Syntax : Number of formulae : 155 ( 19 unt; 0 typ; 8 def)
% Number of atoms : 904 ( 113 equ; 0 cnn)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 3240 ( 475 ~; 493 |; 79 &;2096 @)
% ( 2 <=>; 95 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 8 con; 0-3 aty)
% Number of variables : 210 ( 8 ^; 189 !; 5 ?; 210 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf(antisymmetric_relstr_decl,type,
antisymmetric_relstr: $i > $o ).
thf(rel_str_decl,type,
rel_str: $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(join_on_relstr_decl,type,
join_on_relstr: $i > $i > $i ).
thf(ex_sup_of_relstr_set_decl,type,
ex_sup_of_relstr_set: $i > $i > $o ).
thf(relstr_set_smaller_decl,type,
relstr_set_smaller: $i > $i > $i > $o ).
thf(related_decl,type,
related: $i > $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $o ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ! [C: $i] :
( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) )
& ( B @ ( C @ ( A @ relstr_set_smaller ) ) ) )
=> ( ( C @ ( A @ ex_sup_of_relstr_set ) )
& ( B
= ( C @ ( A @ join_on_relstr ) ) ) ) )
& ! [C: $i] :
( ( ( C @ ( A @ ex_sup_of_relstr_set ) )
& ( B
= ( C @ ( A @ join_on_relstr ) ) ) )
=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) )
& ( B @ ( C @ ( A @ relstr_set_smaller ) ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( sk1 @ the_carrier @ ( A @ element ) )
=> ( ! [B: $i] :
( ( ! [C: $i] :
( ( sk1 @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( sk1 @ relstr_set_smaller ) ) )
=> ( C @ ( A @ ( sk1 @ related ) ) ) ) )
& ( A @ ( B @ ( sk1 @ relstr_set_smaller ) ) ) )
=> ( ( B @ ( sk1 @ ex_sup_of_relstr_set ) )
& ( A
= ( B @ ( sk1 @ join_on_relstr ) ) ) ) )
& ! [B: $i] :
( ( ( B @ ( sk1 @ ex_sup_of_relstr_set ) )
& ( A
= ( B @ ( sk1 @ join_on_relstr ) ) ) )
=> ( ! [C: $i] :
( ( sk1 @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( sk1 @ relstr_set_smaller ) ) )
=> ( C @ ( A @ ( sk1 @ related ) ) ) ) )
& ( A @ ( B @ ( sk1 @ relstr_set_smaller ) ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ( A @ ( sk1 @ ex_sup_of_relstr_set ) )
& ( sk2
= ( A @ ( sk1 @ join_on_relstr ) ) ) )
=> ( ! [B: $i] :
( ( sk1 @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ ( sk1 @ relstr_set_smaller ) ) )
=> ( B @ ( sk2 @ ( sk1 @ related ) ) ) ) )
& ( sk2 @ ( A @ ( sk1 @ relstr_set_smaller ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( sk1 @ the_carrier @ ( A @ element ) )
=> ( ( A @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) )
=> ( A @ ( sk2 @ ( sk1 @ related ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ( ! [B: $i] :
( ( sk1 @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ ( sk1 @ relstr_set_smaller ) ) )
=> ( B @ ( sk2 @ ( sk1 @ related ) ) ) ) )
& ( sk2 @ ( A @ ( sk1 @ relstr_set_smaller ) ) ) )
=> ( ( A @ ( sk1 @ ex_sup_of_relstr_set ) )
& ( sk2
= ( A @ ( sk1 @ join_on_relstr ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( C @ relstr_set_smaller ) ) )
=> ( D @ ( A @ ( C @ related ) ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ! [D: $i] :
( ( B @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( A @ ( B @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( B @ related ) ) ) ) )
& ( C @ ( A @ ( B @ relstr_set_smaller ) ) )
& ( B @ the_carrier @ ( C @ element ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( C @ relstr_set_smaller ) ) )
=> ( D @ ( A @ ( C @ related ) ) ) ) ) ) ) ).
thf(12,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( B @ ( A @ ex_sup_of_relstr_set ) )
<=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_yellow_0) ).
thf(57,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) )
=> ( B @ ( A @ ex_sup_of_relstr_set ) ) )
& ( ( B @ ( A @ ex_sup_of_relstr_set ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(58,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ( ! [B: $i] :
( ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) )
=> ( B @ ( A @ ex_sup_of_relstr_set ) ) )
& ! [B: $i] :
( ( B @ ( A @ ex_sup_of_relstr_set ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) ) ) ) ),
inference(miniscope,[status(thm)],[57]) ).
thf(59,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ ( D @ ( E @ sk12 ) ) @ ( E @ ( A @ related ) ) )
| ~ ( E @ ( D @ ( A @ relstr_set_smaller ) ) )
| ~ ( A @ the_carrier @ ( E @ element ) )
| ~ ( A @ rel_str )
| ~ ( A @ antisymmetric_relstr ) )
& ( ( D @ ( A @ ex_sup_of_relstr_set ) )
| ( A @ ( D @ ( E @ sk12 ) ) @ ( D @ ( A @ relstr_set_smaller ) ) )
| ~ ( E @ ( D @ ( A @ relstr_set_smaller ) ) )
| ~ ( A @ the_carrier @ ( E @ element ) )
| ~ ( A @ rel_str )
| ~ ( A @ antisymmetric_relstr ) )
& ( ( D @ ( A @ ex_sup_of_relstr_set ) )
| ( A @ the_carrier @ ( A @ ( D @ ( E @ sk12 ) ) @ element ) )
| ~ ( E @ ( D @ ( A @ relstr_set_smaller ) ) )
| ~ ( A @ the_carrier @ ( E @ element ) )
| ~ ( A @ rel_str )
| ~ ( A @ antisymmetric_relstr ) )
& ( ( C @ ( A @ ( B @ sk11 ) @ ( A @ related ) ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ rel_str )
| ~ ( A @ antisymmetric_relstr ) )
& ( ( A @ ( B @ sk11 ) @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ rel_str )
| ~ ( A @ antisymmetric_relstr ) )
& ( ( A @ the_carrier @ ( A @ ( B @ sk11 ) @ element ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ rel_str )
| ~ ( A @ antisymmetric_relstr ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ex_sup_of_relstr_set ) )
| ( A @ ( B @ ( C @ sk12 ) ) @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ~ ( A @ antisymmetric_relstr ) ),
inference(cnfConj,[status(thm)],[59]) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ex_sup_of_relstr_set ) )
| ( A @ ( B @ ( C @ sk12 ) ) @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ~ ( A @ antisymmetric_relstr ) ),
inference(simp,[status(thm)],[64]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) )
& ( B @ ( C @ ( A @ relstr_set_smaller ) ) ) )
=> ( ( C @ ( A @ ex_sup_of_relstr_set ) )
& ( B
= ( C @ ( A @ join_on_relstr ) ) ) ) )
& ( ( ( C @ ( A @ ex_sup_of_relstr_set ) )
& ( B
= ( C @ ( A @ join_on_relstr ) ) ) )
=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) )
& ( B @ ( C @ ( A @ relstr_set_smaller ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_yellow_0) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) )
& ( B @ ( C @ ( A @ relstr_set_smaller ) ) ) )
=> ( ( C @ ( A @ ex_sup_of_relstr_set ) )
& ( B
= ( C @ ( A @ join_on_relstr ) ) ) ) )
& ( ( ( C @ ( A @ ex_sup_of_relstr_set ) )
& ( B
= ( C @ ( A @ join_on_relstr ) ) ) )
=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) )
& ( B @ ( C @ ( A @ relstr_set_smaller ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) )
& ( B @ ( C @ ( A @ relstr_set_smaller ) ) ) )
=> ( ( C @ ( A @ ex_sup_of_relstr_set ) )
& ( B
= ( C @ ( A @ join_on_relstr ) ) ) ) )
& ( ( ( C @ ( A @ ex_sup_of_relstr_set ) )
& ( B
= ( C @ ( A @ join_on_relstr ) ) ) )
=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) )
& ( B @ ( C @ ( A @ relstr_set_smaller ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
~ ! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ! [C: $i] :
( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) )
& ( B @ ( C @ ( A @ relstr_set_smaller ) ) ) )
=> ( ( C @ ( A @ ex_sup_of_relstr_set ) )
& ( B
= ( C @ ( A @ join_on_relstr ) ) ) ) )
& ! [C: $i] :
( ( ( C @ ( A @ ex_sup_of_relstr_set ) )
& ( B
= ( C @ ( A @ join_on_relstr ) ) ) )
=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( C @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( B @ ( A @ related ) ) ) ) )
& ( B @ ( C @ ( A @ relstr_set_smaller ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[13]) ).
thf(15,plain,
! [A: $i] :
( ( ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ( sk2
!= ( sk6 @ ( sk1 @ join_on_relstr ) ) )
| sk3 )
& ( ( A @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( A @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( sk1 @ the_carrier @ ( A @ element ) )
| sk3 )
& ( ( sk2 @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| sk3 )
& ( ~ sk3
| ~ ( sk5 @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) ) )
& ( ~ sk3
| ( sk5 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) ) )
& ( ~ sk3
| ( sk1 @ the_carrier @ ( sk5 @ element ) )
| ~ ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) ) )
& ( ~ sk3
| ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) ) )
& ( ~ sk3
| ( sk2
= ( sk4 @ ( sk1 @ join_on_relstr ) ) ) )
& ( sk1 @ the_carrier @ ( sk2 @ element ) )
& ( sk1 @ rel_str )
& ( sk1 @ antisymmetric_relstr ) ),
inference(cnf,[status(esa)],[14]) ).
thf(26,plain,
( ( sk2 @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| sk3 ),
inference(cnfConj,[status(thm)],[15]) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ex_sup_of_relstr_set ) )
| ( A @ the_carrier @ ( A @ ( B @ ( C @ sk12 ) ) @ element ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ~ ( A @ antisymmetric_relstr ) ),
inference(cnfConj,[status(thm)],[59]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ex_sup_of_relstr_set ) )
| ( A @ the_carrier @ ( A @ ( B @ ( C @ sk12 ) ) @ element ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ~ ( A @ antisymmetric_relstr ) ),
inference(simp,[status(thm)],[65]) ).
thf(4026,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
!= ( C @ ( B @ ( A @ relstr_set_smaller ) ) ) )
| ( B @ ( A @ ex_sup_of_relstr_set ) )
| ( A @ the_carrier @ ( A @ ( B @ ( C @ sk12 ) ) @ element ) )
| ~ $true
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ~ ( A @ antisymmetric_relstr )
| sk3 ),
inference(paramod_ordered,[status(thm)],[26,67]) ).
thf(4027,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
!= ( C @ ( B @ ( A @ relstr_set_smaller ) ) ) )
| ( B @ ( A @ ex_sup_of_relstr_set ) )
| ( A @ the_carrier @ ( A @ ( B @ ( C @ sk12 ) ) @ element ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ~ ( A @ antisymmetric_relstr )
| sk3 ),
inference(simp,[status(thm)],[4026]) ).
thf(4028,plain,
( ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ( sk1 @ the_carrier @ ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ element ) )
| ~ ( sk1 @ the_carrier @ ( sk2 @ element ) )
| ~ ( sk1 @ rel_str )
| ~ ( sk1 @ antisymmetric_relstr )
| sk3 ),
inference(pattern_uni,[status(thm)],[4027:[bind(A,$thf( sk1 )),bind(B,$thf( sk6 )),bind(C,$thf( sk2 ))]]) ).
thf(16,plain,
sk1 @ rel_str,
inference(cnfConj,[status(thm)],[15]) ).
thf(18,plain,
sk1 @ antisymmetric_relstr,
inference(cnfConj,[status(thm)],[15]) ).
thf(20,plain,
sk1 @ the_carrier @ ( sk2 @ element ),
inference(cnfConj,[status(thm)],[15]) ).
thf(10613,plain,
( ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ( sk1 @ the_carrier @ ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ element ) )
| ~ $true
| ~ $true
| ~ $true
| sk3 ),
inference(rewrite,[status(thm)],[4028,16,18,20]) ).
thf(10614,plain,
( ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ( sk1 @ the_carrier @ ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ element ) )
| sk3 ),
inference(simp,[status(thm)],[10613]) ).
thf(23,plain,
! [A: $i] :
( ( A @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( A @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( sk1 @ the_carrier @ ( A @ element ) )
| sk3 ),
inference(cnfConj,[status(thm)],[15]) ).
thf(10771,plain,
! [A: $i] :
( ( ( sk1 @ the_carrier @ ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ element ) )
!= ( sk1 @ the_carrier @ ( A @ element ) ) )
| ( A @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( A @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ $true
| sk3
| ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[10614,23]) ).
thf(10772,plain,
! [A: $i] :
( ( ( sk1 @ the_carrier @ ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ element ) )
!= ( sk1 @ the_carrier @ ( A @ element ) ) )
| ( A @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( A @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| sk3 ),
inference(simp,[status(thm)],[10771]) ).
thf(10773,plain,
( ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| sk3 ),
inference(pattern_uni,[status(thm)],[10772:[bind(A,$thf( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) ))]]) ).
thf(17,plain,
( ~ sk3
| ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(21,plain,
( ~ sk3
| ( sk2
= ( sk4 @ ( sk1 @ join_on_relstr ) ) ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(27,plain,
( ~ sk3
| ( ( sk4 @ ( sk1 @ join_on_relstr ) )
= sk2 ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( B @ ( A @ join_on_relstr ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow_0) ).
thf(43,plain,
! [A: $i,B: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( B @ ( A @ join_on_relstr ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(44,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] : ( A @ the_carrier @ ( B @ ( A @ join_on_relstr ) @ element ) ) ),
inference(miniscope,[status(thm)],[43]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( A @ the_carrier @ ( B @ ( A @ join_on_relstr ) @ element ) )
| ~ ( A @ rel_str ) ),
inference(cnf,[status(esa)],[44]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ rel_str )
!= ( A @ rel_str ) )
| ( A @ the_carrier @ ( B @ ( A @ join_on_relstr ) @ element ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16,45]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ rel_str )
!= ( A @ rel_str ) )
| ( A @ the_carrier @ ( B @ ( A @ join_on_relstr ) @ element ) ) ),
inference(simp,[status(thm)],[199]) ).
thf(201,plain,
! [A: $i] : ( sk1 @ the_carrier @ ( A @ ( sk1 @ join_on_relstr ) @ element ) ),
inference(pattern_uni,[status(thm)],[200:[bind(A,$thf( sk1 ))]]) ).
thf(219,plain,
! [A: $i] : ( sk1 @ the_carrier @ ( A @ ( sk1 @ join_on_relstr ) @ element ) ),
inference(simp,[status(thm)],[201]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i,C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( B @ ( A @ ex_sup_of_relstr_set ) )
=> ( ( C
= ( B @ ( A @ join_on_relstr ) ) )
<=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_yellow_0) ).
thf(29,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i,C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( B @ ( A @ ex_sup_of_relstr_set ) )
=> ( ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) ) )
=> ( C
= ( B @ ( A @ join_on_relstr ) ) ) )
& ( ( C
= ( B @ ( A @ join_on_relstr ) ) )
=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C
= ( B @ ( A @ join_on_relstr ) ) )
| ~ ( A @ ( B @ ( C @ sk7 ) ) @ ( C @ ( A @ related ) ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str ) )
& ( ( C
= ( B @ ( A @ join_on_relstr ) ) )
| ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str ) )
& ( ( C
= ( B @ ( A @ join_on_relstr ) ) )
| ( A @ the_carrier @ ( A @ ( B @ ( C @ sk7 ) ) @ element ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str ) )
& ( ( D @ ( C @ ( A @ related ) ) )
| ~ ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( A @ the_carrier @ ( D @ element ) )
| ( C
!= ( B @ ( A @ join_on_relstr ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str ) )
& ( ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ( C
!= ( B @ ( A @ join_on_relstr ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ( C
!= ( B @ ( A @ join_on_relstr ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ( C
!= ( B @ ( A @ join_on_relstr ) ) ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join_on_relstr ) @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( B @ ( A @ join_on_relstr ) @ element ) )
| ~ ( A @ rel_str ) ),
inference(simp,[status(thm)],[41]) ).
thf(2539,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ the_carrier @ ( A @ ( sk1 @ join_on_relstr ) @ element ) )
!= ( B @ the_carrier @ ( C @ ( B @ join_on_relstr ) @ element ) ) )
| ( C @ ( B @ join_on_relstr ) @ ( C @ ( B @ relstr_set_smaller ) ) )
| ~ ( C @ ( B @ ex_sup_of_relstr_set ) )
| ~ $true
| ~ ( B @ rel_str ) ),
inference(paramod_ordered,[status(thm)],[219,42]) ).
thf(2540,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ the_carrier @ ( A @ ( sk1 @ join_on_relstr ) @ element ) )
!= ( B @ the_carrier @ ( C @ ( B @ join_on_relstr ) @ element ) ) )
| ( C @ ( B @ join_on_relstr ) @ ( C @ ( B @ relstr_set_smaller ) ) )
| ~ ( C @ ( B @ ex_sup_of_relstr_set ) )
| ~ ( B @ rel_str ) ),
inference(simp,[status(thm)],[2539]) ).
thf(2541,plain,
! [A: $i] :
( ( A @ ( sk1 @ join_on_relstr ) @ ( A @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( A @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ ( sk1 @ rel_str ) ),
inference(pattern_uni,[status(thm)],[2540:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(3237,plain,
! [A: $i] :
( ( A @ ( sk1 @ join_on_relstr ) @ ( A @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( A @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ $true ),
inference(rewrite,[status(thm)],[2541,16]) ).
thf(3238,plain,
! [A: $i] :
( ( A @ ( sk1 @ join_on_relstr ) @ ( A @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( A @ ( sk1 @ ex_sup_of_relstr_set ) ) ),
inference(simp,[status(thm)],[3237]) ).
thf(3268,plain,
! [A: $i] :
( ( ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
!= ( A @ ( sk1 @ ex_sup_of_relstr_set ) ) )
| ( A @ ( sk1 @ join_on_relstr ) @ ( A @ ( sk1 @ relstr_set_smaller ) ) )
| ~ $true
| ~ sk3 ),
inference(paramod_ordered,[status(thm)],[17,3238]) ).
thf(3269,plain,
! [A: $i] :
( ( ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
!= ( A @ ( sk1 @ ex_sup_of_relstr_set ) ) )
| ( A @ ( sk1 @ join_on_relstr ) @ ( A @ ( sk1 @ relstr_set_smaller ) ) )
| ~ sk3 ),
inference(simp,[status(thm)],[3268]) ).
thf(3270,plain,
( ( sk4 @ ( sk1 @ join_on_relstr ) @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ sk3 ),
inference(pattern_uni,[status(thm)],[3269:[bind(A,$thf( sk4 ))]]) ).
thf(3380,plain,
( ( ( sk4 @ ( sk1 @ join_on_relstr ) )
!= ( sk4 @ ( sk1 @ join_on_relstr ) ) )
| ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ sk3
| ~ sk3 ),
inference(paramod_ordered,[status(thm)],[27,3270]) ).
thf(3381,plain,
( ( ( sk4 @ ( sk1 @ join_on_relstr ) )
!= ( sk4 @ ( sk1 @ join_on_relstr ) ) )
| ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ sk3 ),
inference(simp,[status(thm)],[3380]) ).
thf(3382,plain,
( ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ sk3 ),
inference(pattern_uni,[status(thm)],[3381:[]]) ).
thf(19,plain,
( ~ sk3
| ( sk1 @ the_carrier @ ( sk5 @ element ) )
| ~ ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(3496,plain,
( ( ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) )
!= ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) ) )
| ~ sk3
| ( sk1 @ the_carrier @ ( sk5 @ element ) )
| ~ $true
| ~ sk3 ),
inference(paramod_ordered,[status(thm)],[3382,19]) ).
thf(3497,plain,
( ( ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) )
!= ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) ) )
| ( sk1 @ the_carrier @ ( sk5 @ element ) )
| ~ sk3 ),
inference(simp,[status(thm)],[3496]) ).
thf(3498,plain,
( ( sk1 @ the_carrier @ ( sk5 @ element ) )
| ~ sk3 ),
inference(pattern_uni,[status(thm)],[3497:[]]) ).
thf(25,plain,
( ~ sk3
| ( sk5 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ related ) ) )
| ~ ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( A @ the_carrier @ ( D @ element ) )
| ( C
!= ( B @ ( A @ join_on_relstr ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(36,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ related ) ) )
| ~ ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( A @ the_carrier @ ( D @ element ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ( C
!= ( B @ ( A @ join_on_relstr ) ) ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join_on_relstr ) @ ( A @ related ) ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( B @ ( A @ join_on_relstr ) @ element ) )
| ~ ( A @ rel_str ) ),
inference(simp,[status(thm)],[36]) ).
thf(319,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) )
!= ( C @ ( B @ ( A @ relstr_set_smaller ) ) ) )
| ( C @ ( B @ ( A @ join_on_relstr ) @ ( A @ related ) ) )
| ~ $true
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( B @ ( A @ join_on_relstr ) @ element ) )
| ~ ( A @ rel_str )
| ~ sk3
| ~ ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,37]) ).
thf(320,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) )
!= ( C @ ( B @ ( A @ relstr_set_smaller ) ) ) )
| ( C @ ( B @ ( A @ join_on_relstr ) @ ( A @ related ) ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( B @ ( A @ join_on_relstr ) @ element ) )
| ~ ( A @ rel_str )
| ~ sk3
| ~ ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) ) ),
inference(simp,[status(thm)],[319]) ).
thf(321,plain,
( ( sk5 @ ( sk4 @ ( sk1 @ join_on_relstr ) @ ( sk1 @ related ) ) )
| ~ ( sk1 @ the_carrier @ ( sk5 @ element ) )
| ~ ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ ( sk1 @ the_carrier @ ( sk4 @ ( sk1 @ join_on_relstr ) @ element ) )
| ~ ( sk1 @ rel_str )
| ~ sk3
| ~ ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) ) ),
inference(pattern_uni,[status(thm)],[320:[bind(A,$thf( sk1 )),bind(B,$thf( sk4 )),bind(C,$thf( sk5 ))]]) ).
thf(13480,plain,
( ( sk5 @ ( sk4 @ ( sk1 @ join_on_relstr ) @ ( sk1 @ related ) ) )
| ~ ( sk1 @ the_carrier @ ( sk5 @ element ) )
| ~ ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ $true
| ~ $true
| ~ sk3
| ~ ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) ) ),
inference(rewrite,[status(thm)],[321,16,219]) ).
thf(13481,plain,
( ( sk5 @ ( sk4 @ ( sk1 @ join_on_relstr ) @ ( sk1 @ related ) ) )
| ~ ( sk1 @ the_carrier @ ( sk5 @ element ) )
| ~ ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ sk3
| ~ ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) ) ),
inference(simp,[status(thm)],[13480]) ).
thf(13488,plain,
( ( ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) )
!= ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) ) )
| ( sk5 @ ( sk4 @ ( sk1 @ join_on_relstr ) @ ( sk1 @ related ) ) )
| ~ ( sk1 @ the_carrier @ ( sk5 @ element ) )
| ~ ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ sk3
| ~ $true
| ~ sk3 ),
inference(paramod_ordered,[status(thm)],[3382,13481]) ).
thf(13489,plain,
( ( ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) )
!= ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) ) )
| ( sk5 @ ( sk4 @ ( sk1 @ join_on_relstr ) @ ( sk1 @ related ) ) )
| ~ ( sk1 @ the_carrier @ ( sk5 @ element ) )
| ~ ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ sk3 ),
inference(simp,[status(thm)],[13488]) ).
thf(13490,plain,
( ( sk5 @ ( sk4 @ ( sk1 @ join_on_relstr ) @ ( sk1 @ related ) ) )
| ~ ( sk1 @ the_carrier @ ( sk5 @ element ) )
| ~ ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ sk3 ),
inference(pattern_uni,[status(thm)],[13489:[]]) ).
thf(14066,plain,
( ( ( sk1 @ the_carrier @ ( sk5 @ element ) )
!= ( sk1 @ the_carrier @ ( sk5 @ element ) ) )
| ( sk5 @ ( sk4 @ ( sk1 @ join_on_relstr ) @ ( sk1 @ related ) ) )
| ~ $true
| ~ ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ sk3
| ~ sk3 ),
inference(paramod_ordered,[status(thm)],[3498,13490]) ).
thf(14067,plain,
( ( ( sk1 @ the_carrier @ ( sk5 @ element ) )
!= ( sk1 @ the_carrier @ ( sk5 @ element ) ) )
| ( sk5 @ ( sk4 @ ( sk1 @ join_on_relstr ) @ ( sk1 @ related ) ) )
| ~ ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ sk3 ),
inference(simp,[status(thm)],[14066]) ).
thf(14068,plain,
( ( sk5 @ ( sk4 @ ( sk1 @ join_on_relstr ) @ ( sk1 @ related ) ) )
| ~ ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ sk3 ),
inference(pattern_uni,[status(thm)],[14067:[]]) ).
thf(22,plain,
( ~ sk3
| ~ ( sk5 @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(3472,plain,
( ( ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) )
!= ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) ) )
| ~ sk3
| ~ ( sk5 @ ( sk2 @ ( sk1 @ related ) ) )
| ~ $true
| ~ sk3 ),
inference(paramod_ordered,[status(thm)],[3382,22]) ).
thf(3473,plain,
( ( ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) )
!= ( sk2 @ ( sk4 @ ( sk1 @ relstr_set_smaller ) ) ) )
| ~ ( sk5 @ ( sk2 @ ( sk1 @ related ) ) )
| ~ sk3 ),
inference(simp,[status(thm)],[3472]) ).
thf(3474,plain,
( ~ ( sk5 @ ( sk2 @ ( sk1 @ related ) ) )
| ~ sk3 ),
inference(pattern_uni,[status(thm)],[3473:[]]) ).
thf(14256,plain,
( ( ( sk5 @ ( sk4 @ ( sk1 @ join_on_relstr ) @ ( sk1 @ related ) ) )
!= ( sk5 @ ( sk2 @ ( sk1 @ related ) ) ) )
| ~ $true
| ~ sk3
| ~ ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ sk3 ),
inference(paramod_ordered,[status(thm)],[14068,3474]) ).
thf(14257,plain,
( ( ( sk5 @ ( sk4 @ ( sk1 @ join_on_relstr ) @ ( sk1 @ related ) ) )
!= ( sk5 @ ( sk2 @ ( sk1 @ related ) ) ) )
| ~ ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ sk3 ),
inference(simp,[status(thm)],[14256]) ).
thf(14259,plain,
( ( sk5 != sk5 )
| ( ( sk4 @ ( sk1 @ join_on_relstr ) )
!= sk2 )
| ( sk1 != sk1 )
| ~ ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ sk3 ),
inference(simp,[status(thm)],[14257]) ).
thf(14266,plain,
( ( ( sk4 @ ( sk1 @ join_on_relstr ) )
!= sk2 )
| ~ ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ sk3 ),
inference(simp,[status(thm)],[14259]) ).
thf(14282,plain,
( ( ( sk4 @ ( sk1 @ join_on_relstr ) )
!= ( sk4 @ ( sk1 @ join_on_relstr ) ) )
| ( sk2 != sk2 )
| ~ ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ sk3
| ~ sk3 ),
inference(paramod_ordered,[status(thm)],[27,14266]) ).
thf(14283,plain,
( ( ( sk4 @ ( sk1 @ join_on_relstr ) )
!= ( sk4 @ ( sk1 @ join_on_relstr ) ) )
| ~ ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ sk3 ),
inference(simp,[status(thm)],[14282]) ).
thf(14284,plain,
( ~ ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ sk3 ),
inference(pattern_uni,[status(thm)],[14283:[]]) ).
thf(14308,plain,
( ( ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
!= ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) ) )
| ~ $true
| ~ sk3
| ~ sk3 ),
inference(paramod_ordered,[status(thm)],[17,14284]) ).
thf(14309,plain,
( ( ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) )
!= ( sk4 @ ( sk1 @ ex_sup_of_relstr_set ) ) )
| ~ sk3 ),
inference(simp,[status(thm)],[14308]) ).
thf(14310,plain,
~ sk3,
inference(pattern_uni,[status(thm)],[14309:[]]) ).
thf(14399,plain,
( ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| $false ),
inference(rewrite,[status(thm)],[10773,14310]) ).
thf(14400,plain,
( ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) ) ),
inference(simp,[status(thm)],[14399]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ join_on_relstr ) ) )
| ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ( C
= ( B @ ( A @ join_on_relstr ) ) ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ join_on_relstr ) ) )
| ( A @ the_carrier @ ( A @ ( B @ ( C @ sk7 ) ) @ element ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ the_carrier @ ( A @ ( B @ ( C @ sk7 ) ) @ element ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ( C
= ( B @ ( A @ join_on_relstr ) ) ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(1073,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
!= ( C @ ( B @ ( A @ relstr_set_smaller ) ) ) )
| ( A @ the_carrier @ ( A @ ( B @ ( C @ sk7 ) ) @ element ) )
| ~ $true
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ( C
= ( B @ ( A @ join_on_relstr ) ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[26,39]) ).
thf(1074,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
!= ( C @ ( B @ ( A @ relstr_set_smaller ) ) ) )
| ( A @ the_carrier @ ( A @ ( B @ ( C @ sk7 ) ) @ element ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ( C
= ( B @ ( A @ join_on_relstr ) ) )
| sk3 ),
inference(simp,[status(thm)],[1073]) ).
thf(1075,plain,
( ( sk1 @ the_carrier @ ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ element ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ ( sk1 @ the_carrier @ ( sk2 @ element ) )
| ~ ( sk1 @ rel_str )
| ( ( sk6 @ ( sk1 @ join_on_relstr ) )
= sk2 )
| sk3 ),
inference(pattern_uni,[status(thm)],[1074:[bind(A,$thf( sk1 )),bind(B,$thf( sk6 )),bind(C,$thf( sk2 ))]]) ).
thf(2224,plain,
( ( sk1 @ the_carrier @ ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ element ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ $true
| ~ $true
| ( ( sk6 @ ( sk1 @ join_on_relstr ) )
= sk2 )
| sk3 ),
inference(rewrite,[status(thm)],[1075,16,20]) ).
thf(2225,plain,
( ( sk1 @ the_carrier @ ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ element ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ( ( sk6 @ ( sk1 @ join_on_relstr ) )
= sk2 )
| sk3 ),
inference(simp,[status(thm)],[2224]) ).
thf(24,plain,
( ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ( sk2
!= ( sk6 @ ( sk1 @ join_on_relstr ) ) )
| sk3 ),
inference(cnfConj,[status(thm)],[15]) ).
thf(28,plain,
( ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| sk3
| ( ( sk6 @ ( sk1 @ join_on_relstr ) )
!= sk2 ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(2260,plain,
( ( ( sk6 @ ( sk1 @ join_on_relstr ) )
!= ( sk6 @ ( sk1 @ join_on_relstr ) ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| sk3
| ( sk2 != sk2 )
| ( sk1 @ the_carrier @ ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ element ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[2225,28]) ).
thf(2261,plain,
( ( ( sk6 @ ( sk1 @ join_on_relstr ) )
!= ( sk6 @ ( sk1 @ join_on_relstr ) ) )
| ( sk1 @ the_carrier @ ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ element ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| sk3 ),
inference(simp,[status(thm)],[2260]) ).
thf(2262,plain,
( ( sk1 @ the_carrier @ ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ element ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| sk3 ),
inference(pattern_uni,[status(thm)],[2261:[]]) ).
thf(2455,plain,
! [A: $i] :
( ( ( sk1 @ the_carrier @ ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ element ) )
!= ( sk1 @ the_carrier @ ( A @ element ) ) )
| ( A @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( A @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ $true
| sk3
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[2262,23]) ).
thf(2456,plain,
! [A: $i] :
( ( ( sk1 @ the_carrier @ ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ element ) )
!= ( sk1 @ the_carrier @ ( A @ element ) ) )
| ( A @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( A @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| sk3 ),
inference(simp,[status(thm)],[2455]) ).
thf(2457,plain,
( ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| sk3 ),
inference(pattern_uni,[status(thm)],[2456:[bind(A,$thf( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) ))]]) ).
thf(14359,plain,
( ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| $false ),
inference(rewrite,[status(thm)],[2457,14310]) ).
thf(14360,plain,
( ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) ) ),
inference(simp,[status(thm)],[14359]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ join_on_relstr ) ) )
| ~ ( A @ ( B @ ( C @ sk7 ) ) @ ( C @ ( A @ related ) ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ sk7 ) ) @ ( C @ ( A @ related ) ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ( C
= ( B @ ( A @ join_on_relstr ) ) ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(14335,plain,
( ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| $false
| ( ( sk6 @ ( sk1 @ join_on_relstr ) )
!= sk2 ) ),
inference(rewrite,[status(thm)],[28,14310]) ).
thf(14336,plain,
( ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ( ( sk6 @ ( sk1 @ join_on_relstr ) )
!= sk2 ) ),
inference(simp,[status(thm)],[14335]) ).
thf(14660,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ join_on_relstr ) )
!= ( sk6 @ ( sk1 @ join_on_relstr ) ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ( C != sk2 )
| ~ ( A @ ( B @ ( C @ sk7 ) ) @ ( C @ ( A @ related ) ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str ) ),
inference(paramod_ordered,[status(thm)],[38,14336]) ).
thf(14661,plain,
! [A: $i] :
( ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ( A != sk2 )
| ~ ( sk1 @ ( sk6 @ ( A @ sk7 ) ) @ ( A @ ( sk1 @ related ) ) )
| ~ ( A @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ ( sk1 @ the_carrier @ ( A @ element ) )
| ~ ( sk1 @ rel_str ) ),
inference(pattern_uni,[status(thm)],[14660:[bind(A,$thf( sk1 )),bind(B,$thf( sk6 ))]]) ).
thf(14670,plain,
( ~ ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( sk2 @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ ( sk1 @ the_carrier @ ( sk2 @ element ) )
| ~ ( sk1 @ rel_str ) ),
inference(simp,[status(thm)],[14661]) ).
thf(14387,plain,
( ( sk2 @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| $false ),
inference(rewrite,[status(thm)],[26,14310]) ).
thf(14388,plain,
sk2 @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ),
inference(simp,[status(thm)],[14387]) ).
thf(23707,plain,
( ~ ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ ( sk2 @ ( sk1 @ related ) ) )
| ~ $true
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[14670,16,20,14388]) ).
thf(23708,plain,
( ~ ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) ) ),
inference(simp,[status(thm)],[23707]) ).
thf(23825,plain,
( ( ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ ( sk2 @ ( sk1 @ related ) ) )
!= ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ ( sk2 @ ( sk1 @ related ) ) ) )
| ~ $true
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) ) ),
inference(paramod_ordered,[status(thm)],[14360,23708]) ).
thf(23826,plain,
( ( ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ ( sk2 @ ( sk1 @ related ) ) )
!= ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ ( sk2 @ ( sk1 @ related ) ) ) )
| ~ ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) ) ),
inference(simp,[status(thm)],[23825]) ).
thf(23827,plain,
( ~ ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) ) ),
inference(pattern_uni,[status(thm)],[23826:[]]) ).
thf(24322,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ ( A @ relstr_set_smaller ) ) )
!= ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) ) )
| ~ $true
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ( C
= ( B @ ( A @ join_on_relstr ) ) ) ),
inference(paramod_ordered,[status(thm)],[40,23827]) ).
thf(24323,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ ( A @ relstr_set_smaller ) ) )
!= ( sk1 @ ( sk6 @ ( sk2 @ sk7 ) ) @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ( C
= ( B @ ( A @ join_on_relstr ) ) ) ),
inference(simp,[status(thm)],[24322]) ).
thf(24324,plain,
( ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ ( sk2 @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ ( sk1 @ the_carrier @ ( sk2 @ element ) )
| ~ ( sk1 @ rel_str )
| ( ( sk6 @ ( sk1 @ join_on_relstr ) )
= sk2 ) ),
inference(pattern_uni,[status(thm)],[24323:[bind(A,$thf( sk1 )),bind(B,$thf( sk6 )),bind(C,$thf( sk2 ))]]) ).
thf(24344,plain,
( ~ ( sk2 @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ ( sk1 @ the_carrier @ ( sk2 @ element ) )
| ~ ( sk1 @ rel_str )
| ( ( sk6 @ ( sk1 @ join_on_relstr ) )
= sk2 ) ),
inference(simp,[status(thm)],[24324]) ).
thf(52876,plain,
( ~ $true
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ $true
| ~ $true
| ( ( sk6 @ ( sk1 @ join_on_relstr ) )
= sk2 ) ),
inference(rewrite,[status(thm)],[24344,16,20,14388]) ).
thf(52877,plain,
( ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ( ( sk6 @ ( sk1 @ join_on_relstr ) )
= sk2 ) ),
inference(simp,[status(thm)],[52876]) ).
thf(53117,plain,
( ( ( sk6 @ ( sk1 @ join_on_relstr ) )
!= ( sk6 @ ( sk1 @ join_on_relstr ) ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ( sk2 != sk2 )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) ) ),
inference(paramod_ordered,[status(thm)],[52877,14336]) ).
thf(53118,plain,
( ( ( sk6 @ ( sk1 @ join_on_relstr ) )
!= ( sk6 @ ( sk1 @ join_on_relstr ) ) )
| ~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) ) ),
inference(simp,[status(thm)],[53117]) ).
thf(53119,plain,
~ ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) ),
inference(pattern_uni,[status(thm)],[53118:[]]) ).
thf(54523,plain,
( ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| $false ),
inference(rewrite,[status(thm)],[14400,53119]) ).
thf(54524,plain,
( ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) ) ),
inference(simp,[status(thm)],[54523]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ ( B @ ( C @ sk12 ) ) @ ( C @ ( A @ related ) ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ~ ( A @ antisymmetric_relstr ) ),
inference(cnfConj,[status(thm)],[59]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ ( B @ ( C @ sk12 ) ) @ ( C @ ( A @ related ) ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ~ ( A @ antisymmetric_relstr ) ),
inference(simp,[status(thm)],[61]) ).
thf(14615,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
!= ( C @ ( B @ ( A @ relstr_set_smaller ) ) ) )
| ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ ( B @ ( C @ sk12 ) ) @ ( C @ ( A @ related ) ) )
| ~ $true
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ~ ( A @ antisymmetric_relstr ) ),
inference(paramod_ordered,[status(thm)],[14388,66]) ).
thf(14616,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
!= ( C @ ( B @ ( A @ relstr_set_smaller ) ) ) )
| ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( A @ ( B @ ( C @ sk12 ) ) @ ( C @ ( A @ related ) ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ~ ( A @ antisymmetric_relstr ) ),
inference(simp,[status(thm)],[14615]) ).
thf(14617,plain,
( ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ ( sk2 @ ( sk1 @ related ) ) )
| ~ ( sk1 @ the_carrier @ ( sk2 @ element ) )
| ~ ( sk1 @ rel_str )
| ~ ( sk1 @ antisymmetric_relstr ) ),
inference(pattern_uni,[status(thm)],[14616:[bind(A,$thf( sk1 )),bind(B,$thf( sk6 )),bind(C,$thf( sk2 ))]]) ).
thf(84774,plain,
( $false
| ~ ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ ( sk2 @ ( sk1 @ related ) ) )
| ~ $true
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[14617,16,18,20,53119]) ).
thf(84775,plain,
~ ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ ( sk2 @ ( sk1 @ related ) ) ),
inference(simp,[status(thm)],[84774]) ).
thf(84800,plain,
( $false
| ~ ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) ) ),
inference(rewrite,[status(thm)],[54524,84775]) ).
thf(84801,plain,
~ ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) ),
inference(simp,[status(thm)],[84800]) ).
thf(86810,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk12 ) ) @ ( B @ ( A @ relstr_set_smaller ) ) )
!= ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) ) )
| ~ $true
| ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ~ ( A @ antisymmetric_relstr ) ),
inference(paramod_ordered,[status(thm)],[68,84801]) ).
thf(86811,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk12 ) ) @ ( B @ ( A @ relstr_set_smaller ) ) )
!= ( sk1 @ ( sk6 @ ( sk2 @ sk12 ) ) @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) ) )
| ( B @ ( A @ ex_sup_of_relstr_set ) )
| ~ ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
| ~ ( A @ the_carrier @ ( C @ element ) )
| ~ ( A @ rel_str )
| ~ ( A @ antisymmetric_relstr ) ),
inference(simp,[status(thm)],[86810]) ).
thf(86812,plain,
( ( sk6 @ ( sk1 @ ex_sup_of_relstr_set ) )
| ~ ( sk2 @ ( sk6 @ ( sk1 @ relstr_set_smaller ) ) )
| ~ ( sk1 @ the_carrier @ ( sk2 @ element ) )
| ~ ( sk1 @ rel_str )
| ~ ( sk1 @ antisymmetric_relstr ) ),
inference(pattern_uni,[status(thm)],[86811:[bind(A,$thf( sk1 )),bind(B,$thf( sk6 )),bind(C,$thf( sk2 ))]]) ).
thf(90628,plain,
( $false
| ~ $true
| ~ $true
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[86812,16,18,20,14388,53119]) ).
thf(90629,plain,
$false,
inference(simp,[status(thm)],[90628]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU359+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % 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
% 0.07/5.96 % Computer : n012.cluster.edu
% 0.07/5.96 % Model : x86_64 x86_64
% 0.07/5.96 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.96 % Memory : 8046.5625MB
% 0.07/5.96 % OS : Linux 6.8.0-71-generic
% 0.07/5.96 % CPULimit : 300
% 0.07/5.96 % WCLimit : 300
% 0.07/5.96 % DateTime : Sat Sep 26 09:18:52 UTC 2026
% 0.07/5.96 % CPUTime :
% 0.07/5.96 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
% 0.43/6.25 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.60/6.34 % [INFO] Parsing done (89ms).
% 0.60/6.35 % [INFO] Running in sequential loop mode.
% 0.95/6.54 % [INFO] eprover registered as external prover.
% 0.95/6.54 % [INFO] Scanning for conjecture ...
% 0.95/6.59 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 1.15/6.62 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.15/6.63 % [INFO] Problem is first-order (TPTP FOF).
% 1.15/6.63 % [INFO] Type checking passed.
% 1.15/6.63 % [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 ...
% 58.71/32.93 % [INFO] Killing All external provers ...
% 58.71/32.93 % Time passed: 26885ms (effective reasoning time: 26570ms)
% 58.71/32.93 % 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)>
% 58.71/32.93 % Axioms used in derivation (3): t15_yellow_0, dt_k1_yellow_0, d9_yellow_0
% 58.71/32.93 % No. of inferences in proof: 147
% 58.71/32.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 26885 ms resp. 26570 ms w/o parsing
% 58.71/32.98 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 58.71/32.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------