%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET993+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n020.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 08:31:29 AM UTC 2026
% Result : Theorem 105.68s 24.13s
% Output : Refutation 106.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 52
% Syntax : Number of formulae : 902 ( 357 unt; 0 typ; 18 def)
% Number of atoms : 2494 ( 935 equ; 0 cnn)
% Maximal formula atoms : 42 ( 2 avg)
% Number of connectives : 6557 (1320 ~; 854 |; 131 &;4181 @)
% ( 5 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 11 con; 0-3 aty)
% Number of variables : 1021 ( 18 ^; 940 !; 45 ?;1021 :)
% ( 0 !>; 0 ?*; 0 @-; 18 @+)
% Comments :
%------------------------------------------------------------------------------
thf(empty_set_decl,type,
empty_set: $i ).
thf(relation_decl,type,
relation: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(relation_dom_decl,type,
relation_dom: $i > $i ).
thf(relation_rng_decl,type,
relation_rng: $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(relation_empty_yielding_decl,type,
relation_empty_yielding: $i > $o ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i ).
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 ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i > $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i > $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i > $o ).
thf(sk15_decl,type,
sk15: $i > $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i > $i ).
thf(sk18_decl,type,
sk18: $i ).
thf(sk19_decl,type,
sk19: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( A != empty_set )
=> ! [B: $i] :
? [C: $i] :
( ( ( C @ relation_rng )
= ( B @ singleton ) )
& ( ( C @ relation_dom )
= A )
& ( C @ function )
& ( C @ relation ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ? [B: $i] :
( ( ( B @ relation_rng )
= ( A @ singleton ) )
& ( ( B @ relation_dom )
= sk1 )
& ( B @ function )
& ( B @ relation ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ element ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
( ( A @ relation )
& ( A @ empty ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ( C = B ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C = B )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ( A
= ( D @ ( C @ apply ) ) )
& ( C @ relation_dom @ ( D @ in ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ? [D: $i] :
( ( C
= ( D @ ( B @ apply ) ) )
& ( B @ relation_dom @ ( D @ in ) ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ? [D: $i] :
( ( C
= ( D @ ( B @ apply ) ) )
& ( B @ relation_dom @ ( D @ in ) ) )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( ( B @ ( A @ sk16 ) )
= ( C @ ( B @ apply ) ) )
& ( B @ relation_dom @ ( C @ in ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( @+[A: $i] :
( ( A @ function )
& ( A @ relation ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ! [D: $i] :
( ( B @ ( D @ in ) )
=> ( ( D @ ( C @ apply ) )
= A ) )
& ( ( C @ relation_dom )
= B )
& ( C @ function )
& ( C @ relation ) ) ) ) ).
thf(11,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(69,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(42,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(43,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(cnf,[status(esa)],[42]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( B @ powerset @ ( A @ element ) ) )
& ( ( B @ powerset @ ( A @ element ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(45,plain,
( ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B @ powerset @ ( A @ element ) ) )
& ! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(miniscope,[status(thm)],[44]) ).
thf(46,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ powerset @ ( C @ element ) )
| ~ ( D @ ( C @ subset ) ) )
& ( ( B @ ( A @ subset ) )
| ~ ( B @ powerset @ ( A @ element ) ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( B @ powerset @ ( A @ element ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[46]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( B @ powerset @ ( A @ element ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(226,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( C @ powerset @ ( B @ element ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,49]) ).
thf(227,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( C @ powerset @ ( B @ element ) ) ),
inference(simp,[status(thm)],[226]) ).
thf(228,plain,
! [A: $i] : ( A @ powerset @ ( A @ element ) ),
inference(pattern_uni,[status(thm)],[227:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(77,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ in ) )
| ( B @ empty )
| ~ ( B @ ( A @ element ) ) ),
inference(cnf,[status(esa)],[77]) ).
thf(1332,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ element ) )
!= ( C @ ( B @ element ) ) )
| ( C @ ( B @ in ) )
| ( C @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[228,78]) ).
thf(1333,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ element ) )
!= ( C @ ( B @ element ) ) )
| ( C @ ( B @ in ) )
| ( C @ empty ) ),
inference(simp,[status(thm)],[1332]) ).
thf(1334,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
| ( A @ powerset @ empty ) ),
inference(pattern_uni,[status(thm)],[1333:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ powerset ))]]) ).
thf(1362,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
| ( A @ powerset @ empty ) ),
inference(simp,[status(thm)],[1334]) ).
thf(16,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(81,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(82,plain,
~ ? [A: $i] : ( A @ powerset @ empty ),
inference(miniscope,[status(thm)],[81]) ).
thf(83,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(cnf,[status(esa)],[82]) ).
thf(17735,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
| $false ),
inference(rewrite,[status(thm)],[1362,83]) ).
thf(17736,plain,
! [A: $i] : ( A @ powerset @ ( A @ in ) ),
inference(simp,[status(thm)],[17735]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(112,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ( ( B
= ( A @ singleton ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(113,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
=> ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(miniscope,[status(thm)],[112]) ).
thf(114,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk12 ) @ in ) )
| ( ( E @ ( F @ sk11 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk12 ) )
= E )
| ( ( E @ ( F @ sk11 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk12 ) @ in ) )
| ( F @ ( E @ ( F @ sk11 ) @ in ) ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk12 ) )
= E )
| ( F @ ( E @ ( F @ sk11 ) @ in ) ) )
& ( ( B @ ( D @ in ) )
| ( D != A )
| ( B
!= ( A @ singleton ) ) )
& ( ( C = A )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ singleton ) ) ) ),
inference(cnf,[status(esa)],[113]) ).
thf(118,plain,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ singleton ) ) ),
inference(cnfConj,[status(thm)],[114]) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ in ) )
| ( C = A )
| ( B
!= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[118]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ~ ( A @ singleton @ ( B @ in ) )
| ( B = A ) ),
inference(simp,[status(thm)],[125]) ).
thf(22,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(101,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(23,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(102,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(103,plain,
( ( sk10 @ relation )
& ~ ( sk10 @ empty ) ),
inference(cnf,[status(esa)],[102]) ).
thf(104,plain,
~ ( sk10 @ empty ),
inference(cnfConj,[status(thm)],[103]) ).
thf(210,plain,
( ( ( sk10 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,104]) ).
thf(211,plain,
( ( sk10 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[210]) ).
thf(213,plain,
sk10 != empty_set,
inference(simp,[status(thm)],[211]) ).
thf(2918,plain,
! [B: $i,A: $i] :
( ( A != sk10 )
| ( B != empty_set )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,213]) ).
thf(2919,plain,
! [A: $i] :
( ( A != empty_set )
| ~ ( sk10 @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2918:[bind(A,$thf( sk10 ))]]) ).
thf(3456,plain,
~ ( sk10 @ singleton @ ( empty_set @ in ) ),
inference(simp,[status(thm)],[2919]) ).
thf(17791,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk10 @ singleton @ ( empty_set @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,3456]) ).
thf(17792,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk10 @ singleton @ ( empty_set @ in ) ) ),
inference(simp,[status(thm)],[17791]) ).
thf(17898,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk10 @ singleton ) )
| ( A != empty_set ) ),
inference(simp,[status(thm)],[17792]) ).
thf(17953,plain,
( ( empty_set @ powerset )
!= ( sk10 @ singleton ) ),
inference(simp,[status(thm)],[17898]) ).
thf(18113,plain,
! [B: $i,A: $i] :
( ( A
!= ( empty_set @ powerset ) )
| ( B
!= ( sk10 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,17953]) ).
thf(18114,plain,
! [A: $i] :
( ( A
!= ( sk10 @ singleton ) )
| ~ ( empty_set @ powerset @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[18113:[bind(A,$thf( empty_set @ powerset )),bind(B,$thf( B ))]]) ).
thf(18117,plain,
~ ( empty_set @ powerset @ singleton @ ( sk10 @ singleton @ in ) ),
inference(simp,[status(thm)],[18114]) ).
thf(20174,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ powerset @ singleton @ ( sk10 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,18117]) ).
thf(20175,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ powerset @ singleton @ ( sk10 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[20174]) ).
thf(20246,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( empty_set @ powerset @ singleton ) )
| ( A
!= ( sk10 @ singleton ) ) ),
inference(simp,[status(thm)],[20175]) ).
thf(20256,plain,
( ( sk10 @ singleton @ powerset )
!= ( empty_set @ powerset @ singleton ) ),
inference(simp,[status(thm)],[20246]) ).
thf(2916,plain,
! [B: $i,A: $i] :
( ( B != sk10 )
| ( A != empty_set )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,213]) ).
thf(2917,plain,
! [A: $i] :
( ( A != empty_set )
| ~ ( A @ singleton @ ( sk10 @ in ) ) ),
inference(pattern_uni,[status(thm)],[2916:[bind(A,$thf( A )),bind(B,$thf( sk10 ))]]) ).
thf(3455,plain,
~ ( empty_set @ singleton @ ( sk10 @ in ) ),
inference(simp,[status(thm)],[2917]) ).
thf(17809,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ singleton @ ( sk10 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,3455]) ).
thf(17810,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ singleton @ ( sk10 @ in ) ) ),
inference(simp,[status(thm)],[17809]) ).
thf(17903,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( empty_set @ singleton ) )
| ( A != sk10 ) ),
inference(simp,[status(thm)],[17810]) ).
thf(17959,plain,
( ( sk10 @ powerset )
!= ( empty_set @ singleton ) ),
inference(simp,[status(thm)],[17903]) ).
thf(116,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C != A )
| ( B
!= ( A @ singleton ) ) ),
inference(cnfConj,[status(thm)],[114]) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C != A )
| ( B
!= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[116]) ).
thf(122,plain,
! [A: $i] : ( A @ singleton @ ( A @ in ) ),
inference(simp,[status(thm)],[121]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(72,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ element ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[72]) ).
thf(1292,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ( C @ ( B @ element ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,73]) ).
thf(1293,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ( C @ ( B @ element ) ) ),
inference(simp,[status(thm)],[1292]) ).
thf(1294,plain,
! [A: $i] : ( A @ singleton @ ( A @ element ) ),
inference(pattern_uni,[status(thm)],[1293:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ singleton ))]]) ).
thf(1295,plain,
! [A: $i] : ( A @ singleton @ ( A @ element ) ),
inference(simp,[status(thm)],[1294]) ).
thf(18,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(86,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(87,plain,
( ( sk8 @ relation_empty_yielding )
& ( sk8 @ relation ) ),
inference(cnf,[status(esa)],[86]) ).
thf(88,plain,
sk8 @ relation,
inference(cnfConj,[status(thm)],[87]) ).
thf(13,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(74,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(75,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[74]) ).
thf(76,plain,
~ ( sk7 @ empty ),
inference(cnf,[status(esa)],[75]) ).
thf(208,plain,
( ( ( sk7 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,76]) ).
thf(209,plain,
( ( sk7 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[208]) ).
thf(212,plain,
sk7 != empty_set,
inference(simp,[status(thm)],[209]) ).
thf(2722,plain,
! [B: $i,A: $i] :
( ( A != sk7 )
| ( B != empty_set )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,212]) ).
thf(2723,plain,
! [A: $i] :
( ( A != empty_set )
| ~ ( sk7 @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2722:[bind(A,$thf( sk7 ))]]) ).
thf(3379,plain,
~ ( sk7 @ singleton @ ( empty_set @ in ) ),
inference(simp,[status(thm)],[2723]) ).
thf(17841,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk7 @ singleton @ ( empty_set @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,3379]) ).
thf(17842,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk7 @ singleton @ ( empty_set @ in ) ) ),
inference(simp,[status(thm)],[17841]) ).
thf(17895,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk7 @ singleton ) )
| ( A != empty_set ) ),
inference(simp,[status(thm)],[17842]) ).
thf(17950,plain,
( ( empty_set @ powerset )
!= ( sk7 @ singleton ) ),
inference(simp,[status(thm)],[17895]) ).
thf(9,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(64,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(65,plain,
sk6 @ empty,
inference(cnf,[status(esa)],[64]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(133,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(134,plain,
! [A: $i] :
( ( ( A @ relation_dom @ relation )
| ~ ( A @ empty ) )
& ( ( A @ relation_dom @ empty )
| ~ ( A @ empty ) ) ),
inference(cnf,[status(esa)],[133]) ).
thf(135,plain,
! [A: $i] :
( ( A @ relation_dom @ empty )
| ~ ( A @ empty ) ),
inference(cnfConj,[status(thm)],[134]) ).
thf(5147,plain,
! [A: $i] :
( ( ( sk6 @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,135]) ).
thf(5148,plain,
! [A: $i] :
( ( ( sk6 @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty ) ),
inference(simp,[status(thm)],[5147]) ).
thf(5149,plain,
sk6 @ relation_dom @ empty,
inference(pattern_uni,[status(thm)],[5148:[bind(A,$thf( sk6 ))]]) ).
thf(5317,plain,
! [A: $i] :
( ( ( sk6 @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5149,135]) ).
thf(5318,plain,
! [A: $i] :
( ( ( sk6 @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty ) ),
inference(simp,[status(thm)],[5317]) ).
thf(5319,plain,
sk6 @ relation_dom @ relation_dom @ empty,
inference(pattern_uni,[status(thm)],[5318:[bind(A,$thf( sk6 @ relation_dom ))]]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(137,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(138,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[137]) ).
thf(139,plain,
! [A: $i] :
( ~ ( A @ empty )
| ( A = empty_set ) ),
inference(lifteq,[status(thm)],[138]) ).
thf(6071,plain,
! [A: $i] :
( ( ( sk6 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[65,139]) ).
thf(6072,plain,
! [A: $i] :
( ( ( sk6 @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[6071]) ).
thf(6073,plain,
sk6 = empty_set,
inference(pattern_uni,[status(thm)],[6072:[bind(A,$thf( sk6 ))]]) ).
thf(9118,plain,
empty_set @ relation_dom @ relation_dom @ empty,
inference(rewrite,[status(thm)],[5319,6073]) ).
thf(8,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(60,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(61,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ( B @ empty )
& ( A != B ) )
& ( A @ empty ) ),
inference(miniscope,[status(thm)],[60]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ( A = B )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[61]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( A @ empty )
| ( A = B ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(33,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(173,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(174,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(cnf,[status(esa)],[173]) ).
thf(177,plain,
empty_set @ relation_empty_yielding,
inference(cnfConj,[status(thm)],[174]) ).
thf(430,plain,
! [B: $i,A: $i] :
( ( B != empty_set )
| ( A @ relation_empty_yielding )
| ~ ( B @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[63,177]) ).
thf(431,plain,
! [A: $i] :
( ( A @ relation_empty_yielding )
| ~ ( empty_set @ empty )
| ~ ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[430:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(16977,plain,
! [A: $i] :
( ( A @ relation_empty_yielding )
| ~ $true
| ~ ( A @ empty ) ),
inference(rewrite,[status(thm)],[431,101]) ).
thf(16978,plain,
! [A: $i] :
( ( A @ relation_empty_yielding )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[16977]) ).
thf(17000,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ relation_empty_yielding )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9118,16978]) ).
thf(17001,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ relation_empty_yielding ) ),
inference(simp,[status(thm)],[17000]) ).
thf(17002,plain,
empty_set @ relation_dom @ relation_dom @ relation_empty_yielding,
inference(pattern_uni,[status(thm)],[17001:[bind(A,$thf( empty_set @ relation_dom @ relation_dom ))]]) ).
thf(5129,plain,
! [A: $i] :
( ( ( empty_set @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,135]) ).
thf(5130,plain,
! [A: $i] :
( ( ( empty_set @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty ) ),
inference(simp,[status(thm)],[5129]) ).
thf(5131,plain,
empty_set @ relation_dom @ empty,
inference(pattern_uni,[status(thm)],[5130:[bind(A,$thf( empty_set ))]]) ).
thf(5887,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[5131,139]) ).
thf(5888,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[5887]) ).
thf(5889,plain,
( ( empty_set @ relation_dom )
= empty_set ),
inference(pattern_uni,[status(thm)],[5888:[bind(A,$thf( empty_set @ relation_dom ))]]) ).
thf(17072,plain,
empty_set @ relation_dom @ relation_empty_yielding,
inference(rewrite,[status(thm)],[17002,5889]) ).
thf(31,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_rng @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(169,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_rng @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(170,plain,
! [A: $i] :
( ~ ( A @ relation_rng @ empty )
| ~ ( A @ relation )
| ( A @ empty ) ),
inference(cnf,[status(esa)],[169]) ).
thf(35,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( ( D @ ( C @ apply ) )
= B ) )
& ( ( C @ relation_dom )
= A )
& ( C @ function )
& ( C @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e2_13__funct_1) ).
thf(182,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( ( D @ ( C @ apply ) )
= B ) )
& ( ( C @ relation_dom )
= A )
& ( C @ function )
& ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(183,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ( C @ ( A @ ( B @ sk19 ) @ apply ) )
= B )
| ~ ( A @ ( C @ in ) ) )
& ( ( A @ ( B @ sk19 ) @ relation_dom )
= A )
& ( A @ ( B @ sk19 ) @ function )
& ( A @ ( B @ sk19 ) @ relation ) ),
inference(cnf,[status(esa)],[182]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk19 ) @ relation_dom )
= A ),
inference(cnfConj,[status(thm)],[183]) ).
thf(188,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk19 ) @ relation_dom )
= A ),
inference(lifteq,[status(thm)],[186]) ).
thf(185,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk19 ) @ function ),
inference(cnfConj,[status(thm)],[183]) ).
thf(1,conjecture,
! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
? [C: $i] :
( ( ( C @ relation_rng )
= ( B @ singleton ) )
& ( ( C @ relation_dom )
= A )
& ( C @ function )
& ( C @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funct_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
? [C: $i] :
( ( ( C @ relation_rng )
= ( B @ singleton ) )
& ( ( C @ relation_dom )
= A )
& ( C @ function )
& ( C @ relation ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(36,plain,
~ ! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
? [C: $i] :
( ( ( C @ relation_rng )
= ( B @ singleton ) )
& ( ( C @ relation_dom )
= A )
& ( C @ function )
& ( C @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(37,plain,
! [A: $i] :
( ( ( ( A @ relation_rng )
!= ( sk2 @ singleton ) )
| ( ( A @ relation_dom )
!= sk1 )
| ~ ( A @ function )
| ~ ( A @ relation ) )
& ( sk1 != empty_set ) ),
inference(cnf,[status(esa)],[36]) ).
thf(39,plain,
! [A: $i] :
( ( ( A @ relation_rng )
!= ( sk2 @ singleton ) )
| ( ( A @ relation_dom )
!= sk1 )
| ~ ( A @ function )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(41,plain,
! [A: $i] :
( ~ ( A @ function )
| ~ ( A @ relation )
| ( ( A @ relation_rng )
!= ( sk2 @ singleton ) )
| ( ( A @ relation_dom )
!= sk1 ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(196,plain,
! [A: $i] :
( ( ( sk8 @ relation )
!= ( A @ relation ) )
| ~ ( A @ function )
| ~ $true
| ( ( A @ relation_rng )
!= ( sk2 @ singleton ) )
| ( ( A @ relation_dom )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[88,41]) ).
thf(197,plain,
! [A: $i] :
( ( ( sk8 @ relation )
!= ( A @ relation ) )
| ~ ( A @ function )
| ( ( A @ relation_rng )
!= ( sk2 @ singleton ) )
| ( ( A @ relation_dom )
!= sk1 ) ),
inference(simp,[status(thm)],[196]) ).
thf(198,plain,
( ~ ( sk8 @ function )
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) )
| ( ( sk8 @ relation_dom )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[197:[bind(A,$thf( sk8 ))]]) ).
thf(312,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk19 ) @ function )
!= ( sk8 @ function ) )
| ~ $true
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) )
| ( ( sk8 @ relation_dom )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[185,198]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk19 ) @ function )
!= ( sk8 @ function ) )
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) )
| ( ( sk8 @ relation_dom )
!= sk1 ) ),
inference(simp,[status(thm)],[312]) ).
thf(317,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk19 ) )
!= sk8 )
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) )
| ( ( sk8 @ relation_dom )
!= sk1 ) ),
inference(simp,[status(thm)],[313]) ).
thf(366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk19 ) @ relation_dom )
!= ( sk8 @ relation_dom ) )
| ( ( C @ ( D @ sk19 ) )
!= sk8 )
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[188,317]) ).
thf(373,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ sk19 ) @ relation_dom )
!= ( sk8 @ relation_dom ) )
| ( ( B @ ( C @ sk19 ) )
!= sk8 )
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) ) ),
inference(simp,[status(thm)],[366]) ).
thf(405,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ sk19 ) @ relation_dom )
!= ( sk8 @ relation_dom ) )
| ( ( B @ ( C @ sk19 ) )
!= sk8 )
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) ) ),
inference(simp,[status(thm)],[373]) ).
thf(14468,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ relation_dom )
!= sk1 )
| ( ( A @ ( B @ sk19 ) )
!= sk8 )
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) ) ),
inference(rewrite,[status(thm)],[405,188]) ).
thf(21,axiom,
! [A: $i] :
~ ( A @ singleton @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(98,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(99,plain,
~ ? [A: $i] : ( A @ singleton @ empty ),
inference(miniscope,[status(thm)],[98]) ).
thf(100,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(cnf,[status(esa)],[99]) ).
thf(269,plain,
! [A: $i] :
( ( ( A @ singleton @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,100]) ).
thf(270,plain,
! [A: $i] :
( ( A @ singleton @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[269]) ).
thf(276,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(simp,[status(thm)],[270]) ).
thf(358,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk19 ) @ relation_dom )
!= ( C @ relation_dom ) )
| ~ ( C @ function )
| ~ ( C @ relation )
| ( ( C @ relation_rng )
!= ( sk2 @ singleton ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[188,41]) ).
thf(359,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ sk19 ) @ function )
| ~ ( B @ ( A @ sk19 ) @ relation )
| ( ( B @ ( A @ sk19 ) @ relation_rng )
!= ( sk2 @ singleton ) )
| ( B != sk1 ) ),
inference(pattern_uni,[status(thm)],[358:[bind(A,$thf( E )),bind(B,$thf( D )),bind(C,$thf( E @ ( D @ sk19 ) ))]]) ).
thf(400,plain,
! [A: $i] :
( ~ ( sk1 @ ( A @ sk19 ) @ function )
| ~ ( sk1 @ ( A @ sk19 ) @ relation )
| ( ( sk1 @ ( A @ sk19 ) @ relation_rng )
!= ( sk2 @ singleton ) ) ),
inference(simp,[status(thm)],[359]) ).
thf(184,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk19 ) @ relation ),
inference(cnfConj,[status(thm)],[183]) ).
thf(13992,plain,
! [A: $i] :
( ~ $true
| ~ $true
| ( ( sk1 @ ( A @ sk19 ) @ relation_rng )
!= ( sk2 @ singleton ) ) ),
inference(rewrite,[status(thm)],[400,184,185]) ).
thf(13993,plain,
! [A: $i] :
( ( sk1 @ ( A @ sk19 ) @ relation_rng )
!= ( sk2 @ singleton ) ),
inference(simp,[status(thm)],[13992]) ).
thf(190,plain,
( ( ( sk7 @ empty )
!= ( sk6 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,76]) ).
thf(191,plain,
( ( sk7 @ empty )
!= ( sk6 @ empty ) ),
inference(simp,[status(thm)],[190]) ).
thf(192,plain,
sk7 != sk6,
inference(simp,[status(thm)],[191]) ).
thf(2589,plain,
! [B: $i,A: $i] :
( ( B != sk7 )
| ( A != sk6 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,192]) ).
thf(2590,plain,
! [A: $i] :
( ( A != sk6 )
| ~ ( A @ singleton @ ( sk7 @ in ) ) ),
inference(pattern_uni,[status(thm)],[2589:[bind(A,$thf( A )),bind(B,$thf( sk7 ))]]) ).
thf(3327,plain,
~ ( sk6 @ singleton @ ( sk7 @ in ) ),
inference(simp,[status(thm)],[2590]) ).
thf(4369,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk6 @ singleton @ ( sk7 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,3327]) ).
thf(4370,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk6 @ singleton @ ( sk7 @ in ) ) ),
inference(simp,[status(thm)],[4369]) ).
thf(4371,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk6 @ singleton ) )
| ( A != sk7 ) ),
inference(simp,[status(thm)],[4370]) ).
thf(4376,plain,
( ( sk7 @ singleton )
!= ( sk6 @ singleton ) ),
inference(simp,[status(thm)],[4371]) ).
thf(7199,plain,
( ( sk7 @ singleton )
!= ( empty_set @ singleton ) ),
inference(rewrite,[status(thm)],[4376,6073]) ).
thf(7219,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk7 @ singleton ) )
| ( A
!= ( empty_set @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,7199]) ).
thf(7220,plain,
! [A: $i] :
( ( A
!= ( empty_set @ singleton ) )
| ~ ( A @ singleton @ ( sk7 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[7219:[bind(A,$thf( A )),bind(B,$thf( sk7 @ singleton ))]]) ).
thf(7231,plain,
~ ( empty_set @ singleton @ singleton @ ( sk7 @ singleton @ in ) ),
inference(simp,[status(thm)],[7220]) ).
thf(17843,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk7 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,7231]) ).
thf(17844,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk7 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[17843]) ).
thf(17875,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( empty_set @ singleton @ singleton ) )
| ( A
!= ( sk7 @ singleton ) ) ),
inference(simp,[status(thm)],[17844]) ).
thf(17929,plain,
( ( sk7 @ singleton @ powerset )
!= ( empty_set @ singleton @ singleton ) ),
inference(simp,[status(thm)],[17875]) ).
thf(38,plain,
sk1 != empty_set,
inference(cnfConj,[status(thm)],[37]) ).
thf(40,plain,
sk1 != empty_set,
inference(lifteq,[status(thm)],[38]) ).
thf(432,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B != empty_set )
| ~ ( B @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[63,40]) ).
thf(433,plain,
! [A: $i] :
( ( A != empty_set )
| ~ ( A @ empty )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[432:[bind(A,$thf( sk1 ))]]) ).
thf(1108,plain,
( ~ ( empty_set @ empty )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[433]) ).
thf(1194,plain,
( ~ $true
| ~ ( sk1 @ empty ) ),
inference(rewrite,[status(thm)],[1108,101]) ).
thf(1195,plain,
~ ( sk1 @ empty ),
inference(simp,[status(thm)],[1194]) ).
thf(5239,plain,
( ( ( empty_set @ relation_dom @ empty )
!= ( sk1 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5131,1195]) ).
thf(5240,plain,
( ( empty_set @ relation_dom @ empty )
!= ( sk1 @ empty ) ),
inference(simp,[status(thm)],[5239]) ).
thf(5291,plain,
( ( empty_set @ relation_dom )
!= sk1 ),
inference(simp,[status(thm)],[5240]) ).
thf(5543,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk19 ) @ relation_dom )
!= ( empty_set @ relation_dom ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[188,5291]) ).
thf(5563,plain,
! [A: $i] :
( ( sk1 @ ( A @ sk19 ) )
!= empty_set ),
inference(simp,[status(thm)],[5543]) ).
thf(5569,plain,
! [A: $i] :
( ( sk1 @ ( A @ sk19 ) )
!= empty_set ),
inference(simp,[status(thm)],[5563]) ).
thf(11247,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ ( B @ sk19 ) ) )
| ( empty_set != empty_set )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[139,5569]) ).
thf(11248,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ ( B @ sk19 ) ) )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[11247]) ).
thf(11249,plain,
! [A: $i] :
~ ( sk1 @ ( A @ sk19 ) @ empty ),
inference(pattern_uni,[status(thm)],[11248:[bind(A,$thf( sk1 @ ( C @ sk19 ) )),bind(B,$thf( C ))]]) ).
thf(11266,plain,
! [A: $i] :
~ ( sk1 @ ( A @ sk19 ) @ empty ),
inference(simp,[status(thm)],[11249]) ).
thf(18069,plain,
! [B: $i,A: $i] :
( ( B
!= ( empty_set @ powerset ) )
| ( A
!= ( sk7 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,17950]) ).
thf(18070,plain,
! [A: $i] :
( ( A
!= ( sk7 @ singleton ) )
| ~ ( A @ singleton @ ( empty_set @ powerset @ in ) ) ),
inference(pattern_uni,[status(thm)],[18069:[bind(A,$thf( A )),bind(B,$thf( empty_set @ powerset ))]]) ).
thf(18080,plain,
~ ( sk7 @ singleton @ singleton @ ( empty_set @ powerset @ in ) ),
inference(simp,[status(thm)],[18070]) ).
thf(19978,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk7 @ singleton @ singleton @ ( empty_set @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,18080]) ).
thf(19979,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk7 @ singleton @ singleton @ ( empty_set @ powerset @ in ) ) ),
inference(simp,[status(thm)],[19978]) ).
thf(19981,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk7 @ singleton @ singleton ) )
| ( A
!= ( empty_set @ powerset ) ) ),
inference(simp,[status(thm)],[19979]) ).
thf(19994,plain,
( ( empty_set @ powerset @ singleton )
!= ( sk7 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[19981]) ).
thf(18185,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk10 @ powerset ) )
| ( A
!= ( empty_set @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,17959]) ).
thf(18186,plain,
! [A: $i] :
( ( A
!= ( empty_set @ singleton ) )
| ~ ( A @ singleton @ ( sk10 @ powerset @ in ) ) ),
inference(pattern_uni,[status(thm)],[18185:[bind(A,$thf( A )),bind(B,$thf( sk10 @ powerset ))]]) ).
thf(18193,plain,
~ ( empty_set @ singleton @ singleton @ ( sk10 @ powerset @ in ) ),
inference(simp,[status(thm)],[18186]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_rng @ relation )
& ( A @ relation_rng @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(90,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_rng @ relation )
& ( A @ relation_rng @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(91,plain,
! [A: $i] :
( ( ( A @ relation_rng @ relation )
| ~ ( A @ empty ) )
& ( ( A @ relation_rng @ empty )
| ~ ( A @ empty ) ) ),
inference(cnf,[status(esa)],[90]) ).
thf(92,plain,
! [A: $i] :
( ( A @ relation_rng @ empty )
| ~ ( A @ empty ) ),
inference(cnfConj,[status(thm)],[91]) ).
thf(1576,plain,
! [A: $i] :
( ( ( sk6 @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,92]) ).
thf(1577,plain,
! [A: $i] :
( ( ( sk6 @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty ) ),
inference(simp,[status(thm)],[1576]) ).
thf(1578,plain,
sk6 @ relation_rng @ empty,
inference(pattern_uni,[status(thm)],[1577:[bind(A,$thf( sk6 ))]]) ).
thf(1665,plain,
! [A: $i] :
( ( ( sk6 @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1578,92]) ).
thf(1666,plain,
! [A: $i] :
( ( ( sk6 @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty ) ),
inference(simp,[status(thm)],[1665]) ).
thf(1667,plain,
sk6 @ relation_rng @ relation_rng @ empty,
inference(pattern_uni,[status(thm)],[1666:[bind(A,$thf( sk6 @ relation_rng ))]]) ).
thf(136,plain,
! [A: $i] :
( ( A @ relation_dom @ relation )
| ~ ( A @ empty ) ),
inference(cnfConj,[status(thm)],[134]) ).
thf(5634,plain,
! [A: $i] :
( ( ( sk6 @ relation_rng @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1667,136]) ).
thf(5635,plain,
! [A: $i] :
( ( ( sk6 @ relation_rng @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ relation ) ),
inference(simp,[status(thm)],[5634]) ).
thf(5636,plain,
sk6 @ relation_rng @ relation_rng @ relation_dom @ relation,
inference(pattern_uni,[status(thm)],[5635:[bind(A,$thf( sk6 @ relation_rng @ relation_rng ))]]) ).
thf(12971,plain,
empty_set @ relation_rng @ relation_rng @ relation_dom @ relation,
inference(rewrite,[status(thm)],[5636,6073]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(167,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(168,plain,
! [A: $i] :
( ( A @ function )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[167]) ).
thf(10832,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ function )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9118,168]) ).
thf(10833,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ function ) ),
inference(simp,[status(thm)],[10832]) ).
thf(10834,plain,
empty_set @ relation_dom @ relation_dom @ function,
inference(pattern_uni,[status(thm)],[10833:[bind(A,$thf( empty_set @ relation_dom @ relation_dom ))]]) ).
thf(11468,plain,
empty_set @ relation_dom @ function,
inference(rewrite,[status(thm)],[10834,5889]) ).
thf(1668,plain,
( ( ( sk6 @ relation_rng @ empty )
!= ( sk1 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1578,1195]) ).
thf(1669,plain,
( ( sk6 @ relation_rng @ empty )
!= ( sk1 @ empty ) ),
inference(simp,[status(thm)],[1668]) ).
thf(1704,plain,
( ( sk6 @ relation_rng )
!= sk1 ),
inference(simp,[status(thm)],[1669]) ).
thf(2442,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk6 @ relation_rng ) )
| ( A != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,1704]) ).
thf(2443,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( A @ singleton @ ( sk6 @ relation_rng @ in ) ) ),
inference(pattern_uni,[status(thm)],[2442:[bind(A,$thf( A )),bind(B,$thf( sk6 @ relation_rng ))]]) ).
thf(3266,plain,
~ ( sk1 @ singleton @ ( sk6 @ relation_rng @ in ) ),
inference(simp,[status(thm)],[2443]) ).
thf(8342,plain,
~ ( sk1 @ singleton @ ( empty_set @ relation_rng @ in ) ),
inference(rewrite,[status(thm)],[3266,6073]) ).
thf(20,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(94,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(95,plain,
( ( sk9 @ relation )
& ( sk9 @ empty ) ),
inference(cnf,[status(esa)],[94]) ).
thf(96,plain,
sk9 @ empty,
inference(cnfConj,[status(thm)],[95]) ).
thf(1583,plain,
! [A: $i] :
( ( ( sk9 @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[96,92]) ).
thf(1584,plain,
! [A: $i] :
( ( ( sk9 @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty ) ),
inference(simp,[status(thm)],[1583]) ).
thf(1585,plain,
sk9 @ relation_rng @ empty,
inference(pattern_uni,[status(thm)],[1584:[bind(A,$thf( sk9 ))]]) ).
thf(5640,plain,
! [A: $i] :
( ( ( sk9 @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1585,136]) ).
thf(5641,plain,
! [A: $i] :
( ( ( sk9 @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ relation ) ),
inference(simp,[status(thm)],[5640]) ).
thf(5642,plain,
sk9 @ relation_rng @ relation_dom @ relation,
inference(pattern_uni,[status(thm)],[5641:[bind(A,$thf( sk9 @ relation_rng ))]]) ).
thf(6144,plain,
! [A: $i] :
( ( ( sk9 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[96,139]) ).
thf(6145,plain,
! [A: $i] :
( ( ( sk9 @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[6144]) ).
thf(6146,plain,
sk9 = empty_set,
inference(pattern_uni,[status(thm)],[6145:[bind(A,$thf( sk9 ))]]) ).
thf(10484,plain,
empty_set @ relation_rng @ relation_dom @ relation,
inference(rewrite,[status(thm)],[5642,6146]) ).
thf(5302,plain,
! [A: $i] :
( ( ( sk6 @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5149,92]) ).
thf(5303,plain,
! [A: $i] :
( ( ( sk6 @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty ) ),
inference(simp,[status(thm)],[5302]) ).
thf(5304,plain,
sk6 @ relation_dom @ relation_rng @ empty,
inference(pattern_uni,[status(thm)],[5303:[bind(A,$thf( sk6 @ relation_dom ))]]) ).
thf(9008,plain,
empty_set @ relation_dom @ relation_rng @ empty,
inference(rewrite,[status(thm)],[5304,6073]) ).
thf(9029,plain,
( ( ( empty_set @ relation_dom @ relation_rng @ empty )
!= ( sk7 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9008,76]) ).
thf(9030,plain,
( ( empty_set @ relation_dom @ relation_rng @ empty )
!= ( sk7 @ empty ) ),
inference(simp,[status(thm)],[9029]) ).
thf(9108,plain,
( ( empty_set @ relation_dom @ relation_rng )
!= sk7 ),
inference(simp,[status(thm)],[9030]) ).
thf(10959,plain,
( ( empty_set @ relation_rng )
!= sk7 ),
inference(rewrite,[status(thm)],[9108,5889]) ).
thf(1567,plain,
! [A: $i] :
( ( ( empty_set @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,92]) ).
thf(1568,plain,
! [A: $i] :
( ( ( empty_set @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty ) ),
inference(simp,[status(thm)],[1567]) ).
thf(1569,plain,
empty_set @ relation_rng @ empty,
inference(pattern_uni,[status(thm)],[1568:[bind(A,$thf( empty_set ))]]) ).
thf(5132,plain,
! [A: $i] :
( ( ( empty_set @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1569,135]) ).
thf(5133,plain,
! [A: $i] :
( ( ( empty_set @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty ) ),
inference(simp,[status(thm)],[5132]) ).
thf(5134,plain,
empty_set @ relation_rng @ relation_dom @ empty,
inference(pattern_uni,[status(thm)],[5133:[bind(A,$thf( empty_set @ relation_rng ))]]) ).
thf(5903,plain,
! [A: $i] :
( ( ( empty_set @ relation_rng @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[1569,139]) ).
thf(5904,plain,
! [A: $i] :
( ( ( empty_set @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[5903]) ).
thf(5905,plain,
( ( empty_set @ relation_rng )
= empty_set ),
inference(pattern_uni,[status(thm)],[5904:[bind(A,$thf( empty_set @ relation_rng ))]]) ).
thf(7235,plain,
empty_set @ relation_dom @ empty,
inference(rewrite,[status(thm)],[5134,5905]) ).
thf(5,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(50,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(51,plain,
! [A: $i] :
( ( ~ ( A @ sk3 @ empty )
| ( A @ empty ) )
& ( ( A @ powerset @ ( A @ sk3 @ element ) )
| ( A @ empty ) ) ),
inference(cnf,[status(esa)],[50]) ).
thf(52,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ sk3 @ element ) )
| ( A @ empty ) ),
inference(cnfConj,[status(thm)],[51]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ powerset @ ( A @ element ) ) ),
inference(cnfConj,[status(thm)],[46]) ).
thf(285,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ sk3 @ element ) )
!= ( C @ powerset @ ( B @ element ) ) )
| ( C @ ( B @ subset ) )
| ~ $true
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[52,47]) ).
thf(286,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ sk3 @ element ) )
!= ( C @ powerset @ ( B @ element ) ) )
| ( C @ ( B @ subset ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[285]) ).
thf(287,plain,
! [A: $i] :
( ( A @ ( A @ sk3 @ subset ) )
| ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[286:[bind(A,$thf( D )),bind(B,$thf( D @ sk3 )),bind(C,$thf( D ))]]) ).
thf(288,plain,
! [A: $i] :
( ( A @ ( A @ sk3 @ subset ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[287]) ).
thf(93,plain,
! [A: $i] :
( ( A @ relation_rng @ relation )
| ~ ( A @ empty ) ),
inference(cnfConj,[status(thm)],[91]) ).
thf(5233,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5131,93]) ).
thf(5234,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ relation ) ),
inference(simp,[status(thm)],[5233]) ).
thf(5235,plain,
empty_set @ relation_dom @ relation_rng @ relation,
inference(pattern_uni,[status(thm)],[5234:[bind(A,$thf( empty_set @ relation_dom ))]]) ).
thf(7993,plain,
empty_set @ relation_rng @ relation,
inference(rewrite,[status(thm)],[5235,5889]) ).
thf(3030,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B != empty_set )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,40]) ).
thf(3031,plain,
! [A: $i] :
( ( A != empty_set )
| ~ ( sk1 @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[3030:[bind(A,$thf( sk1 ))]]) ).
thf(3502,plain,
~ ( sk1 @ singleton @ ( empty_set @ in ) ),
inference(simp,[status(thm)],[3031]) ).
thf(1708,plain,
! [A: $i] :
( ( ( sk9 @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1585,92]) ).
thf(1709,plain,
! [A: $i] :
( ( ( sk9 @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty ) ),
inference(simp,[status(thm)],[1708]) ).
thf(1710,plain,
sk9 @ relation_rng @ relation_rng @ empty,
inference(pattern_uni,[status(thm)],[1709:[bind(A,$thf( sk9 @ relation_rng ))]]) ).
thf(2140,plain,
( ( ( sk9 @ relation_rng @ relation_rng @ empty )
!= ( sk1 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1710,1195]) ).
thf(2141,plain,
( ( sk9 @ relation_rng @ relation_rng @ empty )
!= ( sk1 @ empty ) ),
inference(simp,[status(thm)],[2140]) ).
thf(2181,plain,
( ( sk9 @ relation_rng @ relation_rng )
!= sk1 ),
inference(simp,[status(thm)],[2141]) ).
thf(2637,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk9 @ relation_rng @ relation_rng ) )
| ( A != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,2181]) ).
thf(2638,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( A @ singleton @ ( sk9 @ relation_rng @ relation_rng @ in ) ) ),
inference(pattern_uni,[status(thm)],[2637:[bind(A,$thf( A )),bind(B,$thf( sk9 @ relation_rng @ relation_rng ))]]) ).
thf(3344,plain,
~ ( sk1 @ singleton @ ( sk9 @ relation_rng @ relation_rng @ in ) ),
inference(simp,[status(thm)],[2638]) ).
thf(14793,plain,
~ ( sk1 @ singleton @ ( empty_set @ relation_rng @ relation_rng @ in ) ),
inference(rewrite,[status(thm)],[3344,6146]) ).
thf(2720,plain,
! [B: $i,A: $i] :
( ( B != sk7 )
| ( A != empty_set )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,212]) ).
thf(2721,plain,
! [A: $i] :
( ( A != empty_set )
| ~ ( A @ singleton @ ( sk7 @ in ) ) ),
inference(pattern_uni,[status(thm)],[2720:[bind(A,$thf( A )),bind(B,$thf( sk7 ))]]) ).
thf(3378,plain,
~ ( empty_set @ singleton @ ( sk7 @ in ) ),
inference(simp,[status(thm)],[2721]) ).
thf(17752,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ singleton @ ( sk7 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,3378]) ).
thf(17753,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ singleton @ ( sk7 @ in ) ) ),
inference(simp,[status(thm)],[17752]) ).
thf(17899,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( empty_set @ singleton ) )
| ( A != sk7 ) ),
inference(simp,[status(thm)],[17753]) ).
thf(17954,plain,
( ( sk7 @ powerset )
!= ( empty_set @ singleton ) ),
inference(simp,[status(thm)],[17899]) ).
thf(18147,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk7 @ powerset ) )
| ( A
!= ( empty_set @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,17954]) ).
thf(18148,plain,
! [A: $i] :
( ( A
!= ( empty_set @ singleton ) )
| ~ ( A @ singleton @ ( sk7 @ powerset @ in ) ) ),
inference(pattern_uni,[status(thm)],[18147:[bind(A,$thf( A )),bind(B,$thf( sk7 @ powerset ))]]) ).
thf(18155,plain,
~ ( empty_set @ singleton @ singleton @ ( sk7 @ powerset @ in ) ),
inference(simp,[status(thm)],[18148]) ).
thf(16991,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_empty_yielding )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9008,16978]) ).
thf(16992,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_empty_yielding ) ),
inference(simp,[status(thm)],[16991]) ).
thf(16993,plain,
empty_set @ relation_dom @ relation_rng @ relation_empty_yielding,
inference(pattern_uni,[status(thm)],[16992:[bind(A,$thf( empty_set @ relation_dom @ relation_rng ))]]) ).
thf(17017,plain,
empty_set @ relation_rng @ relation_empty_yielding,
inference(rewrite,[status(thm)],[16993,5889]) ).
thf(1696,plain,
! [A: $i] :
( ( ( A @ powerset @ empty )
!= ( sk6 @ relation_rng @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1578,83]) ).
thf(1697,plain,
! [A: $i] :
( ( A @ powerset @ empty )
!= ( sk6 @ relation_rng @ empty ) ),
inference(simp,[status(thm)],[1696]) ).
thf(1702,plain,
! [A: $i] :
( ( A @ powerset )
!= ( sk6 @ relation_rng ) ),
inference(simp,[status(thm)],[1697]) ).
thf(17270,plain,
! [A: $i] :
( ( A @ powerset )
!= ( empty_set @ relation_rng ) ),
inference(rewrite,[status(thm)],[1702,6073]) ).
thf(5334,plain,
( ( ( sk6 @ relation_dom @ empty )
!= ( sk10 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5149,104]) ).
thf(5335,plain,
( ( sk6 @ relation_dom @ empty )
!= ( sk10 @ empty ) ),
inference(simp,[status(thm)],[5334]) ).
thf(5357,plain,
( ( sk6 @ relation_dom )
!= sk10 ),
inference(simp,[status(thm)],[5335]) ).
thf(5692,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk6 @ relation_dom ) )
| ( A != sk10 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,5357]) ).
thf(5693,plain,
! [A: $i] :
( ( A != sk10 )
| ~ ( A @ singleton @ ( sk6 @ relation_dom @ in ) ) ),
inference(pattern_uni,[status(thm)],[5692:[bind(A,$thf( A )),bind(B,$thf( sk6 @ relation_dom ))]]) ).
thf(5709,plain,
~ ( sk10 @ singleton @ ( sk6 @ relation_dom @ in ) ),
inference(simp,[status(thm)],[5693]) ).
thf(13553,plain,
~ ( sk10 @ singleton @ ( empty_set @ relation_dom @ in ) ),
inference(rewrite,[status(thm)],[5709,6073]) ).
thf(3028,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( A != empty_set )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,40]) ).
thf(3029,plain,
! [A: $i] :
( ( A != empty_set )
| ~ ( A @ singleton @ ( sk1 @ in ) ) ),
inference(pattern_uni,[status(thm)],[3028:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(3501,plain,
~ ( empty_set @ singleton @ ( sk1 @ in ) ),
inference(simp,[status(thm)],[3029]) ).
thf(17827,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ singleton @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,3501]) ).
thf(17828,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ singleton @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[17827]) ).
thf(17885,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( empty_set @ singleton ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[17828]) ).
thf(17939,plain,
( ( sk1 @ powerset )
!= ( empty_set @ singleton ) ),
inference(simp,[status(thm)],[17885]) ).
thf(17988,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ powerset ) )
| ( A
!= ( empty_set @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,17939]) ).
thf(17989,plain,
! [A: $i] :
( ( A
!= ( empty_set @ singleton ) )
| ~ ( A @ singleton @ ( sk1 @ powerset @ in ) ) ),
inference(pattern_uni,[status(thm)],[17988:[bind(A,$thf( A )),bind(B,$thf( sk1 @ powerset ))]]) ).
thf(17996,plain,
~ ( empty_set @ singleton @ singleton @ ( sk1 @ powerset @ in ) ),
inference(simp,[status(thm)],[17989]) ).
thf(19447,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk1 @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,17996]) ).
thf(19448,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk1 @ powerset @ in ) ) ),
inference(simp,[status(thm)],[19447]) ).
thf(19455,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( empty_set @ singleton @ singleton ) )
| ( A
!= ( sk1 @ powerset ) ) ),
inference(simp,[status(thm)],[19448]) ).
thf(19472,plain,
( ( sk1 @ powerset @ singleton )
!= ( empty_set @ singleton @ singleton ) ),
inference(simp,[status(thm)],[19455]) ).
thf(5299,plain,
! [A: $i] :
( ( ( sk6 @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5149,93]) ).
thf(5300,plain,
! [A: $i] :
( ( ( sk6 @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ relation ) ),
inference(simp,[status(thm)],[5299]) ).
thf(5301,plain,
sk6 @ relation_dom @ relation_rng @ relation,
inference(pattern_uni,[status(thm)],[5300:[bind(A,$thf( sk6 @ relation_dom ))]]) ).
thf(8919,plain,
empty_set @ relation_dom @ relation_rng @ relation,
inference(rewrite,[status(thm)],[5301,6073]) ).
thf(17739,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ singleton @ ( empty_set @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,3502]) ).
thf(17740,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ singleton @ ( empty_set @ in ) ) ),
inference(simp,[status(thm)],[17739]) ).
thf(17900,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ singleton ) )
| ( A != empty_set ) ),
inference(simp,[status(thm)],[17740]) ).
thf(17955,plain,
( ( empty_set @ powerset )
!= ( sk1 @ singleton ) ),
inference(simp,[status(thm)],[17900]) ).
thf(18028,plain,
! [B: $i,A: $i] :
( ( B
!= ( empty_set @ powerset ) )
| ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,17955]) ).
thf(18029,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( empty_set @ powerset @ in ) ) ),
inference(pattern_uni,[status(thm)],[18028:[bind(A,$thf( A )),bind(B,$thf( empty_set @ powerset ))]]) ).
thf(18037,plain,
~ ( sk1 @ singleton @ singleton @ ( empty_set @ powerset @ in ) ),
inference(simp,[status(thm)],[18029]) ).
thf(19709,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( empty_set @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,18037]) ).
thf(19710,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( empty_set @ powerset @ in ) ) ),
inference(simp,[status(thm)],[19709]) ).
thf(19713,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton @ singleton ) )
| ( A
!= ( empty_set @ powerset ) ) ),
inference(simp,[status(thm)],[19710]) ).
thf(19719,plain,
( ( empty_set @ powerset @ singleton )
!= ( sk1 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[19713]) ).
thf(187,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ sk19 ) @ apply ) )
= B )
| ~ ( A @ ( C @ in ) ) ),
inference(cnfConj,[status(thm)],[183]) ).
thf(189,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ in ) )
| ( ( C @ ( A @ ( B @ sk19 ) @ apply ) )
= B ) ),
inference(lifteq,[status(thm)],[187]) ).
thf(17745,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( B @ ( D @ in ) ) )
| ~ $true
| ( ( D @ ( B @ ( C @ sk19 ) @ apply ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[17736,189]) ).
thf(17746,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( B @ ( D @ in ) ) )
| ( ( D @ ( B @ ( C @ sk19 ) @ apply ) )
= C ) ),
inference(simp,[status(thm)],[17745]) ).
thf(17747,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ powerset @ ( A @ sk19 ) @ apply ) )
= A ),
inference(pattern_uni,[status(thm)],[17746:[bind(A,$thf( E )),bind(B,$thf( E @ powerset )),bind(C,$thf( C )),bind(D,$thf( E ))]]) ).
thf(17928,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ powerset @ ( A @ sk19 ) @ apply ) )
= A ),
inference(simp,[status(thm)],[17747]) ).
thf(17992,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ powerset ) )
| ( B
!= ( empty_set @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,17939]) ).
thf(17993,plain,
! [A: $i] :
( ( A
!= ( empty_set @ singleton ) )
| ~ ( sk1 @ powerset @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[17992:[bind(A,$thf( sk1 @ powerset )),bind(B,$thf( B ))]]) ).
thf(17997,plain,
~ ( sk1 @ powerset @ singleton @ ( empty_set @ singleton @ in ) ),
inference(simp,[status(thm)],[17993]) ).
thf(19512,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ powerset @ singleton @ ( empty_set @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,17997]) ).
thf(19513,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ powerset @ singleton @ ( empty_set @ singleton @ in ) ) ),
inference(simp,[status(thm)],[19512]) ).
thf(19587,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ powerset @ singleton ) )
| ( A
!= ( empty_set @ singleton ) ) ),
inference(simp,[status(thm)],[19513]) ).
thf(19589,plain,
( ( empty_set @ singleton @ powerset )
!= ( sk1 @ powerset @ singleton ) ),
inference(simp,[status(thm)],[19587]) ).
thf(4656,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( empty_set @ singleton @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,3501]) ).
thf(4657,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( empty_set @ singleton @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[4656]) ).
thf(4659,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( empty_set @ singleton ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[4657]) ).
thf(4664,plain,
( ( sk1 @ singleton )
!= ( empty_set @ singleton ) ),
inference(simp,[status(thm)],[4659]) ).
thf(29,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i] :
( ( B
= ( A @ relation_rng ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
thf(140,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) )
=> ( B
= ( A @ relation_rng ) ) )
& ( ( B
= ( A @ relation_rng ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(141,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ! [B: $i] :
( ( ! [C: $i] :
( ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) )
=> ( B
= ( A @ relation_rng ) ) )
& ! [B: $i] :
( ( B
= ( A @ relation_rng ) )
=> ( ! [C: $i] :
( ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[140]) ).
thf(142,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( A @ relation_rng ) )
| ~ ( F @ ( A @ ( F @ sk16 ) @ in ) )
| ( F @ ( A @ sk14 ) )
| ~ ( A @ function )
| ~ ( A @ relation ) )
& ( ( F
= ( A @ relation_rng ) )
| ( ( A @ ( F @ sk16 ) )
= ( A @ ( F @ sk17 ) @ ( A @ apply ) ) )
| ( F @ ( A @ sk14 ) )
| ~ ( A @ function )
| ~ ( A @ relation ) )
& ( ( F
= ( A @ relation_rng ) )
| ( A @ relation_dom @ ( A @ ( F @ sk17 ) @ in ) )
| ( F @ ( A @ sk14 ) )
| ~ ( A @ function )
| ~ ( A @ relation ) )
& ( ( F
= ( A @ relation_rng ) )
| ~ ( F @ ( A @ sk14 ) )
| ( ( A @ ( F @ sk15 ) )
!= ( G @ ( A @ apply ) ) )
| ~ ( A @ relation_dom @ ( G @ in ) )
| ~ ( A @ function )
| ~ ( A @ relation ) )
& ( ( F
= ( A @ relation_rng ) )
| ~ ( F @ ( A @ sk14 ) )
| ( F @ ( A @ ( F @ sk15 ) @ in ) )
| ~ ( A @ function )
| ~ ( A @ relation ) )
& ( ( B @ ( D @ in ) )
| ( D
!= ( E @ ( A @ apply ) ) )
| ~ ( A @ relation_dom @ ( E @ in ) )
| ( B
!= ( A @ relation_rng ) )
| ~ ( A @ function )
| ~ ( A @ relation ) )
& ( ( C
= ( A @ ( B @ ( C @ sk13 ) ) @ ( A @ apply ) ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ relation_rng ) )
| ~ ( A @ function )
| ~ ( A @ relation ) )
& ( ( A @ relation_dom @ ( A @ ( B @ ( C @ sk13 ) ) @ in ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ relation_rng ) )
| ~ ( A @ function )
| ~ ( A @ relation ) ) ),
inference(cnf,[status(esa)],[141]) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ relation_rng ) )
| ~ ( B @ ( A @ sk14 ) )
| ( ( A @ ( B @ sk15 ) )
!= ( C @ ( A @ apply ) ) )
| ~ ( A @ relation_dom @ ( C @ in ) )
| ~ ( A @ function )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[142]) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ sk14 ) )
| ~ ( A @ relation_dom @ ( C @ in ) )
| ~ ( A @ function )
| ~ ( A @ relation )
| ( B
= ( A @ relation_rng ) )
| ( ( A @ ( B @ sk15 ) )
!= ( C @ ( A @ apply ) ) ) ),
inference(lifteq,[status(thm)],[147]) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ sk14 ) )
| ~ ( A @ relation_dom @ ( C @ in ) )
| ~ ( A @ function )
| ~ ( A @ relation )
| ( B
= ( A @ relation_rng ) )
| ( ( A @ ( B @ sk15 ) )
!= ( C @ ( A @ apply ) ) ) ),
inference(simp,[status(thm)],[151]) ).
thf(19912,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk7 @ singleton @ singleton @ ( empty_set @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,18080]) ).
thf(19913,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk7 @ singleton @ singleton @ ( empty_set @ powerset @ in ) ) ),
inference(simp,[status(thm)],[19912]) ).
thf(19986,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk7 @ singleton @ singleton ) )
| ( A
!= ( empty_set @ powerset ) ) ),
inference(simp,[status(thm)],[19913]) ).
thf(19995,plain,
( ( empty_set @ powerset @ powerset )
!= ( sk7 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[19986]) ).
thf(105,plain,
sk10 @ relation,
inference(cnfConj,[status(thm)],[103]) ).
thf(214,plain,
! [A: $i] :
( ( ( sk10 @ relation )
!= ( A @ relation ) )
| ~ ( A @ function )
| ~ $true
| ( ( A @ relation_rng )
!= ( sk2 @ singleton ) )
| ( ( A @ relation_dom )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[105,41]) ).
thf(215,plain,
! [A: $i] :
( ( ( sk10 @ relation )
!= ( A @ relation ) )
| ~ ( A @ function )
| ( ( A @ relation_rng )
!= ( sk2 @ singleton ) )
| ( ( A @ relation_dom )
!= sk1 ) ),
inference(simp,[status(thm)],[214]) ).
thf(216,plain,
( ~ ( sk10 @ function )
| ( ( sk2 @ singleton )
!= ( sk10 @ relation_rng ) )
| ( ( sk10 @ relation_dom )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[215:[bind(A,$thf( sk10 ))]]) ).
thf(10814,plain,
! [A: $i] :
( ( ( empty_set @ empty )
!= ( A @ empty ) )
| ( A @ function )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,168]) ).
thf(10815,plain,
! [A: $i] :
( ( ( empty_set @ empty )
!= ( A @ empty ) )
| ( A @ function ) ),
inference(simp,[status(thm)],[10814]) ).
thf(10816,plain,
empty_set @ function,
inference(pattern_uni,[status(thm)],[10815:[bind(A,$thf( empty_set ))]]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(84,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(148,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ relation_dom @ ( A @ ( B @ ( C @ sk13 ) ) @ in ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ relation_rng ) )
| ~ ( A @ function )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[142]) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ relation_dom @ ( A @ ( B @ ( C @ sk13 ) ) @ in ) )
| ~ ( B @ ( C @ in ) )
| ~ ( A @ function )
| ~ ( A @ relation )
| ( B
!= ( A @ relation_rng ) ) ),
inference(lifteq,[status(thm)],[148]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( A @ relation_dom @ ( A @ ( A @ relation_rng @ ( B @ sk13 ) ) @ in ) )
| ~ ( A @ relation_rng @ ( B @ in ) )
| ~ ( A @ function )
| ~ ( A @ relation ) ),
inference(simp,[status(thm)],[163]) ).
thf(7,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(58,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(59,plain,
! [A: $i] : ( A @ ( A @ sk5 @ element ) ),
inference(cnf,[status(esa)],[58]) ).
thf(1344,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk5 @ element ) )
!= ( C @ ( B @ element ) ) )
| ( C @ ( B @ in ) )
| ( C @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,78]) ).
thf(1345,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk5 @ element ) )
!= ( C @ ( B @ element ) ) )
| ( C @ ( B @ in ) )
| ( C @ empty ) ),
inference(simp,[status(thm)],[1344]) ).
thf(1346,plain,
! [A: $i] :
( ( A @ ( A @ sk5 @ in ) )
| ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[1345:[bind(A,$thf( D )),bind(B,$thf( D @ sk5 )),bind(C,$thf( D ))]]) ).
thf(1360,plain,
! [A: $i] :
( ( A @ ( A @ sk5 @ in ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[1346]) ).
thf(1431,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk5 @ in ) )
!= ( C @ ( B @ in ) ) )
| ( C @ ( B @ element ) )
| ~ $true
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[1360,73]) ).
thf(1432,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk5 @ in ) )
!= ( C @ ( B @ in ) ) )
| ( C @ ( B @ element ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[1431]) ).
thf(1433,plain,
! [A: $i] :
( ( A @ ( A @ sk5 @ element ) )
| ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[1432:[bind(A,$thf( D )),bind(B,$thf( D @ sk5 )),bind(C,$thf( D ))]]) ).
thf(1465,plain,
! [A: $i] :
( ( A @ ( A @ sk5 @ element ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[1433]) ).
thf(193,plain,
( ( ( sk10 @ empty )
!= ( sk6 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,104]) ).
thf(194,plain,
( ( sk10 @ empty )
!= ( sk6 @ empty ) ),
inference(simp,[status(thm)],[193]) ).
thf(195,plain,
sk10 != sk6,
inference(simp,[status(thm)],[194]) ).
thf(3112,plain,
! [B: $i,A: $i] :
( ( B != sk10 )
| ( A != sk6 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,195]) ).
thf(3113,plain,
! [A: $i] :
( ( A != sk6 )
| ~ ( A @ singleton @ ( sk10 @ in ) ) ),
inference(pattern_uni,[status(thm)],[3112:[bind(A,$thf( A )),bind(B,$thf( sk10 ))]]) ).
thf(3190,plain,
~ ( sk6 @ singleton @ ( sk10 @ in ) ),
inference(simp,[status(thm)],[3113]) ).
thf(3613,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk6 @ singleton @ ( sk10 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,3190]) ).
thf(3614,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk6 @ singleton @ ( sk10 @ in ) ) ),
inference(simp,[status(thm)],[3613]) ).
thf(3615,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk6 @ singleton ) )
| ( A != sk10 ) ),
inference(simp,[status(thm)],[3614]) ).
thf(3624,plain,
( ( sk10 @ singleton )
!= ( sk6 @ singleton ) ),
inference(simp,[status(thm)],[3615]) ).
thf(7163,plain,
( ( sk10 @ singleton )
!= ( empty_set @ singleton ) ),
inference(rewrite,[status(thm)],[3624,6073]) ).
thf(7187,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk10 @ singleton ) )
| ( B
!= ( empty_set @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,7163]) ).
thf(7188,plain,
! [A: $i] :
( ( A
!= ( empty_set @ singleton ) )
| ~ ( sk10 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[7187:[bind(A,$thf( sk10 @ singleton )),bind(B,$thf( B ))]]) ).
thf(7196,plain,
~ ( sk10 @ singleton @ singleton @ ( empty_set @ singleton @ in ) ),
inference(simp,[status(thm)],[7188]) ).
thf(17819,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk10 @ singleton @ singleton @ ( empty_set @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,7196]) ).
thf(17820,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk10 @ singleton @ singleton @ ( empty_set @ singleton @ in ) ) ),
inference(simp,[status(thm)],[17819]) ).
thf(17863,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk10 @ singleton @ singleton ) )
| ( A
!= ( empty_set @ singleton ) ) ),
inference(simp,[status(thm)],[17820]) ).
thf(17916,plain,
( ( empty_set @ singleton @ powerset )
!= ( sk10 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[17863]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(106,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(6,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(54,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(55,plain,
! [A: $i] :
( ( A @ sk4 @ empty )
& ( A @ powerset @ ( A @ sk4 @ element ) ) ),
inference(cnf,[status(esa)],[54]) ).
thf(56,plain,
! [A: $i] : ( A @ powerset @ ( A @ sk4 @ element ) ),
inference(cnfConj,[status(thm)],[55]) ).
thf(57,plain,
! [A: $i] : ( A @ sk4 @ empty ),
inference(cnfConj,[status(thm)],[55]) ).
thf(5983,plain,
! [B: $i,A: $i] :
( ( ( A @ sk4 @ empty )
!= ( B @ empty ) )
| ~ $true
| ( B = empty_set ) ),
inference(paramod_ordered,[status(thm)],[57,139]) ).
thf(5984,plain,
! [B: $i,A: $i] :
( ( ( A @ sk4 @ empty )
!= ( B @ empty ) )
| ( B = empty_set ) ),
inference(simp,[status(thm)],[5983]) ).
thf(5985,plain,
! [A: $i] :
( ( A @ sk4 )
= empty_set ),
inference(pattern_uni,[status(thm)],[5984:[bind(A,$thf( C )),bind(B,$thf( C @ sk4 ))]]) ).
thf(6616,plain,
! [A: $i] :
( ( A @ sk4 )
= empty_set ),
inference(simp,[status(thm)],[5985]) ).
thf(14592,plain,
! [A: $i] : ( A @ powerset @ ( empty_set @ element ) ),
inference(rewrite,[status(thm)],[56,6616]) ).
thf(17121,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( empty_set @ element ) )
!= ( C @ ( B @ element ) ) )
| ( C @ ( B @ in ) )
| ( C @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14592,78]) ).
thf(17122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( empty_set @ element ) )
!= ( C @ ( B @ element ) ) )
| ( C @ ( B @ in ) )
| ( C @ empty ) ),
inference(simp,[status(thm)],[17121]) ).
thf(17123,plain,
! [A: $i] :
( ( A @ powerset @ ( empty_set @ in ) )
| ( A @ powerset @ empty ) ),
inference(pattern_uni,[status(thm)],[17122:[bind(A,$thf( D )),bind(B,$thf( empty_set )),bind(C,$thf( D @ powerset ))]]) ).
thf(17168,plain,
! [A: $i] :
( ( A @ powerset @ ( empty_set @ in ) )
| ( A @ powerset @ empty ) ),
inference(simp,[status(thm)],[17123]) ).
thf(17348,plain,
! [A: $i] :
( ( A @ powerset @ ( empty_set @ in ) )
| $false ),
inference(rewrite,[status(thm)],[17168,83]) ).
thf(17349,plain,
! [A: $i] : ( A @ powerset @ ( empty_set @ in ) ),
inference(simp,[status(thm)],[17348]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk12 ) )
= A )
| ( B @ ( A @ ( B @ sk11 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[114]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk11 ) @ in ) )
| ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk12 ) )
= A ) ),
inference(lifteq,[status(thm)],[120]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk11 ) @ in ) )
| ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk12 ) )
= A ) ),
inference(simp,[status(thm)],[131]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(79,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(1383,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ ( A @ in ) ) ),
inference(eqfactor_ordered,[status(thm)],[80]) ).
thf(1384,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[1383:[bind(A,$thf( B ))]]) ).
thf(1387,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(simp,[status(thm)],[1384]) ).
thf(1391,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( B @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,1387]) ).
thf(1392,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( B @ in ) ) ),
inference(simp,[status(thm)],[1391]) ).
thf(1393,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[1392]) ).
thf(1394,plain,
! [A: $i] :
( ( A @ singleton )
!= A ),
inference(simp,[status(thm)],[1393]) ).
thf(1329,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ sk3 @ element ) )
!= ( C @ ( B @ element ) ) )
| ( C @ ( B @ in ) )
| ( C @ empty )
| ~ $true
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[52,78]) ).
thf(1330,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ sk3 @ element ) )
!= ( C @ ( B @ element ) ) )
| ( C @ ( B @ in ) )
| ( C @ empty )
| ( A @ empty ) ),
inference(simp,[status(thm)],[1329]) ).
thf(1331,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ sk3 @ in ) )
| ( A @ powerset @ empty )
| ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[1330:[bind(A,$thf( E )),bind(B,$thf( E @ sk3 )),bind(C,$thf( E @ powerset ))]]) ).
thf(1361,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ sk3 @ in ) )
| ( A @ powerset @ empty )
| ( A @ empty ) ),
inference(simp,[status(thm)],[1331]) ).
thf(21541,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ sk3 @ in ) )
| $false
| ( A @ empty ) ),
inference(rewrite,[status(thm)],[1361,83]) ).
thf(21542,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ sk3 @ in ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[21541]) ).
thf(89,plain,
sk8 @ relation_empty_yielding,
inference(cnfConj,[status(thm)],[87]) ).
thf(1698,plain,
! [A: $i] :
( ( ( A @ singleton @ empty )
!= ( sk6 @ relation_rng @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1578,100]) ).
thf(1699,plain,
! [A: $i] :
( ( A @ singleton @ empty )
!= ( sk6 @ relation_rng @ empty ) ),
inference(simp,[status(thm)],[1698]) ).
thf(1705,plain,
! [A: $i] :
( ( A @ singleton )
!= ( sk6 @ relation_rng ) ),
inference(simp,[status(thm)],[1699]) ).
thf(17298,plain,
! [A: $i] :
( ( A @ singleton )
!= ( empty_set @ relation_rng ) ),
inference(rewrite,[status(thm)],[1705,6073]) ).
thf(2661,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk5 @ in ) )
!= ( B @ singleton @ ( C @ in ) ) )
| ~ $true
| ( C = B )
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[1360,126]) ).
thf(2662,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk5 @ in ) )
!= ( B @ singleton @ ( C @ in ) ) )
| ( C = B )
| ( A @ empty ) ),
inference(simp,[status(thm)],[2661]) ).
thf(2663,plain,
! [A: $i] :
( ( ( A @ singleton @ sk5 )
= A )
| ( A @ singleton @ empty ) ),
inference(pattern_uni,[status(thm)],[2662:[bind(A,$thf( E @ singleton )),bind(B,$thf( E )),bind(C,$thf( E @ singleton @ sk5 ))]]) ).
thf(3353,plain,
! [A: $i] :
( ( ( A @ singleton @ sk5 )
= A )
| ( A @ singleton @ empty ) ),
inference(simp,[status(thm)],[2663]) ).
thf(18411,plain,
! [A: $i] :
( ( ( A @ singleton @ sk5 )
= A )
| $false ),
inference(rewrite,[status(thm)],[3353,100]) ).
thf(18412,plain,
! [A: $i] :
( ( A @ singleton @ sk5 )
= A ),
inference(simp,[status(thm)],[18411]) ).
thf(2446,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk6 @ relation_rng ) )
| ( B != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,1704]) ).
thf(2447,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( sk6 @ relation_rng @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2446:[bind(A,$thf( sk6 @ relation_rng )),bind(B,$thf( B ))]]) ).
thf(3267,plain,
~ ( sk6 @ relation_rng @ singleton @ ( sk1 @ in ) ),
inference(simp,[status(thm)],[2447]) ).
thf(9703,plain,
~ ( empty_set @ relation_rng @ singleton @ ( sk1 @ in ) ),
inference(rewrite,[status(thm)],[3267,6073]) ).
thf(34,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(178,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(179,plain,
( ( sk18 @ function )
& ( sk18 @ relation ) ),
inference(cnf,[status(esa)],[178]) ).
thf(180,plain,
sk18 @ relation,
inference(cnfConj,[status(thm)],[179]) ).
thf(223,plain,
! [A: $i] :
( ( ( sk18 @ relation )
!= ( A @ relation ) )
| ~ ( A @ function )
| ~ $true
| ( ( A @ relation_rng )
!= ( sk2 @ singleton ) )
| ( ( A @ relation_dom )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[180,41]) ).
thf(224,plain,
! [A: $i] :
( ( ( sk18 @ relation )
!= ( A @ relation ) )
| ~ ( A @ function )
| ( ( A @ relation_rng )
!= ( sk2 @ singleton ) )
| ( ( A @ relation_dom )
!= sk1 ) ),
inference(simp,[status(thm)],[223]) ).
thf(225,plain,
( ~ ( sk18 @ function )
| ( ( sk2 @ singleton )
!= ( sk18 @ relation_rng ) )
| ( ( sk18 @ relation_dom )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[224:[bind(A,$thf( sk18 ))]]) ).
thf(181,plain,
sk18 @ function,
inference(cnfConj,[status(thm)],[179]) ).
thf(232,plain,
( ~ $true
| ( ( sk2 @ singleton )
!= ( sk18 @ relation_rng ) )
| ( ( sk18 @ relation_dom )
!= sk1 ) ),
inference(rewrite,[status(thm)],[225,181]) ).
thf(233,plain,
( ( ( sk2 @ singleton )
!= ( sk18 @ relation_rng ) )
| ( ( sk18 @ relation_dom )
!= sk1 ) ),
inference(simp,[status(thm)],[232]) ).
thf(6328,plain,
! [A: $i] :
( ( ( sk6 @ relation_rng @ relation_rng @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[1667,139]) ).
thf(6329,plain,
! [A: $i] :
( ( ( sk6 @ relation_rng @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[6328]) ).
thf(6330,plain,
( ( sk6 @ relation_rng @ relation_rng )
= empty_set ),
inference(pattern_uni,[status(thm)],[6329:[bind(A,$thf( sk6 @ relation_rng @ relation_rng ))]]) ).
thf(10593,plain,
( ( empty_set @ relation_rng @ relation_rng )
= empty_set ),
inference(rewrite,[status(thm)],[6330,6073]) ).
thf(20512,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk7 @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,18155]) ).
thf(20513,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk7 @ powerset @ in ) ) ),
inference(simp,[status(thm)],[20512]) ).
thf(20518,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( empty_set @ singleton @ singleton ) )
| ( A
!= ( sk7 @ powerset ) ) ),
inference(simp,[status(thm)],[20513]) ).
thf(20528,plain,
( ( sk7 @ powerset @ singleton )
!= ( empty_set @ singleton @ singleton ) ),
inference(simp,[status(thm)],[20518]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ element ) )
| ~ ( C @ powerset @ ( B @ element ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[84]) ).
thf(2113,plain,
( ( ( sk6 @ relation_rng @ relation_rng @ empty )
!= ( sk10 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1667,104]) ).
thf(2114,plain,
( ( sk6 @ relation_rng @ relation_rng @ empty )
!= ( sk10 @ empty ) ),
inference(simp,[status(thm)],[2113]) ).
thf(2129,plain,
( ( sk6 @ relation_rng @ relation_rng )
!= sk10 ),
inference(simp,[status(thm)],[2114]) ).
thf(2900,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk6 @ relation_rng @ relation_rng ) )
| ( A != sk10 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,2129]) ).
thf(2901,plain,
! [A: $i] :
( ( A != sk10 )
| ~ ( A @ singleton @ ( sk6 @ relation_rng @ relation_rng @ in ) ) ),
inference(pattern_uni,[status(thm)],[2900:[bind(A,$thf( A )),bind(B,$thf( sk6 @ relation_rng @ relation_rng ))]]) ).
thf(3450,plain,
~ ( sk10 @ singleton @ ( sk6 @ relation_rng @ relation_rng @ in ) ),
inference(simp,[status(thm)],[2901]) ).
thf(15392,plain,
~ ( sk10 @ singleton @ ( empty_set @ relation_rng @ relation_rng @ in ) ),
inference(rewrite,[status(thm)],[3450,6073]) ).
thf(5604,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5131,136]) ).
thf(5605,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ relation ) ),
inference(simp,[status(thm)],[5604]) ).
thf(5606,plain,
empty_set @ relation_dom @ relation_dom @ relation,
inference(pattern_uni,[status(thm)],[5605:[bind(A,$thf( empty_set @ relation_dom ))]]) ).
thf(9544,plain,
empty_set @ relation_dom @ relation,
inference(rewrite,[status(thm)],[5606,5889]) ).
thf(18073,plain,
! [B: $i,A: $i] :
( ( A
!= ( empty_set @ powerset ) )
| ( B
!= ( sk7 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,17950]) ).
thf(18074,plain,
! [A: $i] :
( ( A
!= ( sk7 @ singleton ) )
| ~ ( empty_set @ powerset @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[18073:[bind(A,$thf( empty_set @ powerset )),bind(B,$thf( B ))]]) ).
thf(18081,plain,
~ ( empty_set @ powerset @ singleton @ ( sk7 @ singleton @ in ) ),
inference(simp,[status(thm)],[18074]) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ ( B @ ( C @ sk13 ) ) @ ( A @ apply ) ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ relation_rng ) )
| ~ ( A @ function )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[142]) ).
thf(159,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ in ) )
| ~ ( A @ function )
| ~ ( A @ relation )
| ( ( A @ ( B @ ( C @ sk13 ) ) @ ( A @ apply ) )
= C )
| ( B
!= ( A @ relation_rng ) ) ),
inference(lifteq,[status(thm)],[143]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ~ ( A @ relation_rng @ ( B @ in ) )
| ~ ( A @ function )
| ~ ( A @ relation )
| ( ( A @ ( A @ relation_rng @ ( B @ sk13 ) ) @ ( A @ apply ) )
= B ) ),
inference(simp,[status(thm)],[159]) ).
thf(1202,plain,
( ( ( sk9 @ empty )
!= ( sk1 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[96,1195]) ).
thf(1203,plain,
( ( sk9 @ empty )
!= ( sk1 @ empty ) ),
inference(simp,[status(thm)],[1202]) ).
thf(1211,plain,
sk9 != sk1,
inference(simp,[status(thm)],[1203]) ).
thf(2362,plain,
! [B: $i,A: $i] :
( ( B != sk9 )
| ( A != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,1211]) ).
thf(2363,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( A @ singleton @ ( sk9 @ in ) ) ),
inference(pattern_uni,[status(thm)],[2362:[bind(A,$thf( A )),bind(B,$thf( sk9 ))]]) ).
thf(3234,plain,
~ ( sk1 @ singleton @ ( sk9 @ in ) ),
inference(simp,[status(thm)],[2363]) ).
thf(3733,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk9 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,3234]) ).
thf(3734,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk9 @ in ) ) ),
inference(simp,[status(thm)],[3733]) ).
thf(3735,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton ) )
| ( A != sk9 ) ),
inference(simp,[status(thm)],[3734]) ).
thf(3742,plain,
( ( sk9 @ singleton )
!= ( sk1 @ singleton ) ),
inference(simp,[status(thm)],[3735]) ).
thf(5118,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk9 @ singleton ) )
| ( B
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,3742]) ).
thf(5119,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( sk9 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[5118:[bind(A,$thf( sk9 @ singleton )),bind(B,$thf( B ))]]) ).
thf(5128,plain,
~ ( sk9 @ singleton @ singleton @ ( sk1 @ singleton @ in ) ),
inference(simp,[status(thm)],[5119]) ).
thf(15830,plain,
~ ( empty_set @ singleton @ singleton @ ( sk1 @ singleton @ in ) ),
inference(rewrite,[status(thm)],[5128,6146]) ).
thf(17767,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk1 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,15830]) ).
thf(17768,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk1 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[17767]) ).
thf(17890,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( empty_set @ singleton @ singleton ) )
| ( A
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[17768]) ).
thf(17945,plain,
( ( sk1 @ singleton @ powerset )
!= ( empty_set @ singleton @ singleton ) ),
inference(simp,[status(thm)],[17890]) ).
thf(9012,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9008,92]) ).
thf(9013,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty ) ),
inference(simp,[status(thm)],[9012]) ).
thf(9014,plain,
empty_set @ relation_dom @ relation_rng @ relation_rng @ empty,
inference(pattern_uni,[status(thm)],[9013:[bind(A,$thf( empty_set @ relation_dom @ relation_rng ))]]) ).
thf(13810,plain,
empty_set @ relation_rng @ relation_rng @ empty,
inference(rewrite,[status(thm)],[9014,5889]) ).
thf(10826,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ function )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9008,168]) ).
thf(10827,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ function ) ),
inference(simp,[status(thm)],[10826]) ).
thf(10828,plain,
empty_set @ relation_dom @ relation_rng @ function,
inference(pattern_uni,[status(thm)],[10827:[bind(A,$thf( empty_set @ relation_dom @ relation_rng ))]]) ).
thf(11376,plain,
empty_set @ relation_rng @ function,
inference(rewrite,[status(thm)],[10828,5889]) ).
thf(9009,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9008,93]) ).
thf(9010,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ relation ) ),
inference(simp,[status(thm)],[9009]) ).
thf(9011,plain,
empty_set @ relation_dom @ relation_rng @ relation_rng @ relation,
inference(pattern_uni,[status(thm)],[9010:[bind(A,$thf( empty_set @ relation_dom @ relation_rng ))]]) ).
thf(13681,plain,
empty_set @ relation_rng @ relation_rng @ relation,
inference(rewrite,[status(thm)],[9011,5889]) ).
thf(5159,plain,
! [A: $i] :
( ( ( sk9 @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[96,135]) ).
thf(5160,plain,
! [A: $i] :
( ( ( sk9 @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty ) ),
inference(simp,[status(thm)],[5159]) ).
thf(5161,plain,
sk9 @ relation_dom @ empty,
inference(pattern_uni,[status(thm)],[5160:[bind(A,$thf( sk9 ))]]) ).
thf(5610,plain,
! [A: $i] :
( ( ( sk9 @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5161,136]) ).
thf(5611,plain,
! [A: $i] :
( ( ( sk9 @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ relation ) ),
inference(simp,[status(thm)],[5610]) ).
thf(5612,plain,
sk9 @ relation_dom @ relation_dom @ relation,
inference(pattern_uni,[status(thm)],[5611:[bind(A,$thf( sk9 @ relation_dom ))]]) ).
thf(9613,plain,
empty_set @ relation_dom @ relation_dom @ relation,
inference(rewrite,[status(thm)],[5612,6146]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ relation_rng ) )
| ( ( A @ ( B @ sk16 ) )
= ( A @ ( B @ sk17 ) @ ( A @ apply ) ) )
| ( B @ ( A @ sk14 ) )
| ~ ( A @ function )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[142]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk14 ) )
| ~ ( A @ function )
| ~ ( A @ relation )
| ( B
= ( A @ relation_rng ) )
| ( ( A @ ( B @ sk16 ) )
= ( A @ ( B @ sk17 ) @ ( A @ apply ) ) ) ),
inference(lifteq,[status(thm)],[145]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk14 ) )
| ~ ( A @ function )
| ~ ( A @ relation )
| ( B
= ( A @ relation_rng ) )
| ( ( A @ ( B @ sk16 ) )
= ( A @ ( B @ sk17 ) @ ( A @ apply ) ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(53,plain,
! [A: $i] :
( ~ ( A @ sk3 @ empty )
| ( A @ empty ) ),
inference(cnfConj,[status(thm)],[51]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk12 ) )
= A )
| ( ( A @ ( B @ sk11 ) )
!= A ) ),
inference(cnfConj,[status(thm)],[114]) ).
thf(123,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk12 ) )
= A )
| ( ( A @ ( B @ sk11 ) )
!= A ) ),
inference(lifteq,[status(thm)],[117]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk12 ) )
= A )
| ( ( A @ ( B @ sk11 ) )
!= A ) ),
inference(simp,[status(thm)],[123]) ).
thf(70,plain,
~ ? [A: $i,B: $i] :
( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(miniscope,[status(thm)],[69]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(337,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ empty )
!= ( B @ empty ) )
| ~ $true
| ~ ( B @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[101,71]) ).
thf(338,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ empty )
!= ( B @ empty ) )
| ~ ( B @ ( A @ in ) ) ),
inference(simp,[status(thm)],[337]) ).
thf(339,plain,
! [A: $i] :
~ ( empty_set @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[338:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(301,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk19 ) @ relation )
!= ( C @ relation ) )
| ~ ( C @ function )
| ~ $true
| ( ( C @ relation_rng )
!= ( sk2 @ singleton ) )
| ( ( C @ relation_dom )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[184,41]) ).
thf(302,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk19 ) @ relation )
!= ( C @ relation ) )
| ~ ( C @ function )
| ( ( C @ relation_rng )
!= ( sk2 @ singleton ) )
| ( ( C @ relation_dom )
!= sk1 ) ),
inference(simp,[status(thm)],[301]) ).
thf(303,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ sk19 ) @ function )
| ( ( B @ ( A @ sk19 ) @ relation_rng )
!= ( sk2 @ singleton ) )
| ( ( B @ ( A @ sk19 ) @ relation_dom )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[302:[bind(A,$thf( E )),bind(B,$thf( D )),bind(C,$thf( E @ ( D @ sk19 ) ))]]) ).
thf(304,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ sk19 ) @ function )
| ( ( B @ ( A @ sk19 ) @ relation_rng )
!= ( sk2 @ singleton ) )
| ( ( B @ ( A @ sk19 ) @ relation_dom )
!= sk1 ) ),
inference(simp,[status(thm)],[303]) ).
thf(12817,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ sk19 ) @ relation_rng )
!= ( sk2 @ singleton ) )
| ( B != sk1 ) ),
inference(rewrite,[status(thm)],[304,185,188]) ).
thf(12818,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ relation_rng )
!= ( sk2 @ singleton ) )
| ( B != sk1 ) ),
inference(simp,[status(thm)],[12817]) ).
thf(241,plain,
( ( ( sk18 @ function )
!= ( sk8 @ function ) )
| ~ $true
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) )
| ( ( sk8 @ relation_dom )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[181,198]) ).
thf(242,plain,
( ( ( sk18 @ function )
!= ( sk8 @ function ) )
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) )
| ( ( sk8 @ relation_dom )
!= sk1 ) ),
inference(simp,[status(thm)],[241]) ).
thf(246,plain,
( ( sk18 != sk8 )
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) )
| ( ( sk8 @ relation_dom )
!= sk1 ) ),
inference(simp,[status(thm)],[242]) ).
thf(369,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk19 ) @ relation_dom )
!= ( sk8 @ relation_dom ) )
| ( sk18 != sk8 )
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[188,246]) ).
thf(384,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ sk19 ) )
!= sk8 )
| ( sk18 != sk8 )
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) ) ),
inference(simp,[status(thm)],[369]) ).
thf(393,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ sk19 ) )
!= sk8 )
| ( sk18 != sk8 )
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) ) ),
inference(simp,[status(thm)],[384]) ).
thf(5696,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk6 @ relation_dom ) )
| ( B != sk10 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,5357]) ).
thf(5697,plain,
! [A: $i] :
( ( A != sk10 )
| ~ ( sk6 @ relation_dom @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[5696:[bind(A,$thf( sk6 @ relation_dom )),bind(B,$thf( B ))]]) ).
thf(5702,plain,
~ ( sk6 @ relation_dom @ singleton @ ( sk10 @ in ) ),
inference(simp,[status(thm)],[5697]) ).
thf(13451,plain,
~ ( empty_set @ relation_dom @ singleton @ ( sk10 @ in ) ),
inference(rewrite,[status(thm)],[5702,6073]) ).
thf(17358,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( empty_set @ in ) )
!= ( B @ ( D @ in ) ) )
| ~ $true
| ( ( D @ ( B @ ( C @ sk19 ) @ apply ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[17349,189]) ).
thf(17359,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( empty_set @ in ) )
!= ( B @ ( D @ in ) ) )
| ( ( D @ ( B @ ( C @ sk19 ) @ apply ) )
= C ) ),
inference(simp,[status(thm)],[17358]) ).
thf(17360,plain,
! [B: $i,A: $i] :
( ( empty_set @ ( B @ powerset @ ( A @ sk19 ) @ apply ) )
= A ),
inference(pattern_uni,[status(thm)],[17359:[bind(A,$thf( E )),bind(B,$thf( E @ powerset )),bind(C,$thf( C )),bind(D,$thf( empty_set ))]]) ).
thf(17546,plain,
! [B: $i,A: $i] :
( ( empty_set @ ( B @ powerset @ ( A @ sk19 ) @ apply ) )
= A ),
inference(simp,[status(thm)],[17360]) ).
thf(20446,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk7 @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,18155]) ).
thf(20447,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk7 @ powerset @ in ) ) ),
inference(simp,[status(thm)],[20446]) ).
thf(20519,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( empty_set @ singleton @ singleton ) )
| ( A
!= ( sk7 @ powerset ) ) ),
inference(simp,[status(thm)],[20447]) ).
thf(20529,plain,
( ( sk7 @ powerset @ powerset )
!= ( empty_set @ singleton @ singleton ) ),
inference(simp,[status(thm)],[20519]) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ~ ( B @ ( A @ ( B @ sk12 ) @ in ) )
| ( B @ ( A @ ( B @ sk11 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[114]) ).
thf(127,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk12 ) @ in ) )
| ( B @ ( A @ ( B @ sk11 ) @ in ) )
| ( B
= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[119]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk12 ) @ in ) )
| ( B @ ( A @ ( B @ sk11 ) @ in ) )
| ( B
= ( A @ singleton ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(5188,plain,
! [A: $i] :
( ( ( sk9 @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1585,135]) ).
thf(5189,plain,
! [A: $i] :
( ( ( sk9 @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty ) ),
inference(simp,[status(thm)],[5188]) ).
thf(5190,plain,
sk9 @ relation_rng @ relation_dom @ empty,
inference(pattern_uni,[status(thm)],[5189:[bind(A,$thf( sk9 @ relation_rng ))]]) ).
thf(7412,plain,
empty_set @ relation_rng @ relation_dom @ empty,
inference(rewrite,[status(thm)],[5190,6146]) ).
thf(7419,plain,
( ( ( empty_set @ relation_rng @ relation_dom @ empty )
!= ( sk1 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7412,1195]) ).
thf(7420,plain,
( ( empty_set @ relation_rng @ relation_dom @ empty )
!= ( sk1 @ empty ) ),
inference(simp,[status(thm)],[7419]) ).
thf(7499,plain,
( ( empty_set @ relation_rng @ relation_dom )
!= sk1 ),
inference(simp,[status(thm)],[7420]) ).
thf(8049,plain,
( ( empty_set @ relation_dom )
!= sk1 ),
inference(rewrite,[status(thm)],[7499,5905]) ).
thf(2906,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk6 @ relation_rng @ relation_rng ) )
| ( B != sk10 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,2129]) ).
thf(2907,plain,
! [A: $i] :
( ( A != sk10 )
| ~ ( sk6 @ relation_rng @ relation_rng @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2906:[bind(A,$thf( sk6 @ relation_rng @ relation_rng )),bind(B,$thf( B ))]]) ).
thf(3451,plain,
~ ( sk6 @ relation_rng @ relation_rng @ singleton @ ( sk10 @ in ) ),
inference(simp,[status(thm)],[2907]) ).
thf(15538,plain,
~ ( empty_set @ relation_rng @ relation_rng @ singleton @ ( sk10 @ in ) ),
inference(rewrite,[status(thm)],[3451,6073]) ).
thf(20043,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ powerset @ singleton @ ( sk7 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,18081]) ).
thf(20044,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ powerset @ singleton @ ( sk7 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[20043]) ).
thf(20113,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( empty_set @ powerset @ singleton ) )
| ( A
!= ( sk7 @ singleton ) ) ),
inference(simp,[status(thm)],[20044]) ).
thf(20125,plain,
( ( sk7 @ singleton @ powerset )
!= ( empty_set @ powerset @ singleton ) ),
inference(simp,[status(thm)],[20113]) ).
thf(540,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ~ ( sk10 @ function )
| ( ( A @ singleton )
!= ( sk10 @ relation_rng ) )
| ( ( sk10 @ relation_dom )
!= sk1 )
| ~ ( B @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[63,216]) ).
thf(541,plain,
! [A: $i] :
( ~ ( sk10 @ function )
| ( ( A @ singleton )
!= ( sk10 @ relation_rng ) )
| ( ( sk10 @ relation_dom )
!= sk1 )
| ~ ( sk2 @ empty )
| ~ ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[540:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(291,plain,
! [A: $i] :
( ( ( A @ sk3 @ empty )
!= ( empty_set @ empty ) )
| ~ $true
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[101,53]) ).
thf(292,plain,
! [A: $i] :
( ( ( A @ sk3 @ empty )
!= ( empty_set @ empty ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[291]) ).
thf(298,plain,
! [A: $i] :
( ( ( A @ sk3 )
!= empty_set )
| ( A @ empty ) ),
inference(simp,[status(thm)],[292]) ).
thf(362,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk19 ) @ relation_dom )
!= ( sk10 @ relation_dom ) )
| ~ ( sk10 @ function )
| ( ( sk2 @ singleton )
!= ( sk10 @ relation_rng ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[188,216]) ).
thf(380,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ sk19 ) )
!= sk10 )
| ~ ( sk10 @ function )
| ( ( sk2 @ singleton )
!= ( sk10 @ relation_rng ) ) ),
inference(simp,[status(thm)],[362]) ).
thf(412,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ sk19 ) )
!= sk10 )
| ~ ( sk10 @ function )
| ( ( sk2 @ singleton )
!= ( sk10 @ relation_rng ) ) ),
inference(simp,[status(thm)],[380]) ).
thf(2083,plain,
! [A: $i] :
( ( ( sk6 @ relation_rng @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1667,92]) ).
thf(2084,plain,
! [A: $i] :
( ( ( sk6 @ relation_rng @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty ) ),
inference(simp,[status(thm)],[2083]) ).
thf(2085,plain,
sk6 @ relation_rng @ relation_rng @ relation_rng @ empty,
inference(pattern_uni,[status(thm)],[2084:[bind(A,$thf( sk6 @ relation_rng @ relation_rng ))]]) ).
thf(11710,plain,
empty_set @ relation_rng @ relation_rng @ relation_rng @ empty,
inference(rewrite,[status(thm)],[2085,6073]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ relation_rng ) )
| ( A @ relation_dom @ ( A @ ( B @ sk17 ) @ in ) )
| ( B @ ( A @ sk14 ) )
| ~ ( A @ function )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[142]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( A @ relation_dom @ ( A @ ( B @ sk17 ) @ in ) )
| ( B @ ( A @ sk14 ) )
| ~ ( A @ function )
| ~ ( A @ relation )
| ( B
= ( A @ relation_rng ) ) ),
inference(lifteq,[status(thm)],[149]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( A @ relation_dom @ ( A @ ( B @ sk17 ) @ in ) )
| ( B @ ( A @ sk14 ) )
| ~ ( A @ function )
| ~ ( A @ relation )
| ( B
= ( A @ relation_rng ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(257,plain,
! [A: $i] :
( ( ( A @ powerset @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,83]) ).
thf(258,plain,
! [A: $i] :
( ( A @ powerset @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[257]) ).
thf(264,plain,
! [A: $i] :
( ( A @ powerset )
!= empty_set ),
inference(simp,[status(thm)],[258]) ).
thf(5350,plain,
! [A: $i] :
( ( ( A @ powerset @ empty )
!= ( sk6 @ relation_dom @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5149,83]) ).
thf(5351,plain,
! [A: $i] :
( ( A @ powerset @ empty )
!= ( sk6 @ relation_dom @ empty ) ),
inference(simp,[status(thm)],[5350]) ).
thf(5359,plain,
! [A: $i] :
( ( A @ powerset )
!= ( sk6 @ relation_dom ) ),
inference(simp,[status(thm)],[5351]) ).
thf(17703,plain,
! [A: $i] :
( ( A @ powerset )
!= ( empty_set @ relation_dom ) ),
inference(rewrite,[status(thm)],[5359,6073]) ).
thf(18032,plain,
! [B: $i,A: $i] :
( ( A
!= ( empty_set @ powerset ) )
| ( B
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,17955]) ).
thf(18033,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( empty_set @ powerset @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[18032:[bind(A,$thf( empty_set @ powerset )),bind(B,$thf( B ))]]) ).
thf(18038,plain,
~ ( empty_set @ powerset @ singleton @ ( sk1 @ singleton @ in ) ),
inference(simp,[status(thm)],[18033]) ).
thf(19781,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ powerset @ singleton @ ( sk1 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,18038]) ).
thf(19782,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ powerset @ singleton @ ( sk1 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[19781]) ).
thf(19852,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( empty_set @ powerset @ singleton ) )
| ( A
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[19782]) ).
thf(19861,plain,
( ( sk1 @ singleton @ powerset )
!= ( empty_set @ powerset @ singleton ) ),
inference(simp,[status(thm)],[19852]) ).
thf(368,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk19 ) @ relation_dom )
!= ( sk8 @ relation_dom ) )
| ~ ( sk8 @ function )
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[188,198]) ).
thf(392,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ sk19 ) )
!= sk8 )
| ~ ( sk8 @ function )
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) ) ),
inference(simp,[status(thm)],[368]) ).
thf(402,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ sk19 ) )
!= sk8 )
| ~ ( sk8 @ function )
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) ) ),
inference(simp,[status(thm)],[392]) ).
thf(5114,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk9 @ singleton ) )
| ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,3742]) ).
thf(5115,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( sk9 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[5114:[bind(A,$thf( A )),bind(B,$thf( sk9 @ singleton ))]]) ).
thf(5127,plain,
~ ( sk1 @ singleton @ singleton @ ( sk9 @ singleton @ in ) ),
inference(simp,[status(thm)],[5115]) ).
thf(15699,plain,
~ ( sk1 @ singleton @ singleton @ ( empty_set @ singleton @ in ) ),
inference(rewrite,[status(thm)],[5127,6146]) ).
thf(15803,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( empty_set @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,15699]) ).
thf(15804,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( empty_set @ singleton @ in ) ) ),
inference(simp,[status(thm)],[15803]) ).
thf(15809,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton @ singleton ) )
| ( A
!= ( empty_set @ singleton ) ) ),
inference(simp,[status(thm)],[15804]) ).
thf(15821,plain,
( ( sk1 @ singleton @ singleton )
!= ( empty_set @ singleton @ singleton ) ),
inference(simp,[status(thm)],[15809]) ).
thf(9058,plain,
( ( ( empty_set @ relation_dom @ relation_rng @ empty )
!= ( sk10 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9008,104]) ).
thf(9059,plain,
( ( empty_set @ relation_dom @ relation_rng @ empty )
!= ( sk10 @ empty ) ),
inference(simp,[status(thm)],[9058]) ).
thf(9105,plain,
( ( empty_set @ relation_dom @ relation_rng )
!= sk10 ),
inference(simp,[status(thm)],[9059]) ).
thf(10906,plain,
( ( empty_set @ relation_rng )
!= sk10 ),
inference(rewrite,[status(thm)],[9105,5889]) ).
thf(1675,plain,
( ( ( sk6 @ relation_rng @ empty )
!= ( sk7 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1578,76]) ).
thf(1676,plain,
( ( sk6 @ relation_rng @ empty )
!= ( sk7 @ empty ) ),
inference(simp,[status(thm)],[1675]) ).
thf(1703,plain,
( ( sk6 @ relation_rng )
!= sk7 ),
inference(simp,[status(thm)],[1676]) ).
thf(2402,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk6 @ relation_rng ) )
| ( A != sk7 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,1703]) ).
thf(2403,plain,
! [A: $i] :
( ( A != sk7 )
| ~ ( A @ singleton @ ( sk6 @ relation_rng @ in ) ) ),
inference(pattern_uni,[status(thm)],[2402:[bind(A,$thf( A )),bind(B,$thf( sk6 @ relation_rng ))]]) ).
thf(3250,plain,
~ ( sk7 @ singleton @ ( sk6 @ relation_rng @ in ) ),
inference(simp,[status(thm)],[2403]) ).
thf(12184,plain,
~ ( sk7 @ singleton @ ( empty_set @ relation_rng @ in ) ),
inference(rewrite,[status(thm)],[3250,6073]) ).
thf(7223,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk7 @ singleton ) )
| ( B
!= ( empty_set @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,7199]) ).
thf(7224,plain,
! [A: $i] :
( ( A
!= ( empty_set @ singleton ) )
| ~ ( sk7 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[7223:[bind(A,$thf( sk7 @ singleton )),bind(B,$thf( B ))]]) ).
thf(7232,plain,
~ ( sk7 @ singleton @ singleton @ ( empty_set @ singleton @ in ) ),
inference(simp,[status(thm)],[7224]) ).
thf(17803,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk7 @ singleton @ singleton @ ( empty_set @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,7232]) ).
thf(17804,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk7 @ singleton @ singleton @ ( empty_set @ singleton @ in ) ) ),
inference(simp,[status(thm)],[17803]) ).
thf(17897,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk7 @ singleton @ singleton ) )
| ( A
!= ( empty_set @ singleton ) ) ),
inference(simp,[status(thm)],[17804]) ).
thf(17952,plain,
( ( empty_set @ singleton @ powerset )
!= ( sk7 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[17897]) ).
thf(5236,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5131,92]) ).
thf(5237,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty ) ),
inference(simp,[status(thm)],[5236]) ).
thf(5238,plain,
empty_set @ relation_dom @ relation_rng @ empty,
inference(pattern_uni,[status(thm)],[5237:[bind(A,$thf( empty_set @ relation_dom ))]]) ).
thf(8249,plain,
empty_set @ relation_rng @ empty,
inference(rewrite,[status(thm)],[5238,5889]) ).
thf(20774,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk10 @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,18193]) ).
thf(20775,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk10 @ powerset @ in ) ) ),
inference(simp,[status(thm)],[20774]) ).
thf(20781,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( empty_set @ singleton @ singleton ) )
| ( A
!= ( sk10 @ powerset ) ) ),
inference(simp,[status(thm)],[20775]) ).
thf(20791,plain,
( ( sk10 @ powerset @ singleton )
!= ( empty_set @ singleton @ singleton ) ),
inference(simp,[status(thm)],[20781]) ).
thf(2643,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk9 @ relation_rng @ relation_rng ) )
| ( B != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,2181]) ).
thf(2644,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( sk9 @ relation_rng @ relation_rng @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2643:[bind(A,$thf( sk9 @ relation_rng @ relation_rng )),bind(B,$thf( B ))]]) ).
thf(3345,plain,
~ ( sk9 @ relation_rng @ relation_rng @ singleton @ ( sk1 @ in ) ),
inference(simp,[status(thm)],[2644]) ).
thf(14942,plain,
~ ( empty_set @ relation_rng @ relation_rng @ singleton @ ( sk1 @ in ) ),
inference(rewrite,[status(thm)],[3345,6146]) ).
thf(374,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ sk19 ) )
!= sk8 )
| ( ( B @ ( C @ sk19 ) )
!= sk8 )
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) ) ),
inference(simp,[status(thm)],[366]) ).
thf(406,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ sk19 ) )
!= sk8 )
| ( ( B @ ( C @ sk19 ) )
!= sk8 )
| ( ( sk2 @ singleton )
!= ( sk8 @ relation_rng ) ) ),
inference(simp,[status(thm)],[374]) ).
thf(32,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(171,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(172,plain,
! [A: $i] :
( ~ ( A @ relation_dom @ empty )
| ~ ( A @ relation )
| ( A @ empty ) ),
inference(cnf,[status(esa)],[171]) ).
thf(18109,plain,
! [B: $i,A: $i] :
( ( B
!= ( empty_set @ powerset ) )
| ( A
!= ( sk10 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,17953]) ).
thf(18110,plain,
! [A: $i] :
( ( A
!= ( sk10 @ singleton ) )
| ~ ( A @ singleton @ ( empty_set @ powerset @ in ) ) ),
inference(pattern_uni,[status(thm)],[18109:[bind(A,$thf( A )),bind(B,$thf( empty_set @ powerset ))]]) ).
thf(18122,plain,
~ ( sk10 @ singleton @ singleton @ ( empty_set @ powerset @ in ) ),
inference(simp,[status(thm)],[18110]) ).
thf(20315,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk10 @ singleton @ singleton @ ( empty_set @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,18122]) ).
thf(20316,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk10 @ singleton @ singleton @ ( empty_set @ powerset @ in ) ) ),
inference(simp,[status(thm)],[20315]) ).
thf(20388,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk10 @ singleton @ singleton ) )
| ( A
!= ( empty_set @ powerset ) ) ),
inference(simp,[status(thm)],[20316]) ).
thf(20398,plain,
( ( empty_set @ powerset @ powerset )
!= ( sk10 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[20388]) ).
thf(234,plain,
( ( ( sk18 @ function )
!= ( sk10 @ function ) )
| ~ $true
| ( ( sk2 @ singleton )
!= ( sk10 @ relation_rng ) )
| ( ( sk10 @ relation_dom )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[181,216]) ).
thf(235,plain,
( ( ( sk18 @ function )
!= ( sk10 @ function ) )
| ( ( sk2 @ singleton )
!= ( sk10 @ relation_rng ) )
| ( ( sk10 @ relation_dom )
!= sk1 ) ),
inference(simp,[status(thm)],[234]) ).
thf(245,plain,
( ( sk18 != sk10 )
| ( ( sk2 @ singleton )
!= ( sk10 @ relation_rng ) )
| ( ( sk10 @ relation_dom )
!= sk1 ) ),
inference(simp,[status(thm)],[235]) ).
thf(5305,plain,
( ( ( sk6 @ relation_dom @ empty )
!= ( sk1 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5149,1195]) ).
thf(5306,plain,
( ( sk6 @ relation_dom @ empty )
!= ( sk1 @ empty ) ),
inference(simp,[status(thm)],[5305]) ).
thf(5355,plain,
( ( sk6 @ relation_dom )
!= sk1 ),
inference(simp,[status(thm)],[5306]) ).
thf(5583,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk6 @ relation_dom ) )
| ( A != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,5355]) ).
thf(5584,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( A @ singleton @ ( sk6 @ relation_dom @ in ) ) ),
inference(pattern_uni,[status(thm)],[5583:[bind(A,$thf( A )),bind(B,$thf( sk6 @ relation_dom ))]]) ).
thf(5593,plain,
~ ( sk1 @ singleton @ ( sk6 @ relation_dom @ in ) ),
inference(simp,[status(thm)],[5584]) ).
thf(11554,plain,
~ ( sk1 @ singleton @ ( empty_set @ relation_dom @ in ) ),
inference(rewrite,[status(thm)],[5593,6073]) ).
thf(2134,plain,
! [A: $i] :
( ( ( sk9 @ relation_rng @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1710,93]) ).
thf(2135,plain,
! [A: $i] :
( ( ( sk9 @ relation_rng @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ relation ) ),
inference(simp,[status(thm)],[2134]) ).
thf(2136,plain,
sk9 @ relation_rng @ relation_rng @ relation_rng @ relation,
inference(pattern_uni,[status(thm)],[2135:[bind(A,$thf( sk9 @ relation_rng @ relation_rng ))]]) ).
thf(11883,plain,
empty_set @ relation_rng @ relation_rng @ relation_rng @ relation,
inference(rewrite,[status(thm)],[2136,6146]) ).
thf(11286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk5 @ in ) )
!= ( B @ ( D @ in ) ) )
| ~ $true
| ( ( D @ ( B @ ( C @ sk19 ) @ apply ) )
= C )
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[1360,189]) ).
thf(11287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk5 @ in ) )
!= ( B @ ( D @ in ) ) )
| ( ( D @ ( B @ ( C @ sk19 ) @ apply ) )
= C )
| ( A @ empty ) ),
inference(simp,[status(thm)],[11286]) ).
thf(11288,plain,
! [B: $i,A: $i] :
( ( ( B @ sk5 @ ( B @ ( A @ sk19 ) @ apply ) )
= A )
| ( B @ empty ) ),
inference(pattern_uni,[status(thm)],[11287:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( E @ sk5 ))]]) ).
thf(11355,plain,
! [B: $i,A: $i] :
( ( ( B @ sk5 @ ( B @ ( A @ sk19 ) @ apply ) )
= A )
| ( B @ empty ) ),
inference(simp,[status(thm)],[11288]) ).
thf(566,plain,
! [B: $i,A: $i] :
( ( B != sk18 )
| ( ( sk2 @ singleton )
!= ( sk18 @ relation_rng ) )
| ( ( A @ relation_dom )
!= sk1 )
| ~ ( B @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[63,233]) ).
thf(567,plain,
! [A: $i] :
( ( ( sk2 @ singleton )
!= ( sk18 @ relation_rng ) )
| ( ( A @ relation_dom )
!= sk1 )
| ~ ( sk18 @ empty )
| ~ ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[566:[bind(A,$thf( A )),bind(B,$thf( sk18 ))]]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(66,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9015,plain,
( ( ( empty_set @ relation_dom @ relation_rng @ empty )
!= ( sk1 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9008,1195]) ).
thf(9016,plain,
( ( empty_set @ relation_dom @ relation_rng @ empty )
!= ( sk1 @ empty ) ),
inference(simp,[status(thm)],[9015]) ).
thf(9103,plain,
( ( empty_set @ relation_dom @ relation_rng )
!= sk1 ),
inference(simp,[status(thm)],[9016]) ).
thf(9228,plain,
( ( empty_set @ relation_rng )
!= sk1 ),
inference(rewrite,[status(thm)],[9103,5889]) ).
thf(25,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(108,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(18151,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk7 @ powerset ) )
| ( B
!= ( empty_set @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,17954]) ).
thf(18152,plain,
! [A: $i] :
( ( A
!= ( empty_set @ singleton ) )
| ~ ( sk7 @ powerset @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[18151:[bind(A,$thf( sk7 @ powerset )),bind(B,$thf( B ))]]) ).
thf(18156,plain,
~ ( sk7 @ powerset @ singleton @ ( empty_set @ singleton @ in ) ),
inference(simp,[status(thm)],[18152]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ~ ( B @ ( A @ ( B @ sk12 ) @ in ) )
| ( ( A @ ( B @ sk11 ) )
!= A ) ),
inference(cnfConj,[status(thm)],[114]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk12 ) @ in ) )
| ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk11 ) )
!= A ) ),
inference(lifteq,[status(thm)],[115]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk12 ) @ in ) )
| ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk11 ) )
!= A ) ),
inference(simp,[status(thm)],[129]) ).
thf(363,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk19 ) @ relation_dom )
!= ( sk18 @ relation_dom ) )
| ( ( sk2 @ singleton )
!= ( sk18 @ relation_rng ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[188,233]) ).
thf(390,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ sk19 ) )
!= sk18 )
| ( ( sk2 @ singleton )
!= ( sk18 @ relation_rng ) ) ),
inference(simp,[status(thm)],[363]) ).
thf(399,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ sk19 ) )
!= sk18 )
| ( ( sk2 @ singleton )
!= ( sk18 @ relation_rng ) ) ),
inference(simp,[status(thm)],[390]) ).
thf(1691,plain,
( ( ( sk6 @ relation_rng @ empty )
!= ( sk10 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1578,104]) ).
thf(1692,plain,
( ( sk6 @ relation_rng @ empty )
!= ( sk10 @ empty ) ),
inference(simp,[status(thm)],[1691]) ).
thf(1700,plain,
( ( sk6 @ relation_rng )
!= sk10 ),
inference(simp,[status(thm)],[1692]) ).
thf(2716,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk6 @ relation_rng ) )
| ( B != sk10 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,1700]) ).
thf(2717,plain,
! [A: $i] :
( ( A != sk10 )
| ~ ( sk6 @ relation_rng @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2716:[bind(A,$thf( sk6 @ relation_rng )),bind(B,$thf( B ))]]) ).
thf(3376,plain,
~ ( sk6 @ relation_rng @ singleton @ ( sk10 @ in ) ),
inference(simp,[status(thm)],[2717]) ).
thf(12534,plain,
~ ( empty_set @ relation_rng @ singleton @ ( sk10 @ in ) ),
inference(rewrite,[status(thm)],[3376,6073]) ).
thf(21557,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ sk3 @ in ) )
!= ( B @ ( D @ in ) ) )
| ~ $true
| ( ( D @ ( B @ ( C @ sk19 ) @ apply ) )
= C )
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[21542,189]) ).
thf(21558,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ sk3 @ in ) )
!= ( B @ ( D @ in ) ) )
| ( ( D @ ( B @ ( C @ sk19 ) @ apply ) )
= C )
| ( A @ empty ) ),
inference(simp,[status(thm)],[21557]) ).
thf(21559,plain,
! [B: $i,A: $i] :
( ( ( B @ sk3 @ ( B @ powerset @ ( A @ sk19 ) @ apply ) )
= A )
| ( B @ empty ) ),
inference(pattern_uni,[status(thm)],[21558:[bind(A,$thf( F )),bind(B,$thf( F @ powerset )),bind(C,$thf( C )),bind(D,$thf( F @ sk3 ))]]) ).
thf(21776,plain,
! [B: $i,A: $i] :
( ( ( B @ sk3 @ ( B @ powerset @ ( A @ sk19 ) @ apply ) )
= A )
| ( B @ empty ) ),
inference(simp,[status(thm)],[21559]) ).
thf(20577,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk7 @ powerset @ singleton @ ( empty_set @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,18156]) ).
thf(20578,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk7 @ powerset @ singleton @ ( empty_set @ singleton @ in ) ) ),
inference(simp,[status(thm)],[20577]) ).
thf(20650,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk7 @ powerset @ singleton ) )
| ( A
!= ( empty_set @ singleton ) ) ),
inference(simp,[status(thm)],[20578]) ).
thf(20660,plain,
( ( empty_set @ singleton @ powerset )
!= ( sk7 @ powerset @ singleton ) ),
inference(simp,[status(thm)],[20650]) ).
thf(324,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ sk4 @ element ) )
!= ( C @ powerset @ ( B @ element ) ) )
| ( C @ ( B @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[56,47]) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ sk4 @ element ) )
!= ( C @ powerset @ ( B @ element ) ) )
| ( C @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[324]) ).
thf(326,plain,
! [A: $i] : ( A @ ( A @ sk4 @ subset ) ),
inference(pattern_uni,[status(thm)],[325:[bind(A,$thf( D )),bind(B,$thf( D @ sk4 )),bind(C,$thf( D ))]]) ).
thf(327,plain,
! [A: $i] : ( A @ ( A @ sk4 @ subset ) ),
inference(simp,[status(thm)],[326]) ).
thf(14599,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(rewrite,[status(thm)],[327,6616]) ).
thf(7183,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk10 @ singleton ) )
| ( A
!= ( empty_set @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,7163]) ).
thf(7184,plain,
! [A: $i] :
( ( A
!= ( empty_set @ singleton ) )
| ~ ( A @ singleton @ ( sk10 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[7183:[bind(A,$thf( A )),bind(B,$thf( sk10 @ singleton ))]]) ).
thf(7195,plain,
~ ( empty_set @ singleton @ singleton @ ( sk10 @ singleton @ in ) ),
inference(simp,[status(thm)],[7184]) ).
thf(17860,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk10 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,7195]) ).
thf(17861,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk10 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[17860]) ).
thf(17868,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( empty_set @ singleton @ singleton ) )
| ( A
!= ( sk10 @ singleton ) ) ),
inference(simp,[status(thm)],[17861]) ).
thf(17921,plain,
( ( sk10 @ singleton @ powerset )
!= ( empty_set @ singleton @ singleton ) ),
inference(simp,[status(thm)],[17868]) ).
thf(1377,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ~ ( B @ ( C @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,80]) ).
thf(1378,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ~ ( B @ ( C @ in ) ) ),
inference(simp,[status(thm)],[1377]) ).
thf(1379,plain,
! [A: $i] :
~ ( A @ ( A @ singleton @ in ) ),
inference(pattern_uni,[status(thm)],[1378:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ singleton ))]]) ).
thf(1385,plain,
! [A: $i] :
~ ( A @ ( A @ singleton @ in ) ),
inference(simp,[status(thm)],[1379]) ).
thf(1409,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( B @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,1385]) ).
thf(1410,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( B @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1409]) ).
thf(1411,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= B )
| ( A
!= ( B @ singleton ) ) ),
inference(simp,[status(thm)],[1410]) ).
thf(1413,plain,
! [A: $i] :
( ( A @ singleton @ singleton )
!= A ),
inference(simp,[status(thm)],[1411]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ relation_rng ) )
| ~ ( B @ ( A @ ( B @ sk16 ) @ in ) )
| ( B @ ( A @ sk14 ) )
| ~ ( A @ function )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[142]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk16 ) @ in ) )
| ( B @ ( A @ sk14 ) )
| ~ ( A @ function )
| ~ ( A @ relation )
| ( B
= ( A @ relation_rng ) ) ),
inference(lifteq,[status(thm)],[146]) ).
thf(162,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk16 ) @ in ) )
| ( B @ ( A @ sk14 ) )
| ~ ( A @ function )
| ~ ( A @ relation )
| ( B
= ( A @ relation_rng ) ) ),
inference(simp,[status(thm)],[161]) ).
thf(2093,plain,
( ( ( sk6 @ relation_rng @ relation_rng @ empty )
!= ( sk7 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1667,76]) ).
thf(2094,plain,
( ( sk6 @ relation_rng @ relation_rng @ empty )
!= ( sk7 @ empty ) ),
inference(simp,[status(thm)],[2093]) ).
thf(2125,plain,
( ( sk6 @ relation_rng @ relation_rng )
!= sk7 ),
inference(simp,[status(thm)],[2094]) ).
thf(2744,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk6 @ relation_rng @ relation_rng ) )
| ( A != sk7 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,2125]) ).
thf(2745,plain,
! [A: $i] :
( ( A != sk7 )
| ~ ( A @ singleton @ ( sk6 @ relation_rng @ relation_rng @ in ) ) ),
inference(pattern_uni,[status(thm)],[2744:[bind(A,$thf( A )),bind(B,$thf( sk6 @ relation_rng @ relation_rng ))]]) ).
thf(3388,plain,
~ ( sk7 @ singleton @ ( sk6 @ relation_rng @ relation_rng @ in ) ),
inference(simp,[status(thm)],[2745]) ).
thf(15090,plain,
~ ( sk7 @ singleton @ ( empty_set @ relation_rng @ relation_rng @ in ) ),
inference(rewrite,[status(thm)],[3388,6073]) ).
thf(5587,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk6 @ relation_dom ) )
| ( B != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,5355]) ).
thf(5588,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( sk6 @ relation_dom @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[5587:[bind(A,$thf( sk6 @ relation_dom )),bind(B,$thf( B ))]]) ).
thf(5594,plain,
~ ( sk6 @ relation_dom @ singleton @ ( sk1 @ in ) ),
inference(simp,[status(thm)],[5588]) ).
thf(12043,plain,
~ ( empty_set @ relation_dom @ singleton @ ( sk1 @ in ) ),
inference(rewrite,[status(thm)],[5594,6073]) ).
thf(279,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk5 @ element ) )
!= ( C @ powerset @ ( B @ element ) ) )
| ( C @ ( B @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,47]) ).
thf(280,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk5 @ element ) )
!= ( C @ powerset @ ( B @ element ) ) )
| ( C @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[279]) ).
thf(281,plain,
! [A: $i] : ( A @ ( A @ powerset @ sk5 @ subset ) ),
inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( E @ powerset )),bind(B,$thf( E @ powerset @ sk5 )),bind(C,$thf( E ))]]) ).
thf(282,plain,
! [A: $i] : ( A @ ( A @ powerset @ sk5 @ subset ) ),
inference(simp,[status(thm)],[281]) ).
thf(367,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk19 ) @ relation_dom )
!= ( sk10 @ relation_dom ) )
| ( sk18 != sk10 )
| ( ( sk2 @ singleton )
!= ( sk10 @ relation_rng ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[188,245]) ).
thf(382,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ sk19 ) )
!= sk10 )
| ( sk18 != sk10 )
| ( ( sk2 @ singleton )
!= ( sk10 @ relation_rng ) ) ),
inference(simp,[status(thm)],[367]) ).
thf(414,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ sk19 ) )
!= sk10 )
| ( sk18 != sk10 )
| ( ( sk2 @ singleton )
!= ( sk10 @ relation_rng ) ) ),
inference(simp,[status(thm)],[382]) ).
thf(20240,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( empty_set @ powerset @ singleton @ ( sk10 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,18117]) ).
thf(20241,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( empty_set @ powerset @ singleton @ ( sk10 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[20240]) ).
thf(20248,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( empty_set @ powerset @ singleton ) )
| ( A
!= ( sk10 @ singleton ) ) ),
inference(simp,[status(thm)],[20241]) ).
thf(20257,plain,
( ( empty_set @ powerset @ singleton )
!= ( sk10 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[20248]) ).
thf(17831,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( empty_set @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,15699]) ).
thf(17832,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( empty_set @ singleton @ in ) ) ),
inference(simp,[status(thm)],[17831]) ).
thf(17893,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ singleton @ singleton ) )
| ( A
!= ( empty_set @ singleton ) ) ),
inference(simp,[status(thm)],[17832]) ).
thf(17948,plain,
( ( empty_set @ singleton @ powerset )
!= ( sk1 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[17893]) ).
thf(144,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C
!= ( D @ ( A @ apply ) ) )
| ~ ( A @ relation_dom @ ( D @ in ) )
| ( B
!= ( A @ relation_rng ) )
| ~ ( A @ function )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[142]) ).
thf(153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( A @ relation_dom @ ( D @ in ) )
| ~ ( A @ function )
| ~ ( A @ relation )
| ( C
!= ( D @ ( A @ apply ) ) )
| ( B
!= ( A @ relation_rng ) ) ),
inference(lifteq,[status(thm)],[144]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ( A @ relation_rng @ ( B @ ( A @ apply ) @ in ) )
| ~ ( A @ relation_dom @ ( B @ in ) )
| ~ ( A @ function )
| ~ ( A @ relation ) ),
inference(simp,[status(thm)],[153]) ).
thf(11340,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( D @ in ) ) )
| ~ $true
| ( ( D @ ( B @ ( C @ sk19 ) @ apply ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[122,189]) ).
thf(11341,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( D @ in ) ) )
| ( ( D @ ( B @ ( C @ sk19 ) @ apply ) )
= C ) ),
inference(simp,[status(thm)],[11340]) ).
thf(11342,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ singleton @ ( A @ sk19 ) @ apply ) )
= A ),
inference(pattern_uni,[status(thm)],[11341:[bind(A,$thf( E )),bind(B,$thf( E @ singleton )),bind(C,$thf( C )),bind(D,$thf( E ))]]) ).
thf(11351,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ singleton @ ( A @ sk19 ) @ apply ) )
= A ),
inference(simp,[status(thm)],[11342]) ).
thf(570,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( ( A @ singleton )
!= ( sk18 @ relation_rng ) )
| ( ( sk18 @ relation_dom )
!= sk1 )
| ~ ( B @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[63,233]) ).
thf(571,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk18 @ relation_rng ) )
| ( ( sk18 @ relation_dom )
!= sk1 )
| ~ ( sk2 @ empty )
| ~ ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[570:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(5172,plain,
! [A: $i] :
( ( ( sk6 @ relation_rng @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1667,135]) ).
thf(5173,plain,
! [A: $i] :
( ( ( sk6 @ relation_rng @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty ) ),
inference(simp,[status(thm)],[5172]) ).
thf(5174,plain,
sk6 @ relation_rng @ relation_rng @ relation_dom @ empty,
inference(pattern_uni,[status(thm)],[5173:[bind(A,$thf( sk6 @ relation_rng @ relation_rng ))]]) ).
thf(12652,plain,
empty_set @ relation_rng @ relation_rng @ relation_dom @ empty,
inference(rewrite,[status(thm)],[5174,6073]) ).
thf(16066,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk10 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,7195]) ).
thf(16067,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk10 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[16066]) ).
thf(16069,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( empty_set @ singleton @ singleton ) )
| ( A
!= ( sk10 @ singleton ) ) ),
inference(simp,[status(thm)],[16067]) ).
thf(16085,plain,
( ( sk10 @ singleton @ singleton )
!= ( empty_set @ singleton @ singleton ) ),
inference(simp,[status(thm)],[16069]) ).
thf(17352,plain,
! [A: $i] :
( ( ( A @ powerset @ ( empty_set @ in ) )
!= ( sk1 @ singleton @ ( empty_set @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17349,3502]) ).
thf(17353,plain,
! [A: $i] :
( ( A @ powerset @ ( empty_set @ in ) )
!= ( sk1 @ singleton @ ( empty_set @ in ) ) ),
inference(simp,[status(thm)],[17352]) ).
thf(17506,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ singleton ) )
| ( empty_set != empty_set ) ),
inference(simp,[status(thm)],[17353]) ).
thf(17553,plain,
! [A: $i] :
( ( A @ powerset )
!= ( sk1 @ singleton ) ),
inference(simp,[status(thm)],[17506]) ).
thf(16330,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk7 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,7231]) ).
thf(16331,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk7 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[16330]) ).
thf(16337,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( empty_set @ singleton @ singleton ) )
| ( A
!= ( sk7 @ singleton ) ) ),
inference(simp,[status(thm)],[16331]) ).
thf(16350,plain,
( ( sk7 @ singleton @ singleton )
!= ( empty_set @ singleton @ singleton ) ),
inference(simp,[status(thm)],[16337]) ).
thf(7456,plain,
( ( ( empty_set @ relation_rng @ relation_dom @ empty )
!= ( sk10 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7412,104]) ).
thf(7457,plain,
( ( empty_set @ relation_rng @ relation_dom @ empty )
!= ( sk10 @ empty ) ),
inference(simp,[status(thm)],[7456]) ).
thf(7500,plain,
( ( empty_set @ relation_rng @ relation_dom )
!= sk10 ),
inference(simp,[status(thm)],[7457]) ).
thf(10767,plain,
( ( empty_set @ relation_dom )
!= sk10 ),
inference(rewrite,[status(thm)],[7500,5905]) ).
thf(308,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk19 ) @ function )
!= ( sk10 @ function ) )
| ~ $true
| ( ( sk2 @ singleton )
!= ( sk10 @ relation_rng ) )
| ( ( sk10 @ relation_dom )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[185,216]) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk19 ) @ function )
!= ( sk10 @ function ) )
| ( ( sk2 @ singleton )
!= ( sk10 @ relation_rng ) )
| ( ( sk10 @ relation_dom )
!= sk1 ) ),
inference(simp,[status(thm)],[308]) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk19 ) )
!= sk10 )
| ( ( sk2 @ singleton )
!= ( sk10 @ relation_rng ) )
| ( ( sk10 @ relation_dom )
!= sk1 ) ),
inference(simp,[status(thm)],[309]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ relation_rng ) )
| ~ ( B @ ( A @ sk14 ) )
| ( B @ ( A @ ( B @ sk15 ) @ in ) )
| ~ ( A @ function )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[142]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ sk14 ) )
| ( B @ ( A @ ( B @ sk15 ) @ in ) )
| ~ ( A @ function )
| ~ ( A @ relation )
| ( B
= ( A @ relation_rng ) ) ),
inference(lifteq,[status(thm)],[150]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ sk14 ) )
| ( B @ ( A @ ( B @ sk15 ) @ in ) )
| ~ ( A @ function )
| ~ ( A @ relation )
| ( B
= ( A @ relation_rng ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(5352,plain,
! [A: $i] :
( ( ( A @ singleton @ empty )
!= ( sk6 @ relation_dom @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5149,100]) ).
thf(5353,plain,
! [A: $i] :
( ( A @ singleton @ empty )
!= ( sk6 @ relation_dom @ empty ) ),
inference(simp,[status(thm)],[5352]) ).
thf(5356,plain,
! [A: $i] :
( ( A @ singleton )
!= ( sk6 @ relation_dom ) ),
inference(simp,[status(thm)],[5353]) ).
thf(17672,plain,
! [A: $i] :
( ( A @ singleton )
!= ( empty_set @ relation_dom ) ),
inference(rewrite,[status(thm)],[5356,6073]) ).
thf(18189,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk10 @ powerset ) )
| ( B
!= ( empty_set @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,17959]) ).
thf(18190,plain,
! [A: $i] :
( ( A
!= ( empty_set @ singleton ) )
| ~ ( sk10 @ powerset @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[18189:[bind(A,$thf( sk10 @ powerset )),bind(B,$thf( B ))]]) ).
thf(18194,plain,
~ ( sk10 @ powerset @ singleton @ ( empty_set @ singleton @ in ) ),
inference(simp,[status(thm)],[18190]) ).
thf(2406,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk6 @ relation_rng ) )
| ( B != sk7 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,1703]) ).
thf(2407,plain,
! [A: $i] :
( ( A != sk7 )
| ~ ( sk6 @ relation_rng @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2406:[bind(A,$thf( sk6 @ relation_rng )),bind(B,$thf( B ))]]) ).
thf(3251,plain,
~ ( sk6 @ relation_rng @ singleton @ ( sk7 @ in ) ),
inference(simp,[status(thm)],[2407]) ).
thf(12298,plain,
~ ( empty_set @ relation_rng @ singleton @ ( sk7 @ in ) ),
inference(rewrite,[status(thm)],[3251,6073]) ).
thf(5315,plain,
( ( ( sk6 @ relation_dom @ empty )
!= ( sk7 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5149,76]) ).
thf(5316,plain,
( ( sk6 @ relation_dom @ empty )
!= ( sk7 @ empty ) ),
inference(simp,[status(thm)],[5315]) ).
thf(5354,plain,
( ( sk6 @ relation_dom )
!= sk7 ),
inference(simp,[status(thm)],[5316]) ).
thf(5667,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk6 @ relation_dom ) )
| ( B != sk7 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,5354]) ).
thf(5668,plain,
! [A: $i] :
( ( A != sk7 )
| ~ ( sk6 @ relation_dom @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[5667:[bind(A,$thf( sk6 @ relation_dom )),bind(B,$thf( B ))]]) ).
thf(5674,plain,
~ ( sk6 @ relation_dom @ singleton @ ( sk7 @ in ) ),
inference(simp,[status(thm)],[5668]) ).
thf(13349,plain,
~ ( empty_set @ relation_dom @ singleton @ ( sk7 @ in ) ),
inference(rewrite,[status(thm)],[5674,6073]) ).
thf(5312,plain,
! [B: $i,A: $i] :
( ( ( sk6 @ relation_dom @ empty )
!= ( B @ empty ) )
| ~ $true
| ~ ( B @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[5149,71]) ).
thf(5313,plain,
! [B: $i,A: $i] :
( ( ( sk6 @ relation_dom @ empty )
!= ( B @ empty ) )
| ~ ( B @ ( A @ in ) ) ),
inference(simp,[status(thm)],[5312]) ).
thf(5314,plain,
! [A: $i] :
~ ( sk6 @ relation_dom @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[5313:[bind(A,$thf( A )),bind(B,$thf( sk6 @ relation_dom ))]]) ).
thf(17597,plain,
! [A: $i] :
~ ( empty_set @ relation_dom @ ( A @ in ) ),
inference(rewrite,[status(thm)],[5314,6073]) ).
thf(1672,plain,
! [B: $i,A: $i] :
( ( ( sk6 @ relation_rng @ empty )
!= ( B @ empty ) )
| ~ $true
| ~ ( B @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[1578,71]) ).
thf(1673,plain,
! [B: $i,A: $i] :
( ( ( sk6 @ relation_rng @ empty )
!= ( B @ empty ) )
| ~ ( B @ ( A @ in ) ) ),
inference(simp,[status(thm)],[1672]) ).
thf(1674,plain,
! [A: $i] :
~ ( sk6 @ relation_rng @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[1673:[bind(A,$thf( A )),bind(B,$thf( sk6 @ relation_rng ))]]) ).
thf(17184,plain,
! [A: $i] :
~ ( empty_set @ relation_rng @ ( A @ in ) ),
inference(rewrite,[status(thm)],[1674,6073]) ).
thf(107,plain,
! [A: $i] :
( ( A @ relation )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[106]) ).
thf(2750,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk6 @ relation_rng @ relation_rng ) )
| ( B != sk7 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,2125]) ).
thf(2751,plain,
! [A: $i] :
( ( A != sk7 )
| ~ ( sk6 @ relation_rng @ relation_rng @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2750:[bind(A,$thf( sk6 @ relation_rng @ relation_rng )),bind(B,$thf( B ))]]) ).
thf(3389,plain,
~ ( sk6 @ relation_rng @ relation_rng @ singleton @ ( sk7 @ in ) ),
inference(simp,[status(thm)],[2751]) ).
thf(15236,plain,
~ ( empty_set @ relation_rng @ relation_rng @ singleton @ ( sk7 @ in ) ),
inference(rewrite,[status(thm)],[3389,6073]) ).
thf(19643,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( empty_set @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,18037]) ).
thf(19644,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( empty_set @ powerset @ in ) ) ),
inference(simp,[status(thm)],[19643]) ).
thf(19715,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( sk1 @ singleton @ singleton ) )
| ( A
!= ( empty_set @ powerset ) ) ),
inference(simp,[status(thm)],[19644]) ).
thf(19720,plain,
( ( empty_set @ powerset @ powerset )
!= ( sk1 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[19715]) ).
thf(19381,plain,
! [A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk1 @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17736,17996]) ).
thf(19382,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( empty_set @ singleton @ singleton @ ( sk1 @ powerset @ in ) ) ),
inference(simp,[status(thm)],[19381]) ).
thf(19449,plain,
! [A: $i] :
( ( ( A @ powerset )
!= ( empty_set @ singleton @ singleton ) )
| ( A
!= ( sk1 @ powerset ) ) ),
inference(simp,[status(thm)],[19382]) ).
thf(19469,plain,
( ( sk1 @ powerset @ powerset )
!= ( empty_set @ singleton @ singleton ) ),
inference(simp,[status(thm)],[19449]) ).
thf(2712,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk6 @ relation_rng ) )
| ( A != sk10 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,1700]) ).
thf(2713,plain,
! [A: $i] :
( ( A != sk10 )
| ~ ( A @ singleton @ ( sk6 @ relation_rng @ in ) ) ),
inference(pattern_uni,[status(thm)],[2712:[bind(A,$thf( A )),bind(B,$thf( sk6 @ relation_rng ))]]) ).
thf(3375,plain,
~ ( sk10 @ singleton @ ( sk6 @ relation_rng @ in ) ),
inference(simp,[status(thm)],[2713]) ).
thf(12420,plain,
~ ( sk10 @ singleton @ ( empty_set @ relation_rng @ in ) ),
inference(rewrite,[status(thm)],[3375,6073]) ).
thf(5663,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk6 @ relation_dom ) )
| ( A != sk7 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[126,5354]) ).
thf(5664,plain,
! [A: $i] :
( ( A != sk7 )
| ~ ( A @ singleton @ ( sk6 @ relation_dom @ in ) ) ),
inference(pattern_uni,[status(thm)],[5663:[bind(A,$thf( A )),bind(B,$thf( sk6 @ relation_dom ))]]) ).
thf(5673,plain,
~ ( sk7 @ singleton @ ( sk6 @ relation_dom @ in ) ),
inference(simp,[status(thm)],[5664]) ).
thf(13247,plain,
~ ( sk7 @ singleton @ ( empty_set @ relation_dom @ in ) ),
inference(rewrite,[status(thm)],[5673,6073]) ).
thf(67,plain,
~ ? [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ empty )
& ( C @ powerset @ ( B @ element ) ) )
& ( B @ ( A @ in ) ) ),
inference(miniscope,[status(thm)],[66]) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ empty )
| ~ ( C @ powerset @ ( B @ element ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[67]) ).
thf(109,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(cnf,[status(esa)],[108]) ).
thf(111,plain,
empty_set @ relation,
inference(cnfConj,[status(thm)],[109]) ).
thf(7433,plain,
( ( ( empty_set @ relation_rng @ relation_dom @ empty )
!= ( sk7 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7412,76]) ).
thf(7434,plain,
( ( empty_set @ relation_rng @ relation_dom @ empty )
!= ( sk7 @ empty ) ),
inference(simp,[status(thm)],[7433]) ).
thf(7498,plain,
( ( empty_set @ relation_rng @ relation_dom )
!= sk7 ),
inference(simp,[status(thm)],[7434]) ).
thf(10723,plain,
( ( empty_set @ relation_dom )
!= sk7 ),
inference(rewrite,[status(thm)],[7498,5905]) ).
thf(28758,plain,
$false,
inference(e,[status(thm)],[69,20256,17959,1295,88,101,17950,17072,170,14468,276,13993,17929,11266,19994,18193,12971,11468,8342,10484,10959,185,7235,288,7993,3502,42,52,14793,184,18155,17017,17270,13553,19472,8919,19719,17928,19589,4664,93,152,228,78,19995,17955,189,216,10816,84,18037,164,1465,17916,106,17349,132,1394,6616,21542,89,133,74,17298,18412,3378,9703,233,60,10593,20528,85,15392,102,9544,16978,18081,1387,160,137,17945,92,13810,11376,1195,13681,9613,1360,317,156,188,53,169,5889,17939,124,339,77,12818,5905,15830,212,393,173,13451,17546,20529,41,73,128,8049,105,15538,20125,9008,541,298,412,18080,11710,166,264,64,17703,180,19861,402,15821,10906,44,18038,12184,59,71,54,17952,8249,49,20791,181,14942,86,406,172,81,20398,245,11554,98,11883,9118,11355,76,567,3456,140,213,66,9228,198,108,18156,130,399,12534,21776,20660,80,14599,135,17921,7232,167,1413,162,112,3455,17736,15090,12043,63,17953,282,414,7196,20257,6146,50,17948,17996,177,182,6073,17997,154,7163,72,11351,571,43,12652,16085,17553,16350,10767,7412,104,1385,18117,319,40,158,17672,171,18194,3501,139,58,246,14592,15699,12298,13349,36,18122,17597,17184,3379,168,7231,107,7199,79,15236,19720,94,126,136,19469,12420,13247,47,68,17954,178,7195,83,5569,100,90,111,122,10723]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET993+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.21/0.48 % Computer : n020.cluster.edu
% 0.21/0.48 % Model : x86_64 x86_64
% 0.21/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.48 % Memory : 8046.5625MB
% 0.21/0.48 % OS : Linux 6.8.0-71-generic
% 0.21/0.48 % CPULimit : 300
% 0.21/0.48 % WCLimit : 300
% 0.21/0.48 % DateTime : Sat Sep 26 08:30:34 UTC 2026
% 0.21/0.49 % CPUTime :
% 0.21/0.49 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
% 1.40/1.31 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.73/1.55 % [INFO] Parsing done (240ms).
% 1.73/1.57 % [INFO] Running in sequential loop mode.
% 2.74/2.14 % [INFO] eprover registered as external prover.
% 2.96/2.16 % [INFO] Scanning for conjecture ...
% 3.18/2.30 % [INFO] Found a conjecture (or negated_conjecture) and 33 axioms. Running axiom selection ...
% 3.36/2.41 % [INFO] Axiom selection finished. Selected 33 axioms (removed 0 axioms).
% 3.36/2.48 % [INFO] Problem is first-order (TPTP FOF).
% 3.36/2.49 % [INFO] Type checking passed.
% 3.36/2.49 % [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 ...
% 108.21/24.13 % External prover 'e' found a proof!
% 108.21/24.13 % [INFO] Killing All external provers ...
% 108.21/24.13 % Time passed: 23443ms (effective reasoning time: 22553ms)
% 108.21/24.13 % 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)>
% 105.68/24.13 % Axioms used in derivation (33): d1_tarski, cc1_relat_1, rc1_funct_1, t5_subset, fc2_subset_1, t4_subset, rc1_subset_1, rc2_relat_1, fc6_relat_1, d5_funct_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, fc4_relat_1, t1_subset, rc3_relat_1, t6_boole, rc2_subset_1, t7_boole, cc1_funct_1, fc1_subset_1, fc5_relat_1, s3_funct_1__e2_13__funct_1, t3_subset, existence_m1_subset_1, rc1_relat_1, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1, fc12_relat_1, fc8_relat_1
% 105.68/24.13 % No. of inferences in proof: 884
% 105.68/24.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 23443 ms resp. 22553 ms w/o parsing
% 106.33/24.37 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 106.33/24.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------