TSTP Solution File: SEV153^5 by Leo-III---1.7.15
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV153^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n027.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 78.99s 17.82s
% Output : Refutation 79.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 1
% Syntax : Number of formulae : 791 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 4924 ( 582 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 9142 (1924 ~;2675 |; 57 &;4408 @)
% ( 0 <=>; 78 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 295 ( 295 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 51 usr; 30 con; 0-2 aty)
% Number of variables : 1220 ( 748 ^ 472 !; 0 ?;1220 :)
% 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: ( a > $o ) > $o ).
thf(sk8_type,type,
sk8: ( a > $o ) > a ).
thf(sk9_type,type,
sk9: ( a > $o ) > a ).
thf(sk10_type,type,
sk10: ( a > $o ) > a ).
thf(sk11_type,type,
sk11: $o ).
thf(sk12_type,type,
sk12: a ).
thf(sk13_type,type,
sk13: a ).
thf(sk14_type,type,
sk14: $o ).
thf(sk15_type,type,
sk15: ( a > $o ) > a ).
thf(sk16_type,type,
sk16: ( a > $o ) > a ).
thf(sk17_type,type,
sk17: ( a > $o ) > a ).
thf(sk18_type,type,
sk18: ( a > $o ) > a ).
thf(sk19_type,type,
sk19: ( a > $o ) > a ).
thf(sk20_type,type,
sk20: ( a > $o ) > a ).
thf(sk21_type,type,
sk21: a > $o ).
thf(sk22_type,type,
sk22: a ).
thf(sk23_type,type,
sk23: a ).
thf(sk24_type,type,
sk24: 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 ) > $o ).
thf(sk30_type,type,
sk30: ( a > $o ) > a ).
thf(sk31_type,type,
sk31: ( a > $o ) > a ).
thf(sk32_type,type,
sk32: ( a > $o ) > a ).
thf(sk33_type,type,
sk33: a > $o ).
thf(sk34_type,type,
sk34: a ).
thf(sk35_type,type,
sk35: a ).
thf(sk36_type,type,
sk36: a ).
thf(sk37_type,type,
sk37: a ).
thf(sk38_type,type,
sk38: 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(sk44_type,type,
sk44: a ).
thf(sk45_type,type,
sk45: 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(sk50_type,type,
sk50: a ).
thf(sk51_type,type,
sk51: a ).
thf(sk52_type,type,
sk52: 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 > $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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM251H_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 > $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 ) ) ) ) ),
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 > $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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(34,plain,
! [B: a,A: a] :
( sk6
| sk11
| ~ ( sk33 @ A )
| ~ ( sk2 @ A @ B )
| ( sk33 @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(69,plain,
! [B: a,A: a] :
( sk6
| sk11
| ~ ( sk33 @ A )
| ~ ( sk2 @ A @ B )
| ( sk33 @ B ) ),
inference(simp,[status(thm)],[34]) ).
thf(10,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk1 @ sk23 @ ( sk30 @ A ) )
| ( sk2 @ sk23 @ ( sk30 @ A ) )
| ~ ( sk29 @ A )
| ( A @ sk24 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(47,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk1 @ sk23 @ ( sk30 @ A ) )
| ( sk2 @ sk23 @ ( sk30 @ A ) )
| ~ ( sk29 @ A )
| ( A @ sk24 ) ),
inference(simp,[status(thm)],[10]) ).
thf(340,plain,
! [B: a > a,A: a > a] :
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
| ~ ( sk29
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk1 @ ( A @ sk24 ) @ ( B @ sk24 ) ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [D: a] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(365,plain,
! [B: a > a,A: a > a] :
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
| ~ ( sk29
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk1 @ ( A @ sk24 ) @ ( B @ sk24 ) ) ),
inference(simp,[status(thm)],[340]) ).
thf(45,plain,
! [A: a > $o] :
( ( sk7 @ A )
| ( A @ ( sk9 @ A ) )
| ( A @ sk4 )
| ~ sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(66,plain,
! [A: a > $o] :
( ( sk7 @ A )
| ( A @ ( sk9 @ A ) )
| ( A @ sk4 )
| ~ sk6 ),
inference(simp,[status(thm)],[45]) ).
thf(2731,plain,
( ( sk7
@ ^ [A: a] : $false )
| $false
| $false
| ~ sk6 ),
inference(prim_subst,[status(thm)],[66:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(2815,plain,
( ( sk7
@ ^ [A: a] : $false )
| ~ sk6 ),
inference(simp,[status(thm)],[2731]) ).
thf(39,plain,
! [A: a > $o] :
( ( sk1 @ sk3 @ ( sk8 @ A ) )
| ( sk2 @ sk3 @ ( sk8 @ A ) )
| ~ ( sk7 @ A )
| ( A @ sk4 )
| ~ sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(74,plain,
! [A: a > $o] :
( ( sk1 @ sk3 @ ( sk8 @ A ) )
| ( sk2 @ sk3 @ ( sk8 @ A ) )
| ~ ( sk7 @ A )
| ( A @ sk4 )
| ~ sk6 ),
inference(simp,[status(thm)],[39]) ).
thf(7783,plain,
! [A: a > $o] :
( ~ sk6
| ( sk1 @ sk3 @ ( sk8 @ A ) )
| ( sk2 @ sk3 @ ( sk8 @ A ) )
| ( A @ sk4 )
| ( ( sk7
@ ^ [B: a] : $false )
!= ( sk7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2815,74]) ).
thf(7784,plain,
( ~ sk6
| ( sk1 @ sk3
@ ( sk8
@ ^ [A: a] : $false ) )
| ( sk2 @ sk3
@ ( sk8
@ ^ [A: a] : $false ) )
| $false ),
inference(pattern_uni,[status(thm)],[7783:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(7851,plain,
( ~ sk6
| ( sk1 @ sk3
@ ( sk8
@ ^ [A: a] : $false ) )
| ( sk2 @ sk3
@ ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[7784]) ).
thf(36,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ( sk5 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7901,plain,
! [A: a] :
( ~ sk6
| ( sk1 @ sk3
@ ( sk8
@ ^ [B: a] : $false ) )
| ( sk5 @ A )
| ( ( sk2 @ sk3
@ ( sk8
@ ^ [B: a] : $false ) )
!= ( sk2 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7851,36]) ).
thf(7902,plain,
( ~ sk6
| ( sk1 @ sk3
@ ( sk8
@ ^ [A: a] : $false ) )
| ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[7901:[bind(A,$thf( sk8 @ ^ [B: a] : $false ))]]) ).
thf(21,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ( sk5 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7943,plain,
! [A: a] :
( ~ sk6
| ( sk5
@ ( sk8
@ ^ [B: a] : $false ) )
| ( sk5 @ A )
| ( ( sk1 @ sk3
@ ( sk8
@ ^ [B: a] : $false ) )
!= ( sk1 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7902,21]) ).
thf(7944,plain,
( ~ sk6
| ( sk5
@ ( sk8
@ ^ [A: a] : $false ) )
| ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[7943:[bind(A,$thf( sk8 @ ^ [B: a] : $false ))]]) ).
thf(7992,plain,
( ~ sk6
| ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[7944]) ).
thf(43,plain,
! [A: a > $o] :
( ~ ( A @ ( sk8 @ A ) )
| ~ ( sk7 @ A )
| ( A @ sk4 )
| ~ sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(78,plain,
! [A: a > $o] :
( ~ ( A @ ( sk8 @ A ) )
| ~ ( sk7 @ A )
| ( A @ sk4 )
| ~ sk6 ),
inference(simp,[status(thm)],[43]) ).
thf(98,plain,
( ~ ( sk5 @ ( sk8 @ sk5 ) )
| ~ ( sk7 @ sk5 )
| ( sk5 @ sk4 )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[78:[bind(A,$thf( sk5 ))]]) ).
thf(38,plain,
~ ( sk5 @ sk4 ),
inference(cnf,[status(esa)],[3]) ).
thf(307,plain,
( ~ ( sk5 @ ( sk8 @ sk5 ) )
| ~ ( sk7 @ sk5 )
| $false
| ~ sk6 ),
inference(rewrite,[status(thm)],[98,38]) ).
thf(308,plain,
( ~ ( sk5 @ ( sk8 @ sk5 ) )
| ~ ( sk7 @ sk5 )
| ~ sk6 ),
inference(simp,[status(thm)],[307]) ).
thf(2863,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk7 @ sk5 )
!= ( sk7
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[2815,308]) ).
thf(2907,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( sk5
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[2863]) ).
thf(8049,plain,
( ~ sk6
| ( sk5
!= ( ^ [A: a] : $false ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,2907]) ).
thf(8082,plain,
( ~ sk6
| ( sk5
!= ( ^ [A: a] : $false ) )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[8049]) ).
thf(8140,plain,
( ~ sk6
| ( sk5
!= ( ^ [A: a] : $false ) )
| ( sk5
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[8082]) ).
thf(8164,plain,
( ~ sk6
| ( sk5
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[8140]) ).
thf(8167,plain,
( ( sk5 @ sk45 )
| ~ sk6 ),
inference(func_ext,[status(esa)],[8164]) ).
thf(7,plain,
! [A: a > $o] :
( ( sk7 @ A )
| ~ ( A @ ( sk10 @ A ) )
| ( A @ sk4 )
| ~ sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(73,plain,
! [A: a > $o] :
( ( sk7 @ A )
| ~ ( A @ ( sk10 @ A ) )
| ( A @ sk4 )
| ~ sk6 ),
inference(simp,[status(thm)],[7]) ).
thf(7390,plain,
( ( sk7 @ sk5 )
| ~ ( sk5 @ ( sk10 @ sk5 ) )
| ( sk5 @ sk4 )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[73:[bind(A,$thf( sk5 ))]]) ).
thf(21863,plain,
( ( sk7 @ sk5 )
| ~ ( sk5 @ ( sk10 @ sk5 ) )
| $false
| ~ sk6 ),
inference(rewrite,[status(thm)],[7390,38]) ).
thf(21864,plain,
( ( sk7 @ sk5 )
| ~ ( sk5 @ ( sk10 @ sk5 ) )
| ~ sk6 ),
inference(simp,[status(thm)],[21863]) ).
thf(21867,plain,
( ~ ( sk5 @ ( sk10 @ sk5 ) )
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk7 @ sk5 )
!= ( sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[21864,308]) ).
thf(21868,plain,
( ~ ( sk5 @ ( sk10 @ sk5 ) )
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[21867:[]]) ).
thf(22134,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ ( sk8 @ sk5 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21868]) ).
thf(22149,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk10 @ sk5 )
!= ( sk8 @ sk5 ) ) ),
inference(simp,[status(thm)],[22134]) ).
thf(23553,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk8 @ sk5 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,22149]) ).
thf(23595,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk8 @ sk5 ) )
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[23553]) ).
thf(41,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk25 @ A )
| ( A @ ( sk27 @ A ) )
| ( A @ sk23 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(65,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk25 @ A )
| ( A @ ( sk27 @ A ) )
| ( A @ sk23 ) ),
inference(simp,[status(thm)],[41]) ).
thf(5160,plain,
( sk6
| sk11
| ( sk25
@ ^ [A: a] : $false )
| $false
| $false ),
inference(prim_subst,[status(thm)],[65:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(5279,plain,
( sk6
| sk11
| ( sk25
@ ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[5160]) ).
thf(20,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk1 @ sk22 @ ( sk26 @ A ) )
| ( sk2 @ sk22 @ ( sk26 @ A ) )
| ~ ( sk25 @ A )
| ( A @ sk23 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(60,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk1 @ sk22 @ ( sk26 @ A ) )
| ( sk2 @ sk22 @ ( sk26 @ A ) )
| ~ ( sk25 @ A )
| ( A @ sk23 ) ),
inference(simp,[status(thm)],[20]) ).
thf(5390,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk1 @ sk22 @ ( sk26 @ A ) )
| ( sk2 @ sk22 @ ( sk26 @ A ) )
| ( A @ sk23 )
| ( ( sk25
@ ^ [B: a] : $false )
!= ( sk25 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5279,60]) ).
thf(5391,plain,
( sk6
| sk11
| ( sk1 @ sk22
@ ( sk26
@ ^ [A: a] : $false ) )
| ( sk2 @ sk22
@ ( sk26
@ ^ [A: a] : $false ) )
| $false ),
inference(pattern_uni,[status(thm)],[5390:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(5409,plain,
( sk6
| sk11
| ( sk1 @ sk22
@ ( sk26
@ ^ [A: a] : $false ) )
| ( sk2 @ sk22
@ ( sk26
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[5391]) ).
thf(18,plain,
! [A: a] :
( sk6
| sk11
| ~ ( sk2 @ sk22 @ A )
| ( sk33 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(52,plain,
! [A: a] :
( sk6
| sk11
| ~ ( sk2 @ sk22 @ A )
| ( sk33 @ A ) ),
inference(simp,[status(thm)],[18]) ).
thf(31999,plain,
! [A: a] :
( sk6
| sk11
| ( sk1 @ sk22
@ ( sk26
@ ^ [B: a] : $false ) )
| ( sk33 @ A )
| ( ( sk2 @ sk22
@ ( sk26
@ ^ [B: a] : $false ) )
!= ( sk2 @ sk22 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5409,52]) ).
thf(32000,plain,
( sk6
| sk11
| ( sk1 @ sk22
@ ( sk26
@ ^ [A: a] : $false ) )
| ( sk33
@ ( sk26
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[31999:[bind(A,$thf( sk26 @ ^ [B: a] : $false ))]]) ).
thf(17,plain,
! [A: a] :
( sk6
| sk11
| ~ ( sk1 @ sk22 @ A )
| ( sk33 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(67,plain,
! [A: a] :
( sk6
| sk11
| ~ ( sk1 @ sk22 @ A )
| ( sk33 @ A ) ),
inference(simp,[status(thm)],[17]) ).
thf(32338,plain,
! [A: a] :
( sk6
| sk11
| ( sk33
@ ( sk26
@ ^ [B: a] : $false ) )
| ( sk33 @ A )
| ( ( sk1 @ sk22
@ ( sk26
@ ^ [B: a] : $false ) )
!= ( sk1 @ sk22 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[32000,67]) ).
thf(32339,plain,
( sk6
| sk11
| ( sk33
@ ( sk26
@ ^ [A: a] : $false ) )
| ( sk33
@ ( sk26
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[32338:[bind(A,$thf( sk26 @ ^ [B: a] : $false ))]]) ).
thf(32383,plain,
( sk6
| sk11
| ( sk33
@ ( sk26
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[32339]) ).
thf(2728,plain,
( ( sk7 @ sk5 )
| ( sk5 @ ( sk9 @ sk5 ) )
| ( sk5 @ sk4 )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[66:[bind(A,$thf( sk5 ))]]) ).
thf(3891,plain,
( ( sk7 @ sk5 )
| ( sk5 @ ( sk9 @ sk5 ) )
| $false
| ~ sk6 ),
inference(rewrite,[status(thm)],[2728,38]) ).
thf(3892,plain,
( ( sk7 @ sk5 )
| ( sk5 @ ( sk9 @ sk5 ) )
| ~ sk6 ),
inference(simp,[status(thm)],[3891]) ).
thf(21967,plain,
( ( sk7 @ sk5 )
| ~ sk6
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ ( sk9 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3892,21864]) ).
thf(21993,plain,
( ( sk7 @ sk5 )
| ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk9 @ sk5 ) ) ),
inference(simp,[status(thm)],[21967]) ).
thf(5170,plain,
( sk6
| sk11
| ( sk25
@ ^ [A: a] : sk6 )
| sk6
| sk6 ),
inference(prim_subst,[status(thm)],[65:[bind(A,$thf( ^ [B: a] : sk6 ))]]) ).
thf(5288,plain,
( sk6
| sk11
| ( sk25
@ ^ [A: a] : sk6 ) ),
inference(simp,[status(thm)],[5170]) ).
thf(29,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk29 @ A )
| ( A @ ( sk31 @ A ) )
| ( A @ sk24 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(61,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk29 @ A )
| ( A @ ( sk31 @ A ) )
| ( A @ sk24 ) ),
inference(simp,[status(thm)],[29]) ).
thf(150,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] :
~ ( A @ B ) )
| ~ ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
| ~ ( A @ sk24 ) ),
inference(prim_subst,[status(thm)],[61:[bind(A,$thf( ^ [C: a] : ~ ( B @ C ) ))]]) ).
thf(182,plain,
! [A: a > $o] :
( ~ ( A @ sk24 )
| ~ ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
| ( sk29
@ ^ [B: a] :
~ ( A @ B ) )
| sk11
| sk6 ),
inference(cnf,[status(esa)],[150]) ).
thf(183,plain,
! [A: a > $o] :
( ~ ( A @ sk24 )
| ~ ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
| ( sk29
@ ^ [B: a] :
~ ( A @ B ) )
| sk11
| sk6 ),
inference(simp,[status(thm)],[182]) ).
thf(21159,plain,
! [A: a > $o] :
( sk6
| sk11
| ~ ( A @ sk24 )
| ( sk29
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( sk25
@ ^ [B: a] : sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[5288,183]) ).
thf(21460,plain,
( sk6
| sk11
| ~ ( sk25
@ ^ [A: a] : sk6 )
| ( sk29
@ ^ [A: a] :
~ ( sk25
@ ^ [B: a] : sk6 ) ) ),
inference(pre_uni,[status(thm)],[21159:[bind(A,$thf( ^ [B: a] : ( sk25 @ ^ [C: a] : sk6 ) ))]]) ).
thf(39696,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] :
~ ( sk25
@ ^ [B: a] : sk6 ) )
| ( ( sk25
@ ^ [A: a] : sk6 )
!= ( sk25
@ ^ [A: a] : sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[5288,21460]) ).
thf(39697,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] :
~ ( sk25
@ ^ [B: a] : sk6 ) ) ),
inference(pattern_uni,[status(thm)],[39696:[]]) ).
thf(2730,plain,
( ( sk7
@ ^ [A: a] : sk11 )
| sk11
| sk11
| ~ sk6 ),
inference(prim_subst,[status(thm)],[66:[bind(A,$thf( ^ [B: a] : sk11 ))]]) ).
thf(2814,plain,
( ( sk7
@ ^ [A: a] : sk11 )
| sk11
| ~ sk6 ),
inference(simp,[status(thm)],[2730]) ).
thf(3112,plain,
( sk11
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk7 @ sk5 )
!= ( sk7
@ ^ [A: a] : sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[2814,308]) ).
thf(3158,plain,
( sk11
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( sk5
!= ( ^ [A: a] : sk11 ) ) ),
inference(simp,[status(thm)],[3112]) ).
thf(3798,plain,
( ( ( sk5 @ sk37 )
!= sk11 )
| sk11
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[3158]) ).
thf(5,plain,
! [A: a > $o] :
( sk6
| ( sk1 @ sk12 @ ( sk15 @ A ) )
| ( A @ ( sk16 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11 ),
inference(cnf,[status(esa)],[3]) ).
thf(46,plain,
! [A: a > $o] :
( sk6
| ( sk1 @ sk12 @ ( sk15 @ A ) )
| ( A @ ( sk16 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11 ),
inference(simp,[status(thm)],[5]) ).
thf(218,plain,
! [A: a > $o] :
( sk6
| ( sk1 @ sk12 @ ( sk15 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11
| ( ( A @ ( sk16 @ A ) )
!= sk6 )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[46]) ).
thf(257,plain,
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [A: a] : sk6 ) )
| sk6
| sk14
| ~ sk11 ),
inference(pre_uni,[status(thm)],[218:[bind(A,$thf( ^ [B: a] : sk6 ))]]) ).
thf(261,plain,
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [A: a] : sk6 ) )
| sk14
| ~ sk11 ),
inference(simp,[status(thm)],[257]) ).
thf(22,plain,
! [A: a] :
( sk6
| ~ ( sk1 @ sk12 @ A )
| ( sk21 @ A )
| ~ sk11 ),
inference(cnf,[status(esa)],[3]) ).
thf(70,plain,
! [A: a] :
( sk6
| ~ ( sk1 @ sk12 @ A )
| ( sk21 @ A )
| ~ sk11 ),
inference(simp,[status(thm)],[22]) ).
thf(1682,plain,
! [A: a] :
( sk6
| sk14
| ~ sk11
| ( sk21 @ A )
| ( ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : sk6 ) )
!= ( sk1 @ sk12 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[261,70]) ).
thf(1683,plain,
( sk6
| sk14
| ~ sk11
| ( sk21
@ ( sk15
@ ^ [A: a] : sk6 ) ) ),
inference(pattern_uni,[status(thm)],[1682:[bind(A,$thf( sk15 @ ^ [B: a] : sk6 ))]]) ).
thf(40,plain,
( sk6
| ~ ( sk21 @ sk13 )
| ~ sk11 ),
inference(cnf,[status(esa)],[3]) ).
thf(1707,plain,
( sk6
| sk14
| ~ sk11
| ( ( sk21
@ ( sk15
@ ^ [A: a] : sk6 ) )
!= ( sk21 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[1683,40]) ).
thf(1729,plain,
( sk6
| sk14
| ~ sk11
| ( ( sk15
@ ^ [A: a] : sk6 )
!= sk13 ) ),
inference(simp,[status(thm)],[1707]) ).
thf(37,plain,
! [B: a,A: a] :
( ~ ( sk5 @ A )
| ~ ( sk1 @ A @ B )
| ( sk5 @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(58,plain,
! [B: a,A: a] :
( ~ ( sk5 @ A )
| ~ ( sk1 @ A @ B )
| ( sk5 @ B ) ),
inference(simp,[status(thm)],[37]) ).
thf(554,plain,
! [B: a,A: a] :
( sk6
| sk14
| ~ sk11
| ~ ( sk5 @ A )
| ( sk5 @ B )
| ( ( sk1 @ sk12
@ ( sk15
@ ^ [C: a] : sk6 ) )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[261,58]) ).
thf(555,plain,
( sk6
| sk14
| ~ sk11
| ~ ( sk5 @ sk12 )
| ( sk5
@ ( sk15
@ ^ [A: a] : sk6 ) ) ),
inference(pattern_uni,[status(thm)],[554:[bind(A,$thf( sk12 )),bind(B,$thf( sk15 @ ^ [C: a] : sk6 ))]]) ).
thf(2992,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[2907]) ).
thf(8048,plain,
( ~ sk6
| ( sk5 @ sk34 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,2992]) ).
thf(8077,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[8048]) ).
thf(352,plain,
( sk6
| sk11
| ( sk1 @ sk23 @ ( sk30 @ sk5 ) )
| ( sk2 @ sk23 @ ( sk30 @ sk5 ) )
| ~ ( sk29 @ sk5 )
| ( sk5 @ sk24 ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( sk5 ))]]) ).
thf(3917,plain,
( ( sk7 @ sk5 )
| ~ sk6
| ( ( sk5 @ ( sk9 @ sk5 ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[3892,38]) ).
thf(3979,plain,
( ( sk7 @ sk5 )
| ~ sk6
| ( ( sk9 @ sk5 )
!= sk4 ) ),
inference(simp,[status(thm)],[3917]) ).
thf(202,plain,
! [A: a > $o] :
( sk6
| ( sk1 @ sk12 @ ( sk15 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11
| ( ( A @ ( sk16 @ A ) )
!= ( sk21 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[46,40]) ).
thf(249,plain,
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [A: a] : ( sk21 @ sk13 ) ) )
| ( sk21 @ sk13 )
| sk14
| ~ sk11 ),
inference(pre_uni,[status(thm)],[202:[bind(A,$thf( ^ [B: a] : ( sk21 @ sk13 ) ))]]) ).
thf(138,plain,
! [A: a > a] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) )
| ( sk21
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) ) ) )
| ( sk21 @ ( A @ sk24 ) ) ),
inference(prim_subst,[status(thm)],[61:[bind(A,$thf( ^ [C: a] : ( sk21 @ ( B @ C ) ) ))]]) ).
thf(170,plain,
! [A: a > a] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) )
| ( sk21
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) ) ) )
| ( sk21 @ ( A @ sk24 ) ) ),
inference(simp,[status(thm)],[138]) ).
thf(102,plain,
! [A: a > a > $o] :
( ~ ( sk25
@ ( A
@ ( sk8
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) ) ) )
| ~ ( sk7
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) )
| ( sk25 @ ( A @ sk4 ) )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[78:[bind(A,$thf( ^ [C: a] : ( sk25 @ ( B @ C ) ) ))]]) ).
thf(115,plain,
! [A: a > a > $o] :
( ~ ( sk25
@ ( A
@ ( sk8
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) ) ) )
| ~ ( sk7
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) )
| ( sk25 @ ( A @ sk4 ) )
| ~ sk6 ),
inference(simp,[status(thm)],[102]) ).
thf(2727,plain,
! [A: a > $o] :
( ( sk7 @ A )
| ( A @ sk4 )
| ~ sk6
| ( ( A @ ( sk9 @ A ) )
!= ~ sk6 )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[66]) ).
thf(2778,plain,
( ( sk7
@ ^ [A: a] : ~ sk6 )
| ~ sk6
| ~ sk6 ),
inference(pre_uni,[status(thm)],[2727:[bind(A,$thf( ^ [B: a] : ~ ( sk6 ) ))]]) ).
thf(2846,plain,
( ~ sk6
| ~ sk6
| ( sk7
@ ^ [A: a] : ~ sk6 ) ),
inference(cnf,[status(esa)],[2778]) ).
thf(2847,plain,
( ~ sk6
| ( sk7
@ ^ [A: a] : ~ sk6 ) ),
inference(simp,[status(thm)],[2846]) ).
thf(7785,plain,
! [A: a > $o] :
( ~ sk6
| ( sk1 @ sk3 @ ( sk8 @ A ) )
| ( sk2 @ sk3 @ ( sk8 @ A ) )
| ( A @ sk4 )
| ( ( sk7
@ ^ [B: a] : ~ sk6 )
!= ( sk7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2847,74]) ).
thf(7786,plain,
( ~ sk6
| ( sk1 @ sk3
@ ( sk8
@ ^ [A: a] : ~ sk6 ) )
| ( sk2 @ sk3
@ ( sk8
@ ^ [A: a] : ~ sk6 ) )
| ~ sk6 ),
inference(pattern_uni,[status(thm)],[7785:[bind(A,$thf( ^ [B: a] : ~ ( sk6 ) ))]]) ).
thf(7852,plain,
( ~ sk6
| ( sk2 @ sk3
@ ( sk8
@ ^ [A: a] : ~ sk6 ) )
| ( sk1 @ sk3
@ ( sk8
@ ^ [A: a] : ~ sk6 ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[7786]) ).
thf(7853,plain,
( ~ sk6
| ( sk2 @ sk3
@ ( sk8
@ ^ [A: a] : ~ sk6 ) )
| ( sk1 @ sk3
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[7852]) ).
thf(11903,plain,
! [A: a] :
( ~ sk6
| ( sk1 @ sk3
@ ( sk8
@ ^ [B: a] : ~ sk6 ) )
| ( sk5 @ A )
| ( ( sk2 @ sk3
@ ( sk8
@ ^ [B: a] : ~ sk6 ) )
!= ( sk2 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7853,36]) ).
thf(11904,plain,
( ~ sk6
| ( sk1 @ sk3
@ ( sk8
@ ^ [A: a] : ~ sk6 ) )
| ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[11903:[bind(A,$thf( sk8 @ ^ [B: a] : ~ ( sk6 ) ))]]) ).
thf(11962,plain,
! [A: a] :
( ~ sk6
| ( sk5
@ ( sk8
@ ^ [B: a] : ~ sk6 ) )
| ( sk5 @ A )
| ( ( sk1 @ sk3
@ ( sk8
@ ^ [B: a] : ~ sk6 ) )
!= ( sk1 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11904,21]) ).
thf(11963,plain,
( ~ sk6
| ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) )
| ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[11962:[bind(A,$thf( sk8 @ ^ [B: a] : ~ ( sk6 ) ))]]) ).
thf(12046,plain,
( ~ sk6
| ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[11963]) ).
thf(12053,plain,
( ~ sk6
| ~ ( sk7 @ sk5 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12046,308]) ).
thf(12157,plain,
( ~ sk6
| ~ ( sk7 @ sk5 )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[12053]) ).
thf(13132,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) )
| ( ( sk7 @ sk5 )
!= ( sk7
@ ^ [A: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[2847,12157]) ).
thf(13160,plain,
( ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk6 ) )
| ( sk5
!= ( ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[13132]) ).
thf(13168,plain,
( ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[13160]) ).
thf(13169,plain,
( ( ( sk5 @ sk50 )
!= ~ sk6 )
| ~ sk6 ),
inference(func_ext,[status(esa)],[13168]) ).
thf(13200,plain,
( ~ sk6
| ( sk5 @ sk50 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[13169]) ).
thf(13249,plain,
( ~ sk6
| ( sk5 @ sk50 )
| ~ sk6 ),
inference(cnf,[status(esa)],[13200]) ).
thf(13250,plain,
( ~ sk6
| ( sk5 @ sk50 ) ),
inference(simp,[status(thm)],[13249]) ).
thf(13276,plain,
( ~ sk6
| ( ( sk5 @ sk50 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,38]) ).
thf(13341,plain,
( ~ sk6
| ( sk50 != sk4 ) ),
inference(simp,[status(thm)],[13276]) ).
thf(91,plain,
! [A: a > $o] :
( ~ ~ ( A
@ ( sk8
@ ^ [B: a] :
~ ( A @ B ) ) )
| ~ ( sk7
@ ^ [B: a] :
~ ( A @ B ) )
| ~ ( A @ sk4 )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[78:[bind(A,$thf( ^ [C: a] : ~ ( B @ C ) ))]]) ).
thf(117,plain,
! [A: a > $o] :
( ~ sk6
| ~ ( A @ sk4 )
| ~ ( sk7
@ ^ [B: a] :
~ ( A @ B ) )
| ( A
@ ( sk8
@ ^ [B: a] :
~ ( A @ B ) ) ) ),
inference(cnf,[status(esa)],[91]) ).
thf(118,plain,
! [A: a > $o] :
( ~ sk6
| ~ ( A @ sk4 )
| ~ ( sk7
@ ^ [B: a] :
~ ( A @ B ) )
| ( A
@ ( sk8
@ ^ [B: a] :
~ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(457,plain,
! [A: a > $o] :
( ~ sk6
| ~ ( A @ sk4 )
| ~ ( sk7
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( A
@ ( sk8
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( ~ ( A @ sk4 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[118]) ).
thf(480,plain,
! [A: a > $o] :
( ~ sk6
| ~ ( A @ sk4 )
| ~ ( sk7
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( A
@ ( sk8
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( ~ ( A @ sk4 ) ) ) ),
inference(simp,[status(thm)],[457]) ).
thf(906,plain,
( ~ sk6
| ~ ( sk33 @ sk4 )
| ~ ( sk7
@ ^ [A: a] :
~ ( sk33 @ A ) )
| ( ( sk33
@ ( sk8
@ ^ [A: a] :
~ ( sk33 @ A ) ) )
!= ( ~ ( sk33 @ sk4 ) ) ) ),
inference(prim_subst,[status(thm)],[480:[bind(A,$thf( sk33 ))]]) ).
thf(2864,plain,
( ~ sk6
| ~ ( sk33 @ sk4 )
| ( ( sk33
@ ( sk8
@ ^ [A: a] :
~ ( sk33 @ A ) ) )
!= ( ~ ( sk33 @ sk4 ) ) )
| ( ( sk7
@ ^ [A: a] :
~ ( sk33 @ A ) )
!= ( sk7
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[2815,906]) ).
thf(2908,plain,
( ~ sk6
| ~ ( sk33 @ sk4 )
| ( ( sk33
@ ( sk8
@ ^ [A: a] :
~ ( sk33 @ A ) ) )
!= ( ~ ( sk33 @ sk4 ) ) )
| ( ( ^ [A: a] :
~ ( sk33 @ A ) )
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[2864]) ).
thf(95,plain,
! [A: a > a > $o] :
( ~ ( sk29
@ ( A
@ ( sk8
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) ) ) )
| ~ ( sk7
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) )
| ( sk29 @ ( A @ sk4 ) )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[78:[bind(A,$thf( ^ [C: a] : ( sk29 @ ( B @ C ) ) ))]]) ).
thf(120,plain,
! [A: a > a > $o] :
( ~ ( sk29
@ ( A
@ ( sk8
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) ) ) )
| ~ ( sk7
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) )
| ( sk29 @ ( A @ sk4 ) )
| ~ sk6 ),
inference(simp,[status(thm)],[95]) ).
thf(2922,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk7 @ sk5 )
!= ( sk7
@ ^ [A: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[2847,308]) ).
thf(2964,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( sk5
!= ( ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[2922]) ).
thf(3023,plain,
( ( ( sk5 @ sk35 )
!= ~ sk6 )
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[2964]) ).
thf(3333,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( sk5 @ sk35 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[3023]) ).
thf(3373,plain,
( ~ sk6
| ( sk5 @ sk35 )
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[3333]) ).
thf(3374,plain,
( ~ sk6
| ( sk5 @ sk35 )
| ~ ( sk5 @ ( sk8 @ sk5 ) ) ),
inference(simp,[status(thm)],[3373]) ).
thf(3899,plain,
( ( sk7 @ sk5 )
| ~ sk6
| ( sk5 @ sk35 )
| ( ( sk5 @ ( sk9 @ sk5 ) )
!= ( sk5 @ ( sk8 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3892,3374]) ).
thf(3959,plain,
( ( sk7 @ sk5 )
| ( sk5 @ sk35 )
| ~ sk6
| ( ( sk9 @ sk5 )
!= ( sk8 @ sk5 ) ) ),
inference(simp,[status(thm)],[3899]) ).
thf(44,plain,
! [A: a > $o] :
( sk6
| ~ sk14
| ( sk2 @ sk12 @ ( sk18 @ A ) )
| ( A @ ( sk19 @ A ) )
| ( A @ sk13 )
| ~ sk11 ),
inference(cnf,[status(esa)],[3]) ).
thf(71,plain,
! [A: a > $o] :
( sk6
| ~ sk14
| ( sk2 @ sk12 @ ( sk18 @ A ) )
| ( A @ ( sk19 @ A ) )
| ( A @ sk13 )
| ~ sk11 ),
inference(simp,[status(thm)],[44]) ).
thf(6316,plain,
( sk6
| ~ sk14
| ( sk2 @ sk12
@ ( sk18
@ ^ [A: a] : sk6 ) )
| sk6
| sk6
| ~ sk11 ),
inference(prim_subst,[status(thm)],[71:[bind(A,$thf( ^ [B: a] : sk6 ))]]) ).
thf(6426,plain,
( sk6
| ~ sk14
| ( sk2 @ sk12
@ ( sk18
@ ^ [A: a] : sk6 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[6316]) ).
thf(22081,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,21868]) ).
thf(22171,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk10 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[22081]) ).
thf(22646,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= sk45 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,22171]) ).
thf(22666,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= sk45 )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[22646]) ).
thf(231,plain,
! [A: a > a > $o] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) )
| ( sk7
@ ( A
@ ( sk16
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
| ( sk7 @ ( A @ sk13 ) )
| sk14
| ~ sk11 ),
inference(prim_subst,[status(thm)],[46:[bind(A,$thf( ^ [C: a] : ( sk7 @ ( B @ C ) ) ))]]) ).
thf(269,plain,
! [A: a > a > $o] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) )
| ( sk7
@ ( A
@ ( sk16
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
| ( sk7 @ ( A @ sk13 ) )
| sk14
| ~ sk11 ),
inference(simp,[status(thm)],[231]) ).
thf(223,plain,
! [A: a > $o] :
( sk6
| ( sk1 @ sk12 @ ( sk15 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11
| ( ( A @ ( sk16 @ A ) )
!= ~ sk11 )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[46]) ).
thf(255,plain,
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [A: a] : ~ sk11 ) )
| ~ sk11
| sk14
| ~ sk11 ),
inference(pre_uni,[status(thm)],[223:[bind(A,$thf( ^ [B: a] : ~ ( sk11 ) ))]]) ).
thf(285,plain,
( ~ sk11
| sk14
| ~ sk11
| ( sk1 @ sk12
@ ( sk15
@ ^ [A: a] : ~ sk11 ) )
| sk6 ),
inference(cnf,[status(esa)],[255]) ).
thf(286,plain,
( ~ sk11
| sk14
| ( sk1 @ sk12
@ ( sk15
@ ^ [A: a] : ~ sk11 ) )
| sk6 ),
inference(simp,[status(thm)],[285]) ).
thf(676,plain,
! [B: a,A: a] :
( ~ sk11
| sk14
| sk6
| ~ ( sk5 @ A )
| ( sk5 @ B )
| ( ( sk1 @ sk12
@ ( sk15
@ ^ [C: a] : ~ sk11 ) )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[286,58]) ).
thf(677,plain,
( ~ sk11
| sk14
| sk6
| ~ ( sk5 @ sk12 )
| ( sk5
@ ( sk15
@ ^ [A: a] : ~ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[676:[bind(A,$thf( sk12 )),bind(B,$thf( sk15 @ ^ [C: a] : ~ ( sk11 ) ))]]) ).
thf(22067,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,21868]) ).
thf(22175,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk10 @ sk5 )
!= sk50 ) ),
inference(simp,[status(thm)],[22067]) ).
thf(22739,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= sk50 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,22175]) ).
thf(22770,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= sk50 )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[22739]) ).
thf(561,plain,
! [A: a] :
( sk6
| sk14
| ~ sk11
| ( sk5 @ A )
| ( ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : sk6 ) )
!= ( sk1 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[261,21]) ).
thf(562,plain,
! [A: a] :
( sk6
| sk14
| ( sk5 @ A )
| ~ sk11
| ( sk12 != sk3 )
| ( ( sk15
@ ^ [B: a] : sk6 )
!= A ) ),
inference(simp,[status(thm)],[561]) ).
thf(566,plain,
( sk6
| sk14
| ( sk5
@ ( sk15
@ ^ [A: a] : sk6 ) )
| ~ sk11
| ( sk12 != sk3 ) ),
inference(simp,[status(thm)],[562]) ).
thf(1029,plain,
( sk6
| sk14
| ~ sk11
| ( sk12 != sk3 )
| ( ( sk5
@ ( sk15
@ ^ [A: a] : sk6 ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[566,38]) ).
thf(1041,plain,
( sk6
| sk14
| ~ sk11
| ( sk12 != sk3 )
| ( ( sk15
@ ^ [A: a] : sk6 )
!= sk4 ) ),
inference(simp,[status(thm)],[1029]) ).
thf(8052,plain,
! [B: a,A: a] :
( ~ sk6
| ~ ( sk1 @ A @ B )
| ( sk5 @ B )
| ( ( sk5
@ ( sk8
@ ^ [C: a] : $false ) )
!= ( sk5 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7992,58]) ).
thf(8053,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1
@ ( sk8
@ ^ [B: a] : $false )
@ A )
| ( sk5 @ A ) ),
inference(pattern_uni,[status(thm)],[8052:[bind(A,$thf( sk8 @ ^ [C: a] : $false )),bind(B,$thf( B ))]]) ).
thf(8101,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1
@ ( sk8
@ ^ [B: a] : $false )
@ A )
| ( sk5 @ A ) ),
inference(simp,[status(thm)],[8053]) ).
thf(42,plain,
! [A: a > $o] :
( sk6
| ~ ( A @ ( sk15 @ A ) )
| ( sk1 @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11 ),
inference(cnf,[status(esa)],[3]) ).
thf(56,plain,
! [A: a > $o] :
( sk6
| ~ ( A @ ( sk15 @ A ) )
| ( sk1 @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11 ),
inference(simp,[status(thm)],[42]) ).
thf(225,plain,
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [A: a] : $false ) )
| $false
| $false
| sk14
| ~ sk11 ),
inference(prim_subst,[status(thm)],[46:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(265,plain,
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [A: a] : $false ) )
| sk14
| ~ sk11 ),
inference(simp,[status(thm)],[225]) ).
thf(1686,plain,
! [A: a] :
( sk6
| sk14
| ~ sk11
| ( sk21 @ A )
| ( ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : $false ) )
!= ( sk1 @ sk12 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[265,70]) ).
thf(1687,plain,
( sk6
| sk14
| ~ sk11
| ( sk21
@ ( sk15
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[1686:[bind(A,$thf( sk15 @ ^ [B: a] : $false ))]]) ).
thf(1738,plain,
( sk6
| sk14
| ~ sk11
| ( ( sk21
@ ( sk15
@ ^ [A: a] : $false ) )
!= ( sk21 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[1687,40]) ).
thf(1761,plain,
( sk6
| sk14
| ~ sk11
| ( ( sk15
@ ^ [A: a] : $false )
!= sk13 ) ),
inference(simp,[status(thm)],[1738]) ).
thf(6315,plain,
( sk6
| ~ sk14
| ( sk2 @ sk12
@ ( sk18
@ ^ [A: a] : $false ) )
| $false
| $false
| ~ sk11 ),
inference(prim_subst,[status(thm)],[71:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(6425,plain,
( sk6
| ~ sk14
| ( sk2 @ sk12
@ ( sk18
@ ^ [A: a] : $false ) )
| ~ sk11 ),
inference(simp,[status(thm)],[6315]) ).
thf(6535,plain,
! [A: a] :
( sk6
| ~ sk14
| ~ sk11
| ( sk5 @ A )
| ( ( sk2 @ sk12
@ ( sk18
@ ^ [B: a] : $false ) )
!= ( sk2 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6425,36]) ).
thf(6558,plain,
! [A: a] :
( sk6
| ( sk5 @ A )
| ~ sk14
| ~ sk11
| ( sk12 != sk3 )
| ( ( sk18
@ ^ [B: a] : $false )
!= A ) ),
inference(simp,[status(thm)],[6535]) ).
thf(6565,plain,
( sk6
| ( sk5
@ ( sk18
@ ^ [A: a] : $false ) )
| ~ sk14
| ~ sk11
| ( sk12 != sk3 ) ),
inference(simp,[status(thm)],[6558]) ).
thf(24051,plain,
( sk6
| ~ sk14
| ~ sk11
| ( sk12 != sk3 )
| ( ( sk5
@ ( sk18
@ ^ [A: a] : $false ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[6565,38]) ).
thf(24166,plain,
( sk6
| ~ sk14
| ~ sk11
| ( sk12 != sk3 )
| ( ( sk18
@ ^ [A: a] : $false )
!= sk4 ) ),
inference(simp,[status(thm)],[24051]) ).
thf(919,plain,
( ~ sk6
| ~ ( sk21 @ sk4 )
| ~ ( sk7
@ ^ [A: a] :
~ ( sk21 @ A ) )
| ( ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
!= ( ~ ( sk21 @ sk4 ) ) ) ),
inference(prim_subst,[status(thm)],[480:[bind(A,$thf( sk21 ))]]) ).
thf(2950,plain,
( ~ sk6
| ~ ( sk21 @ sk4 )
| ( ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
!= ( ~ ( sk21 @ sk4 ) ) )
| ( ( sk7
@ ^ [A: a] :
~ ( sk21 @ A ) )
!= ( sk7
@ ^ [A: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[2847,919]) ).
thf(2963,plain,
( ~ sk6
| ~ ( sk21 @ sk4 )
| ( ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
!= ( ~ ( sk21 @ sk4 ) ) )
| ( ( ^ [A: a] :
~ ( sk21 @ A ) )
!= ( ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[2950]) ).
thf(7147,plain,
( ~ sk6
| ~ ( sk21 @ sk4 )
| ( ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
!= ( ~ ( sk21 @ sk4 ) ) )
| ( sk21
!= ( ^ [A: a] : sk6 ) ) ),
inference(simp,[status(thm)],[2963]) ).
thf(217,plain,
! [A: a > $o] :
( sk6
| ( A @ ( sk16 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11
| ( ( sk1 @ sk12 @ ( sk15 @ A ) )
!= ( A @ sk13 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[46]) ).
thf(248,plain,
! [A: a > $o] :
( sk6
| ( A @ ( sk16 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11
| ( ( sk1 @ sk12 @ ( sk15 @ A ) )
!= ( A @ sk13 ) ) ),
inference(simp,[status(thm)],[217]) ).
thf(26392,plain,
( sk6
| sk14
| sk14
| sk14
| ~ sk11
| ( ( sk1 @ sk12
@ ( sk15
@ ^ [A: a] : sk14 ) )
!= sk14 ) ),
inference(prim_subst,[status(thm)],[248:[bind(A,$thf( ^ [B: a] : sk14 ))]]) ).
thf(26863,plain,
( sk6
| sk14
| ~ sk11
| ( ( sk1 @ sk12
@ ( sk15
@ ^ [A: a] : sk14 ) )
!= sk14 ) ),
inference(simp,[status(thm)],[26392]) ).
thf(685,plain,
! [A: a] :
( ~ sk11
| sk14
| sk6
| ( sk5 @ A )
| ( ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : ~ sk11 ) )
!= ( sk1 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[286,21]) ).
thf(693,plain,
! [A: a] :
( sk14
| sk6
| ( sk5 @ A )
| ~ sk11
| ( sk12 != sk3 )
| ( ( sk15
@ ^ [B: a] : ~ sk11 )
!= A ) ),
inference(simp,[status(thm)],[685]) ).
thf(698,plain,
( sk14
| sk6
| ( sk5
@ ( sk15
@ ^ [A: a] : ~ sk11 ) )
| ~ sk11
| ( sk12 != sk3 ) ),
inference(simp,[status(thm)],[693]) ).
thf(143,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] : $false )
| $false
| $false ),
inference(prim_subst,[status(thm)],[61:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(174,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[143]) ).
thf(153,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] : sk6 )
| sk6
| sk6 ),
inference(prim_subst,[status(thm)],[61:[bind(A,$thf( ^ [B: a] : sk6 ))]]) ).
thf(185,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] : sk6 ) ),
inference(simp,[status(thm)],[153]) ).
thf(35,plain,
! [A: a] :
( sk6
| ~ ( sk2 @ sk12 @ A )
| ( sk21 @ A )
| ~ sk11 ),
inference(cnf,[status(esa)],[3]) ).
thf(51,plain,
! [A: a] :
( sk6
| ~ ( sk2 @ sk12 @ A )
| ( sk21 @ A )
| ~ sk11 ),
inference(simp,[status(thm)],[35]) ).
thf(6903,plain,
! [A: a] :
( sk6
| ~ sk14
| ~ sk11
| ( sk21 @ A )
| ( ( sk2 @ sk12
@ ( sk18
@ ^ [B: a] : sk6 ) )
!= ( sk2 @ sk12 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6426,51]) ).
thf(6904,plain,
( sk6
| ~ sk14
| ~ sk11
| ( sk21
@ ( sk18
@ ^ [A: a] : sk6 ) ) ),
inference(pattern_uni,[status(thm)],[6903:[bind(A,$thf( sk18 @ ^ [B: a] : sk6 ))]]) ).
thf(2729,plain,
( ( sk7
@ ^ [A: a] : sk14 )
| sk14
| sk14
| ~ sk6 ),
inference(prim_subst,[status(thm)],[66:[bind(A,$thf( ^ [B: a] : sk14 ))]]) ).
thf(2813,plain,
( ( sk7
@ ^ [A: a] : sk14 )
| sk14
| ~ sk6 ),
inference(simp,[status(thm)],[2729]) ).
thf(3054,plain,
( sk14
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk7 @ sk5 )
!= ( sk7
@ ^ [A: a] : sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[2813,308]) ).
thf(3090,plain,
( sk14
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( sk5
!= ( ^ [A: a] : sk14 ) ) ),
inference(simp,[status(thm)],[3054]) ).
thf(13277,plain,
( ~ sk6
| sk14
| ( sk5
!= ( ^ [A: a] : sk14 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,3090]) ).
thf(13335,plain,
( sk14
| ~ sk6
| ( sk5
!= ( ^ [A: a] : sk14 ) )
| ( ( sk8 @ sk5 )
!= sk50 ) ),
inference(simp,[status(thm)],[13277]) ).
thf(17843,plain,
( ( ( sk5 @ sk52 )
!= sk14 )
| sk14
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 ) ),
inference(func_ext,[status(esa)],[13335]) ).
thf(14,plain,
( sk6
| sk11
| ~ ( sk33 @ sk24 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(13316,plain,
! [B: a,A: a] :
( ~ sk6
| ~ ( sk1 @ A @ B )
| ( sk5 @ B )
| ( ( sk5 @ sk50 )
!= ( sk5 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13250,58]) ).
thf(13317,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1 @ sk50 @ A )
| ( sk5 @ A ) ),
inference(pattern_uni,[status(thm)],[13316:[bind(A,$thf( sk50 ))]]) ).
thf(13360,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1 @ sk50 @ A )
| ( sk5 @ A ) ),
inference(simp,[status(thm)],[13317]) ).
thf(151,plain,
! [B: a > a,A: a > a] :
( sk6
| sk11
| ( sk29
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk1
@ ( A
@ ( sk31
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk31
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ( sk1 @ ( A @ sk24 ) @ ( B @ sk24 ) ) ),
inference(prim_subst,[status(thm)],[61:[bind(A,$thf( ^ [D: a] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(184,plain,
! [B: a > a,A: a > a] :
( sk6
| sk11
| ( sk29
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk1
@ ( A
@ ( sk31
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk31
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ( sk1 @ ( A @ sk24 ) @ ( B @ sk24 ) ) ),
inference(simp,[status(thm)],[151]) ).
thf(3893,plain,
( ( sk5 @ ( sk9 @ sk5 ) )
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk7 @ sk5 )
!= ( sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[3892,308]) ).
thf(3894,plain,
( ( sk5 @ ( sk9 @ sk5 ) )
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[3893:[]]) ).
thf(4022,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk5 @ ( sk9 @ sk5 ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[3894,38]) ).
thf(4059,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk9 @ sk5 )
!= sk4 ) ),
inference(simp,[status(thm)],[4022]) ).
thf(12072,plain,
( ~ sk6
| ( ( sk9 @ sk5 )
!= sk4 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12046,4059]) ).
thf(12154,plain,
( ~ sk6
| ( ( sk9 @ sk5 )
!= sk4 )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[12072]) ).
thf(89,plain,
( ~ ( sk21 @ ( sk8 @ sk21 ) )
| ~ ( sk7 @ sk21 )
| ( sk21 @ sk4 )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[78:[bind(A,$thf( sk21 ))]]) ).
thf(2875,plain,
( ~ sk6
| ~ ( sk21 @ ( sk8 @ sk21 ) )
| ( sk21 @ sk4 )
| ( ( sk7 @ sk21 )
!= ( sk7
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[2815,89]) ).
thf(2909,plain,
( ( sk21 @ sk4 )
| ~ sk6
| ~ ( sk21 @ ( sk8 @ sk21 ) )
| ( sk21
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[2875]) ).
thf(4654,plain,
( ( sk21 @ sk39 )
| ( sk21 @ sk4 )
| ~ sk6
| ~ ( sk21 @ ( sk8 @ sk21 ) ) ),
inference(func_ext,[status(esa)],[2909]) ).
thf(22148,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ ( sk8 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[22134]) ).
thf(27843,plain,
( ~ sk6
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ ( sk8 @ sk5 ) ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12046,22148]) ).
thf(27973,plain,
( ~ sk6
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ ( sk8 @ sk5 ) ) )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[27843]) ).
thf(12075,plain,
( ~ sk6
| ( sk5 @ ( sk9 @ sk5 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12046,3894]) ).
thf(12161,plain,
( ( sk5 @ ( sk9 @ sk5 ) )
| ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[12075]) ).
thf(5171,plain,
( sk6
| sk11
| ( sk25
@ ^ [A: a] : sk14 )
| sk14
| sk14 ),
inference(prim_subst,[status(thm)],[65:[bind(A,$thf( ^ [B: a] : sk14 ))]]) ).
thf(5289,plain,
( sk6
| sk11
| ( sk25
@ ^ [A: a] : sk14 )
| sk14 ),
inference(simp,[status(thm)],[5171]) ).
thf(8195,plain,
( ~ sk6
| ~ ( sk7 @ sk5 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,308]) ).
thf(8259,plain,
( ~ sk6
| ~ ( sk7 @ sk5 )
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[8195]) ).
thf(21912,plain,
( ~ ( sk5 @ ( sk10 @ sk5 ) )
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 )
| ( ( sk7 @ sk5 )
!= ( sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[21864,8259]) ).
thf(21913,plain,
( ~ ( sk5 @ ( sk10 @ sk5 ) )
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(pattern_uni,[status(thm)],[21912:[]]) ).
thf(22444,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12046,21913]) ).
thf(22493,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 )
| ( ( sk10 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[22444]) ).
thf(126,plain,
! [B: a,A: a > $o] :
( sk6
| sk11
| ( sk29 @ A )
| ( A @ sk24 )
| ( sk5 @ B )
| ( ( A @ ( sk31 @ A ) )
!= ( sk2 @ sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[61,36]) ).
thf(167,plain,
! [A: a > a] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] : ( sk2 @ sk3 @ ( A @ B ) ) )
| ( sk2 @ sk3 @ ( A @ sk24 ) )
| ( sk5
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk2 @ sk3 @ ( A @ B ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[126:[bind(A,$thf( ^ [D: a] : ( sk2 @ sk3 @ ( D @ D ) ) )),bind(B,$thf( D @ ( sk31 @ ^ [D: a] : ( sk2 @ sk3 @ ( D @ D ) ) ) ))]]) ).
thf(191,plain,
! [A: a > a] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] : ( sk2 @ sk3 @ ( A @ B ) ) )
| ( sk2 @ sk3 @ ( A @ sk24 ) )
| ( sk5
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk2 @ sk3 @ ( A @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[167]) ).
thf(24222,plain,
! [A: a > a] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] : ( sk2 @ sk3 @ ( A @ B ) ) )
| ( sk2 @ sk3 @ ( A @ sk24 ) )
| ( ( sk5
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk2 @ sk3 @ ( A @ B ) ) ) ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[191,38]) ).
thf(24345,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] : ( sk2 @ sk3 @ sk4 ) )
| ( sk2 @ sk3 @ sk4 ) ),
inference(pre_uni,[status(thm)],[24222:[bind(A,$thf( ^ [B: a] : sk4 ))]]) ).
thf(344,plain,
( sk6
| sk11
| ( sk1 @ sk23 @ ( sk30 @ sk33 ) )
| ( sk2 @ sk23 @ ( sk30 @ sk33 ) )
| ~ ( sk29 @ sk33 )
| ( sk33 @ sk24 ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( sk33 ))]]) ).
thf(32391,plain,
( sk6
| sk11
| ( ( sk33
@ ( sk26
@ ^ [A: a] : $false ) )
!= ( sk33 @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[32383,14]) ).
thf(32462,plain,
( sk6
| sk11
| ( ( sk26
@ ^ [A: a] : $false )
!= sk24 ) ),
inference(simp,[status(thm)],[32391]) ).
thf(131,plain,
! [B: a,A: a > $o] :
( sk6
| sk11
| ( sk29 @ A )
| ( A @ sk24 )
| ( sk5 @ B )
| ( ( A @ ( sk31 @ A ) )
!= ( sk1 @ sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[61,21]) ).
thf(162,plain,
! [A: a > a] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] : ( sk1 @ sk3 @ ( A @ B ) ) )
| ( sk1 @ sk3 @ ( A @ sk24 ) )
| ( sk5
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk1 @ sk3 @ ( A @ B ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[131:[bind(A,$thf( ^ [D: a] : ( sk1 @ sk3 @ ( D @ D ) ) )),bind(B,$thf( D @ ( sk31 @ ^ [D: a] : ( sk1 @ sk3 @ ( D @ D ) ) ) ))]]) ).
thf(189,plain,
! [A: a > a] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] : ( sk1 @ sk3 @ ( A @ B ) ) )
| ( sk1 @ sk3 @ ( A @ sk24 ) )
| ( sk5
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk1 @ sk3 @ ( A @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[162]) ).
thf(92,plain,
( ~ ( sk33 @ ( sk8 @ sk33 ) )
| ~ ( sk7 @ sk33 )
| ( sk33 @ sk4 )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[78:[bind(A,$thf( sk33 ))]]) ).
thf(2876,plain,
( ~ sk6
| ~ ( sk33 @ ( sk8 @ sk33 ) )
| ( sk33 @ sk4 )
| ( ( sk7 @ sk33 )
!= ( sk7
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[2815,92]) ).
thf(2896,plain,
( ( sk33 @ sk4 )
| ~ sk6
| ~ ( sk33 @ ( sk8 @ sk33 ) )
| ( sk33
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[2876]) ).
thf(4622,plain,
( ( sk33 @ sk38 )
| ( sk33 @ sk4 )
| ~ sk6
| ~ ( sk33 @ ( sk8 @ sk33 ) ) ),
inference(func_ext,[status(esa)],[2896]) ).
thf(24,plain,
! [A: a > $o] :
( sk6
| ~ sk14
| ~ ( A @ ( sk18 @ A ) )
| ~ ( A @ ( sk20 @ A ) )
| ( A @ sk13 )
| ~ sk11 ),
inference(cnf,[status(esa)],[3]) ).
thf(57,plain,
! [A: a > $o] :
( sk6
| ~ sk14
| ~ ( A @ ( sk18 @ A ) )
| ~ ( A @ ( sk20 @ A ) )
| ( A @ sk13 )
| ~ sk11 ),
inference(simp,[status(thm)],[24]) ).
thf(8204,plain,
( ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk6 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,2964]) ).
thf(8255,plain,
( ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk6 ) )
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[8204]) ).
thf(9497,plain,
( ( ( sk5 @ sk46 )
!= ~ sk6 )
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(func_ext,[status(esa)],[8255]) ).
thf(7638,plain,
( sk11
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( sk5 @ sk37 )
| sk11 ),
inference(bool_ext,[status(thm)],[3798]) ).
thf(7694,plain,
( sk11
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( sk5 @ sk37 ) ),
inference(simp,[status(thm)],[7638]) ).
thf(13323,plain,
( ~ sk6
| sk11
| ( sk5 @ sk37 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,7694]) ).
thf(13350,plain,
( sk11
| ( sk5 @ sk37 )
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 ) ),
inference(simp,[status(thm)],[13323]) ).
thf(8231,plain,
( ~ sk6
| ( sk5 @ sk34 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,2992]) ).
thf(8252,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[8231]) ).
thf(8208,plain,
( ~ sk6
| ( ( sk9 @ sk5 )
!= sk4 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,4059]) ).
thf(8257,plain,
( ~ sk6
| ( ( sk9 @ sk5 )
!= sk4 )
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[8208]) ).
thf(5698,plain,
( ~ ( sk33 @ sk40 )
| ~ sk6
| ~ ( sk33 @ sk4 )
| ( ( sk33
@ ( sk8
@ ^ [A: a] :
~ ( sk33 @ A ) ) )
!= ( ~ ( sk33 @ sk4 ) ) ) ),
inference(func_ext,[status(esa)],[2908]) ).
thf(5744,plain,
( ( ( sk33
@ ( sk8
@ ^ [A: a] :
~ ( sk33 @ A ) ) )
!= ( ~ ( sk33 @ sk4 ) ) )
| ~ ( sk33 @ sk4 )
| ~ sk6
| ~ ( sk33 @ sk40 ) ),
inference(cnf,[status(esa)],[5698]) ).
thf(13261,plain,
( ~ sk6
| ~ ( sk7 @ sk5 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,308]) ).
thf(13356,plain,
( ~ sk6
| ~ ( sk7 @ sk5 )
| ( ( sk8 @ sk5 )
!= sk50 ) ),
inference(simp,[status(thm)],[13261]) ).
thf(147,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] : sk14 )
| sk14
| sk14 ),
inference(prim_subst,[status(thm)],[61:[bind(A,$thf( ^ [B: a] : sk14 ))]]) ).
thf(179,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] : sk14 )
| sk14 ),
inference(simp,[status(thm)],[147]) ).
thf(28,plain,
! [B: a,A: a] :
( ~ ( sk5 @ A )
| ~ ( sk2 @ A @ B )
| ( sk5 @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(63,plain,
! [B: a,A: a] :
( ~ ( sk5 @ A )
| ~ ( sk2 @ A @ B )
| ( sk5 @ B ) ),
inference(simp,[status(thm)],[28]) ).
thf(6894,plain,
! [B: a,A: a] :
( sk6
| ~ sk14
| ~ sk11
| ~ ( sk5 @ A )
| ( sk5 @ B )
| ( ( sk2 @ sk12
@ ( sk18
@ ^ [C: a] : sk6 ) )
!= ( sk2 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6426,63]) ).
thf(6895,plain,
( sk6
| ~ sk14
| ~ sk11
| ~ ( sk5 @ sk12 )
| ( sk5
@ ( sk18
@ ^ [A: a] : sk6 ) ) ),
inference(pattern_uni,[status(thm)],[6894:[bind(A,$thf( sk12 )),bind(B,$thf( sk18 @ ^ [C: a] : sk6 ))]]) ).
thf(83,plain,
! [A: a > $o] :
( ~ ( sk7 @ A )
| ( A @ sk4 )
| ~ sk6
| ( ( A @ ( sk8 @ A ) )
!= ( ~ ( A @ sk4 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[78]) ).
thf(106,plain,
! [A: a > $o] :
( ( A @ sk4 )
| ~ ( sk7 @ A )
| ~ sk6
| ( ( A @ ( sk8 @ A ) )
!= ( ~ ( A @ sk4 ) ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(5156,plain,
( sk6
| sk11
| ( sk25 @ sk21 )
| ( sk21 @ ( sk27 @ sk21 ) )
| ( sk21 @ sk23 ) ),
inference(prim_subst,[status(thm)],[65:[bind(A,$thf( sk21 ))]]) ).
thf(8211,plain,
( ~ sk6
| ( sk5 @ ( sk9 @ sk5 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,3894]) ).
thf(8246,plain,
( ( sk5 @ ( sk9 @ sk5 ) )
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[8211]) ).
thf(8141,plain,
( ( sk5 @ sk44 )
| ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(func_ext,[status(esa)],[8082]) ).
thf(6902,plain,
! [A: a] :
( sk6
| ~ sk14
| ~ sk11
| ( sk5 @ A )
| ( ( sk2 @ sk12
@ ( sk18
@ ^ [B: a] : sk6 ) )
!= ( sk2 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6426,36]) ).
thf(6924,plain,
! [A: a] :
( sk6
| ( sk5 @ A )
| ~ sk14
| ~ sk11
| ( sk12 != sk3 )
| ( ( sk18
@ ^ [B: a] : sk6 )
!= A ) ),
inference(simp,[status(thm)],[6902]) ).
thf(6932,plain,
( sk6
| ( sk5
@ ( sk18
@ ^ [A: a] : sk6 ) )
| ~ sk14
| ~ sk11
| ( sk12 != sk3 ) ),
inference(simp,[status(thm)],[6924]) ).
thf(132,plain,
! [A: a > $o] :
( sk6
| sk11
| ( A @ ( sk31 @ A ) )
| ( A @ sk24 )
| ( ( sk29 @ A )
!= ( A @ sk24 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[61]) ).
thf(163,plain,
! [A: a > $o] :
( sk6
| sk11
| ( A @ ( sk31 @ A ) )
| ( A @ sk24 )
| ( ( sk29 @ A )
!= ( A @ sk24 ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(15946,plain,
( sk6
| sk11
| sk6
| sk6
| ( ( sk29
@ ^ [A: a] : sk6 )
!= sk6 ) ),
inference(prim_subst,[status(thm)],[163:[bind(A,$thf( ^ [B: a] : sk6 ))]]) ).
thf(16187,plain,
( sk6
| sk11
| ( ( sk29
@ ^ [A: a] : sk6 )
!= sk6 ) ),
inference(simp,[status(thm)],[15946]) ).
thf(103,plain,
! [B: a > a,A: a > a] :
( ~ ( sk2
@ ( A
@ ( sk8
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk8
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ~ ( sk7
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk2 @ ( A @ sk4 ) @ ( B @ sk4 ) )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[78:[bind(A,$thf( ^ [D: a] : ( sk2 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(116,plain,
! [B: a > a,A: a > a] :
( ~ ( sk2
@ ( A
@ ( sk8
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk8
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ~ ( sk7
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk2 @ ( A @ sk4 ) @ ( B @ sk4 ) )
| ~ sk6 ),
inference(simp,[status(thm)],[103]) ).
thf(8004,plain,
( ~ sk6
| ~ ( sk7 @ sk5 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,308]) ).
thf(8083,plain,
( ~ sk6
| ~ ( sk7 @ sk5 )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[8004]) ).
thf(21957,plain,
( ~ ( sk5 @ ( sk10 @ sk5 ) )
| ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) )
| ( ( sk7 @ sk5 )
!= ( sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[21864,8083]) ).
thf(21958,plain,
( ~ ( sk5 @ ( sk10 @ sk5 ) )
| ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[21957:[]]) ).
thf(22997,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,21958]) ).
thf(23038,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) )
| ( ( sk10 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[22997]) ).
thf(36814,plain,
( sk14
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 )
| ( sk5 @ sk52 )
| sk14 ),
inference(bool_ext,[status(thm)],[17843]) ).
thf(36896,plain,
( sk14
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 )
| ( sk5 @ sk52 ) ),
inference(simp,[status(thm)],[36814]) ).
thf(2937,plain,
( ~ sk6
| ~ ( sk21 @ ( sk8 @ sk21 ) )
| ( sk21 @ sk4 )
| ( ( sk7 @ sk21 )
!= ( sk7
@ ^ [A: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[2847,89]) ).
thf(2965,plain,
( ( sk21 @ sk4 )
| ~ sk6
| ~ ( sk21 @ ( sk8 @ sk21 ) )
| ( sk21
!= ( ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[2937]) ).
thf(5754,plain,
( ~ ( sk33 @ sk4 )
| ~ sk6
| ~ ( sk33 @ sk40 )
| ( sk33
@ ( sk8
@ ^ [A: a] :
~ ( sk33 @ A ) ) )
| ~ ( sk33 @ sk4 ) ),
inference(bool_ext,[status(thm)],[5744]) ).
thf(5818,plain,
( ~ ( sk33 @ sk4 )
| ( sk33
@ ( sk8
@ ^ [A: a] :
~ ( sk33 @ A ) ) )
| ~ ( sk33 @ sk40 )
| ~ sk6
| ~ ( sk33 @ sk4 ) ),
inference(cnf,[status(esa)],[5754]) ).
thf(5819,plain,
( ~ ( sk33 @ sk4 )
| ( sk33
@ ( sk8
@ ^ [A: a] :
~ ( sk33 @ A ) ) )
| ~ ( sk33 @ sk40 )
| ~ sk6 ),
inference(simp,[status(thm)],[5818]) ).
thf(13293,plain,
( ~ sk6
| ( ( sk5 @ sk35 )
!= ~ sk6 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,3023]) ).
thf(13352,plain,
( ~ sk6
| ( ( sk5 @ sk35 )
!= ~ sk6 )
| ( ( sk8 @ sk5 )
!= sk50 ) ),
inference(simp,[status(thm)],[13293]) ).
thf(2885,plain,
( ~ sk6
| ~ ( sk21 @ sk4 )
| ( ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
!= ( ~ ( sk21 @ sk4 ) ) )
| ( ( sk7
@ ^ [A: a] :
~ ( sk21 @ A ) )
!= ( sk7
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[2815,919]) ).
thf(2910,plain,
( ~ sk6
| ~ ( sk21 @ sk4 )
| ( ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
!= ( ~ ( sk21 @ sk4 ) ) )
| ( ( ^ [A: a] :
~ ( sk21 @ A ) )
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[2885]) ).
thf(232,plain,
! [A: a > a] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) ) )
| ( sk5
@ ( A
@ ( sk16
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) ) ) )
| ( sk5 @ ( A @ sk13 ) )
| sk14
| ~ sk11 ),
inference(prim_subst,[status(thm)],[46:[bind(A,$thf( ^ [C: a] : ( sk5 @ ( B @ C ) ) ))]]) ).
thf(270,plain,
! [A: a > a] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) ) )
| ( sk5
@ ( A
@ ( sk16
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) ) ) )
| ( sk5 @ ( A @ sk13 ) )
| sk14
| ~ sk11 ),
inference(simp,[status(thm)],[232]) ).
thf(8021,plain,
( ~ sk6
| sk14
| ( sk5
!= ( ^ [A: a] : sk14 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,3090]) ).
thf(8078,plain,
( sk14
| ~ sk6
| ( sk5
!= ( ^ [A: a] : sk14 ) )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[8021]) ).
thf(5419,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk1 @ sk22 @ ( sk26 @ A ) )
| ( sk2 @ sk22 @ ( sk26 @ A ) )
| ( A @ sk23 )
| ( ( sk25
@ ^ [B: a] : sk6 )
!= ( sk25 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5288,60]) ).
thf(5420,plain,
( sk6
| sk11
| ( sk1 @ sk22
@ ( sk26
@ ^ [A: a] : sk6 ) )
| ( sk2 @ sk22
@ ( sk26
@ ^ [A: a] : sk6 ) )
| sk6 ),
inference(pattern_uni,[status(thm)],[5419:[bind(A,$thf( ^ [B: a] : sk6 ))]]) ).
thf(5438,plain,
( sk6
| sk11
| ( sk1 @ sk22
@ ( sk26
@ ^ [A: a] : sk6 ) )
| ( sk2 @ sk22
@ ( sk26
@ ^ [A: a] : sk6 ) ) ),
inference(simp,[status(thm)],[5420]) ).
thf(21175,plain,
! [A: a > $o] :
( sk6
| sk11
| ~ ( A @ sk24 )
| ( sk29
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( sk25
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[5279,183]) ).
thf(21401,plain,
( sk6
| sk11
| ~ ( sk25
@ ^ [A: a] : $false )
| ( sk29
@ ^ [A: a] :
~ ( sk25
@ ^ [B: a] : $false ) ) ),
inference(pre_uni,[status(thm)],[21175:[bind(A,$thf( ^ [B: a] : ( sk25 @ ^ [C: a] : $false ) ))]]) ).
thf(36964,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] :
~ ( sk25
@ ^ [B: a] : $false ) )
| ( ( sk25
@ ^ [A: a] : $false )
!= ( sk25
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[5279,21401]) ).
thf(36965,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] :
~ ( sk25
@ ^ [B: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[36964:[]]) ).
thf(3767,plain,
( ( ( sk5 @ sk36 )
!= sk14 )
| sk14
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[3090]) ).
thf(2737,plain,
( ( sk7 @ sk21 )
| ( sk21 @ ( sk9 @ sk21 ) )
| ( sk21 @ sk4 )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[66:[bind(A,$thf( sk21 ))]]) ).
thf(341,plain,
! [A: a > a > $o] :
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) )
| ~ ( sk29
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( sk7 @ ( A @ sk24 ) ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [C: a] : ( sk7 @ ( B @ C ) ) ))]]) ).
thf(366,plain,
! [A: a > a > $o] :
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) )
| ~ ( sk29
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( sk7 @ ( A @ sk24 ) ) ),
inference(simp,[status(thm)],[341]) ).
thf(8197,plain,
( ~ sk6
| ( sk5 @ sk35 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,3374]) ).
thf(8265,plain,
( ( sk5 @ sk35 )
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[8197]) ).
thf(6527,plain,
! [B: a,A: a] :
( sk6
| ~ sk14
| ~ sk11
| ~ ( sk5 @ A )
| ( sk5 @ B )
| ( ( sk2 @ sk12
@ ( sk18
@ ^ [C: a] : $false ) )
!= ( sk2 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6425,63]) ).
thf(6528,plain,
( sk6
| ~ sk14
| ~ sk11
| ~ ( sk5 @ sk12 )
| ( sk5
@ ( sk18
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[6527:[bind(A,$thf( sk12 )),bind(B,$thf( sk18 @ ^ [C: a] : $false ))]]) ).
thf(8006,plain,
( ~ sk6
| ( sk5 @ sk35 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,3374]) ).
thf(8091,plain,
( ( sk5 @ sk35 )
| ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[8006]) ).
thf(237,plain,
! [A: a > a] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) ) )
| ( sk21
@ ( A
@ ( sk16
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) ) ) )
| ( sk21 @ ( A @ sk13 ) )
| sk14
| ~ sk11 ),
inference(prim_subst,[status(thm)],[46:[bind(A,$thf( ^ [C: a] : ( sk21 @ ( B @ C ) ) ))]]) ).
thf(275,plain,
! [A: a > a] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) ) )
| ( sk21
@ ( A
@ ( sk16
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) ) ) )
| ( sk21 @ ( A @ sk13 ) )
| sk14
| ~ sk11 ),
inference(simp,[status(thm)],[237]) ).
thf(7378,plain,
( ( sk7 @ sk33 )
| ~ ( sk33 @ ( sk10 @ sk33 ) )
| ( sk33 @ sk4 )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[73:[bind(A,$thf( sk33 ))]]) ).
thf(467,plain,
( ~ sk6
| ~ ( sk33 @ sk4 )
| ~ ( sk7
@ ^ [A: a] :
~ ( sk33 @ A ) )
| ( sk33
@ ( sk8
@ ^ [A: a] :
~ ( sk33 @ A ) ) ) ),
inference(prim_subst,[status(thm)],[118:[bind(A,$thf( sk33 ))]]) ).
thf(22448,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ ( sk9 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8246,21913]) ).
thf(22492,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 )
| ( ( sk10 @ sk5 )
!= ( sk9 @ sk5 ) ) ),
inference(simp,[status(thm)],[22448]) ).
thf(8022,plain,
( ~ sk6
| ( sk5 @ ( sk9 @ sk5 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,3894]) ).
thf(8067,plain,
( ( sk5 @ ( sk9 @ sk5 ) )
| ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[8022]) ).
thf(22998,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ ( sk9 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8067,21958]) ).
thf(23018,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) )
| ( ( sk10 @ sk5 )
!= ( sk9 @ sk5 ) ) ),
inference(simp,[status(thm)],[22998]) ).
thf(229,plain,
( sk6
| ( sk1 @ sk12 @ ( sk15 @ sk21 ) )
| ( sk21 @ ( sk16 @ sk21 ) )
| ( sk21 @ sk13 )
| sk14
| ~ sk11 ),
inference(prim_subst,[status(thm)],[46:[bind(A,$thf( sk21 ))]]) ).
thf(220,plain,
! [A: a > $o] :
( sk6
| ( sk1 @ sk12 @ ( sk15 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11
| ( ( A @ ( sk16 @ A ) )
!= ( A @ sk13 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[46]) ).
thf(251,plain,
! [A: a > $o] :
( sk6
| ( sk1 @ sk12 @ ( sk15 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11
| ( ( A @ ( sk16 @ A ) )
!= ( A @ sk13 ) ) ),
inference(pre_uni,[status(thm)],[220:[]]) ).
thf(252,plain,
! [A: a > $o] :
( ~ sk11
| sk14
| ( A @ sk13 )
| ( sk1 @ sk12 @ ( sk15 @ A ) )
| sk6
| ( ( A @ ( sk16 @ A ) )
!= ( A @ sk13 ) ) ),
inference(pre_uni,[status(thm)],[251:[]]) ).
thf(222,plain,
! [A: a > $o] :
( sk6
| ( sk1 @ sk12 @ ( sk15 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11
| ( ( A @ ( sk16 @ A ) )
!= sk14 )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[46]) ).
thf(260,plain,
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [A: a] : sk14 ) )
| sk14
| sk14
| ~ sk11 ),
inference(pre_uni,[status(thm)],[222:[bind(A,$thf( ^ [B: a] : sk14 ))]]) ).
thf(263,plain,
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [A: a] : sk14 ) )
| sk14
| ~ sk11 ),
inference(simp,[status(thm)],[260]) ).
thf(1692,plain,
! [A: a] :
( sk6
| sk14
| ~ sk11
| ( sk21 @ A )
| ( ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : sk14 ) )
!= ( sk1 @ sk12 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[263,70]) ).
thf(1693,plain,
( sk6
| sk14
| ~ sk11
| ( sk21
@ ( sk15
@ ^ [A: a] : sk14 ) ) ),
inference(pattern_uni,[status(thm)],[1692:[bind(A,$thf( sk15 @ ^ [B: a] : sk14 ))]]) ).
thf(1811,plain,
( sk6
| sk14
| ~ sk11
| ( ( sk21
@ ( sk15
@ ^ [A: a] : sk14 ) )
!= ( sk21 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[1693,40]) ).
thf(1837,plain,
( sk6
| sk14
| ~ sk11
| ( ( sk15
@ ^ [A: a] : sk14 )
!= sk13 ) ),
inference(simp,[status(thm)],[1811]) ).
thf(149,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] : sk11 )
| sk11
| sk11 ),
inference(prim_subst,[status(thm)],[61:[bind(A,$thf( ^ [B: a] : sk11 ))]]) ).
thf(181,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] : sk11 ) ),
inference(simp,[status(thm)],[149]) ).
thf(326,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk1 @ sk23 @ ( sk30 @ A ) )
| ( sk2 @ sk23 @ ( sk30 @ A ) )
| ( A @ sk24 )
| ( ( sk29
@ ^ [B: a] : sk11 )
!= ( sk29 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[181,47]) ).
thf(327,plain,
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [A: a] : sk11 ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [A: a] : sk11 ) )
| sk11 ),
inference(pattern_uni,[status(thm)],[326:[bind(A,$thf( ^ [B: a] : sk11 ))]]) ).
thf(361,plain,
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [A: a] : sk11 ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [A: a] : sk11 ) ) ),
inference(simp,[status(thm)],[327]) ).
thf(8241,plain,
( ~ sk6
| sk11
| ( sk5 @ sk37 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,7694]) ).
thf(8270,plain,
( sk11
| ( sk5 @ sk37 )
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[8241]) ).
thf(8027,plain,
( ~ sk6
| sk11
| ( sk5
!= ( ^ [A: a] : sk11 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,3158]) ).
thf(8085,plain,
( sk11
| ~ sk6
| ( sk5
!= ( ^ [A: a] : sk11 ) )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[8027]) ).
thf(26393,plain,
( sk6
| sk6
| sk6
| sk14
| ~ sk11
| ( ( sk1 @ sk12
@ ( sk15
@ ^ [A: a] : sk6 ) )
!= sk6 ) ),
inference(prim_subst,[status(thm)],[248:[bind(A,$thf( ^ [B: a] : sk6 ))]]) ).
thf(26864,plain,
( sk6
| sk14
| ~ sk11
| ( ( sk1 @ sk12
@ ( sk15
@ ^ [A: a] : sk6 ) )
!= sk6 ) ),
inference(simp,[status(thm)],[26393]) ).
thf(13308,plain,
( ~ sk6
| ( sk5 @ sk34 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,2992]) ).
thf(13347,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 ) ),
inference(simp,[status(thm)],[13308]) ).
thf(8,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk29 @ A )
| ( sk1 @ ( sk31 @ A ) @ ( sk32 @ A ) )
| ( sk2 @ ( sk31 @ A ) @ ( sk32 @ A ) )
| ( A @ sk24 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(53,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk29 @ A )
| ( sk1 @ ( sk31 @ A ) @ ( sk32 @ A ) )
| ( sk2 @ ( sk31 @ A ) @ ( sk32 @ A ) )
| ( A @ sk24 ) ),
inference(simp,[status(thm)],[8]) ).
thf(136,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk29 @ A )
| ( A @ sk24 )
| ( ( A @ ( sk31 @ A ) )
!= ( A @ sk24 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[61]) ).
thf(168,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk29 @ A )
| ( A @ sk24 )
| ( ( A @ ( sk31 @ A ) )
!= ( A @ sk24 ) ) ),
inference(pre_uni,[status(thm)],[136:[]]) ).
thf(169,plain,
! [A: a > $o] :
( ( A @ sk24 )
| ( sk29 @ A )
| sk11
| sk6
| ( ( A @ ( sk31 @ A ) )
!= ( A @ sk24 ) ) ),
inference(pre_uni,[status(thm)],[168:[]]) ).
thf(8014,plain,
( ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk6 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,2964]) ).
thf(8081,plain,
( ~ sk6
| ( sk5
!= ( ^ [A: a] : ~ sk6 ) )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[8014]) ).
thf(10052,plain,
( ( ( sk5 @ sk47 )
!= ~ sk6 )
| ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(func_ext,[status(esa)],[8081]) ).
thf(21954,plain,
( ~ ( sk5 @ ( sk10 @ sk5 ) )
| ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) )
| ( ( sk7 @ sk5 )
!= ( sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[21864,12157]) ).
thf(21955,plain,
( ~ ( sk5 @ ( sk10 @ sk5 ) )
| ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[21954:[]]) ).
thf(24981,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12046,21955]) ).
thf(25034,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) )
| ( ( sk10 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[24981]) ).
thf(22451,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,21913]) ).
thf(22503,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 )
| ( ( sk10 @ sk5 )
!= sk50 ) ),
inference(simp,[status(thm)],[22451]) ).
thf(99,plain,
! [A: a > a > $o] :
( ~ ( sk7
@ ( A
@ ( sk8
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
| ~ ( sk7
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( sk7 @ ( A @ sk4 ) )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[78:[bind(A,$thf( ^ [C: a] : ( sk7 @ ( B @ C ) ) ))]]) ).
thf(109,plain,
! [A: a > a > $o] :
( ~ ( sk7
@ ( A
@ ( sk8
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
| ~ ( sk7
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( sk7 @ ( A @ sk4 ) )
| ~ sk6 ),
inference(simp,[status(thm)],[99]) ).
thf(12123,plain,
! [B: a,A: a] :
( ~ sk6
| ~ ( sk1 @ A @ B )
| ( sk5 @ B )
| ( ( sk5
@ ( sk8
@ ^ [C: a] : ~ sk6 ) )
!= ( sk5 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12046,58]) ).
thf(12124,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1
@ ( sk8
@ ^ [B: a] : ~ sk6 )
@ A )
| ( sk5 @ A ) ),
inference(pattern_uni,[status(thm)],[12123:[bind(A,$thf( sk8 @ ^ [C: a] : ~ ( sk6 ) )),bind(B,$thf( B ))]]) ).
thf(12179,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1
@ ( sk8
@ ^ [B: a] : ~ sk6 )
@ A )
| ( sk5 @ A ) ),
inference(simp,[status(thm)],[12124]) ).
thf(11,plain,
! [B: a,A: a] :
( sk6
| ~ ( sk21 @ A )
| ~ ( sk2 @ A @ B )
| ( sk21 @ B )
| ~ sk11 ),
inference(cnf,[status(esa)],[3]) ).
thf(77,plain,
! [B: a,A: a] :
( sk6
| ~ ( sk21 @ A )
| ~ ( sk2 @ A @ B )
| ( sk21 @ B )
| ~ sk11 ),
inference(simp,[status(thm)],[11]) ).
thf(8215,plain,
( ~ sk6
| sk11
| ( sk5
!= ( ^ [A: a] : sk11 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,3158]) ).
thf(8258,plain,
( sk11
| ~ sk6
| ( sk5
!= ( ^ [A: a] : sk11 ) )
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[8215]) ).
thf(140,plain,
( sk6
| sk11
| ( sk29 @ sk21 )
| ( sk21 @ ( sk31 @ sk21 ) )
| ( sk21 @ sk24 ) ),
inference(prim_subst,[status(thm)],[61:[bind(A,$thf( sk21 ))]]) ).
thf(1010,plain,
( sk6
| sk11
| ( sk29 @ sk21 )
| ( sk21 @ sk24 )
| ( ( sk21 @ ( sk31 @ sk21 ) )
!= ( sk21 @ sk24 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[140]) ).
thf(1016,plain,
( sk6
| sk11
| ( sk29 @ sk21 )
| ( sk21 @ sk24 )
| ( ( sk31 @ sk21 )
!= sk24 ) ),
inference(simp,[status(thm)],[1010]) ).
thf(27868,plain,
( ~ sk6
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ ( sk8 @ sk5 ) ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,22148]) ).
thf(27963,plain,
( ~ sk6
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ ( sk8 @ sk5 ) ) )
| ( ( sk8 @ sk5 )
!= sk50 ) ),
inference(simp,[status(thm)],[27868]) ).
thf(8042,plain,
! [B: a,A: a] :
( ~ sk6
| ~ ( sk2 @ A @ B )
| ( sk5 @ B )
| ( ( sk5
@ ( sk8
@ ^ [C: a] : $false ) )
!= ( sk5 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7992,63]) ).
thf(8043,plain,
! [A: a] :
( ~ sk6
| ~ ( sk2
@ ( sk8
@ ^ [B: a] : $false )
@ A )
| ( sk5 @ A ) ),
inference(pattern_uni,[status(thm)],[8042:[bind(A,$thf( sk8 @ ^ [C: a] : $false )),bind(B,$thf( B ))]]) ).
thf(8100,plain,
! [A: a] :
( ~ sk6
| ~ ( sk2
@ ( sk8
@ ^ [B: a] : $false )
@ A )
| ( sk5 @ A ) ),
inference(simp,[status(thm)],[8043]) ).
thf(2938,plain,
( ~ sk6
| ~ ( sk33 @ ( sk8 @ sk33 ) )
| ( sk33 @ sk4 )
| ( ( sk7 @ sk33 )
!= ( sk7
@ ^ [A: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[2847,92]) ).
thf(2968,plain,
( ( sk33 @ sk4 )
| ~ sk6
| ~ ( sk33 @ ( sk8 @ sk33 ) )
| ( sk33
!= ( ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[2938]) ).
thf(8060,plain,
( ~ sk6
| sk11
| ( sk5 @ sk37 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,7694]) ).
thf(8072,plain,
( sk11
| ( sk5 @ sk37 )
| ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[8060]) ).
thf(27884,plain,
( ~ sk6
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ ( sk8 @ sk5 ) ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,22148]) ).
thf(27954,plain,
( ~ sk6
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ ( sk8 @ sk5 ) ) )
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[27884]) ).
thf(142,plain,
! [A: a > a > $o] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) )
| ( sk25
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) ) ) )
| ( sk25 @ ( A @ sk24 ) ) ),
inference(prim_subst,[status(thm)],[61:[bind(A,$thf( ^ [C: a] : ( sk25 @ ( B @ C ) ) ))]]) ).
thf(173,plain,
! [A: a > a > $o] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) )
| ( sk25
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) ) ) )
| ( sk25 @ ( A @ sk24 ) ) ),
inference(simp,[status(thm)],[142]) ).
thf(22100,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,21868]) ).
thf(22168,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk10 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[22100]) ).
thf(6979,plain,
( sk6
| ~ sk14
| ~ sk11
| ( ( sk21
@ ( sk18
@ ^ [A: a] : sk6 ) )
!= ( sk21 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[6904,40]) ).
thf(6988,plain,
( sk6
| ~ sk14
| ~ sk11
| ( ( sk18
@ ^ [A: a] : sk6 )
!= sk13 ) ),
inference(simp,[status(thm)],[6979]) ).
thf(85,plain,
! [A: a > $o] :
( ~ ( A @ ( sk8 @ A ) )
| ( A @ sk4 )
| ~ sk6
| ( ( sk7 @ A )
!= ( A @ ( sk8 @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[78]) ).
thf(105,plain,
! [A: a > $o] :
( ( A @ sk4 )
| ~ ( A @ ( sk8 @ A ) )
| ~ sk6
| ( ( sk7 @ A )
!= ( A @ ( sk8 @ A ) ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(226,plain,
! [B: a > a,A: a > a] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
| ( sk1
@ ( A
@ ( sk16
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk16
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ( sk1 @ ( A @ sk13 ) @ ( B @ sk13 ) )
| sk14
| ~ sk11 ),
inference(prim_subst,[status(thm)],[46:[bind(A,$thf( ^ [D: a] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(266,plain,
! [B: a > a,A: a > a] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
| ( sk1
@ ( A
@ ( sk16
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk16
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ( sk1 @ ( A @ sk13 ) @ ( B @ sk13 ) )
| sk14
| ~ sk11 ),
inference(simp,[status(thm)],[226]) ).
thf(324,plain,
! [A: a > $o] :
( sk6
| sk11
| sk14
| ( sk1 @ sk23 @ ( sk30 @ A ) )
| ( sk2 @ sk23 @ ( sk30 @ A ) )
| ( A @ sk24 )
| ( ( sk29
@ ^ [B: a] : sk14 )
!= ( sk29 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,47]) ).
thf(325,plain,
( sk6
| sk11
| sk14
| ( sk1 @ sk23
@ ( sk30
@ ^ [A: a] : sk14 ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [A: a] : sk14 ) )
| sk14 ),
inference(pattern_uni,[status(thm)],[324:[bind(A,$thf( ^ [B: a] : sk14 ))]]) ).
thf(360,plain,
( sk6
| sk11
| sk14
| ( sk1 @ sk23
@ ( sk30
@ ^ [A: a] : sk14 ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [A: a] : sk14 ) ) ),
inference(simp,[status(thm)],[325]) ).
thf(21871,plain,
( ~ sk6
| ( sk7 @ sk5 )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12046,21864]) ).
thf(21989,plain,
( ( sk7 @ sk5 )
| ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[21871]) ).
thf(21941,plain,
( ~ sk6
| ( sk7 @ sk5 )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,21864]) ).
thf(22017,plain,
( ( sk7 @ sk5 )
| ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[21941]) ).
thf(5172,plain,
( sk6
| sk11
| ( sk25
@ ^ [A: a] : sk11 )
| sk11
| sk11 ),
inference(prim_subst,[status(thm)],[65:[bind(A,$thf( ^ [B: a] : sk11 ))]]) ).
thf(5290,plain,
( sk6
| sk11
| ( sk25
@ ^ [A: a] : sk11 ) ),
inference(simp,[status(thm)],[5172]) ).
thf(21353,plain,
! [A: a > $o] :
( sk6
| sk11
| ~ ( A @ sk24 )
| ( sk29
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( sk25
@ ^ [B: a] : sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[5290,183]) ).
thf(21402,plain,
( sk6
| sk11
| ~ ( sk25
@ ^ [A: a] : sk11 )
| ( sk29
@ ^ [A: a] :
~ ( sk25
@ ^ [B: a] : sk11 ) ) ),
inference(pre_uni,[status(thm)],[21353:[bind(A,$thf( ^ [B: a] : ( sk25 @ ^ [C: a] : sk11 ) ))]]) ).
thf(37840,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] :
~ ( sk25
@ ^ [B: a] : sk11 ) )
| ( ( sk25
@ ^ [A: a] : sk11 )
!= ( sk25
@ ^ [A: a] : sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[5290,21402]) ).
thf(37841,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] :
~ ( sk25
@ ^ [B: a] : sk11 ) ) ),
inference(pattern_uni,[status(thm)],[37840:[]]) ).
thf(1688,plain,
! [A: a] :
( ~ sk11
| sk14
| sk6
| ( sk21 @ A )
| ( ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : ~ sk11 ) )
!= ( sk1 @ sk12 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[286,70]) ).
thf(1689,plain,
( ~ sk11
| sk14
| sk6
| ( sk21
@ ( sk15
@ ^ [A: a] : ~ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[1688:[bind(A,$thf( sk15 @ ^ [B: a] : ~ ( sk11 ) ))]]) ).
thf(2157,plain,
( ~ sk11
| sk14
| sk6
| ( ( sk21
@ ( sk15
@ ^ [A: a] : ~ sk11 ) )
!= ( sk21 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[1689,40]) ).
thf(2189,plain,
( sk14
| sk6
| ~ sk11
| ( ( sk15
@ ^ [A: a] : ~ sk11 )
!= sk13 ) ),
inference(simp,[status(thm)],[2157]) ).
thf(661,plain,
! [B: a,A: a] :
( sk6
| sk14
| ~ sk11
| ~ ( sk5 @ A )
| ( sk5 @ B )
| ( ( sk1 @ sk12
@ ( sk15
@ ^ [C: a] : $false ) )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[265,58]) ).
thf(662,plain,
( sk6
| sk14
| ~ sk11
| ~ ( sk5 @ sk12 )
| ( sk5
@ ( sk15
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[661:[bind(A,$thf( sk12 )),bind(B,$thf( sk15 @ ^ [C: a] : $false ))]]) ).
thf(135,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk29 @ A )
| ( A @ sk24 )
| ( ( A @ ( sk31 @ A ) )
!= ( sk29 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[61]) ).
thf(166,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk29 @ A )
| ( A @ sk24 )
| ( ( A @ ( sk31 @ A ) )
!= ( sk29 @ A ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(224,plain,
! [A: a > a > $o] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) ) )
| ( sk25
@ ( A
@ ( sk16
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) ) ) )
| ( sk25 @ ( A @ sk13 ) )
| sk14
| ~ sk11 ),
inference(prim_subst,[status(thm)],[46:[bind(A,$thf( ^ [C: a] : ( sk25 @ ( B @ C ) ) ))]]) ).
thf(264,plain,
! [A: a > a > $o] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) ) )
| ( sk25
@ ( A
@ ( sk16
@ ^ [B: a] : ( sk25 @ ( A @ B ) ) ) ) )
| ( sk25 @ ( A @ sk13 ) )
| sk14
| ~ sk11 ),
inference(simp,[status(thm)],[224]) ).
thf(27903,plain,
( ~ sk6
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ ( sk8 @ sk5 ) ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,22148]) ).
thf(28012,plain,
( ~ sk6
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ ( sk8 @ sk5 ) ) )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[27903]) ).
thf(6296,plain,
! [A: a > $o] :
( sk6
| ~ sk14
| ( sk2 @ sk12 @ ( sk18 @ A ) )
| ( A @ sk13 )
| ~ sk11
| ( ( A @ ( sk19 @ A ) )
!= ~ sk14 )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[71]) ).
thf(6353,plain,
( sk6
| ~ sk14
| ( sk2 @ sk12
@ ( sk18
@ ^ [A: a] : ~ sk14 ) )
| ~ sk14
| ~ sk11 ),
inference(pre_uni,[status(thm)],[6296:[bind(A,$thf( ^ [B: a] : ~ ( sk14 ) ))]]) ).
thf(6453,plain,
( ~ sk11
| ~ sk14
| ( sk2 @ sk12
@ ( sk18
@ ^ [A: a] : ~ sk14 ) )
| ~ sk14
| sk6 ),
inference(cnf,[status(esa)],[6353]) ).
thf(6454,plain,
( ~ sk11
| ~ sk14
| ( sk2 @ sk12
@ ( sk18
@ ^ [A: a] : ~ sk14 ) )
| sk6 ),
inference(simp,[status(thm)],[6453]) ).
thf(148,plain,
! [A: a > a] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] : ( sk33 @ ( A @ B ) ) )
| ( sk33
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk33 @ ( A @ B ) ) ) ) )
| ( sk33 @ ( A @ sk24 ) ) ),
inference(prim_subst,[status(thm)],[61:[bind(A,$thf( ^ [C: a] : ( sk33 @ ( B @ C ) ) ))]]) ).
thf(180,plain,
! [A: a > a] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] : ( sk33 @ ( A @ B ) ) )
| ( sk33
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk33 @ ( A @ B ) ) ) ) )
| ( sk33 @ ( A @ sk24 ) ) ),
inference(simp,[status(thm)],[148]) ).
thf(22619,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= sk45 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12046,22171]) ).
thf(22669,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= sk45 )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[22619]) ).
thf(204,plain,
! [B: a,A: a > $o] :
( sk6
| ( sk1 @ sk12 @ ( sk15 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11
| ( sk5 @ B )
| ( ( A @ ( sk16 @ A ) )
!= ( sk2 @ sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[46,36]) ).
thf(244,plain,
! [A: a > a] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : ( sk2 @ sk3 @ ( A @ B ) ) ) )
| ( sk2 @ sk3 @ ( A @ sk13 ) )
| sk14
| ~ sk11
| ( sk5
@ ( A
@ ( sk16
@ ^ [B: a] : ( sk2 @ sk3 @ ( A @ B ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[204:[bind(A,$thf( ^ [D: a] : ( sk2 @ sk3 @ ( D @ D ) ) )),bind(B,$thf( D @ ( sk16 @ ^ [D: a] : ( sk2 @ sk3 @ ( D @ D ) ) ) ))]]) ).
thf(279,plain,
! [A: a > a] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : ( sk2 @ sk3 @ ( A @ B ) ) ) )
| ( sk2 @ sk3 @ ( A @ sk13 ) )
| sk14
| ~ sk11
| ( sk5
@ ( A
@ ( sk16
@ ^ [B: a] : ( sk2 @ sk3 @ ( A @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[244]) ).
thf(13,plain,
! [B: a,A: a] :
( sk6
| sk11
| ~ ( sk33 @ A )
| ~ ( sk1 @ A @ B )
| ( sk33 @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(64,plain,
! [B: a,A: a] :
( sk6
| sk11
| ~ ( sk33 @ A )
| ~ ( sk1 @ A @ B )
| ( sk33 @ B ) ),
inference(simp,[status(thm)],[13]) ).
thf(22712,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= sk50 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12046,22175]) ).
thf(22787,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= sk50 )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[22712]) ).
thf(353,plain,
! [A: a > a] :
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [B: a] : ( sk33 @ ( A @ B ) ) ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [B: a] : ( sk33 @ ( A @ B ) ) ) )
| ~ ( sk29
@ ^ [B: a] : ( sk33 @ ( A @ B ) ) )
| ( sk33 @ ( A @ sk24 ) ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [C: a] : ( sk33 @ ( B @ C ) ) ))]]) ).
thf(375,plain,
! [A: a > a] :
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [B: a] : ( sk33 @ ( A @ B ) ) ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [B: a] : ( sk33 @ ( A @ B ) ) ) )
| ~ ( sk29
@ ^ [B: a] : ( sk33 @ ( A @ B ) ) )
| ( sk33 @ ( A @ sk24 ) ) ),
inference(simp,[status(thm)],[353]) ).
thf(6300,plain,
! [A: a > $o] :
( sk6
| ~ sk14
| ( sk2 @ sk12 @ ( sk18 @ A ) )
| ( A @ sk13 )
| ~ sk11
| ( ( A @ ( sk19 @ A ) )
!= ~ sk11 )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[71]) ).
thf(6350,plain,
( sk6
| ~ sk14
| ( sk2 @ sk12
@ ( sk18
@ ^ [A: a] : ~ sk11 ) )
| ~ sk11
| ~ sk11 ),
inference(pre_uni,[status(thm)],[6300:[bind(A,$thf( ^ [B: a] : ~ ( sk11 ) ))]]) ).
thf(6448,plain,
( ~ sk11
| ~ sk11
| ( sk2 @ sk12
@ ( sk18
@ ^ [A: a] : ~ sk11 ) )
| ~ sk14
| sk6 ),
inference(cnf,[status(esa)],[6350]) ).
thf(6449,plain,
( ~ sk11
| ( sk2 @ sk12
@ ( sk18
@ ^ [A: a] : ~ sk11 ) )
| ~ sk14
| sk6 ),
inference(simp,[status(thm)],[6448]) ).
thf(20446,plain,
! [A: a] :
( ~ sk11
| ~ sk14
| sk6
| ( sk21 @ A )
| ( ( sk2 @ sk12
@ ( sk18
@ ^ [B: a] : ~ sk11 ) )
!= ( sk2 @ sk12 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6449,51]) ).
thf(20447,plain,
( ~ sk11
| ~ sk14
| sk6
| ( sk21
@ ( sk18
@ ^ [A: a] : ~ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[20446:[bind(A,$thf( sk18 @ ^ [B: a] : ~ ( sk11 ) ))]]) ).
thf(23631,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12046,22168]) ).
thf(23687,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[23631]) ).
thf(650,plain,
! [A: a] :
( sk6
| sk14
| ~ sk11
| ( sk5 @ A )
| ( ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : sk14 ) )
!= ( sk1 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[263,21]) ).
thf(653,plain,
! [A: a] :
( sk6
| sk14
| ( sk5 @ A )
| ~ sk11
| ( sk12 != sk3 )
| ( ( sk15
@ ^ [B: a] : sk14 )
!= A ) ),
inference(simp,[status(thm)],[650]) ).
thf(656,plain,
( sk6
| sk14
| ( sk5
@ ( sk15
@ ^ [A: a] : sk14 ) )
| ~ sk11
| ( sk12 != sk3 ) ),
inference(simp,[status(thm)],[653]) ).
thf(1516,plain,
( sk6
| sk14
| ~ sk11
| ( sk12 != sk3 )
| ( ( sk5
@ ( sk15
@ ^ [A: a] : sk14 ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[656,38]) ).
thf(1535,plain,
( sk6
| sk14
| ~ sk11
| ( sk12 != sk3 )
| ( ( sk15
@ ^ [A: a] : sk14 )
!= sk4 ) ),
inference(simp,[status(thm)],[1516]) ).
thf(4863,plain,
( sk14
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( sk5 @ sk36 )
| sk14 ),
inference(bool_ext,[status(thm)],[3767]) ).
thf(4917,plain,
( sk14
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( sk5 @ sk36 ) ),
inference(simp,[status(thm)],[4863]) ).
thf(8055,plain,
( ~ sk6
| sk14
| ( sk5 @ sk36 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,4917]) ).
thf(8092,plain,
( sk14
| ( sk5 @ sk36 )
| ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[8055]) ).
thf(22471,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,21913]) ).
thf(22510,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 )
| ( ( sk10 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[22471]) ).
thf(13318,plain,
( ~ sk6
| sk14
| ( sk5 @ sk36 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,4917]) ).
thf(13338,plain,
( sk14
| ( sk5 @ sk36 )
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 ) ),
inference(simp,[status(thm)],[13318]) ).
thf(2673,plain,
! [A: a > $o] :
( ( A @ ( sk9 @ A ) )
| ( A @ sk4 )
| ~ sk6
| ~ ( sk21 @ sk4 )
| ( ( sk21
@ ( sk8
@ ^ [B: a] :
~ ( sk21 @ B ) ) )
!= ( ~ ( sk21 @ sk4 ) ) )
| ( ( sk7 @ A )
!= ( sk7
@ ^ [B: a] :
~ ( sk21 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[66,919]) ).
thf(2674,plain,
( ~ ( sk21
@ ( sk9
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
| ~ ( sk21 @ sk4 )
| ~ sk6
| ~ ( sk21 @ sk4 )
| ( ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
!= ( ~ ( sk21 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[2673:[bind(A,$thf( ^ [B: a] : ~ ( sk21 @ B ) ))]]) ).
thf(2858,plain,
( ( ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
!= ( ~ ( sk21 @ sk4 ) ) )
| ~ ( sk21 @ sk4 )
| ~ sk6
| ~ ( sk21 @ sk4 )
| ~ ( sk21
@ ( sk9
@ ^ [A: a] :
~ ( sk21 @ A ) ) ) ),
inference(cnf,[status(esa)],[2674]) ).
thf(2859,plain,
( ( ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
!= ( ~ ( sk21 @ sk4 ) ) )
| ~ ( sk21 @ sk4 )
| ~ sk6
| ~ ( sk21
@ ( sk9
@ ^ [A: a] :
~ ( sk21 @ A ) ) ) ),
inference(simp,[status(thm)],[2858]) ).
thf(11358,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) )
| ( sk5 @ sk47 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[10052]) ).
thf(11410,plain,
( ~ sk6
| ( sk5 @ sk47 )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[11358]) ).
thf(11411,plain,
( ~ sk6
| ( sk5 @ sk47 )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[11410]) ).
thf(12055,plain,
( ~ sk6
| ( sk5 @ sk35 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12046,3374]) ).
thf(12143,plain,
( ( sk5 @ sk35 )
| ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[12055]) ).
thf(25,plain,
! [A: a > $o] :
( sk6
| ~ sk14
| ( sk2 @ sk12 @ ( sk18 @ A ) )
| ~ ( A @ ( sk20 @ A ) )
| ( A @ sk13 )
| ~ sk11 ),
inference(cnf,[status(esa)],[3]) ).
thf(59,plain,
! [A: a > $o] :
( sk6
| ~ sk14
| ( sk2 @ sk12 @ ( sk18 @ A ) )
| ~ ( A @ ( sk20 @ A ) )
| ( A @ sk13 )
| ~ sk11 ),
inference(simp,[status(thm)],[25]) ).
thf(15952,plain,
( sk6
| sk11
| sk11
| sk11
| ( ( sk29
@ ^ [A: a] : sk11 )
!= sk11 ) ),
inference(prim_subst,[status(thm)],[163:[bind(A,$thf( ^ [B: a] : sk11 ))]]) ).
thf(16194,plain,
( sk6
| sk11
| ( ( sk29
@ ^ [A: a] : sk11 )
!= sk11 ) ),
inference(simp,[status(thm)],[15952]) ).
thf(22071,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ ( sk9 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3894,21868]) ).
thf(22142,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk10 @ sk5 )
!= ( sk9 @ sk5 ) ) ),
inference(simp,[status(thm)],[22071]) ).
thf(23443,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk9 @ sk5 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12046,22142]) ).
thf(23509,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk9 @ sk5 ) )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[23443]) ).
thf(22055,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12046,21868]) ).
thf(22155,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( sk10 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[22055]) ).
thf(23537,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk8 @ sk5 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12046,22149]) ).
thf(23593,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk8 @ sk5 ) )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[23537]) ).
thf(8237,plain,
( ~ sk6
| sk14
| ( sk5 @ sk36 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,4917]) ).
thf(8249,plain,
( sk14
| ( sk5 @ sk36 )
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[8237]) ).
thf(9,plain,
! [A: a > $o] :
( sk6
| ~ sk14
| ~ ( A @ ( sk18 @ A ) )
| ( sk2 @ ( sk19 @ A ) @ ( sk20 @ A ) )
| ( A @ sk13 )
| ~ sk11 ),
inference(cnf,[status(esa)],[3]) ).
thf(49,plain,
! [A: a > $o] :
( sk6
| ~ sk14
| ~ ( A @ ( sk18 @ A ) )
| ( sk2 @ ( sk19 @ A ) @ ( sk20 @ A ) )
| ( A @ sk13 )
| ~ sk11 ),
inference(simp,[status(thm)],[9]) ).
thf(236,plain,
( sk6
| ( sk1 @ sk12 @ ( sk15 @ sk33 ) )
| ( sk33 @ ( sk16 @ sk33 ) )
| ( sk33 @ sk13 )
| sk14
| ~ sk11 ),
inference(prim_subst,[status(thm)],[46:[bind(A,$thf( sk33 ))]]) ).
thf(5158,plain,
( sk6
| sk11
| ( sk25 @ sk33 )
| ( sk33 @ ( sk27 @ sk33 ) )
| ( sk33 @ sk23 ) ),
inference(prim_subst,[status(thm)],[65:[bind(A,$thf( sk33 ))]]) ).
thf(12113,plain,
( ~ sk6
| ( sk5 @ sk34 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12046,2992]) ).
thf(12167,plain,
( ( sk5 @ sk34 )
| ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[12113]) ).
thf(21919,plain,
( ~ sk6
| ( sk7 @ sk5 )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,21864]) ).
thf(22010,plain,
( ( sk7 @ sk5 )
| ~ sk6
| ( ( sk10 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[21919]) ).
thf(121,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk29 @ A )
| ( A @ sk24 )
| ( ( A @ ( sk31 @ A ) )
!= ( sk33 @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[61,14]) ).
thf(159,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] : ( sk33 @ sk24 ) )
| ( sk33 @ sk24 ) ),
inference(pre_uni,[status(thm)],[121:[bind(A,$thf( ^ [B: a] : ( sk33 @ sk24 ) ))]]) ).
thf(13274,plain,
( ~ sk6
| ( ( sk5 @ sk36 )
!= sk14 )
| sk14
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,3767]) ).
thf(13358,plain,
( sk14
| ~ sk6
| ( ( sk5 @ sk36 )
!= sk14 )
| ( ( sk8 @ sk5 )
!= sk50 ) ),
inference(simp,[status(thm)],[13274]) ).
thf(4,plain,
! [A: a > $o] :
( sk6
| ( sk1 @ sk12 @ ( sk15 @ A ) )
| ( sk1 @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11 ),
inference(cnf,[status(esa)],[3]) ).
thf(54,plain,
! [A: a > $o] :
( sk6
| ( sk1 @ sk12 @ ( sk15 @ A ) )
| ( sk1 @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11 ),
inference(simp,[status(thm)],[4]) ).
thf(3944,plain,
( ( sk7 @ sk5 )
| ~ sk6
| ( sk5 @ sk34 )
| ( ( sk5 @ ( sk9 @ sk5 ) )
!= ( sk5 @ ( sk8 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3892,2992]) ).
thf(3964,plain,
( ( sk7 @ sk5 )
| ( sk5 @ sk34 )
| ~ sk6
| ( ( sk9 @ sk5 )
!= ( sk8 @ sk5 ) ) ),
inference(simp,[status(thm)],[3944]) ).
thf(100,plain,
! [B: a > $o,A: a > $o] :
( ~ ( ( A
@ ( sk8
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( B
@ ( sk8
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) ) )
| ~ ( sk7
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ( A @ sk4 )
| ( B @ sk4 )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[78:[bind(A,$thf( ^ [D: a] : ( ( B @ D ) | ( C @ D ) ) ))]]) ).
thf(111,plain,
! [B: a > $o,A: a > $o] :
( ~ sk6
| ( A @ sk4 )
| ( B @ sk4 )
| ~ ( sk7
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ~ ( B
@ ( sk8
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) ) ),
inference(cnf,[status(esa)],[100]) ).
thf(113,plain,
! [B: a > $o,A: a > $o] :
( ~ sk6
| ( A @ sk4 )
| ( B @ sk4 )
| ~ ( sk7
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ~ ( B
@ ( sk8
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(235,plain,
! [A: a > $o] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] :
~ ( A @ B ) ) )
| ~ ( A
@ ( sk16
@ ^ [B: a] :
~ ( A @ B ) ) )
| ~ ( A @ sk13 )
| sk14
| ~ sk11 ),
inference(prim_subst,[status(thm)],[46:[bind(A,$thf( ^ [C: a] : ~ ( B @ C ) ))]]) ).
thf(273,plain,
! [A: a > $o] :
( ~ sk11
| sk14
| ~ ( A @ sk13 )
| ~ ( A
@ ( sk16
@ ^ [B: a] :
~ ( A @ B ) ) )
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] :
~ ( A @ B ) ) )
| sk6 ),
inference(cnf,[status(esa)],[235]) ).
thf(274,plain,
! [A: a > $o] :
( ~ sk11
| sk14
| ~ ( A @ sk13 )
| ~ ( A
@ ( sk16
@ ^ [B: a] :
~ ( A @ B ) ) )
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] :
~ ( A @ B ) ) )
| sk6 ),
inference(simp,[status(thm)],[273]) ).
thf(30,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk25 @ A )
| ( sk1 @ ( sk27 @ A ) @ ( sk28 @ A ) )
| ( sk2 @ ( sk27 @ A ) @ ( sk28 @ A ) )
| ( A @ sk23 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(81,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk25 @ A )
| ( sk1 @ ( sk27 @ A ) @ ( sk28 @ A ) )
| ( sk2 @ ( sk27 @ A ) @ ( sk28 @ A ) )
| ( A @ sk23 ) ),
inference(simp,[status(thm)],[30]) ).
thf(7379,plain,
( ( sk7 @ sk21 )
| ~ ( sk21 @ ( sk10 @ sk21 ) )
| ( sk21 @ sk4 )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[73:[bind(A,$thf( sk21 ))]]) ).
thf(1560,plain,
( sk6
| sk14
| ~ sk11
| ~ ( sk5 @ sk12 )
| ( ( sk5
@ ( sk15
@ ^ [A: a] : $false ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[662,38]) ).
thf(1589,plain,
( sk6
| sk14
| ~ sk11
| ~ ( sk5 @ sk12 )
| ( ( sk15
@ ^ [A: a] : $false )
!= sk4 ) ),
inference(simp,[status(thm)],[1560]) ).
thf(8210,plain,
( ~ sk6
| sk14
| ( sk5
!= ( ^ [A: a] : sk14 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,3090]) ).
thf(8254,plain,
( sk14
| ~ sk6
| ( sk5
!= ( ^ [A: a] : sk14 ) )
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[8210]) ).
thf(11118,plain,
( ( ( sk5 @ sk49 )
!= sk11 )
| sk11
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(func_ext,[status(esa)],[8258]) ).
thf(32186,plain,
( sk11
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 )
| ( sk5 @ sk49 )
| sk11 ),
inference(bool_ext,[status(thm)],[11118]) ).
thf(32259,plain,
( sk11
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 )
| ( sk5 @ sk49 ) ),
inference(simp,[status(thm)],[32186]) ).
thf(2743,plain,
( ( sk7 @ sk33 )
| ( sk33 @ ( sk9 @ sk33 ) )
| ( sk33 @ sk4 )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[66:[bind(A,$thf( sk33 ))]]) ).
thf(4601,plain,
( ( sk7 @ sk33 )
| ( sk33 @ sk4 )
| ~ sk6
| ( ( sk33 @ ( sk9 @ sk33 ) )
!= ( sk33 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2743]) ).
thf(4616,plain,
( ( sk7 @ sk33 )
| ( sk33 @ sk4 )
| ~ sk6
| ( ( sk9 @ sk33 )
!= sk4 ) ),
inference(simp,[status(thm)],[4601]) ).
thf(21880,plain,
( ~ ( sk5 @ ( sk10 @ sk5 ) )
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 )
| ( ( sk7 @ sk5 )
!= ( sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[21864,13356]) ).
thf(21881,plain,
( ~ ( sk5 @ ( sk10 @ sk5 ) )
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 ) ),
inference(pattern_uni,[status(thm)],[21880:[]]) ).
thf(22202,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12046,21881]) ).
thf(22273,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 )
| ( ( sk10 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[22202]) ).
thf(141,plain,
! [A: a > a > $o] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( sk7
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
| ( sk7 @ ( A @ sk24 ) ) ),
inference(prim_subst,[status(thm)],[61:[bind(A,$thf( ^ [C: a] : ( sk7 @ ( B @ C ) ) ))]]) ).
thf(172,plain,
! [A: a > a > $o] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( sk7
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
| ( sk7 @ ( A @ sk24 ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(8019,plain,
( ~ sk6
| ( ( sk9 @ sk5 )
!= sk4 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,4059]) ).
thf(8088,plain,
( ~ sk6
| ( ( sk9 @ sk5 )
!= sk4 )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[8019]) ).
thf(329,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk1 @ sk23 @ ( sk30 @ A ) )
| ( sk2 @ sk23 @ ( sk30 @ A ) )
| ( A @ sk24 )
| ( ( sk29
@ ^ [B: a] : $false )
!= ( sk29 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[174,47]) ).
thf(330,plain,
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [A: a] : $false ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [A: a] : $false ) )
| $false ),
inference(pattern_uni,[status(thm)],[329:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(362,plain,
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [A: a] : $false ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[330]) ).
thf(31,plain,
! [A: a > $o] :
( sk6
| sk11
| ~ ( A @ ( sk30 @ A ) )
| ~ ( sk29 @ A )
| ( A @ sk24 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(76,plain,
! [A: a > $o] :
( sk6
| sk11
| ~ ( A @ ( sk30 @ A ) )
| ~ ( sk29 @ A )
| ( A @ sk24 ) ),
inference(simp,[status(thm)],[31]) ).
thf(219,plain,
! [A: a > $o] :
( sk6
| ( sk1 @ sk12 @ ( sk15 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11
| ( ( A @ ( sk16 @ A ) )
!= ( sk1 @ sk12 @ ( sk15 @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[46]) ).
thf(245,plain,
! [A: a > $o] :
( sk6
| ( sk1 @ sk12 @ ( sk15 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11
| ( ( A @ ( sk16 @ A ) )
!= ( sk1 @ sk12 @ ( sk15 @ A ) ) ) ),
inference(simp,[status(thm)],[219]) ).
thf(8207,plain,
( ~ sk6
| ( ( sk5 @ sk36 )
!= sk14 )
| sk14
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,3767]) ).
thf(8269,plain,
( sk14
| ~ sk6
| ( ( sk5 @ sk36 )
!= sk14 )
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[8207]) ).
thf(233,plain,
! [A: a > a] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : ( sk33 @ ( A @ B ) ) ) )
| ( sk33
@ ( A
@ ( sk16
@ ^ [B: a] : ( sk33 @ ( A @ B ) ) ) ) )
| ( sk33 @ ( A @ sk13 ) )
| sk14
| ~ sk11 ),
inference(prim_subst,[status(thm)],[46:[bind(A,$thf( ^ [C: a] : ( sk33 @ ( B @ C ) ) ))]]) ).
thf(271,plain,
! [A: a > a] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : ( sk33 @ ( A @ B ) ) ) )
| ( sk33
@ ( A
@ ( sk16
@ ^ [B: a] : ( sk33 @ ( A @ B ) ) ) ) )
| ( sk33 @ ( A @ sk13 ) )
| sk14
| ~ sk11 ),
inference(simp,[status(thm)],[233]) ).
thf(2583,plain,
! [A: a > $o] :
( ( A @ ( sk9 @ A ) )
| ( A @ sk4 )
| ~ sk6
| ~ ( sk33 @ sk4 )
| ( ( sk33
@ ( sk8
@ ^ [B: a] :
~ ( sk33 @ B ) ) )
!= ( ~ ( sk33 @ sk4 ) ) )
| ( ( sk7 @ A )
!= ( sk7
@ ^ [B: a] :
~ ( sk33 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[66,906]) ).
thf(2584,plain,
( ~ ( sk33
@ ( sk9
@ ^ [A: a] :
~ ( sk33 @ A ) ) )
| ~ ( sk33 @ sk4 )
| ~ sk6
| ~ ( sk33 @ sk4 )
| ( ( sk33
@ ( sk8
@ ^ [A: a] :
~ ( sk33 @ A ) ) )
!= ( ~ ( sk33 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[2583:[bind(A,$thf( ^ [B: a] : ~ ( sk33 @ B ) ))]]) ).
thf(2811,plain,
( ( ( sk33
@ ( sk8
@ ^ [A: a] :
~ ( sk33 @ A ) ) )
!= ( ~ ( sk33 @ sk4 ) ) )
| ~ ( sk33 @ sk4 )
| ~ sk6
| ~ ( sk33 @ sk4 )
| ~ ( sk33
@ ( sk9
@ ^ [A: a] :
~ ( sk33 @ A ) ) ) ),
inference(cnf,[status(esa)],[2584]) ).
thf(2812,plain,
( ( ( sk33
@ ( sk8
@ ^ [A: a] :
~ ( sk33 @ A ) ) )
!= ( ~ ( sk33 @ sk4 ) ) )
| ~ ( sk33 @ sk4 )
| ~ sk6
| ~ ( sk33
@ ( sk9
@ ^ [A: a] :
~ ( sk33 @ A ) ) ) ),
inference(simp,[status(thm)],[2811]) ).
thf(22217,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,21881]) ).
thf(22253,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 )
| ( ( sk10 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[22217]) ).
thf(240,plain,
( sk6
| ( sk1 @ sk12 @ ( sk15 @ sk5 ) )
| ( sk5 @ ( sk16 @ sk5 ) )
| ( sk5 @ sk13 )
| sk14
| ~ sk11 ),
inference(prim_subst,[status(thm)],[46:[bind(A,$thf( sk5 ))]]) ).
thf(23863,plain,
( sk6
| ~ sk14
| ~ sk11
| ~ ( sk5 @ sk12 )
| ( ( sk5
@ ( sk18
@ ^ [A: a] : $false ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[6528,38]) ).
thf(24011,plain,
( sk6
| ~ sk14
| ~ sk11
| ~ ( sk5 @ sk12 )
| ( ( sk18
@ ^ [A: a] : $false )
!= sk4 ) ),
inference(simp,[status(thm)],[23863]) ).
thf(155,plain,
( sk6
| sk11
| ( sk29 @ sk5 )
| ( sk5 @ ( sk31 @ sk5 ) )
| ( sk5 @ sk24 ) ),
inference(prim_subst,[status(thm)],[61:[bind(A,$thf( sk5 ))]]) ).
thf(97,plain,
! [A: a > a] :
( ~ ( sk5
@ ( A
@ ( sk8
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) ) ) )
| ~ ( sk7
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) )
| ( sk5 @ ( A @ sk4 ) )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[78:[bind(A,$thf( ^ [C: a] : ( sk5 @ ( B @ C ) ) ))]]) ).
thf(108,plain,
! [A: a > a] :
( ~ ( sk5
@ ( A
@ ( sk8
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) ) ) )
| ~ ( sk7
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) )
| ( sk5 @ ( A @ sk4 ) )
| ~ sk6 ),
inference(simp,[status(thm)],[97]) ).
thf(11095,plain,
( ( ( sk5 @ sk48 )
!= sk14 )
| sk14
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(func_ext,[status(esa)],[8254]) ).
thf(154,plain,
( sk6
| sk11
| ( sk29 @ sk33 )
| ( sk33 @ ( sk31 @ sk33 ) )
| ( sk33 @ sk24 ) ),
inference(prim_subst,[status(thm)],[61:[bind(A,$thf( sk33 ))]]) ).
thf(1498,plain,
( sk6
| sk11
| ( sk29 @ sk33 )
| ( sk33 @ sk24 )
| ( ( sk33 @ ( sk31 @ sk33 ) )
!= ( sk33 @ sk24 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[154]) ).
thf(1502,plain,
( sk6
| sk11
| ( sk29 @ sk33 )
| ( sk33 @ sk24 )
| ( ( sk31 @ sk33 )
!= sk24 ) ),
inference(simp,[status(thm)],[1498]) ).
thf(49218,plain,
( sk6
| sk11
| ( sk29 @ sk33 )
| ( ( sk31 @ sk33 )
!= sk24 )
| ( ( sk33 @ sk24 )
!= ( sk33 @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[1502,14]) ).
thf(49219,plain,
( sk6
| sk11
| ( sk29 @ sk33 )
| ( ( sk31 @ sk33 )
!= sk24 ) ),
inference(pattern_uni,[status(thm)],[49218:[]]) ).
thf(2577,plain,
! [A: a > $o] :
( ( sk7 @ A )
| ( A @ sk4 )
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) )
| ( ( A @ ( sk9 @ A ) )
!= ( sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[66,308]) ).
thf(2770,plain,
( ( sk7
@ ^ [A: a] : ( sk7 @ sk5 ) )
| ( sk7 @ sk5 )
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) ) ),
inference(pre_uni,[status(thm)],[2577:[bind(A,$thf( ^ [B: a] : ( sk7 @ sk5 ) ))]]) ).
thf(5874,plain,
( ~ ( sk21 @ sk41 )
| ~ sk6
| ~ ( sk21 @ sk4 )
| ( ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
!= ( ~ ( sk21 @ sk4 ) ) ) ),
inference(func_ext,[status(esa)],[2910]) ).
thf(5931,plain,
( ( ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
!= ( ~ ( sk21 @ sk4 ) ) )
| ~ ( sk21 @ sk4 )
| ~ sk6
| ~ ( sk21 @ sk41 ) ),
inference(cnf,[status(esa)],[5874]) ).
thf(241,plain,
! [B: a > $o,A: a > $o] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( A
@ ( sk16
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( B
@ ( sk16
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( A @ sk13 )
| ( B @ sk13 )
| sk14
| ~ sk11 ),
inference(prim_subst,[status(thm)],[46:[bind(A,$thf( ^ [D: a] : ( ( B @ D ) | ( C @ D ) ) ))]]) ).
thf(277,plain,
! [B: a > $o,A: a > $o] :
( ~ sk11
| sk14
| ( A @ sk13 )
| ( B @ sk13 )
| ( A
@ ( sk16
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( B
@ ( sk16
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( sk1 @ sk12
@ ( sk15
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| sk6 ),
inference(cnf,[status(esa)],[241]) ).
thf(278,plain,
! [B: a > $o,A: a > $o] :
( ~ sk11
| sk14
| ( A @ sk13 )
| ( B @ sk13 )
| ( A
@ ( sk16
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( B
@ ( sk16
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( sk1 @ sk12
@ ( sk15
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| sk6 ),
inference(simp,[status(thm)],[277]) ).
thf(20591,plain,
( ~ sk11
| ~ sk14
| sk6
| ( ( sk21
@ ( sk18
@ ^ [A: a] : ~ sk11 ) )
!= ( sk21 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[20447,40]) ).
thf(20617,plain,
( sk6
| ~ sk11
| ~ sk14
| ( ( sk18
@ ^ [A: a] : ~ sk11 )
!= sk13 ) ),
inference(simp,[status(thm)],[20591]) ).
thf(12106,plain,
! [B: a,A: a] :
( ~ sk6
| ~ ( sk2 @ A @ B )
| ( sk5 @ B )
| ( ( sk5
@ ( sk8
@ ^ [C: a] : ~ sk6 ) )
!= ( sk5 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12046,63]) ).
thf(12107,plain,
! [A: a] :
( ~ sk6
| ~ ( sk2
@ ( sk8
@ ^ [B: a] : ~ sk6 )
@ A )
| ( sk5 @ A ) ),
inference(pattern_uni,[status(thm)],[12106:[bind(A,$thf( sk8 @ ^ [C: a] : ~ ( sk6 ) )),bind(B,$thf( B ))]]) ).
thf(12178,plain,
! [A: a] :
( ~ sk6
| ~ ( sk2
@ ( sk8
@ ^ [B: a] : ~ sk6 )
@ A )
| ( sk5 @ A ) ),
inference(simp,[status(thm)],[12107]) ).
thf(13263,plain,
( ~ sk6
| ( sk5 @ sk35 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,3374]) ).
thf(13330,plain,
( ( sk5 @ sk35 )
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 ) ),
inference(simp,[status(thm)],[13263]) ).
thf(21391,plain,
( ~ sk14
| ~ sk14
| ( sk29
@ ^ [A: a] : ~ sk14 )
| sk11
| sk6 ),
inference(prim_subst,[status(thm)],[183:[bind(A,$thf( ^ [B: a] : sk14 ))]]) ).
thf(21544,plain,
( ~ sk14
| ( sk29
@ ^ [A: a] : ~ sk14 )
| sk11
| sk6 ),
inference(simp,[status(thm)],[21391]) ).
thf(27953,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk8 @ sk5 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(simp,[status(thm)],[27884]) ).
thf(23,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk25 @ A )
| ~ ( A @ ( sk28 @ A ) )
| ( A @ sk23 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(80,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk25 @ A )
| ~ ( A @ ( sk28 @ A ) )
| ( A @ sk23 ) ),
inference(simp,[status(thm)],[23]) ).
thf(36070,plain,
! [A: a] :
( sk6
| sk11
| ( sk1 @ sk22
@ ( sk26
@ ^ [B: a] : sk6 ) )
| ( sk33 @ A )
| ( ( sk2 @ sk22
@ ( sk26
@ ^ [B: a] : sk6 ) )
!= ( sk2 @ sk22 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5438,52]) ).
thf(36071,plain,
( sk6
| sk11
| ( sk1 @ sk22
@ ( sk26
@ ^ [A: a] : sk6 ) )
| ( sk33
@ ( sk26
@ ^ [A: a] : sk6 ) ) ),
inference(pattern_uni,[status(thm)],[36070:[bind(A,$thf( sk26 @ ^ [B: a] : sk6 ))]]) ).
thf(36605,plain,
! [A: a] :
( sk6
| sk11
| ( sk33
@ ( sk26
@ ^ [B: a] : sk6 ) )
| ( sk33 @ A )
| ( ( sk1 @ sk22
@ ( sk26
@ ^ [B: a] : sk6 ) )
!= ( sk1 @ sk22 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[36071,67]) ).
thf(36606,plain,
( sk6
| sk11
| ( sk33
@ ( sk26
@ ^ [A: a] : sk6 ) )
| ( sk33
@ ( sk26
@ ^ [A: a] : sk6 ) ) ),
inference(pattern_uni,[status(thm)],[36605:[bind(A,$thf( sk26 @ ^ [B: a] : sk6 ))]]) ).
thf(36651,plain,
( sk6
| sk11
| ( sk33
@ ( sk26
@ ^ [A: a] : sk6 ) ) ),
inference(simp,[status(thm)],[36606]) ).
thf(36658,plain,
( sk6
| sk11
| ( ( sk33
@ ( sk26
@ ^ [A: a] : sk6 ) )
!= ( sk33 @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[36651,14]) ).
thf(36741,plain,
( sk6
| sk11
| ( ( sk26
@ ^ [A: a] : sk6 )
!= sk24 ) ),
inference(simp,[status(thm)],[36658]) ).
thf(27148,plain,
( sk6
| ~ sk14
| ~ sk11
| ~ ( sk5 @ sk12 )
| ( ( sk5
@ ( sk18
@ ^ [A: a] : sk6 ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[6895,38]) ).
thf(27289,plain,
( sk6
| ~ sk14
| ~ sk11
| ~ ( sk5 @ sk12 )
| ( ( sk18
@ ^ [A: a] : sk6 )
!= sk4 ) ),
inference(simp,[status(thm)],[27148]) ).
thf(110,plain,
! [B: a > $o,A: a > $o] :
( ~ sk6
| ( A @ sk4 )
| ( B @ sk4 )
| ~ ( sk7
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ~ ( A
@ ( sk8
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) ) ),
inference(cnf,[status(esa)],[100]) ).
thf(112,plain,
! [B: a > $o,A: a > $o] :
( ~ sk6
| ( A @ sk4 )
| ( B @ sk4 )
| ~ ( sk7
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ~ ( A
@ ( sk8
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(22229,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,21881]) ).
thf(22251,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 )
| ( ( sk10 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[22229]) ).
thf(351,plain,
! [B: a > $o,A: a > $o] :
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ~ ( sk29
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ( A @ sk24 )
| ( B @ sk24 ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [D: a] : ( ( B @ D ) | ( C @ D ) ) ))]]) ).
thf(373,plain,
! [B: a > $o,A: a > $o] :
( ( A @ sk24 )
| ( B @ sk24 )
| ~ ( sk29
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( sk1 @ sk23
@ ( sk30
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| sk11
| sk6 ),
inference(cnf,[status(esa)],[351]) ).
thf(374,plain,
! [B: a > $o,A: a > $o] :
( ( A @ sk24 )
| ( B @ sk24 )
| ~ ( sk29
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( sk1 @ sk23
@ ( sk30
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| sk11
| sk6 ),
inference(simp,[status(thm)],[373]) ).
thf(5165,plain,
( sk6
| sk11
| ( sk25 @ sk5 )
| ( sk5 @ ( sk27 @ sk5 ) )
| ( sk5 @ sk23 ) ),
inference(prim_subst,[status(thm)],[65:[bind(A,$thf( sk5 ))]]) ).
thf(5938,plain,
( ~ ( sk21 @ sk4 )
| ~ sk6
| ~ ( sk21 @ sk41 )
| ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
| ~ ( sk21 @ sk4 ) ),
inference(bool_ext,[status(thm)],[5931]) ).
thf(6011,plain,
( ~ ( sk21 @ sk4 )
| ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
| ~ ( sk21 @ sk41 )
| ~ sk6
| ~ ( sk21 @ sk4 ) ),
inference(cnf,[status(esa)],[5938]) ).
thf(6012,plain,
( ~ ( sk21 @ sk4 )
| ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
| ~ ( sk21 @ sk41 )
| ~ sk6 ),
inference(simp,[status(thm)],[6011]) ).
thf(13278,plain,
( ~ sk6
| ( sk5 @ ( sk9 @ sk5 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,3894]) ).
thf(13354,plain,
( ( sk5 @ ( sk9 @ sk5 ) )
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 ) ),
inference(simp,[status(thm)],[13278]) ).
thf(22233,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ ( sk9 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[13354,21881]) ).
thf(22266,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 )
| ( ( sk10 @ sk5 )
!= ( sk9 @ sk5 ) ) ),
inference(simp,[status(thm)],[22233]) ).
thf(6,plain,
! [A: a > $o] :
( ( sk7 @ A )
| ( sk1 @ ( sk9 @ A ) @ ( sk10 @ A ) )
| ( sk2 @ ( sk9 @ A ) @ ( sk10 @ A ) )
| ( A @ sk4 )
| ~ sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(48,plain,
! [A: a > $o] :
( ( sk7 @ A )
| ( sk1 @ ( sk9 @ A ) @ ( sk10 @ A ) )
| ( sk2 @ ( sk9 @ A ) @ ( sk10 @ A ) )
| ( A @ sk4 )
| ~ sk6 ),
inference(simp,[status(thm)],[6]) ).
thf(27962,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk8 @ sk5 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(simp,[status(thm)],[27868]) ).
thf(21160,plain,
! [A: a > $o] :
( sk6
| sk11
| ~ ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
| ( sk29
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk29
@ ^ [B: a] : $false )
!= ( A @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[174,183]) ).
thf(21413,plain,
( sk6
| sk11
| ~ ( sk29
@ ^ [A: a] : $false )
| ( sk29
@ ^ [A: a] :
~ ( sk29
@ ^ [B: a] : $false ) ) ),
inference(pre_uni,[status(thm)],[21160:[bind(A,$thf( ^ [B: a] : ( sk29 @ ^ [C: a] : $false ) ))]]) ).
thf(38095,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] :
~ ( sk29
@ ^ [B: a] : $false ) )
| ( ( sk29
@ ^ [A: a] : $false )
!= ( sk29
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[174,21413]) ).
thf(38096,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] :
~ ( sk29
@ ^ [B: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[38095:[]]) ).
thf(216,plain,
! [B: a,A: a > $o] :
( sk6
| ( sk1 @ sk12 @ ( sk15 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11
| ( sk5 @ B )
| ( ( A @ ( sk16 @ A ) )
!= ( sk1 @ sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[46,21]) ).
thf(250,plain,
! [A: a > a] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : ( sk1 @ sk3 @ ( A @ B ) ) ) )
| ( sk1 @ sk3 @ ( A @ sk13 ) )
| sk14
| ~ sk11
| ( sk5
@ ( A
@ ( sk16
@ ^ [B: a] : ( sk1 @ sk3 @ ( A @ B ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[216:[bind(A,$thf( ^ [D: a] : ( sk1 @ sk3 @ ( D @ D ) ) )),bind(B,$thf( D @ ( sk16 @ ^ [D: a] : ( sk1 @ sk3 @ ( D @ D ) ) ) ))]]) ).
thf(282,plain,
! [A: a > a] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : ( sk1 @ sk3 @ ( A @ B ) ) ) )
| ( sk1 @ sk3 @ ( A @ sk13 ) )
| sk14
| ~ sk11
| ( sk5
@ ( A
@ ( sk16
@ ^ [B: a] : ( sk1 @ sk3 @ ( A @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[250]) ).
thf(21162,plain,
! [A: a > $o] :
( sk6
| sk11
| ~ ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
| ( sk29
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk29
@ ^ [B: a] : sk6 )
!= ( A @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[185,183]) ).
thf(21452,plain,
( sk6
| sk11
| ~ ( sk29
@ ^ [A: a] : sk6 )
| ( sk29
@ ^ [A: a] :
~ ( sk29
@ ^ [B: a] : sk6 ) ) ),
inference(pre_uni,[status(thm)],[21162:[bind(A,$thf( ^ [B: a] : ( sk29 @ ^ [C: a] : sk6 ) ))]]) ).
thf(39058,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] :
~ ( sk29
@ ^ [B: a] : sk6 ) )
| ( ( sk29
@ ^ [A: a] : sk6 )
!= ( sk29
@ ^ [A: a] : sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[185,21452]) ).
thf(39059,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] :
~ ( sk29
@ ^ [B: a] : sk6 ) ) ),
inference(pattern_uni,[status(thm)],[39058:[]]) ).
thf(21258,plain,
! [A: a > $o] :
( sk6
| sk11
| ~ ( A
@ ( sk31
@ ^ [B: a] :
~ ( A @ B ) ) )
| ( sk29
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk29
@ ^ [B: a] : sk11 )
!= ( A @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[181,183]) ).
thf(21437,plain,
( sk6
| sk11
| ~ ( sk29
@ ^ [A: a] : sk11 )
| ( sk29
@ ^ [A: a] :
~ ( sk29
@ ^ [B: a] : sk11 ) ) ),
inference(pre_uni,[status(thm)],[21258:[bind(A,$thf( ^ [B: a] : ( sk29 @ ^ [C: a] : sk11 ) ))]]) ).
thf(38635,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] :
~ ( sk29
@ ^ [B: a] : sk11 ) )
| ( ( sk29
@ ^ [A: a] : sk11 )
!= ( sk29
@ ^ [A: a] : sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[181,21437]) ).
thf(38636,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] :
~ ( sk29
@ ^ [B: a] : sk11 ) ) ),
inference(pattern_uni,[status(thm)],[38635:[]]) ).
thf(28011,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk8 @ sk5 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(simp,[status(thm)],[27903]) ).
thf(12,plain,
! [A: a > $o] :
( sk6
| ~ ( A @ ( sk15 @ A ) )
| ( A @ ( sk16 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11 ),
inference(cnf,[status(esa)],[3]) ).
thf(50,plain,
! [A: a > $o] :
( sk6
| ~ ( A @ ( sk15 @ A ) )
| ( A @ ( sk16 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11 ),
inference(simp,[status(thm)],[12]) ).
thf(668,plain,
! [A: a] :
( sk6
| sk14
| ~ sk11
| ( sk5 @ A )
| ( ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : $false ) )
!= ( sk1 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[265,21]) ).
thf(669,plain,
! [A: a] :
( sk6
| sk14
| ( sk5 @ A )
| ~ sk11
| ( sk12 != sk3 )
| ( ( sk15
@ ^ [B: a] : $false )
!= A ) ),
inference(simp,[status(thm)],[668]) ).
thf(673,plain,
( sk6
| sk14
| ( sk5
@ ( sk15
@ ^ [A: a] : $false ) )
| ~ sk11
| ( sk12 != sk3 ) ),
inference(simp,[status(thm)],[669]) ).
thf(13303,plain,
! [B: a,A: a] :
( ~ sk6
| ~ ( sk2 @ A @ B )
| ( sk5 @ B )
| ( ( sk5 @ sk50 )
!= ( sk5 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13250,63]) ).
thf(13304,plain,
! [A: a] :
( ~ sk6
| ~ ( sk2 @ sk50 @ A )
| ( sk5 @ A ) ),
inference(pattern_uni,[status(thm)],[13303:[bind(A,$thf( sk50 ))]]) ).
thf(13369,plain,
! [A: a] :
( ~ sk6
| ~ ( sk2 @ sk50 @ A )
| ( sk5 @ A ) ),
inference(simp,[status(thm)],[13304]) ).
thf(21614,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk25 @ A )
| ( A @ sk23 )
| ~ sk14
| ( sk29
@ ^ [B: a] : $true )
| ( ( A @ ( sk27 @ A ) )
!= ~ sk14 ) ),
inference(paramod_ordered,[status(thm)],[65,21544]) ).
thf(21696,plain,
( sk6
| sk11
| ( sk25
@ ^ [A: a] : ~ sk14 )
| ~ sk14
| ~ sk14
| ( sk29
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[21614:[bind(A,$thf( ^ [B: a] : ~ ( sk14 ) ))]]) ).
thf(21705,plain,
( ( sk29
@ ^ [A: a] : $true )
| ~ sk14
| ~ sk14
| ( sk25
@ ^ [A: a] : ~ sk14 )
| sk11
| sk6 ),
inference(cnf,[status(esa)],[21696]) ).
thf(21706,plain,
( ( sk29
@ ^ [A: a] : $true )
| ~ sk14
| ( sk25
@ ^ [A: a] : ~ sk14 )
| sk11
| sk6 ),
inference(simp,[status(thm)],[21705]) ).
thf(347,plain,
! [B: a > a,A: a > a] :
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
| ~ ( sk29
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk2 @ ( A @ sk24 ) @ ( B @ sk24 ) ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [D: a] : ( sk2 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(370,plain,
! [B: a > a,A: a > a] :
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
| ~ ( sk29
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk2 @ ( A @ sk24 ) @ ( B @ sk24 ) ) ),
inference(simp,[status(thm)],[347]) ).
thf(710,plain,
( sk6
| sk14
| ~ sk11
| ~ ( sk5 @ sk12 )
| ( ( sk5
@ ( sk15
@ ^ [A: a] : sk6 ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[555,38]) ).
thf(717,plain,
( sk6
| sk14
| ~ sk11
| ~ ( sk5 @ sk12 )
| ( ( sk15
@ ^ [A: a] : sk6 )
!= sk4 ) ),
inference(simp,[status(thm)],[710]) ).
thf(8020,plain,
( ~ sk6
| ( ( sk5
@ ( sk8
@ ^ [A: a] : $false ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[7992,38]) ).
thf(8071,plain,
( ~ sk6
| ( ( sk8
@ ^ [A: a] : $false )
!= sk4 ) ),
inference(simp,[status(thm)],[8020]) ).
thf(470,plain,
( ~ sk6
| ~ ( sk21 @ sk4 )
| ~ ( sk7
@ ^ [A: a] :
~ ( sk21 @ A ) )
| ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) ) ),
inference(prim_subst,[status(thm)],[118:[bind(A,$thf( sk21 ))]]) ).
thf(4980,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk25 @ A )
| ( A @ sk23 )
| ( ( A @ ( sk27 @ A ) )
!= ( sk33 @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[65,14]) ).
thf(5186,plain,
( sk6
| sk11
| ( sk25
@ ^ [A: a] : ( sk33 @ sk24 ) )
| ( sk33 @ sk24 ) ),
inference(pre_uni,[status(thm)],[4980:[bind(A,$thf( ^ [B: a] : ( sk33 @ sk24 ) ))]]) ).
thf(22209,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,21881]) ).
thf(22256,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 )
| ( ( sk10 @ sk5 )
!= sk50 ) ),
inference(simp,[status(thm)],[22209]) ).
thf(145,plain,
! [B: a > $o,A: a > $o] :
( sk6
| sk11
| ( sk29
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ( A
@ ( sk31
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( B
@ ( sk31
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( A @ sk24 )
| ( B @ sk24 ) ),
inference(prim_subst,[status(thm)],[61:[bind(A,$thf( ^ [D: a] : ( ( B @ D ) | ( C @ D ) ) ))]]) ).
thf(176,plain,
! [B: a > $o,A: a > $o] :
( ( A @ sk24 )
| ( B @ sk24 )
| ( A
@ ( sk31
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( B
@ ( sk31
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( sk29
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| sk11
| sk6 ),
inference(cnf,[status(esa)],[145]) ).
thf(177,plain,
! [B: a > $o,A: a > $o] :
( ( A @ sk24 )
| ( B @ sk24 )
| ( A
@ ( sk31
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( B
@ ( sk31
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( sk29
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| sk11
| sk6 ),
inference(simp,[status(thm)],[176]) ).
thf(27,plain,
! [B: a,A: a] :
( sk6
| ~ ( sk21 @ A )
| ~ ( sk1 @ A @ B )
| ( sk21 @ B )
| ~ sk11 ),
inference(cnf,[status(esa)],[3]) ).
thf(72,plain,
! [B: a,A: a] :
( sk6
| ~ ( sk21 @ A )
| ~ ( sk1 @ A @ B )
| ( sk21 @ B )
| ~ sk11 ),
inference(simp,[status(thm)],[27]) ).
thf(144,plain,
! [A: a > a > $o] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) )
| ( sk29
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) ) ) )
| ( sk29 @ ( A @ sk24 ) ) ),
inference(prim_subst,[status(thm)],[61:[bind(A,$thf( ^ [C: a] : ( sk29 @ ( B @ C ) ) ))]]) ).
thf(175,plain,
! [A: a > a > $o] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) )
| ( sk29
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) ) ) )
| ( sk29 @ ( A @ sk24 ) ) ),
inference(simp,[status(thm)],[144]) ).
thf(13287,plain,
( ~ sk6
| sk11
| ( sk5
!= ( ^ [A: a] : sk11 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,3158]) ).
thf(13329,plain,
( sk11
| ~ sk6
| ( sk5
!= ( ^ [A: a] : sk11 ) )
| ( ( sk8 @ sk5 )
!= sk50 ) ),
inference(simp,[status(thm)],[13287]) ).
thf(17817,plain,
( ( ( sk5 @ sk51 )
!= sk11 )
| sk11
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 ) ),
inference(func_ext,[status(esa)],[13329]) ).
thf(8035,plain,
( ~ sk6
| ( ( sk5 @ sk35 )
!= ~ sk6 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,3023]) ).
thf(8087,plain,
( ~ sk6
| ( ( sk5 @ sk35 )
!= ~ sk6 )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[8035]) ).
thf(22459,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,21913]) ).
thf(22501,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 )
| ( ( sk10 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[22459]) ).
thf(6536,plain,
! [A: a] :
( sk6
| ~ sk14
| ~ sk11
| ( sk21 @ A )
| ( ( sk2 @ sk12
@ ( sk18
@ ^ [B: a] : $false ) )
!= ( sk2 @ sk12 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6425,51]) ).
thf(6537,plain,
( sk6
| ~ sk14
| ~ sk11
| ( sk21
@ ( sk18
@ ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[6536:[bind(A,$thf( sk18 @ ^ [B: a] : $false ))]]) ).
thf(6610,plain,
( sk6
| ~ sk14
| ~ sk11
| ( ( sk21
@ ( sk18
@ ^ [A: a] : $false ) )
!= ( sk21 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[6537,40]) ).
thf(6622,plain,
( sk6
| ~ sk14
| ~ sk11
| ( ( sk18
@ ^ [A: a] : $false )
!= sk13 ) ),
inference(simp,[status(thm)],[6610]) ).
thf(27352,plain,
( sk6
| ~ sk14
| ~ sk11
| ( sk12 != sk3 )
| ( ( sk5
@ ( sk18
@ ^ [A: a] : sk6 ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[6932,38]) ).
thf(27469,plain,
( sk6
| ~ sk14
| ~ sk11
| ( sk12 != sk3 )
| ( ( sk18
@ ^ [A: a] : sk6 )
!= sk4 ) ),
inference(simp,[status(thm)],[27352]) ).
thf(12094,plain,
( ~ sk6
| ( ( sk5 @ sk35 )
!= ~ sk6 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12046,3023]) ).
thf(12145,plain,
( ~ sk6
| ( ( sk5 @ sk35 )
!= ~ sk6 )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[12094]) ).
thf(31866,plain,
( sk14
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 )
| ( sk5 @ sk48 )
| sk14 ),
inference(bool_ext,[status(thm)],[11095]) ).
thf(31948,plain,
( sk14
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 )
| ( sk5 @ sk48 ) ),
inference(simp,[status(thm)],[31866]) ).
thf(23226,plain,
! [A: a > a] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] : ( sk1 @ sk3 @ ( A @ B ) ) )
| ( sk1 @ sk3 @ ( A @ sk24 ) )
| ( ( sk5
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk1 @ sk3 @ ( A @ B ) ) ) ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[189,38]) ).
thf(23360,plain,
( sk6
| sk11
| ( sk29
@ ^ [A: a] : ( sk1 @ sk3 @ sk4 ) )
| ( sk1 @ sk3 @ sk4 ) ),
inference(pre_uni,[status(thm)],[23226:[bind(A,$thf( ^ [B: a] : sk4 ))]]) ).
thf(331,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk1 @ sk23 @ ( sk30 @ A ) )
| ( sk2 @ sk23 @ ( sk30 @ A ) )
| ( A @ sk24 )
| ( ( sk29
@ ^ [B: a] : sk6 )
!= ( sk29 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[185,47]) ).
thf(332,plain,
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [A: a] : sk6 ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [A: a] : sk6 ) )
| sk6 ),
inference(pattern_uni,[status(thm)],[331:[bind(A,$thf( ^ [B: a] : sk6 ))]]) ).
thf(363,plain,
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [A: a] : sk6 ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [A: a] : sk6 ) ) ),
inference(simp,[status(thm)],[332]) ).
thf(27972,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk8 @ sk5 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(simp,[status(thm)],[27843]) ).
thf(343,plain,
! [A: a > a] :
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) ) )
| ~ ( sk29
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) )
| ( sk21 @ ( A @ sk24 ) ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [C: a] : ( sk21 @ ( B @ C ) ) ))]]) ).
thf(368,plain,
! [A: a > a] :
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) ) )
| ~ ( sk29
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) )
| ( sk21 @ ( A @ sk24 ) ) ),
inference(simp,[status(thm)],[343]) ).
thf(13275,plain,
( ~ sk6
| ( ( sk9 @ sk5 )
!= sk4 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,4059]) ).
thf(13345,plain,
( ~ sk6
| ( ( sk9 @ sk5 )
!= sk4 )
| ( ( sk8 @ sk5 )
!= sk50 ) ),
inference(simp,[status(thm)],[13275]) ).
thf(21895,plain,
( ~ sk6
| ( sk7 @ sk5 )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,21864]) ).
thf(22025,plain,
( ( sk7 @ sk5 )
| ~ sk6
| ( ( sk10 @ sk5 )
!= sk50 ) ),
inference(simp,[status(thm)],[21895]) ).
thf(139,plain,
! [A: a > a] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) )
| ( sk5
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) ) ) )
| ( sk5 @ ( A @ sk24 ) ) ),
inference(prim_subst,[status(thm)],[61:[bind(A,$thf( ^ [C: a] : ( sk5 @ ( B @ C ) ) ))]]) ).
thf(171,plain,
! [A: a > a] :
( sk6
| sk11
| ( sk29
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) )
| ( sk5
@ ( A
@ ( sk31
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) ) ) )
| ( sk5 @ ( A @ sk24 ) ) ),
inference(simp,[status(thm)],[139]) ).
thf(36477,plain,
( sk11
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 )
| ( sk5 @ sk51 )
| sk11 ),
inference(bool_ext,[status(thm)],[17817]) ).
thf(36559,plain,
( sk11
| ~ sk6
| ( ( sk8 @ sk5 )
!= sk50 )
| ( sk5 @ sk51 ) ),
inference(simp,[status(thm)],[36477]) ).
thf(22970,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) )
| ( ( sk5 @ ( sk10 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12046,21958]) ).
thf(23029,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) )
| ( ( sk10 @ sk5 )
!= ( sk8
@ ^ [A: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[22970]) ).
thf(15,plain,
! [A: a > $o] :
( sk6
| ~ ( A @ ( sk15 @ A ) )
| ~ ( A @ ( sk17 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11 ),
inference(cnf,[status(esa)],[3]) ).
thf(55,plain,
! [A: a > $o] :
( sk6
| ~ ( A @ ( sk15 @ A ) )
| ~ ( A @ ( sk17 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11 ),
inference(simp,[status(thm)],[15]) ).
thf(101,plain,
! [B: a > a,A: a > a] :
( ~ ( sk1
@ ( A
@ ( sk8
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk8
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ~ ( sk7
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk1 @ ( A @ sk4 ) @ ( B @ sk4 ) )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[78:[bind(A,$thf( ^ [D: a] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(114,plain,
! [B: a > a,A: a > a] :
( ~ ( sk1
@ ( A
@ ( sk8
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk8
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ~ ( sk7
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk1 @ ( A @ sk4 ) @ ( B @ sk4 ) )
| ~ sk6 ),
inference(simp,[status(thm)],[101]) ).
thf(16,plain,
! [A: a > $o] :
( sk6
| ~ sk14
| ~ ( A @ ( sk18 @ A ) )
| ( A @ ( sk19 @ A ) )
| ( A @ sk13 )
| ~ sk11 ),
inference(cnf,[status(esa)],[3]) ).
thf(75,plain,
! [A: a > $o] :
( sk6
| ~ sk14
| ~ ( A @ ( sk18 @ A ) )
| ( A @ ( sk19 @ A ) )
| ( A @ sk13 )
| ~ sk11 ),
inference(simp,[status(thm)],[16]) ).
thf(23565,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk8 @ sk5 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5
@ ( sk8
@ ^ [A: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7992,22149]) ).
thf(23605,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk8 @ sk5 ) )
| ( ( sk8 @ sk5 )
!= ( sk8
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[23565]) ).
thf(20841,plain,
! [A: a] :
( ~ sk11
| ~ sk14
| sk6
| ( sk21 @ A )
| ( ( sk2 @ sk12
@ ( sk18
@ ^ [B: a] : ~ sk14 ) )
!= ( sk2 @ sk12 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6454,51]) ).
thf(20842,plain,
( ~ sk11
| ~ sk14
| sk6
| ( sk21
@ ( sk18
@ ^ [A: a] : ~ sk14 ) ) ),
inference(pattern_uni,[status(thm)],[20841:[bind(A,$thf( sk18 @ ^ [B: a] : ~ ( sk14 ) ))]]) ).
thf(20986,plain,
( ~ sk11
| ~ sk14
| sk6
| ( ( sk21
@ ( sk18
@ ^ [A: a] : ~ sk14 ) )
!= ( sk21 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[20842,40]) ).
thf(21011,plain,
( sk6
| ~ sk11
| ~ sk14
| ( ( sk18
@ ^ [A: a] : ~ sk14 )
!= sk13 ) ),
inference(simp,[status(thm)],[20986]) ).
thf(643,plain,
! [B: a,A: a] :
( sk6
| sk14
| ~ sk11
| ~ ( sk5 @ A )
| ( sk5 @ B )
| ( ( sk1 @ sk12
@ ( sk15
@ ^ [C: a] : sk14 ) )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[263,58]) ).
thf(644,plain,
( sk6
| sk14
| ~ sk11
| ~ ( sk5 @ sk12 )
| ( sk5
@ ( sk15
@ ^ [A: a] : sk14 ) ) ),
inference(pattern_uni,[status(thm)],[643:[bind(A,$thf( sk12 )),bind(B,$thf( sk15 @ ^ [C: a] : sk14 ))]]) ).
thf(1061,plain,
( sk6
| sk14
| ~ sk11
| ~ ( sk5 @ sk12 )
| ( ( sk5
@ ( sk15
@ ^ [A: a] : sk14 ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[644,38]) ).
thf(1077,plain,
( sk6
| sk14
| ~ sk11
| ~ ( sk5 @ sk12 )
| ( ( sk15
@ ^ [A: a] : sk14 )
!= sk4 ) ),
inference(simp,[status(thm)],[1061]) ).
thf(234,plain,
! [B: a > a,A: a > a] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
| ( sk2
@ ( A
@ ( sk16
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk16
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ( sk2 @ ( A @ sk13 ) @ ( B @ sk13 ) )
| sk14
| ~ sk11 ),
inference(prim_subst,[status(thm)],[46:[bind(A,$thf( ^ [D: a] : ( sk2 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(272,plain,
! [B: a > a,A: a > a] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
| ( sk2
@ ( A
@ ( sk16
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk16
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ( sk2 @ ( A @ sk13 ) @ ( B @ sk13 ) )
| sk14
| ~ sk11 ),
inference(simp,[status(thm)],[234]) ).
thf(12073,plain,
( ~ sk6
| ( ( sk5
@ ( sk8
@ ^ [A: a] : ~ sk6 ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[12046,38]) ).
thf(12152,plain,
( ~ sk6
| ( ( sk8
@ ^ [A: a] : ~ sk6 )
!= sk4 ) ),
inference(simp,[status(thm)],[12073]) ).
thf(4555,plain,
( ( sk7 @ sk21 )
| ( sk21 @ sk4 )
| ~ sk6
| ( ( sk21 @ ( sk9 @ sk21 ) )
!= ( sk21 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2737]) ).
thf(4570,plain,
( ( sk7 @ sk21 )
| ( sk21 @ sk4 )
| ~ sk6
| ( ( sk9 @ sk21 )
!= sk4 ) ),
inference(simp,[status(thm)],[4555]) ).
thf(19,plain,
! [A: a > $o] :
( sk6
| sk11
| ~ ( A @ ( sk26 @ A ) )
| ~ ( sk25 @ A )
| ( A @ sk23 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(82,plain,
! [A: a > $o] :
( sk6
| sk11
| ~ ( A @ ( sk26 @ A ) )
| ~ ( sk25 @ A )
| ( A @ sk23 ) ),
inference(simp,[status(thm)],[19]) ).
thf(8226,plain,
! [B: a,A: a] :
( ~ sk6
| ~ ( sk2 @ A @ B )
| ( sk5 @ B )
| ( ( sk5 @ sk45 )
!= ( sk5 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8167,63]) ).
thf(8227,plain,
! [A: a] :
( ~ sk6
| ~ ( sk2 @ sk45 @ A )
| ( sk5 @ A ) ),
inference(pattern_uni,[status(thm)],[8226:[bind(A,$thf( sk45 ))]]) ).
thf(8272,plain,
! [A: a] :
( ~ sk6
| ~ ( sk2 @ sk45 @ A )
| ( sk5 @ A ) ),
inference(simp,[status(thm)],[8227]) ).
thf(93,plain,
! [A: a > a] :
( ~ ( sk21
@ ( A
@ ( sk8
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) ) ) )
| ~ ( sk7
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) )
| ( sk21 @ ( A @ sk4 ) )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[78:[bind(A,$thf( ^ [C: a] : ( sk21 @ ( B @ C ) ) ))]]) ).
thf(119,plain,
! [A: a > a] :
( ~ ( sk21
@ ( A
@ ( sk8
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) ) ) )
| ~ ( sk7
@ ^ [B: a] : ( sk21 @ ( A @ B ) ) )
| ( sk21 @ ( A @ sk4 ) )
| ~ sk6 ),
inference(simp,[status(thm)],[93]) ).
thf(346,plain,
( sk6
| sk11
| ( sk1 @ sk23 @ ( sk30 @ sk21 ) )
| ( sk2 @ sk23 @ ( sk30 @ sk21 ) )
| ~ ( sk29 @ sk21 )
| ( sk21 @ sk24 ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( sk21 ))]]) ).
thf(8209,plain,
( ~ sk6
| ( ( sk5 @ sk45 )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,38]) ).
thf(8267,plain,
( ~ sk6
| ( sk45 != sk4 ) ),
inference(simp,[status(thm)],[8209]) ).
thf(7148,plain,
( ( ( ~ ( sk21 @ sk42 ) )
!= ~ sk6 )
| ~ sk6
| ~ ( sk21 @ sk4 )
| ( ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
!= ( ~ ( sk21 @ sk4 ) ) ) ),
inference(func_ext,[status(esa)],[2963]) ).
thf(7216,plain,
( ( ( sk21 @ sk42 )
!= sk6 )
| ~ sk6
| ~ ( sk21 @ sk4 )
| ( ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
!= ( ~ ( sk21 @ sk4 ) ) ) ),
inference(simp,[status(thm)],[7148]) ).
thf(15950,plain,
( sk6
| sk11
| sk14
| sk14
| ( ( sk29
@ ^ [A: a] : sk14 )
!= sk14 ) ),
inference(prim_subst,[status(thm)],[163:[bind(A,$thf( ^ [B: a] : sk14 ))]]) ).
thf(16192,plain,
( sk6
| sk11
| sk14
| ( ( sk29
@ ^ [A: a] : sk14 )
!= sk14 ) ),
inference(simp,[status(thm)],[15950]) ).
thf(13259,plain,
( ~ sk6
| ( ( sk5 @ sk37 )
!= sk11 )
| sk11
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,3798]) ).
thf(13349,plain,
( sk11
| ~ sk6
| ( ( sk5 @ sk37 )
!= sk11 )
| ( ( sk8 @ sk5 )
!= sk50 ) ),
inference(simp,[status(thm)],[13259]) ).
thf(215,plain,
! [B: a,A: a > $o] :
( sk6
| ( A @ ( sk16 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11
| ( sk5 @ B )
| ( ( sk1 @ sk12 @ ( sk15 @ A ) )
!= ( sk1 @ sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[46,21]) ).
thf(259,plain,
! [B: a,A: a > $o] :
( sk6
| ( A @ ( sk16 @ A ) )
| ( A @ sk13 )
| sk14
| ( sk5 @ B )
| ~ sk11
| ( sk12 != sk3 )
| ( ( sk15 @ A )
!= B ) ),
inference(simp,[status(thm)],[215]) ).
thf(262,plain,
! [A: a > $o] :
( sk6
| ( A @ ( sk16 @ A ) )
| ( A @ sk13 )
| sk14
| ( sk5 @ ( sk15 @ A ) )
| ~ sk11
| ( sk12 != sk3 ) ),
inference(simp,[status(thm)],[259]) ).
thf(7474,plain,
( ~ sk6
| ~ ( sk21 @ sk4 )
| ( sk21
!= ( ^ [A: a] : sk6 ) )
| ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
| ~ ( sk21 @ sk4 ) ),
inference(bool_ext,[status(thm)],[7147]) ).
thf(7541,plain,
( ~ ( sk21 @ sk4 )
| ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
| ( sk21
!= ( ^ [A: a] : sk6 ) )
| ~ ( sk21 @ sk4 )
| ~ sk6 ),
inference(cnf,[status(esa)],[7474]) ).
thf(7542,plain,
( ~ ( sk21 @ sk4 )
| ( sk21
@ ( sk8
@ ^ [A: a] :
~ ( sk21 @ A ) ) )
| ( sk21
!= ( ^ [A: a] : sk6 ) )
| ~ sk6 ),
inference(simp,[status(thm)],[7541]) ).
thf(10603,plain,
( ~ sk6
| ( ( sk8 @ sk5 )
!= sk45 )
| ( sk5 @ sk46 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[9497]) ).
thf(10648,plain,
( ~ sk6
| ( sk5 @ sk46 )
| ( ( sk8 @ sk5 )
!= sk45 )
| ~ sk6 ),
inference(cnf,[status(esa)],[10603]) ).
thf(10649,plain,
( ~ sk6
| ( sk5 @ sk46 )
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[10648]) ).
thf(96,plain,
! [A: a > a] :
( ~ ( sk33
@ ( A
@ ( sk8
@ ^ [B: a] : ( sk33 @ ( A @ B ) ) ) ) )
| ~ ( sk7
@ ^ [B: a] : ( sk33 @ ( A @ B ) ) )
| ( sk33 @ ( A @ sk4 ) )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[78:[bind(A,$thf( ^ [C: a] : ( sk33 @ ( B @ C ) ) ))]]) ).
thf(107,plain,
! [A: a > a] :
( ~ ( sk33
@ ( A
@ ( sk8
@ ^ [B: a] : ( sk33 @ ( A @ B ) ) ) ) )
| ~ ( sk7
@ ^ [B: a] : ( sk33 @ ( A @ B ) ) )
| ( sk33 @ ( A @ sk4 ) )
| ~ sk6 ),
inference(simp,[status(thm)],[96]) ).
thf(228,plain,
! [A: a > a > $o] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) ) )
| ( sk29
@ ( A
@ ( sk16
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) ) ) )
| ( sk29 @ ( A @ sk13 ) )
| sk14
| ~ sk11 ),
inference(prim_subst,[status(thm)],[46:[bind(A,$thf( ^ [C: a] : ( sk29 @ ( B @ C ) ) ))]]) ).
thf(268,plain,
! [A: a > a > $o] :
( sk6
| ( sk1 @ sk12
@ ( sk15
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) ) )
| ( sk29
@ ( A
@ ( sk16
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) ) ) )
| ( sk29 @ ( A @ sk13 ) )
| sk14
| ~ sk11 ),
inference(simp,[status(thm)],[228]) ).
thf(338,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk1 @ sk23 @ ( sk30 @ A ) )
| ~ ( sk29 @ A )
| ( A @ sk24 )
| ( ( sk2 @ sk23 @ ( sk30 @ A ) )
!= ( A @ sk24 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[47]) ).
thf(358,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk1 @ sk23 @ ( sk30 @ A ) )
| ( A @ sk24 )
| ~ ( sk29 @ A )
| ( ( sk2 @ sk23 @ ( sk30 @ A ) )
!= ( A @ sk24 ) ) ),
inference(simp,[status(thm)],[338]) ).
thf(26,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk29 @ A )
| ~ ( A @ ( sk32 @ A ) )
| ( A @ sk24 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(79,plain,
! [A: a > $o] :
( sk6
| sk11
| ( sk29 @ A )
| ~ ( A @ ( sk32 @ A ) )
| ( A @ sk24 ) ),
inference(simp,[status(thm)],[26]) ).
thf(8193,plain,
( ~ sk6
| ( ( sk5 @ sk37 )
!= sk11 )
| sk11
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,3798]) ).
thf(8268,plain,
( sk11
| ~ sk6
| ( ( sk5 @ sk37 )
!= sk11 )
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[8193]) ).
thf(23545,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk8 @ sk5 ) )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk50 ) ) ),
inference(paramod_ordered,[status(thm)],[13250,22149]) ).
thf(23606,plain,
( ~ sk6
| ( ( sk10 @ sk5 )
!= ( sk8 @ sk5 ) )
| ( ( sk8 @ sk5 )
!= sk50 ) ),
inference(simp,[status(thm)],[23545]) ).
thf(32,plain,
! [A: a > $o] :
( sk6
| ( sk1 @ sk12 @ ( sk15 @ A ) )
| ~ ( A @ ( sk17 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11 ),
inference(cnf,[status(esa)],[3]) ).
thf(68,plain,
! [A: a > $o] :
( sk6
| ( sk1 @ sk12 @ ( sk15 @ A ) )
| ~ ( A @ ( sk17 @ A ) )
| ( A @ sk13 )
| sk14
| ~ sk11 ),
inference(simp,[status(thm)],[32]) ).
thf(33,plain,
! [A: a > $o] :
( sk6
| ~ sk14
| ( sk2 @ sk12 @ ( sk18 @ A ) )
| ( sk2 @ ( sk19 @ A ) @ ( sk20 @ A ) )
| ( A @ sk13 )
| ~ sk11 ),
inference(cnf,[status(esa)],[3]) ).
thf(62,plain,
! [A: a > $o] :
( sk6
| ~ sk14
| ( sk2 @ sk12 @ ( sk18 @ A ) )
| ( sk2 @ ( sk19 @ A ) @ ( sk20 @ A ) )
| ( A @ sk13 )
| ~ sk11 ),
inference(simp,[status(thm)],[33]) ).
thf(2246,plain,
( sk6
| sk14
| ~ sk11
| ( sk12 != sk3 )
| ( ( sk5
@ ( sk15
@ ^ [A: a] : $false ) )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[673,38]) ).
thf(2270,plain,
( sk6
| sk14
| ~ sk11
| ( sk12 != sk3 )
| ( ( sk15
@ ^ [A: a] : $false )
!= sk4 ) ),
inference(simp,[status(thm)],[2246]) ).
thf(345,plain,
! [A: a > a > $o] :
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) ) )
| ~ ( sk29
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) )
| ( sk29 @ ( A @ sk24 ) ) ),
inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [C: a] : ( sk29 @ ( B @ C ) ) ))]]) ).
thf(369,plain,
! [A: a > a > $o] :
( sk6
| sk11
| ( sk1 @ sk23
@ ( sk30
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) ) )
| ( sk2 @ sk23
@ ( sk30
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) ) )
| ~ ( sk29
@ ^ [B: a] : ( sk29 @ ( A @ B ) ) )
| ( sk29 @ ( A @ sk24 ) ) ),
inference(simp,[status(thm)],[345]) ).
thf(146,plain,
! [B: a > a,A: a > a] :
( sk6
| sk11
| ( sk29
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk2
@ ( A
@ ( sk31
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk31
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ( sk2 @ ( A @ sk24 ) @ ( B @ sk24 ) ) ),
inference(prim_subst,[status(thm)],[61:[bind(A,$thf( ^ [D: a] : ( sk2 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(178,plain,
! [B: a > a,A: a > a] :
( sk6
| sk11
| ( sk29
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk2
@ ( A
@ ( sk31
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk31
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ( sk2 @ ( A @ sk24 ) @ ( B @ sk24 ) ) ),
inference(simp,[status(thm)],[146]) ).
thf(8234,plain,
! [B: a,A: a] :
( ~ sk6
| ~ ( sk1 @ A @ B )
| ( sk5 @ B )
| ( ( sk5 @ sk45 )
!= ( sk5 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8167,58]) ).
thf(8235,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1 @ sk45 @ A )
| ( sk5 @ A ) ),
inference(pattern_uni,[status(thm)],[8234:[bind(A,$thf( sk45 ))]]) ).
thf(8273,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1 @ sk45 @ A )
| ( sk5 @ A ) ),
inference(simp,[status(thm)],[8235]) ).
thf(8221,plain,
( ~ sk6
| ( ( sk5 @ sk35 )
!= ~ sk6 )
| ( ( sk5 @ ( sk8 @ sk5 ) )
!= ( sk5 @ sk45 ) ) ),
inference(paramod_ordered,[status(thm)],[8167,3023]) ).
thf(8264,plain,
( ~ sk6
| ( ( sk5 @ sk35 )
!= ~ sk6 )
| ( ( sk8 @ sk5 )
!= sk45 ) ),
inference(simp,[status(thm)],[8221]) ).
thf(335,plain,
! [B: a > $o,A: a > $o] :
( sk6
| sk11
| ( A @ ( sk31 @ A ) )
| ( A @ sk24 )
| ( sk1 @ sk23 @ ( sk30 @ B ) )
| ( sk2 @ sk23 @ ( sk30 @ B ) )
| ( B @ sk24 )
| ( ( sk29 @ A )
!= ( sk29 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[61,47]) ).
thf(336,plain,
! [A: a > $o] :
( sk6
| sk11
| ( A @ ( sk31 @ A ) )
| ( A @ sk24 )
| ( sk1 @ sk23 @ ( sk30 @ A ) )
| ( sk2 @ sk23 @ ( sk30 @ A ) )
| ( A @ sk24 ) ),
inference(pattern_uni,[status(thm)],[335:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(364,plain,
! [A: a > $o] :
( sk6
| sk11
| ( A @ ( sk31 @ A ) )
| ( A @ sk24 )
| ( sk1 @ sk23 @ ( sk30 @ A ) )
| ( sk2 @ sk23 @ ( sk30 @ A ) ) ),
inference(simp,[status(thm)],[336]) ).
thf(55086,plain,
$false,
inference(e,[status(thm)],[69,365,23595,32383,21993,39697,3798,1729,555,8077,352,3979,249,170,115,13341,2908,120,308,3959,6426,22666,269,677,22770,1041,8101,56,22175,5288,1761,24166,7147,26863,698,174,185,6904,17843,14,13360,2814,184,12046,12154,4654,27973,12161,5289,52,22493,24345,344,5279,32462,3374,189,46,4622,57,9497,78,13350,8252,261,8257,5744,13356,179,6895,106,5156,8246,480,61,8141,6932,89,16187,116,74,23038,36896,2965,265,5819,13352,248,60,2910,270,8078,5438,36965,3767,4059,2737,366,8265,6528,38,70,6565,21958,13335,8091,275,21,7378,13250,92,467,3090,1687,3894,22492,7853,23018,229,566,252,1837,361,22149,65,8270,8085,26864,13347,53,169,10052,25034,22503,109,1683,12179,77,8258,1016,27963,8100,2968,8072,13169,27954,173,22168,2813,6988,73,105,266,360,21989,2963,22017,37841,2189,662,2909,906,166,264,28012,6454,180,3158,8164,22669,279,64,22787,375,20447,23687,1535,8092,22510,191,8259,13338,2859,11411,286,12143,59,118,8167,16194,23509,3023,22155,23593,8249,49,236,919,181,5158,12167,22010,159,71,13358,54,3964,113,274,81,7379,1589,22148,8254,32259,4616,22273,172,8088,362,76,245,8269,271,2896,2812,22253,140,66,240,24011,155,108,11095,49219,2770,5931,6449,278,20617,3,12178,13330,21544,27953,80,36741,13168,27289,112,7992,22251,374,8067,5165,6012,22266,48,63,27962,38096,282,39059,38636,263,22142,28011,50,13354,673,13369,21706,370,717,8071,470,5186,67,22256,177,21955,22171,2992,656,72,175,17817,8087,154,22501,6622,27469,12145,31948,23360,6425,363,27972,2743,368,36651,12157,13345,22025,171,8083,36559,23029,40,55,114,75,1689,23605,21011,5409,1077,272,12152,11118,4570,82,8272,119,58,346,8267,7216,20842,16192,13349,36,262,13329,3892,51,2815,183,7542,4917,10649,107,7851,21881,1693,6537,268,5290,358,79,8268,23606,2847,644,47,68,62,2270,369,163,21913,7694,178,21864,8273,8264,364,21868]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEV153^5 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:10:55 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.96/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.98 % [INFO] Parsing done (115ms).
% 1.20/0.99 % [INFO] Running in sequential loop mode.
% 1.70/1.20 % [INFO] eprover registered as external prover.
% 1.70/1.20 % [INFO] Scanning for conjecture ...
% 1.90/1.28 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.90/1.31 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.90/1.31 % [INFO] Problem is higher-order (TPTP THF).
% 1.90/1.32 % [INFO] Type checking passed.
% 1.90/1.32 % [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 ...
% 78.99/17.82 % External prover 'e' found a proof!
% 78.99/17.82 % [INFO] Killing All external provers ...
% 78.99/17.82 % Time passed: 17292ms (effective reasoning time: 16824ms)
% 78.99/17.82 % 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)>
% 78.99/17.82 % Axioms used in derivation (0):
% 78.99/17.82 % No. of inferences in proof: 791
% 78.99/17.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 17292 ms resp. 16824 ms w/o parsing
% 79.55/18.01 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 79.55/18.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------