TSTP Solution File: SEV154^5 by Leo-III---1.7.15
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV154^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 15:58:21 EDT 2024
% Result : Theorem 89.42s 18.70s
% Output : Refutation 90.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 1
% Syntax : Number of formulae : 647 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 3833 ( 505 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 6957 (1818 ~;2092 |; 54 &;2912 @)
% ( 0 <=>; 81 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 224 ( 224 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 48 usr; 27 con; 0-2 aty)
% Number of variables : 919 ( 566 ^ 353 !; 0 ?; 919 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_type,type,
sk1: a > a > $o ).
thf(sk2_type,type,
sk2: a > a > $o ).
thf(sk3_type,type,
sk3: a ).
thf(sk4_type,type,
sk4: a ).
thf(sk5_type,type,
sk5: a > $o ).
thf(sk6_type,type,
sk6: $o ).
thf(sk7_type,type,
sk7: $o ).
thf(sk8_type,type,
sk8: a ).
thf(sk9_type,type,
sk9: a ).
thf(sk10_type,type,
sk10: $o ).
thf(sk11_type,type,
sk11: ( a > $o ) > a ).
thf(sk12_type,type,
sk12: ( a > $o ) > a ).
thf(sk13_type,type,
sk13: ( a > $o ) > a ).
thf(sk14_type,type,
sk14: ( a > $o ) > a ).
thf(sk15_type,type,
sk15: ( a > $o ) > a ).
thf(sk16_type,type,
sk16: ( a > $o ) > a ).
thf(sk17_type,type,
sk17: a > $o ).
thf(sk18_type,type,
sk18: a ).
thf(sk19_type,type,
sk19: a ).
thf(sk20_type,type,
sk20: a ).
thf(sk21_type,type,
sk21: ( a > $o ) > $o ).
thf(sk22_type,type,
sk22: ( a > $o ) > a ).
thf(sk23_type,type,
sk23: ( a > $o ) > a ).
thf(sk24_type,type,
sk24: ( a > $o ) > a ).
thf(sk25_type,type,
sk25: ( a > $o ) > $o ).
thf(sk26_type,type,
sk26: ( a > $o ) > a ).
thf(sk27_type,type,
sk27: ( a > $o ) > a ).
thf(sk28_type,type,
sk28: ( a > $o ) > a ).
thf(sk29_type,type,
sk29: a > $o ).
thf(sk30_type,type,
sk30: ( a > $o ) > $o ).
thf(sk31_type,type,
sk31: ( a > $o ) > a ).
thf(sk32_type,type,
sk32: ( a > $o ) > a ).
thf(sk33_type,type,
sk33: ( a > $o ) > a ).
thf(sk34_type,type,
sk34: a ).
thf(sk35_type,type,
sk35: a ).
thf(sk36_type,type,
sk36: a ).
thf(sk39_type,type,
sk39: a ).
thf(sk40_type,type,
sk40: a ).
thf(sk41_type,type,
sk41: a ).
thf(sk42_type,type,
sk42: a ).
thf(sk43_type,type,
sk43: a ).
thf(sk46_type,type,
sk46: a ).
thf(sk47_type,type,
sk47: a ).
thf(sk48_type,type,
sk48: a ).
thf(sk49_type,type,
sk49: a ).
thf(sk51_type,type,
sk51: a ).
thf(sk52_type,type,
sk52: a ).
thf(sk66_type,type,
sk66: a ).
thf(1,conjecture,
! [A: a > a > $o,B: a > a > $o,C: a,D: a] :
( ! [E: a > $o] :
( ( ! [F: a] :
( ( ( A @ C @ F )
| ( B @ C @ F ) )
=> ( E @ F ) )
& ! [F: a,G: a] :
( ( ( E @ F )
& ( ( A @ F @ G )
| ( B @ F @ G ) ) )
=> ( E @ G ) ) )
=> ( E @ D ) )
| ~ ( ( ! [E: a,F: a] :
( ( ! [G: a > $o] :
( ( ! [H: a] :
( ( A @ E @ H )
=> ( G @ H ) )
& ! [H: a,I: a] :
( ( ( G @ H )
& ( A @ H @ I ) )
=> ( G @ I ) ) )
=> ( G @ F ) )
| ! [G: a > $o] :
( ( ! [H: a] :
( ( B @ E @ H )
=> ( G @ H ) )
& ! [H: a,I: a] :
( ( ( G @ H )
& ( B @ H @ I ) )
=> ( G @ I ) ) )
=> ( G @ F ) ) )
=> ! [G: a > $o] :
( ( ! [H: a] :
( ( ( A @ E @ H )
| ( B @ E @ H ) )
=> ( G @ H ) )
& ! [H: a,I: a] :
( ( ( G @ H )
& ( ( A @ H @ I )
| ( B @ H @ I ) ) )
=> ( G @ I ) ) )
=> ( G @ F ) ) )
& ! [E: a,F: a,G: a] :
( ( ! [H: a > $o] :
( ( ! [I: a] :
( ( ( A @ E @ I )
| ( B @ E @ I ) )
=> ( H @ I ) )
& ! [I: a,J: a] :
( ( ( H @ I )
& ( ( A @ I @ J )
| ( B @ I @ J ) ) )
=> ( H @ J ) ) )
=> ( H @ F ) )
& ! [H: a > $o] :
( ( ! [I: a] :
( ( ( A @ F @ I )
| ( B @ F @ I ) )
=> ( H @ I ) )
& ! [I: a,J: a] :
( ( ( H @ I )
& ( ( A @ I @ J )
| ( B @ I @ J ) ) )
=> ( H @ J ) ) )
=> ( H @ G ) ) )
=> ! [H: a > $o] :
( ( ! [I: a] :
( ( ( A @ E @ I )
| ( B @ E @ I ) )
=> ( H @ I ) )
& ! [I: a,J: a] :
( ( ( H @ I )
& ( ( A @ I @ J )
| ( B @ I @ J ) ) )
=> ( H @ J ) ) )
=> ( H @ G ) ) ) )
=> ! [E: a > $o] :
( ( ! [F: a] :
( ( ( A @ C @ F )
| ( B @ C @ F ) )
=> ( E @ F ) )
& ! [F: a,G: a] :
( ( ( E @ F )
& ( ( A @ F @ G )
| ( B @ F @ G ) ) )
=> ( E @ G ) ) )
=> ( E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM251G_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > a > $o,B: a > a > $o,C: a,D: a] :
( ! [E: a > $o] :
( ( ! [F: a] :
( ( ( A @ C @ F )
| ( B @ C @ F ) )
=> ( E @ F ) )
& ! [F: a,G: a] :
( ( ( E @ F )
& ( ( A @ F @ G )
| ( B @ F @ G ) ) )
=> ( E @ G ) ) )
=> ( E @ D ) )
| ~ ( ( ! [E: a,F: a] :
( ( ! [G: a > $o] :
( ( ! [H: a] :
( ( A @ E @ H )
=> ( G @ H ) )
& ! [H: a,I: a] :
( ( ( G @ H )
& ( A @ H @ I ) )
=> ( G @ I ) ) )
=> ( G @ F ) )
| ! [G: a > $o] :
( ( ! [H: a] :
( ( B @ E @ H )
=> ( G @ H ) )
& ! [H: a,I: a] :
( ( ( G @ H )
& ( B @ H @ I ) )
=> ( G @ I ) ) )
=> ( G @ F ) ) )
=> ! [G: a > $o] :
( ( ! [H: a] :
( ( ( A @ E @ H )
| ( B @ E @ H ) )
=> ( G @ H ) )
& ! [H: a,I: a] :
( ( ( G @ H )
& ( ( A @ H @ I )
| ( B @ H @ I ) ) )
=> ( G @ I ) ) )
=> ( G @ F ) ) )
& ! [E: a,F: a,G: a] :
( ( ! [H: a > $o] :
( ( ! [I: a] :
( ( ( A @ E @ I )
| ( B @ E @ I ) )
=> ( H @ I ) )
& ! [I: a,J: a] :
( ( ( H @ I )
& ( ( A @ I @ J )
| ( B @ I @ J ) ) )
=> ( H @ J ) ) )
=> ( H @ F ) )
& ! [H: a > $o] :
( ( ! [I: a] :
( ( ( A @ F @ I )
| ( B @ F @ I ) )
=> ( H @ I ) )
& ! [I: a,J: a] :
( ( ( H @ I )
& ( ( A @ I @ J )
| ( B @ I @ J ) ) )
=> ( H @ J ) ) )
=> ( H @ G ) ) )
=> ! [H: a > $o] :
( ( ! [I: a] :
( ( ( A @ E @ I )
| ( B @ E @ I ) )
=> ( H @ I ) )
& ! [I: a,J: a] :
( ( ( H @ I )
& ( ( A @ I @ J )
| ( B @ I @ J ) ) )
=> ( H @ J ) ) )
=> ( H @ G ) ) ) )
=> ! [E: a > $o] :
( ( ! [F: a] :
( ( ( A @ C @ F )
| ( B @ C @ F ) )
=> ( E @ F ) )
& ! [F: a,G: a] :
( ( ( E @ F )
& ( ( A @ F @ G )
| ( B @ F @ G ) ) )
=> ( E @ G ) ) )
=> ( E @ D ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > a > $o,B: a > a > $o,C: a,D: a] :
( ! [E: a > $o] :
( ( ! [F: a] :
( ( ( A @ C @ F )
| ( B @ C @ F ) )
=> ( E @ F ) )
& ! [F: a,G: a] :
( ( ( E @ F )
& ( ( A @ F @ G )
| ( B @ F @ G ) ) )
=> ( E @ G ) ) )
=> ( E @ D ) )
| ~ ( ( ! [E: a,F: a] :
( ( ! [G: a > $o] :
( ( ! [H: a] :
( ( A @ E @ H )
=> ( G @ H ) )
& ! [H: a,I: a] :
( ( ( G @ H )
& ( A @ H @ I ) )
=> ( G @ I ) ) )
=> ( G @ F ) )
| ! [G: a > $o] :
( ( ! [H: a] :
( ( B @ E @ H )
=> ( G @ H ) )
& ! [H: a,I: a] :
( ( ( G @ H )
& ( B @ H @ I ) )
=> ( G @ I ) ) )
=> ( G @ F ) ) )
=> ! [G: a > $o] :
( ( ! [H: a] :
( ( ( A @ E @ H )
| ( B @ E @ H ) )
=> ( G @ H ) )
& ! [H: a,I: a] :
( ( ( G @ H )
& ( ( A @ H @ I )
| ( B @ H @ I ) ) )
=> ( G @ I ) ) )
=> ( G @ F ) ) )
& ! [E: a,F: a,G: a] :
( ( ! [H: a > $o] :
( ( ! [I: a] :
( ( ( A @ E @ I )
| ( B @ E @ I ) )
=> ( H @ I ) )
& ! [I: a,J: a] :
( ( ( H @ I )
& ( ( A @ I @ J )
| ( B @ I @ J ) ) )
=> ( H @ J ) ) )
=> ( H @ F ) )
& ! [H: a > $o] :
( ( ! [I: a] :
( ( ( A @ F @ I )
| ( B @ F @ I ) )
=> ( H @ I ) )
& ! [I: a,J: a] :
( ( ( H @ I )
& ( ( A @ I @ J )
| ( B @ I @ J ) ) )
=> ( H @ J ) ) )
=> ( H @ G ) ) )
=> ! [H: a > $o] :
( ( ! [I: a] :
( ( ( A @ E @ I )
| ( B @ E @ I ) )
=> ( H @ I ) )
& ! [I: a,J: a] :
( ( ( H @ I )
& ( ( A @ I @ J )
| ( B @ I @ J ) ) )
=> ( H @ J ) ) )
=> ( H @ G ) ) ) )
=> ! [E: a > $o] :
( ( ! [F: a] :
( ( ( A @ C @ F )
| ( B @ C @ F ) )
=> ( E @ F ) )
& ! [F: a,G: a] :
( ( ( E @ F )
& ( ( A @ F @ G )
| ( B @ F @ G ) ) )
=> ( E @ G ) ) )
=> ( E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
! [A: a > $o] :
( ~ sk10
| ( sk2 @ sk8 @ ( sk14 @ A ) )
| ~ ( A @ ( sk16 @ A ) )
| ( A @ sk9 )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(69,plain,
! [A: a > $o] :
( ~ sk10
| ( sk2 @ sk8 @ ( sk14 @ A ) )
| ~ ( A @ ( sk16 @ A ) )
| ( A @ sk9 )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[22]) ).
thf(41,plain,
! [A: a > $o] :
( ~ sk6
| ( sk30 @ A )
| ~ ( A @ ( sk33 @ A ) )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(64,plain,
! [A: a > $o] :
( ~ sk6
| ( sk30 @ A )
| ~ ( A @ ( sk33 @ A ) )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[41]) ).
thf(3962,plain,
( ~ sk6
| ( sk30 @ sk29 )
| ~ ( sk29 @ ( sk33 @ sk29 ) )
| ( sk29 @ sk4 ) ),
inference(prim_subst,[status(thm)],[64:[bind(A,$thf( sk29 ))]]) ).
thf(3973,plain,
( ~ sk6
| ( sk30 @ sk5 )
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ( sk5 @ sk4 ) ),
inference(prim_subst,[status(thm)],[64:[bind(A,$thf( sk5 ))]]) ).
thf(11,plain,
~ ( sk5 @ sk4 ),
inference(cnf,[status(esa)],[3]) ).
thf(5126,plain,
( ~ sk6
| ( sk30 @ sk5 )
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| $false ),
inference(rewrite,[status(thm)],[3973,11]) ).
thf(5127,plain,
( ~ sk6
| ( sk30 @ sk5 )
| ~ ( sk5 @ ( sk33 @ sk5 ) ) ),
inference(simp,[status(thm)],[5126]) ).
thf(10,plain,
! [A: a > $o] :
( ~ sk6
| ~ ( A @ ( sk31 @ A ) )
| ~ ( sk30 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(47,plain,
! [A: a > $o] :
( ~ sk6
| ~ ( A @ ( sk31 @ A ) )
| ~ ( sk30 @ A )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[10]) ).
thf(86,plain,
( ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ~ ( sk30 @ sk5 )
| ( sk5 @ sk4 ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( sk5 ))]]) ).
thf(121,plain,
( ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ~ ( sk30 @ sk5 )
| $false ),
inference(rewrite,[status(thm)],[86,11]) ).
thf(122,plain,
( ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ~ ( sk30 @ sk5 ) ),
inference(simp,[status(thm)],[121]) ).
thf(5200,plain,
( ~ sk6
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk30 @ sk5 )
!= ( sk30 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[5127,122]) ).
thf(5201,plain,
( ~ sk6
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ~ ( sk5 @ ( sk31 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[5200:[]]) ).
thf(5314,plain,
( ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5 @ ( sk31 @ sk5 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[5201]) ).
thf(5320,plain,
( ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk33 @ sk5 )
!= ( sk31 @ sk5 ) ) ),
inference(simp,[status(thm)],[5314]) ).
thf(5,plain,
! [A: a > $o] :
( ( sk1 @ sk8 @ ( sk11 @ A ) )
| ( sk1 @ ( sk12 @ A ) @ ( sk13 @ A ) )
| ( A @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(46,plain,
! [A: a > $o] :
( ( sk1 @ sk8 @ ( sk11 @ A ) )
| ( sk1 @ ( sk12 @ A ) @ ( sk13 @ A ) )
| ( A @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[5]) ).
thf(221,plain,
! [A: a > $o] :
( ( sk1 @ sk8 @ ( sk11 @ A ) )
| ( sk1 @ ( sk12 @ A ) @ ( sk13 @ A ) )
| sk10
| ~ sk7
| sk6
| ( ( A @ sk9 )
!= ( sk1 @ ( sk12 @ A ) @ ( sk13 @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[46]) ).
thf(249,plain,
! [A: a > $o] :
( ( sk1 @ sk8 @ ( sk11 @ A ) )
| ( sk1 @ ( sk12 @ A ) @ ( sk13 @ A ) )
| sk10
| sk6
| ~ sk7
| ( ( A @ sk9 )
!= ( sk1 @ ( sk12 @ A ) @ ( sk13 @ A ) ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(43,plain,
! [A: a > $o] :
( ~ sk6
| ( sk30 @ A )
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(76,plain,
! [A: a > $o] :
( ~ sk6
| ( sk30 @ A )
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[43]) ).
thf(9398,plain,
! [A: a > $o] :
( ~ sk6
| ( sk30 @ A )
| ( A @ sk4 )
| ( ( A @ ( sk32 @ A ) )
!= ~ sk6 )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[76]) ).
thf(9553,plain,
( ~ sk6
| ( sk30
@ ^ [A: a] : ~ sk6 )
| ~ sk6 ),
inference(pre_uni,[status(thm)],[9398:[bind(A,$thf( ^ [B: a] : ~ ( sk6 ) ))]]) ).
thf(9730,plain,
( ~ sk6
| ( sk30
@ ^ [A: a] : ~ sk6 )
| ~ sk6 ),
inference(cnf,[status(esa)],[9553]) ).
thf(9731,plain,
( ~ sk6
| ( sk30
@ ^ [A: a] : ~ sk6 ) ),
inference(simp,[status(thm)],[9730]) ).
thf(3969,plain,
( ~ sk6
| ( sk30 @ sk17 )
| ~ ( sk17 @ ( sk33 @ sk17 ) )
| ( sk17 @ sk4 ) ),
inference(prim_subst,[status(thm)],[64:[bind(A,$thf( sk17 ))]]) ).
thf(96,plain,
! [A: a > $o] :
( ~ sk6
| ~ ~ ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
| ~ ( sk30
@ ^ [B: a] :
~ ( A @ B ) )
| ~ ( A @ sk4 ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [C: a] : ~ ( B @ C ) ))]]) ).
thf(107,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ~ ( sk30
@ ^ [B: a] :
~ ( A @ B ) )
| ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[96]) ).
thf(108,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ~ ( sk30
@ ^ [B: a] :
~ ( A @ B ) )
| ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
| ~ sk6 ),
inference(simp,[status(thm)],[107]) ).
thf(460,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ~ ( sk30
@ ^ [B: a] :
~ ( A @ B ) )
| ~ sk6
| ( ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( ~ ( sk30
@ ^ [B: a] :
~ ( A @ B ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[108]) ).
thf(482,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ~ ( sk30
@ ^ [B: a] :
~ ( A @ B ) )
| ~ sk6
| ( ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( ~ ( sk30
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(simp,[status(thm)],[460]) ).
thf(2733,plain,
( ~ sk6
| ~ ( sk30
@ ^ [A: a] : ~ sk6 )
| ~ sk6
| ( ( ~ ( sk30
@ ^ [A: a] : ~ sk6 ) )
!= sk6 ) ),
inference(prim_subst,[status(thm)],[482:[bind(A,$thf( ^ [B: a] : sk6 ))]]) ).
thf(2768,plain,
( ~ sk6
| ~ ( sk30
@ ^ [A: a] : ~ sk6 )
| ( ( ~ ( sk30
@ ^ [A: a] : ~ sk6 ) )
!= sk6 ) ),
inference(simp,[status(thm)],[2733]) ).
thf(2807,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ~ ( sk30
@ ^ [B: a] :
~ ( A @ B ) )
| ~ sk6
| ~ ( sk30
@ ^ [B: a] : ~ sk6 )
| ( ( ~ ( sk30
@ ^ [B: a] : $false ) )
!= sk6 )
| ( ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
!= sk6 ) ),
inference(paramod_ordered,[status(thm)],[108,2768]) ).
thf(2832,plain,
( ~ sk6
| ~ ( sk30
@ ^ [A: a] : ~ sk6 )
| ~ sk6
| ~ ( sk30
@ ^ [A: a] : ~ sk6 )
| ( ( ~ ( sk30
@ ^ [A: a] : $false ) )
!= sk6 ) ),
inference(pre_uni,[status(thm)],[2807:[bind(A,$thf( ^ [B: a] : sk6 ))]]) ).
thf(2847,plain,
( ~ sk6
| ~ ( sk30
@ ^ [A: a] : ~ sk6 )
| ( ( ~ ( sk30
@ ^ [A: a] : $false ) )
!= sk6 ) ),
inference(simp,[status(thm)],[2832]) ).
thf(2862,plain,
( ~ sk6
| ~ ( sk30
@ ^ [A: a] : ~ sk6 )
| ~ ~ ( sk30
@ ^ [A: a] : $false )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[2847]) ).
thf(2919,plain,
( ~ sk6
| ( sk30
@ ^ [A: a] : $false )
| ~ ( sk30
@ ^ [A: a] : ~ sk6 )
| ~ sk6 ),
inference(cnf,[status(esa)],[2862]) ).
thf(2920,plain,
( ~ sk6
| ( sk30
@ ^ [A: a] : $false )
| ~ ( sk30
@ ^ [A: a] : ~ sk6 ) ),
inference(simp,[status(thm)],[2919]) ).
thf(9240,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ( sk30
@ ^ [B: a] : $false )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[76,2920]) ).
thf(9241,plain,
( ~ sk6
| ~ sk6
| ~ sk6
| ( sk30
@ ^ [A: a] : $false ) ),
inference(pattern_uni,[status(thm)],[9240:[bind(A,$thf( ^ [B: a] : ~ ( sk6 ) ))]]) ).
thf(9624,plain,
( ( sk30
@ ^ [A: a] : $false )
| ~ sk6
| ~ sk6
| ~ sk6 ),
inference(cnf,[status(esa)],[9241]) ).
thf(9625,plain,
( ( sk30
@ ^ [A: a] : $false )
| ~ sk6 ),
inference(simp,[status(thm)],[9624]) ).
thf(9356,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ( ( ~ ( sk30
@ ^ [B: a] : $false ) )
!= sk6 )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[76,2847]) ).
thf(9357,plain,
( ~ sk6
| ~ sk6
| ~ sk6
| ( ( ~ ( sk30
@ ^ [A: a] : $false ) )
!= sk6 ) ),
inference(pattern_uni,[status(thm)],[9356:[bind(A,$thf( ^ [B: a] : ~ ( sk6 ) ))]]) ).
thf(9644,plain,
( ( ( ~ ( sk30
@ ^ [A: a] : $false ) )
!= sk6 )
| ~ sk6
| ~ sk6
| ~ sk6 ),
inference(cnf,[status(esa)],[9357]) ).
thf(9645,plain,
( ( ( ~ ( sk30
@ ^ [A: a] : $false ) )
!= sk6 )
| ~ sk6 ),
inference(simp,[status(thm)],[9644]) ).
thf(11260,plain,
! [A: a > $o] :
( ~ sk6
| ( sk30 @ A )
| ( A @ sk4 )
| ( ( A @ ( sk32 @ A ) )
!= ( ~ ( sk30
@ ^ [B: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,9645]) ).
thf(11289,plain,
( ~ sk6
| ( sk30
@ ^ [A: a] :
~ ( sk30
@ ^ [B: a] : $false ) )
| ~ ( sk30
@ ^ [A: a] : $false ) ),
inference(pre_uni,[status(thm)],[11260:[bind(A,$thf( ^ [B: a] : ~ ( sk30 @ ^ [C: a] : $false ) ))]]) ).
thf(11309,plain,
( ~ ( sk30
@ ^ [A: a] : $false )
| ( sk30
@ ^ [A: a] :
~ ( sk30
@ ^ [B: a] : $false ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[11289]) ).
thf(17187,plain,
( ~ sk6
| ( sk30
@ ^ [A: a] :
~ ( sk30
@ ^ [B: a] : $false ) )
| ( ( sk30
@ ^ [A: a] : $false )
!= ( sk30
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[9625,11309]) ).
thf(17188,plain,
( ~ sk6
| ( sk30
@ ^ [A: a] :
~ ( sk30
@ ^ [B: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[17187:[]]) ).
thf(15,plain,
! [A: a > $o] :
( ~ sk6
| ( sk1 @ sk3 @ ( sk31 @ A ) )
| ( sk2 @ sk3 @ ( sk31 @ A ) )
| ~ ( sk30 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(55,plain,
! [A: a > $o] :
( ~ sk6
| ( sk1 @ sk3 @ ( sk31 @ A ) )
| ( sk2 @ sk3 @ ( sk31 @ A ) )
| ~ ( sk30 @ A )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[15]) ).
thf(1746,plain,
( ~ sk6
| ( sk1 @ sk3
@ ( sk31
@ ^ [A: a] : $false ) )
| ( sk2 @ sk3
@ ( sk31
@ ^ [A: a] : $false ) )
| ~ ( sk30
@ ^ [A: a] : $false )
| $false ),
inference(prim_subst,[status(thm)],[55:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(1773,plain,
( ~ sk6
| ( sk1 @ sk3
@ ( sk31
@ ^ [A: a] : $false ) )
| ( sk2 @ sk3
@ ( sk31
@ ^ [A: a] : $false ) )
| ~ ( sk30
@ ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[1746]) ).
thf(38,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ( sk5 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(1898,plain,
! [A: a] :
( ~ sk6
| ( sk1 @ sk3
@ ( sk31
@ ^ [B: a] : $false ) )
| ~ ( sk30
@ ^ [B: a] : $false )
| ( sk5 @ A )
| ( ( sk2 @ sk3
@ ( sk31
@ ^ [B: a] : $false ) )
!= ( sk2 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1773,38]) ).
thf(1899,plain,
( ~ sk6
| ( sk1 @ sk3
@ ( sk31
@ ^ [A: a] : $false ) )
| ~ ( sk30
@ ^ [A: a] : $false )
| ( sk5
@ ( sk31
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[1898:[bind(A,$thf( sk31 @ ^ [B: a] : $false ))]]) ).
thf(18,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ( sk5 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(3565,plain,
! [A: a] :
( ~ sk6
| ~ ( sk30
@ ^ [B: a] : $false )
| ( sk5
@ ( sk31
@ ^ [B: a] : $false ) )
| ( sk5 @ A )
| ( ( sk1 @ sk3
@ ( sk31
@ ^ [B: a] : $false ) )
!= ( sk1 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1899,18]) ).
thf(3566,plain,
( ~ sk6
| ~ ( sk30
@ ^ [A: a] : $false )
| ( sk5
@ ( sk31
@ ^ [A: a] : $false ) )
| ( sk5
@ ( sk31
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[3565:[bind(A,$thf( sk31 @ ^ [B: a] : $false ))]]) ).
thf(3601,plain,
( ~ sk6
| ~ ( sk30
@ ^ [A: a] : $false )
| ( sk5
@ ( sk31
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[3566]) ).
thf(3642,plain,
( ~ sk6
| ~ ( sk30
@ ^ [A: a] : $false )
| ~ ( sk30 @ sk5 )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5
@ ( sk31
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[3601,122]) ).
thf(3654,plain,
( ~ sk6
| ~ ( sk30
@ ^ [A: a] : $false )
| ~ ( sk30 @ sk5 )
| ( ( sk31 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[3642]) ).
thf(3701,plain,
( ~ sk6
| ~ ( sk30
@ ^ [A: a] : $false )
| ~ ( sk30 @ sk5 )
| ( sk5
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[3654]) ).
thf(3756,plain,
( ~ sk6
| ~ ( sk30
@ ^ [A: a] : $false )
| ( sk5
!= ( ^ [A: a] : $false ) )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : $false ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3701]) ).
thf(3760,plain,
( ~ sk6
| ~ ( sk30
@ ^ [A: a] : $false )
| ( sk5
!= ( ^ [A: a] : $false ) )
| ( sk5
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[3756]) ).
thf(3767,plain,
( ~ sk6
| ~ ( sk30
@ ^ [A: a] : $false )
| ( sk5
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[3760]) ).
thf(3773,plain,
( ( sk5 @ sk35 )
| ~ sk6
| ~ ( sk30
@ ^ [A: a] : $false ) ),
inference(func_ext,[status(esa)],[3767]) ).
thf(9185,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ( sk5 @ sk35 )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[76,3773]) ).
thf(9186,plain,
( ~ sk6
| $false
| $false
| ( sk5 @ sk35 ) ),
inference(pattern_uni,[status(thm)],[9185:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(9770,plain,
( ~ sk6
| ( sk5 @ sk35 ) ),
inference(simp,[status(thm)],[9186]) ).
thf(9991,plain,
( ~ sk6
| ~ ( sk30 @ sk5 )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[9770,122]) ).
thf(10019,plain,
( ~ sk6
| ~ ( sk30 @ sk5 )
| ( ( sk31 @ sk5 )
!= sk35 ) ),
inference(simp,[status(thm)],[9991]) ).
thf(17529,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= sk35 )
| ( ( sk30
@ ^ [A: a] :
~ ( sk30
@ ^ [B: a] : $false ) )
!= ( sk30 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[17188,10019]) ).
thf(17656,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= sk35 )
| ( ( ^ [A: a] :
~ ( sk30
@ ^ [B: a] : $false ) )
!= sk5 ) ),
inference(simp,[status(thm)],[17529]) ).
thf(35,plain,
! [A: a > $o] :
( ~ sk10
| ( sk2 @ sk8 @ ( sk14 @ A ) )
| ( A @ ( sk15 @ A ) )
| ( A @ sk9 )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(52,plain,
! [A: a > $o] :
( ~ sk10
| ( sk2 @ sk8 @ ( sk14 @ A ) )
| ( A @ ( sk15 @ A ) )
| ( A @ sk9 )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[35]) ).
thf(665,plain,
( ~ sk10
| ( sk2 @ sk8
@ ( sk14
@ ^ [A: a] : sk6 ) )
| sk6
| sk6
| ~ sk7
| sk6 ),
inference(prim_subst,[status(thm)],[52:[bind(A,$thf( ^ [B: a] : sk6 ))]]) ).
thf(722,plain,
( ~ sk10
| ( sk2 @ sk8
@ ( sk14
@ ^ [A: a] : sk6 ) )
| sk6
| ~ sk7 ),
inference(simp,[status(thm)],[665]) ).
thf(759,plain,
! [A: a] :
( ~ sk10
| sk6
| ~ sk7
| ( sk5 @ A )
| ( ( sk2 @ sk8
@ ( sk14
@ ^ [B: a] : sk6 ) )
!= ( sk2 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[722,38]) ).
thf(772,plain,
! [A: a] :
( sk6
| ( sk5 @ A )
| ~ sk10
| ~ sk7
| ( sk8 != sk3 )
| ( ( sk14
@ ^ [B: a] : sk6 )
!= A ) ),
inference(simp,[status(thm)],[759]) ).
thf(776,plain,
( sk6
| ( sk5
@ ( sk14
@ ^ [A: a] : sk6 ) )
| ~ sk10
| ~ sk7
| ( sk8 != sk3 ) ),
inference(simp,[status(thm)],[772]) ).
thf(1387,plain,
( sk6
| ~ sk10
| ~ sk7
| ( sk8 != sk3 )
| ( ( sk5
@ ( sk14
@ ^ [A: a] : sk6 ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[776,11]) ).
thf(1406,plain,
( sk6
| ~ sk10
| ~ sk7
| ( sk8 != sk3 )
| ( ( sk14
@ ^ [A: a] : sk6 )
!= sk4 ) ),
inference(simp,[status(thm)],[1387]) ).
thf(32,plain,
! [A: a > $o] :
( ( sk1 @ sk8 @ ( sk11 @ A ) )
| ( A @ ( sk12 @ A ) )
| ( A @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(67,plain,
! [A: a > $o] :
( ( sk1 @ sk8 @ ( sk11 @ A ) )
| ( A @ ( sk12 @ A ) )
| ( A @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[32]) ).
thf(5666,plain,
( ( sk1 @ sk8
@ ( sk11
@ ^ [A: a] : sk6 ) )
| sk6
| sk6
| sk10
| ~ sk7
| sk6 ),
inference(prim_subst,[status(thm)],[67:[bind(A,$thf( ^ [B: a] : sk6 ))]]) ).
thf(5786,plain,
( ( sk1 @ sk8
@ ( sk11
@ ^ [A: a] : sk6 ) )
| sk6
| sk10
| ~ sk7 ),
inference(simp,[status(thm)],[5666]) ).
thf(31,plain,
! [A: a] :
( ~ ( sk1 @ sk8 @ A )
| ( sk17 @ A )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(75,plain,
! [A: a] :
( ~ ( sk1 @ sk8 @ A )
| ( sk17 @ A )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[31]) ).
thf(8550,plain,
! [A: a] :
( sk6
| sk10
| ~ sk7
| ( sk17 @ A )
| ( ( sk1 @ sk8
@ ( sk11
@ ^ [B: a] : sk6 ) )
!= ( sk1 @ sk8 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5786,75]) ).
thf(8551,plain,
( sk6
| sk10
| ~ sk7
| ( sk17
@ ( sk11
@ ^ [A: a] : sk6 ) ) ),
inference(pattern_uni,[status(thm)],[8550:[bind(A,$thf( sk11 @ ^ [B: a] : sk6 ))]]) ).
thf(42,plain,
( ~ ( sk17 @ sk9 )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(8673,plain,
( sk6
| sk10
| ~ sk7
| ( ( sk17
@ ( sk11
@ ^ [A: a] : sk6 ) )
!= ( sk17 @ sk9 ) ) ),
inference(paramod_ordered,[status(thm)],[8551,42]) ).
thf(8723,plain,
( sk6
| sk10
| ~ sk7
| ( ( sk11
@ ^ [A: a] : sk6 )
!= sk9 ) ),
inference(simp,[status(thm)],[8673]) ).
thf(675,plain,
( ~ sk10
| ( sk2 @ sk8
@ ( sk14
@ ^ [A: a] : $false ) )
| $false
| $false
| ~ sk7
| sk6 ),
inference(prim_subst,[status(thm)],[52:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(730,plain,
( ~ sk10
| ( sk2 @ sk8
@ ( sk14
@ ^ [A: a] : $false ) )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[675]) ).
thf(656,plain,
! [A: a > $o] :
( ~ sk10
| ( sk2 @ sk8 @ ( sk14 @ A ) )
| ( A @ sk9 )
| ~ sk7
| sk6
| ( ( A @ ( sk15 @ A ) )
!= ~ sk10 )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[52]) ).
thf(705,plain,
( ~ sk10
| ( sk2 @ sk8
@ ( sk14
@ ^ [A: a] : ~ sk10 ) )
| ~ sk10
| ~ sk7
| sk6 ),
inference(pre_uni,[status(thm)],[656:[bind(A,$thf( ^ [B: a] : ~ ( sk10 ) ))]]) ).
thf(712,plain,
( sk6
| ~ sk7
| ~ sk10
| ( sk2 @ sk8
@ ( sk14
@ ^ [A: a] : ~ sk10 ) )
| ~ sk10 ),
inference(cnf,[status(esa)],[705]) ).
thf(713,plain,
( sk6
| ~ sk7
| ~ sk10
| ( sk2 @ sk8
@ ( sk14
@ ^ [A: a] : ~ sk10 ) ) ),
inference(simp,[status(thm)],[712]) ).
thf(24,plain,
! [A: a] :
( ~ ( sk2 @ sk8 @ A )
| ( sk17 @ A )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(56,plain,
! [A: a] :
( ~ ( sk2 @ sk8 @ A )
| ( sk17 @ A )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[24]) ).
thf(1521,plain,
! [A: a] :
( sk6
| ~ sk7
| ~ sk10
| ( sk17 @ A )
| ( ( sk2 @ sk8
@ ( sk14
@ ^ [B: a] : ~ sk10 ) )
!= ( sk2 @ sk8 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[713,56]) ).
thf(1522,plain,
( sk6
| ~ sk7
| ~ sk10
| ( sk17
@ ( sk14
@ ^ [A: a] : ~ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[1521:[bind(A,$thf( sk14 @ ^ [B: a] : ~ ( sk10 ) ))]]) ).
thf(5671,plain,
( ( sk1 @ sk8
@ ( sk11
@ ^ [A: a] : $false ) )
| $false
| $false
| sk10
| ~ sk7
| sk6 ),
inference(prim_subst,[status(thm)],[67:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(5793,plain,
( ( sk1 @ sk8
@ ( sk11
@ ^ [A: a] : $false ) )
| sk10
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[5671]) ).
thf(9419,plain,
( ~ sk6
| ( sk30
@ ^ [A: a] : sk7 )
| sk7
| sk7 ),
inference(prim_subst,[status(thm)],[76:[bind(A,$thf( ^ [B: a] : sk7 ))]]) ).
thf(9664,plain,
( ~ sk6
| ( sk30
@ ^ [A: a] : sk7 )
| sk7 ),
inference(simp,[status(thm)],[9419]) ).
thf(3735,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ~ ( sk30
@ ^ [A: a] : $false )
| ~ ( sk30 @ sk5 ) ),
inference(func_ext,[status(esa)],[3701]) ).
thf(9110,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ( sk5 @ sk34 )
| ~ ( sk30 @ sk5 )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[76,3735]) ).
thf(9111,plain,
( ~ sk6
| $false
| $false
| ( sk5 @ sk34 )
| ~ ( sk30 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[9110:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(9765,plain,
( ~ sk6
| ( sk5 @ sk34 )
| ~ ( sk30 @ sk5 ) ),
inference(simp,[status(thm)],[9111]) ).
thf(11992,plain,
( ~ sk6
| sk7
| ( sk5 @ sk34 )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[9664,9765]) ).
thf(12011,plain,
( sk7
| ( sk5 @ sk34 )
| ~ sk6
| ( sk5
!= ( ^ [A: a] : sk7 ) ) ),
inference(simp,[status(thm)],[11992]) ).
thf(14446,plain,
( ( ( sk5 @ sk43 )
!= sk7 )
| sk7
| ( sk5 @ sk34 )
| ~ sk6 ),
inference(func_ext,[status(esa)],[12011]) ).
thf(17514,plain,
( ~ sk6
| ( sk5 @ sk34 )
| ( ( sk30
@ ^ [A: a] :
~ ( sk30
@ ^ [B: a] : $false ) )
!= ( sk30 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[17188,9765]) ).
thf(17612,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( ( ^ [A: a] :
~ ( sk30
@ ^ [B: a] : $false ) )
!= sk5 ) ),
inference(simp,[status(thm)],[17514]) ).
thf(20637,plain,
( ~ sk6
| ( ( ^ [A: a] :
~ ( sk30
@ ^ [B: a] : $false ) )
!= sk5 )
| ( ( sk5 @ sk34 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[17612,11]) ).
thf(20658,plain,
( ~ sk6
| ( ( ^ [A: a] :
~ ( sk30
@ ^ [B: a] : $false ) )
!= sk5 )
| ( sk34 != sk4 ) ),
inference(simp,[status(thm)],[20637]) ).
thf(5152,plain,
( ~ sk6
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ( sk5 @ sk34 )
| ~ ( sk30
@ ^ [A: a] : $false )
| ( ( sk30 @ sk5 )
!= ( sk30 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[5127,3735]) ).
thf(5153,plain,
( ~ sk6
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ( sk5 @ sk34 )
| ~ ( sk30
@ ^ [A: a] : $false ) ),
inference(pattern_uni,[status(thm)],[5152:[]]) ).
thf(9171,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ( sk5 @ sk34 )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[76,5153]) ).
thf(9172,plain,
( ~ sk6
| $false
| $false
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ( sk5 @ sk34 ) ),
inference(pattern_uni,[status(thm)],[9171:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(9769,plain,
( ~ sk6
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ( sk5 @ sk34 ) ),
inference(simp,[status(thm)],[9172]) ).
thf(95,plain,
! [A: a > a > $o] :
( ~ sk6
| ~ ( sk25
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) ) ) )
| ~ ( sk30
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) )
| ( sk25 @ ( A @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [C: a] : ( sk25 @ ( B @ C ) ) ))]]) ).
thf(120,plain,
! [A: a > a > $o] :
( ~ sk6
| ~ ( sk25
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) ) ) )
| ~ ( sk30
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) )
| ( sk25 @ ( A @ sk4 ) ) ),
inference(simp,[status(thm)],[95]) ).
thf(202,plain,
! [A: a > $o] :
( ( sk1 @ sk8 @ ( sk11 @ A ) )
| ( sk1 @ ( sk12 @ A ) @ ( sk13 @ A ) )
| sk10
| ~ sk7
| sk6
| ( ( A @ sk9 )
!= ( sk17 @ sk9 ) ) ),
inference(paramod_ordered,[status(thm)],[46,42]) ).
thf(247,plain,
( ( sk1 @ sk8 @ ( sk11 @ sk17 ) )
| ( sk1 @ ( sk12 @ sk17 ) @ ( sk13 @ sk17 ) )
| sk10
| ~ sk7
| sk6 ),
inference(pre_uni,[status(thm)],[202:[bind(A,$thf( sk17 ))]]) ).
thf(20530,plain,
( ( ( ~ ( sk30
@ ^ [A: a] : $false ) )
!= ( sk5 @ sk51 ) )
| ( sk5 @ sk34 )
| ~ sk6 ),
inference(func_ext,[status(esa)],[17612]) ).
thf(27052,plain,
( ~ sk6
| ( sk5 @ sk51 )
| ( sk5 @ sk34 )
| ( ( sk30
@ ^ [A: a] : $false )
!= ( sk30
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[9625,20530]) ).
thf(27053,plain,
( ~ sk6
| ( sk5 @ sk51 )
| ( sk5 @ sk34 ) ),
inference(pattern_uni,[status(thm)],[27052:[]]) ).
thf(27464,plain,
( ~ sk6
| ( sk5 @ sk34 )
| ( ( sk5 @ sk51 )
!= ( sk5 @ sk34 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[27053]) ).
thf(27492,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( sk51 != sk34 ) ),
inference(simp,[status(thm)],[27464]) ).
thf(2739,plain,
( ~ sk10
| ~ ( sk30
@ ^ [A: a] : ~ sk10 )
| ~ sk6
| ( ( ~ ( sk30
@ ^ [A: a] : ~ sk10 ) )
!= sk10 ) ),
inference(prim_subst,[status(thm)],[482:[bind(A,$thf( ^ [B: a] : sk10 ))]]) ).
thf(9301,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ~ sk10
| ( ( ~ ( sk30
@ ^ [B: a] : ~ sk10 ) )
!= sk10 )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : ~ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[76,2739]) ).
thf(9302,plain,
( ~ sk6
| ~ sk10
| ~ sk10
| ~ sk10
| ( ( ~ ( sk30
@ ^ [A: a] : ~ sk10 ) )
!= sk10 ) ),
inference(pattern_uni,[status(thm)],[9301:[bind(A,$thf( ^ [B: a] : ~ ( sk10 ) ))]]) ).
thf(9637,plain,
( ( ( ~ ( sk30
@ ^ [A: a] : ~ sk10 ) )
!= sk10 )
| ~ sk10
| ~ sk10
| ~ sk10
| ~ sk6 ),
inference(cnf,[status(esa)],[9302]) ).
thf(9638,plain,
( ( ( ~ ( sk30
@ ^ [A: a] : ~ sk10 ) )
!= sk10 )
| ~ sk10
| ~ sk6 ),
inference(simp,[status(thm)],[9637]) ).
thf(13203,plain,
( ~ sk10
| ~ sk6
| ~ ~ ( sk30
@ ^ [A: a] : ~ sk10 )
| ~ sk10 ),
inference(bool_ext,[status(thm)],[9638]) ).
thf(13303,plain,
( ~ sk10
| ( sk30
@ ^ [A: a] : ~ sk10 )
| ~ sk6
| ~ sk10 ),
inference(cnf,[status(esa)],[13203]) ).
thf(13304,plain,
( ~ sk10
| ( sk30
@ ^ [A: a] : ~ sk10 )
| ~ sk6 ),
inference(simp,[status(thm)],[13303]) ).
thf(13451,plain,
( ~ sk10
| ~ sk6
| ( sk5 @ sk34 )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : ~ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[13304,9765]) ).
thf(13538,plain,
( ( sk5 @ sk34 )
| ~ sk10
| ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk10 ) ) ),
inference(simp,[status(thm)],[13451]) ).
thf(24914,plain,
( ~ sk10
| ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk10 ) )
| ( ( sk5 @ sk34 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[13538,11]) ).
thf(24946,plain,
( ~ sk10
| ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk10 ) )
| ( sk34 != sk4 ) ),
inference(simp,[status(thm)],[24914]) ).
thf(11963,plain,
( ~ sk6
| ( sk5 @ sk34 )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[9731,9765]) ).
thf(12001,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[11963]) ).
thf(14010,plain,
( ( ( sk5 @ sk40 )
!= ~ sk6 )
| ( sk5 @ sk34 )
| ~ sk6 ),
inference(func_ext,[status(esa)],[12001]) ).
thf(18158,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( sk5 @ sk40 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[14010]) ).
thf(18208,plain,
( ~ sk6
| ( sk5 @ sk40 )
| ~ sk6
| ( sk5 @ sk34 ) ),
inference(cnf,[status(esa)],[18158]) ).
thf(18209,plain,
( ~ sk6
| ( sk5 @ sk40 )
| ( sk5 @ sk34 ) ),
inference(simp,[status(thm)],[18208]) ).
thf(18271,plain,
( ~ sk6
| ( sk5 @ sk34 )
| ( ( sk5 @ sk40 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18209,11]) ).
thf(18295,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( sk40 != sk4 ) ),
inference(simp,[status(thm)],[18271]) ).
thf(18408,plain,
( ~ sk6
| ( sk40 != sk4 )
| ~ ( sk30 @ sk5 )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk34 ) ) ),
inference(paramod_ordered,[status(thm)],[18295,122]) ).
thf(18438,plain,
( ~ sk6
| ( sk40 != sk4 )
| ~ ( sk30 @ sk5 )
| ( ( sk31 @ sk5 )
!= sk34 ) ),
inference(simp,[status(thm)],[18408]) ).
thf(14054,plain,
( ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk6 ) )
| ( ( sk5 @ sk34 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[12001,11]) ).
thf(14084,plain,
( ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk6 ) )
| ( sk34 != sk4 ) ),
inference(simp,[status(thm)],[14054]) ).
thf(13,plain,
! [A: a > $o] :
( sk7
| ( sk25 @ A )
| ( A @ ( sk27 @ A ) )
| ( A @ sk20 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(63,plain,
! [A: a > $o] :
( sk7
| ( sk25 @ A )
| ( A @ ( sk27 @ A ) )
| ( A @ sk20 )
| sk6 ),
inference(simp,[status(thm)],[13]) ).
thf(2087,plain,
( sk7
| ( sk25
@ ^ [A: a] : sk7 )
| sk7
| sk7
| sk6 ),
inference(prim_subst,[status(thm)],[63:[bind(A,$thf( ^ [B: a] : sk7 ))]]) ).
thf(2168,plain,
( sk7
| ( sk25
@ ^ [A: a] : sk7 )
| sk6 ),
inference(simp,[status(thm)],[2087]) ).
thf(9416,plain,
( ~ sk6
| ( sk30
@ ^ [A: a] : sk10 )
| sk10
| sk10 ),
inference(prim_subst,[status(thm)],[76:[bind(A,$thf( ^ [B: a] : sk10 ))]]) ).
thf(9661,plain,
( ~ sk6
| ( sk30
@ ^ [A: a] : sk10 )
| sk10 ),
inference(simp,[status(thm)],[9416]) ).
thf(11974,plain,
( ~ sk6
| sk10
| ( sk5 @ sk34 )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[9661,9765]) ).
thf(12009,plain,
( sk10
| ( sk5 @ sk34 )
| ~ sk6
| ( sk5
!= ( ^ [A: a] : sk10 ) ) ),
inference(simp,[status(thm)],[11974]) ).
thf(14349,plain,
( ( ( sk5 @ sk42 )
!= sk10 )
| sk10
| ( sk5 @ sk34 )
| ~ sk6 ),
inference(func_ext,[status(esa)],[12009]) ).
thf(28795,plain,
( sk10
| ( sk5 @ sk34 )
| ~ sk6
| ( sk5 @ sk42 )
| sk10 ),
inference(bool_ext,[status(thm)],[14349]) ).
thf(28871,plain,
( sk10
| ( sk5 @ sk34 )
| ~ sk6
| ( sk5 @ sk42 ) ),
inference(simp,[status(thm)],[28795]) ).
thf(28942,plain,
( sk10
| ( sk5 @ sk34 )
| ~ sk6
| ( ( sk5 @ sk42 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[28871,11]) ).
thf(28982,plain,
( sk10
| ( sk5 @ sk34 )
| ~ sk6
| ( sk42 != sk4 ) ),
inference(simp,[status(thm)],[28942]) ).
thf(29376,plain,
( sk10
| ~ sk6
| ( sk42 != sk4 )
| ( ( sk5 @ sk34 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[28982,11]) ).
thf(29401,plain,
( sk10
| ~ sk6
| ( sk42 != sk4 )
| ( sk34 != sk4 ) ),
inference(simp,[status(thm)],[29376]) ).
thf(9,plain,
! [A: a > $o] :
( sk7
| ( sk21 @ A )
| ( A @ ( sk23 @ A ) )
| ( A @ sk19 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(50,plain,
! [A: a > $o] :
( sk7
| ( sk21 @ A )
| ( A @ ( sk23 @ A ) )
| ( A @ sk19 )
| sk6 ),
inference(simp,[status(thm)],[9]) ).
thf(154,plain,
( sk7
| ( sk21
@ ^ [A: a] : sk10 )
| sk10
| sk10
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( ^ [B: a] : sk10 ))]]) ).
thf(185,plain,
( sk7
| ( sk21
@ ^ [A: a] : sk10 )
| sk10
| sk6 ),
inference(simp,[status(thm)],[154]) ).
thf(9340,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ( sk5
@ ( sk31
@ ^ [B: a] : $false ) )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[76,3601]) ).
thf(9341,plain,
( ~ sk6
| $false
| $false
| ( sk5
@ ( sk31
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[9340:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(9641,plain,
( ~ sk6
| ( sk5
@ ( sk31
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[9341]) ).
thf(5319,plain,
( ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5 @ ( sk31 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[5314]) ).
thf(9982,plain,
( ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5 @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[9770,5319]) ).
thf(9994,plain,
( ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk33 @ sk5 )
!= sk35 ) ),
inference(simp,[status(thm)],[9982]) ).
thf(14304,plain,
( ~ sk6
| ( ( sk33 @ sk5 )
!= sk35 )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5
@ ( sk31
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[9641,9994]) ).
thf(14333,plain,
( ~ sk6
| ( ( sk33 @ sk5 )
!= sk35 )
| ( ( sk31 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[14304]) ).
thf(31254,plain,
( sk7
| ( sk5 @ sk34 )
| ~ sk6
| ( sk5 @ sk43 )
| sk7 ),
inference(bool_ext,[status(thm)],[14446]) ).
thf(31325,plain,
( sk7
| ( sk5 @ sk34 )
| ~ sk6
| ( sk5 @ sk43 ) ),
inference(simp,[status(thm)],[31254]) ).
thf(5149,plain,
( ~ sk6
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ( sk5
!= ( ^ [A: a] : $false ) )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[5127,3767]) ).
thf(5208,plain,
( ~ sk6
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ( sk5
!= ( ^ [A: a] : $false ) )
| ( sk5
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[5149]) ).
thf(5246,plain,
( ~ sk6
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ( sk5
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[5208]) ).
thf(5252,plain,
( ( sk5 @ sk36 )
| ~ sk6
| ~ ( sk5 @ ( sk33 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[5246]) ).
thf(1511,plain,
! [A: a] :
( ~ sk10
| ~ sk7
| sk6
| ( sk17 @ A )
| ( ( sk2 @ sk8
@ ( sk14
@ ^ [B: a] : $false ) )
!= ( sk2 @ sk8 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[730,56]) ).
thf(1512,plain,
( ~ sk10
| ~ sk7
| sk6
| ( sk17
@ ( sk14
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[1511:[bind(A,$thf( sk14 @ ^ [B: a] : $false ))]]) ).
thf(1549,plain,
( ~ sk10
| ~ sk7
| sk6
| ( ( sk17
@ ( sk14
@ ^ [A: a] : $false ) )
!= ( sk17 @ sk9 ) ) ),
inference(paramod_ordered,[status(thm)],[1512,42]) ).
thf(1576,plain,
( sk6
| ~ sk10
| ~ sk7
| ( ( sk14
@ ^ [A: a] : $false )
!= sk9 ) ),
inference(simp,[status(thm)],[1549]) ).
thf(28963,plain,
( sk10
| ( sk5 @ sk34 )
| ~ sk6
| ( ( sk5 @ sk42 )
!= ( sk5 @ sk34 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[28871]) ).
thf(28989,plain,
( sk10
| ( sk5 @ sk34 )
| ~ sk6
| ( sk42 != sk34 ) ),
inference(simp,[status(thm)],[28963]) ).
thf(29532,plain,
( sk10
| ~ sk6
| ( sk42 != sk34 )
| ( ( sk5 @ sk34 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[28989,11]) ).
thf(29572,plain,
( sk10
| ~ sk6
| ( sk42 != sk34 )
| ( sk34 != sk4 ) ),
inference(simp,[status(thm)],[29532]) ).
thf(143,plain,
! [A: a > a > $o] :
( sk7
| ( sk21
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) )
| ( sk21
@ ( A
@ ( sk23
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) ) ) )
| ( sk21 @ ( A @ sk19 ) )
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( ^ [C: a] : ( sk21 @ ( B @ C ) ) ))]]) ).
thf(174,plain,
! [A: a > a > $o] :
( sk7
| ( sk21
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) )
| ( sk21
@ ( A
@ ( sk23
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) ) ) )
| ( sk21 @ ( A @ sk19 ) )
| sk6 ),
inference(simp,[status(thm)],[143]) ).
thf(153,plain,
! [A: a > a > $o] :
( sk7
| ( sk21
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) )
| ( sk25
@ ( A
@ ( sk23
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) ) ) )
| ( sk25 @ ( A @ sk19 ) )
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( ^ [C: a] : ( sk25 @ ( B @ C ) ) ))]]) ).
thf(184,plain,
! [A: a > a > $o] :
( sk7
| ( sk21
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) )
| ( sk25
@ ( A
@ ( sk23
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) ) ) )
| ( sk25 @ ( A @ sk19 ) )
| sk6 ),
inference(simp,[status(thm)],[153]) ).
thf(23,plain,
! [B: a,A: a] :
( ~ ( sk5 @ A )
| ~ ( sk2 @ A @ B )
| ( sk5 @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(79,plain,
! [B: a,A: a] :
( ~ ( sk5 @ A )
| ~ ( sk2 @ A @ B )
| ( sk5 @ B ) ),
inference(simp,[status(thm)],[23]) ).
thf(784,plain,
! [B: a,A: a] :
( ~ sk10
| ~ sk7
| sk6
| ~ ( sk5 @ A )
| ( sk5 @ B )
| ( ( sk2 @ sk8
@ ( sk14
@ ^ [C: a] : $false ) )
!= ( sk2 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[730,79]) ).
thf(785,plain,
( ~ sk10
| ~ sk7
| sk6
| ~ ( sk5 @ sk8 )
| ( sk5
@ ( sk14
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[784:[bind(A,$thf( sk8 )),bind(B,$thf( sk14 @ ^ [C: a] : $false ))]]) ).
thf(25278,plain,
( ( ( sk5 @ sk66 )
!= ~ sk10 )
| ~ sk10
| ~ sk6
| ( sk34 != sk4 ) ),
inference(func_ext,[status(esa)],[24946]) ).
thf(32066,plain,
( ~ sk10
| ~ sk6
| ( sk34 != sk4 )
| ( sk5 @ sk66 )
| ~ sk10 ),
inference(bool_ext,[status(thm)],[25278]) ).
thf(32160,plain,
( ~ sk10
| ( sk5 @ sk66 )
| ( sk34 != sk4 )
| ~ sk6
| ~ sk10 ),
inference(cnf,[status(esa)],[32066]) ).
thf(32161,plain,
( ~ sk10
| ( sk5 @ sk66 )
| ( sk34 != sk4 )
| ~ sk6 ),
inference(simp,[status(thm)],[32160]) ).
thf(18396,plain,
( ~ sk6
| ( sk40 != sk4 )
| ( ( sk5 @ sk34 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18295,11]) ).
thf(18436,plain,
( ~ sk6
| ( sk40 != sk4 )
| ( sk34 != sk4 ) ),
inference(simp,[status(thm)],[18396]) ).
thf(98,plain,
! [A: a > a] :
( ~ sk6
| ~ ( sk29
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) ) ) )
| ~ ( sk30
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) )
| ( sk29 @ ( A @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [C: a] : ( sk29 @ ( B @ C ) ) ))]]) ).
thf(110,plain,
! [A: a > a] :
( ~ sk6
| ~ ( sk29
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) ) ) )
| ~ ( sk30
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) )
| ( sk29 @ ( A @ sk4 ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(14322,plain,
( ~ sk6
| ( ( sk33 @ sk5 )
!= sk35 )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[9770,9994]) ).
thf(14331,plain,
( ~ sk6
| ( ( sk33 @ sk5 )
!= sk35 )
| ( ( sk31 @ sk5 )
!= sk35 ) ),
inference(simp,[status(thm)],[14322]) ).
thf(10526,plain,
( ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[9731,122]) ).
thf(10563,plain,
( ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( sk5
!= ( ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[10526]) ).
thf(15991,plain,
( ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk6 ) )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk34 ) ) ),
inference(paramod_ordered,[status(thm)],[12001,10563]) ).
thf(16004,plain,
( ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk6 ) )
| ( ( sk31 @ sk5 )
!= sk34 ) ),
inference(simp,[status(thm)],[15991]) ).
thf(20313,plain,
( ( ( sk5 @ sk49 )
!= ~ sk6 )
| ~ sk6
| ( ( sk31 @ sk5 )
!= sk34 ) ),
inference(func_ext,[status(esa)],[16004]) ).
thf(756,plain,
! [B: a,A: a] :
( ~ sk10
| sk6
| ~ sk7
| ~ ( sk5 @ A )
| ( sk5 @ B )
| ( ( sk2 @ sk8
@ ( sk14
@ ^ [C: a] : sk6 ) )
!= ( sk2 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[722,79]) ).
thf(757,plain,
( ~ sk10
| sk6
| ~ sk7
| ~ ( sk5 @ sk8 )
| ( sk5
@ ( sk14
@ ^ [A: a] : sk6 ) ) ),
inference(pattern_uni,[status(thm)],[756:[bind(A,$thf( sk8 )),bind(B,$thf( sk14 @ ^ [C: a] : sk6 ))]]) ).
thf(1062,plain,
( ~ sk10
| sk6
| ~ sk7
| ~ ( sk5 @ sk8 )
| ( ( sk5
@ ( sk14
@ ^ [A: a] : sk6 ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[757,11]) ).
thf(1087,plain,
( sk6
| ~ sk10
| ~ sk7
| ~ ( sk5 @ sk8 )
| ( ( sk14
@ ^ [A: a] : sk6 )
!= sk4 ) ),
inference(simp,[status(thm)],[1062]) ).
thf(11786,plain,
( ~ sk6
| sk7
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[9664,122]) ).
thf(11802,plain,
( sk7
| ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( sk5
!= ( ^ [A: a] : sk7 ) ) ),
inference(simp,[status(thm)],[11786]) ).
thf(8542,plain,
! [A: a] :
( sk10
| ~ sk7
| sk6
| ( sk17 @ A )
| ( ( sk1 @ sk8
@ ( sk11
@ ^ [B: a] : $false ) )
!= ( sk1 @ sk8 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5793,75]) ).
thf(8543,plain,
( sk10
| ~ sk7
| sk6
| ( sk17
@ ( sk11
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[8542:[bind(A,$thf( sk11 @ ^ [B: a] : $false ))]]) ).
thf(5312,plain,
( ~ sk6
| ~ ( sk30
@ ^ [A: a] : $false )
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5
@ ( sk31
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[3601,5201]) ).
thf(5323,plain,
( ~ sk6
| ~ ( sk30
@ ^ [A: a] : $false )
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk33 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[5312]) ).
thf(9031,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk33 @ sk5 )
!= ( sk31
@ ^ [B: a] : $false ) )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[76,5323]) ).
thf(9032,plain,
( ~ sk6
| $false
| $false
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk33 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[9031:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(9725,plain,
( ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk33 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[9032]) ).
thf(37,plain,
! [A: a > $o] :
( ~ ( A @ ( sk11 @ A ) )
| ~ ( A @ ( sk13 @ A ) )
| ( A @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(57,plain,
! [A: a > $o] :
( ~ ( A @ ( sk11 @ A ) )
| ~ ( A @ ( sk13 @ A ) )
| ( A @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[37]) ).
thf(9100,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ( sk5
!= ( ^ [B: a] : $false ) )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[76,3767]) ).
thf(9101,plain,
( ~ sk6
| $false
| $false
| ( sk5
!= ( ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[9100:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(9755,plain,
( ~ sk6
| ( sk5
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[9101]) ).
thf(9916,plain,
( ( sk5 @ sk39 )
| ~ sk6 ),
inference(func_ext,[status(esa)],[9755]) ).
thf(10067,plain,
( ~ sk6
| ( sk30 @ sk5 )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5 @ sk39 ) ) ),
inference(paramod_ordered,[status(thm)],[9916,5127]) ).
thf(10117,plain,
( ( sk30 @ sk5 )
| ~ sk6
| ( ( sk33 @ sk5 )
!= sk39 ) ),
inference(simp,[status(thm)],[10067]) ).
thf(26,plain,
! [A: a > $o] :
( ~ sk10
| ( sk2 @ sk8 @ ( sk14 @ A ) )
| ( sk2 @ ( sk15 @ A ) @ ( sk16 @ A ) )
| ( A @ sk9 )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(78,plain,
! [A: a > $o] :
( ~ sk10
| ( sk2 @ sk8 @ ( sk14 @ A ) )
| ( sk2 @ ( sk15 @ A ) @ ( sk16 @ A ) )
| ( A @ sk9 )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[26]) ).
thf(123,plain,
! [B: a,A: a > $o] :
( sk7
| ( sk21 @ A )
| ( A @ sk19 )
| sk6
| ( sk5 @ B )
| ( ( A @ ( sk23 @ A ) )
!= ( sk1 @ sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[50,18]) ).
thf(169,plain,
! [A: a > a] :
( sk7
| ( sk21
@ ^ [B: a] : ( sk1 @ sk3 @ ( A @ B ) ) )
| ( sk1 @ sk3 @ ( A @ sk19 ) )
| sk6
| ( sk5
@ ( A
@ ( sk23
@ ^ [B: a] : ( sk1 @ sk3 @ ( A @ B ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[123:[bind(A,$thf( ^ [D: a] : ( sk1 @ sk3 @ ( D @ D ) ) )),bind(B,$thf( D @ ( sk23 @ ^ [D: a] : ( sk1 @ sk3 @ ( D @ D ) ) ) ))]]) ).
thf(192,plain,
! [A: a > a] :
( sk7
| ( sk21
@ ^ [B: a] : ( sk1 @ sk3 @ ( A @ B ) ) )
| ( sk1 @ sk3 @ ( A @ sk19 ) )
| sk6
| ( sk5
@ ( A
@ ( sk23
@ ^ [B: a] : ( sk1 @ sk3 @ ( A @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[169]) ).
thf(26320,plain,
! [A: a > a] :
( sk7
| ( sk21
@ ^ [B: a] : ( sk1 @ sk3 @ ( A @ B ) ) )
| ( sk1 @ sk3 @ ( A @ sk19 ) )
| sk6
| ( ( sk5
@ ( A
@ ( sk23
@ ^ [B: a] : ( sk1 @ sk3 @ ( A @ B ) ) ) ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[192,11]) ).
thf(26374,plain,
( sk7
| ( sk21
@ ^ [A: a] : ( sk1 @ sk3 @ sk4 ) )
| ( sk1 @ sk3 @ sk4 )
| sk6 ),
inference(pre_uni,[status(thm)],[26320:[bind(A,$thf( ^ [B: a] : sk4 ))]]) ).
thf(9158,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ~ ( sk30 @ sk5 )
| ( ( sk31 @ sk5 )
!= ( sk31
@ ^ [B: a] : $false ) )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[76,3654]) ).
thf(9159,plain,
( ~ sk6
| $false
| $false
| ~ ( sk30 @ sk5 )
| ( ( sk31 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[9158:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(9768,plain,
( ~ sk6
| ~ ( sk30 @ sk5 )
| ( ( sk31 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[9159]) ).
thf(26923,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= sk34 )
| ( sk5 @ sk49 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[20313]) ).
thf(27001,plain,
( ~ sk6
| ( sk5 @ sk49 )
| ( ( sk31 @ sk5 )
!= sk34 )
| ~ sk6 ),
inference(cnf,[status(esa)],[26923]) ).
thf(27002,plain,
( ~ sk6
| ( sk5 @ sk49 )
| ( ( sk31 @ sk5 )
!= sk34 ) ),
inference(simp,[status(thm)],[27001]) ).
thf(10078,plain,
( ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5 @ sk39 ) ) ),
inference(paramod_ordered,[status(thm)],[9916,5201]) ).
thf(10114,plain,
( ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk33 @ sk5 )
!= sk39 ) ),
inference(simp,[status(thm)],[10078]) ).
thf(14880,plain,
( ~ sk6
| ( ( sk33 @ sk5 )
!= sk39 )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5
@ ( sk31
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[9641,10114]) ).
thf(14904,plain,
( ~ sk6
| ( ( sk33 @ sk5 )
!= sk39 )
| ( ( sk31 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[14880]) ).
thf(12156,plain,
( ~ sk6
| ( sk5 @ sk34 )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5
@ ( sk31
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[9641,9769]) ).
thf(12185,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( ( sk33 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[12156]) ).
thf(134,plain,
! [A: a > $o] :
( sk7
| ( A @ ( sk23 @ A ) )
| ( A @ sk19 )
| sk6
| ( ( sk21 @ A )
!= ( A @ sk19 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[50]) ).
thf(164,plain,
! [A: a > $o] :
( sk7
| ( A @ ( sk23 @ A ) )
| ( A @ sk19 )
| sk6
| ( ( sk21 @ A )
!= ( A @ sk19 ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(148,plain,
! [B: a > $o,A: a > $o] :
( sk7
| ( sk21
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ( A
@ ( sk23
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( B
@ ( sk23
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( A @ sk19 )
| ( B @ sk19 )
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( ^ [D: a] : ( ( B @ D ) | ( C @ D ) ) ))]]) ).
thf(178,plain,
! [B: a > $o,A: a > $o] :
( sk6
| ( A @ sk19 )
| ( B @ sk19 )
| ( A
@ ( sk23
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( B
@ ( sk23
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( sk21
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| sk7 ),
inference(cnf,[status(esa)],[148]) ).
thf(179,plain,
! [B: a > $o,A: a > $o] :
( sk6
| ( A @ sk19 )
| ( B @ sk19 )
| ( A
@ ( sk23
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( B
@ ( sk23
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( sk21
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| sk7 ),
inference(simp,[status(thm)],[178]) ).
thf(12211,plain,
( ~ sk6
| sk10
| ( ( sk31 @ sk5 )
!= sk35 )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[9661,10019]) ).
thf(12236,plain,
( sk10
| ~ sk6
| ( ( sk31 @ sk5 )
!= sk35 )
| ( sk5
!= ( ^ [A: a] : sk10 ) ) ),
inference(simp,[status(thm)],[12211]) ).
thf(2073,plain,
( sk7
| ( sk25 @ sk17 )
| ( sk17 @ ( sk27 @ sk17 ) )
| ( sk17 @ sk20 )
| sk6 ),
inference(prim_subst,[status(thm)],[63:[bind(A,$thf( sk17 ))]]) ).
thf(2730,plain,
( ~ sk7
| ~ ( sk30
@ ^ [A: a] : ~ sk7 )
| ~ sk6
| ( ( ~ ( sk30
@ ^ [A: a] : ~ sk7 ) )
!= sk7 ) ),
inference(prim_subst,[status(thm)],[482:[bind(A,$thf( ^ [B: a] : sk7 ))]]) ).
thf(9062,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ~ sk7
| ( ( ~ ( sk30
@ ^ [B: a] : ~ sk7 ) )
!= sk7 )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : ~ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[76,2730]) ).
thf(9063,plain,
( ~ sk6
| ~ sk7
| ~ sk7
| ~ sk7
| ( ( ~ ( sk30
@ ^ [A: a] : ~ sk7 ) )
!= sk7 ) ),
inference(pattern_uni,[status(thm)],[9062:[bind(A,$thf( ^ [B: a] : ~ ( sk7 ) ))]]) ).
thf(9744,plain,
( ( ( ~ ( sk30
@ ^ [A: a] : ~ sk7 ) )
!= sk7 )
| ~ sk7
| ~ sk7
| ~ sk7
| ~ sk6 ),
inference(cnf,[status(esa)],[9063]) ).
thf(9745,plain,
( ( ( ~ ( sk30
@ ^ [A: a] : ~ sk7 ) )
!= sk7 )
| ~ sk7
| ~ sk6 ),
inference(simp,[status(thm)],[9744]) ).
thf(13307,plain,
( ~ sk7
| ~ sk6
| ~ ~ ( sk30
@ ^ [A: a] : ~ sk7 )
| ~ sk7 ),
inference(bool_ext,[status(thm)],[9745]) ).
thf(13410,plain,
( ~ sk7
| ( sk30
@ ^ [A: a] : ~ sk7 )
| ~ sk6
| ~ sk7 ),
inference(cnf,[status(esa)],[13307]) ).
thf(13411,plain,
( ~ sk7
| ( sk30
@ ^ [A: a] : ~ sk7 )
| ~ sk6 ),
inference(simp,[status(thm)],[13410]) ).
thf(13627,plain,
( ~ sk7
| ~ sk6
| ( ( sk31 @ sk5 )
!= sk35 )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : ~ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[13411,10019]) ).
thf(13719,plain,
( ~ sk7
| ~ sk6
| ( ( sk31 @ sk5 )
!= sk35 )
| ( sk5
!= ( ^ [A: a] : ~ sk7 ) ) ),
inference(simp,[status(thm)],[13627]) ).
thf(102,plain,
( ~ sk6
| ~ ( sk17 @ ( sk31 @ sk17 ) )
| ~ ( sk30 @ sk17 )
| ( sk17 @ sk4 ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( sk17 ))]]) ).
thf(3871,plain,
! [A: a > $o] :
( ~ sk6
| ~ ( A @ ( sk33 @ A ) )
| ( A @ sk4 )
| ~ ( sk17 @ ( sk31 @ sk17 ) )
| ( sk17 @ sk4 )
| ( ( sk30 @ A )
!= ( sk30 @ sk17 ) ) ),
inference(paramod_ordered,[status(thm)],[64,102]) ).
thf(3872,plain,
( ~ sk6
| ~ ( sk17 @ ( sk33 @ sk17 ) )
| ( sk17 @ sk4 )
| ~ ( sk17 @ ( sk31 @ sk17 ) )
| ( sk17 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[3871:[bind(A,$thf( sk17 ))]]) ).
thf(4033,plain,
( ~ sk6
| ~ ( sk17 @ ( sk33 @ sk17 ) )
| ( sk17 @ sk4 )
| ~ ( sk17 @ ( sk31 @ sk17 ) ) ),
inference(simp,[status(thm)],[3872]) ).
thf(33,plain,
! [A: a > $o] :
( ~ sk10
| ~ ( A @ ( sk14 @ A ) )
| ( sk2 @ ( sk15 @ A ) @ ( sk16 @ A ) )
| ( A @ sk9 )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(61,plain,
! [A: a > $o] :
( ~ sk10
| ~ ( A @ ( sk14 @ A ) )
| ( sk2 @ ( sk15 @ A ) @ ( sk16 @ A ) )
| ( A @ sk9 )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[33]) ).
thf(13617,plain,
( ~ sk7
| ~ sk6
| ( sk5 @ sk34 )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : ~ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[13411,9765]) ).
thf(13717,plain,
( ( sk5 @ sk34 )
| ~ sk7
| ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk7 ) ) ),
inference(simp,[status(thm)],[13617]) ).
thf(26838,plain,
( ~ sk7
| ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk7 ) )
| ( ( sk5 @ sk34 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[13717,11]) ).
thf(26887,plain,
( ~ sk7
| ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk7 ) )
| ( sk34 != sk4 ) ),
inference(simp,[status(thm)],[26838]) ).
thf(91,plain,
! [B: a > $o,A: a > $o] :
( ~ sk6
| ~ ( ( A
@ ( sk31
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( B
@ ( sk31
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) ) )
| ~ ( sk30
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ( A @ sk4 )
| ( B @ sk4 ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [D: a] : ( ( B @ D ) | ( C @ D ) ) ))]]) ).
thf(114,plain,
! [B: a > $o,A: a > $o] :
( ( A @ sk4 )
| ( B @ sk4 )
| ~ ( sk30
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ~ ( A
@ ( sk31
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[91]) ).
thf(116,plain,
! [B: a > $o,A: a > $o] :
( ( A @ sk4 )
| ( B @ sk4 )
| ~ ( sk30
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ~ ( A
@ ( sk31
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ~ sk6 ),
inference(simp,[status(thm)],[114]) ).
thf(1672,plain,
( sk6
| ~ sk7
| ~ sk10
| ( ( sk17
@ ( sk14
@ ^ [A: a] : ~ sk10 ) )
!= ( sk17 @ sk9 ) ) ),
inference(paramod_ordered,[status(thm)],[1522,42]) ).
thf(1697,plain,
( sk6
| ~ sk7
| ~ sk10
| ( ( sk14
@ ^ [A: a] : ~ sk10 )
!= sk9 ) ),
inference(simp,[status(thm)],[1672]) ).
thf(459,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ~ ( sk30
@ ^ [B: a] :
~ ( A @ B ) )
| ~ sk6
| ( ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( ~ ( A @ sk4 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[108]) ).
thf(507,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ~ ( sk30
@ ^ [B: a] :
~ ( A @ B ) )
| ~ sk6
| ( ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( ~ ( A @ sk4 ) ) ) ),
inference(simp,[status(thm)],[459]) ).
thf(16,plain,
! [A: a > $o] :
( sk7
| ~ ( A @ ( sk26 @ A ) )
| ~ ( sk25 @ A )
| ( A @ sk20 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(74,plain,
! [A: a > $o] :
( sk7
| ~ ( A @ ( sk26 @ A ) )
| ~ ( sk25 @ A )
| ( A @ sk20 )
| sk6 ),
inference(simp,[status(thm)],[16]) ).
thf(3636,plain,
( ~ sk6
| ~ ( sk30
@ ^ [A: a] : $false )
| ( ( sk5
@ ( sk31
@ ^ [A: a] : $false ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[3601,11]) ).
thf(3649,plain,
( ~ sk6
| ~ ( sk30
@ ^ [A: a] : $false )
| ( ( sk31
@ ^ [A: a] : $false )
!= sk4 ) ),
inference(simp,[status(thm)],[3636]) ).
thf(8995,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ( ( sk31
@ ^ [B: a] : $false )
!= sk4 )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[76,3649]) ).
thf(8996,plain,
( ~ sk6
| $false
| $false
| ( ( sk31
@ ^ [A: a] : $false )
!= sk4 ) ),
inference(pattern_uni,[status(thm)],[8995:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(9703,plain,
( ~ sk6
| ( ( sk31
@ ^ [A: a] : $false )
!= sk4 ) ),
inference(simp,[status(thm)],[8996]) ).
thf(10298,plain,
( ~ sk6
| ( sk5 @ sk36 )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5
@ ( sk31
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[9641,5252]) ).
thf(10374,plain,
( ( sk5 @ sk36 )
| ~ sk6
| ( ( sk33 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[10298]) ).
thf(29,plain,
! [A: a] :
( sk7
| ~ ( sk1 @ sk18 @ A )
| ( sk29 @ A )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(60,plain,
! [A: a] :
( sk7
| ~ ( sk1 @ sk18 @ A )
| ( sk29 @ A )
| sk6 ),
inference(simp,[status(thm)],[29]) ).
thf(115,plain,
! [B: a > $o,A: a > $o] :
( ( A @ sk4 )
| ( B @ sk4 )
| ~ ( sk30
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ~ ( B
@ ( sk31
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[91]) ).
thf(117,plain,
! [B: a > $o,A: a > $o] :
( ( A @ sk4 )
| ( B @ sk4 )
| ~ ( sk30
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ~ ( B
@ ( sk31
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ~ sk6 ),
inference(simp,[status(thm)],[115]) ).
thf(19491,plain,
( sk7
| sk7
| sk7
| sk6
| ( ( sk21
@ ^ [A: a] : sk7 )
!= sk7 ) ),
inference(prim_subst,[status(thm)],[164:[bind(A,$thf( ^ [B: a] : sk7 ))]]) ).
thf(19727,plain,
( sk7
| sk6
| ( ( sk21
@ ^ [A: a] : sk7 )
!= sk7 ) ),
inference(simp,[status(thm)],[19491]) ).
thf(17584,plain,
( ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk30
@ ^ [A: a] :
~ ( sk30
@ ^ [B: a] : $false ) )
!= ( sk30 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[17188,122]) ).
thf(17632,plain,
( ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( ^ [A: a] :
~ ( sk30
@ ^ [B: a] : $false ) )
!= sk5 ) ),
inference(simp,[status(thm)],[17584]) ).
thf(25999,plain,
( ~ sk6
| ( ( ^ [A: a] :
~ ( sk30
@ ^ [B: a] : $false ) )
!= sk5 )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk34 ) ) ),
inference(paramod_ordered,[status(thm)],[17612,17632]) ).
thf(26047,plain,
( ~ sk6
| ( ( ^ [A: a] :
~ ( sk30
@ ^ [B: a] : $false ) )
!= sk5 )
| ( ( sk31 @ sk5 )
!= sk34 ) ),
inference(simp,[status(thm)],[25999]) ).
thf(10108,plain,
( ~ sk6
| ~ ( sk30 @ sk5 )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk39 ) ) ),
inference(paramod_ordered,[status(thm)],[9916,122]) ).
thf(10136,plain,
( ~ sk6
| ~ ( sk30 @ sk5 )
| ( ( sk31 @ sk5 )
!= sk39 ) ),
inference(simp,[status(thm)],[10108]) ).
thf(12539,plain,
( ~ sk6
| sk7
| ( ( sk31 @ sk5 )
!= sk39 )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[9664,10136]) ).
thf(12542,plain,
( sk7
| ~ sk6
| ( ( sk31 @ sk5 )
!= sk39 )
| ( sk5
!= ( ^ [A: a] : sk7 ) ) ),
inference(simp,[status(thm)],[12539]) ).
thf(18284,plain,
( ~ sk6
| ( sk5 @ sk34 )
| ( ( sk5 @ sk40 )
!= ( sk5 @ sk34 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[18209]) ).
thf(18300,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( sk40 != sk34 ) ),
inference(simp,[status(thm)],[18284]) ).
thf(44,plain,
! [A: a > $o] :
( ~ ( A @ ( sk11 @ A ) )
| ( sk1 @ ( sk12 @ A ) @ ( sk13 @ A ) )
| ( A @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(70,plain,
! [A: a > $o] :
( ~ ( A @ ( sk11 @ A ) )
| ( sk1 @ ( sk12 @ A ) @ ( sk13 @ A ) )
| ( A @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[44]) ).
thf(21,plain,
( sk7
| ~ ( sk29 @ sk20 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(1515,plain,
! [A: a] :
( ~ sk10
| sk6
| ~ sk7
| ( sk17 @ A )
| ( ( sk2 @ sk8
@ ( sk14
@ ^ [B: a] : sk6 ) )
!= ( sk2 @ sk8 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[722,56]) ).
thf(1516,plain,
( ~ sk10
| sk6
| ~ sk7
| ( sk17
@ ( sk14
@ ^ [A: a] : sk6 ) ) ),
inference(pattern_uni,[status(thm)],[1515:[bind(A,$thf( sk14 @ ^ [B: a] : sk6 ))]]) ).
thf(1591,plain,
( ~ sk10
| sk6
| ~ sk7
| ( ( sk17
@ ( sk14
@ ^ [A: a] : sk6 ) )
!= ( sk17 @ sk9 ) ) ),
inference(paramod_ordered,[status(thm)],[1516,42]) ).
thf(1619,plain,
( sk6
| ~ sk10
| ~ sk7
| ( ( sk14
@ ^ [A: a] : sk6 )
!= sk9 ) ),
inference(simp,[status(thm)],[1591]) ).
thf(9334,plain,
! [A: a > $o] :
( ~ sk6
| ( sk30 @ A )
| ( A @ sk4 )
| ~ ( sk30
@ ^ [B: a] : ~ sk6 )
| ( ( A @ ( sk32 @ A ) )
!= ( ~ ( sk30
@ ^ [B: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,2768]) ).
thf(9559,plain,
( ~ sk6
| ( sk30
@ ^ [A: a] :
~ ( sk30
@ ^ [B: a] : ~ sk6 ) )
| ~ ( sk30
@ ^ [A: a] : ~ sk6 )
| ~ ( sk30
@ ^ [A: a] : ~ sk6 ) ),
inference(pre_uni,[status(thm)],[9334:[bind(A,$thf( ^ [B: a] : ~ ( sk30 @ ^ [C: a] : ~ ( sk6 ) ) ))]]) ).
thf(9734,plain,
( ~ ( sk30
@ ^ [A: a] : ~ sk6 )
| ~ ( sk30
@ ^ [A: a] : ~ sk6 )
| ( sk30
@ ^ [A: a] :
~ ( sk30
@ ^ [B: a] : ~ sk6 ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[9559]) ).
thf(9735,plain,
( ~ ( sk30
@ ^ [A: a] : ~ sk6 )
| ( sk30
@ ^ [A: a] :
~ ( sk30
@ ^ [B: a] : ~ sk6 ) )
| ~ sk6 ),
inference(simp,[status(thm)],[9734]) ).
thf(30283,plain,
( ~ sk6
| ( sk30
@ ^ [A: a] :
~ ( sk30
@ ^ [B: a] : ~ sk6 ) )
| ( ( sk30
@ ^ [A: a] : ~ sk6 )
!= ( sk30
@ ^ [A: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[9731,9735]) ).
thf(30284,plain,
( ~ sk6
| ( sk30
@ ^ [A: a] :
~ ( sk30
@ ^ [B: a] : ~ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[30283:[]]) ).
thf(30757,plain,
( ~ sk6
| ( sk5 @ sk34 )
| ( ( sk30
@ ^ [A: a] :
~ ( sk30
@ ^ [B: a] : ~ sk6 ) )
!= ( sk30 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[30284,9765]) ).
thf(30924,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( ( ^ [A: a] :
~ ( sk30
@ ^ [B: a] : ~ sk6 ) )
!= sk5 ) ),
inference(simp,[status(thm)],[30757]) ).
thf(45,plain,
! [A: a > $o] :
( sk7
| ( sk25 @ A )
| ~ ( A @ ( sk28 @ A ) )
| ( A @ sk20 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(65,plain,
! [A: a > $o] :
( sk7
| ( sk25 @ A )
| ~ ( A @ ( sk28 @ A ) )
| ( A @ sk20 )
| sk6 ),
inference(simp,[status(thm)],[45]) ).
thf(18530,plain,
( ~ sk6
| ( sk40 != sk34 )
| ~ ( sk30 @ sk5 )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk34 ) ) ),
inference(paramod_ordered,[status(thm)],[18300,122]) ).
thf(18535,plain,
( ~ sk6
| ( sk40 != sk34 )
| ~ ( sk30 @ sk5 )
| ( ( sk31 @ sk5 )
!= sk34 ) ),
inference(simp,[status(thm)],[18530]) ).
thf(10100,plain,
( ~ sk6
| ( ( sk5 @ sk39 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[9916,11]) ).
thf(10131,plain,
( ~ sk6
| ( sk39 != sk4 ) ),
inference(simp,[status(thm)],[10100]) ).
thf(27842,plain,
( ~ sk6
| ( sk51 != sk34 )
| ( ( sk5 @ sk34 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[27492,11]) ).
thf(27886,plain,
( ~ sk6
| ( sk51 != sk34 )
| ( sk34 != sk4 ) ),
inference(simp,[status(thm)],[27842]) ).
thf(156,plain,
( sk7
| ( sk21 @ sk17 )
| ( sk17 @ ( sk23 @ sk17 ) )
| ( sk17 @ sk19 )
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( sk17 ))]]) ).
thf(12510,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= sk39 )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[9731,10136]) ).
thf(12546,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= sk39 )
| ( sk5
!= ( ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[12510]) ).
thf(8,plain,
! [A: a > $o] :
( ~ sk10
| ~ ( A @ ( sk14 @ A ) )
| ~ ( A @ ( sk16 @ A ) )
| ( A @ sk9 )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(53,plain,
! [A: a > $o] :
( ~ sk10
| ~ ( A @ ( sk14 @ A ) )
| ~ ( A @ ( sk16 @ A ) )
| ( A @ sk9 )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[8]) ).
thf(5676,plain,
( ( sk1 @ sk8
@ ( sk11
@ ^ [A: a] : sk10 ) )
| sk10
| sk10
| sk10
| ~ sk7
| sk6 ),
inference(prim_subst,[status(thm)],[67:[bind(A,$thf( ^ [B: a] : sk10 ))]]) ).
thf(5796,plain,
( ( sk1 @ sk8
@ ( sk11
@ ^ [A: a] : sk10 ) )
| sk10
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[5676]) ).
thf(8564,plain,
! [A: a] :
( sk10
| ~ sk7
| sk6
| ( sk17 @ A )
| ( ( sk1 @ sk8
@ ( sk11
@ ^ [B: a] : sk10 ) )
!= ( sk1 @ sk8 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5796,75]) ).
thf(8565,plain,
( sk10
| ~ sk7
| sk6
| ( sk17
@ ( sk11
@ ^ [A: a] : sk10 ) ) ),
inference(pattern_uni,[status(thm)],[8564:[bind(A,$thf( sk11 @ ^ [B: a] : sk10 ))]]) ).
thf(8744,plain,
( sk10
| ~ sk7
| sk6
| ( ( sk17
@ ( sk11
@ ^ [A: a] : sk10 ) )
!= ( sk17 @ sk9 ) ) ),
inference(paramod_ordered,[status(thm)],[8565,42]) ).
thf(8800,plain,
( sk10
| sk6
| ~ sk7
| ( ( sk11
@ ^ [A: a] : sk10 )
!= sk9 ) ),
inference(simp,[status(thm)],[8744]) ).
thf(5662,plain,
! [A: a > $o] :
( ( sk1 @ sk8 @ ( sk11 @ A ) )
| ( A @ sk9 )
| sk10
| ~ sk7
| sk6
| ( ( A @ ( sk12 @ A ) )
!= ~ sk7 )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[67]) ).
thf(5728,plain,
( ( sk1 @ sk8
@ ( sk11
@ ^ [A: a] : ~ sk7 ) )
| ~ sk7
| sk10
| ~ sk7
| sk6 ),
inference(pre_uni,[status(thm)],[5662:[bind(A,$thf( ^ [B: a] : ~ ( sk7 ) ))]]) ).
thf(5834,plain,
( sk6
| ~ sk7
| sk10
| ~ sk7
| ( sk1 @ sk8
@ ( sk11
@ ^ [A: a] : ~ sk7 ) ) ),
inference(cnf,[status(esa)],[5728]) ).
thf(5835,plain,
( sk6
| ~ sk7
| sk10
| ( sk1 @ sk8
@ ( sk11
@ ^ [A: a] : ~ sk7 ) ) ),
inference(simp,[status(thm)],[5834]) ).
thf(8566,plain,
! [A: a] :
( sk6
| ~ sk7
| sk10
| ( sk17 @ A )
| ( ( sk1 @ sk8
@ ( sk11
@ ^ [B: a] : ~ sk7 ) )
!= ( sk1 @ sk8 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5835,75]) ).
thf(8567,plain,
( sk6
| ~ sk7
| sk10
| ( sk17
@ ( sk11
@ ^ [A: a] : ~ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[8566:[bind(A,$thf( sk11 @ ^ [B: a] : ~ ( sk7 ) ))]]) ).
thf(97,plain,
! [A: a > a] :
( ~ sk6
| ~ ( sk17
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk17 @ ( A @ B ) ) ) ) )
| ~ ( sk30
@ ^ [B: a] : ( sk17 @ ( A @ B ) ) )
| ( sk17 @ ( A @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [C: a] : ( sk17 @ ( B @ C ) ) ))]]) ).
thf(109,plain,
! [A: a > a] :
( ~ sk6
| ~ ( sk17
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk17 @ ( A @ B ) ) ) ) )
| ~ ( sk30
@ ^ [B: a] : ( sk17 @ ( A @ B ) ) )
| ( sk17 @ ( A @ sk4 ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(9324,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ( ( ~ ( sk30
@ ^ [B: a] : ~ sk6 ) )
!= sk6 )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[76,2768]) ).
thf(9325,plain,
( ~ sk6
| ~ sk6
| ~ sk6
| ( ( ~ ( sk30
@ ^ [A: a] : ~ sk6 ) )
!= sk6 ) ),
inference(pattern_uni,[status(thm)],[9324:[bind(A,$thf( ^ [B: a] : ~ ( sk6 ) ))]]) ).
thf(9639,plain,
( ( ( ~ ( sk30
@ ^ [A: a] : ~ sk6 ) )
!= sk6 )
| ~ sk6
| ~ sk6
| ~ sk6 ),
inference(cnf,[status(esa)],[9325]) ).
thf(9640,plain,
( ( ( ~ ( sk30
@ ^ [A: a] : ~ sk6 ) )
!= sk6 )
| ~ sk6 ),
inference(simp,[status(thm)],[9639]) ).
thf(14491,plain,
( sk7
| ~ sk6
| ( sk5
!= ( ^ [A: a] : sk7 ) )
| ( ( sk5 @ sk34 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[12011,11]) ).
thf(14529,plain,
( sk7
| ~ sk6
| ( sk5
!= ( ^ [A: a] : sk7 ) )
| ( sk34 != sk4 ) ),
inference(simp,[status(thm)],[14491]) ).
thf(40,plain,
! [A: a > $o] :
( sk7
| ( sk21 @ A )
| ( sk1 @ ( sk23 @ A ) @ ( sk24 @ A ) )
| ( sk2 @ ( sk23 @ A ) @ ( sk24 @ A ) )
| ( A @ sk19 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(77,plain,
! [A: a > $o] :
( sk7
| ( sk21 @ A )
| ( sk1 @ ( sk23 @ A ) @ ( sk24 @ A ) )
| ( sk2 @ ( sk23 @ A ) @ ( sk24 @ A ) )
| ( A @ sk19 )
| sk6 ),
inference(simp,[status(thm)],[40]) ).
thf(901,plain,
( ~ ( sk29 @ sk4 )
| ~ ( sk30
@ ^ [A: a] :
~ ( sk29 @ A ) )
| ~ sk6
| ( ( sk29
@ ( sk31
@ ^ [A: a] :
~ ( sk29 @ A ) ) )
!= ( ~ ( sk29 @ sk4 ) ) ) ),
inference(prim_subst,[status(thm)],[507:[bind(A,$thf( sk29 ))]]) ).
thf(8602,plain,
( sk10
| ~ sk7
| sk6
| ( ( sk17
@ ( sk11
@ ^ [A: a] : $false ) )
!= ( sk17 @ sk9 ) ) ),
inference(paramod_ordered,[status(thm)],[8543,42]) ).
thf(8658,plain,
( sk10
| sk6
| ~ sk7
| ( ( sk11
@ ^ [A: a] : $false )
!= sk9 ) ),
inference(simp,[status(thm)],[8602]) ).
thf(142,plain,
( sk7
| ( sk21
@ ^ [A: a] : $false )
| $false
| $false
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(173,plain,
( sk7
| ( sk21
@ ^ [A: a] : $false )
| sk6 ),
inference(simp,[status(thm)],[142]) ).
thf(12200,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= sk35 )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[9731,10019]) ).
thf(12235,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= sk35 )
| ( sk5
!= ( ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[12200]) ).
thf(17678,plain,
( ( ( sk5 @ sk47 )
!= ~ sk6 )
| ~ sk6
| ( ( sk31 @ sk5 )
!= sk35 ) ),
inference(func_ext,[status(esa)],[12235]) ).
thf(31424,plain,
( sk7
| ( sk5 @ sk34 )
| ~ sk6
| ( ( sk5 @ sk43 )
!= ( sk5 @ sk34 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[31325]) ).
thf(31464,plain,
( sk7
| ( sk5 @ sk34 )
| ~ sk6
| ( sk43 != sk34 ) ),
inference(simp,[status(thm)],[31424]) ).
thf(660,plain,
! [A: a > $o] :
( ~ sk10
| ( sk2 @ sk8 @ ( sk14 @ A ) )
| ( A @ sk9 )
| ~ sk7
| sk6
| ( ( A @ ( sk15 @ A ) )
!= ~ sk7 )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[52]) ).
thf(683,plain,
( ~ sk10
| ( sk2 @ sk8
@ ( sk14
@ ^ [A: a] : ~ sk7 ) )
| ~ sk7
| ~ sk7
| sk6 ),
inference(pre_uni,[status(thm)],[660:[bind(A,$thf( ^ [B: a] : ~ ( sk7 ) ))]]) ).
thf(734,plain,
( sk6
| ~ sk7
| ~ sk7
| ( sk2 @ sk8
@ ( sk14
@ ^ [A: a] : ~ sk7 ) )
| ~ sk10 ),
inference(cnf,[status(esa)],[683]) ).
thf(735,plain,
( sk6
| ~ sk7
| ( sk2 @ sk8
@ ( sk14
@ ^ [A: a] : ~ sk7 ) )
| ~ sk10 ),
inference(simp,[status(thm)],[734]) ).
thf(1527,plain,
! [A: a] :
( sk6
| ~ sk7
| ~ sk10
| ( sk17 @ A )
| ( ( sk2 @ sk8
@ ( sk14
@ ^ [B: a] : ~ sk7 ) )
!= ( sk2 @ sk8 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[735,56]) ).
thf(1528,plain,
( sk6
| ~ sk7
| ~ sk10
| ( sk17
@ ( sk14
@ ^ [A: a] : ~ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[1527:[bind(A,$thf( sk14 @ ^ [B: a] : ~ ( sk7 ) ))]]) ).
thf(1798,plain,
( sk6
| ~ sk7
| ~ sk10
| ( ( sk17
@ ( sk14
@ ^ [A: a] : ~ sk7 ) )
!= ( sk17 @ sk9 ) ) ),
inference(paramod_ordered,[status(thm)],[1528,42]) ).
thf(1825,plain,
( sk6
| ~ sk7
| ~ sk10
| ( ( sk14
@ ^ [A: a] : ~ sk7 )
!= sk9 ) ),
inference(simp,[status(thm)],[1798]) ).
thf(31926,plain,
( ~ sk6
| ( ( ^ [A: a] :
~ ( sk30
@ ^ [B: a] : ~ sk6 ) )
!= sk5 )
| ( ( sk5 @ sk34 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[30924,11]) ).
thf(32002,plain,
( ~ sk6
| ( ( ^ [A: a] :
~ ( sk30
@ ^ [B: a] : ~ sk6 ) )
!= sk5 )
| ( sk34 != sk4 ) ),
inference(simp,[status(thm)],[31926]) ).
thf(12165,plain,
( ~ sk6
| ( sk5 @ sk34 )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5 @ sk39 ) ) ),
inference(paramod_ordered,[status(thm)],[9916,9769]) ).
thf(12191,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( ( sk33 @ sk5 )
!= sk39 ) ),
inference(simp,[status(thm)],[12165]) ).
thf(13462,plain,
( ~ sk10
| ~ sk6
| ( ( sk31 @ sk5 )
!= sk35 )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : ~ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[13304,10019]) ).
thf(13522,plain,
( ~ sk10
| ~ sk6
| ( ( sk31 @ sk5 )
!= sk35 )
| ( sk5
!= ( ^ [A: a] : ~ sk10 ) ) ),
inference(simp,[status(thm)],[13462]) ).
thf(39,plain,
! [B: a,A: a] :
( ~ ( sk5 @ A )
| ~ ( sk1 @ A @ B )
| ( sk5 @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(73,plain,
! [B: a,A: a] :
( ~ ( sk5 @ A )
| ~ ( sk1 @ A @ B )
| ( sk5 @ B ) ),
inference(simp,[status(thm)],[39]) ).
thf(12173,plain,
( ~ sk6
| ( sk5 @ sk34 )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5 @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[9770,9769]) ).
thf(12183,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( ( sk33 @ sk5 )
!= sk35 ) ),
inference(simp,[status(thm)],[12173]) ).
thf(85,plain,
! [A: a > $o] :
( ~ sk6
| ~ ( A @ ( sk31 @ A ) )
| ( A @ sk4 )
| ( ( sk30 @ A )
!= ( A @ ( sk31 @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[47]) ).
thf(105,plain,
! [A: a > $o] :
( ( A @ sk4 )
| ~ sk6
| ~ ( A @ ( sk31 @ A ) )
| ( ( sk30 @ A )
!= ( A @ ( sk31 @ A ) ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(10079,plain,
( ~ sk6
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk39 ) ) ),
inference(paramod_ordered,[status(thm)],[9916,5201]) ).
thf(10129,plain,
( ~ sk6
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ( ( sk31 @ sk5 )
!= sk39 ) ),
inference(simp,[status(thm)],[10079]) ).
thf(14937,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= sk39 )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5
@ ( sk31
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[9641,10129]) ).
thf(14961,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= sk39 )
| ( ( sk33 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[14937]) ).
thf(787,plain,
! [A: a] :
( ~ sk10
| ~ sk7
| sk6
| ( sk5 @ A )
| ( ( sk2 @ sk8
@ ( sk14
@ ^ [B: a] : $false ) )
!= ( sk2 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[730,38]) ).
thf(799,plain,
! [A: a] :
( sk6
| ( sk5 @ A )
| ~ sk10
| ~ sk7
| ( sk8 != sk3 )
| ( ( sk14
@ ^ [B: a] : $false )
!= A ) ),
inference(simp,[status(thm)],[787]) ).
thf(805,plain,
( sk6
| ( sk5
@ ( sk14
@ ^ [A: a] : $false ) )
| ~ sk10
| ~ sk7
| ( sk8 != sk3 ) ),
inference(simp,[status(thm)],[799]) ).
thf(9962,plain,
( ~ sk6
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[9770,5201]) ).
thf(10011,plain,
( ~ sk6
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ( ( sk31 @ sk5 )
!= sk35 ) ),
inference(simp,[status(thm)],[9962]) ).
thf(2089,plain,
( sk7
| ( sk25 @ sk29 )
| ( sk29 @ ( sk27 @ sk29 ) )
| ( sk29 @ sk20 )
| sk6 ),
inference(prim_subst,[status(thm)],[63:[bind(A,$thf( sk29 ))]]) ).
thf(19506,plain,
( sk7
| sk10
| sk10
| sk6
| ( ( sk21
@ ^ [A: a] : sk10 )
!= sk10 ) ),
inference(prim_subst,[status(thm)],[164:[bind(A,$thf( ^ [B: a] : sk10 ))]]) ).
thf(19740,plain,
( sk7
| sk10
| sk6
| ( ( sk21
@ ^ [A: a] : sk10 )
!= sk10 ) ),
inference(simp,[status(thm)],[19506]) ).
thf(137,plain,
! [A: a > $o] :
( sk7
| ( sk21 @ A )
| ( A @ sk19 )
| sk6
| ( ( A @ ( sk23 @ A ) )
!= ( A @ sk19 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[50]) ).
thf(160,plain,
! [A: a > $o] :
( sk7
| ( sk21 @ A )
| ( A @ sk19 )
| sk6
| ( ( A @ ( sk23 @ A ) )
!= ( A @ sk19 ) ) ),
inference(pre_uni,[status(thm)],[137:[]]) ).
thf(161,plain,
! [A: a > $o] :
( sk6
| ( A @ sk19 )
| ( sk21 @ A )
| sk7
| ( ( A @ ( sk23 @ A ) )
!= ( A @ sk19 ) ) ),
inference(pre_uni,[status(thm)],[160:[]]) ).
thf(149,plain,
! [A: a > a] :
( sk7
| ( sk21
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) )
| ( sk5
@ ( A
@ ( sk23
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) ) ) )
| ( sk5 @ ( A @ sk19 ) )
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( ^ [C: a] : ( sk5 @ ( B @ C ) ) ))]]) ).
thf(180,plain,
! [A: a > a] :
( sk7
| ( sk21
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) )
| ( sk5
@ ( A
@ ( sk23
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) ) ) )
| ( sk5 @ ( A @ sk19 ) )
| sk6 ),
inference(simp,[status(thm)],[149]) ).
thf(15961,plain,
( ( ( sk5 @ sk46 )
!= ~ sk6 )
| ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[10563]) ).
thf(25148,plain,
( ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( sk5 @ sk46 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[15961]) ).
thf(25276,plain,
( ~ sk6
| ( sk5 @ sk46 )
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[25148]) ).
thf(25277,plain,
( ~ sk6
| ( sk5 @ sk46 )
| ~ ( sk5 @ ( sk31 @ sk5 ) ) ),
inference(simp,[status(thm)],[25276]) ).
thf(25378,plain,
( ~ sk6
| ( sk5 @ sk46 )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[9770,25277]) ).
thf(25389,plain,
( ( sk5 @ sk46 )
| ~ sk6
| ( ( sk31 @ sk5 )
!= sk35 ) ),
inference(simp,[status(thm)],[25378]) ).
thf(145,plain,
( sk7
| ( sk21
@ ^ [A: a] : sk7 )
| sk7
| sk7
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( ^ [B: a] : sk7 ))]]) ).
thf(176,plain,
( sk7
| ( sk21
@ ^ [A: a] : sk7 )
| sk6 ),
inference(simp,[status(thm)],[145]) ).
thf(132,plain,
! [B: a,A: a > $o] :
( sk7
| ( sk21 @ A )
| ( A @ sk19 )
| sk6
| ( sk5 @ B )
| ( ( A @ ( sk23 @ A ) )
!= ( sk2 @ sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[50,38]) ).
thf(167,plain,
! [A: a > a] :
( sk7
| ( sk21
@ ^ [B: a] : ( sk2 @ sk3 @ ( A @ B ) ) )
| ( sk2 @ sk3 @ ( A @ sk19 ) )
| sk6
| ( sk5
@ ( A
@ ( sk23
@ ^ [B: a] : ( sk2 @ sk3 @ ( A @ B ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[132:[bind(A,$thf( ^ [D: a] : ( sk2 @ sk3 @ ( D @ D ) ) )),bind(B,$thf( D @ ( sk23 @ ^ [D: a] : ( sk2 @ sk3 @ ( D @ D ) ) ) ))]]) ).
thf(191,plain,
! [A: a > a] :
( sk7
| ( sk21
@ ^ [B: a] : ( sk2 @ sk3 @ ( A @ B ) ) )
| ( sk2 @ sk3 @ ( A @ sk19 ) )
| sk6
| ( sk5
@ ( A
@ ( sk23
@ ^ [B: a] : ( sk2 @ sk3 @ ( A @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[167]) ).
thf(14728,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= sk35 )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5
@ ( sk31
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[9641,10011]) ).
thf(14760,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= sk35 )
| ( ( sk33 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[14728]) ).
thf(25222,plain,
( ~ sk6
| ( ( sk5 @ sk46 )
!= ~ sk6 )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[9770,15961]) ).
thf(25241,plain,
( ~ sk6
| ( ( sk5 @ sk46 )
!= ~ sk6 )
| ( ( sk31 @ sk5 )
!= sk35 ) ),
inference(simp,[status(thm)],[25222]) ).
thf(31402,plain,
( sk7
| ( sk5 @ sk34 )
| ~ sk6
| ( ( sk5 @ sk43 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[31325,11]) ).
thf(31434,plain,
( sk7
| ( sk5 @ sk34 )
| ~ sk6
| ( sk43 != sk4 ) ),
inference(simp,[status(thm)],[31402]) ).
thf(20,plain,
! [A: a > $o] :
( sk7
| ( sk21 @ A )
| ~ ( A @ ( sk24 @ A ) )
| ( A @ sk19 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(59,plain,
! [A: a > $o] :
( sk7
| ( sk21 @ A )
| ~ ( A @ ( sk24 @ A ) )
| ( A @ sk19 )
| sk6 ),
inference(simp,[status(thm)],[20]) ).
thf(92,plain,
! [A: a > a] :
( ~ sk6
| ~ ( sk5
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) ) ) )
| ~ ( sk30
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) )
| ( sk5 @ ( A @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [C: a] : ( sk5 @ ( B @ C ) ) ))]]) ).
thf(118,plain,
! [A: a > a] :
( ~ sk6
| ~ ( sk5
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) ) ) )
| ~ ( sk30
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) )
| ( sk5 @ ( A @ sk4 ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(2079,plain,
( sk7
| ( sk25
@ ^ [A: a] : sk10 )
| sk10
| sk10
| sk6 ),
inference(prim_subst,[status(thm)],[63:[bind(A,$thf( ^ [B: a] : sk10 ))]]) ).
thf(2161,plain,
( sk7
| ( sk25
@ ^ [A: a] : sk10 )
| sk10
| sk6 ),
inference(simp,[status(thm)],[2079]) ).
thf(6,plain,
! [B: a,A: a] :
( ~ ( sk17 @ A )
| ~ ( sk1 @ A @ B )
| ( sk17 @ B )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(49,plain,
! [B: a,A: a] :
( ~ ( sk17 @ A )
| ~ ( sk1 @ A @ B )
| ( sk17 @ B )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[6]) ).
thf(17535,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= sk39 )
| ( ( sk30
@ ^ [A: a] :
~ ( sk30
@ ^ [B: a] : $false ) )
!= ( sk30 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[17188,10136]) ).
thf(17611,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= sk39 )
| ( ( ^ [A: a] :
~ ( sk30
@ ^ [B: a] : $false ) )
!= sk5 ) ),
inference(simp,[status(thm)],[17535]) ).
thf(150,plain,
! [A: a > a > $o] :
( sk7
| ( sk21
@ ^ [B: a] : ( sk30 @ ( A @ B ) ) )
| ( sk30
@ ( A
@ ( sk23
@ ^ [B: a] : ( sk30 @ ( A @ B ) ) ) ) )
| ( sk30 @ ( A @ sk19 ) )
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( ^ [C: a] : ( sk30 @ ( B @ C ) ) ))]]) ).
thf(181,plain,
! [A: a > a > $o] :
( sk7
| ( sk21
@ ^ [B: a] : ( sk30 @ ( A @ B ) ) )
| ( sk30
@ ( A
@ ( sk23
@ ^ [B: a] : ( sk30 @ ( A @ B ) ) ) ) )
| ( sk30 @ ( A @ sk19 ) )
| sk6 ),
inference(simp,[status(thm)],[150]) ).
thf(12521,plain,
( ~ sk6
| sk10
| ( ( sk31 @ sk5 )
!= sk39 )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[9661,10136]) ).
thf(12547,plain,
( sk10
| ~ sk6
| ( ( sk31 @ sk5 )
!= sk39 )
| ( sk5
!= ( ^ [A: a] : sk10 ) ) ),
inference(simp,[status(thm)],[12521]) ).
thf(18299,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( ( sk5 @ sk40 )
!= ( sk5 @ sk34 ) ) ),
inference(simp,[status(thm)],[18284]) ).
thf(27,plain,
! [A: a > $o] :
( ~ sk6
| ( sk30 @ A )
| ( sk1 @ ( sk32 @ A ) @ ( sk33 @ A ) )
| ( sk2 @ ( sk32 @ A ) @ ( sk33 @ A ) )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(71,plain,
! [A: a > $o] :
( ~ sk6
| ( sk30 @ A )
| ( sk1 @ ( sk32 @ A ) @ ( sk33 @ A ) )
| ( sk2 @ ( sk32 @ A ) @ ( sk33 @ A ) )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[27]) ).
thf(27445,plain,
( ~ sk6
| ( sk5 @ sk34 )
| ( ( sk5 @ sk51 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[27053,11]) ).
thf(27490,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( sk51 != sk4 ) ),
inference(simp,[status(thm)],[27445]) ).
thf(4,plain,
! [B: a,A: a] :
( ~ ( sk17 @ A )
| ~ ( sk2 @ A @ B )
| ( sk17 @ B )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(54,plain,
! [B: a,A: a] :
( ~ ( sk17 @ A )
| ~ ( sk2 @ A @ B )
| ( sk17 @ B )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[4]) ).
thf(157,plain,
! [B: a > a,A: a > a] :
( sk7
| ( sk21
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk1
@ ( A
@ ( sk23
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk23
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ( sk1 @ ( A @ sk19 ) @ ( B @ sk19 ) )
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( ^ [D: a] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(187,plain,
! [B: a > a,A: a > a] :
( sk7
| ( sk21
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk1
@ ( A
@ ( sk23
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk23
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ( sk1 @ ( A @ sk19 ) @ ( B @ sk19 ) )
| sk6 ),
inference(simp,[status(thm)],[157]) ).
thf(90,plain,
! [A: a > a > $o] :
( ~ sk6
| ~ ( sk21
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) ) ) )
| ~ ( sk30
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) )
| ( sk21 @ ( A @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [C: a] : ( sk21 @ ( B @ C ) ) ))]]) ).
thf(113,plain,
! [A: a > a > $o] :
( ~ sk6
| ~ ( sk21
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) ) ) )
| ~ ( sk30
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) )
| ( sk21 @ ( A @ sk4 ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(30,plain,
! [A: a > $o] :
( sk7
| ( sk1 @ sk19 @ ( sk26 @ A ) )
| ( sk2 @ sk19 @ ( sk26 @ A ) )
| ~ ( sk25 @ A )
| ( A @ sk20 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(81,plain,
! [A: a > $o] :
( sk7
| ( sk1 @ sk19 @ ( sk26 @ A ) )
| ( sk2 @ sk19 @ ( sk26 @ A ) )
| ~ ( sk25 @ A )
| ( A @ sk20 )
| sk6 ),
inference(simp,[status(thm)],[30]) ).
thf(4070,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ~ ( sk30
@ ^ [A: a] : $false )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : $false ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3735]) ).
thf(4073,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ~ ( sk30
@ ^ [A: a] : $false )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[4070]) ).
thf(9201,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ( sk5 @ sk34 )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [B: a] : $false ) )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[76,4073]) ).
thf(9202,plain,
( ~ sk6
| $false
| $false
| ( sk5 @ sk34 )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[9201:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(9771,plain,
( ~ sk6
| ( sk5 @ sk34 )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[9202]) ).
thf(13633,plain,
( ~ sk7
| ~ sk6
| ( ( sk31 @ sk5 )
!= sk39 )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : ~ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[13411,10136]) ).
thf(13705,plain,
( ~ sk7
| ~ sk6
| ( ( sk31 @ sk5 )
!= sk39 )
| ( sk5
!= ( ^ [A: a] : ~ sk7 ) ) ),
inference(simp,[status(thm)],[13633]) ).
thf(25786,plain,
! [A: a > a] :
( sk7
| ( sk21
@ ^ [B: a] : ( sk2 @ sk3 @ ( A @ B ) ) )
| ( sk2 @ sk3 @ ( A @ sk19 ) )
| sk6
| ( ( sk5
@ ( A
@ ( sk23
@ ^ [B: a] : ( sk2 @ sk3 @ ( A @ B ) ) ) ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[191,11]) ).
thf(25866,plain,
( sk7
| ( sk21
@ ^ [A: a] : ( sk2 @ sk3 @ sk4 ) )
| ( sk2 @ sk3 @ sk4 )
| sk6 ),
inference(pre_uni,[status(thm)],[25786:[bind(A,$thf( ^ [B: a] : sk4 ))]]) ).
thf(10062,plain,
( ~ sk6
| ( sk5 @ sk36 )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5 @ sk39 ) ) ),
inference(paramod_ordered,[status(thm)],[9916,5252]) ).
thf(10115,plain,
( ( sk5 @ sk36 )
| ~ sk6
| ( ( sk33 @ sk5 )
!= sk39 ) ),
inference(simp,[status(thm)],[10062]) ).
thf(11660,plain,
( ~ sk6
| sk10
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[9661,122]) ).
thf(11686,plain,
( sk10
| ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( sk5
!= ( ^ [A: a] : sk10 ) ) ),
inference(simp,[status(thm)],[11660]) ).
thf(141,plain,
! [A: a > a] :
( sk7
| ( sk21
@ ^ [B: a] : ( sk17 @ ( A @ B ) ) )
| ( sk17
@ ( A
@ ( sk23
@ ^ [B: a] : ( sk17 @ ( A @ B ) ) ) ) )
| ( sk17 @ ( A @ sk19 ) )
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( ^ [C: a] : ( sk17 @ ( B @ C ) ) ))]]) ).
thf(172,plain,
! [A: a > a] :
( sk7
| ( sk21
@ ^ [B: a] : ( sk17 @ ( A @ B ) ) )
| ( sk17
@ ( A
@ ( sk23
@ ^ [B: a] : ( sk17 @ ( A @ B ) ) ) ) )
| ( sk17 @ ( A @ sk19 ) )
| sk6 ),
inference(simp,[status(thm)],[141]) ).
thf(18220,plain,
( ~ sk6
| ( sk5 @ sk34 )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5 @ sk40 ) ) ),
inference(paramod_ordered,[status(thm)],[18209,9769]) ).
thf(18331,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( ( sk33 @ sk5 )
!= sk40 ) ),
inference(simp,[status(thm)],[18220]) ).
thf(9981,plain,
( ~ sk6
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5 @ ( sk31 @ sk5 ) ) )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[9770,5319]) ).
thf(10000,plain,
( ~ sk6
| ( ( sk33 @ sk5 )
!= ( sk31 @ sk5 ) )
| ( ( sk31 @ sk5 )
!= sk35 ) ),
inference(simp,[status(thm)],[9981]) ).
thf(20747,plain,
( ( ( ~ ( sk30
@ ^ [A: a] : $false ) )
!= ( sk5 @ sk52 ) )
| ~ sk6
| ( sk34 != sk4 ) ),
inference(func_ext,[status(esa)],[20658]) ).
thf(28232,plain,
( ~ sk6
| ( sk5 @ sk52 )
| ( sk34 != sk4 )
| ( ( sk30
@ ^ [A: a] : $false )
!= ( sk30
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[9625,20747]) ).
thf(28233,plain,
( ~ sk6
| ( sk5 @ sk52 )
| ( sk34 != sk4 ) ),
inference(pattern_uni,[status(thm)],[28232:[]]) ).
thf(28490,plain,
( ~ sk6
| ( sk34 != sk4 )
| ( ( sk5 @ sk52 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[28233,11]) ).
thf(28529,plain,
( ~ sk6
| ( sk34 != sk4 )
| ( sk52 != sk4 ) ),
inference(simp,[status(thm)],[28490]) ).
thf(14738,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= sk35 )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5 @ sk39 ) ) ),
inference(paramod_ordered,[status(thm)],[9916,10011]) ).
thf(14767,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= sk35 )
| ( ( sk33 @ sk5 )
!= sk39 ) ),
inference(simp,[status(thm)],[14738]) ).
thf(140,plain,
( sk7
| ( sk21 @ sk5 )
| ( sk5 @ ( sk23 @ sk5 ) )
| ( sk5 @ sk19 )
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( sk5 ))]]) ).
thf(14137,plain,
( ( ( sk5 @ sk41 )
!= ~ sk6 )
| ~ sk6
| ( sk34 != sk4 ) ),
inference(func_ext,[status(esa)],[14084]) ).
thf(13513,plain,
( ~ sk10
| ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : ~ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[13304,122]) ).
thf(13518,plain,
( ~ sk10
| ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( sk5
!= ( ^ [A: a] : ~ sk10 ) ) ),
inference(simp,[status(thm)],[13513]) ).
thf(17,plain,
! [A: a > $o] :
( ~ ( A @ ( sk11 @ A ) )
| ( A @ ( sk12 @ A ) )
| ( A @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(66,plain,
! [A: a > $o] :
( ~ ( A @ ( sk11 @ A ) )
| ( A @ ( sk12 @ A ) )
| ( A @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[17]) ).
thf(32243,plain,
( sk7
| ~ sk6
| ( sk43 != sk4 )
| ( ( sk5 @ sk34 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[31434,11]) ).
thf(32291,plain,
( sk7
| ~ sk6
| ( sk43 != sk4 )
| ( sk34 != sk4 ) ),
inference(simp,[status(thm)],[32243]) ).
thf(220,plain,
! [A: a > $o] :
( ( sk1 @ sk8 @ ( sk11 @ A ) )
| ( sk1 @ ( sk12 @ A ) @ ( sk13 @ A ) )
| sk10
| ~ sk7
| sk6
| ( ( A @ sk9 )
!= ( sk1 @ sk8 @ ( sk11 @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[46]) ).
thf(251,plain,
! [A: a > $o] :
( ( sk1 @ sk8 @ ( sk11 @ A ) )
| ( sk1 @ ( sk12 @ A ) @ ( sk13 @ A ) )
| sk10
| sk6
| ~ sk7
| ( ( A @ sk9 )
!= ( sk1 @ sk8 @ ( sk11 @ A ) ) ) ),
inference(simp,[status(thm)],[220]) ).
thf(1427,plain,
( ~ sk10
| ~ sk7
| sk6
| ~ ( sk5 @ sk8 )
| ( ( sk5
@ ( sk14
@ ^ [A: a] : $false ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[785,11]) ).
thf(1460,plain,
( sk6
| ~ sk10
| ~ sk7
| ~ ( sk5 @ sk8 )
| ( ( sk14
@ ^ [A: a] : $false )
!= sk4 ) ),
inference(simp,[status(thm)],[1427]) ).
thf(36,plain,
! [A: a > $o] :
( sk7
| ( sk1 @ sk18 @ ( sk22 @ A ) )
| ( sk2 @ sk18 @ ( sk22 @ A ) )
| ~ ( sk21 @ A )
| ( A @ sk19 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(80,plain,
! [A: a > $o] :
( sk7
| ( sk1 @ sk18 @ ( sk22 @ A ) )
| ( sk2 @ sk18 @ ( sk22 @ A ) )
| ~ ( sk21 @ A )
| ( A @ sk19 )
| sk6 ),
inference(simp,[status(thm)],[36]) ).
thf(18518,plain,
( ~ sk6
| ( sk40 != sk34 )
| ( ( sk5 @ sk34 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18300,11]) ).
thf(18567,plain,
( ~ sk6
| ( sk40 != sk34 )
| ( sk34 != sk4 ) ),
inference(simp,[status(thm)],[18518]) ).
thf(14313,plain,
( ~ sk6
| ( ( sk33 @ sk5 )
!= sk35 )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk39 ) ) ),
inference(paramod_ordered,[status(thm)],[9916,9994]) ).
thf(14329,plain,
( ~ sk6
| ( ( sk33 @ sk5 )
!= sk35 )
| ( ( sk31 @ sk5 )
!= sk39 ) ),
inference(simp,[status(thm)],[14313]) ).
thf(26427,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= sk35 )
| ( sk5 @ sk47 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[17678]) ).
thf(26503,plain,
( ~ sk6
| ( sk5 @ sk47 )
| ( ( sk31 @ sk5 )
!= sk35 )
| ~ sk6 ),
inference(cnf,[status(esa)],[26427]) ).
thf(26504,plain,
( ~ sk6
| ( sk5 @ sk47 )
| ( ( sk31 @ sk5 )
!= sk35 ) ),
inference(simp,[status(thm)],[26503]) ).
thf(88,plain,
! [B: a > a,A: a > a] :
( ~ sk6
| ~ ( sk1
@ ( A
@ ( sk31
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk31
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ~ ( sk30
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk1 @ ( A @ sk4 ) @ ( B @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [D: a] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(112,plain,
! [B: a > a,A: a > a] :
( ~ sk6
| ~ ( sk1
@ ( A
@ ( sk31
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk31
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ~ ( sk30
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk1 @ ( A @ sk4 ) @ ( B @ sk4 ) ) ),
inference(simp,[status(thm)],[88]) ).
thf(18774,plain,
( ~ sk6
| ( sk34 != sk4 )
| ( sk5 @ sk41 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[14137]) ).
thf(18834,plain,
( ~ sk6
| ( sk5 @ sk41 )
| ( sk34 != sk4 )
| ~ sk6 ),
inference(cnf,[status(esa)],[18774]) ).
thf(18835,plain,
( ~ sk6
| ( sk5 @ sk41 )
| ( sk34 != sk4 ) ),
inference(simp,[status(thm)],[18834]) ).
thf(18891,plain,
( ~ sk6
| ( sk34 != sk4 )
| ( ( sk5 @ sk41 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18835,11]) ).
thf(18913,plain,
( ~ sk6
| ( sk34 != sk4 )
| ( sk41 != sk4 ) ),
inference(simp,[status(thm)],[18891]) ).
thf(12229,plain,
( ~ sk6
| sk7
| ( ( sk31 @ sk5 )
!= sk35 )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[9664,10019]) ).
thf(12234,plain,
( sk7
| ~ sk6
| ( ( sk31 @ sk5 )
!= sk35 )
| ( sk5
!= ( ^ [A: a] : sk7 ) ) ),
inference(simp,[status(thm)],[12229]) ).
thf(14,plain,
! [A: a > $o] :
( sk7
| ~ ( A @ ( sk22 @ A ) )
| ~ ( sk21 @ A )
| ( A @ sk19 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(48,plain,
! [A: a > $o] :
( sk7
| ~ ( A @ ( sk22 @ A ) )
| ~ ( sk21 @ A )
| ( A @ sk19 )
| sk6 ),
inference(simp,[status(thm)],[14]) ).
thf(9945,plain,
( ~ sk6
| ( sk5 @ sk36 )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5 @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[9770,5252]) ).
thf(10001,plain,
( ( sk5 @ sk36 )
| ~ sk6
| ( ( sk33 @ sk5 )
!= sk35 ) ),
inference(simp,[status(thm)],[9945]) ).
thf(10061,plain,
( ~ sk6
| ( ( sk33 @ sk5 )
!= ( sk31 @ sk5 ) )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk39 ) ) ),
inference(paramod_ordered,[status(thm)],[9916,5320]) ).
thf(10112,plain,
( ~ sk6
| ( ( sk33 @ sk5 )
!= ( sk31 @ sk5 ) )
| ( ( sk31 @ sk5 )
!= sk39 ) ),
inference(simp,[status(thm)],[10061]) ).
thf(2078,plain,
( sk7
| ( sk25
@ ^ [A: a] : sk6 )
| sk6
| sk6
| sk6 ),
inference(prim_subst,[status(thm)],[63:[bind(A,$thf( ^ [B: a] : sk6 ))]]) ).
thf(2160,plain,
( sk7
| ( sk25
@ ^ [A: a] : sk6 )
| sk6 ),
inference(simp,[status(thm)],[2078]) ).
thf(13842,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[9731,9768]) ).
thf(13893,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) )
| ( sk5
!= ( ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[13842]) ).
thf(3307,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ~ ( sk30
@ ^ [B: a] :
~ ( A @ B ) )
| ~ sk6
| ~ sk10
| ~ ( sk30
@ ^ [B: a] : ~ sk10 )
| ( ( ~ ( sk30
@ ^ [B: a] : $false ) )
!= sk10 )
| ( ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
!= sk10 ) ),
inference(paramod_ordered,[status(thm)],[108,2739]) ).
thf(3333,plain,
( ~ sk10
| ~ ( sk30
@ ^ [A: a] : ~ sk10 )
| ~ sk6
| ~ sk10
| ~ ( sk30
@ ^ [A: a] : ~ sk10 )
| ( ( ~ ( sk30
@ ^ [A: a] : $false ) )
!= sk10 ) ),
inference(pre_uni,[status(thm)],[3307:[bind(A,$thf( ^ [B: a] : sk10 ))]]) ).
thf(3346,plain,
( ~ sk10
| ~ ( sk30
@ ^ [A: a] : ~ sk10 )
| ~ sk6
| ( ( ~ ( sk30
@ ^ [A: a] : $false ) )
!= sk10 ) ),
inference(simp,[status(thm)],[3333]) ).
thf(9277,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ~ sk10
| ( ( ~ ( sk30
@ ^ [B: a] : $false ) )
!= sk10 )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : ~ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[76,3346]) ).
thf(9278,plain,
( ~ sk6
| ~ sk10
| ~ sk10
| ~ sk10
| ( ( ~ ( sk30
@ ^ [A: a] : $false ) )
!= sk10 ) ),
inference(pattern_uni,[status(thm)],[9277:[bind(A,$thf( ^ [B: a] : ~ ( sk10 ) ))]]) ).
thf(9633,plain,
( ( ( ~ ( sk30
@ ^ [A: a] : $false ) )
!= sk10 )
| ~ sk10
| ~ sk10
| ~ sk10
| ~ sk6 ),
inference(cnf,[status(esa)],[9278]) ).
thf(9634,plain,
( ( ( ~ ( sk30
@ ^ [A: a] : $false ) )
!= sk10 )
| ~ sk10
| ~ sk6 ),
inference(simp,[status(thm)],[9633]) ).
thf(147,plain,
( sk7
| ( sk21
@ ^ [A: a] : sk6 )
| sk6
| sk6
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( ^ [B: a] : sk6 ))]]) ).
thf(177,plain,
( sk7
| ( sk21
@ ^ [A: a] : sk6 )
| sk6 ),
inference(simp,[status(thm)],[147]) ).
thf(7,plain,
! [A: a > $o] :
( sk7
| ( sk25 @ A )
| ( sk1 @ ( sk27 @ A ) @ ( sk28 @ A ) )
| ( sk2 @ ( sk27 @ A ) @ ( sk28 @ A ) )
| ( A @ sk20 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(72,plain,
! [A: a > $o] :
( sk7
| ( sk25 @ A )
| ( sk1 @ ( sk27 @ A ) @ ( sk28 @ A ) )
| ( sk2 @ ( sk27 @ A ) @ ( sk28 @ A ) )
| ( A @ sk20 )
| sk6 ),
inference(simp,[status(thm)],[7]) ).
thf(144,plain,
! [A: a > a] :
( sk7
| ( sk21
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) )
| ( sk29
@ ( A
@ ( sk23
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) ) ) )
| ( sk29 @ ( A @ sk19 ) )
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( ^ [C: a] : ( sk29 @ ( B @ C ) ) ))]]) ).
thf(175,plain,
! [A: a > a] :
( sk7
| ( sk21
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) )
| ( sk29
@ ( A
@ ( sk23
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) ) ) )
| ( sk29 @ ( A @ sk19 ) )
| sk6 ),
inference(simp,[status(thm)],[144]) ).
thf(27686,plain,
( ~ sk6
| ( sk51 != sk4 )
| ( ( sk5 @ sk34 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[27490,11]) ).
thf(27759,plain,
( ~ sk6
| ( sk51 != sk4 )
| ( sk34 != sk4 ) ),
inference(simp,[status(thm)],[27686]) ).
thf(17836,plain,
( ( ( sk5 @ sk48 )
!= ~ sk6 )
| ~ sk6
| ( ( sk31 @ sk5 )
!= sk39 ) ),
inference(func_ext,[status(esa)],[12546]) ).
thf(26550,plain,
( ~ sk6
| ( ( sk31 @ sk5 )
!= sk39 )
| ( sk5 @ sk48 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[17836]) ).
thf(26627,plain,
( ~ sk6
| ( sk5 @ sk48 )
| ( ( sk31 @ sk5 )
!= sk39 )
| ~ sk6 ),
inference(cnf,[status(esa)],[26550]) ).
thf(26628,plain,
( ~ sk6
| ( sk5 @ sk48 )
| ( ( sk31 @ sk5 )
!= sk39 ) ),
inference(simp,[status(thm)],[26627]) ).
thf(9950,plain,
( ~ sk6
| ( sk30 @ sk5 )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5 @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[9770,5127]) ).
thf(9995,plain,
( ( sk30 @ sk5 )
| ~ sk6
| ( ( sk33 @ sk5 )
!= sk35 ) ),
inference(simp,[status(thm)],[9950]) ).
thf(13678,plain,
( ~ sk7
| ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : ~ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[13411,122]) ).
thf(13729,plain,
( ~ sk7
| ~ sk6
| ~ ( sk5 @ ( sk31 @ sk5 ) )
| ( sk5
!= ( ^ [A: a] : ~ sk7 ) ) ),
inference(simp,[status(thm)],[13678]) ).
thf(465,plain,
( ~ ( sk29 @ sk4 )
| ~ ( sk30
@ ^ [A: a] :
~ ( sk29 @ A ) )
| ( sk29
@ ( sk31
@ ^ [A: a] :
~ ( sk29 @ A ) ) )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[108:[bind(A,$thf( sk29 ))]]) ).
thf(27491,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( ( sk5 @ sk51 )
!= ( sk5 @ sk34 ) ) ),
inference(simp,[status(thm)],[27464]) ).
thf(84,plain,
! [A: a > $o] :
( ~ sk6
| ~ ( sk30 @ A )
| ( A @ sk4 )
| ( ( A @ ( sk31 @ A ) )
!= ( ~ ( A @ sk4 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[47]) ).
thf(104,plain,
! [A: a > $o] :
( ( A @ sk4 )
| ~ sk6
| ~ ( sk30 @ A )
| ( ( A @ ( sk31 @ A ) )
!= ( ~ ( A @ sk4 ) ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(5192,plain,
( ~ sk6
| ~ ( sk30
@ ^ [A: a] : $false )
| ( sk30 @ sk5 )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5
@ ( sk31
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[3601,5127]) ).
thf(5226,plain,
( ( sk30 @ sk5 )
| ~ sk6
| ~ ( sk30
@ ^ [A: a] : $false )
| ( ( sk33 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[5192]) ).
thf(9257,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ( sk30 @ sk5 )
| ( ( sk33 @ sk5 )
!= ( sk31
@ ^ [B: a] : $false ) )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[76,5226]) ).
thf(9258,plain,
( ~ sk6
| $false
| $false
| ( sk30 @ sk5 )
| ( ( sk33 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[9257:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(9628,plain,
( ~ sk6
| ( sk30 @ sk5 )
| ( ( sk33 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[9258]) ).
thf(27380,plain,
( ~ sk6
| ( sk5 @ sk34 )
| ( ( sk5 @ ( sk33 @ sk5 ) )
!= ( sk5 @ sk51 ) ) ),
inference(paramod_ordered,[status(thm)],[27053,9769]) ).
thf(27508,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( ( sk33 @ sk5 )
!= sk51 ) ),
inference(simp,[status(thm)],[27380]) ).
thf(155,plain,
! [B: a > a,A: a > a] :
( sk7
| ( sk21
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk2
@ ( A
@ ( sk23
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk23
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ( sk2 @ ( A @ sk19 ) @ ( B @ sk19 ) )
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( ^ [D: a] : ( sk2 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(186,plain,
! [B: a > a,A: a > a] :
( sk7
| ( sk21
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk2
@ ( A
@ ( sk23
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk23
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ( sk2 @ ( A @ sk19 ) @ ( B @ sk19 ) )
| sk6 ),
inference(simp,[status(thm)],[155]) ).
thf(136,plain,
! [A: a > $o] :
( sk7
| ( sk21 @ A )
| ( A @ sk19 )
| sk6
| ( ( A @ ( sk23 @ A ) )
!= ( sk21 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[50]) ).
thf(171,plain,
! [A: a > $o] :
( sk7
| ( sk21 @ A )
| ( A @ sk19 )
| sk6
| ( ( A @ ( sk23 @ A ) )
!= ( sk21 @ A ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(24899,plain,
( ~ sk10
| ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk10 ) )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk34 ) ) ),
inference(paramod_ordered,[status(thm)],[13538,13518]) ).
thf(24962,plain,
( ~ sk10
| ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk10 ) )
| ( ( sk31 @ sk5 )
!= sk34 ) ),
inference(simp,[status(thm)],[24899]) ).
thf(25205,plain,
( ~ sk6
| ( ( sk5 @ sk46 )
!= ~ sk6 )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk39 ) ) ),
inference(paramod_ordered,[status(thm)],[9916,15961]) ).
thf(25259,plain,
( ~ sk6
| ( ( sk5 @ sk46 )
!= ~ sk6 )
| ( ( sk31 @ sk5 )
!= sk39 ) ),
inference(simp,[status(thm)],[25205]) ).
thf(2080,plain,
( sk7
| ( sk25
@ ^ [A: a] : $false )
| $false
| $false
| sk6 ),
inference(prim_subst,[status(thm)],[63:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(2162,plain,
( sk7
| ( sk25
@ ^ [A: a] : $false )
| sk6 ),
inference(simp,[status(thm)],[2080]) ).
thf(899,plain,
( ~ ( sk17 @ sk4 )
| ~ ( sk30
@ ^ [A: a] :
~ ( sk17 @ A ) )
| ~ sk6
| ( ( sk17
@ ( sk31
@ ^ [A: a] :
~ ( sk17 @ A ) ) )
!= ( ~ ( sk17 @ sk4 ) ) ) ),
inference(prim_subst,[status(thm)],[507:[bind(A,$thf( sk17 ))]]) ).
thf(2006,plain,
! [A: a > $o] :
( sk7
| ( sk25 @ A )
| ( A @ sk20 )
| sk6
| ( ( A @ ( sk27 @ A ) )
!= ( sk29 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[63,21]) ).
thf(2120,plain,
( sk7
| ( sk25
@ ^ [A: a] : ( sk29 @ sk20 ) )
| ( sk29 @ sk20 )
| sk6 ),
inference(pre_uni,[status(thm)],[2006:[bind(A,$thf( ^ [B: a] : ( sk29 @ sk20 ) ))]]) ).
thf(25368,plain,
( ~ sk6
| ( sk5 @ sk46 )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk39 ) ) ),
inference(paramod_ordered,[status(thm)],[9916,25277]) ).
thf(25414,plain,
( ( sk5 @ sk46 )
| ~ sk6
| ( ( sk31 @ sk5 )
!= sk39 ) ),
inference(simp,[status(thm)],[25368]) ).
thf(151,plain,
! [A: a > $o] :
( sk7
| ( sk21
@ ^ [B: a] :
~ ( A @ B ) )
| ~ ( A
@ ( sk23
@ ^ [B: a] :
~ ( A @ B ) ) )
| ~ ( A @ sk19 )
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( ^ [C: a] : ~ ( B @ C ) ))]]) ).
thf(182,plain,
! [A: a > $o] :
( sk6
| ~ ( A @ sk19 )
| ~ ( A
@ ( sk23
@ ^ [B: a] :
~ ( A @ B ) ) )
| ( sk21
@ ^ [B: a] :
~ ( A @ B ) )
| sk7 ),
inference(cnf,[status(esa)],[151]) ).
thf(183,plain,
! [A: a > $o] :
( sk6
| ~ ( A @ sk19 )
| ~ ( A
@ ( sk23
@ ^ [B: a] :
~ ( A @ B ) ) )
| ( sk21
@ ^ [B: a] :
~ ( A @ B ) )
| sk7 ),
inference(simp,[status(thm)],[182]) ).
thf(23858,plain,
( sk6
| ~ sk10
| ~ sk10
| ( sk21
@ ^ [A: a] : ~ sk10 )
| sk7 ),
inference(prim_subst,[status(thm)],[183:[bind(A,$thf( ^ [B: a] : sk10 ))]]) ).
thf(23993,plain,
( sk6
| ~ sk10
| ( sk21
@ ^ [A: a] : ~ sk10 )
| sk7 ),
inference(simp,[status(thm)],[23858]) ).
thf(19,plain,
! [A: a > $o] :
( ( sk1 @ sk8 @ ( sk11 @ A ) )
| ~ ( A @ ( sk13 @ A ) )
| ( A @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(82,plain,
! [A: a > $o] :
( ( sk1 @ sk8 @ ( sk11 @ A ) )
| ~ ( A @ ( sk13 @ A ) )
| ( A @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[19]) ).
thf(5159,plain,
( ~ sk6
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ~ ( sk30
@ ^ [A: a] : $false )
| ( ( sk31 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) )
| ( ( sk30 @ sk5 )
!= ( sk30 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[5127,3654]) ).
thf(5160,plain,
( ~ sk6
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ~ ( sk30
@ ^ [A: a] : $false )
| ( ( sk31 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[5159:[]]) ).
thf(9017,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ( ( sk31 @ sk5 )
!= ( sk31
@ ^ [B: a] : $false ) )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[76,5160]) ).
thf(9018,plain,
( ~ sk6
| $false
| $false
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ( ( sk31 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[9017:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(9718,plain,
( ~ sk6
| ~ ( sk5 @ ( sk33 @ sk5 ) )
| ( ( sk31 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[9018]) ).
thf(2081,plain,
( sk7
| ( sk25 @ sk5 )
| ( sk5 @ ( sk27 @ sk5 ) )
| ( sk5 @ sk20 )
| sk6 ),
inference(prim_subst,[status(thm)],[63:[bind(A,$thf( sk5 ))]]) ).
thf(94,plain,
! [A: a > a > $o] :
( ~ sk6
| ~ ( sk30
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk30 @ ( A @ B ) ) ) ) )
| ~ ( sk30
@ ^ [B: a] : ( sk30 @ ( A @ B ) ) )
| ( sk30 @ ( A @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [C: a] : ( sk30 @ ( B @ C ) ) ))]]) ).
thf(119,plain,
! [A: a > a > $o] :
( ~ sk6
| ~ ( sk30
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk30 @ ( A @ B ) ) ) ) )
| ~ ( sk30
@ ^ [B: a] : ( sk30 @ ( A @ B ) ) )
| ( sk30 @ ( A @ sk4 ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(25,plain,
! [B: a,A: a] :
( sk7
| ~ ( sk29 @ A )
| ~ ( sk2 @ A @ B )
| ( sk29 @ B )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(58,plain,
! [B: a,A: a] :
( sk7
| ~ ( sk29 @ A )
| ~ ( sk2 @ A @ B )
| ( sk29 @ B )
| sk6 ),
inference(simp,[status(thm)],[25]) ).
thf(235,plain,
( ( sk1 @ sk8 @ ( sk11 @ sk5 ) )
| ( sk1 @ ( sk12 @ sk5 ) @ ( sk13 @ sk5 ) )
| ( sk5 @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(prim_subst,[status(thm)],[46:[bind(A,$thf( sk5 ))]]) ).
thf(246,plain,
( ( sk1 @ sk8
@ ( sk11
@ ^ [A: a] : ( sk17 @ sk9 ) ) )
| ( sk1
@ ( sk12
@ ^ [A: a] : ( sk17 @ sk9 ) )
@ ( sk13
@ ^ [A: a] : ( sk17 @ sk9 ) ) )
| sk10
| ~ sk7
| sk6 ),
inference(pre_uni,[status(thm)],[202:[bind(A,$thf( ^ [B: a] : ( sk17 @ sk9 ) ))]]) ).
thf(100,plain,
( ~ sk6
| ~ ( sk29 @ ( sk31 @ sk29 ) )
| ~ ( sk30 @ sk29 )
| ( sk29 @ sk4 ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( sk29 ))]]) ).
thf(3956,plain,
! [A: a > $o] :
( ~ sk6
| ~ ( A @ ( sk33 @ A ) )
| ( A @ sk4 )
| ~ ( sk29 @ ( sk31 @ sk29 ) )
| ( sk29 @ sk4 )
| ( ( sk30 @ A )
!= ( sk30 @ sk29 ) ) ),
inference(paramod_ordered,[status(thm)],[64,100]) ).
thf(3957,plain,
( ~ sk6
| ~ ( sk29 @ ( sk33 @ sk29 ) )
| ( sk29 @ sk4 )
| ~ ( sk29 @ ( sk31 @ sk29 ) )
| ( sk29 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[3956:[bind(A,$thf( sk29 ))]]) ).
thf(4039,plain,
( ~ sk6
| ~ ( sk29 @ ( sk33 @ sk29 ) )
| ( sk29 @ sk4 )
| ~ ( sk29 @ ( sk31 @ sk29 ) ) ),
inference(simp,[status(thm)],[3957]) ).
thf(146,plain,
( sk7
| ( sk21 @ sk29 )
| ( sk29 @ ( sk23 @ sk29 ) )
| ( sk29 @ sk19 )
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( sk29 ))]]) ).
thf(12,plain,
! [A: a] :
( sk7
| ~ ( sk2 @ sk18 @ A )
| ( sk29 @ A )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(51,plain,
! [A: a] :
( sk7
| ~ ( sk2 @ sk18 @ A )
| ( sk29 @ A )
| sk6 ),
inference(simp,[status(thm)],[12]) ).
thf(14394,plain,
( sk10
| ~ sk6
| ( sk5
!= ( ^ [A: a] : sk10 ) )
| ( ( sk5 @ sk34 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[12009,11]) ).
thf(14411,plain,
( sk10
| ~ sk6
| ( sk5
!= ( ^ [A: a] : sk10 ) )
| ( sk34 != sk4 ) ),
inference(simp,[status(thm)],[14394]) ).
thf(9037,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ( sk1 @ sk3
@ ( sk31
@ ^ [B: a] : $false ) )
| ( sk2 @ sk3
@ ( sk31
@ ^ [B: a] : $false ) )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[76,1773]) ).
thf(9038,plain,
( ~ sk6
| $false
| $false
| ( sk1 @ sk3
@ ( sk31
@ ^ [A: a] : $false ) )
| ( sk2 @ sk3
@ ( sk31
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[9037:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(9728,plain,
( ~ sk6
| ( sk1 @ sk3
@ ( sk31
@ ^ [A: a] : $false ) )
| ( sk2 @ sk3
@ ( sk31
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[9038]) ).
thf(133,plain,
! [A: a > $o] :
( sk7
| ( sk21 @ A )
| ( A @ sk19 )
| sk6
| ( ( A @ ( sk23 @ A ) )
!= ( sk29 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[50,21]) ).
thf(168,plain,
( sk7
| ( sk21
@ ^ [A: a] : ( sk29 @ sk20 ) )
| ( sk29 @ sk20 )
| sk6 ),
inference(pre_uni,[status(thm)],[133:[bind(A,$thf( ^ [B: a] : ( sk29 @ sk20 ) ))]]) ).
thf(242,plain,
( ( sk1 @ sk8 @ ( sk11 @ sk29 ) )
| ( sk1 @ ( sk12 @ sk29 ) @ ( sk13 @ sk29 ) )
| ( sk29 @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(prim_subst,[status(thm)],[46:[bind(A,$thf( sk29 ))]]) ).
thf(474,plain,
( ~ ( sk17 @ sk4 )
| ~ ( sk30
@ ^ [A: a] :
~ ( sk17 @ A ) )
| ( sk17
@ ( sk31
@ ^ [A: a] :
~ ( sk17 @ A ) ) )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[108:[bind(A,$thf( sk17 ))]]) ).
thf(19497,plain,
( sk7
| sk6
| sk6
| sk6
| ( ( sk21
@ ^ [A: a] : sk6 )
!= sk6 ) ),
inference(prim_subst,[status(thm)],[164:[bind(A,$thf( ^ [B: a] : sk6 ))]]) ).
thf(19733,plain,
( sk7
| sk6
| ( ( sk21
@ ^ [A: a] : sk6 )
!= sk6 ) ),
inference(simp,[status(thm)],[19497]) ).
thf(14890,plain,
( ~ sk6
| ( ( sk33 @ sk5 )
!= sk39 )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk39 ) ) ),
inference(paramod_ordered,[status(thm)],[9916,10114]) ).
thf(14903,plain,
( ~ sk6
| ( ( sk33 @ sk5 )
!= sk39 )
| ( ( sk31 @ sk5 )
!= sk39 ) ),
inference(simp,[status(thm)],[14890]) ).
thf(9983,plain,
( ~ sk6
| ( ( sk5 @ sk35 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[9770,11]) ).
thf(10009,plain,
( ~ sk6
| ( sk35 != sk4 ) ),
inference(simp,[status(thm)],[9983]) ).
thf(2982,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ~ ( sk30
@ ^ [B: a] :
~ ( A @ B ) )
| ~ sk6
| ~ sk7
| ~ ( sk30
@ ^ [B: a] : ~ sk7 )
| ( ( ~ ( sk30
@ ^ [B: a] : $false ) )
!= sk7 )
| ( ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
!= sk7 ) ),
inference(paramod_ordered,[status(thm)],[108,2730]) ).
thf(3010,plain,
( ~ sk7
| ~ ( sk30
@ ^ [A: a] : ~ sk7 )
| ~ sk6
| ~ sk7
| ~ ( sk30
@ ^ [A: a] : ~ sk7 )
| ( ( ~ ( sk30
@ ^ [A: a] : $false ) )
!= sk7 ) ),
inference(pre_uni,[status(thm)],[2982:[bind(A,$thf( ^ [B: a] : sk7 ))]]) ).
thf(3014,plain,
( ~ sk7
| ~ ( sk30
@ ^ [A: a] : ~ sk7 )
| ~ sk6
| ( ( ~ ( sk30
@ ^ [A: a] : $false ) )
!= sk7 ) ),
inference(simp,[status(thm)],[3010]) ).
thf(9050,plain,
! [A: a > $o] :
( ~ sk6
| ( A @ ( sk32 @ A ) )
| ( A @ sk4 )
| ~ sk7
| ( ( ~ ( sk30
@ ^ [B: a] : $false ) )
!= sk7 )
| ( ( sk30 @ A )
!= ( sk30
@ ^ [B: a] : ~ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[76,3014]) ).
thf(9051,plain,
( ~ sk6
| ~ sk7
| ~ sk7
| ~ sk7
| ( ( ~ ( sk30
@ ^ [A: a] : $false ) )
!= sk7 ) ),
inference(pattern_uni,[status(thm)],[9050:[bind(A,$thf( ^ [B: a] : ~ ( sk7 ) ))]]) ).
thf(9736,plain,
( ( ( ~ ( sk30
@ ^ [A: a] : $false ) )
!= sk7 )
| ~ sk7
| ~ sk7
| ~ sk7
| ~ sk6 ),
inference(cnf,[status(esa)],[9051]) ).
thf(9737,plain,
( ( ( ~ ( sk30
@ ^ [A: a] : $false ) )
!= sk7 )
| ~ sk7
| ~ sk6 ),
inference(simp,[status(thm)],[9736]) ).
thf(34,plain,
! [A: a > $o] :
( ~ sk10
| ~ ( A @ ( sk14 @ A ) )
| ( A @ ( sk15 @ A ) )
| ( A @ sk9 )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(68,plain,
! [A: a > $o] :
( ~ sk10
| ~ ( A @ ( sk14 @ A ) )
| ( A @ ( sk15 @ A ) )
| ( A @ sk9 )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[34]) ).
thf(28,plain,
! [B: a,A: a] :
( sk7
| ~ ( sk29 @ A )
| ~ ( sk1 @ A @ B )
| ( sk29 @ B )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(62,plain,
! [B: a,A: a] :
( sk7
| ~ ( sk29 @ A )
| ~ ( sk1 @ A @ B )
| ( sk29 @ B )
| sk6 ),
inference(simp,[status(thm)],[28]) ).
thf(101,plain,
! [B: a > a,A: a > a] :
( ~ sk6
| ~ ( sk2
@ ( A
@ ( sk31
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk31
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ~ ( sk30
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk2 @ ( A @ sk4 ) @ ( B @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [D: a] : ( sk2 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(111,plain,
! [B: a > a,A: a > a] :
( ~ sk6
| ~ ( sk2
@ ( A
@ ( sk31
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk31
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ~ ( sk30
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk2 @ ( A @ sk4 ) @ ( B @ sk4 ) ) ),
inference(simp,[status(thm)],[101]) ).
thf(18903,plain,
( ~ sk6
| ( sk34 != sk4 )
| ~ ( sk30 @ sk5 )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5 @ sk41 ) ) ),
inference(paramod_ordered,[status(thm)],[18835,122]) ).
thf(18939,plain,
( ~ sk6
| ( sk34 != sk4 )
| ~ ( sk30 @ sk5 )
| ( ( sk31 @ sk5 )
!= sk41 ) ),
inference(simp,[status(thm)],[18903]) ).
thf(25357,plain,
( ~ sk6
| ( sk5 @ sk46 )
| ( ( sk5 @ ( sk31 @ sk5 ) )
!= ( sk5
@ ( sk31
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[9641,25277]) ).
thf(25408,plain,
( ( sk5 @ sk46 )
| ~ sk6
| ( ( sk31 @ sk5 )
!= ( sk31
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[25357]) ).
thf(13468,plain,
( ~ sk10
| ~ sk6
| ( ( sk31 @ sk5 )
!= sk39 )
| ( ( sk30 @ sk5 )
!= ( sk30
@ ^ [A: a] : ~ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[13304,10136]) ).
thf(13537,plain,
( ~ sk10
| ~ sk6
| ( ( sk31 @ sk5 )
!= sk39 )
| ( sk5
!= ( ^ [A: a] : ~ sk10 ) ) ),
inference(simp,[status(thm)],[13468]) ).
thf(39468,plain,
$false,
inference(e,[status(thm)],[69,3962,5320,249,9731,3969,17656,1406,8723,730,1522,5793,14446,20658,9769,120,247,27492,24946,56,18438,14084,2168,29401,8551,185,14333,31325,5252,42,1576,9994,12009,29572,9625,174,52,184,785,32161,18436,110,14331,20313,1087,5127,46,11802,8543,9725,57,10117,78,9661,26374,9768,27002,14904,12185,164,179,13538,12236,2073,13719,4033,61,20530,26887,116,1697,507,74,9703,10374,60,117,19727,102,26047,12542,38,18300,70,192,18209,9745,21,1619,30924,65,18535,5201,757,13411,9641,10131,27886,156,12546,16004,53,8800,8567,109,9640,14529,77,901,5786,9645,8658,173,17678,31464,1825,32002,12191,13522,73,12183,105,14961,805,10011,2089,9765,28871,19740,161,64,180,25389,176,191,14760,25241,12011,31434,59,118,2161,14010,713,49,17611,181,27053,25277,12547,18299,71,27490,9638,54,187,113,81,9771,76,13705,25866,10115,11686,172,18331,10000,10019,28529,14767,140,14137,13518,108,66,32291,15961,10136,251,13304,1460,1528,9916,80,28989,13717,18567,14329,3,30284,26504,722,14349,112,18913,12234,776,48,10001,18,10112,2160,18835,13893,1516,63,50,67,9634,177,17632,12001,5319,10129,17188,11,72,175,27759,8565,26628,9995,9770,13729,18295,465,17612,25278,9664,10114,27491,20747,104,9628,482,9755,27508,186,171,55,24962,10563,75,25259,2162,899,2120,25414,23993,82,9718,2081,119,58,235,246,4039,1512,5796,146,51,183,14411,9728,735,168,28233,242,5835,17836,474,19733,79,14903,10009,28982,12235,9737,47,68,62,111,18939,122,25408,100,13537]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SEV154^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.13 % Command : run_Leo-III %s %d THM
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 21 19:24:25 EDT 2024
% 0.13/0.34 % CPUTime :
% 1.00/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.13/1.01 % [INFO] Parsing done (128ms).
% 1.38/1.02 % [INFO] Running in sequential loop mode.
% 1.83/1.25 % [INFO] eprover registered as external prover.
% 1.83/1.26 % [INFO] Scanning for conjecture ...
% 1.83/1.34 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.11/1.37 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.11/1.37 % [INFO] Problem is higher-order (TPTP THF).
% 2.11/1.38 % [INFO] Type checking passed.
% 2.11/1.38 % [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 ...
% 89.42/18.69 % External prover 'e' found a proof!
% 89.42/18.69 % [INFO] Killing All external provers ...
% 89.42/18.70 % Time passed: 18153ms (effective reasoning time: 17674ms)
% 89.42/18.70 % 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)>
% 89.42/18.70 % Axioms used in derivation (0):
% 89.42/18.70 % No. of inferences in proof: 647
% 89.42/18.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 18153 ms resp. 17674 ms w/o parsing
% 90.73/18.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 90.73/18.93 % [INFO] Killing All external provers ...
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