TSTP Solution File: SEV148^5 by Leo-III---1.7.15
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV148^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n017.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 15:58:20 EDT 2024
% Result : Theorem 221.52s 62.21s
% Output : Refutation 221.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 1
% Syntax : Number of formulae : 273 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 1430 ( 231 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 3093 ( 564 ~; 652 |; 36 &;1784 @)
% ( 0 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 175 ( 175 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 34 usr; 15 con; 0-2 aty)
% Number of variables : 400 ( 165 ^ 235 !; 0 ?; 400 :)
% 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 ) > $o ).
thf(sk6_type,type,
sk6: ( a > $o ) > a ).
thf(sk7_type,type,
sk7: ( a > $o ) > $o ).
thf(sk8_type,type,
sk8: ( a > $o ) > ( a > $o ) > a ).
thf(sk9_type,type,
sk9: ( a > $o ) > ( a > $o ) > a ).
thf(sk10_type,type,
sk10: ( a > $o ) > ( a > $o ) > a ).
thf(sk11_type,type,
sk11: ( a > $o ) > ( a > $o ) > a ).
thf(sk12_type,type,
sk12: ( a > $o ) > ( a > $o ) > a ).
thf(sk13_type,type,
sk13: ( a > $o ) > ( a > $o ) > a ).
thf(sk14_type,type,
sk14: ( a > $o ) > a ).
thf(sk15_type,type,
sk15: ( a > $o ) > a ).
thf(sk16_type,type,
sk16: ( a > $o ) > $o ).
thf(sk17_type,type,
sk17: ( a > $o ) > ( a > $o ) > a ).
thf(sk18_type,type,
sk18: ( a > $o ) > ( a > $o ) > a ).
thf(sk19_type,type,
sk19: ( a > $o ) > ( a > $o ) > a ).
thf(sk20_type,type,
sk20: ( a > $o ) > ( a > $o ) > a ).
thf(sk21_type,type,
sk21: ( a > $o ) > ( a > $o ) > a ).
thf(sk22_type,type,
sk22: ( a > $o ) > ( a > $o ) > a ).
thf(sk23_type,type,
sk23: a > $o ).
thf(sk24_type,type,
sk24: a ).
thf(sk25_type,type,
sk25: a ).
thf(sk26_type,type,
sk26: a ).
thf(sk28_type,type,
sk28: a ).
thf(sk29_type,type,
sk29: a ).
thf(sk32_type,type,
sk32: a ).
thf(sk33_type,type,
sk33: a ).
thf(sk34_type,type,
sk34: a ).
thf(sk36_type,type,
sk36: a ).
thf(sk38_type,type,
sk38: a ).
thf(sk39_type,type,
sk39: a ).
thf(1,conjecture,
! [A: a > a > $o,B: a > a > $o,C: a,D: a] :
( ! [E: a > $o] :
( ( ! [F: a] :
( ( ! [G: a > $o] :
( ( ! [H: a] :
( ( A @ C @ H )
=> ( G @ H ) )
& ! [H: a,I: a] :
( ( ( G @ H )
& ( A @ H @ I ) )
=> ( G @ I ) ) )
=> ( G @ F ) )
| ! [G: a > $o] :
( ( ! [H: a] :
( ( B @ C @ H )
=> ( G @ H ) )
& ! [H: a,I: a] :
( ( ( G @ H )
& ( B @ H @ I ) )
=> ( G @ I ) ) )
=> ( G @ F ) ) )
=> ( E @ F ) )
& ! [F: a,G: a] :
( ( ( E @ F )
& ( ! [H: a > $o] :
( ( ! [I: a] :
( ( A @ F @ I )
=> ( H @ I ) )
& ! [I: a,J: a] :
( ( ( H @ I )
& ( A @ I @ J ) )
=> ( H @ J ) ) )
=> ( H @ G ) )
| ! [H: a > $o] :
( ( ! [I: a] :
( ( B @ F @ I )
=> ( H @ I ) )
& ! [I: a,J: a] :
( ( ( H @ I )
& ( B @ I @ J ) )
=> ( H @ J ) ) )
=> ( H @ 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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM251C_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > a > $o,B: a > a > $o,C: a,D: a] :
( ! [E: a > $o] :
( ( ! [F: a] :
( ( ! [G: a > $o] :
( ( ! [H: a] :
( ( A @ C @ H )
=> ( G @ H ) )
& ! [H: a,I: a] :
( ( ( G @ H )
& ( A @ H @ I ) )
=> ( G @ I ) ) )
=> ( G @ F ) )
| ! [G: a > $o] :
( ( ! [H: a] :
( ( B @ C @ H )
=> ( G @ H ) )
& ! [H: a,I: a] :
( ( ( G @ H )
& ( B @ H @ I ) )
=> ( G @ I ) ) )
=> ( G @ F ) ) )
=> ( E @ F ) )
& ! [F: a,G: a] :
( ( ( E @ F )
& ( ! [H: a > $o] :
( ( ! [I: a] :
( ( A @ F @ I )
=> ( H @ I ) )
& ! [I: a,J: a] :
( ( ( H @ I )
& ( A @ I @ J ) )
=> ( H @ J ) ) )
=> ( H @ G ) )
| ! [H: a > $o] :
( ( ! [I: a] :
( ( B @ F @ I )
=> ( H @ I ) )
& ! [I: a,J: a] :
( ( ( H @ I )
& ( B @ I @ J ) )
=> ( H @ J ) ) )
=> ( H @ 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 ) ) ),
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] :
( ( ! [G: a > $o] :
( ( ! [H: a] :
( ( A @ C @ H )
=> ( G @ H ) )
& ! [H: a,I: a] :
( ( ( G @ H )
& ( A @ H @ I ) )
=> ( G @ I ) ) )
=> ( G @ F ) )
| ! [G: a > $o] :
( ( ! [H: a] :
( ( B @ C @ H )
=> ( G @ H ) )
& ! [H: a,I: a] :
( ( ( G @ H )
& ( B @ H @ I ) )
=> ( G @ I ) ) )
=> ( G @ F ) ) )
=> ( E @ F ) )
& ! [F: a,G: a] :
( ( ( E @ F )
& ( ! [H: a > $o] :
( ( ! [I: a] :
( ( A @ F @ I )
=> ( H @ I ) )
& ! [I: a,J: a] :
( ( ( H @ I )
& ( A @ I @ J ) )
=> ( H @ J ) ) )
=> ( H @ G ) )
| ! [H: a > $o] :
( ( ! [I: a] :
( ( B @ F @ I )
=> ( H @ I ) )
& ! [I: a,J: a] :
( ( ( H @ I )
& ( B @ I @ J ) )
=> ( H @ J ) ) )
=> ( H @ 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
! [A: a > $o] :
( ( sk5 @ A )
| ( A @ ( sk14 @ A ) )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(70,plain,
( ( sk5
@ ^ [A: a] : $false )
| $false
| $false ),
inference(prim_subst,[status(thm)],[8:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(90,plain,
( sk5
@ ^ [A: a] : $false ),
inference(simp,[status(thm)],[70]) ).
thf(21,plain,
! [A: a > $o] :
( ~ ( A @ ( sk6 @ A ) )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(113,plain,
! [A: a > $o] :
( ~ ~ ( A
@ ( sk6
@ ^ [B: a] :
~ ( A @ B ) ) )
| ~ ( sk5
@ ^ [B: a] :
~ ( A @ B ) )
| ~ ( A @ sk4 ) ),
inference(prim_subst,[status(thm)],[21:[bind(A,$thf( ^ [C: a] : ~ ( B @ C ) ))]]) ).
thf(131,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ~ ( sk5
@ ^ [B: a] :
~ ( A @ B ) )
| ( A
@ ( sk6
@ ^ [B: a] :
~ ( A @ B ) ) ) ),
inference(cnf,[status(esa)],[113]) ).
thf(132,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ~ ( sk5
@ ^ [B: a] :
~ ( A @ B ) )
| ( A
@ ( sk6
@ ^ [B: a] :
~ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(905,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ~ ( sk5
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( A
@ ( sk6
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( ~ ( A @ sk4 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[132]) ).
thf(918,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ~ ( sk5
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( A
@ ( sk6
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( ~ ( A @ sk4 ) ) ) ),
inference(simp,[status(thm)],[905]) ).
thf(1768,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ( ( A
@ ( sk6
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( ~ ( A @ sk4 ) ) )
| ( ( sk5
@ ^ [B: a] :
~ ( A @ B ) )
!= ( sk5
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[90,918]) ).
thf(1879,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ( ( A
@ ( sk6
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( ~ ( A @ sk4 ) ) )
| ( ( ^ [B: a] :
~ ( A @ B ) )
!= ( ^ [B: a] : $false ) ) ),
inference(simp,[status(thm)],[1768]) ).
thf(107,plain,
( ~ ( sk23 @ ( sk6 @ sk23 ) )
| ~ ( sk5 @ sk23 )
| ( sk23 @ sk4 ) ),
inference(prim_subst,[status(thm)],[21:[bind(A,$thf( sk23 ))]]) ).
thf(31,plain,
~ ( sk23 @ sk4 ),
inference(cnf,[status(esa)],[3]) ).
thf(137,plain,
( ~ ( sk23 @ ( sk6 @ sk23 ) )
| ~ ( sk5 @ sk23 )
| $false ),
inference(rewrite,[status(thm)],[107,31]) ).
thf(138,plain,
( ~ ( sk23 @ ( sk6 @ sk23 ) )
| ~ ( sk5 @ sk23 ) ),
inference(simp,[status(thm)],[137]) ).
thf(73,plain,
( ( sk5 @ sk23 )
| ( sk23 @ ( sk14 @ sk23 ) )
| ( sk23 @ sk4 ) ),
inference(prim_subst,[status(thm)],[8:[bind(A,$thf( sk23 ))]]) ).
thf(269,plain,
( ( sk5 @ sk23 )
| ( sk23 @ ( sk14 @ sk23 ) )
| $false ),
inference(rewrite,[status(thm)],[73,31]) ).
thf(270,plain,
( ( sk5 @ sk23 )
| ( sk23 @ ( sk14 @ sk23 ) ) ),
inference(simp,[status(thm)],[269]) ).
thf(71,plain,
! [A: a > $o] :
( ( sk5
@ ^ [B: a] :
~ ( A @ B ) )
| ~ ( A
@ ( sk14
@ ^ [B: a] :
~ ( A @ B ) ) )
| ~ ( A @ sk4 ) ),
inference(prim_subst,[status(thm)],[8:[bind(A,$thf( ^ [C: a] : ~ ( B @ C ) ))]]) ).
thf(91,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ~ ( A
@ ( sk14
@ ^ [B: a] :
~ ( A @ B ) ) )
| ( sk5
@ ^ [B: a] :
~ ( A @ B ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(92,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ~ ( A
@ ( sk14
@ ^ [B: a] :
~ ( A @ B ) ) )
| ( sk5
@ ^ [B: a] :
~ ( A @ B ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(285,plain,
! [A: a > $o] :
( ( sk5 @ sk23 )
| ~ ( A
@ ( sk14
@ ^ [B: a] :
~ ( A @ B ) ) )
| ( sk5
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk23 @ ( sk14 @ sk23 ) )
!= ( A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[270,92]) ).
thf(312,plain,
( ( sk5 @ sk23 )
| ~ ( sk23 @ ( sk14 @ sk23 ) )
| ( sk5
@ ^ [A: a] :
~ ( sk23 @ ( sk14 @ sk23 ) ) ) ),
inference(pre_uni,[status(thm)],[285:[bind(A,$thf( ^ [B: a] : ( sk23 @ ( sk14 @ sk23 ) ) ))]]) ).
thf(3934,plain,
( ( sk5 @ sk23 )
| ( sk5
@ ^ [A: a] :
~ ( sk23 @ ( sk14 @ sk23 ) ) )
| ( ( sk23 @ ( sk14 @ sk23 ) )
!= ( sk23 @ ( sk14 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[270,312]) ).
thf(3935,plain,
( ( sk5 @ sk23 )
| ( sk5
@ ^ [A: a] :
~ ( sk23 @ ( sk14 @ sk23 ) ) ) ),
inference(pattern_uni,[status(thm)],[3934:[]]) ).
thf(4188,plain,
( ( sk5 @ sk23 )
| ( ( sk5
@ ^ [A: a] :
~ ( sk23 @ ( sk14 @ sk23 ) ) )
!= ( sk5 @ sk23 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3935]) ).
thf(4203,plain,
( ( sk5 @ sk23 )
| ( ( ^ [A: a] :
~ ( sk23 @ ( sk14 @ sk23 ) ) )
!= sk23 ) ),
inference(simp,[status(thm)],[4188]) ).
thf(4699,plain,
( ( sk5 @ sk23 )
| ( sk23
!= ( ^ [A: a] : $false ) )
| ( ( sk23 @ ( sk14 @ sk23 ) )
!= ( sk23 @ ( sk14 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[270,4203]) ).
thf(4700,plain,
( ( sk5 @ sk23 )
| ( sk23
!= ( ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[4699:[]]) ).
thf(4870,plain,
! [A: a > $o] :
( ( sk23
!= ( ^ [B: a] : $false ) )
| ~ ( A @ sk4 )
| ( sk5
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk5 @ sk23 )
!= ( A
@ ( sk14
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4700,92]) ).
thf(4900,plain,
( ( sk23
!= ( ^ [A: a] : $false ) )
| ~ ( sk5 @ sk23 )
| ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) ),
inference(pre_uni,[status(thm)],[4870:[bind(A,$thf( ^ [B: a] : ( sk5 @ sk23 ) ))]]) ).
thf(15330,plain,
( ( sk23
!= ( ^ [A: a] : $false ) )
| ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) )
| ( ( sk5 @ sk23 )
!= ( sk5 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[4700,4900]) ).
thf(15331,plain,
( ( sk23
!= ( ^ [A: a] : $false ) )
| ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[15330:[]]) ).
thf(15629,plain,
( ( sk23 @ sk38 )
| ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) ),
inference(func_ext,[status(esa)],[15331]) ).
thf(906,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ~ ( sk5
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( A
@ ( sk6
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( ~ ( sk5
@ ^ [B: a] :
~ ( A @ B ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[132]) ).
thf(946,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ~ ( sk5
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( A
@ ( sk6
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( ~ ( sk5
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(simp,[status(thm)],[906]) ).
thf(4882,plain,
! [A: a > $o] :
( ( sk23
!= ( ^ [B: a] : $false ) )
| ~ ( sk5
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( A
@ ( sk6
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( ~ ( sk5
@ ^ [B: a] :
~ ( A @ B ) ) ) )
| ( ( sk5 @ sk23 )
!= ( A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[4700,946]) ).
thf(4911,plain,
( ( sk23
!= ( ^ [A: a] : $false ) )
| ~ ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) )
| ( ( ~ ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) )
!= ( sk5 @ sk23 ) ) ),
inference(pre_uni,[status(thm)],[4882:[bind(A,$thf( ^ [B: a] : ( sk5 @ sk23 ) ))]]) ).
thf(8120,plain,
( ( sk23
!= ( ^ [A: a] : $false ) )
| ~ ( sk5
@ ^ [A: a] : $false )
| ( ( ~ ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) )
!= ( sk5 @ sk23 ) )
| ( ( sk5 @ sk23 )
!= ( sk5 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[4700,4911]) ).
thf(8121,plain,
( ( sk23
!= ( ^ [A: a] : $false ) )
| ~ ( sk5
@ ^ [A: a] : $false )
| ( ( ~ ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) )
!= ( sk5 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[8120:[]]) ).
thf(8385,plain,
( ( sk23
!= ( ^ [A: a] : $false ) )
| ~ $true
| ( ( ~ ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) )
!= ( sk5 @ sk23 ) ) ),
inference(rewrite,[status(thm)],[8121,90]) ).
thf(8386,plain,
( ( sk23
!= ( ^ [A: a] : $false ) )
| ( ( ~ ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) )
!= ( sk5 @ sk23 ) ) ),
inference(simp,[status(thm)],[8385]) ).
thf(8387,plain,
( ( sk23 @ sk36 )
| ( ( ~ ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) )
!= ( sk5 @ sk23 ) ) ),
inference(func_ext,[status(esa)],[8386]) ).
thf(16009,plain,
( ( sk23 @ sk38 )
| ( sk23 @ sk36 )
| ( sk5 @ sk23 )
| ( ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) )
!= ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[15629,8387]) ).
thf(16010,plain,
( ( sk23 @ sk38 )
| ( sk23 @ sk36 )
| ( sk5 @ sk23 ) ),
inference(pattern_uni,[status(thm)],[16009:[]]) ).
thf(17864,plain,
( ( sk23 @ sk36 )
| ( sk5 @ sk23 )
| ( ( sk23 @ sk38 )
!= ( sk23 @ sk36 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[16010]) ).
thf(17950,plain,
( ( sk23 @ sk36 )
| ( sk5 @ sk23 )
| ( sk38 != sk36 ) ),
inference(simp,[status(thm)],[17864]) ).
thf(307,plain,
! [A: a > $o] :
( ~ ~ ( A @ sk4 )
| ~ ~ ( A
@ ( sk14
@ ^ [B: a] :
~ ~ ( A @ B ) ) )
| ( sk5
@ ^ [B: a] :
~ ~ ( A @ B ) ) ),
inference(prim_subst,[status(thm)],[92:[bind(A,$thf( ^ [C: a] : ~ ( B @ C ) ))]]) ).
thf(341,plain,
! [A: a > $o] :
( ( sk5
@ ^ [B: a] :
~ ~ ( A @ B ) )
| ( A
@ ( sk14
@ ^ [B: a] :
~ ~ ( A @ B ) ) )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[307]) ).
thf(342,plain,
! [A: a > $o] :
( ( sk5 @ A )
| ( A @ ( sk14 @ A ) )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[341]) ).
thf(1442,plain,
( ( sk5 @ sk23 )
| ( sk23 @ ( sk14 @ sk23 ) )
| ( sk23 @ sk4 ) ),
inference(prim_subst,[status(thm)],[342:[bind(A,$thf( sk23 ))]]) ).
thf(1700,plain,
( ( sk5 @ sk23 )
| ( sk23 @ ( sk14 @ sk23 ) )
| $false ),
inference(rewrite,[status(thm)],[1442,31]) ).
thf(1701,plain,
( ( sk5 @ sk23 )
| ( sk23 @ ( sk14 @ sk23 ) ) ),
inference(simp,[status(thm)],[1700]) ).
thf(4698,plain,
( ( ( ~ ( sk23 @ ( sk14 @ sk23 ) ) )
!= ( sk23 @ sk32 ) )
| ( sk5 @ sk23 ) ),
inference(func_ext,[status(esa)],[4203]) ).
thf(5963,plain,
( ( sk5 @ sk23 )
| ( sk23 @ sk32 )
| ( ( sk23 @ ( sk14 @ sk23 ) )
!= ( sk23 @ ( sk14 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1701,4698]) ).
thf(5964,plain,
( ( sk5 @ sk23 )
| ( sk23 @ sk32 ) ),
inference(pattern_uni,[status(thm)],[5963:[]]) ).
thf(23,plain,
! [A: a > $o] :
( ( sk5 @ A )
| ~ ( A @ ( sk15 @ A ) )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(1098,plain,
( ( sk5 @ sk23 )
| ~ ( sk23 @ ( sk15 @ sk23 ) )
| ( sk23 @ sk4 ) ),
inference(prim_subst,[status(thm)],[23:[bind(A,$thf( sk23 ))]]) ).
thf(1384,plain,
( ( sk5 @ sk23 )
| ~ ( sk23 @ ( sk15 @ sk23 ) )
| $false ),
inference(rewrite,[status(thm)],[1098,31]) ).
thf(1385,plain,
( ( sk5 @ sk23 )
| ~ ( sk23 @ ( sk15 @ sk23 ) ) ),
inference(simp,[status(thm)],[1384]) ).
thf(6228,plain,
( ( sk5 @ sk23 )
| ( ( sk23 @ ( sk15 @ sk23 ) )
!= ( sk23 @ sk32 ) ) ),
inference(paramod_ordered,[status(thm)],[5964,1385]) ).
thf(6285,plain,
( ( sk5 @ sk23 )
| ( ( sk15 @ sk23 )
!= sk32 ) ),
inference(simp,[status(thm)],[6228]) ).
thf(68,plain,
! [A: a > a > $o] :
( ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( sk7
@ ( A
@ ( sk14
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
| ( sk7 @ ( A @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[8:[bind(A,$thf( ^ [C: a] : ( sk7 @ ( B @ C ) ) ))]]) ).
thf(88,plain,
! [A: a > a > $o] :
( ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( sk7
@ ( A
@ ( sk14
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
| ( sk7 @ ( A @ sk4 ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(4709,plain,
( ( ( ^ [A: a] :
~ ( sk23 @ ( sk14 @ sk23 ) ) )
!= sk23 )
| ~ ( sk23 @ ( sk6 @ sk23 ) )
| ( ( sk5 @ sk23 )
!= ( sk5 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[4203,138]) ).
thf(4710,plain,
( ( ( ^ [A: a] :
~ ( sk23 @ ( sk14 @ sk23 ) ) )
!= sk23 )
| ~ ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[4709:[]]) ).
thf(4931,plain,
( ( ( ~ ( sk23 @ ( sk14 @ sk23 ) ) )
!= ( sk23 @ sk34 ) )
| ~ ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(func_ext,[status(esa)],[4710]) ).
thf(6211,plain,
( ( sk5 @ sk23 )
| ( ( sk23 @ sk32 )
!= ( sk23 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[5964,31]) ).
thf(6281,plain,
( ( sk5 @ sk23 )
| ( sk32 != sk4 ) ),
inference(simp,[status(thm)],[6211]) ).
thf(6332,plain,
( ( sk32 != sk4 )
| ~ ( sk23 @ ( sk6 @ sk23 ) )
| ( ( sk5 @ sk23 )
!= ( sk5 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[6281,138]) ).
thf(6333,plain,
( ( sk32 != sk4 )
| ~ ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[6332:[]]) ).
thf(9087,plain,
( ( ( ~ ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) )
!= ( sk5 @ sk23 ) )
| ( sk32 != sk4 )
| ( ( sk23 @ ( sk6 @ sk23 ) )
!= ( sk23 @ sk36 ) ) ),
inference(paramod_ordered,[status(thm)],[8387,6333]) ).
thf(9251,plain,
( ( ( ~ ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) )
!= ( sk5 @ sk23 ) )
| ( sk32 != sk4 )
| ( ( sk6 @ sk23 )
!= sk36 ) ),
inference(simp,[status(thm)],[9087]) ).
thf(1389,plain,
! [A: a > $o] :
( ( sk5 @ A )
| ( A @ sk4 )
| ( sk5 @ sk23 )
| ( ( A @ ( sk14 @ A ) )
!= ( sk23 @ ( sk15 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,1385]) ).
thf(1398,plain,
( ( sk5
@ ^ [A: a] : ( sk23 @ ( sk15 @ sk23 ) ) )
| ( sk23 @ ( sk15 @ sk23 ) )
| ( sk5 @ sk23 ) ),
inference(pre_uni,[status(thm)],[1389:[bind(A,$thf( ^ [B: a] : ( sk23 @ ( sk15 @ sk23 ) ) ))]]) ).
thf(1967,plain,
( ( sk23 @ ( sk15 @ sk23 ) )
| ( sk5 @ sk23 )
| ( ( sk5
@ ^ [A: a] : ( sk23 @ ( sk15 @ sk23 ) ) )
!= ( sk5 @ sk23 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1398]) ).
thf(1973,plain,
( ( sk23 @ ( sk15 @ sk23 ) )
| ( sk5 @ sk23 )
| ( ( ^ [A: a] : ( sk23 @ ( sk15 @ sk23 ) ) )
!= sk23 ) ),
inference(simp,[status(thm)],[1967]) ).
thf(2513,plain,
( ( sk23 @ ( sk15 @ sk23 ) )
| ( sk5 @ sk23 )
| ( ( ^ [A: a] : ( sk15 @ sk23 ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1973]) ).
thf(2800,plain,
( ( sk5 @ sk23 )
| ( ( ^ [A: a] : ( sk15 @ sk23 ) )
!= ( ^ [A: a] : A ) )
| ( ( sk23 @ ( sk15 @ sk23 ) )
!= ( sk23 @ ( sk15 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2513,1385]) ).
thf(2801,plain,
( ( sk5 @ sk23 )
| ( ( ^ [A: a] : ( sk15 @ sk23 ) )
!= ( ^ [A: a] : A ) ) ),
inference(pattern_uni,[status(thm)],[2800:[]]) ).
thf(2837,plain,
( ( ( sk15 @ sk23 )
!= sk29 )
| ( sk5 @ sk23 ) ),
inference(func_ext,[status(esa)],[2801]) ).
thf(30,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk7 @ A )
| ( sk2 @ sk3 @ ( sk11 @ B @ A ) )
| ( sk2 @ ( sk12 @ B @ A ) @ ( sk13 @ B @ A ) )
| ( B @ ( sk6 @ A ) )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(56,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk7 @ A )
| ( sk2 @ sk3 @ ( sk11 @ B @ A ) )
| ( sk2 @ ( sk12 @ B @ A ) @ ( sk13 @ B @ A ) )
| ( B @ ( sk6 @ A ) )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[30]) ).
thf(3490,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ( ( A
@ ( sk6
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( ~ ( sk5
@ ^ [B: a] :
~ ( A @ B ) ) ) )
| ( ( sk5
@ ^ [B: a] :
~ ( A @ B ) )
!= ( sk5
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[90,946]) ).
thf(3577,plain,
! [A: a > $o] :
( ~ ( A @ sk4 )
| ( ( A
@ ( sk6
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( ~ ( sk5
@ ^ [B: a] :
~ ( A @ B ) ) ) )
| ( ( ^ [B: a] :
~ ( A @ B ) )
!= ( ^ [B: a] : $false ) ) ),
inference(simp,[status(thm)],[3490]) ).
thf(140,plain,
! [A: a > $o] :
( ( sk5 @ A )
| ( A @ sk4 )
| ~ ( sk5 @ sk23 )
| ( ( A @ ( sk14 @ A ) )
!= ( sk23 @ ( sk6 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,138]) ).
thf(142,plain,
( ( sk5
@ ^ [A: a] : ( sk23 @ ( sk6 @ sk23 ) ) )
| ( sk23 @ ( sk6 @ sk23 ) )
| ~ ( sk5 @ sk23 ) ),
inference(pre_uni,[status(thm)],[140:[bind(A,$thf( ^ [B: a] : ( sk23 @ ( sk6 @ sk23 ) ) ))]]) ).
thf(4843,plain,
( ( sk23 @ sk33 )
| ( sk5 @ sk23 ) ),
inference(func_ext,[status(esa)],[4700]) ).
thf(5058,plain,
! [A: a > $o] :
( ( sk5 @ sk23 )
| ~ ( A
@ ( sk14
@ ^ [B: a] :
~ ( A @ B ) ) )
| ( sk5
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk23 @ sk33 )
!= ( A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[4843,92]) ).
thf(5113,plain,
( ( sk5 @ sk23 )
| ~ ( sk23 @ sk33 )
| ( sk5
@ ^ [A: a] :
~ ( sk23 @ sk33 ) ) ),
inference(pre_uni,[status(thm)],[5058:[bind(A,$thf( ^ [B: a] : ( sk23 @ sk33 ) ))]]) ).
thf(22082,plain,
( ( sk5 @ sk23 )
| ( sk5
@ ^ [A: a] :
~ ( sk23 @ sk33 ) )
| ( ( sk23 @ sk33 )
!= ( sk23 @ sk33 ) ) ),
inference(paramod_ordered,[status(thm)],[4843,5113]) ).
thf(22083,plain,
( ( sk5 @ sk23 )
| ( sk5
@ ^ [A: a] :
~ ( sk23 @ sk33 ) ) ),
inference(pattern_uni,[status(thm)],[22082:[]]) ).
thf(17837,plain,
( ( sk23 @ sk36 )
| ( sk5 @ sk23 )
| ( ( sk23 @ ( sk15 @ sk23 ) )
!= ( sk23 @ sk38 ) ) ),
inference(paramod_ordered,[status(thm)],[16010,1385]) ).
thf(17924,plain,
( ( sk23 @ sk36 )
| ( sk5 @ sk23 )
| ( ( sk15 @ sk23 )
!= sk38 ) ),
inference(simp,[status(thm)],[17837]) ).
thf(12,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ( sk1 @ ( sk14 @ A ) @ ( sk17 @ B @ A ) )
| ~ ( B @ ( sk19 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( sk16 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(42,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ( sk1 @ ( sk14 @ A ) @ ( sk17 @ B @ A ) )
| ~ ( B @ ( sk19 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( sk16 @ A )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[12]) ).
thf(16046,plain,
( ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) )
| ( ( sk23 @ sk38 )
!= ( sk23 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[15629,31]) ).
thf(16268,plain,
( ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) )
| ( sk38 != sk4 ) ),
inference(simp,[status(thm)],[16046]) ).
thf(10,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ( sk23 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(37,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ( sk23 @ A ) ),
inference(simp,[status(thm)],[10]) ).
thf(5023,plain,
( ( sk23 @ sk33 )
| ~ ( sk23 @ ( sk6 @ sk23 ) )
| ( ( sk5 @ sk23 )
!= ( sk5 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[4843,138]) ).
thf(5024,plain,
( ( sk23 @ sk33 )
| ~ ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[5023:[]]) ).
thf(32,plain,
! [B: a,A: a] :
( ~ ( sk23 @ A )
| ~ ( sk1 @ A @ B )
| ( sk23 @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(52,plain,
! [B: a,A: a] :
( ~ ( sk23 @ A )
| ~ ( sk1 @ A @ B )
| ( sk23 @ B ) ),
inference(simp,[status(thm)],[32]) ).
thf(16820,plain,
( ( sk38 != sk4 )
| ( sk23 @ sk36 )
| ( sk5 @ sk23 )
| ( ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) )
!= ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16268,8387]) ).
thf(16821,plain,
( ( sk38 != sk4 )
| ( sk23 @ sk36 )
| ( sk5 @ sk23 ) ),
inference(pattern_uni,[status(thm)],[16820:[]]) ).
thf(5073,plain,
( ( sk5 @ sk23 )
| ( ( sk23 @ sk33 )
!= ( sk23 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[4843,31]) ).
thf(5166,plain,
( ( sk5 @ sk23 )
| ( sk33 != sk4 ) ),
inference(simp,[status(thm)],[5073]) ).
thf(5181,plain,
( ( sk33 != sk4 )
| ~ ( sk23 @ ( sk6 @ sk23 ) )
| ( ( sk5 @ sk23 )
!= ( sk5 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[5166,138]) ).
thf(5182,plain,
( ( sk33 != sk4 )
| ~ ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[5181:[]]) ).
thf(15,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ( sk1 @ ( sk14 @ A ) @ ( sk17 @ B @ A ) )
| ( B @ ( sk18 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( sk16 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(46,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ( sk1 @ ( sk14 @ A ) @ ( sk17 @ B @ A ) )
| ( B @ ( sk18 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( sk16 @ A )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[15]) ).
thf(72,plain,
! [A: a > a > $o] :
( ( sk5
@ ^ [B: a] : ( sk16 @ ( A @ B ) ) )
| ( sk16
@ ( A
@ ( sk14
@ ^ [B: a] : ( sk16 @ ( A @ B ) ) ) ) )
| ( sk16 @ ( A @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[8:[bind(A,$thf( ^ [C: a] : ( sk16 @ ( B @ C ) ) ))]]) ).
thf(93,plain,
! [A: a > a > $o] :
( ( sk5
@ ^ [B: a] : ( sk16 @ ( A @ B ) ) )
| ( sk16
@ ( A
@ ( sk14
@ ^ [B: a] : ( sk16 @ ( A @ B ) ) ) ) )
| ( sk16 @ ( A @ sk4 ) ) ),
inference(simp,[status(thm)],[72]) ).
thf(144,plain,
( ~ ( sk23 @ ( sk6 @ sk23 ) )
| ( ( sk5 @ sk23 )
!= ( sk5
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[90,138]) ).
thf(149,plain,
( ~ ( sk23 @ ( sk6 @ sk23 ) )
| ( sk23
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[144]) ).
thf(273,plain,
( ( sk5 @ sk23 )
| ( sk23
!= ( ^ [A: a] : $false ) )
| ( ( sk23 @ ( sk14 @ sk23 ) )
!= ( sk23 @ ( sk6 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[270,149]) ).
thf(282,plain,
( ( sk5 @ sk23 )
| ( sk23
!= ( ^ [A: a] : $false ) )
| ( ( sk14 @ sk23 )
!= ( sk6 @ sk23 ) ) ),
inference(simp,[status(thm)],[273]) ).
thf(284,plain,
( ( sk23 @ sk25 )
| ( sk5 @ sk23 )
| ( ( sk14 @ sk23 )
!= ( sk6 @ sk23 ) ) ),
inference(func_ext,[status(esa)],[282]) ).
thf(19,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk7 @ A )
| ( sk2 @ sk3 @ ( sk11 @ B @ A ) )
| ~ ( B @ ( sk13 @ B @ A ) )
| ( B @ ( sk6 @ A ) )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(57,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk7 @ A )
| ( sk2 @ sk3 @ ( sk11 @ B @ A ) )
| ~ ( B @ ( sk13 @ B @ A ) )
| ( B @ ( sk6 @ A ) )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[19]) ).
thf(61,plain,
! [A: a > $o] :
( ( A @ ( sk14 @ A ) )
| ( A @ sk4 )
| ( ( sk5 @ A )
!= ( A @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8]) ).
thf(78,plain,
! [A: a > $o] :
( ( A @ ( sk14 @ A ) )
| ( A @ sk4 )
| ( ( sk5 @ A )
!= ( A @ sk4 ) ) ),
inference(simp,[status(thm)],[61]) ).
thf(19849,plain,
( ( sk5 @ sk23 )
| ( sk38 != sk36 )
| ( ( sk23 @ sk36 )
!= ( sk23 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[17950,31]) ).
thf(19995,plain,
( ( sk5 @ sk23 )
| ( sk38 != sk36 )
| ( sk36 != sk4 ) ),
inference(simp,[status(thm)],[19849]) ).
thf(29,plain,
! [B: a > $o,A: a > $o] :
( ( sk1 @ sk3 @ ( sk8 @ B @ A ) )
| ~ ( B @ ( sk10 @ B @ A ) )
| ( B @ ( sk6 @ A ) )
| ( sk7 @ A )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5026,plain,
( ( sk23 @ sk33 )
| ( sk5
@ ^ [A: a] : ( sk23 @ ( sk6 @ sk23 ) ) )
| ( sk23 @ ( sk6 @ sk23 ) )
| ( ( sk5 @ sk23 )
!= ( sk5 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[4843,142]) ).
thf(5027,plain,
( ( sk23 @ sk33 )
| ( sk5
@ ^ [A: a] : ( sk23 @ ( sk6 @ sk23 ) ) )
| ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[5026:[]]) ).
thf(263,plain,
( ( sk23 @ sk24 )
| ~ ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(func_ext,[status(esa)],[149]) ).
thf(6146,plain,
( ( sk5 @ sk23 )
| ( sk23 @ sk24 )
| ( ( sk23 @ ( sk6 @ sk23 ) )
!= ( sk23 @ sk32 ) ) ),
inference(paramod_ordered,[status(thm)],[5964,263]) ).
thf(6300,plain,
( ( sk5 @ sk23 )
| ( sk23 @ sk24 )
| ( ( sk6 @ sk23 )
!= sk32 ) ),
inference(simp,[status(thm)],[6146]) ).
thf(62,plain,
! [A: a > $o] :
( ( sk5 @ A )
| ( A @ sk4 )
| ( ( A @ ( sk14 @ A ) )
!= ( sk5 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8]) ).
thf(84,plain,
! [A: a > $o] :
( ( sk5 @ A )
| ( A @ sk4 )
| ( ( A @ ( sk14 @ A ) )
!= ( sk5 @ A ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(910,plain,
! [A: a > $o] :
( ~ ~ ( A @ sk4 )
| ~ ( sk5
@ ^ [B: a] :
~ ~ ( A @ B ) )
| ~ ( A
@ ( sk6
@ ^ [B: a] :
~ ~ ( A @ B ) ) ) ),
inference(prim_subst,[status(thm)],[132:[bind(A,$thf( ^ [C: a] : ~ ( B @ C ) ))]]) ).
thf(980,plain,
! [A: a > $o] :
( ~ ( A
@ ( sk6
@ ^ [B: a] :
~ ~ ( A @ B ) ) )
| ~ ( sk5
@ ^ [B: a] :
~ ~ ( A @ B ) )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[910]) ).
thf(981,plain,
! [A: a > $o] :
( ~ ( A @ ( sk6 @ A ) )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[980]) ).
thf(274,plain,
( ( sk5 @ sk23 )
| ( sk23 @ sk24 )
| ( ( sk23 @ ( sk14 @ sk23 ) )
!= ( sk23 @ ( sk6 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[270,263]) ).
thf(280,plain,
( ( sk5 @ sk23 )
| ( sk23 @ sk24 )
| ( ( sk14 @ sk23 )
!= ( sk6 @ sk23 ) ) ),
inference(simp,[status(thm)],[274]) ).
thf(69,plain,
! [B: a > a,A: a > a] :
( ( sk5
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk2
@ ( A
@ ( sk14
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk14
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ( sk2 @ ( A @ sk4 ) @ ( B @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[8:[bind(A,$thf( ^ [D: a] : ( sk2 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(89,plain,
! [B: a > a,A: a > a] :
( ( sk5
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk2
@ ( A
@ ( sk14
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk14
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ( sk2 @ ( A @ sk4 ) @ ( B @ sk4 ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(5016,plain,
( ( sk5 @ sk23 )
| ( sk23 @ sk24 )
| ( ( sk23 @ ( sk6 @ sk23 ) )
!= ( sk23 @ sk33 ) ) ),
inference(paramod_ordered,[status(thm)],[4843,263]) ).
thf(5137,plain,
( ( sk5 @ sk23 )
| ( sk23 @ sk24 )
| ( ( sk6 @ sk23 )
!= sk33 ) ),
inference(simp,[status(thm)],[5016]) ).
thf(264,plain,
! [A: a > $o] :
( ( sk5 @ A )
| ( A @ sk4 )
| ( sk23
!= ( ^ [B: a] : $false ) )
| ( ( A @ ( sk14 @ A ) )
!= ( sk23 @ ( sk6 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,149]) ).
thf(265,plain,
( ( sk5
@ ^ [A: a] : ( sk23 @ ( sk6 @ sk23 ) ) )
| ( sk23 @ ( sk6 @ sk23 ) )
| ( sk23
!= ( ^ [A: a] : $false ) ) ),
inference(pre_uni,[status(thm)],[264:[bind(A,$thf( ^ [B: a] : ( sk23 @ ( sk6 @ sk23 ) ) ))]]) ).
thf(5087,plain,
( ( sk5 @ sk23 )
| ( ( sk23 @ ( sk15 @ sk23 ) )
!= ( sk23 @ sk33 ) ) ),
inference(paramod_ordered,[status(thm)],[4843,1385]) ).
thf(5157,plain,
( ( sk5 @ sk23 )
| ( ( sk15 @ sk23 )
!= sk33 ) ),
inference(simp,[status(thm)],[5087]) ).
thf(65,plain,
! [A: a > a] :
( ( sk5
@ ^ [B: a] : ( sk23 @ ( A @ B ) ) )
| ( sk23
@ ( A
@ ( sk14
@ ^ [B: a] : ( sk23 @ ( A @ B ) ) ) ) )
| ( sk23 @ ( A @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[8:[bind(A,$thf( ^ [C: a] : ( sk23 @ ( B @ C ) ) ))]]) ).
thf(85,plain,
! [A: a > a] :
( ( sk5
@ ^ [B: a] : ( sk23 @ ( A @ B ) ) )
| ( sk23
@ ( A
@ ( sk14
@ ^ [B: a] : ( sk23 @ ( A @ B ) ) ) ) )
| ( sk23 @ ( A @ sk4 ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(14,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk7 @ A )
| ~ ( B @ ( sk11 @ B @ A ) )
| ( B @ ( sk12 @ B @ A ) )
| ( B @ ( sk6 @ A ) )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(38,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk7 @ A )
| ~ ( B @ ( sk11 @ B @ A ) )
| ( B @ ( sk12 @ B @ A ) )
| ( B @ ( sk6 @ A ) )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[14]) ).
thf(5598,plain,
( ( sk5 @ sk23 )
| ( sk23 @ sk34 )
| ~ ( sk23 @ ( sk6 @ sk23 ) )
| ( ( sk23 @ ( sk14 @ sk23 ) )
!= ( sk23 @ ( sk14 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1701,4931]) ).
thf(5599,plain,
( ( sk5 @ sk23 )
| ( sk23 @ sk34 )
| ~ ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[5598:[]]) ).
thf(10390,plain,
( ( sk5 @ sk23 )
| ( sk23 @ sk34 )
| ( ( sk23 @ ( sk6 @ sk23 ) )
!= ( sk23 @ sk32 ) ) ),
inference(paramod_ordered,[status(thm)],[5964,5599]) ).
thf(10426,plain,
( ( sk5 @ sk23 )
| ( sk23 @ sk34 )
| ( ( sk6 @ sk23 )
!= sk32 ) ),
inference(simp,[status(thm)],[10390]) ).
thf(815,plain,
( ( sk23 @ sk26 )
| ( sk5
@ ^ [A: a] : ( sk23 @ ( sk6 @ sk23 ) ) )
| ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(func_ext,[status(esa)],[265]) ).
thf(33,plain,
! [B: a > $o,A: a > $o] :
( ~ ( B @ ( sk8 @ B @ A ) )
| ( B @ ( sk9 @ B @ A ) )
| ( B @ ( sk6 @ A ) )
| ( sk7 @ A )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(141,plain,
! [A: a > $o] :
( ( sk5 @ A )
| ( A @ sk4 )
| ~ ( sk23 @ ( sk6 @ sk23 ) )
| ( ( A @ ( sk14 @ A ) )
!= ( sk5 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[8,138]) ).
thf(143,plain,
( ( sk5
@ ^ [A: a] : ( sk5 @ sk23 ) )
| ( sk5 @ sk23 )
| ~ ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(pre_uni,[status(thm)],[141:[bind(A,$thf( ^ [B: a] : ( sk5 @ sk23 ) ))]]) ).
thf(563,plain,
( ( sk5 @ sk23 )
| ( sk5
@ ^ [A: a] : ( sk5 @ sk23 ) )
| ( ( sk23 @ ( sk14 @ sk23 ) )
!= ( sk23 @ ( sk6 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[270,143]) ).
thf(566,plain,
( ( sk5 @ sk23 )
| ( sk5
@ ^ [A: a] : ( sk5 @ sk23 ) )
| ( ( sk14 @ sk23 )
!= ( sk6 @ sk23 ) ) ),
inference(simp,[status(thm)],[563]) ).
thf(6152,plain,
( ( sk23 @ sk32 )
| ~ ( sk23 @ ( sk6 @ sk23 ) )
| ( ( sk5 @ sk23 )
!= ( sk5 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[5964,138]) ).
thf(6153,plain,
( ( sk23 @ sk32 )
| ~ ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[6152:[]]) ).
thf(20552,plain,
( ( sk38 != sk36 )
| ( sk36 != sk4 )
| ~ ( sk23 @ ( sk6 @ sk23 ) )
| ( ( sk5 @ sk23 )
!= ( sk5 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[19995,138]) ).
thf(20553,plain,
( ( sk38 != sk36 )
| ( sk36 != sk4 )
| ~ ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[20552:[]]) ).
thf(34,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ( sk23 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(53,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ( sk23 @ A ) ),
inference(simp,[status(thm)],[34]) ).
thf(1386,plain,
( ( sk5 @ sk23 )
| ( ( sk14 @ sk23 )
!= ( sk6 @ sk23 ) )
| ( ( sk23 @ ( sk15 @ sk23 ) )
!= ( sk23 @ sk25 ) ) ),
inference(paramod_ordered,[status(thm)],[284,1385]) ).
thf(1397,plain,
( ( sk5 @ sk23 )
| ( ( sk14 @ sk23 )
!= ( sk6 @ sk23 ) )
| ( ( sk15 @ sk23 )
!= sk25 ) ),
inference(simp,[status(thm)],[1386]) ).
thf(9086,plain,
( ( ( ~ ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) )
!= ( sk5 @ sk23 ) )
| ( ( sk23 @ sk36 )
!= ( sk23 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[8387,31]) ).
thf(9214,plain,
( ( ( ~ ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) )
!= ( sk5 @ sk23 ) )
| ( sk36 != sk4 ) ),
inference(simp,[status(thm)],[9086]) ).
thf(16843,plain,
( ( sk38 != sk4 )
| ( sk5 @ sk23 )
| ( sk36 != sk4 )
| ( ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) )
!= ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16268,9214]) ).
thf(16844,plain,
( ( sk38 != sk4 )
| ( sk5 @ sk23 )
| ( sk36 != sk4 ) ),
inference(pattern_uni,[status(thm)],[16843:[]]) ).
thf(2058,plain,
( ~ ( sk23 @ ( sk6 @ sk23 ) )
| ~ ( sk5 @ sk23 )
| ( sk23 @ sk4 ) ),
inference(prim_subst,[status(thm)],[981:[bind(A,$thf( sk23 ))]]) ).
thf(2471,plain,
( ~ ( sk23 @ ( sk6 @ sk23 ) )
| ~ ( sk5 @ sk23 )
| $false ),
inference(rewrite,[status(thm)],[2058,31]) ).
thf(2472,plain,
( ~ ( sk23 @ ( sk6 @ sk23 ) )
| ~ ( sk5 @ sk23 ) ),
inference(simp,[status(thm)],[2471]) ).
thf(18920,plain,
( ( sk38 != sk4 )
| ( sk5 @ sk23 )
| ( ( sk23 @ ( sk15 @ sk23 ) )
!= ( sk23 @ sk36 ) ) ),
inference(paramod_ordered,[status(thm)],[16821,1385]) ).
thf(18975,plain,
( ( sk5 @ sk23 )
| ( sk38 != sk4 )
| ( ( sk15 @ sk23 )
!= sk36 ) ),
inference(simp,[status(thm)],[18920]) ).
thf(13,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ~ ( sk16 @ A )
| ~ ( B @ ( sk20 @ B @ A ) )
| ( sk2 @ ( sk21 @ B @ A ) @ ( sk22 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(41,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ~ ( sk16 @ A )
| ~ ( B @ ( sk20 @ B @ A ) )
| ( sk2 @ ( sk21 @ B @ A ) @ ( sk22 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[13]) ).
thf(1387,plain,
( ( sk5 @ sk23 )
| ( ( sk23 @ ( sk15 @ sk23 ) )
!= ( sk23 @ ( sk14 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[270,1385]) ).
thf(1393,plain,
( ( sk5 @ sk23 )
| ( ( sk15 @ sk23 )
!= ( sk14 @ sk23 ) ) ),
inference(simp,[status(thm)],[1387]) ).
thf(19332,plain,
( ( sk38 != sk4 )
| ( sk36 != sk4 )
| ~ ( sk23 @ ( sk6 @ sk23 ) )
| ( ( sk5 @ sk23 )
!= ( sk5 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[16844,138]) ).
thf(19333,plain,
( ( sk38 != sk4 )
| ( sk36 != sk4 )
| ~ ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[19332:[]]) ).
thf(16037,plain,
( ( sk23 @ sk38 )
| ( sk5 @ sk23 )
| ( sk36 != sk4 )
| ( ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) )
!= ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[15629,9214]) ).
thf(16038,plain,
( ( sk23 @ sk38 )
| ( sk5 @ sk23 )
| ( sk36 != sk4 ) ),
inference(pattern_uni,[status(thm)],[16037:[]]) ).
thf(18403,plain,
( ( sk5 @ sk23 )
| ( sk36 != sk4 )
| ( ( sk23 @ ( sk15 @ sk23 ) )
!= ( sk23 @ sk38 ) ) ),
inference(paramod_ordered,[status(thm)],[16038,1385]) ).
thf(18489,plain,
( ( sk5 @ sk23 )
| ( sk36 != sk4 )
| ( ( sk15 @ sk23 )
!= sk38 ) ),
inference(simp,[status(thm)],[18403]) ).
thf(2779,plain,
( ( ( sk15 @ sk23 )
!= sk28 )
| ( sk23 @ ( sk15 @ sk23 ) )
| ( sk5 @ sk23 ) ),
inference(func_ext,[status(esa)],[2513]) ).
thf(3041,plain,
( ( ( sk15 @ sk23 )
!= sk28 )
| ( sk5 @ sk23 )
| ( ( sk23 @ ( sk15 @ sk23 ) )
!= ( sk23 @ ( sk15 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2779,1385]) ).
thf(3042,plain,
( ( ( sk15 @ sk23 )
!= sk28 )
| ( sk5 @ sk23 ) ),
inference(pattern_uni,[status(thm)],[3041:[]]) ).
thf(11,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk7 @ A )
| ~ ( B @ ( sk11 @ B @ A ) )
| ~ ( B @ ( sk13 @ B @ A ) )
| ( B @ ( sk6 @ A ) )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(45,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk7 @ A )
| ~ ( B @ ( sk11 @ B @ A ) )
| ~ ( B @ ( sk13 @ B @ A ) )
| ( B @ ( sk6 @ A ) )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[11]) ).
thf(275,plain,
( ( sk5 @ sk23 )
| ( ( sk23 @ ( sk14 @ sk23 ) )
!= ( sk23 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[270,31]) ).
thf(279,plain,
( ( sk5 @ sk23 )
| ( ( sk14 @ sk23 )
!= sk4 ) ),
inference(simp,[status(thm)],[275]) ).
thf(18,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ~ ( B @ ( sk17 @ B @ A ) )
| ~ ( B @ ( sk19 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( sk16 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(44,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ~ ( B @ ( sk17 @ B @ A ) )
| ~ ( B @ ( sk19 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( sk16 @ A )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[18]) ).
thf(18261,plain,
( ( sk23 @ sk38 )
| ( sk36 != sk4 )
| ~ ( sk23 @ ( sk6 @ sk23 ) )
| ( ( sk5 @ sk23 )
!= ( sk5 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[16038,138]) ).
thf(18262,plain,
( ( sk23 @ sk38 )
| ( sk36 != sk4 )
| ~ ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[18261:[]]) ).
thf(22,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk7 @ A )
| ~ ( B @ ( sk11 @ B @ A ) )
| ( sk2 @ ( sk12 @ B @ A ) @ ( sk13 @ B @ A ) )
| ( B @ ( sk6 @ A ) )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(54,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk7 @ A )
| ~ ( B @ ( sk11 @ B @ A ) )
| ( sk2 @ ( sk12 @ B @ A ) @ ( sk13 @ B @ A ) )
| ( B @ ( sk6 @ A ) )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[22]) ).
thf(595,plain,
( ( sk5 @ sk23 )
| ( ( sk14 @ sk23 )
!= ( sk6 @ sk23 ) )
| ( ( sk23 @ sk25 )
!= ( sk23 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[284,31]) ).
thf(611,plain,
( ( sk5 @ sk23 )
| ( ( sk14 @ sk23 )
!= ( sk6 @ sk23 ) )
| ( sk25 != sk4 ) ),
inference(simp,[status(thm)],[595]) ).
thf(20,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ~ ( B @ ( sk17 @ B @ A ) )
| ( sk1 @ ( sk18 @ B @ A ) @ ( sk19 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( sk16 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(49,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ~ ( B @ ( sk17 @ B @ A ) )
| ( sk1 @ ( sk18 @ B @ A ) @ ( sk19 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( sk16 @ A )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[20]) ).
thf(66,plain,
! [A: a > a > $o] :
( ( sk5
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) )
| ( sk5
@ ( A
@ ( sk14
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) ) ) )
| ( sk5 @ ( A @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[8:[bind(A,$thf( ^ [C: a] : ( sk5 @ ( B @ C ) ) ))]]) ).
thf(86,plain,
! [A: a > a > $o] :
( ( sk5
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) )
| ( sk5
@ ( A
@ ( sk14
@ ^ [B: a] : ( sk5 @ ( A @ B ) ) ) ) )
| ( sk5 @ ( A @ sk4 ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(7,plain,
! [B: a > $o,A: a > $o] :
( ( sk1 @ sk3 @ ( sk8 @ B @ A ) )
| ( sk1 @ ( sk9 @ B @ A ) @ ( sk10 @ B @ A ) )
| ( B @ ( sk6 @ A ) )
| ( sk7 @ A )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk7 @ A )
| ( sk2 @ sk3 @ ( sk11 @ B @ A ) )
| ( B @ ( sk12 @ B @ A ) )
| ( B @ ( sk6 @ A ) )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(39,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk7 @ A )
| ( sk2 @ sk3 @ ( sk11 @ B @ A ) )
| ( B @ ( sk12 @ B @ A ) )
| ( B @ ( sk6 @ A ) )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[6]) ).
thf(8982,plain,
( ( ( ~ ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) )
!= ( sk5 @ sk23 ) )
| ( sk33 != sk4 )
| ( ( sk23 @ ( sk6 @ sk23 ) )
!= ( sk23 @ sk36 ) ) ),
inference(paramod_ordered,[status(thm)],[8387,5182]) ).
thf(9228,plain,
( ( ( ~ ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) )
!= ( sk5 @ sk23 ) )
| ( sk33 != sk4 )
| ( ( sk6 @ sk23 )
!= sk36 ) ),
inference(simp,[status(thm)],[8982]) ).
thf(10041,plain,
( ( sk5 @ sk23 )
| ( ( sk6 @ sk23 )
!= sk33 )
| ( ( sk23 @ sk24 )
!= ( sk23 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[5137,31]) ).
thf(10119,plain,
( ( sk5 @ sk23 )
| ( ( sk6 @ sk23 )
!= sk33 )
| ( sk24 != sk4 ) ),
inference(simp,[status(thm)],[10041]) ).
thf(18774,plain,
( ( sk38 != sk4 )
| ( sk23 @ sk36 )
| ~ ( sk23 @ ( sk6 @ sk23 ) )
| ( ( sk5 @ sk23 )
!= ( sk5 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[16821,138]) ).
thf(18775,plain,
( ( sk38 != sk4 )
| ( sk23 @ sk36 )
| ~ ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[18774:[]]) ).
thf(14154,plain,
( ( sk5 @ sk23 )
| ( ( sk6 @ sk23 )
!= sk32 )
| ( ( sk23 @ sk34 )
!= ( sk23 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[10426,31]) ).
thf(14230,plain,
( ( sk5 @ sk23 )
| ( ( sk6 @ sk23 )
!= sk32 )
| ( sk34 != sk4 ) ),
inference(simp,[status(thm)],[14154]) ).
thf(17695,plain,
( ( sk23 @ sk38 )
| ( sk23 @ sk36 )
| ~ ( sk23 @ ( sk6 @ sk23 ) )
| ( ( sk5 @ sk23 )
!= ( sk5 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[16010,138]) ).
thf(17696,plain,
( ( sk23 @ sk38 )
| ( sk23 @ sk36 )
| ~ ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[17695:[]]) ).
thf(25,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ~ ( sk16 @ A )
| ( sk2 @ ( sk14 @ A ) @ ( sk20 @ B @ A ) )
| ~ ( B @ ( sk22 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(48,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ~ ( sk16 @ A )
| ( sk2 @ ( sk14 @ A ) @ ( sk20 @ B @ A ) )
| ~ ( B @ ( sk22 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[25]) ).
thf(28,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ~ ( sk16 @ A )
| ( sk2 @ ( sk14 @ A ) @ ( sk20 @ B @ A ) )
| ( sk2 @ ( sk21 @ B @ A ) @ ( sk22 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(50,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ~ ( sk16 @ A )
| ( sk2 @ ( sk14 @ A ) @ ( sk20 @ B @ A ) )
| ( sk2 @ ( sk21 @ B @ A ) @ ( sk22 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[28]) ).
thf(16,plain,
! [B: a > $o,A: a > $o] :
( ( sk1 @ sk3 @ ( sk8 @ B @ A ) )
| ( B @ ( sk9 @ B @ A ) )
| ( B @ ( sk6 @ A ) )
| ( sk7 @ A )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6158,plain,
( ( sk23 @ sk32 )
| ( sk5
@ ^ [A: a] : ( sk23 @ ( sk6 @ sk23 ) ) )
| ( sk23 @ ( sk6 @ sk23 ) )
| ( ( sk5 @ sk23 )
!= ( sk5 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[5964,142]) ).
thf(6159,plain,
( ( sk23 @ sk32 )
| ( sk5
@ ^ [A: a] : ( sk23 @ ( sk6 @ sk23 ) ) )
| ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[6158:[]]) ).
thf(9010,plain,
( ( ( ~ ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) )
!= ( sk5 @ sk23 ) )
| ~ ( sk5 @ sk23 )
| ( ( sk23 @ ( sk6 @ sk23 ) )
!= ( sk23 @ sk36 ) ) ),
inference(paramod_ordered,[status(thm)],[8387,138]) ).
thf(9194,plain,
( ( ( ~ ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) ) )
!= ( sk5 @ sk23 ) )
| ~ ( sk5 @ sk23 )
| ( ( sk6 @ sk23 )
!= sk36 ) ),
inference(simp,[status(thm)],[9010]) ).
thf(4202,plain,
( ( sk5 @ sk23 )
| ( ( sk5
@ ^ [A: a] :
~ ( sk23 @ ( sk14 @ sk23 ) ) )
!= ( sk5 @ sk23 ) ) ),
inference(simp,[status(thm)],[4188]) ).
thf(35,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ~ ( B @ ( sk17 @ B @ A ) )
| ( B @ ( sk18 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( sk16 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(43,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ~ ( B @ ( sk17 @ B @ A ) )
| ( B @ ( sk18 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( sk16 @ A )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[35]) ).
thf(67,plain,
! [B: a > a,A: a > a] :
( ( sk5
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk1
@ ( A
@ ( sk14
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk14
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ( sk1 @ ( A @ sk4 ) @ ( B @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[8:[bind(A,$thf( ^ [D: a] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(87,plain,
! [B: a > a,A: a > a] :
( ( sk5
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk1
@ ( A
@ ( sk14
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk14
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ( sk1 @ ( A @ sk4 ) @ ( B @ sk4 ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(574,plain,
( ( sk5 @ sk23 )
| ( ( sk14 @ sk23 )
!= ( sk6 @ sk23 ) )
| ( ( sk23 @ sk24 )
!= ( sk23 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[280,31]) ).
thf(581,plain,
( ( sk5 @ sk23 )
| ( ( sk14 @ sk23 )
!= ( sk6 @ sk23 ) )
| ( sk24 != sk4 ) ),
inference(simp,[status(thm)],[574]) ).
thf(10408,plain,
( ( sk5 @ sk23 )
| ( sk23 @ sk34 )
| ( ( sk23 @ ( sk6 @ sk23 ) )
!= ( sk23 @ sk33 ) ) ),
inference(paramod_ordered,[status(thm)],[4843,5599]) ).
thf(10421,plain,
( ( sk5 @ sk23 )
| ( sk23 @ sk34 )
| ( ( sk6 @ sk23 )
!= sk33 ) ),
inference(simp,[status(thm)],[10408]) ).
thf(14012,plain,
( ( sk5 @ sk23 )
| ( ( sk6 @ sk23 )
!= sk33 )
| ( ( sk23 @ sk34 )
!= ( sk23 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[10421,31]) ).
thf(14083,plain,
( ( sk5 @ sk23 )
| ( ( sk6 @ sk23 )
!= sk33 )
| ( sk34 != sk4 ) ),
inference(simp,[status(thm)],[14012]) ).
thf(9,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ~ ( sk16 @ A )
| ( sk2 @ ( sk14 @ A ) @ ( sk20 @ B @ A ) )
| ( B @ ( sk21 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(40,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ~ ( sk16 @ A )
| ( sk2 @ ( sk14 @ A ) @ ( sk20 @ B @ A ) )
| ( B @ ( sk21 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[9]) ).
thf(26,plain,
! [B: a > $o,A: a > $o] :
( ~ ( B @ ( sk8 @ B @ A ) )
| ( sk1 @ ( sk9 @ B @ A ) @ ( sk10 @ B @ A ) )
| ( B @ ( sk6 @ A ) )
| ( sk7 @ A )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(27,plain,
! [B: a,A: a] :
( ~ ( sk23 @ A )
| ~ ( sk2 @ A @ B )
| ( sk23 @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(55,plain,
! [B: a,A: a] :
( ~ ( sk23 @ A )
| ~ ( sk2 @ A @ B )
| ( sk23 @ B ) ),
inference(simp,[status(thm)],[27]) ).
thf(16749,plain,
( ( sk38 != sk4 )
| ~ ( sk23 @ ( sk6 @ sk23 ) )
| ( ( sk5
@ ^ [A: a] :
~ ( sk5 @ sk23 ) )
!= ( sk5 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[16268,138]) ).
thf(16963,plain,
( ( sk38 != sk4 )
| ~ ( sk23 @ ( sk6 @ sk23 ) )
| ( ( ^ [A: a] :
~ ( sk5 @ sk23 ) )
!= sk23 ) ),
inference(simp,[status(thm)],[16749]) ).
thf(63,plain,
! [A: a > $o] :
( ( sk5 @ A )
| ( A @ sk4 )
| ( ( A @ ( sk14 @ A ) )
!= ( A @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8]) ).
thf(81,plain,
! [A: a > $o] :
( ( sk5 @ A )
| ( A @ sk4 )
| ( ( A @ ( sk14 @ A ) )
!= ( A @ sk4 ) ) ),
inference(pre_uni,[status(thm)],[63:[]]) ).
thf(82,plain,
! [A: a > $o] :
( ( A @ sk4 )
| ( sk5 @ A )
| ( ( A @ ( sk14 @ A ) )
!= ( A @ sk4 ) ) ),
inference(pre_uni,[status(thm)],[81:[]]) ).
thf(19878,plain,
( ( sk5 @ sk23 )
| ( sk38 != sk36 )
| ( ( sk23 @ ( sk15 @ sk23 ) )
!= ( sk23 @ sk36 ) ) ),
inference(paramod_ordered,[status(thm)],[17950,1385]) ).
thf(19970,plain,
( ( sk5 @ sk23 )
| ( sk38 != sk36 )
| ( ( sk15 @ sk23 )
!= sk36 ) ),
inference(simp,[status(thm)],[19878]) ).
thf(5,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ~ ( sk16 @ A )
| ~ ( B @ ( sk20 @ B @ A ) )
| ~ ( B @ ( sk22 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(36,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ~ ( sk16 @ A )
| ~ ( B @ ( sk20 @ B @ A ) )
| ~ ( B @ ( sk22 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[5]) ).
thf(17024,plain,
( ( ( ~ ( sk5 @ sk23 ) )
!= ( sk23 @ sk39 ) )
| ( sk38 != sk4 )
| ~ ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(func_ext,[status(esa)],[16963]) ).
thf(1390,plain,
( ( sk5 @ sk23 )
| ( ( sk14 @ sk23 )
!= ( sk6 @ sk23 ) )
| ( ( sk23 @ ( sk15 @ sk23 ) )
!= ( sk23 @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[280,1385]) ).
thf(1395,plain,
( ( sk5 @ sk23 )
| ( ( sk14 @ sk23 )
!= ( sk6 @ sk23 ) )
| ( ( sk15 @ sk23 )
!= sk24 ) ),
inference(simp,[status(thm)],[1390]) ).
thf(17,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ( sk1 @ ( sk14 @ A ) @ ( sk17 @ B @ A ) )
| ( sk1 @ ( sk18 @ B @ A ) @ ( sk19 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( sk16 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(51,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ( sk1 @ ( sk14 @ A ) @ ( sk17 @ B @ A ) )
| ( sk1 @ ( sk18 @ B @ A ) @ ( sk19 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( sk16 @ A )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[17]) ).
thf(4,plain,
! [B: a > $o,A: a > $o] :
( ~ ( B @ ( sk8 @ B @ A ) )
| ~ ( B @ ( sk10 @ B @ A ) )
| ( B @ ( sk6 @ A ) )
| ( sk7 @ A )
| ~ ( sk5 @ A )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(267,plain,
! [A: a > $o] :
( ( sk5 @ A )
| ( A @ sk4 )
| ( sk23 @ sk24 )
| ( ( A @ ( sk14 @ A ) )
!= ( sk23 @ ( sk6 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,263]) ).
thf(268,plain,
( ( sk5
@ ^ [A: a] : ( sk23 @ ( sk6 @ sk23 ) ) )
| ( sk23 @ ( sk6 @ sk23 ) )
| ( sk23 @ sk24 ) ),
inference(pre_uni,[status(thm)],[267:[bind(A,$thf( ^ [B: a] : ( sk23 @ ( sk6 @ sk23 ) ) ))]]) ).
thf(19732,plain,
( ( sk23 @ sk36 )
| ( sk38 != sk36 )
| ~ ( sk23 @ ( sk6 @ sk23 ) )
| ( ( sk5 @ sk23 )
!= ( sk5 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[17950,138]) ).
thf(19733,plain,
( ( sk23 @ sk36 )
| ( sk38 != sk36 )
| ~ ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[19732:[]]) ).
thf(12452,plain,
( ( sk5 @ sk23 )
| ( ( sk6 @ sk23 )
!= sk32 )
| ( ( sk23 @ sk24 )
!= ( sk23 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[6300,31]) ).
thf(12530,plain,
( ( sk5 @ sk23 )
| ( ( sk6 @ sk23 )
!= sk32 )
| ( sk24 != sk4 ) ),
inference(simp,[status(thm)],[12452]) ).
thf(5974,plain,
( ( ( ~ ( sk23 @ ( sk14 @ sk23 ) ) )
!= ( sk23 @ sk32 ) )
| ~ ( sk23 @ ( sk6 @ sk23 ) )
| ( ( sk5 @ sk23 )
!= ( sk5 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[4698,138]) ).
thf(5975,plain,
( ( ( ~ ( sk23 @ ( sk14 @ sk23 ) ) )
!= ( sk23 @ sk32 ) )
| ~ ( sk23 @ ( sk6 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[5974:[]]) ).
thf(24,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ~ ( sk16 @ A )
| ~ ( B @ ( sk20 @ B @ A ) )
| ( B @ ( sk21 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(47,plain,
! [B: a > $o,A: a > $o] :
( ( sk5 @ A )
| ~ ( sk16 @ A )
| ~ ( B @ ( sk20 @ B @ A ) )
| ( B @ ( sk21 @ B @ A ) )
| ( B @ ( sk15 @ A ) )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[24]) ).
thf(133110,plain,
$false,
inference(e,[status(thm)],[1879,138,17950,6285,88,4931,9251,2837,56,15331,3577,142,22083,17924,42,16268,37,5024,52,16821,5182,46,93,284,1398,57,78,19995,29,5027,6300,84,981,280,132,89,5137,265,4700,5157,270,85,38,10426,21,815,33,92,566,8386,2801,6153,20553,53,1397,5166,16844,2472,3935,18975,41,1393,5964,19333,18489,3042,45,279,149,44,18262,1701,54,611,49,8387,6281,86,7,39,16010,4203,5599,9228,3,10119,1973,18775,14230,342,17696,48,263,50,9214,16,6159,31,9194,6333,4202,143,43,4698,87,581,14083,40,26,946,55,23,4710,1385,8,16963,82,16038,19970,4843,36,17024,1395,51,4,918,268,19733,10421,12530,5975,47,90,15629]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV148^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 21 19:26:55 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.94/0.93 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/1.05 % [INFO] Parsing done (119ms).
% 1.22/1.06 % [INFO] Running in sequential loop mode.
% 1.74/1.25 % [INFO] eprover registered as external prover.
% 1.74/1.25 % [INFO] Scanning for conjecture ...
% 1.89/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.09/1.35 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.09/1.35 % [INFO] Problem is higher-order (TPTP THF).
% 2.09/1.35 % [INFO] Type checking passed.
% 2.09/1.36 % [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 ...
% 221.52/62.21 % External prover 'e' found a proof!
% 221.52/62.21 % [INFO] Killing All external provers ...
% 221.52/62.21 % Time passed: 61659ms (effective reasoning time: 61150ms)
% 221.52/62.21 % 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)>
% 221.52/62.21 % Axioms used in derivation (0):
% 221.52/62.21 % No. of inferences in proof: 273
% 221.52/62.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 61659 ms resp. 61150 ms w/o parsing
% 221.52/62.31 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 221.52/62.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------