TSTP Solution File: SEV245^5 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV245^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n032.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 15:58:36 EDT 2024
% Result : Theorem 129.74s 33.84s
% Output : Refutation 130.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 1
% Syntax : Number of formulae : 625 ( 83 unt; 0 typ; 0 def)
% Number of atoms : 2910 ( 454 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 5676 ( 968 ~; 794 |; 75 &;3749 @)
% ( 0 <=>; 90 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 555 ( 555 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 18 con; 0-2 aty)
% Number of variables : 1275 ( 567 ^ 633 !; 75 ?;1275 :)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_type,type,
sk1: ( $i > $o ) > $i > $o ).
thf(sk2_type,type,
sk2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i > $o ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: ( $i > $o ) > $i ).
thf(sk7_type,type,
sk7: $i > $o ).
thf(sk14_type,type,
sk14: $i > $o ).
thf(sk15_type,type,
sk15: ( $i > $o ) > ( $i > $o ) > $i ).
thf(sk16_type,type,
sk16: $i ).
thf(sk21_type,type,
sk21: $i > $o ).
thf(sk22_type,type,
sk22: $i ).
thf(sk27_type,type,
sk27: $i > $o ).
thf(sk28_type,type,
sk28: $i ).
thf(sk29_type,type,
sk29: ( $i > $o ) > $i ).
thf(sk30_type,type,
sk30: $i ).
thf(sk32_type,type,
sk32: $i > $o ).
thf(sk60_type,type,
sk60: $i ).
thf(sk61_type,type,
sk61: $i ).
thf(sk64_type,type,
sk64: $i ).
thf(sk65_type,type,
sk65: $i ).
thf(sk100_type,type,
sk100: ( $i > $o ) > $i ).
thf(sk102_type,type,
sk102: ( $i > $o ) > $i ).
thf(sk132_type,type,
sk132: $i ).
thf(sk138_type,type,
sk138: $i ).
thf(sk139_type,type,
sk139: $i ).
thf(sk141_type,type,
sk141: $i ).
thf(sk143_type,type,
sk143: $i ).
thf(sk144_type,type,
sk144: $i ).
thf(1,conjecture,
! [A: ( $i > $o ) > $i > $o] :
( ! [B: $i > $o,C: $i > $o] :
( ! [D: $i] :
( ( B @ D )
=> ( C @ D ) )
=> ! [D: $i] :
( ( A @ B @ D )
=> ( A @ C @ D ) ) )
=> ! [B: $i] :
( ? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( A @ C @ D ) )
& ( C @ B ) )
=> ( A
@ ^ [C: $i] :
? [D: $i > $o] :
( ! [E: $i] :
( ( D @ E )
=> ( A @ D @ E ) )
& ( D @ C ) )
@ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM2A_TWO_pme) ).
thf(2,negated_conjecture,
~ ! [A: ( $i > $o ) > $i > $o] :
( ! [B: $i > $o,C: $i > $o] :
( ! [D: $i] :
( ( B @ D )
=> ( C @ D ) )
=> ! [D: $i] :
( ( A @ B @ D )
=> ( A @ C @ D ) ) )
=> ! [B: $i] :
( ? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( A @ C @ D ) )
& ( C @ B ) )
=> ( A
@ ^ [C: $i] :
? [D: $i > $o] :
( ! [E: $i] :
( ( D @ E )
=> ( A @ D @ E ) )
& ( D @ C ) )
@ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: ( $i > $o ) > $i > $o] :
( ! [B: $i > $o,C: $i > $o] :
( ! [D: $i] :
( ( B @ D )
=> ( C @ D ) )
=> ! [D: $i] :
( ( A @ B @ D )
=> ( A @ C @ D ) ) )
=> ! [B: $i] :
( ? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( A @ C @ D ) )
& ( C @ B ) )
=> ( A
@ ^ [C: $i] :
? [D: $i > $o] :
( ! [E: $i] :
( ( D @ E )
=> ( A @ D @ E ) )
& ( D @ C ) )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: $i] :
( ~ ( sk4 @ A )
| ( sk1 @ sk4 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
! [A: $i] :
( ~ ( sk4 @ A )
| ( sk1 @ sk4 @ A ) ),
inference(simp,[status(thm)],[4]) ).
thf(7,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ( A @ ( sk2 @ B @ A ) )
| ~ ( sk1 @ A @ C )
| ( sk1 @ B @ C ) ),
inference(cnf,[status(esa)],[3]) ).
thf(85,plain,
! [D: $i,C: $i > $o,B: $i > $o,A: $i] :
( ~ ( sk4 @ A )
| ( B @ ( sk2 @ C @ B ) )
| ( sk1 @ C @ D )
| ( ( sk1 @ sk4 @ A )
!= ( sk1 @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[9,7]) ).
thf(86,plain,
! [B: $i > $o,A: $i] :
( ~ ( sk4 @ A )
| ( sk4 @ ( sk2 @ B @ sk4 ) )
| ( sk1 @ B @ A ) ),
inference(pattern_uni,[status(thm)],[85:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(138,plain,
! [B: $i > $o,A: $i] :
( ~ ( sk4 @ A )
| ( sk4 @ ( sk2 @ B @ sk4 ) )
| ( sk1 @ B @ A ) ),
inference(simp,[status(thm)],[86]) ).
thf(6,plain,
sk4 @ sk3,
inference(cnf,[status(esa)],[3]) ).
thf(11,plain,
! [A: $i] :
( ( sk1 @ sk4 @ A )
| ( ( sk4 @ sk3 )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6,9]) ).
thf(12,plain,
sk1 @ sk4 @ sk3,
inference(pattern_uni,[status(thm)],[11:[bind(A,$thf( sk3 ))]]) ).
thf(5,plain,
~ ( sk1
@ ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) )
@ sk3 ),
inference(cnf,[status(esa)],[3]) ).
thf(15,plain,
( ( sk1 @ sk4 @ sk3 )
!= ( sk1
@ ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) )
@ sk3 ) ),
inference(paramod_ordered,[status(thm)],[12,5]) ).
thf(16,plain,
( ( sk4
!= ( ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) ) ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[15]) ).
thf(17,plain,
( sk4
!= ( ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(18,plain,
( ( sk4 @ sk5 )
!= ( ? [A: $i > $o] :
( ! [B: $i] :
( ( A @ B )
=> ( sk1 @ A @ B ) )
& ( A @ sk5 ) ) ) ),
inference(func_ext,[status(esa)],[17]) ).
thf(20,plain,
( ( sk4 @ sk5 )
| ? [A: $i > $o] :
( ! [B: $i] :
( ( A @ B )
=> ( sk1 @ A @ B ) )
& ( A @ sk5 ) ) ),
inference(bool_ext,[status(thm)],[18]) ).
thf(25,plain,
( ( sk7 @ sk5 )
| ( sk4 @ sk5 ) ),
inference(cnf,[status(esa)],[20]) ).
thf(19,plain,
( ~ ( sk4 @ sk5 )
| ~ ? [A: $i > $o] :
( ! [B: $i] :
( ( A @ B )
=> ( sk1 @ A @ B ) )
& ( A @ sk5 ) ) ),
inference(bool_ext,[status(thm)],[18]) ).
thf(23,plain,
! [A: $i > $o] :
( ( A @ ( sk6 @ A ) )
| ~ ( A @ sk5 )
| ~ ( sk4 @ sk5 ) ),
inference(cnf,[status(esa)],[19]) ).
thf(47,plain,
( ( sk4 @ ( sk6 @ sk4 ) )
| ~ ( sk4 @ sk5 )
| ~ ( sk4 @ sk5 ) ),
inference(prim_subst,[status(thm)],[23:[bind(A,$thf( sk4 ))]]) ).
thf(66,plain,
( ( sk4 @ ( sk6 @ sk4 ) )
| ~ ( sk4 @ sk5 ) ),
inference(simp,[status(thm)],[47]) ).
thf(24,plain,
! [A: $i > $o] :
( ~ ( sk1 @ A @ ( sk6 @ A ) )
| ~ ( A @ sk5 )
| ~ ( sk4 @ sk5 ) ),
inference(cnf,[status(esa)],[19]) ).
thf(177,plain,
! [B: $i > $o,A: $i] :
( ~ ( sk4 @ A )
| ~ ( B @ sk5 )
| ~ ( sk4 @ sk5 )
| ( ( sk1 @ sk4 @ A )
!= ( sk1 @ B @ ( sk6 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,24]) ).
thf(178,plain,
( ~ ( sk4 @ ( sk6 @ sk4 ) )
| ~ ( sk4 @ sk5 )
| ~ ( sk4 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[177:[bind(A,$thf( sk6 @ sk4 )),bind(B,$thf( sk4 ))]]) ).
thf(247,plain,
( ~ ( sk4 @ ( sk6 @ sk4 ) )
| ~ ( sk4 @ sk5 ) ),
inference(simp,[status(thm)],[178]) ).
thf(252,plain,
( ~ ( sk4 @ sk5 )
| ( ( sk4 @ ( sk6 @ sk4 ) )
!= ( sk4 @ ( sk6 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[66,247]) ).
thf(253,plain,
~ ( sk4 @ sk5 ),
inference(pattern_uni,[status(thm)],[252:[]]) ).
thf(313,plain,
( ( sk7 @ sk5 )
| $false ),
inference(rewrite,[status(thm)],[25,253]) ).
thf(314,plain,
sk7 @ sk5,
inference(simp,[status(thm)],[313]) ).
thf(26,plain,
! [A: $i] :
( ~ ( sk7 @ A )
| ( sk1 @ sk7 @ A )
| ( sk4 @ sk5 ) ),
inference(cnf,[status(esa)],[20]) ).
thf(434,plain,
! [A: $i] :
( ~ ( sk7 @ A )
| ( sk1 @ sk7 @ A )
| $false ),
inference(rewrite,[status(thm)],[26,253]) ).
thf(435,plain,
! [A: $i] :
( ~ ( sk7 @ A )
| ( sk1 @ sk7 @ A ) ),
inference(simp,[status(thm)],[434]) ).
thf(437,plain,
! [A: $i] :
( ( sk1 @ sk7 @ A )
| ( ( sk7 @ sk5 )
!= ( sk7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[314,435]) ).
thf(438,plain,
sk1 @ sk7 @ sk5,
inference(pattern_uni,[status(thm)],[437:[bind(A,$thf( sk5 ))]]) ).
thf(457,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ( A @ ( sk2 @ B @ A ) )
| ( sk1 @ B @ C )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[438,7]) ).
thf(458,plain,
! [A: $i > $o] :
( ( sk7 @ ( sk2 @ A @ sk7 ) )
| ( sk1 @ A @ sk5 ) ),
inference(pattern_uni,[status(thm)],[457:[bind(A,$thf( sk7 )),bind(B,$thf( B )),bind(C,$thf( sk5 ))]]) ).
thf(462,plain,
! [A: $i > $o] :
( ( sk7 @ ( sk2 @ A @ sk7 ) )
| ( sk1 @ A @ sk5 ) ),
inference(simp,[status(thm)],[458]) ).
thf(99,plain,
! [B: $i,A: $i > $o] :
( $false
| ~ ( sk1
@ ^ [C: $i] : $false
@ B )
| ( sk1 @ A @ B ) ),
inference(prim_subst,[status(thm)],[7:[bind(A,$thf( ^ [D: $i] : $false ))]]) ).
thf(118,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk1
@ ^ [C: $i] : $false
@ B )
| ( sk1 @ A @ B ) ),
inference(simp,[status(thm)],[99]) ).
thf(1826,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ( sk7 @ ( sk2 @ A @ sk7 ) )
| ( sk1 @ B @ C )
| ( ( sk1 @ A @ sk5 )
!= ( sk1
@ ^ [D: $i] : $false
@ C ) ) ),
inference(paramod_ordered,[status(thm)],[462,118]) ).
thf(1827,plain,
! [A: $i > $o] :
( ( sk7
@ ( sk2
@ ^ [B: $i] : $false
@ sk7 ) )
| ( sk1 @ A @ sk5 ) ),
inference(pattern_uni,[status(thm)],[1826:[bind(A,$thf( ^ [D: $i] : $false )),bind(B,$thf( B )),bind(C,$thf( sk5 ))]]) ).
thf(1871,plain,
! [A: $i > $o] :
( ( sk7
@ ( sk2
@ ^ [B: $i] : $false
@ sk7 ) )
| ( sk1 @ A @ sk5 ) ),
inference(simp,[status(thm)],[1827]) ).
thf(4520,plain,
! [B: $i,A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk1 @ sk7 @ B )
| ( ( sk7
@ ( sk2
@ ^ [C: $i] : $false
@ sk7 ) )
!= ( sk7 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1871,435]) ).
thf(4521,plain,
! [A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk1 @ sk7
@ ( sk2
@ ^ [B: $i] : $false
@ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[4520:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ^ [C: $i] : $false @ sk7 ))]]) ).
thf(8,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ~ ( B @ ( sk2 @ B @ A ) )
| ~ ( sk1 @ A @ C )
| ( sk1 @ B @ C ) ),
inference(cnf,[status(esa)],[3]) ).
thf(335,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ~ ( B @ ( sk2 @ B @ A ) )
| ( sk1 @ B @ C )
| ( ( sk1 @ sk4 @ sk3 )
!= ( sk1 @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[12,8]) ).
thf(336,plain,
! [A: $i > $o] :
( ~ ( A @ ( sk2 @ A @ sk4 ) )
| ( sk1 @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[335:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(381,plain,
! [A: $i > $o] :
( ~ ( A @ ( sk2 @ A @ sk4 ) )
| ( sk1 @ A @ sk3 ) ),
inference(simp,[status(thm)],[336]) ).
thf(7479,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk1 @ B @ sk3 )
| ( ( sk1 @ sk7
@ ( sk2
@ ^ [C: $i] : $false
@ sk7 ) )
!= ( B @ ( sk2 @ B @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[4521,381]) ).
thf(7569,plain,
! [A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk1
@ ^ [B: $i] :
( sk1 @ sk7
@ ( sk2
@ ^ [C: $i] : $false
@ sk7 ) )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[7479:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : ( sk1 @ sk7 @ ( sk2 @ ^ [D: $i] : $false @ sk7 ) ) ))]]) ).
thf(795,plain,
( ~ ( sk21 @ ( sk2 @ sk21 @ sk4 ) )
| ( sk1 @ sk21 @ sk3 ) ),
inference(prim_subst,[status(thm)],[381:[bind(A,$thf( sk21 ))]]) ).
thf(1798,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk1
@ ^ [C: $i] : $false
@ B )
| ( ( sk1 @ A @ B )
!= ( sk1
@ ^ [C: $i] :
? [D: $i > $o] :
( ! [E: $i] :
( ( D @ E )
=> ( sk1 @ D @ E ) )
& ( D @ C ) )
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[118,5]) ).
thf(1799,plain,
~ ( sk1
@ ^ [A: $i] : $false
@ sk3 ),
inference(pattern_uni,[status(thm)],[1798:[bind(A,$thf( ^ [C: $i] : ? [D: $i > $o] : ( ! [E: $i] : ( ( D @ E ) => ( sk1 @ D @ E ) ) & ( D @ C ) ) )),bind(B,$thf( sk3 ))]]) ).
thf(11797,plain,
( ~ ( sk21 @ ( sk2 @ sk21 @ sk4 ) )
| ( ( sk1 @ sk21 @ sk3 )
!= ( sk1
@ ^ [A: $i] : $false
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[795,1799]) ).
thf(11851,plain,
( ~ ( sk21 @ ( sk2 @ sk21 @ sk4 ) )
| ( sk21
!= ( ^ [A: $i] : $false ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[11797]) ).
thf(11872,plain,
( ~ ( sk21 @ ( sk2 @ sk21 @ sk4 ) )
| ( sk21
!= ( ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[11851]) ).
thf(11895,plain,
( ( sk21 @ sk132 )
| ~ ( sk21 @ ( sk2 @ sk21 @ sk4 ) ) ),
inference(func_ext,[status(esa)],[11872]) ).
thf(87,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ( A @ ( sk2 @ B @ A ) )
| ( sk1 @ B @ C )
| ( ( sk1 @ sk4 @ sk3 )
!= ( sk1 @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[12,7]) ).
thf(88,plain,
! [A: $i > $o] :
( ( sk4 @ ( sk2 @ A @ sk4 ) )
| ( sk1 @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(139,plain,
! [A: $i > $o] :
( ( sk4 @ ( sk2 @ A @ sk4 ) )
| ( sk1 @ A @ sk3 ) ),
inference(simp,[status(thm)],[88]) ).
thf(276,plain,
! [B: $i,A: $i > $o] :
( ( sk1 @ A @ sk3 )
| ( sk1 @ sk4 @ B )
| ( ( sk4 @ ( sk2 @ A @ sk4 ) )
!= ( sk4 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[139,9]) ).
thf(277,plain,
! [A: $i > $o] :
( ( sk1 @ A @ sk3 )
| ( sk1 @ sk4 @ ( sk2 @ A @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[276:[bind(A,$thf( C )),bind(B,$thf( sk2 @ C @ sk4 ))]]) ).
thf(311,plain,
! [A: $i > $o] :
( ( sk1 @ A @ sk3 )
| ( sk1 @ sk4 @ ( sk2 @ A @ sk4 ) ) ),
inference(simp,[status(thm)],[277]) ).
thf(772,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk1 @ A @ sk3 )
| ( sk1 @ B @ sk3 )
| ( ( sk1 @ sk4 @ ( sk2 @ A @ sk4 ) )
!= ( B @ ( sk2 @ B @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,381]) ).
thf(813,plain,
( ( sk1 @ ( sk1 @ sk4 ) @ sk3 )
| ( sk1 @ ( sk1 @ sk4 ) @ sk3 ) ),
inference(pre_uni,[status(thm)],[772:[bind(A,$thf( sk1 @ sk4 )),bind(B,$thf( sk1 @ sk4 ))]]) ).
thf(857,plain,
sk1 @ ( sk1 @ sk4 ) @ sk3,
inference(simp,[status(thm)],[813]) ).
thf(1058,plain,
( ( sk1 @ ( sk1 @ sk4 ) @ sk3 )
!= ( sk1
@ ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) )
@ sk3 ) ),
inference(paramod_ordered,[status(thm)],[857,5]) ).
thf(1070,plain,
( ( ( sk1 @ sk4 )
!= ( ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) ) ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[1058]) ).
thf(1076,plain,
( ( sk1 @ sk4 )
!= ( ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) ) ) ),
inference(simp,[status(thm)],[1070]) ).
thf(1379,plain,
( ( sk1 @ sk4 @ sk30 )
!= ( ? [A: $i > $o] :
( ! [B: $i] :
( ( A @ B )
=> ( sk1 @ A @ B ) )
& ( A @ sk30 ) ) ) ),
inference(func_ext,[status(esa)],[1076]) ).
thf(1479,plain,
( ( sk1 @ sk4 @ sk30 )
| ? [A: $i > $o] :
( ! [B: $i] :
( ( A @ B )
=> ( sk1 @ A @ B ) )
& ( A @ sk30 ) ) ),
inference(bool_ext,[status(thm)],[1379]) ).
thf(1532,plain,
( ( sk32 @ sk30 )
| ( sk1 @ sk4 @ sk30 ) ),
inference(cnf,[status(esa)],[1479]) ).
thf(1622,plain,
! [A: $i > $o] :
( ( sk32 @ sk30 )
| ( sk1 @ A @ sk3 )
| ( ( A @ ( sk2 @ A @ sk4 ) )
!= ( sk1 @ sk4 @ sk30 ) ) ),
inference(paramod_ordered,[status(thm)],[1532,381]) ).
thf(1631,plain,
( ( sk32 @ sk30 )
| ( sk1
@ ^ [A: $i] : ( sk1 @ sk4 @ sk30 )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[1622:[bind(A,$thf( ^ [B: $i] : ( sk1 @ sk4 @ sk30 ) ))]]) ).
thf(1696,plain,
! [A: $i > $o] :
( ( sk32 @ sk30 )
| ( sk1 @ A @ sk3 )
| ( ( A @ ( sk2 @ A @ sk4 ) )
!= ( sk1
@ ^ [B: $i] : ( sk1 @ sk4 @ sk30 )
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[1631,381]) ).
thf(1729,plain,
( ( sk32 @ sk30 )
| ( sk1
@ ^ [A: $i] :
( sk1
@ ^ [B: $i] : ( sk1 @ sk4 @ sk30 )
@ sk3 )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[1696:[bind(A,$thf( ^ [B: $i] : ( sk1 @ ^ [C: $i] : ( sk1 @ sk4 @ sk30 ) @ sk3 ) ))]]) ).
thf(797,plain,
( ~ ( sk7 @ ( sk2 @ sk7 @ sk4 ) )
| ( sk1 @ sk7 @ sk3 ) ),
inference(prim_subst,[status(thm)],[381:[bind(A,$thf( sk7 ))]]) ).
thf(12267,plain,
( ~ ( sk7 @ ( sk2 @ sk7 @ sk4 ) )
| ( ( sk1 @ sk7 @ sk3 )
!= ( sk1
@ ^ [A: $i] : $false
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[797,1799]) ).
thf(12340,plain,
( ~ ( sk7 @ ( sk2 @ sk7 @ sk4 ) )
| ( sk7
!= ( ^ [A: $i] : $false ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[12267]) ).
thf(12365,plain,
( ~ ( sk7 @ ( sk2 @ sk7 @ sk4 ) )
| ( sk7
!= ( ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[12340]) ).
thf(12384,plain,
( ( sk7
!= ( ^ [A: $i] : $false ) )
| ( ( sk7 @ ( sk2 @ sk7 @ sk4 ) )
!= ( sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[314,12365]) ).
thf(12393,plain,
( ( sk7
!= ( ^ [A: $i] : $false ) )
| ( ( sk2 @ sk7 @ sk4 )
!= sk5 ) ),
inference(simp,[status(thm)],[12384]) ).
thf(12440,plain,
( ( sk7 @ sk139 )
| ( ( sk2 @ sk7 @ sk4 )
!= sk5 ) ),
inference(func_ext,[status(esa)],[12393]) ).
thf(1904,plain,
( ( sk1 @ ( sk1 @ sk4 ) @ sk3 )
!= ( sk1
@ ^ [A: $i] : $false
@ sk3 ) ),
inference(paramod_ordered,[status(thm)],[857,1799]) ).
thf(1940,plain,
( ( ( sk1 @ sk4 )
!= ( ^ [A: $i] : $false ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[1904]) ).
thf(1956,plain,
( ( sk1 @ sk4 )
!= ( ^ [A: $i] : $false ) ),
inference(simp,[status(thm)],[1940]) ).
thf(799,plain,
( ~ $true
| ( sk1
@ ^ [A: $i] : $true
@ sk3 ) ),
inference(prim_subst,[status(thm)],[381:[bind(A,$thf( ^ [B: $i] : $true ))]]) ).
thf(850,plain,
( sk1
@ ^ [A: $i] : $true
@ sk3 ),
inference(simp,[status(thm)],[799]) ).
thf(870,plain,
( ( sk1
@ ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) )
@ sk3 )
!= ( sk1
@ ^ [A: $i] : $true
@ sk3 ) ),
inference(paramod_ordered,[status(thm)],[850,5]) ).
thf(878,plain,
( ( ( ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) ) )
!= ( ^ [A: $i] : $true ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[870]) ).
thf(884,plain,
( ( ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) ) )
!= ( ^ [A: $i] : $true ) ),
inference(simp,[status(thm)],[878]) ).
thf(886,plain,
~ ? [A: $i > $o] :
( ! [B: $i] :
( ( A @ B )
=> ( sk1 @ A @ B ) )
& ( A @ sk28 ) ),
inference(func_ext,[status(esa)],[884]) ).
thf(887,plain,
! [A: $i > $o] :
( ( A @ ( sk29 @ A ) )
| ~ ( A @ sk28 ) ),
inference(cnf,[status(esa)],[886]) ).
thf(6398,plain,
! [A: $i > $o] :
( ~ ( A
@ ( sk29
@ ^ [B: $i] :
~ ( A @ B ) ) )
| ~ ~ ( A @ sk28 ) ),
inference(prim_subst,[status(thm)],[887:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).
thf(6678,plain,
! [A: $i > $o] :
( ( A @ sk28 )
| ~ ( A
@ ( sk29
@ ^ [B: $i] :
~ ( A @ B ) ) ) ),
inference(cnf,[status(esa)],[6398]) ).
thf(6679,plain,
! [A: $i > $o] :
( ( A @ sk28 )
| ~ ( A
@ ( sk29
@ ^ [B: $i] :
~ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[6678]) ).
thf(10536,plain,
( ( sk4 @ sk28 )
| ~ ( sk4
@ ( sk29
@ ^ [A: $i] :
~ ( sk4 @ A ) ) ) ),
inference(prim_subst,[status(thm)],[6679:[bind(A,$thf( sk4 ))]]) ).
thf(888,plain,
! [A: $i > $o] :
( ~ ( sk1 @ A @ ( sk29 @ A ) )
| ~ ( A @ sk28 ) ),
inference(cnf,[status(esa)],[886]) ).
thf(908,plain,
! [B: $i > $o,A: $i] :
( ~ ( sk4 @ A )
| ~ ( B @ sk28 )
| ( ( sk1 @ sk4 @ A )
!= ( sk1 @ B @ ( sk29 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,888]) ).
thf(909,plain,
( ~ ( sk4 @ ( sk29 @ sk4 ) )
| ~ ( sk4 @ sk28 ) ),
inference(pattern_uni,[status(thm)],[908:[bind(A,$thf( sk29 @ sk4 )),bind(B,$thf( sk4 ))]]) ).
thf(6222,plain,
! [A: $i > $o] :
( ~ ( A @ sk28 )
| ~ ( sk4 @ sk28 )
| ( ( A @ ( sk29 @ A ) )
!= ( sk4 @ ( sk29 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[887,909]) ).
thf(6582,plain,
( ~ ( sk4 @ sk28 )
| ~ ( sk4 @ sk28 ) ),
inference(pre_uni,[status(thm)],[6222:[bind(A,$thf( sk4 ))]]) ).
thf(6666,plain,
~ ( sk4 @ sk28 ),
inference(simp,[status(thm)],[6582]) ).
thf(11351,plain,
( $false
| ~ ( sk4
@ ( sk29
@ ^ [A: $i] :
~ ( sk4 @ A ) ) ) ),
inference(rewrite,[status(thm)],[10536,6666]) ).
thf(11352,plain,
~ ( sk4
@ ( sk29
@ ^ [A: $i] :
~ ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[11351]) ).
thf(1892,plain,
! [A: $i] :
( ~ ( sk7 @ A )
| ( ( sk1 @ sk7 @ A )
!= ( sk1
@ ^ [B: $i] : $false
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[435,1799]) ).
thf(1924,plain,
! [A: $i] :
( ~ ( sk7 @ A )
| ( sk7
!= ( ^ [B: $i] : $false ) )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[1892]) ).
thf(1947,plain,
( ~ ( sk7 @ sk3 )
| ( sk7
!= ( ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[1924]) ).
thf(2237,plain,
( ( sk7 @ sk65 )
| ~ ( sk7 @ sk3 ) ),
inference(func_ext,[status(esa)],[1947]) ).
thf(2891,plain,
! [A: $i > $o] :
( ~ ( sk7 @ sk3 )
| ( sk1 @ A @ sk3 )
| ( ( A @ ( sk2 @ A @ sk4 ) )
!= ( sk7 @ sk65 ) ) ),
inference(paramod_ordered,[status(thm)],[2237,381]) ).
thf(2915,plain,
( ~ ( sk7 @ sk3 )
| ( sk1
@ ^ [A: $i] : ( sk7 @ sk65 )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[2891:[bind(A,$thf( ^ [B: $i] : ( sk7 @ sk65 ) ))]]) ).
thf(9459,plain,
( ~ ( sk7 @ sk3 )
| ( ( sk1
@ ^ [A: $i] : ( sk7 @ sk65 )
@ sk3 )
!= ( sk1
@ ^ [A: $i] : $false
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[2915,1799]) ).
thf(9545,plain,
( ~ ( sk7 @ sk3 )
| ( ( ^ [A: $i] : ( sk7 @ sk65 ) )
!= ( ^ [A: $i] : $false ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[9459]) ).
thf(9573,plain,
( ~ ( sk7 @ sk3 )
| ( ( ^ [A: $i] : ( sk7 @ sk65 ) )
!= ( ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[9545]) ).
thf(6728,plain,
( ( sk4 @ sk28 )
!= ( sk4 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[6,6666]) ).
thf(6744,plain,
sk28 != sk3,
inference(simp,[status(thm)],[6728]) ).
thf(1065,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ( A @ ( sk2 @ B @ A ) )
| ( sk1 @ B @ C )
| ( ( sk1 @ ( sk1 @ sk4 ) @ sk3 )
!= ( sk1 @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[857,7]) ).
thf(1066,plain,
! [A: $i > $o] :
( ( sk1 @ sk4 @ ( sk2 @ A @ ( sk1 @ sk4 ) ) )
| ( sk1 @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[1065:[bind(A,$thf( sk1 @ sk4 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(1073,plain,
! [A: $i > $o] :
( ( sk1 @ sk4 @ ( sk2 @ A @ ( sk1 @ sk4 ) ) )
| ( sk1 @ A @ sk3 ) ),
inference(simp,[status(thm)],[1066]) ).
thf(4519,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk7
@ ( sk2
@ ^ [C: $i] : $false
@ sk7 ) )
| ( sk1 @ B @ sk3 )
| ( ( sk1 @ A @ sk5 )
!= ( B @ ( sk2 @ B @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1871,381]) ).
thf(4571,plain,
! [A: $i > $i > $o] :
( ( sk7
@ ( sk2
@ ^ [B: $i] : $false
@ sk7 ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ B ) @ sk5 )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[4519:[bind(A,$thf( C @ ( sk2 @ ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) @ sk4 ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) ))]]) ).
thf(4603,plain,
! [A: $i > $i > $o] :
( ( sk7
@ ( sk2
@ ^ [B: $i] : $false
@ sk7 ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ B ) @ sk5 )
@ sk3 ) ),
inference(simp,[status(thm)],[4571]) ).
thf(101,plain,
! [B: $i,A: $i > $o] :
( ( sk7 @ ( sk2 @ A @ sk7 ) )
| ~ ( sk1 @ sk7 @ B )
| ( sk1 @ A @ B ) ),
inference(prim_subst,[status(thm)],[7:[bind(A,$thf( sk7 ))]]) ).
thf(120,plain,
! [B: $i,A: $i > $o] :
( ( sk7 @ ( sk2 @ A @ sk7 ) )
| ~ ( sk1 @ sk7 @ B )
| ( sk1 @ A @ B ) ),
inference(simp,[status(thm)],[101]) ).
thf(328,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ~ ( B @ ( sk2 @ B @ A ) )
| ~ ( sk1 @ A @ C )
| ( ( sk1 @ B @ C )
!= ( sk1
@ ^ [D: $i] :
? [E: $i > $o] :
( ! [F: $i] :
( ( E @ F )
=> ( sk1 @ E @ F ) )
& ( E @ D ) )
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[8,5]) ).
thf(329,plain,
! [A: $i > $o] :
( ~ ? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B
@ ( sk2
@ ^ [C: $i] :
? [D: $i > $o] :
( ! [E: $i] :
( ( D @ E )
=> ( sk1 @ D @ E ) )
& ( D @ C ) )
@ A ) ) )
| ~ ( sk1 @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[328:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ? [E: $i > $o] : ( ! [F: $i] : ( ( E @ F ) => ( sk1 @ E @ F ) ) & ( E @ D ) ) )),bind(C,$thf( sk3 ))]]) ).
thf(379,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( sk1 @ A @ sk3 )
| ~ ( sk1 @ B @ ( sk15 @ B @ A ) )
| ~ ( B
@ ( sk2
@ ^ [C: $i] :
? [D: $i > $o] :
( ! [E: $i] :
( ( D @ E )
=> ( sk1 @ D @ E ) )
& ( D @ C ) )
@ A ) ) ),
inference(cnf,[status(esa)],[329]) ).
thf(315,plain,
? [A: $i > $o] :
( ! [B: $i] :
( ( A @ B )
=> ( sk1 @ A @ B ) )
& ( A @ sk5 ) ),
inference(rewrite,[status(thm)],[18,253]) ).
thf(325,plain,
sk14 @ sk5,
inference(cnf,[status(esa)],[315]) ).
thf(326,plain,
! [A: $i] :
( ~ ( sk14 @ A )
| ( sk1 @ sk14 @ A ) ),
inference(cnf,[status(esa)],[315]) ).
thf(609,plain,
! [A: $i] :
( ( sk1 @ sk14 @ A )
| ( ( sk14 @ sk5 )
!= ( sk14 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[325,326]) ).
thf(610,plain,
sk1 @ sk14 @ sk5,
inference(pattern_uni,[status(thm)],[609:[bind(A,$thf( sk5 ))]]) ).
thf(1806,plain,
! [B: $i,A: $i > $o] :
( ( sk1 @ A @ B )
| ( ( sk1 @ sk14 @ sk5 )
!= ( sk1
@ ^ [C: $i] : $false
@ B ) ) ),
inference(paramod_ordered,[status(thm)],[610,118]) ).
thf(1853,plain,
! [B: $i,A: $i > $o] :
( ( sk1 @ A @ B )
| ( sk14
!= ( ^ [C: $i] : $false ) )
| ( sk5 != B ) ),
inference(simp,[status(thm)],[1806]) ).
thf(1887,plain,
! [A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk14
!= ( ^ [B: $i] : $false ) ) ),
inference(simp,[status(thm)],[1853]) ).
thf(948,plain,
( ~ ( sk1 @ sk21 @ ( sk29 @ sk21 ) )
| ~ ( sk21 @ sk28 ) ),
inference(prim_subst,[status(thm)],[888:[bind(A,$thf( sk21 ))]]) ).
thf(7745,plain,
! [A: $i > $o] :
( ( sk14
!= ( ^ [B: $i] : $false ) )
| ~ ( sk21 @ sk28 )
| ( ( sk1 @ A @ sk5 )
!= ( sk1 @ sk21 @ ( sk29 @ sk21 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1887,948]) ).
thf(7785,plain,
! [A: $i > $o] :
( ( sk14
!= ( ^ [B: $i] : $false ) )
| ~ ( sk21 @ sk28 )
| ( A != sk21 )
| ( ( sk29 @ sk21 )
!= sk5 ) ),
inference(simp,[status(thm)],[7745]) ).
thf(7813,plain,
( ( sk14
!= ( ^ [A: $i] : $false ) )
| ~ ( sk21 @ sk28 )
| ( ( sk29 @ sk21 )
!= sk5 ) ),
inference(simp,[status(thm)],[7785]) ).
thf(350,plain,
! [F: $i,E: $i > $o,D: $i > $o,C: $i,B: $i > $o,A: $i > $o] :
( ~ ( B @ ( sk2 @ B @ A ) )
| ~ ( sk1 @ A @ C )
| ~ ( E @ ( sk2 @ E @ D ) )
| ( sk1 @ E @ F )
| ( ( sk1 @ B @ C )
!= ( sk1 @ D @ F ) ) ),
inference(paramod_ordered,[status(thm)],[8,8]) ).
thf(351,plain,
! [D: $i > $o,C: $i,B: $i > $o,A: $i > $o] :
( ~ ( B @ ( sk2 @ B @ A ) )
| ~ ( sk1 @ A @ C )
| ~ ( D @ ( sk2 @ D @ B ) )
| ( sk1 @ D @ C ) ),
inference(pattern_uni,[status(thm)],[350:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( E )),bind(F,$thf( C ))]]) ).
thf(385,plain,
! [D: $i > $o,C: $i,B: $i > $o,A: $i > $o] :
( ~ ( B @ ( sk2 @ B @ A ) )
| ~ ( sk1 @ A @ C )
| ~ ( D @ ( sk2 @ D @ B ) )
| ( sk1 @ D @ C ) ),
inference(simp,[status(thm)],[351]) ).
thf(347,plain,
! [D: $i,C: $i > $o,B: $i > $o,A: $i > $o] :
( ( sk4 @ ( sk2 @ A @ sk4 ) )
| ~ ( C @ ( sk2 @ C @ B ) )
| ( sk1 @ C @ D )
| ( ( sk1 @ A @ sk3 )
!= ( sk1 @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[139,8]) ).
thf(348,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk4 @ ( sk2 @ A @ sk4 ) )
| ~ ( B @ ( sk2 @ B @ A ) )
| ( sk1 @ B @ sk3 ) ),
inference(pattern_uni,[status(thm)],[347:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( sk3 ))]]) ).
thf(384,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk4 @ ( sk2 @ A @ sk4 ) )
| ~ ( B @ ( sk2 @ B @ A ) )
| ( sk1 @ B @ sk3 ) ),
inference(simp,[status(thm)],[348]) ).
thf(1810,plain,
! [C: $i > $o,B: $i,A: $i > $o] :
( ~ ( sk1
@ ^ [D: $i] : $false
@ B )
| ~ ( C @ sk28 )
| ( ( sk1 @ A @ B )
!= ( sk1 @ C @ ( sk29 @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[118,888]) ).
thf(1811,plain,
! [A: $i > $o] :
( ~ ( sk1
@ ^ [B: $i] : $false
@ ( sk29 @ A ) )
| ~ ( A @ sk28 ) ),
inference(pattern_uni,[status(thm)],[1810:[bind(A,$thf( D )),bind(B,$thf( sk29 @ D )),bind(C,$thf( D ))]]) ).
thf(1867,plain,
! [A: $i > $o] :
( ~ ( sk1
@ ^ [B: $i] : $false
@ ( sk29 @ A ) )
| ~ ( A @ sk28 ) ),
inference(simp,[status(thm)],[1811]) ).
thf(890,plain,
! [B: $i > $o,A: $i] :
( ~ ( sk7 @ A )
| ~ ( B @ sk28 )
| ( ( sk1 @ sk7 @ A )
!= ( sk1 @ B @ ( sk29 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[435,888]) ).
thf(891,plain,
( ~ ( sk7 @ ( sk29 @ sk7 ) )
| ~ ( sk7 @ sk28 ) ),
inference(pattern_uni,[status(thm)],[890:[bind(A,$thf( sk29 @ sk7 )),bind(B,$thf( sk7 ))]]) ).
thf(6354,plain,
! [A: $i > $o] :
( ~ ( A @ sk28 )
| ~ ( sk7 @ sk28 )
| ( ( A @ ( sk29 @ A ) )
!= ( sk7 @ ( sk29 @ sk7 ) ) ) ),
inference(paramod_ordered,[status(thm)],[887,891]) ).
thf(6556,plain,
( ~ ( sk7 @ sk28 )
| ~ ( sk7 @ sk28 ) ),
inference(pre_uni,[status(thm)],[6354:[bind(A,$thf( sk7 ))]]) ).
thf(6655,plain,
~ ( sk7 @ sk28 ),
inference(simp,[status(thm)],[6556]) ).
thf(1341,plain,
! [A: $i > $o] :
( ( sk1 @ sk4 @ ( sk2 @ A @ ( sk1 @ sk4 ) ) )
| ( ( sk1
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ sk3 )
!= ( sk1 @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[1073,5]) ).
thf(1342,plain,
( sk1 @ sk4
@ ( sk2
@ ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) )
@ ( sk1 @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[1341:[bind(A,$thf( ^ [B: $i] : ? [C: $i > $o] : ( ! [D: $i] : ( ( C @ D ) => ( sk1 @ C @ D ) ) & ( C @ B ) ) ))]]) ).
thf(7730,plain,
! [A: $i > $o] :
( ( sk14 @ ( sk102 @ A ) )
| ( sk1 @ A @ sk5 ) ),
inference(func_ext,[status(esa)],[1887]) ).
thf(19941,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ( sk14 @ ( sk102 @ A ) )
| ( sk1 @ B @ C )
| ( ( sk1 @ A @ sk5 )
!= ( sk1
@ ^ [D: $i] : $false
@ C ) ) ),
inference(paramod_ordered,[status(thm)],[7730,118]) ).
thf(19942,plain,
! [A: $i > $o] :
( ( sk14
@ ( sk102
@ ^ [B: $i] : $false ) )
| ( sk1 @ A @ sk5 ) ),
inference(pattern_uni,[status(thm)],[19941:[bind(A,$thf( ^ [D: $i] : $false )),bind(B,$thf( B )),bind(C,$thf( sk5 ))]]) ).
thf(20108,plain,
! [A: $i > $o] :
( ( sk14
@ ( sk102
@ ^ [B: $i] : $false ) )
| ( sk1 @ A @ sk5 ) ),
inference(simp,[status(thm)],[19942]) ).
thf(20179,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk14
@ ( sk102
@ ^ [C: $i] : $false ) )
| ( sk1 @ B @ sk3 )
| ( ( sk1 @ A @ sk5 )
!= ( B @ ( sk2 @ B @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[20108,381]) ).
thf(20243,plain,
! [A: $i > $i > $o] :
( ( sk14
@ ( sk102
@ ^ [B: $i] : $false ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ B ) @ sk5 )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[20179:[bind(A,$thf( C @ ( sk2 @ ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) @ sk4 ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) ))]]) ).
thf(20280,plain,
! [A: $i > $i > $o] :
( ( sk14
@ ( sk102
@ ^ [B: $i] : $false ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ B ) @ sk5 )
@ sk3 ) ),
inference(simp,[status(thm)],[20243]) ).
thf(282,plain,
! [A: $i > $o] :
( ( sk4 @ ( sk2 @ A @ sk4 ) )
| ( ( sk1
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ sk3 )
!= ( sk1 @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[139,5]) ).
thf(283,plain,
( sk4
@ ( sk2
@ ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) )
@ sk4 ) ),
inference(pattern_uni,[status(thm)],[282:[bind(A,$thf( ^ [B: $i] : ? [C: $i > $o] : ( ! [D: $i] : ( ( C @ D ) => ( sk1 @ C @ D ) ) & ( C @ B ) ) ))]]) ).
thf(418,plain,
! [A: $i] :
( ( sk1 @ sk4 @ A )
| ( ( sk4
@ ( sk2
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ sk4 ) )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[283,9]) ).
thf(419,plain,
( sk1 @ sk4
@ ( sk2
@ ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) )
@ sk4 ) ),
inference(pattern_uni,[status(thm)],[418:[bind(A,$thf( sk2 @ ^ [B: $i] : ? [C: $i > $o] : ( ! [D: $i] : ( ( C @ D ) => ( sk1 @ C @ D ) ) & ( C @ B ) ) @ sk4 ))]]) ).
thf(378,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( sk1 @ A @ sk3 )
| ( B @ ( sk15 @ B @ A ) )
| ~ ( B
@ ( sk2
@ ^ [C: $i] :
? [D: $i > $o] :
( ! [E: $i] :
( ( D @ E )
=> ( sk1 @ D @ E ) )
& ( D @ C ) )
@ A ) ) ),
inference(cnf,[status(esa)],[329]) ).
thf(25278,plain,
! [B: $i > $o,A: $i > $o] :
( ( B @ ( sk15 @ B @ A ) )
| ~ ( B
@ ( sk2
@ ^ [C: $i] :
? [D: $i > $o] :
( ! [E: $i] :
( ( D @ E )
=> ( sk1 @ D @ E ) )
& ( D @ C ) )
@ A ) )
| ( ( sk1 @ sk4 @ sk3 )
!= ( sk1 @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[12,378]) ).
thf(25279,plain,
! [A: $i > $o] :
( ( A @ ( sk15 @ A @ sk4 ) )
| ~ ( A
@ ( sk2
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[25278:[bind(A,$thf( sk4 )),bind(B,$thf( B ))]]) ).
thf(26303,plain,
! [A: $i > $o] :
( ( A @ ( sk15 @ A @ sk4 ) )
| ~ ( A
@ ( sk2
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ sk4 ) ) ),
inference(simp,[status(thm)],[25279]) ).
thf(36722,plain,
! [A: $i > $o] :
( ( A @ ( sk15 @ A @ sk4 ) )
| ( ( sk1 @ sk4
@ ( sk2
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ sk4 ) )
!= ( A
@ ( sk2
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[419,26303]) ).
thf(37412,plain,
sk1 @ sk4 @ ( sk15 @ ( sk1 @ sk4 ) @ sk4 ),
inference(pre_uni,[status(thm)],[36722:[bind(A,$thf( sk1 @ sk4 ))]]) ).
thf(1919,plain,
! [A: $i] :
( ~ ( sk14 @ A )
| ( ( sk1 @ sk14 @ A )
!= ( sk1
@ ^ [B: $i] : $false
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[326,1799]) ).
thf(1922,plain,
! [A: $i] :
( ~ ( sk14 @ A )
| ( sk14
!= ( ^ [B: $i] : $false ) )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[1919]) ).
thf(1945,plain,
( ~ ( sk14 @ sk3 )
| ( sk14
!= ( ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[1922]) ).
thf(2229,plain,
( ( sk14 @ sk64 )
| ~ ( sk14 @ sk3 ) ),
inference(func_ext,[status(esa)],[1945]) ).
thf(2468,plain,
! [A: $i] :
( ~ ( sk14 @ sk3 )
| ( sk1 @ sk14 @ A )
| ( ( sk14 @ sk64 )
!= ( sk14 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2229,326]) ).
thf(2469,plain,
( ~ ( sk14 @ sk3 )
| ( sk1 @ sk14 @ sk64 ) ),
inference(pattern_uni,[status(thm)],[2468:[bind(A,$thf( sk64 ))]]) ).
thf(4654,plain,
! [A: $i > $o] :
( ~ ( sk14 @ sk3 )
| ( sk1 @ A @ sk3 )
| ( ( A @ ( sk2 @ A @ sk4 ) )
!= ( sk1 @ sk14 @ sk64 ) ) ),
inference(paramod_ordered,[status(thm)],[2469,381]) ).
thf(4679,plain,
( ~ ( sk14 @ sk3 )
| ( sk1
@ ^ [A: $i] : ( sk1 @ sk14 @ sk64 )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[4654:[bind(A,$thf( ^ [B: $i] : ( sk1 @ sk14 @ sk64 ) ))]]) ).
thf(949,plain,
( ~ ( sk1
@ ^ [A: $i] : $true
@ ( sk29
@ ^ [A: $i] : $true ) )
| ~ $true ),
inference(prim_subst,[status(thm)],[888:[bind(A,$thf( ^ [B: $i] : $true ))]]) ).
thf(1008,plain,
~ ( sk1
@ ^ [A: $i] : $true
@ ( sk29
@ ^ [A: $i] : $true ) ),
inference(simp,[status(thm)],[949]) ).
thf(1080,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ~ ( B @ ( sk2 @ B @ A ) )
| ~ ( sk1 @ A @ C )
| ( ( sk1 @ B @ C )
!= ( sk1
@ ^ [D: $i] : $true
@ ( sk29
@ ^ [D: $i] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,1008]) ).
thf(1081,plain,
! [A: $i > $o] :
( ~ $true
| ~ ( sk1 @ A
@ ( sk29
@ ^ [B: $i] : $true ) ) ),
inference(pattern_uni,[status(thm)],[1080:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : $true )),bind(C,$thf( sk29 @ ^ [D: $i] : $true ))]]) ).
thf(1134,plain,
! [A: $i > $o] :
~ ( sk1 @ A
@ ( sk29
@ ^ [B: $i] : $true ) ),
inference(simp,[status(thm)],[1081]) ).
thf(1466,plain,
! [A: $i > $o] :
( ( sk1 @ sk4
@ ( sk2
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ ( sk1 @ sk4 ) ) )
!= ( sk1 @ A
@ ( sk29
@ ^ [B: $i] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[1342,1134]) ).
thf(1469,plain,
! [A: $i > $o] :
( ( sk4 != A )
| ( ( sk2
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ ( sk1 @ sk4 ) )
!= ( sk29
@ ^ [B: $i] : $true ) ) ),
inference(simp,[status(thm)],[1466]) ).
thf(1475,plain,
( ( sk2
@ ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) )
@ ( sk1 @ sk4 ) )
!= ( sk29
@ ^ [A: $i] : $true ) ),
inference(simp,[status(thm)],[1469]) ).
thf(316,plain,
( ( sk4 @ sk5 )
!= ( sk4 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[6,253]) ).
thf(320,plain,
sk5 != sk3,
inference(simp,[status(thm)],[316]) ).
thf(12293,plain,
( ( sk1 @ sk7 @ sk3 )
| ( ( sk7 @ ( sk2 @ sk7 @ sk4 ) )
!= ( sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[314,797]) ).
thf(12339,plain,
( ( sk1 @ sk7 @ sk3 )
| ( ( sk2 @ sk7 @ sk4 )
!= sk5 ) ),
inference(simp,[status(thm)],[12293]) ).
thf(1828,plain,
! [B: $i,A: $i > $o] :
( ( sk1 @ A @ B )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1
@ ^ [C: $i] : $false
@ B ) ) ),
inference(paramod_ordered,[status(thm)],[438,118]) ).
thf(1849,plain,
! [B: $i,A: $i > $o] :
( ( sk1 @ A @ B )
| ( sk7
!= ( ^ [C: $i] : $false ) )
| ( sk5 != B ) ),
inference(simp,[status(thm)],[1828]) ).
thf(1883,plain,
! [A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk7
!= ( ^ [B: $i] : $false ) ) ),
inference(simp,[status(thm)],[1849]) ).
thf(7636,plain,
! [A: $i > $o] :
( ( sk7 @ ( sk100 @ A ) )
| ( sk1 @ A @ sk5 ) ),
inference(func_ext,[status(esa)],[1883]) ).
thf(18210,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ( sk7 @ ( sk100 @ A ) )
| ( sk1 @ B @ C )
| ( ( sk1 @ A @ sk5 )
!= ( sk1
@ ^ [D: $i] : $false
@ C ) ) ),
inference(paramod_ordered,[status(thm)],[7636,118]) ).
thf(18211,plain,
! [A: $i > $o] :
( ( sk7
@ ( sk100
@ ^ [B: $i] : $false ) )
| ( sk1 @ A @ sk5 ) ),
inference(pattern_uni,[status(thm)],[18210:[bind(A,$thf( ^ [D: $i] : $false )),bind(B,$thf( B )),bind(C,$thf( sk5 ))]]) ).
thf(18323,plain,
! [A: $i > $o] :
( ( sk7
@ ( sk100
@ ^ [B: $i] : $false ) )
| ( sk1 @ A @ sk5 ) ),
inference(simp,[status(thm)],[18211]) ).
thf(18388,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk7
@ ( sk100
@ ^ [C: $i] : $false ) )
| ( sk1 @ B @ sk3 )
| ( ( sk1 @ A @ sk5 )
!= ( B @ ( sk2 @ B @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[18323,381]) ).
thf(18439,plain,
! [A: $i > $i > $o] :
( ( sk7
@ ( sk100
@ ^ [B: $i] : $false ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ B ) @ sk5 )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[18388:[bind(A,$thf( C @ ( sk2 @ ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) @ sk4 ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) ))]]) ).
thf(18468,plain,
! [A: $i > $i > $o] :
( ( sk7
@ ( sk100
@ ^ [B: $i] : $false ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ B ) @ sk5 )
@ sk3 ) ),
inference(simp,[status(thm)],[18439]) ).
thf(1894,plain,
! [A: $i > $o] :
( ( sk4 @ ( sk2 @ A @ sk4 ) )
| ( ( sk1 @ A @ sk3 )
!= ( sk1
@ ^ [B: $i] : $false
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[139,1799]) ).
thf(1895,plain,
( sk4
@ ( sk2
@ ^ [A: $i] : $false
@ sk4 ) ),
inference(pattern_uni,[status(thm)],[1894:[bind(A,$thf( ^ [B: $i] : $false ))]]) ).
thf(1241,plain,
! [B: $i > $o,A: $i] :
( ~ ( sk4 @ A )
| ( ( sk1 @ sk4 @ A )
!= ( sk1 @ B
@ ( sk29
@ ^ [C: $i] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,1134]) ).
thf(1242,plain,
~ ( sk4
@ ( sk29
@ ^ [A: $i] : $true ) ),
inference(pattern_uni,[status(thm)],[1241:[bind(A,$thf( sk29 @ ^ [C: $i] : $true )),bind(B,$thf( sk4 ))]]) ).
thf(2198,plain,
( ( sk4
@ ( sk2
@ ^ [A: $i] : $false
@ sk4 ) )
!= ( sk4
@ ( sk29
@ ^ [A: $i] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[1895,1242]) ).
thf(2217,plain,
( ( sk2
@ ^ [A: $i] : $false
@ sk4 )
!= ( sk29
@ ^ [A: $i] : $true ) ),
inference(simp,[status(thm)],[2198]) ).
thf(801,plain,
( ~ ( sk14 @ ( sk2 @ sk14 @ sk4 ) )
| ( sk1 @ sk14 @ sk3 ) ),
inference(prim_subst,[status(thm)],[381:[bind(A,$thf( sk14 ))]]) ).
thf(12608,plain,
( ( sk1 @ sk14 @ sk3 )
| ( ( sk14 @ ( sk2 @ sk14 @ sk4 ) )
!= ( sk14 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[325,801]) ).
thf(12682,plain,
( ( sk1 @ sk14 @ sk3 )
| ( ( sk2 @ sk14 @ sk4 )
!= sk5 ) ),
inference(simp,[status(thm)],[12608]) ).
thf(1627,plain,
! [A: $i > $o] :
( ( sk32 @ sk30 )
| ( ( sk1 @ sk4 @ sk30 )
!= ( sk1 @ A
@ ( sk29
@ ^ [B: $i] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[1532,1134]) ).
thf(1634,plain,
! [A: $i > $o] :
( ( sk32 @ sk30 )
| ( sk4 != A )
| ( ( sk29
@ ^ [B: $i] : $true )
!= sk30 ) ),
inference(simp,[status(thm)],[1627]) ).
thf(1637,plain,
( ( sk32 @ sk30 )
| ( ( sk29
@ ^ [A: $i] : $true )
!= sk30 ) ),
inference(simp,[status(thm)],[1634]) ).
thf(3772,plain,
! [A: $i > $o] :
( ( ( sk29
@ ^ [B: $i] : $true )
!= sk30 )
| ( sk1 @ A @ sk3 )
| ( ( A @ ( sk2 @ A @ sk4 ) )
!= ( sk32 @ sk30 ) ) ),
inference(paramod_ordered,[status(thm)],[1637,381]) ).
thf(3783,plain,
( ( ( sk29
@ ^ [A: $i] : $true )
!= sk30 )
| ( sk1
@ ^ [A: $i] : ( sk32 @ sk30 )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[3772:[bind(A,$thf( ^ [B: $i] : ( sk32 @ sk30 ) ))]]) ).
thf(13071,plain,
( ( ( sk29
@ ^ [A: $i] : $true )
!= sk30 )
| ( ( sk1
@ ^ [A: $i] : ( sk32 @ sk30 )
@ sk3 )
!= ( sk1
@ ^ [A: $i] : $false
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[3783,1799]) ).
thf(13145,plain,
( ( ( sk29
@ ^ [A: $i] : $true )
!= sk30 )
| ( ( ^ [A: $i] : ( sk32 @ sk30 ) )
!= ( ^ [A: $i] : $false ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[13071]) ).
thf(13183,plain,
( ( ( sk29
@ ^ [A: $i] : $true )
!= sk30 )
| ( ( ^ [A: $i] : ( sk32 @ sk30 ) )
!= ( ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[13145]) ).
thf(25494,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( sk1 @ A @ sk3 )
| ( B @ ( sk15 @ B @ A ) )
| ( ( sk4
@ ( sk2
@ ^ [C: $i] :
? [D: $i > $o] :
( ! [E: $i] :
( ( D @ E )
=> ( sk1 @ D @ E ) )
& ( D @ C ) )
@ sk4 ) )
!= ( B
@ ( sk2
@ ^ [C: $i] :
? [D: $i > $o] :
( ! [E: $i] :
( ( D @ E )
=> ( sk1 @ D @ E ) )
& ( D @ C ) )
@ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[283,378]) ).
thf(25590,plain,
( ~ ( sk1 @ sk4 @ sk3 )
| ( sk4 @ ( sk15 @ sk4 @ sk4 ) ) ),
inference(pre_uni,[status(thm)],[25494:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 ))]]) ).
thf(26727,plain,
( ~ $true
| ( sk4 @ ( sk15 @ sk4 @ sk4 ) ) ),
inference(rewrite,[status(thm)],[25590,12]) ).
thf(26728,plain,
sk4 @ ( sk15 @ sk4 @ sk4 ),
inference(simp,[status(thm)],[26727]) ).
thf(10534,plain,
( ( sk27 @ sk28 )
| ~ ( sk27
@ ( sk29
@ ^ [A: $i] :
~ ( sk27 @ A ) ) ) ),
inference(prim_subst,[status(thm)],[6679:[bind(A,$thf( sk27 ))]]) ).
thf(417,plain,
( ( sk4
@ ( sk2
@ ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) )
@ sk4 ) )
!= ( sk4 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[283,253]) ).
thf(421,plain,
( ( sk2
@ ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) )
@ sk4 )
!= sk5 ),
inference(simp,[status(thm)],[417]) ).
thf(940,plain,
! [B: $i > $o,A: $i] :
( ~ ( sk14 @ A )
| ~ ( B @ sk28 )
| ( ( sk1 @ sk14 @ A )
!= ( sk1 @ B @ ( sk29 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[326,888]) ).
thf(941,plain,
( ~ ( sk14 @ ( sk29 @ sk14 ) )
| ~ ( sk14 @ sk28 ) ),
inference(pattern_uni,[status(thm)],[940:[bind(A,$thf( sk29 @ sk14 )),bind(B,$thf( sk14 ))]]) ).
thf(6224,plain,
! [A: $i > $o] :
( ~ ( A @ sk28 )
| ~ ( sk14 @ sk28 )
| ( ( A @ ( sk29 @ A ) )
!= ( sk14 @ ( sk29 @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[887,941]) ).
thf(6482,plain,
( ~ ( sk14 @ sk28 )
| ~ ( sk14 @ sk28 ) ),
inference(pre_uni,[status(thm)],[6224:[bind(A,$thf( sk14 ))]]) ).
thf(6626,plain,
~ ( sk14 @ sk28 ),
inference(simp,[status(thm)],[6482]) ).
thf(1907,plain,
( ( sk32 @ sk30 )
| ( ( sk1
@ ^ [A: $i] : ( sk1 @ sk4 @ sk30 )
@ sk3 )
!= ( sk1
@ ^ [A: $i] : $false
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[1631,1799]) ).
thf(1923,plain,
( ( sk32 @ sk30 )
| ( ( ^ [A: $i] : ( sk1 @ sk4 @ sk30 ) )
!= ( ^ [A: $i] : $false ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[1907]) ).
thf(1946,plain,
( ( sk32 @ sk30 )
| ( ( ^ [A: $i] : ( sk1 @ sk4 @ sk30 ) )
!= ( ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[1923]) ).
thf(6393,plain,
( ( sk27 @ ( sk29 @ sk27 ) )
| ~ ( sk27 @ sk28 ) ),
inference(prim_subst,[status(thm)],[887:[bind(A,$thf( sk27 ))]]) ).
thf(7157,plain,
! [A: $i > $o] :
( ~ ( sk27 @ sk28 )
| ( sk1 @ A @ sk3 )
| ( ( A @ ( sk2 @ A @ sk4 ) )
!= ( sk27 @ ( sk29 @ sk27 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6393,381]) ).
thf(7175,plain,
( ~ ( sk27 @ sk28 )
| ( sk1
@ ^ [A: $i] : ( sk27 @ ( sk29 @ sk27 ) )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[7157:[bind(A,$thf( ^ [B: $i] : ( sk27 @ ( sk29 @ sk27 ) ) ))]]) ).
thf(2896,plain,
! [A: $i > $o] :
( ~ ( sk7 @ sk3 )
| ~ ( sk1 @ A @ ( sk29 @ A ) )
| ( ( sk7 @ sk65 )
!= ( A @ sk28 ) ) ),
inference(paramod_ordered,[status(thm)],[2237,888]) ).
thf(2925,plain,
( ~ ( sk7 @ sk3 )
| ~ ( sk1
@ ^ [A: $i] : ( sk7 @ sk65 )
@ ( sk29
@ ^ [A: $i] : ( sk7 @ sk65 ) ) ) ),
inference(pre_uni,[status(thm)],[2896:[bind(A,$thf( ^ [B: $i] : ( sk7 @ sk65 ) ))]]) ).
thf(102,plain,
! [D: $i > $i,C: $i > $i > $o,B: $i,A: $i > $o] :
( ( sk1
@ ( C
@ ( sk2 @ A
@ ^ [E: $i] : ( sk1 @ ( C @ E ) @ ( D @ E ) ) ) )
@ ( D
@ ( sk2 @ A
@ ^ [E: $i] : ( sk1 @ ( C @ E ) @ ( D @ E ) ) ) ) )
| ~ ( sk1
@ ^ [E: $i] : ( sk1 @ ( C @ E ) @ ( D @ E ) )
@ B )
| ( sk1 @ A @ B ) ),
inference(prim_subst,[status(thm)],[7:[bind(A,$thf( ^ [F: $i] : ( sk1 @ ( D @ F ) @ ( E @ F ) ) ))]]) ).
thf(121,plain,
! [D: $i > $i,C: $i > $i > $o,B: $i,A: $i > $o] :
( ( sk1
@ ( C
@ ( sk2 @ A
@ ^ [E: $i] : ( sk1 @ ( C @ E ) @ ( D @ E ) ) ) )
@ ( D
@ ( sk2 @ A
@ ^ [E: $i] : ( sk1 @ ( C @ E ) @ ( D @ E ) ) ) ) )
| ~ ( sk1
@ ^ [E: $i] : ( sk1 @ ( C @ E ) @ ( D @ E ) )
@ B )
| ( sk1 @ A @ B ) ),
inference(simp,[status(thm)],[102]) ).
thf(1908,plain,
( ( sk1 @ sk4 @ sk3 )
!= ( sk1
@ ^ [A: $i] : $false
@ sk3 ) ),
inference(paramod_ordered,[status(thm)],[12,1799]) ).
thf(1934,plain,
( ( sk4
!= ( ^ [A: $i] : $false ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[1908]) ).
thf(1951,plain,
( sk4
!= ( ^ [A: $i] : $false ) ),
inference(simp,[status(thm)],[1934]) ).
thf(1959,plain,
sk4 @ sk60,
inference(func_ext,[status(esa)],[1951]) ).
thf(332,plain,
! [D: $i,C: $i > $o,B: $i > $o,A: $i] :
( ~ ( sk4 @ A )
| ~ ( C @ ( sk2 @ C @ B ) )
| ( sk1 @ C @ D )
| ( ( sk1 @ sk4 @ A )
!= ( sk1 @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[9,8]) ).
thf(333,plain,
! [B: $i > $o,A: $i] :
( ~ ( sk4 @ A )
| ~ ( B @ ( sk2 @ B @ sk4 ) )
| ( sk1 @ B @ A ) ),
inference(pattern_uni,[status(thm)],[332:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(380,plain,
! [B: $i > $o,A: $i] :
( ~ ( sk4 @ A )
| ~ ( B @ ( sk2 @ B @ sk4 ) )
| ( sk1 @ B @ A ) ),
inference(simp,[status(thm)],[333]) ).
thf(24529,plain,
( ~ ( sk7 @ sk3 )
| ~ ( sk1
@ ^ [A: $i] : $true
@ ( sk29
@ ^ [A: $i] : ( sk7 @ sk65 ) ) )
| ( ( sk7 @ sk65 )
!= ( sk7 @ sk65 ) ) ),
inference(paramod_ordered,[status(thm)],[2237,2925]) ).
thf(24530,plain,
( ~ ( sk7 @ sk3 )
| ~ ( sk1
@ ^ [A: $i] : $true
@ ( sk29
@ ^ [A: $i] : ( sk7 @ sk65 ) ) ) ),
inference(pattern_uni,[status(thm)],[24529:[]]) ).
thf(28227,plain,
! [B: $i > $o,A: $i] :
( ~ ( sk4 @ A )
| ~ ( B @ ( sk2 @ B @ sk4 ) )
| ~ ( sk7 @ sk3 )
| ( ( sk1 @ B @ A )
!= ( sk1
@ ^ [C: $i] : $true
@ ( sk29
@ ^ [C: $i] : ( sk7 @ sk65 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[380,24530]) ).
thf(28228,plain,
( ~ ( sk4
@ ( sk29
@ ^ [A: $i] : ( sk7 @ sk65 ) ) )
| ~ $true
| ~ ( sk7 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[28227:[bind(A,$thf( sk29 @ ^ [C: $i] : ( sk7 @ sk65 ) )),bind(B,$thf( ^ [C: $i] : $true ))]]) ).
thf(28615,plain,
( ~ ( sk4
@ ( sk29
@ ^ [A: $i] : ( sk7 @ sk65 ) ) )
| ~ ( sk7 @ sk3 ) ),
inference(simp,[status(thm)],[28228]) ).
thf(28796,plain,
( ~ ( sk7 @ sk3 )
| ( ( sk4
@ ( sk29
@ ^ [A: $i] : ( sk7 @ sk65 ) ) )
!= ( sk4 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[1959,28615]) ).
thf(28872,plain,
( ~ ( sk7 @ sk3 )
| ( ( sk29
@ ^ [A: $i] : ( sk7 @ sk65 ) )
!= sk60 ) ),
inference(simp,[status(thm)],[28796]) ).
thf(468,plain,
! [B: $i,A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk1 @ sk7 @ B )
| ( ( sk7 @ ( sk2 @ A @ sk7 ) )
!= ( sk7 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[462,435]) ).
thf(469,plain,
! [A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk1 @ sk7 @ ( sk2 @ A @ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[468:[bind(A,$thf( C )),bind(B,$thf( sk2 @ C @ sk7 ))]]) ).
thf(480,plain,
! [A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk1 @ sk7 @ ( sk2 @ A @ sk7 ) ) ),
inference(simp,[status(thm)],[469]) ).
thf(2892,plain,
! [A: $i] :
( ~ ( sk7 @ sk3 )
| ( sk1 @ sk7 @ A )
| ( ( sk7 @ sk65 )
!= ( sk7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2237,435]) ).
thf(2893,plain,
( ~ ( sk7 @ sk3 )
| ( sk1 @ sk7 @ sk65 ) ),
inference(pattern_uni,[status(thm)],[2892:[bind(A,$thf( sk65 ))]]) ).
thf(84,plain,
! [D: $i,C: $i,B: $i > $o,A: $i > $o] :
( ~ ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( sk1 @ sk4 @ D )
| ( ( A @ ( sk2 @ B @ A ) )
!= ( sk4 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[7,9]) ).
thf(113,plain,
! [C: $i > $i,B: $i,A: $i > $o] :
( ~ ( sk1
@ ^ [D: $i] : ( sk4 @ ( C @ D ) )
@ B )
| ( sk1 @ A @ B )
| ( sk1 @ sk4
@ ( C
@ ( sk2 @ A
@ ^ [D: $i] : ( sk4 @ ( C @ D ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[84:[bind(A,$thf( ^ [F: $i] : ( sk4 @ ( E @ F ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( E @ ( sk2 @ B @ ^ [F: $i] : ( sk4 @ ( E @ F ) ) ) ))]]) ).
thf(132,plain,
! [C: $i > $i,B: $i,A: $i > $o] :
( ~ ( sk1
@ ^ [D: $i] : ( sk4 @ ( C @ D ) )
@ B )
| ( sk1 @ A @ B )
| ( sk1 @ sk4
@ ( C
@ ( sk2 @ A
@ ^ [D: $i] : ( sk4 @ ( C @ D ) ) ) ) ) ),
inference(simp,[status(thm)],[113]) ).
thf(18417,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk7
@ ( sk100
@ ^ [C: $i] : $false ) )
| ( B @ sk28 )
| ( ( sk1 @ A @ sk5 )
!= ( B
@ ( sk29
@ ^ [C: $i] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[18323,6679]) ).
thf(18442,plain,
! [A: $i > $i > $o] :
( ( sk7
@ ( sk100
@ ^ [B: $i] : $false ) )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(pre_uni,[status(thm)],[18417:[bind(A,$thf( C @ ( sk29 @ ^ [D: $i] : ~ ( sk1 @ ( C @ D ) @ sk5 ) ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) ))]]) ).
thf(18475,plain,
! [A: $i > $i > $o] :
( ( sk7
@ ( sk100
@ ^ [B: $i] : $false ) )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(simp,[status(thm)],[18442]) ).
thf(10523,plain,
( ( sk21 @ sk28 )
| ~ ( sk21
@ ( sk29
@ ^ [A: $i] :
~ ( sk21 @ A ) ) ) ),
inference(prim_subst,[status(thm)],[6679:[bind(A,$thf( sk21 ))]]) ).
thf(2460,plain,
! [A: $i > $o] :
( ~ ( sk14 @ sk3 )
| ~ ( sk1 @ A @ ( sk29 @ A ) )
| ( ( sk14 @ sk64 )
!= ( A @ sk28 ) ) ),
inference(paramod_ordered,[status(thm)],[2229,888]) ).
thf(2484,plain,
( ~ ( sk14 @ sk3 )
| ~ ( sk1
@ ^ [A: $i] : ( sk14 @ sk64 )
@ ( sk29
@ ^ [A: $i] : ( sk14 @ sk64 ) ) ) ),
inference(pre_uni,[status(thm)],[2460:[bind(A,$thf( ^ [B: $i] : ( sk14 @ sk64 ) ))]]) ).
thf(22384,plain,
( ~ ( sk14 @ sk3 )
| ~ ( sk1
@ ^ [A: $i] : $true
@ ( sk29
@ ^ [A: $i] : ( sk14 @ sk64 ) ) )
| ( ( sk14 @ sk64 )
!= ( sk14 @ sk64 ) ) ),
inference(paramod_ordered,[status(thm)],[2229,2484]) ).
thf(22385,plain,
( ~ ( sk14 @ sk3 )
| ~ ( sk1
@ ^ [A: $i] : $true
@ ( sk29
@ ^ [A: $i] : ( sk14 @ sk64 ) ) ) ),
inference(pattern_uni,[status(thm)],[22384:[]]) ).
thf(2456,plain,
! [A: $i > $o] :
( ~ ( sk14 @ sk3 )
| ( sk1 @ A @ sk3 )
| ( ( A @ ( sk2 @ A @ sk4 ) )
!= ( sk14 @ sk64 ) ) ),
inference(paramod_ordered,[status(thm)],[2229,381]) ).
thf(2483,plain,
( ~ ( sk14 @ sk3 )
| ( sk1
@ ^ [A: $i] : ( sk14 @ sk64 )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[2456:[bind(A,$thf( ^ [B: $i] : ( sk14 @ sk64 ) ))]]) ).
thf(278,plain,
! [D: $i,C: $i > $o,B: $i > $o,A: $i > $o] :
( ( sk4 @ ( sk2 @ A @ sk4 ) )
| ( B @ ( sk2 @ C @ B ) )
| ( sk1 @ C @ D )
| ( ( sk1 @ A @ sk3 )
!= ( sk1 @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[139,7]) ).
thf(279,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk4 @ ( sk2 @ A @ sk4 ) )
| ( A @ ( sk2 @ B @ A ) )
| ( sk1 @ B @ sk3 ) ),
inference(pattern_uni,[status(thm)],[278:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( sk3 ))]]) ).
thf(312,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk4 @ ( sk2 @ A @ sk4 ) )
| ( A @ ( sk2 @ B @ A ) )
| ( sk1 @ B @ sk3 ) ),
inference(simp,[status(thm)],[279]) ).
thf(2204,plain,
! [A: $i] :
( ( sk1 @ sk4 @ A )
| ( ( sk4
@ ( sk2
@ ^ [B: $i] : $false
@ sk4 ) )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1895,9]) ).
thf(2205,plain,
( sk1 @ sk4
@ ( sk2
@ ^ [A: $i] : $false
@ sk4 ) ),
inference(pattern_uni,[status(thm)],[2204:[bind(A,$thf( sk2 @ ^ [B: $i] : $false @ sk4 ))]]) ).
thf(1063,plain,
! [A: $i > $o] :
( ~ ( A @ sk28 )
| ( ( sk1 @ ( sk1 @ sk4 ) @ sk3 )
!= ( sk1 @ A @ ( sk29 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[857,888]) ).
thf(1067,plain,
! [A: $i > $o] :
( ~ ( A @ sk28 )
| ( ( sk1 @ sk4 )
!= A )
| ( ( sk29 @ A )
!= sk3 ) ),
inference(simp,[status(thm)],[1063]) ).
thf(1074,plain,
( ~ ( sk1 @ sk4 @ sk28 )
| ( ( sk29 @ ( sk1 @ sk4 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[1067]) ).
thf(15212,plain,
( ~ ( sk14 @ sk3 )
| ( ( sk1
@ ^ [A: $i] : ( sk1 @ sk14 @ sk64 )
@ sk3 )
!= ( sk1
@ ^ [A: $i] : $false
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[4679,1799]) ).
thf(15386,plain,
( ~ ( sk14 @ sk3 )
| ( ( ^ [A: $i] : ( sk1 @ sk14 @ sk64 ) )
!= ( ^ [A: $i] : $false ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[15212]) ).
thf(15449,plain,
( ~ ( sk14 @ sk3 )
| ( ( ^ [A: $i] : ( sk1 @ sk14 @ sk64 ) )
!= ( ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[15386]) ).
thf(6388,plain,
( ( sk21 @ ( sk29 @ sk21 ) )
| ~ ( sk21 @ sk28 ) ),
inference(prim_subst,[status(thm)],[887:[bind(A,$thf( sk21 ))]]) ).
thf(339,plain,
! [F: $i,E: $i > $o,D: $i > $o,C: $i,B: $i > $o,A: $i > $o] :
( ~ ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ~ ( sk1 @ D @ F )
| ( sk1 @ E @ F )
| ( ( A @ ( sk2 @ B @ A ) )
!= ( E @ ( sk2 @ E @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,8]) ).
thf(365,plain,
! [F: $i,E: $i > $o,D: $i > $o,C: $i,B: $i > $o,A: $i > $o] :
( ~ ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ~ ( sk1 @ D @ F )
| ( sk1 @ E @ F )
| ( ( A @ ( sk2 @ B @ A ) )
!= ( E @ ( sk2 @ E @ D ) ) ) ),
inference(pre_uni,[status(thm)],[339:[]]) ).
thf(366,plain,
! [F: $i,E: $i > $o,D: $i > $o,C: $i,B: $i > $o,A: $i > $o] :
( ( sk1 @ E @ F )
| ~ ( sk1 @ D @ F )
| ( sk1 @ B @ C )
| ~ ( sk1 @ A @ C )
| ( ( A @ ( sk2 @ B @ A ) )
!= ( E @ ( sk2 @ E @ D ) ) ) ),
inference(pre_uni,[status(thm)],[365:[]]) ).
thf(4518,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk1 @ B @ sk3 )
| ( ( sk7
@ ( sk2
@ ^ [C: $i] : $false
@ sk7 ) )
!= ( B @ ( sk2 @ B @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1871,381]) ).
thf(4576,plain,
! [A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk1
@ ^ [B: $i] :
( sk7
@ ( sk2
@ ^ [C: $i] : $false
@ sk7 ) )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[4518:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : ( sk7 @ ( sk2 @ ^ [D: $i] : $false @ sk7 ) ) ))]]) ).
thf(626,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ( A @ ( sk2 @ B @ A ) )
| ( sk1 @ B @ C )
| ( ( sk1 @ sk14 @ sk5 )
!= ( sk1 @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[610,7]) ).
thf(627,plain,
! [A: $i > $o] :
( ( sk14 @ ( sk2 @ A @ sk14 ) )
| ( sk1 @ A @ sk5 ) ),
inference(pattern_uni,[status(thm)],[626:[bind(A,$thf( sk14 )),bind(B,$thf( B )),bind(C,$thf( sk5 ))]]) ).
thf(631,plain,
! [A: $i > $o] :
( ( sk14 @ ( sk2 @ A @ sk14 ) )
| ( sk1 @ A @ sk5 ) ),
inference(simp,[status(thm)],[627]) ).
thf(1824,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ( sk14 @ ( sk2 @ A @ sk14 ) )
| ( sk1 @ B @ C )
| ( ( sk1 @ A @ sk5 )
!= ( sk1
@ ^ [D: $i] : $false
@ C ) ) ),
inference(paramod_ordered,[status(thm)],[631,118]) ).
thf(1825,plain,
! [A: $i > $o] :
( ( sk14
@ ( sk2
@ ^ [B: $i] : $false
@ sk14 ) )
| ( sk1 @ A @ sk5 ) ),
inference(pattern_uni,[status(thm)],[1824:[bind(A,$thf( ^ [D: $i] : $false )),bind(B,$thf( B )),bind(C,$thf( sk5 ))]]) ).
thf(1870,plain,
! [A: $i > $o] :
( ( sk14
@ ( sk2
@ ^ [B: $i] : $false
@ sk14 ) )
| ( sk1 @ A @ sk5 ) ),
inference(simp,[status(thm)],[1825]) ).
thf(4181,plain,
! [B: $i,A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk1 @ sk14 @ B )
| ( ( sk14
@ ( sk2
@ ^ [C: $i] : $false
@ sk14 ) )
!= ( sk14 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1870,326]) ).
thf(4182,plain,
! [A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk1 @ sk14
@ ( sk2
@ ^ [B: $i] : $false
@ sk14 ) ) ),
inference(pattern_uni,[status(thm)],[4181:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ^ [C: $i] : $false @ sk14 ))]]) ).
thf(10509,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk1 @ sk14
@ ( sk2
@ ^ [C: $i] : $false
@ sk14 ) )
| ( B @ sk28 )
| ( ( sk1 @ A @ sk5 )
!= ( B
@ ( sk29
@ ^ [C: $i] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4182,6679]) ).
thf(10619,plain,
! [A: $i > $i > $o] :
( ( sk1 @ sk14
@ ( sk2
@ ^ [B: $i] : $false
@ sk14 ) )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(pre_uni,[status(thm)],[10509:[bind(A,$thf( C @ ( sk29 @ ^ [D: $i] : ~ ( sk1 @ ( C @ D ) @ sk5 ) ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) ))]]) ).
thf(10697,plain,
! [A: $i > $i > $o] :
( ( sk1 @ sk14
@ ( sk2
@ ^ [B: $i] : $false
@ sk14 ) )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(simp,[status(thm)],[10619]) ).
thf(11461,plain,
! [B: $i > $o,A: $i > $i > $o] :
( ( sk1 @ ( A @ sk28 ) @ sk5 )
| ( sk1 @ B @ sk3 )
| ( ( sk1 @ sk14
@ ( sk2
@ ^ [C: $i] : $false
@ sk14 ) )
!= ( B @ ( sk2 @ B @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[10697,381]) ).
thf(11582,plain,
! [A: $i > $i > $o] :
( ( sk1 @ ( A @ sk28 ) @ sk5 )
| ( sk1
@ ^ [B: $i] :
( sk1 @ sk14
@ ( sk2
@ ^ [C: $i] : $false
@ sk14 ) )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[11461:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : ( sk1 @ sk14 @ ( sk2 @ ^ [D: $i] : $false @ sk14 ) ) ))]]) ).
thf(7127,plain,
! [A: $i > $o] :
( ~ ( sk21 @ sk28 )
| ( sk1 @ A @ sk3 )
| ( ( A @ ( sk2 @ A @ sk4 ) )
!= ( sk21 @ ( sk29 @ sk21 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6388,381]) ).
thf(7146,plain,
( ~ ( sk21 @ sk28 )
| ( sk1
@ ^ [A: $i] : ( sk21 @ ( sk29 @ sk21 ) )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[7127:[bind(A,$thf( ^ [B: $i] : ( sk21 @ ( sk29 @ sk21 ) ) ))]]) ).
thf(16616,plain,
( ~ ( sk21 @ sk28 )
| ( ( sk1
@ ^ [A: $i] : ( sk21 @ ( sk29 @ sk21 ) )
@ sk3 )
!= ( sk1
@ ^ [A: $i] : $false
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[7146,1799]) ).
thf(16685,plain,
( ~ ( sk21 @ sk28 )
| ( ( ^ [A: $i] : ( sk21 @ ( sk29 @ sk21 ) ) )
!= ( ^ [A: $i] : $false ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[16616]) ).
thf(16729,plain,
( ~ ( sk21 @ sk28 )
| ( ( ^ [A: $i] : ( sk21 @ ( sk29 @ sk21 ) ) )
!= ( ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[16685]) ).
thf(436,plain,
! [A: $i] :
( ~ ( sk7 @ A )
| ( ( sk1 @ sk7 @ A )
!= ( sk1
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[435,5]) ).
thf(445,plain,
! [A: $i] :
( ~ ( sk7 @ A )
| ( sk7
!= ( ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) ) ) )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[436]) ).
thf(450,plain,
( ~ ( sk7 @ sk3 )
| ( sk7
!= ( ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) ) ) ) ),
inference(simp,[status(thm)],[445]) ).
thf(491,plain,
( ( ( sk7 @ sk16 )
!= ( ? [A: $i > $o] :
( ! [B: $i] :
( ( A @ B )
=> ( sk1 @ A @ B ) )
& ( A @ sk16 ) ) ) )
| ~ ( sk7 @ sk3 ) ),
inference(func_ext,[status(esa)],[450]) ).
thf(536,plain,
( ~ ( sk7 @ sk3 )
| ( sk7 @ sk16 )
| ? [A: $i > $o] :
( ! [B: $i] :
( ( A @ B )
=> ( sk1 @ A @ B ) )
& ( A @ sk16 ) ) ),
inference(bool_ext,[status(thm)],[491]) ).
thf(561,plain,
( ( sk21 @ sk16 )
| ( sk7 @ sk16 )
| ~ ( sk7 @ sk3 ) ),
inference(cnf,[status(esa)],[536]) ).
thf(4150,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk1 @ B @ sk3 )
| ( ( sk14
@ ( sk2
@ ^ [C: $i] : $false
@ sk14 ) )
!= ( B @ ( sk2 @ B @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1870,381]) ).
thf(4214,plain,
! [A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk1
@ ^ [B: $i] :
( sk14
@ ( sk2
@ ^ [C: $i] : $false
@ sk14 ) )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[4150:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : ( sk14 @ ( sk2 @ ^ [D: $i] : $false @ sk14 ) ) ))]]) ).
thf(10507,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk1
@ ^ [C: $i] :
( sk14
@ ( sk2
@ ^ [D: $i] : $false
@ sk14 ) )
@ sk3 )
| ( B @ sk28 )
| ( ( sk1 @ A @ sk5 )
!= ( B
@ ( sk29
@ ^ [C: $i] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4214,6679]) ).
thf(10541,plain,
! [A: $i > $i > $o] :
( ( sk1
@ ^ [B: $i] :
( sk14
@ ( sk2
@ ^ [C: $i] : $false
@ sk14 ) )
@ sk3 )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(pre_uni,[status(thm)],[10507:[bind(A,$thf( C @ ( sk29 @ ^ [D: $i] : ~ ( sk1 @ ( C @ D ) @ sk5 ) ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) ))]]) ).
thf(10657,plain,
! [A: $i > $i > $o] :
( ( sk1
@ ^ [B: $i] :
( sk14
@ ( sk2
@ ^ [C: $i] : $false
@ sk14 ) )
@ sk3 )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(simp,[status(thm)],[10541]) ).
thf(6682,plain,
( ~ ( sk14 @ sk3 )
| ( ( sk14 @ sk64 )
!= ( sk14 @ sk28 ) ) ),
inference(paramod_ordered,[status(thm)],[2229,6626]) ).
thf(6696,plain,
( ~ ( sk14 @ sk3 )
| ( sk64 != sk28 ) ),
inference(simp,[status(thm)],[6682]) ).
thf(11356,plain,
( ( sk4
@ ( sk2
@ ^ [A: $i] : $false
@ sk4 ) )
!= ( sk4
@ ( sk29
@ ^ [A: $i] :
~ ( sk4 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[1895,11352]) ).
thf(11371,plain,
( ( sk2
@ ^ [A: $i] : $false
@ sk4 )
!= ( sk29
@ ^ [A: $i] :
~ ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[11356]) ).
thf(6399,plain,
( ( sk32 @ ( sk29 @ sk32 ) )
| ~ ( sk32 @ sk28 ) ),
inference(prim_subst,[status(thm)],[887:[bind(A,$thf( sk32 ))]]) ).
thf(7367,plain,
! [A: $i > $o] :
( ~ ( sk32 @ sk28 )
| ( sk1 @ A @ sk3 )
| ( ( A @ ( sk2 @ A @ sk4 ) )
!= ( sk32 @ ( sk29 @ sk32 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6399,381]) ).
thf(7384,plain,
( ~ ( sk32 @ sk28 )
| ( sk1
@ ^ [A: $i] : ( sk32 @ ( sk29 @ sk32 ) )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[7367:[bind(A,$thf( ^ [B: $i] : ( sk32 @ ( sk29 @ sk32 ) ) ))]]) ).
thf(17731,plain,
( ~ ( sk32 @ sk28 )
| ( ( sk1
@ ^ [A: $i] : ( sk32 @ ( sk29 @ sk32 ) )
@ sk3 )
!= ( sk1
@ ^ [A: $i] : $false
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[7384,1799]) ).
thf(17806,plain,
( ~ ( sk32 @ sk28 )
| ( ( ^ [A: $i] : ( sk32 @ ( sk29 @ sk32 ) ) )
!= ( ^ [A: $i] : $false ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[17731]) ).
thf(17844,plain,
( ~ ( sk32 @ sk28 )
| ( ( ^ [A: $i] : ( sk32 @ ( sk29 @ sk32 ) ) )
!= ( ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[17806]) ).
thf(1967,plain,
! [A: $i] :
( ( sk1 @ sk4 @ A )
| ( ( sk4 @ sk60 )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1959,9]) ).
thf(1968,plain,
sk1 @ sk4 @ sk60,
inference(pattern_uni,[status(thm)],[1967:[bind(A,$thf( sk60 ))]]) ).
thf(6730,plain,
( ( sk4
@ ( sk2
@ ^ [A: $i] : $false
@ sk4 ) )
!= ( sk4 @ sk28 ) ),
inference(paramod_ordered,[status(thm)],[1895,6666]) ).
thf(6748,plain,
( ( sk2
@ ^ [A: $i] : $false
@ sk4 )
!= sk28 ),
inference(simp,[status(thm)],[6730]) ).
thf(1233,plain,
! [B: $i > $o,A: $i] :
( ~ ( sk7 @ A )
| ( ( sk1 @ sk7 @ A )
!= ( sk1 @ B
@ ( sk29
@ ^ [C: $i] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[435,1134]) ).
thf(1234,plain,
~ ( sk7
@ ( sk29
@ ^ [A: $i] : $true ) ),
inference(pattern_uni,[status(thm)],[1233:[bind(A,$thf( sk29 @ ^ [C: $i] : $true )),bind(B,$thf( sk7 ))]]) ).
thf(1983,plain,
sk1 @ sk4 @ sk61,
inference(func_ext,[status(esa)],[1956]) ).
thf(10529,plain,
( ( sk32 @ sk28 )
| ~ ( sk32
@ ( sk29
@ ^ [A: $i] :
~ ( sk32 @ A ) ) ) ),
inference(prim_subst,[status(thm)],[6679:[bind(A,$thf( sk32 ))]]) ).
thf(5320,plain,
! [A: $i > $o] :
( ~ ( sk7 @ sk3 )
| ( sk1 @ A @ sk3 )
| ( ( A @ ( sk2 @ A @ sk4 ) )
!= ( sk1 @ sk7 @ sk65 ) ) ),
inference(paramod_ordered,[status(thm)],[2893,381]) ).
thf(5362,plain,
( ~ ( sk7 @ sk3 )
| ( sk1
@ ^ [A: $i] : ( sk1 @ sk7 @ sk65 )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[5320:[bind(A,$thf( ^ [B: $i] : ( sk1 @ sk7 @ sk65 ) ))]]) ).
thf(10531,plain,
( ( sk14 @ sk28 )
| ~ ( sk14
@ ( sk29
@ ^ [A: $i] :
~ ( sk14 @ A ) ) ) ),
inference(prim_subst,[status(thm)],[6679:[bind(A,$thf( sk14 ))]]) ).
thf(11088,plain,
( $false
| ~ ( sk14
@ ( sk29
@ ^ [A: $i] :
~ ( sk14 @ A ) ) ) ),
inference(rewrite,[status(thm)],[10531,6626]) ).
thf(11089,plain,
~ ( sk14
@ ( sk29
@ ^ [A: $i] :
~ ( sk14 @ A ) ) ),
inference(simp,[status(thm)],[11088]) ).
thf(10761,plain,
( ( ( sk29 @ ( sk1 @ sk4 ) )
!= sk3 )
| ( ( sk1 @ sk4 @ sk61 )
!= ( sk1 @ sk4 @ sk28 ) ) ),
inference(paramod_ordered,[status(thm)],[1983,1074]) ).
thf(10836,plain,
( ( ( sk29 @ ( sk1 @ sk4 ) )
!= sk3 )
| ( sk4 != sk4 )
| ( sk61 != sk28 ) ),
inference(simp,[status(thm)],[10761]) ).
thf(10880,plain,
( ( ( sk29 @ ( sk1 @ sk4 ) )
!= sk3 )
| ( sk61 != sk28 ) ),
inference(simp,[status(thm)],[10836]) ).
thf(28154,plain,
! [B: $i > $o,A: $i] :
( ~ ( sk4 @ A )
| ~ ( B @ ( sk2 @ B @ sk4 ) )
| ~ ( sk14 @ sk3 )
| ( ( sk1 @ B @ A )
!= ( sk1
@ ^ [C: $i] : $true
@ ( sk29
@ ^ [C: $i] : ( sk14 @ sk64 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[380,22385]) ).
thf(28155,plain,
( ~ ( sk4
@ ( sk29
@ ^ [A: $i] : ( sk14 @ sk64 ) ) )
| ~ $true
| ~ ( sk14 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[28154:[bind(A,$thf( sk29 @ ^ [C: $i] : ( sk14 @ sk64 ) )),bind(B,$thf( ^ [C: $i] : $true ))]]) ).
thf(28770,plain,
( ~ ( sk4
@ ( sk29
@ ^ [A: $i] : ( sk14 @ sk64 ) ) )
| ~ ( sk14 @ sk3 ) ),
inference(simp,[status(thm)],[28155]) ).
thf(28924,plain,
( ~ ( sk14 @ sk3 )
| ( ( sk4
@ ( sk29
@ ^ [A: $i] : ( sk14 @ sk64 ) ) )
!= ( sk4 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[1959,28770]) ).
thf(28967,plain,
( ~ ( sk14 @ sk3 )
| ( ( sk29
@ ^ [A: $i] : ( sk14 @ sk64 ) )
!= sk60 ) ),
inference(simp,[status(thm)],[28924]) ).
thf(5950,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk1
@ ^ [C: $i] : $false
@ B )
| ~ ( sk21 @ sk28 )
| ( ( sk1 @ A @ B )
!= ( sk1 @ sk21 @ ( sk29 @ sk21 ) ) ) ),
inference(paramod_ordered,[status(thm)],[118,948]) ).
thf(5951,plain,
( ~ ( sk1
@ ^ [A: $i] : $false
@ ( sk29 @ sk21 ) )
| ~ ( sk21 @ sk28 ) ),
inference(pattern_uni,[status(thm)],[5950:[bind(A,$thf( sk21 )),bind(B,$thf( sk29 @ sk21 ))]]) ).
thf(38364,plain,
! [A: $i > $o] :
( ( sk1 @ sk4 @ ( sk15 @ ( sk1 @ sk4 ) @ sk4 ) )
!= ( sk1 @ A
@ ( sk29
@ ^ [B: $i] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[37412,1134]) ).
thf(38410,plain,
! [A: $i > $o] :
( ( sk4 != A )
| ( ( sk15 @ ( sk1 @ sk4 ) @ sk4 )
!= ( sk29
@ ^ [B: $i] : $true ) ) ),
inference(simp,[status(thm)],[38364]) ).
thf(38442,plain,
( ( sk15 @ ( sk1 @ sk4 ) @ sk4 )
!= ( sk29
@ ^ [A: $i] : $true ) ),
inference(simp,[status(thm)],[38410]) ).
thf(104,plain,
! [C: $i > $i,B: $i,A: $i > $o] :
( ( sk7
@ ( C
@ ( sk2 @ A
@ ^ [D: $i] : ( sk7 @ ( C @ D ) ) ) ) )
| ~ ( sk1
@ ^ [D: $i] : ( sk7 @ ( C @ D ) )
@ B )
| ( sk1 @ A @ B ) ),
inference(prim_subst,[status(thm)],[7:[bind(A,$thf( ^ [E: $i] : ( sk7 @ ( D @ E ) ) ))]]) ).
thf(124,plain,
! [C: $i > $i,B: $i,A: $i > $o] :
( ( sk7
@ ( C
@ ( sk2 @ A
@ ^ [D: $i] : ( sk7 @ ( C @ D ) ) ) ) )
| ~ ( sk1
@ ^ [D: $i] : ( sk7 @ ( C @ D ) )
@ B )
| ( sk1 @ A @ B ) ),
inference(simp,[status(thm)],[104]) ).
thf(947,plain,
( ~ ( sk1 @ sk27 @ ( sk29 @ sk27 ) )
| ~ ( sk27 @ sk28 ) ),
inference(prim_subst,[status(thm)],[888:[bind(A,$thf( sk27 ))]]) ).
thf(5840,plain,
( ~ ( sk27 @ sk28 )
| ( ( sk1 @ sk27 @ ( sk29 @ sk27 ) )
!= ( sk1 @ sk4 @ sk61 ) ) ),
inference(paramod_ordered,[status(thm)],[1983,947]) ).
thf(5915,plain,
( ~ ( sk27 @ sk28 )
| ( sk27 != sk4 )
| ( ( sk29 @ sk27 )
!= sk61 ) ),
inference(simp,[status(thm)],[5840]) ).
thf(10429,plain,
! [B: $i > $o,A: $i > $i > $o] :
( ( sk7
@ ( sk2
@ ^ [C: $i] : $false
@ sk7 ) )
| ( B @ sk28 )
| ( ( sk1
@ ^ [C: $i] : ( sk1 @ ( A @ C ) @ sk5 )
@ sk3 )
!= ( B
@ ( sk29
@ ^ [C: $i] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4603,6679]) ).
thf(10600,plain,
! [A: $i > $i > $i > $o] :
( ( sk7
@ ( sk2
@ ^ [B: $i] : $false
@ sk7 ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ sk28 @ B ) @ sk5 )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[10429:[bind(A,$thf( E @ ( sk29 @ ^ [D: $i] : ~ ( sk1 @ ^ [E: $i] : ( sk1 @ ( E @ D @ E ) @ sk5 ) @ sk3 ) ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ^ [E: $i] : ( sk1 @ ( E @ D @ E ) @ sk5 ) @ sk3 ) ))]]) ).
thf(10688,plain,
! [A: $i > $i > $i > $o] :
( ( sk7
@ ( sk2
@ ^ [B: $i] : $false
@ sk7 ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ sk28 @ B ) @ sk5 )
@ sk3 ) ),
inference(simp,[status(thm)],[10600]) ).
thf(5862,plain,
( ~ ( sk27 @ sk28 )
| ( ( sk1 @ sk27 @ ( sk29 @ sk27 ) )
!= ( sk1 @ sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[438,947]) ).
thf(5905,plain,
( ~ ( sk27 @ sk28 )
| ( sk27 != sk7 )
| ( ( sk29 @ sk27 )
!= sk5 ) ),
inference(simp,[status(thm)],[5862]) ).
thf(12618,plain,
( ~ ( sk14 @ ( sk2 @ sk14 @ sk4 ) )
| ( ( sk1 @ sk14 @ sk3 )
!= ( sk1
@ ^ [A: $i] : $false
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[801,1799]) ).
thf(12684,plain,
( ~ ( sk14 @ ( sk2 @ sk14 @ sk4 ) )
| ( sk14
!= ( ^ [A: $i] : $false ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[12618]) ).
thf(12704,plain,
( ~ ( sk14 @ ( sk2 @ sk14 @ sk4 ) )
| ( sk14
!= ( ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[12684]) ).
thf(12724,plain,
( ( sk14 @ sk143 )
| ~ ( sk14 @ ( sk2 @ sk14 @ sk4 ) ) ),
inference(func_ext,[status(esa)],[12704]) ).
thf(12725,plain,
( ( sk14
!= ( ^ [A: $i] : $false ) )
| ( ( sk14 @ ( sk2 @ sk14 @ sk4 ) )
!= ( sk14 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[325,12704]) ).
thf(12739,plain,
( ( sk14
!= ( ^ [A: $i] : $false ) )
| ( ( sk2 @ sk14 @ sk4 )
!= sk5 ) ),
inference(simp,[status(thm)],[12725]) ).
thf(12756,plain,
( ( sk14 @ sk144 )
| ( ( sk2 @ sk14 @ sk4 )
!= sk5 ) ),
inference(func_ext,[status(esa)],[12739]) ).
thf(6739,plain,
( ( sk4
@ ( sk2
@ ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) )
@ sk4 ) )
!= ( sk4 @ sk28 ) ),
inference(paramod_ordered,[status(thm)],[283,6666]) ).
thf(6752,plain,
( ( sk2
@ ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) )
@ sk4 )
!= sk28 ),
inference(simp,[status(thm)],[6739]) ).
thf(1960,plain,
( ( sk4
@ ( sk29
@ ^ [A: $i] : $true ) )
!= ( sk4 @ sk60 ) ),
inference(paramod_ordered,[status(thm)],[1959,1242]) ).
thf(1974,plain,
( ( sk29
@ ^ [A: $i] : $true )
!= sk60 ),
inference(simp,[status(thm)],[1960]) ).
thf(4151,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk14
@ ( sk2
@ ^ [C: $i] : $false
@ sk14 ) )
| ( sk1 @ B @ sk3 )
| ( ( sk1 @ A @ sk5 )
!= ( B @ ( sk2 @ B @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1870,381]) ).
thf(4188,plain,
! [A: $i > $i > $o] :
( ( sk14
@ ( sk2
@ ^ [B: $i] : $false
@ sk14 ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ B ) @ sk5 )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[4151:[bind(A,$thf( C @ ( sk2 @ ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) @ sk4 ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) ))]]) ).
thf(4225,plain,
! [A: $i > $i > $o] :
( ( sk14
@ ( sk2
@ ^ [B: $i] : $false
@ sk14 ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ B ) @ sk5 )
@ sk3 ) ),
inference(simp,[status(thm)],[4188]) ).
thf(10501,plain,
! [B: $i > $o,A: $i > $i > $o] :
( ( sk14
@ ( sk2
@ ^ [C: $i] : $false
@ sk14 ) )
| ( B @ sk28 )
| ( ( sk1
@ ^ [C: $i] : ( sk1 @ ( A @ C ) @ sk5 )
@ sk3 )
!= ( B
@ ( sk29
@ ^ [C: $i] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4225,6679]) ).
thf(10552,plain,
! [A: $i > $i > $i > $o] :
( ( sk14
@ ( sk2
@ ^ [B: $i] : $false
@ sk14 ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ sk28 @ B ) @ sk5 )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[10501:[bind(A,$thf( E @ ( sk29 @ ^ [D: $i] : ~ ( sk1 @ ^ [E: $i] : ( sk1 @ ( E @ D @ E ) @ sk5 ) @ sk3 ) ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ^ [E: $i] : ( sk1 @ ( E @ D @ E ) @ sk5 ) @ sk3 ) ))]]) ).
thf(10666,plain,
! [A: $i > $i > $i > $o] :
( ( sk14
@ ( sk2
@ ^ [B: $i] : $false
@ sk14 ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ sk28 @ B ) @ sk5 )
@ sk3 ) ),
inference(simp,[status(thm)],[10552]) ).
thf(89,plain,
! [F: $i,E: $i > $o,D: $i > $o,C: $i,B: $i > $o,A: $i > $o] :
( ~ ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( D @ ( sk2 @ E @ D ) )
| ( sk1 @ E @ F )
| ( ( A @ ( sk2 @ B @ A ) )
!= ( sk1 @ D @ F ) ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(108,plain,
! [E: $i > $i,D: $i > $i > $o,C: $i > $o,B: $i,A: $i > $o] :
( ~ ( sk1
@ ^ [F: $i] : ( sk1 @ ( D @ F ) @ ( E @ F ) )
@ B )
| ( sk1 @ A @ B )
| ( D
@ ( sk2 @ A
@ ^ [F: $i] : ( sk1 @ ( D @ F ) @ ( E @ F ) ) )
@ ( sk2 @ C
@ ( D
@ ( sk2 @ A
@ ^ [F: $i] : ( sk1 @ ( D @ F ) @ ( E @ F ) ) ) ) ) )
| ( sk1 @ C
@ ( E
@ ( sk2 @ A
@ ^ [F: $i] : ( sk1 @ ( D @ F ) @ ( E @ F ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[89:[bind(A,$thf( ^ [I: $i] : ( sk1 @ ( G @ I ) @ ( H @ I ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G @ ( sk2 @ B @ ^ [I: $i] : ( sk1 @ ( G @ I ) @ ( H @ I ) ) ) )),bind(E,$thf( E )),bind(F,$thf( H @ ( sk2 @ B @ ^ [I: $i] : ( sk1 @ ( G @ I ) @ ( H @ I ) ) ) ))]]) ).
thf(128,plain,
! [E: $i > $i,D: $i > $i > $o,C: $i > $o,B: $i,A: $i > $o] :
( ~ ( sk1
@ ^ [F: $i] : ( sk1 @ ( D @ F ) @ ( E @ F ) )
@ B )
| ( sk1 @ A @ B )
| ( D
@ ( sk2 @ A
@ ^ [F: $i] : ( sk1 @ ( D @ F ) @ ( E @ F ) ) )
@ ( sk2 @ C
@ ( D
@ ( sk2 @ A
@ ^ [F: $i] : ( sk1 @ ( D @ F ) @ ( E @ F ) ) ) ) ) )
| ( sk1 @ C
@ ( E
@ ( sk2 @ A
@ ^ [F: $i] : ( sk1 @ ( D @ F ) @ ( E @ F ) ) ) ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(605,plain,
! [A: $i] :
( ~ ( sk14 @ A )
| ( ( sk1 @ sk14 @ A )
!= ( sk1
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[326,5]) ).
thf(615,plain,
! [A: $i] :
( ~ ( sk14 @ A )
| ( sk14
!= ( ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) ) ) )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[605]) ).
thf(620,plain,
( ~ ( sk14 @ sk3 )
| ( sk14
!= ( ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) ) ) ) ),
inference(simp,[status(thm)],[615]) ).
thf(633,plain,
( ( ( sk14 @ sk22 )
!= ( ? [A: $i > $o] :
( ! [B: $i] :
( ( A @ B )
=> ( sk1 @ A @ B ) )
& ( A @ sk22 ) ) ) )
| ~ ( sk14 @ sk3 ) ),
inference(func_ext,[status(esa)],[620]) ).
thf(10450,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk1
@ ^ [C: $i] :
( sk7
@ ( sk2
@ ^ [D: $i] : $false
@ sk7 ) )
@ sk3 )
| ( B @ sk28 )
| ( ( sk1 @ A @ sk5 )
!= ( B
@ ( sk29
@ ^ [C: $i] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4576,6679]) ).
thf(10602,plain,
! [A: $i > $i > $o] :
( ( sk1
@ ^ [B: $i] :
( sk7
@ ( sk2
@ ^ [C: $i] : $false
@ sk7 ) )
@ sk3 )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(pre_uni,[status(thm)],[10450:[bind(A,$thf( C @ ( sk29 @ ^ [D: $i] : ~ ( sk1 @ ( C @ D ) @ sk5 ) ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) ))]]) ).
thf(10689,plain,
! [A: $i > $i > $o] :
( ( sk1
@ ^ [B: $i] :
( sk7
@ ( sk2
@ ^ [C: $i] : $false
@ sk7 ) )
@ sk3 )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(simp,[status(thm)],[10602]) ).
thf(5982,plain,
( ~ ( sk21 @ sk28 )
| ( ( sk1 @ sk21 @ ( sk29 @ sk21 ) )
!= ( sk1 @ sk4 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[12,948]) ).
thf(6011,plain,
( ~ ( sk21 @ sk28 )
| ( sk21 != sk4 )
| ( ( sk29 @ sk21 )
!= sk3 ) ),
inference(simp,[status(thm)],[5982]) ).
thf(20210,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk14
@ ( sk102
@ ^ [C: $i] : $false ) )
| ( B @ sk28 )
| ( ( sk1 @ A @ sk5 )
!= ( B
@ ( sk29
@ ^ [C: $i] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[20108,6679]) ).
thf(20251,plain,
! [A: $i > $i > $o] :
( ( sk14
@ ( sk102
@ ^ [B: $i] : $false ) )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(pre_uni,[status(thm)],[20210:[bind(A,$thf( C @ ( sk29 @ ^ [D: $i] : ~ ( sk1 @ ( C @ D ) @ sk5 ) ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) ))]]) ).
thf(20290,plain,
! [A: $i > $i > $o] :
( ( sk14
@ ( sk102
@ ^ [B: $i] : $false ) )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(simp,[status(thm)],[20251]) ).
thf(1243,plain,
! [A: $i > $o] :
( ( sk1 @ sk14 @ sk5 )
!= ( sk1 @ A
@ ( sk29
@ ^ [B: $i] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[610,1134]) ).
thf(1268,plain,
! [A: $i > $o] :
( ( sk14 != A )
| ( ( sk29
@ ^ [B: $i] : $true )
!= sk5 ) ),
inference(simp,[status(thm)],[1243]) ).
thf(1286,plain,
( ( sk29
@ ^ [A: $i] : $true )
!= sk5 ),
inference(simp,[status(thm)],[1268]) ).
thf(800,plain,
( ~ ( sk27 @ ( sk2 @ sk27 @ sk4 ) )
| ( sk1 @ sk27 @ sk3 ) ),
inference(prim_subst,[status(thm)],[381:[bind(A,$thf( sk27 ))]]) ).
thf(12456,plain,
( ~ ( sk27 @ ( sk2 @ sk27 @ sk4 ) )
| ( ( sk1 @ sk27 @ sk3 )
!= ( sk1
@ ^ [A: $i] : $false
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[800,1799]) ).
thf(12528,plain,
( ~ ( sk27 @ ( sk2 @ sk27 @ sk4 ) )
| ( sk27
!= ( ^ [A: $i] : $false ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[12456]) ).
thf(12553,plain,
( ~ ( sk27 @ ( sk2 @ sk27 @ sk4 ) )
| ( sk27
!= ( ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[12528]) ).
thf(22325,plain,
( ~ ( sk14 @ sk3 )
| ( ( sk1
@ ^ [A: $i] : ( sk14 @ sk64 )
@ ( sk29
@ ^ [A: $i] : ( sk14 @ sk64 ) ) )
!= ( sk1
@ ^ [A: $i] : ( sk14 @ sk64 )
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[2483,2484]) ).
thf(22505,plain,
( ~ ( sk14 @ sk3 )
| ( ( ^ [A: $i] : ( sk14 @ sk64 ) )
!= ( ^ [A: $i] : ( sk14 @ sk64 ) ) )
| ( ( sk29
@ ^ [A: $i] : ( sk14 @ sk64 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[22325]) ).
thf(22669,plain,
( ~ ( sk14 @ sk3 )
| ( ( sk29
@ ^ [A: $i] : ( sk14 @ sk64 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[22505]) ).
thf(664,plain,
( ~ ( sk14 @ sk3 )
| ( sk14 @ sk22 )
| ? [A: $i > $o] :
( ! [B: $i] :
( ( A @ B )
=> ( sk1 @ A @ B ) )
& ( A @ sk22 ) ) ),
inference(bool_ext,[status(thm)],[633]) ).
thf(689,plain,
( ( sk27 @ sk22 )
| ( sk14 @ sk22 )
| ~ ( sk14 @ sk3 ) ),
inference(cnf,[status(esa)],[664]) ).
thf(7478,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk1 @ sk7
@ ( sk2
@ ^ [C: $i] : $false
@ sk7 ) )
| ( sk1 @ B @ sk3 )
| ( ( sk1 @ A @ sk5 )
!= ( B @ ( sk2 @ B @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[4521,381]) ).
thf(7584,plain,
! [A: $i > $i > $o] :
( ( sk1 @ sk7
@ ( sk2
@ ^ [B: $i] : $false
@ sk7 ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ B ) @ sk5 )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[7478:[bind(A,$thf( C @ ( sk2 @ ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) @ sk4 ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) ))]]) ).
thf(7611,plain,
! [A: $i > $i > $o] :
( ( sk1 @ sk7
@ ( sk2
@ ^ [B: $i] : $false
@ sk7 ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ B ) @ sk5 )
@ sk3 ) ),
inference(simp,[status(thm)],[7584]) ).
thf(13433,plain,
! [A: $i > $o] :
( ~ ( sk7 @ sk3 )
| ~ ( sk1
@ ^ [B: $i] : $false
@ ( sk29 @ A ) )
| ( ( sk7 @ sk65 )
!= ( A @ sk28 ) ) ),
inference(paramod_ordered,[status(thm)],[2237,1867]) ).
thf(13710,plain,
( ~ ( sk7 @ sk3 )
| ~ ( sk1
@ ^ [A: $i] : $false
@ ( sk29
@ ^ [A: $i] : ( sk7 @ sk65 ) ) ) ),
inference(pre_uni,[status(thm)],[13433:[bind(A,$thf( ^ [B: $i] : ( sk7 @ sk65 ) ))]]) ).
thf(26731,plain,
( ( sk4 @ ( sk15 @ sk4 @ sk4 ) )
!= ( sk4
@ ( sk29
@ ^ [A: $i] :
~ ( sk4 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[26728,11352]) ).
thf(26748,plain,
( ( sk15 @ sk4 @ sk4 )
!= ( sk29
@ ^ [A: $i] :
~ ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[26731]) ).
thf(337,plain,
! [F: $i,E: $i > $o,D: $i > $o,C: $i,B: $i > $o,A: $i > $o] :
( ~ ( B @ ( sk2 @ B @ A ) )
| ~ ( sk1 @ A @ C )
| ( D @ ( sk2 @ E @ D ) )
| ( sk1 @ E @ F )
| ( ( sk1 @ B @ C )
!= ( sk1 @ D @ F ) ) ),
inference(paramod_ordered,[status(thm)],[8,7]) ).
thf(338,plain,
! [D: $i > $o,C: $i,B: $i > $o,A: $i > $o] :
( ~ ( B @ ( sk2 @ B @ A ) )
| ~ ( sk1 @ A @ C )
| ( B @ ( sk2 @ D @ B ) )
| ( sk1 @ D @ C ) ),
inference(pattern_uni,[status(thm)],[337:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( E )),bind(F,$thf( C ))]]) ).
thf(382,plain,
! [D: $i > $o,C: $i,B: $i > $o,A: $i > $o] :
( ~ ( B @ ( sk2 @ B @ A ) )
| ~ ( sk1 @ A @ C )
| ( B @ ( sk2 @ D @ B ) )
| ( sk1 @ D @ C ) ),
inference(simp,[status(thm)],[338]) ).
thf(16163,plain,
( ~ ( sk7 @ sk3 )
| ( ( sk1
@ ^ [A: $i] : ( sk1 @ sk7 @ sk65 )
@ sk3 )
!= ( sk1
@ ^ [A: $i] : $false
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[5362,1799]) ).
thf(16310,plain,
( ~ ( sk7 @ sk3 )
| ( ( ^ [A: $i] : ( sk1 @ sk7 @ sk65 ) )
!= ( ^ [A: $i] : $false ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[16163]) ).
thf(16415,plain,
( ~ ( sk7 @ sk3 )
| ( ( ^ [A: $i] : ( sk1 @ sk7 @ sk65 ) )
!= ( ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[16310]) ).
thf(5854,plain,
( ~ ( sk27 @ sk28 )
| ( ( sk1 @ sk27 @ ( sk29 @ sk27 ) )
!= ( sk1 @ sk4 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[12,947]) ).
thf(5908,plain,
( ~ ( sk27 @ sk28 )
| ( sk27 != sk4 )
| ( ( sk29 @ sk27 )
!= sk3 ) ),
inference(simp,[status(thm)],[5854]) ).
thf(1257,plain,
! [B: $i > $o,A: $i] :
( ~ ( sk14 @ A )
| ( ( sk1 @ sk14 @ A )
!= ( sk1 @ B
@ ( sk29
@ ^ [C: $i] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[326,1134]) ).
thf(1258,plain,
~ ( sk14
@ ( sk29
@ ^ [A: $i] : $true ) ),
inference(pattern_uni,[status(thm)],[1257:[bind(A,$thf( sk29 @ ^ [C: $i] : $true )),bind(B,$thf( sk14 ))]]) ).
thf(7754,plain,
! [A: $i > $o] :
( ( sk14
!= ( ^ [B: $i] : $false ) )
| ~ ( sk27 @ sk28 )
| ( ( sk1 @ A @ sk5 )
!= ( sk1 @ sk27 @ ( sk29 @ sk27 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1887,947]) ).
thf(7782,plain,
! [A: $i > $o] :
( ( sk14
!= ( ^ [B: $i] : $false ) )
| ~ ( sk27 @ sk28 )
| ( A != sk27 )
| ( ( sk29 @ sk27 )
!= sk5 ) ),
inference(simp,[status(thm)],[7754]) ).
thf(7810,plain,
( ( sk14
!= ( ^ [A: $i] : $false ) )
| ~ ( sk27 @ sk28 )
| ( ( sk29 @ sk27 )
!= sk5 ) ),
inference(simp,[status(thm)],[7782]) ).
thf(12757,plain,
( ( sk14 @ sk143 )
| ( ( sk14 @ ( sk2 @ sk14 @ sk4 ) )
!= ( sk14 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[325,12724]) ).
thf(12780,plain,
( ( sk14 @ sk143 )
| ( ( sk2 @ sk14 @ sk4 )
!= sk5 ) ),
inference(simp,[status(thm)],[12757]) ).
thf(12369,plain,
( ( sk7 @ sk138 )
| ~ ( sk7 @ ( sk2 @ sk7 @ sk4 ) ) ),
inference(func_ext,[status(esa)],[12365]) ).
thf(319,plain,
! [A: $i > $o] :
( ( sk1 @ A @ sk3 )
| ( ( sk4 @ ( sk2 @ A @ sk4 ) )
!= ( sk4 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[139,253]) ).
thf(323,plain,
! [A: $i > $o] :
( ( sk1 @ A @ sk3 )
| ( ( sk2 @ A @ sk4 )
!= sk5 ) ),
inference(simp,[status(thm)],[319]) ).
thf(90,plain,
! [F: $i,E: $i > $o,D: $i > $o,C: $i,B: $i > $o,A: $i > $o] :
( ( A @ ( sk2 @ B @ A ) )
| ~ ( sk1 @ A @ C )
| ( D @ ( sk2 @ E @ D ) )
| ( sk1 @ E @ F )
| ( ( sk1 @ B @ C )
!= ( sk1 @ D @ F ) ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(91,plain,
! [D: $i > $o,C: $i,B: $i > $o,A: $i > $o] :
( ( A @ ( sk2 @ B @ A ) )
| ~ ( sk1 @ A @ C )
| ( B @ ( sk2 @ D @ B ) )
| ( sk1 @ D @ C ) ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( E )),bind(F,$thf( C ))]]) ).
thf(140,plain,
! [D: $i > $o,C: $i,B: $i > $o,A: $i > $o] :
( ( A @ ( sk2 @ B @ A ) )
| ~ ( sk1 @ A @ C )
| ( B @ ( sk2 @ D @ B ) )
| ( sk1 @ D @ C ) ),
inference(simp,[status(thm)],[91]) ).
thf(11354,plain,
( ( sk4
@ ( sk29
@ ^ [A: $i] :
~ ( sk4 @ A ) ) )
!= ( sk4 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[6,11352]) ).
thf(11375,plain,
( ( sk29
@ ^ [A: $i] :
~ ( sk4 @ A ) )
!= sk3 ),
inference(simp,[status(thm)],[11354]) ).
thf(7651,plain,
! [A: $i > $o] :
( ( sk7
!= ( ^ [B: $i] : $false ) )
| ~ ( sk21 @ sk28 )
| ( ( sk1 @ A @ sk5 )
!= ( sk1 @ sk21 @ ( sk29 @ sk21 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1883,948]) ).
thf(7683,plain,
! [A: $i > $o] :
( ( sk7
!= ( ^ [B: $i] : $false ) )
| ~ ( sk21 @ sk28 )
| ( A != sk21 )
| ( ( sk29 @ sk21 )
!= sk5 ) ),
inference(simp,[status(thm)],[7651]) ).
thf(7699,plain,
( ( sk7
!= ( ^ [A: $i] : $false ) )
| ~ ( sk21 @ sk28 )
| ( ( sk29 @ sk21 )
!= sk5 ) ),
inference(simp,[status(thm)],[7683]) ).
thf(5880,plain,
( ~ ( sk27 @ sk28 )
| ( ( sk1 @ sk27 @ ( sk29 @ sk27 ) )
!= ( sk1
@ ^ [A: $i] : $true
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[850,947]) ).
thf(5920,plain,
( ~ ( sk27 @ sk28 )
| ( sk27
!= ( ^ [A: $i] : $true ) )
| ( ( sk29 @ sk27 )
!= sk3 ) ),
inference(simp,[status(thm)],[5880]) ).
thf(25191,plain,
! [B: $i > $o,A: $i > $o] :
( ( B @ ( sk15 @ B @ A ) )
| ~ ( B
@ ( sk2
@ ^ [C: $i] :
? [D: $i > $o] :
( ! [E: $i] :
( ( D @ E )
=> ( sk1 @ D @ E ) )
& ( D @ C ) )
@ A ) )
| ( ( sk1 @ ( sk1 @ sk4 ) @ sk3 )
!= ( sk1 @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[857,378]) ).
thf(25192,plain,
! [A: $i > $o] :
( ( A @ ( sk15 @ A @ ( sk1 @ sk4 ) ) )
| ~ ( A
@ ( sk2
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ ( sk1 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[25191:[bind(A,$thf( sk1 @ sk4 )),bind(B,$thf( B ))]]) ).
thf(26295,plain,
! [A: $i > $o] :
( ( A @ ( sk15 @ A @ ( sk1 @ sk4 ) ) )
| ~ ( A
@ ( sk2
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ ( sk1 @ sk4 ) ) ) ),
inference(simp,[status(thm)],[25192]) ).
thf(33654,plain,
! [A: $i > $o] :
( ( A @ ( sk15 @ A @ ( sk1 @ sk4 ) ) )
| ( ( sk1 @ sk4
@ ( sk2
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ ( sk1 @ sk4 ) ) )
!= ( A
@ ( sk2
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ ( sk1 @ sk4 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1342,26295]) ).
thf(34269,plain,
sk1 @ sk4 @ ( sk15 @ ( sk1 @ sk4 ) @ ( sk1 @ sk4 ) ),
inference(pre_uni,[status(thm)],[33654:[bind(A,$thf( sk1 @ sk4 ))]]) ).
thf(2894,plain,
( ~ ( sk7 @ sk3 )
| ( ( sk7
@ ( sk29
@ ^ [A: $i] : $true ) )
!= ( sk7 @ sk65 ) ) ),
inference(paramod_ordered,[status(thm)],[2237,1234]) ).
thf(2923,plain,
( ~ ( sk7 @ sk3 )
| ( ( sk29
@ ^ [A: $i] : $true )
!= sk65 ) ),
inference(simp,[status(thm)],[2894]) ).
thf(98,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ( A @ ( sk2 @ B @ A ) )
| ~ ( sk1 @ A @ C )
| ( ( sk1 @ B @ C )
!= ( A @ ( sk2 @ B @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[7]) ).
thf(110,plain,
! [C: $i > $i,B: $i > $i > $o,A: $i > $o] :
( ( sk1
@ ( B
@ ( sk2 @ A
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ) )
@ ( C
@ ( sk2 @ A
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ) ) )
| ~ ( sk1
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk2 @ A
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ) ) )
| ( A
!= ( B
@ ( sk2 @ A
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[98:[bind(A,$thf( ^ [F: $i] : ( sk1 @ ( D @ F ) @ ( E @ F ) ) )),bind(B,$thf( B )),bind(C,$thf( E @ ( sk2 @ B @ ^ [F: $i] : ( sk1 @ ( D @ F ) @ ( E @ F ) ) ) ))]]) ).
thf(111,plain,
! [C: $i > $i,B: $i > $i > $o,A: $i > $o] :
( ~ ( sk1
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk2 @ A
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ) ) )
| ( sk1
@ ( B
@ ( sk2 @ A
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ) )
@ ( C
@ ( sk2 @ A
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ) ) )
| ( A
!= ( B
@ ( sk2 @ A
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[110:[]]) ).
thf(130,plain,
! [C: $i > $i,B: $i > $i > $o,A: $i > $o] :
( ~ ( sk1
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk2 @ A
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ) ) )
| ( sk1
@ ( B
@ ( sk2 @ A
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ) )
@ ( C
@ ( sk2 @ A
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ) ) )
| ( A
!= ( B
@ ( sk2 @ A
@ ^ [D: $i] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ) ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(18790,plain,
! [B: $i > $o,A: $i > $i > $o] :
( ( sk7
@ ( sk100
@ ^ [C: $i] : $false ) )
| ( B @ sk28 )
| ( ( sk1
@ ^ [C: $i] : ( sk1 @ ( A @ C ) @ sk5 )
@ sk3 )
!= ( B
@ ( sk29
@ ^ [C: $i] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[18468,6679]) ).
thf(18825,plain,
! [A: $i > $i > $i > $o] :
( ( sk7
@ ( sk100
@ ^ [B: $i] : $false ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ sk28 @ B ) @ sk5 )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[18790:[bind(A,$thf( E @ ( sk29 @ ^ [D: $i] : ~ ( sk1 @ ^ [E: $i] : ( sk1 @ ( E @ D @ E ) @ sk5 ) @ sk3 ) ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ^ [E: $i] : ( sk1 @ ( E @ D @ E ) @ sk5 ) @ sk3 ) ))]]) ).
thf(18844,plain,
! [A: $i > $i > $i > $o] :
( ( sk7
@ ( sk100
@ ^ [B: $i] : $false ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ sk28 @ B ) @ sk5 )
@ sk3 ) ),
inference(simp,[status(thm)],[18825]) ).
thf(5877,plain,
! [A: $i] :
( ~ ( sk14 @ A )
| ~ ( sk27 @ sk28 )
| ( ( sk1 @ sk14 @ A )
!= ( sk1 @ sk27 @ ( sk29 @ sk27 ) ) ) ),
inference(paramod_ordered,[status(thm)],[326,947]) ).
thf(5894,plain,
! [A: $i] :
( ~ ( sk14 @ A )
| ~ ( sk27 @ sk28 )
| ( sk27 != sk14 )
| ( A
!= ( sk29 @ sk27 ) ) ),
inference(simp,[status(thm)],[5877]) ).
thf(5931,plain,
( ~ ( sk14 @ ( sk29 @ sk27 ) )
| ~ ( sk27 @ sk28 )
| ( sk27 != sk14 ) ),
inference(simp,[status(thm)],[5894]) ).
thf(13511,plain,
! [A: $i > $o] :
( ~ ( sk14 @ sk3 )
| ~ ( sk1
@ ^ [B: $i] : $false
@ ( sk29 @ A ) )
| ( ( sk14 @ sk64 )
!= ( A @ sk28 ) ) ),
inference(paramod_ordered,[status(thm)],[2229,1867]) ).
thf(13666,plain,
( ~ ( sk14 @ sk3 )
| ~ ( sk1
@ ^ [A: $i] : $false
@ ( sk29
@ ^ [A: $i] : ( sk14 @ sk64 ) ) ) ),
inference(pre_uni,[status(thm)],[13511:[bind(A,$thf( ^ [B: $i] : ( sk14 @ sk64 ) ))]]) ).
thf(12556,plain,
( ( sk27 @ sk141 )
| ~ ( sk27 @ ( sk2 @ sk27 @ sk4 ) ) ),
inference(func_ext,[status(esa)],[12553]) ).
thf(11357,plain,
( ( sk4
@ ( sk29
@ ^ [A: $i] :
~ ( sk4 @ A ) ) )
!= ( sk4 @ sk60 ) ),
inference(paramod_ordered,[status(thm)],[1959,11352]) ).
thf(11380,plain,
( ( sk29
@ ^ [A: $i] :
~ ( sk4 @ A ) )
!= sk60 ),
inference(simp,[status(thm)],[11357]) ).
thf(427,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ( A @ ( sk2 @ B @ A ) )
| ( sk1 @ B @ C )
| ( ( sk1 @ sk4
@ ( sk2
@ ^ [D: $i] :
? [E: $i > $o] :
( ! [F: $i] :
( ( E @ F )
=> ( sk1 @ E @ F ) )
& ( E @ D ) )
@ sk4 ) )
!= ( sk1 @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[419,7]) ).
thf(428,plain,
! [A: $i > $o] :
( ( sk4 @ ( sk2 @ A @ sk4 ) )
| ( sk1 @ A
@ ( sk2
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[427:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( sk2 @ ^ [D: $i] : ? [E: $i > $o] : ( ! [F: $i] : ( ( E @ F ) => ( sk1 @ E @ F ) ) & ( E @ D ) ) @ sk4 ))]]) ).
thf(431,plain,
! [A: $i > $o] :
( ( sk4 @ ( sk2 @ A @ sk4 ) )
| ( sk1 @ A
@ ( sk2
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ sk4 ) ) ),
inference(simp,[status(thm)],[428]) ).
thf(10535,plain,
( ( sk7 @ sk28 )
| ~ ( sk7
@ ( sk29
@ ^ [A: $i] :
~ ( sk7 @ A ) ) ) ),
inference(prim_subst,[status(thm)],[6679:[bind(A,$thf( sk7 ))]]) ).
thf(11144,plain,
( $false
| ~ ( sk7
@ ( sk29
@ ^ [A: $i] :
~ ( sk7 @ A ) ) ) ),
inference(rewrite,[status(thm)],[10535,6655]) ).
thf(11145,plain,
~ ( sk7
@ ( sk29
@ ^ [A: $i] :
~ ( sk7 @ A ) ) ),
inference(simp,[status(thm)],[11144]) ).
thf(11159,plain,
( ( sk7
@ ( sk29
@ ^ [A: $i] :
~ ( sk7 @ A ) ) )
!= ( sk7 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[314,11145]) ).
thf(11161,plain,
( ( sk29
@ ^ [A: $i] :
~ ( sk7 @ A ) )
!= sk5 ),
inference(simp,[status(thm)],[11159]) ).
thf(1247,plain,
! [A: $i > $o] :
( ( sk1 @ sk4
@ ( sk2
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ sk4 ) )
!= ( sk1 @ A
@ ( sk29
@ ^ [B: $i] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[419,1134]) ).
thf(1259,plain,
! [A: $i > $o] :
( ( sk4 != A )
| ( ( sk2
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ sk4 )
!= ( sk29
@ ^ [B: $i] : $true ) ) ),
inference(simp,[status(thm)],[1247]) ).
thf(1277,plain,
( ( sk2
@ ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) )
@ sk4 )
!= ( sk29
@ ^ [A: $i] : $true ) ),
inference(simp,[status(thm)],[1259]) ).
thf(5972,plain,
! [A: $i] :
( ~ ( sk4 @ A )
| ~ ( sk21 @ sk28 )
| ( ( sk1 @ sk4 @ A )
!= ( sk1 @ sk21 @ ( sk29 @ sk21 ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,948]) ).
thf(6019,plain,
! [A: $i] :
( ~ ( sk4 @ A )
| ~ ( sk21 @ sk28 )
| ( sk21 != sk4 )
| ( A
!= ( sk29 @ sk21 ) ) ),
inference(simp,[status(thm)],[5972]) ).
thf(6056,plain,
( ~ ( sk4 @ ( sk29 @ sk21 ) )
| ~ ( sk21 @ sk28 )
| ( sk21 != sk4 ) ),
inference(simp,[status(thm)],[6019]) ).
thf(5968,plain,
! [A: $i] :
( ~ ( sk7 @ A )
| ~ ( sk21 @ sk28 )
| ( ( sk1 @ sk7 @ A )
!= ( sk1 @ sk21 @ ( sk29 @ sk21 ) ) ) ),
inference(paramod_ordered,[status(thm)],[435,948]) ).
thf(6014,plain,
! [A: $i] :
( ~ ( sk7 @ A )
| ~ ( sk21 @ sk28 )
| ( sk21 != sk7 )
| ( A
!= ( sk29 @ sk21 ) ) ),
inference(simp,[status(thm)],[5968]) ).
thf(6076,plain,
( ~ ( sk7 @ ( sk29 @ sk21 ) )
| ~ ( sk21 @ sk28 )
| ( sk21 != sk7 ) ),
inference(simp,[status(thm)],[6014]) ).
thf(103,plain,
! [D: $i > $o,C: $i > $o,B: $i,A: $i > $o] :
( ( C
@ ( sk2 @ A
@ ^ [E: $i] :
( ( C @ E )
| ( D @ E ) ) ) )
| ( D
@ ( sk2 @ A
@ ^ [E: $i] :
( ( C @ E )
| ( D @ E ) ) ) )
| ~ ( sk1
@ ^ [E: $i] :
( ( C @ E )
| ( D @ E ) )
@ B )
| ( sk1 @ A @ B ) ),
inference(prim_subst,[status(thm)],[7:[bind(A,$thf( ^ [F: $i] : ( ( D @ F ) | ( E @ F ) ) ))]]) ).
thf(122,plain,
! [D: $i > $o,C: $i > $o,B: $i,A: $i > $o] :
( ( sk1 @ A @ B )
| ~ ( sk1
@ ^ [E: $i] :
( ( C @ E )
| ( D @ E ) )
@ B )
| ( C
@ ( sk2 @ A
@ ^ [E: $i] :
( ( C @ E )
| ( D @ E ) ) ) )
| ( D
@ ( sk2 @ A
@ ^ [E: $i] :
( ( C @ E )
| ( D @ E ) ) ) ) ),
inference(cnf,[status(esa)],[103]) ).
thf(123,plain,
! [D: $i > $o,C: $i > $o,B: $i,A: $i > $o] :
( ( sk1 @ A @ B )
| ~ ( sk1
@ ^ [E: $i] :
( ( C @ E )
| ( D @ E ) )
@ B )
| ( C
@ ( sk2 @ A
@ ^ [E: $i] :
( ( C @ E )
| ( D @ E ) ) ) )
| ( D
@ ( sk2 @ A
@ ^ [E: $i] :
( ( C @ E )
| ( D @ E ) ) ) ) ),
inference(simp,[status(thm)],[122]) ).
thf(2725,plain,
( ( sk32 @ sk30 )
| ( ( sk1
@ ^ [A: $i] :
( sk1
@ ^ [B: $i] : ( sk1 @ sk4 @ sk30 )
@ sk3 )
@ sk3 )
!= ( sk1
@ ^ [A: $i] : $false
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[1729,1799]) ).
thf(2821,plain,
( ( sk32 @ sk30 )
| ( ( ^ [A: $i] :
( sk1
@ ^ [B: $i] : ( sk1 @ sk4 @ sk30 )
@ sk3 ) )
!= ( ^ [A: $i] : $false ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[2725]) ).
thf(2846,plain,
( ( sk32 @ sk30 )
| ( ( ^ [A: $i] :
( sk1
@ ^ [B: $i] : ( sk1 @ sk4 @ sk30 )
@ sk3 ) )
!= ( ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[2821]) ).
thf(5967,plain,
( ~ ( sk21 @ sk28 )
| ( ( sk1 @ sk21 @ ( sk29 @ sk21 ) )
!= ( sk1 @ sk4 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[1968,948]) ).
thf(6012,plain,
( ~ ( sk21 @ sk28 )
| ( sk21 != sk4 )
| ( ( sk29 @ sk21 )
!= sk60 ) ),
inference(simp,[status(thm)],[5967]) ).
thf(5821,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk1
@ ^ [C: $i] : $false
@ B )
| ~ ( sk27 @ sk28 )
| ( ( sk1 @ A @ B )
!= ( sk1 @ sk27 @ ( sk29 @ sk27 ) ) ) ),
inference(paramod_ordered,[status(thm)],[118,947]) ).
thf(5822,plain,
( ~ ( sk1
@ ^ [A: $i] : $false
@ ( sk29 @ sk27 ) )
| ~ ( sk27 @ sk28 ) ),
inference(pattern_uni,[status(thm)],[5821:[bind(A,$thf( sk27 )),bind(B,$thf( sk29 @ sk27 ))]]) ).
thf(10435,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk7
@ ( sk2
@ ^ [C: $i] : $false
@ sk7 ) )
| ( B @ sk28 )
| ( ( sk1 @ A @ sk5 )
!= ( B
@ ( sk29
@ ^ [C: $i] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1871,6679]) ).
thf(10596,plain,
! [A: $i > $i > $o] :
( ( sk7
@ ( sk2
@ ^ [B: $i] : $false
@ sk7 ) )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(pre_uni,[status(thm)],[10435:[bind(A,$thf( C @ ( sk29 @ ^ [D: $i] : ~ ( sk1 @ ( C @ D ) @ sk5 ) ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) ))]]) ).
thf(10685,plain,
! [A: $i > $i > $o] :
( ( sk7
@ ( sk2
@ ^ [B: $i] : $false
@ sk7 ) )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(simp,[status(thm)],[10596]) ).
thf(10453,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk1 @ sk7
@ ( sk2
@ ^ [C: $i] : $false
@ sk7 ) )
| ( B @ sk28 )
| ( ( sk1 @ A @ sk5 )
!= ( B
@ ( sk29
@ ^ [C: $i] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4521,6679]) ).
thf(10632,plain,
! [A: $i > $i > $o] :
( ( sk1 @ sk7
@ ( sk2
@ ^ [B: $i] : $false
@ sk7 ) )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(pre_uni,[status(thm)],[10453:[bind(A,$thf( C @ ( sk29 @ ^ [D: $i] : ~ ( sk1 @ ( C @ D ) @ sk5 ) ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) ))]]) ).
thf(10704,plain,
! [A: $i > $i > $o] :
( ( sk1 @ sk7
@ ( sk2
@ ^ [B: $i] : $false
@ sk7 ) )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(simp,[status(thm)],[10632]) ).
thf(5969,plain,
( ~ ( sk21 @ sk28 )
| ( ( sk1 @ sk21 @ ( sk29 @ sk21 ) )
!= ( sk1 @ sk4 @ sk61 ) ) ),
inference(paramod_ordered,[status(thm)],[1983,948]) ).
thf(6036,plain,
( ~ ( sk21 @ sk28 )
| ( sk21 != sk4 )
| ( ( sk29 @ sk21 )
!= sk61 ) ),
inference(simp,[status(thm)],[5969]) ).
thf(11368,plain,
( ( sk4
@ ( sk2
@ ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) )
@ sk4 ) )
!= ( sk4
@ ( sk29
@ ^ [A: $i] :
~ ( sk4 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[283,11352]) ).
thf(11374,plain,
( ( sk2
@ ^ [A: $i] :
? [B: $i > $o] :
( ! [C: $i] :
( ( B @ C )
=> ( sk1 @ B @ C ) )
& ( B @ A ) )
@ sk4 )
!= ( sk29
@ ^ [A: $i] :
~ ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[11368]) ).
thf(107,plain,
! [C: $i > $i,B: $i,A: $i > $o] :
( ( sk4
@ ( C
@ ( sk2 @ A
@ ^ [D: $i] : ( sk4 @ ( C @ D ) ) ) ) )
| ~ ( sk1
@ ^ [D: $i] : ( sk4 @ ( C @ D ) )
@ B )
| ( sk1 @ A @ B ) ),
inference(prim_subst,[status(thm)],[7:[bind(A,$thf( ^ [E: $i] : ( sk4 @ ( D @ E ) ) ))]]) ).
thf(127,plain,
! [C: $i > $i,B: $i,A: $i > $o] :
( ( sk4
@ ( C
@ ( sk2 @ A
@ ^ [D: $i] : ( sk4 @ ( C @ D ) ) ) ) )
| ~ ( sk1
@ ^ [D: $i] : ( sk4 @ ( C @ D ) )
@ B )
| ( sk1 @ A @ B ) ),
inference(simp,[status(thm)],[107]) ).
thf(11092,plain,
( ~ ( sk14 @ sk3 )
| ( ( sk14
@ ( sk29
@ ^ [A: $i] :
~ ( sk14 @ A ) ) )
!= ( sk14 @ sk64 ) ) ),
inference(paramod_ordered,[status(thm)],[2229,11089]) ).
thf(11109,plain,
( ~ ( sk14 @ sk3 )
| ( ( sk29
@ ^ [A: $i] :
~ ( sk14 @ A ) )
!= sk64 ) ),
inference(simp,[status(thm)],[11092]) ).
thf(9121,plain,
( ~ ( sk14 @ sk3 )
| ( ( sk1
@ ^ [A: $i] : ( sk14 @ sk64 )
@ sk3 )
!= ( sk1
@ ^ [A: $i] : $false
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[2483,1799]) ).
thf(9174,plain,
( ~ ( sk14 @ sk3 )
| ( ( ^ [A: $i] : ( sk14 @ sk64 ) )
!= ( ^ [A: $i] : $false ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[9121]) ).
thf(9220,plain,
( ~ ( sk14 @ sk3 )
| ( ( ^ [A: $i] : ( sk14 @ sk64 ) )
!= ( ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[9174]) ).
thf(5843,plain,
! [A: $i] :
( ~ ( sk4 @ A )
| ~ ( sk27 @ sk28 )
| ( ( sk1 @ sk4 @ A )
!= ( sk1 @ sk27 @ ( sk29 @ sk27 ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,947]) ).
thf(5886,plain,
! [A: $i] :
( ~ ( sk4 @ A )
| ~ ( sk27 @ sk28 )
| ( sk27 != sk4 )
| ( A
!= ( sk29 @ sk27 ) ) ),
inference(simp,[status(thm)],[5843]) ).
thf(5948,plain,
( ~ ( sk4 @ ( sk29 @ sk27 ) )
| ~ ( sk27 @ sk28 )
| ( sk27 != sk4 ) ),
inference(simp,[status(thm)],[5886]) ).
thf(13634,plain,
( ~ ( sk1
@ ^ [A: $i] : $false
@ ( sk29 @ sk32 ) )
| ~ ( sk32 @ sk28 ) ),
inference(prim_subst,[status(thm)],[1867:[bind(A,$thf( sk32 ))]]) ).
thf(1082,plain,
( ( sk1
@ ^ [A: $i] : $true
@ ( sk29
@ ^ [A: $i] : $true ) )
!= ( sk1
@ ^ [A: $i] : $true
@ sk3 ) ),
inference(paramod_ordered,[status(thm)],[850,1008]) ).
thf(1107,plain,
( ( ( ^ [A: $i] : $true )
!= ( ^ [A: $i] : $true ) )
| ( ( sk29
@ ^ [A: $i] : $true )
!= sk3 ) ),
inference(simp,[status(thm)],[1082]) ).
thf(1130,plain,
( ( sk29
@ ^ [A: $i] : $true )
!= sk3 ),
inference(simp,[status(thm)],[1107]) ).
thf(9707,plain,
! [A: $i] :
( ~ ( sk14 @ A )
| ~ ( sk27 @ sk28 )
| ( ( sk1 @ sk14 @ A )
!= ( sk1
@ ^ [B: $i] : $false
@ ( sk29 @ sk27 ) ) ) ),
inference(paramod_ordered,[status(thm)],[326,5822]) ).
thf(9776,plain,
! [A: $i] :
( ~ ( sk14 @ A )
| ~ ( sk27 @ sk28 )
| ( sk14
!= ( ^ [B: $i] : $false ) )
| ( A
!= ( sk29 @ sk27 ) ) ),
inference(simp,[status(thm)],[9707]) ).
thf(9807,plain,
( ~ ( sk14 @ ( sk29 @ sk27 ) )
| ~ ( sk27 @ sk28 )
| ( sk14
!= ( ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[9776]) ).
thf(26734,plain,
( ( sk4 @ ( sk15 @ sk4 @ sk4 ) )
!= ( sk4
@ ( sk29
@ ^ [A: $i] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[26728,1242]) ).
thf(26757,plain,
( ( sk15 @ sk4 @ sk4 )
!= ( sk29
@ ^ [A: $i] : $true ) ),
inference(simp,[status(thm)],[26734]) ).
thf(647,plain,
! [B: $i,A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk1 @ sk14 @ B )
| ( ( sk14 @ ( sk2 @ A @ sk14 ) )
!= ( sk14 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[631,326]) ).
thf(648,plain,
! [A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk1 @ sk14 @ ( sk2 @ A @ sk14 ) ) ),
inference(pattern_uni,[status(thm)],[647:[bind(A,$thf( C )),bind(B,$thf( sk2 @ C @ sk14 ))]]) ).
thf(656,plain,
! [A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk1 @ sk14 @ ( sk2 @ A @ sk14 ) ) ),
inference(simp,[status(thm)],[648]) ).
thf(7208,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk1 @ sk14
@ ( sk2
@ ^ [C: $i] : $false
@ sk14 ) )
| ( sk1 @ B @ sk3 )
| ( ( sk1 @ A @ sk5 )
!= ( B @ ( sk2 @ B @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[4182,381]) ).
thf(7269,plain,
! [A: $i > $i > $o] :
( ( sk1 @ sk14
@ ( sk2
@ ^ [B: $i] : $false
@ sk14 ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ B ) @ sk5 )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[7208:[bind(A,$thf( C @ ( sk2 @ ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) @ sk4 ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) ))]]) ).
thf(7342,plain,
! [A: $i > $i > $o] :
( ( sk1 @ sk14
@ ( sk2
@ ^ [B: $i] : $false
@ sk14 ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ B ) @ sk5 )
@ sk3 ) ),
inference(simp,[status(thm)],[7269]) ).
thf(10433,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk14
!= ( ^ [C: $i] : $false ) )
| ( B @ sk28 )
| ( ( sk1 @ A @ sk5 )
!= ( B
@ ( sk29
@ ^ [C: $i] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1887,6679]) ).
thf(10548,plain,
! [A: $i > $i > $o] :
( ( sk14
!= ( ^ [B: $i] : $false ) )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(pre_uni,[status(thm)],[10433:[bind(A,$thf( C @ ( sk29 @ ^ [D: $i] : ~ ( sk1 @ ( C @ D ) @ sk5 ) ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) ))]]) ).
thf(10663,plain,
! [A: $i > $i > $o] :
( ( sk14
!= ( ^ [B: $i] : $false ) )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(simp,[status(thm)],[10548]) ).
thf(353,plain,
! [C: $i > $i,B: $i,A: $i > $o] :
( ~ ( sk4
@ ( C
@ ( sk2
@ ^ [D: $i] : ( sk4 @ ( C @ D ) )
@ A ) ) )
| ~ ( sk1 @ A @ B )
| ( sk1
@ ^ [D: $i] : ( sk4 @ ( C @ D ) )
@ B ) ),
inference(prim_subst,[status(thm)],[8:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( sk4 @ ( D @ E ) ) ))]]) ).
thf(386,plain,
! [C: $i > $i,B: $i,A: $i > $o] :
( ~ ( sk4
@ ( C
@ ( sk2
@ ^ [D: $i] : ( sk4 @ ( C @ D ) )
@ A ) ) )
| ~ ( sk1 @ A @ B )
| ( sk1
@ ^ [D: $i] : ( sk4 @ ( C @ D ) )
@ B ) ),
inference(simp,[status(thm)],[353]) ).
thf(10455,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk7
!= ( ^ [C: $i] : $false ) )
| ( B @ sk28 )
| ( ( sk1 @ A @ sk5 )
!= ( B
@ ( sk29
@ ^ [C: $i] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1883,6679]) ).
thf(10584,plain,
! [A: $i > $i > $o] :
( ( sk7
!= ( ^ [B: $i] : $false ) )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(pre_uni,[status(thm)],[10455:[bind(A,$thf( C @ ( sk29 @ ^ [D: $i] : ~ ( sk1 @ ( C @ D ) @ sk5 ) ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) ))]]) ).
thf(10680,plain,
! [A: $i > $i > $o] :
( ( sk7
!= ( ^ [B: $i] : $false ) )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(simp,[status(thm)],[10584]) ).
thf(2462,plain,
( ~ ( sk14 @ sk3 )
| ( ( sk14
@ ( sk29
@ ^ [A: $i] : $true ) )
!= ( sk14 @ sk64 ) ) ),
inference(paramod_ordered,[status(thm)],[2229,1258]) ).
thf(2479,plain,
( ~ ( sk14 @ sk3 )
| ( ( sk29
@ ^ [A: $i] : $true )
!= sk64 ) ),
inference(simp,[status(thm)],[2462]) ).
thf(5970,plain,
( ~ ( sk21 @ sk28 )
| ( ( sk1 @ sk21 @ ( sk29 @ sk21 ) )
!= ( sk1 @ sk14 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[610,948]) ).
thf(6013,plain,
( ~ ( sk21 @ sk28 )
| ( sk21 != sk14 )
| ( ( sk29 @ sk21 )
!= sk5 ) ),
inference(simp,[status(thm)],[5970]) ).
thf(20707,plain,
! [B: $i > $o,A: $i > $i > $o] :
( ( sk14
@ ( sk102
@ ^ [C: $i] : $false ) )
| ( B @ sk28 )
| ( ( sk1
@ ^ [C: $i] : ( sk1 @ ( A @ C ) @ sk5 )
@ sk3 )
!= ( B
@ ( sk29
@ ^ [C: $i] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[20280,6679]) ).
thf(20733,plain,
! [A: $i > $i > $i > $o] :
( ( sk14
@ ( sk102
@ ^ [B: $i] : $false ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ sk28 @ B ) @ sk5 )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[20707:[bind(A,$thf( E @ ( sk29 @ ^ [D: $i] : ~ ( sk1 @ ^ [E: $i] : ( sk1 @ ( E @ D @ E ) @ sk5 ) @ sk3 ) ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ^ [E: $i] : ( sk1 @ ( E @ D @ E ) @ sk5 ) @ sk3 ) ))]]) ).
thf(20782,plain,
! [A: $i > $i > $i > $o] :
( ( sk14
@ ( sk102
@ ^ [B: $i] : $false ) )
| ( sk1
@ ^ [B: $i] : ( sk1 @ ( A @ sk28 @ B ) @ sk5 )
@ sk3 ) ),
inference(simp,[status(thm)],[20733]) ).
thf(6731,plain,
( ( sk4 @ sk60 )
!= ( sk4 @ sk28 ) ),
inference(paramod_ordered,[status(thm)],[1959,6666]) ).
thf(6743,plain,
sk60 != sk28,
inference(simp,[status(thm)],[6731]) ).
thf(2202,plain,
( ( sk4
@ ( sk2
@ ^ [A: $i] : $false
@ sk4 ) )
!= ( sk4 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[1895,253]) ).
thf(2215,plain,
( ( sk2
@ ^ [A: $i] : $false
@ sk4 )
!= sk5 ),
inference(simp,[status(thm)],[2202]) ).
thf(5839,plain,
! [A: $i] :
( ~ ( sk7 @ A )
| ~ ( sk27 @ sk28 )
| ( ( sk1 @ sk7 @ A )
!= ( sk1 @ sk27 @ ( sk29 @ sk27 ) ) ) ),
inference(paramod_ordered,[status(thm)],[435,947]) ).
thf(5904,plain,
! [A: $i] :
( ~ ( sk7 @ A )
| ~ ( sk27 @ sk28 )
| ( sk27 != sk7 )
| ( A
!= ( sk29 @ sk27 ) ) ),
inference(simp,[status(thm)],[5839]) ).
thf(5934,plain,
( ~ ( sk7 @ ( sk29 @ sk27 ) )
| ~ ( sk27 @ sk28 )
| ( sk27 != sk7 ) ),
inference(simp,[status(thm)],[5904]) ).
thf(13576,plain,
! [A: $i > $o] :
( ~ ( sk1
@ ^ [B: $i] : $false
@ ( sk29 @ A ) )
| ( ( sk7 @ sk5 )
!= ( A @ sk28 ) ) ),
inference(paramod_ordered,[status(thm)],[314,1867]) ).
thf(13718,plain,
~ ( sk1
@ ^ [A: $i] : $false
@ ( sk29
@ ^ [A: $i] : ( sk7 @ sk5 ) ) ),
inference(pre_uni,[status(thm)],[13576:[bind(A,$thf( ^ [B: $i] : ( sk7 @ sk5 ) ))]]) ).
thf(14172,plain,
~ ( sk1
@ ^ [A: $i] : $false
@ ( sk29
@ ^ [A: $i] : $true ) ),
inference(rewrite,[status(thm)],[13718,314]) ).
thf(6680,plain,
( ( sk14 @ sk28 )
!= ( sk14 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[325,6626]) ).
thf(6689,plain,
sk28 != sk5,
inference(simp,[status(thm)],[6680]) ).
thf(26736,plain,
( ( sk4 @ ( sk15 @ sk4 @ sk4 ) )
!= ( sk4 @ sk28 ) ),
inference(paramod_ordered,[status(thm)],[26728,6666]) ).
thf(26752,plain,
( ( sk15 @ sk4 @ sk4 )
!= sk28 ),
inference(simp,[status(thm)],[26736]) ).
thf(5838,plain,
( ~ ( sk27 @ sk28 )
| ( ( sk1 @ sk27 @ ( sk29 @ sk27 ) )
!= ( sk1 @ sk4 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[1968,947]) ).
thf(5922,plain,
( ~ ( sk27 @ sk28 )
| ( sk27 != sk4 )
| ( ( sk29 @ sk27 )
!= sk60 ) ),
inference(simp,[status(thm)],[5838]) ).
thf(5990,plain,
( ~ ( sk21 @ sk28 )
| ( ( sk1 @ sk21 @ ( sk29 @ sk21 ) )
!= ( sk1 @ sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[438,948]) ).
thf(6023,plain,
( ~ ( sk21 @ sk28 )
| ( sk21 != sk7 )
| ( ( sk29 @ sk21 )
!= sk5 ) ),
inference(simp,[status(thm)],[5990]) ).
thf(26733,plain,
( ( sk4 @ ( sk15 @ sk4 @ sk4 ) )
!= ( sk4 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[26728,253]) ).
thf(26754,plain,
( ( sk15 @ sk4 @ sk4 )
!= sk5 ),
inference(simp,[status(thm)],[26733]) ).
thf(25514,plain,
! [B: $i > $o,A: $i > $o] :
( ( B @ ( sk15 @ B @ A ) )
| ~ ( B
@ ( sk2
@ ^ [C: $i] :
? [D: $i > $o] :
( ! [E: $i] :
( ( D @ E )
=> ( sk1 @ D @ E ) )
& ( D @ C ) )
@ A ) )
| ( ( sk1
@ ^ [C: $i] : $true
@ sk3 )
!= ( sk1 @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[850,378]) ).
thf(25515,plain,
! [A: $i > $o] :
( ( A
@ ( sk15 @ A
@ ^ [B: $i] : $true ) )
| ~ ( A
@ ( sk2
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ ^ [B: $i] : $true ) ) ),
inference(pattern_uni,[status(thm)],[25514:[bind(A,$thf( ^ [C: $i] : $true ))]]) ).
thf(26317,plain,
! [A: $i > $o] :
( ( A
@ ( sk15 @ A
@ ^ [B: $i] : $true ) )
| ~ ( A
@ ( sk2
@ ^ [B: $i] :
? [C: $i > $o] :
( ! [D: $i] :
( ( C @ D )
=> ( sk1 @ C @ D ) )
& ( C @ B ) )
@ ^ [B: $i] : $true ) ) ),
inference(simp,[status(thm)],[25515]) ).
thf(6008,plain,
( ~ ( sk21 @ sk28 )
| ( ( sk1 @ sk21 @ ( sk29 @ sk21 ) )
!= ( sk1
@ ^ [A: $i] : $true
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[850,948]) ).
thf(6045,plain,
( ~ ( sk21 @ sk28 )
| ( sk21
!= ( ^ [A: $i] : $true ) )
| ( ( sk29 @ sk21 )
!= sk3 ) ),
inference(simp,[status(thm)],[6008]) ).
thf(342,plain,
! [F: $i,E: $i > $o,D: $i > $o,C: $i,B: $i > $o,A: $i > $o] :
( ( A @ ( sk2 @ B @ A ) )
| ~ ( sk1 @ A @ C )
| ~ ( E @ ( sk2 @ E @ D ) )
| ( sk1 @ E @ F )
| ( ( sk1 @ B @ C )
!= ( sk1 @ D @ F ) ) ),
inference(paramod_ordered,[status(thm)],[7,8]) ).
thf(343,plain,
! [D: $i > $o,C: $i,B: $i > $o,A: $i > $o] :
( ( A @ ( sk2 @ B @ A ) )
| ~ ( sk1 @ A @ C )
| ~ ( D @ ( sk2 @ D @ B ) )
| ( sk1 @ D @ C ) ),
inference(pattern_uni,[status(thm)],[342:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( E )),bind(F,$thf( C ))]]) ).
thf(383,plain,
! [D: $i > $o,C: $i,B: $i > $o,A: $i > $o] :
( ( A @ ( sk2 @ B @ A ) )
| ~ ( sk1 @ A @ C )
| ~ ( D @ ( sk2 @ D @ B ) )
| ( sk1 @ D @ C ) ),
inference(simp,[status(thm)],[343]) ).
thf(9651,plain,
! [A: $i] :
( ~ ( sk7 @ A )
| ~ ( sk27 @ sk28 )
| ( ( sk1 @ sk7 @ A )
!= ( sk1
@ ^ [B: $i] : $false
@ ( sk29 @ sk27 ) ) ) ),
inference(paramod_ordered,[status(thm)],[435,5822]) ).
thf(9757,plain,
! [A: $i] :
( ~ ( sk7 @ A )
| ~ ( sk27 @ sk28 )
| ( sk7
!= ( ^ [B: $i] : $false ) )
| ( A
!= ( sk29 @ sk27 ) ) ),
inference(simp,[status(thm)],[9651]) ).
thf(9799,plain,
( ~ ( sk7 @ ( sk29 @ sk27 ) )
| ~ ( sk27 @ sk28 )
| ( sk7
!= ( ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[9757]) ).
thf(13556,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( A @ sk28 )
| ~ ( B @ sk28 )
| ( ( A @ ( sk29 @ A ) )
!= ( sk1
@ ^ [C: $i] : $false
@ ( sk29 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[887,1867]) ).
thf(13837,plain,
( ~ ( sk1
@ ^ [A: $i] : $false
@ sk28 )
| ~ ( sk1
@ ^ [A: $i] : $false
@ sk28 ) ),
inference(pre_uni,[status(thm)],[13556:[bind(A,$thf( sk1 @ ^ [C: $i] : $false )),bind(B,$thf( sk1 @ ^ [C: $i] : $false ))]]) ).
thf(13855,plain,
~ ( sk1
@ ^ [A: $i] : $false
@ sk28 ),
inference(simp,[status(thm)],[13837]) ).
thf(100,plain,
! [B: $i,A: $i > $o] :
( ( sk4 @ ( sk2 @ A @ sk4 ) )
| ~ ( sk1 @ sk4 @ B )
| ( sk1 @ A @ B ) ),
inference(prim_subst,[status(thm)],[7:[bind(A,$thf( sk4 ))]]) ).
thf(119,plain,
! [B: $i,A: $i > $o] :
( ( sk4 @ ( sk2 @ A @ sk4 ) )
| ~ ( sk1 @ sk4 @ B )
| ( sk1 @ A @ B ) ),
inference(simp,[status(thm)],[100]) ).
thf(11149,plain,
( ~ ( sk7 @ sk3 )
| ( ( sk7
@ ( sk29
@ ^ [A: $i] :
~ ( sk7 @ A ) ) )
!= ( sk7 @ sk65 ) ) ),
inference(paramod_ordered,[status(thm)],[2237,11145]) ).
thf(11167,plain,
( ~ ( sk7 @ sk3 )
| ( ( sk29
@ ^ [A: $i] :
~ ( sk7 @ A ) )
!= sk65 ) ),
inference(simp,[status(thm)],[11149]) ).
thf(6005,plain,
! [A: $i] :
( ~ ( sk14 @ A )
| ~ ( sk21 @ sk28 )
| ( ( sk1 @ sk14 @ A )
!= ( sk1 @ sk21 @ ( sk29 @ sk21 ) ) ) ),
inference(paramod_ordered,[status(thm)],[326,948]) ).
thf(6016,plain,
! [A: $i] :
( ~ ( sk14 @ A )
| ~ ( sk21 @ sk28 )
| ( sk21 != sk14 )
| ( A
!= ( sk29 @ sk21 ) ) ),
inference(simp,[status(thm)],[6005]) ).
thf(6055,plain,
( ~ ( sk14 @ ( sk29 @ sk21 ) )
| ~ ( sk21 @ sk28 )
| ( sk21 != sk14 ) ),
inference(simp,[status(thm)],[6016]) ).
thf(894,plain,
! [A: $i > $o] :
( ~ ( sk1 @ A @ ( sk29 @ A ) )
| ( ( sk1 @ sk4 @ sk3 )
!= ( A @ sk28 ) ) ),
inference(paramod_ordered,[status(thm)],[12,888]) ).
thf(977,plain,
~ ( sk1
@ ^ [A: $i] : ( sk1 @ sk4 @ sk3 )
@ ( sk29
@ ^ [A: $i] : ( sk1 @ sk4 @ sk3 ) ) ),
inference(pre_uni,[status(thm)],[894:[bind(A,$thf( ^ [B: $i] : ( sk1 @ sk4 @ sk3 ) ))]]) ).
thf(1380,plain,
~ ( sk1
@ ^ [A: $i] : $true
@ ( sk29
@ ^ [A: $i] : $true ) ),
inference(rewrite,[status(thm)],[977,12]) ).
thf(24591,plain,
( ~ ( sk7 @ sk3 )
| ( ( sk1
@ ^ [A: $i] : ( sk7 @ sk65 )
@ ( sk29
@ ^ [A: $i] : ( sk7 @ sk65 ) ) )
!= ( sk1
@ ^ [A: $i] : ( sk7 @ sk65 )
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[2915,2925]) ).
thf(24780,plain,
( ~ ( sk7 @ sk3 )
| ( ( ^ [A: $i] : ( sk7 @ sk65 ) )
!= ( ^ [A: $i] : ( sk7 @ sk65 ) ) )
| ( ( sk29
@ ^ [A: $i] : ( sk7 @ sk65 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[24591]) ).
thf(24873,plain,
( ~ ( sk7 @ sk3 )
| ( ( sk29
@ ^ [A: $i] : ( sk7 @ sk65 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[24780]) ).
thf(36375,plain,
! [A: $i > $o] :
( ( sk1 @ sk4 @ ( sk15 @ ( sk1 @ sk4 ) @ ( sk1 @ sk4 ) ) )
!= ( sk1 @ A
@ ( sk29
@ ^ [B: $i] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[34269,1134]) ).
thf(36411,plain,
! [A: $i > $o] :
( ( sk4 != A )
| ( ( sk15 @ ( sk1 @ sk4 ) @ ( sk1 @ sk4 ) )
!= ( sk29
@ ^ [B: $i] : $true ) ) ),
inference(simp,[status(thm)],[36375]) ).
thf(36454,plain,
( ( sk15 @ ( sk1 @ sk4 ) @ ( sk1 @ sk4 ) )
!= ( sk29
@ ^ [A: $i] : $true ) ),
inference(simp,[status(thm)],[36411]) ).
thf(7660,plain,
! [A: $i > $o] :
( ( sk7
!= ( ^ [B: $i] : $false ) )
| ~ ( sk27 @ sk28 )
| ( ( sk1 @ A @ sk5 )
!= ( sk1 @ sk27 @ ( sk29 @ sk27 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1883,947]) ).
thf(7679,plain,
! [A: $i > $o] :
( ( sk7
!= ( ^ [B: $i] : $false ) )
| ~ ( sk27 @ sk28 )
| ( A != sk27 )
| ( ( sk29 @ sk27 )
!= sk5 ) ),
inference(simp,[status(thm)],[7660]) ).
thf(7727,plain,
( ( sk7
!= ( ^ [A: $i] : $false ) )
| ~ ( sk27 @ sk28 )
| ( ( sk29 @ sk27 )
!= sk5 ) ),
inference(simp,[status(thm)],[7679]) ).
thf(12419,plain,
( ( sk7 @ sk138 )
| ( ( sk7 @ ( sk2 @ sk7 @ sk4 ) )
!= ( sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[314,12369]) ).
thf(12431,plain,
( ( sk7 @ sk138 )
| ( ( sk2 @ sk7 @ sk4 )
!= sk5 ) ),
inference(simp,[status(thm)],[12419]) ).
thf(106,plain,
! [C: $i > $o,B: $i,A: $i > $o] :
( ~ ( C
@ ( sk2 @ A
@ ^ [D: $i] :
~ ( C @ D ) ) )
| ~ ( sk1
@ ^ [D: $i] :
~ ( C @ D )
@ B )
| ( sk1 @ A @ B ) ),
inference(prim_subst,[status(thm)],[7:[bind(A,$thf( ^ [E: $i] : ~ ( D @ E ) ))]]) ).
thf(125,plain,
! [C: $i > $o,B: $i,A: $i > $o] :
( ( sk1 @ A @ B )
| ~ ( sk1
@ ^ [D: $i] :
~ ( C @ D )
@ B )
| ~ ( C
@ ( sk2 @ A
@ ^ [D: $i] :
~ ( C @ D ) ) ) ),
inference(cnf,[status(esa)],[106]) ).
thf(126,plain,
! [C: $i > $o,B: $i,A: $i > $o] :
( ( sk1 @ A @ B )
| ~ ( sk1
@ ^ [D: $i] :
~ ( C @ D )
@ B )
| ~ ( C
@ ( sk2 @ A
@ ^ [D: $i] :
~ ( C @ D ) ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(1965,plain,
( ( sk4 @ sk60 )
!= ( sk4 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[1959,253]) ).
thf(1977,plain,
sk60 != sk5,
inference(simp,[status(thm)],[1965]) ).
thf(26737,plain,
! [A: $i] :
( ( sk1 @ sk4 @ A )
| ( ( sk4 @ ( sk15 @ sk4 @ sk4 ) )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[26728,9]) ).
thf(26738,plain,
sk1 @ sk4 @ ( sk15 @ sk4 @ sk4 ),
inference(pattern_uni,[status(thm)],[26737:[bind(A,$thf( sk15 @ sk4 @ sk4 ))]]) ).
thf(17048,plain,
( ~ ( sk27 @ sk28 )
| ( ( sk1
@ ^ [A: $i] : ( sk27 @ ( sk29 @ sk27 ) )
@ sk3 )
!= ( sk1
@ ^ [A: $i] : $false
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[7175,1799]) ).
thf(17134,plain,
( ~ ( sk27 @ sk28 )
| ( ( ^ [A: $i] : ( sk27 @ ( sk29 @ sk27 ) ) )
!= ( ^ [A: $i] : $false ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[17048]) ).
thf(17177,plain,
( ~ ( sk27 @ sk28 )
| ( ( ^ [A: $i] : ( sk27 @ ( sk29 @ sk27 ) ) )
!= ( ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[17134]) ).
thf(5841,plain,
( ~ ( sk27 @ sk28 )
| ( ( sk1 @ sk27 @ ( sk29 @ sk27 ) )
!= ( sk1 @ sk14 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[610,947]) ).
thf(5891,plain,
( ~ ( sk27 @ sk28 )
| ( sk27 != sk14 )
| ( ( sk29 @ sk27 )
!= sk5 ) ),
inference(simp,[status(thm)],[5841]) ).
thf(6704,plain,
( ~ ( sk7 @ sk3 )
| ( ( sk7 @ sk65 )
!= ( sk7 @ sk28 ) ) ),
inference(paramod_ordered,[status(thm)],[2237,6655]) ).
thf(6718,plain,
( ~ ( sk7 @ sk3 )
| ( sk65 != sk28 ) ),
inference(simp,[status(thm)],[6704]) ).
thf(2037,plain,
! [A: $i > $o] :
( ( sk1 @ sk4 @ sk61 )
!= ( sk1 @ A
@ ( sk29
@ ^ [B: $i] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[1983,1134]) ).
thf(2045,plain,
! [A: $i > $o] :
( ( sk4 != A )
| ( ( sk29
@ ^ [B: $i] : $true )
!= sk61 ) ),
inference(simp,[status(thm)],[2037]) ).
thf(2059,plain,
( ( sk29
@ ^ [A: $i] : $true )
!= sk61 ),
inference(simp,[status(thm)],[2045]) ).
thf(7209,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk1 @ B @ sk3 )
| ( ( sk1 @ sk14
@ ( sk2
@ ^ [C: $i] : $false
@ sk14 ) )
!= ( B @ ( sk2 @ B @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[4182,381]) ).
thf(7274,plain,
! [A: $i > $o] :
( ( sk1 @ A @ sk5 )
| ( sk1
@ ^ [B: $i] :
( sk1 @ sk14
@ ( sk2
@ ^ [C: $i] : $false
@ sk14 ) )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[7209:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : ( sk1 @ sk14 @ ( sk2 @ ^ [D: $i] : $false @ sk14 ) ) ))]]) ).
thf(11090,plain,
( ( sk14
@ ( sk29
@ ^ [A: $i] :
~ ( sk14 @ A ) ) )
!= ( sk14 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[325,11089]) ).
thf(11103,plain,
( ( sk29
@ ^ [A: $i] :
~ ( sk14 @ A ) )
!= sk5 ),
inference(simp,[status(thm)],[11090]) ).
thf(10519,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk14
@ ( sk2
@ ^ [C: $i] : $false
@ sk14 ) )
| ( B @ sk28 )
| ( ( sk1 @ A @ sk5 )
!= ( B
@ ( sk29
@ ^ [C: $i] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1870,6679]) ).
thf(10559,plain,
! [A: $i > $i > $o] :
( ( sk14
@ ( sk2
@ ^ [B: $i] : $false
@ sk14 ) )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(pre_uni,[status(thm)],[10519:[bind(A,$thf( C @ ( sk29 @ ^ [D: $i] : ~ ( sk1 @ ( C @ D ) @ sk5 ) ) )),bind(B,$thf( ^ [D: $i] : ( sk1 @ ( C @ D ) @ sk5 ) ))]]) ).
thf(10669,plain,
! [A: $i > $i > $o] :
( ( sk14
@ ( sk2
@ ^ [B: $i] : $false
@ sk14 ) )
| ( sk1 @ ( A @ sk28 ) @ sk5 ) ),
inference(simp,[status(thm)],[10559]) ).
thf(45593,plain,
$false,
inference(e,[status(thm)],[138,7569,11895,1729,12440,1956,11352,9573,6744,1073,5,4603,120,379,7813,385,384,1867,797,6655,1342,20280,37412,4679,1475,1887,320,12339,18468,1871,2217,12682,13183,325,26728,1379,10534,421,6626,2237,1946,7175,253,2925,121,28872,480,2893,2469,132,1242,18475,10523,22385,2483,312,2205,1074,6,380,15449,381,6388,366,4576,12365,7730,11582,28615,16729,561,10657,4521,6696,11371,1883,17844,20108,1968,435,1951,6666,6748,1234,1983,10529,948,9,5362,11089,610,10880,857,28967,5951,38442,884,124,5915,10688,5905,12724,12756,6752,1974,1799,1947,10666,12393,128,633,311,10689,24530,6011,20290,1286,12553,2915,1895,888,22669,1959,12704,7636,689,17,1631,7611,13710,26748,118,12,382,16415,5908,3783,1258,947,2229,7810,419,7,12780,12369,631,323,140,26303,462,11375,7699,5920,34269,2923,130,18844,5931,13666,12556,11380,3,438,431,1076,11161,795,1277,1134,6056,6076,123,2846,11872,6012,5822,10685,6399,887,10704,6036,1637,11374,127,11109,9220,5948,13634,1130,9807,26757,6679,656,7342,10663,386,4225,314,10680,7146,450,2479,6013,20782,6743,2215,5934,14172,10697,6689,26752,11145,5922,6023,26754,139,7384,4214,26317,6045,28770,383,9799,13855,800,4182,8,119,378,11167,6055,12739,1380,24873,620,36454,7727,326,12431,6393,283,126,801,26295,1977,26738,1532,18323,17177,2484,850,5891,1945,6718,2059,7274,491,11103,10669,1870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV245^5 : TPTP v8.2.0. Released v4.0.0.
% 0.00/0.09 % Command : run_Leo-III %s %d THM
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Fri Jun 21 19:00:55 EDT 2024
% 0.09/0.28 % CPUTime :
% 0.73/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.04/0.88 % [INFO] Parsing done (108ms).
% 1.10/0.88 % [INFO] Running in sequential loop mode.
% 1.44/1.09 % [INFO] eprover registered as external prover.
% 1.44/1.10 % [INFO] Scanning for conjecture ...
% 1.44/1.16 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.65/1.19 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.65/1.19 % [INFO] Problem is higher-order (TPTP THF).
% 1.71/1.19 % [INFO] Type checking passed.
% 1.71/1.20 % [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 ...
% 129.74/33.84 % External prover 'e' found a proof!
% 129.74/33.84 % [INFO] Killing All external provers ...
% 129.74/33.84 % Time passed: 33426ms (effective reasoning time: 32952ms)
% 129.74/33.84 % 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)>
% 129.74/33.84 % Axioms used in derivation (0):
% 129.74/33.84 % No. of inferences in proof: 625
% 129.74/33.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 33426 ms resp. 32952 ms w/o parsing
% 130.00/34.04 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 130.00/34.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------