TSTP Solution File: SEV094^5 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV094^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n022.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 15:58:12 EDT 2024
% Result : Theorem 77.55s 18.55s
% Output : Refutation 77.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 1
% Syntax : Number of formulae : 443 ( 104 unt; 0 typ; 0 def)
% Number of atoms : 1246 ( 345 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 4376 ( 599 ~; 420 |; 24 &;3312 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 214 ( 214 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 1345 (1056 ^ 277 !; 12 ?;1345 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_type,type,
sk1: a > $o ).
thf(sk2_type,type,
sk2: a > $o ).
thf(sk3_type,type,
sk3: a > a ).
thf(sk4_type,type,
sk4: a > a ).
thf(sk5_type,type,
sk5: ( a > a ) > $o ).
thf(sk6_type,type,
sk6: ( a > a ) > a ).
thf(sk7_type,type,
sk7: ( a > a ) > a ).
thf(sk8_type,type,
sk8: a > ( a > a ) > a ).
thf(sk11_type,type,
sk11: a ).
thf(sk12_type,type,
sk12: a ).
thf(sk13_type,type,
sk13: a ).
thf(sk14_type,type,
sk14: a ).
thf(sk15_type,type,
sk15: a ).
thf(sk16_type,type,
sk16: a ).
thf(sk21_type,type,
sk21: a ).
thf(sk22_type,type,
sk22: a ).
thf(sk25_type,type,
sk25: a ).
thf(1,conjecture,
! [A: a > $o,B: a > $o] :
( ? [C: a > a] :
( ! [D: a] :
( ( A @ D )
=> ( B @ ( C @ D ) ) )
& ! [D: a] :
( ( B @ D )
=> ? [E: a] :
( ( A @ E )
& ( D
= ( C @ E ) )
& ! [F: a] :
( ( ( A @ F )
& ( D
= ( C @ F ) ) )
=> ( F = E ) ) ) ) )
=> ? [C: a > a] :
( ! [D: a] :
( ( B @ D )
=> ( A @ ( C @ D ) ) )
& ! [D: a] :
( ( A @ D )
=> ? [E: a] :
( ( B @ E )
& ( D
= ( C @ E ) )
& ! [F: a] :
( ( ( B @ F )
& ( D
= ( C @ F ) ) )
=> ( F = E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEQP1_1B_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o,B: a > $o] :
( ? [C: a > a] :
( ! [D: a] :
( ( A @ D )
=> ( B @ ( C @ D ) ) )
& ! [D: a] :
( ( B @ D )
=> ? [E: a] :
( ( A @ E )
& ( D
= ( C @ E ) )
& ! [F: a] :
( ( ( A @ F )
& ( D
= ( C @ F ) ) )
=> ( F = E ) ) ) ) )
=> ? [C: a > a] :
( ! [D: a] :
( ( B @ D )
=> ( A @ ( C @ D ) ) )
& ! [D: a] :
( ( A @ D )
=> ? [E: a] :
( ( B @ E )
& ( D
= ( C @ E ) )
& ! [F: a] :
( ( ( B @ F )
& ( D
= ( C @ F ) ) )
=> ( F = E ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o,B: a > $o] :
( ? [C: a > a] :
( ! [D: a] :
( ( A @ D )
=> ( B @ ( C @ D ) ) )
& ! [D: a] :
( ( B @ D )
=> ? [E: a] :
( ( A @ E )
& ( D
= ( C @ E ) )
& ! [F: a] :
( ( ( A @ F )
& ( D
= ( C @ F ) ) )
=> ( F = E ) ) ) ) )
=> ? [C: a > a] :
( ! [D: a] :
( ( B @ D )
=> ( A @ ( C @ D ) ) )
& ! [D: a] :
( ( A @ D )
=> ? [E: a] :
( ( B @ E )
& ( D
= ( C @ E ) )
& ! [F: a] :
( ( ( B @ F )
& ( D
= ( C @ F ) ) )
=> ( F = E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,plain,
! [A: a > a] :
( ( sk5 @ A )
| ( sk1 @ ( sk7 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(19,plain,
! [A: a > a] :
( ( sk5 @ A )
| ( sk1 @ ( sk7 @ A ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(6,plain,
! [A: a > a] :
( ~ ( sk1 @ ( A @ ( sk6 @ A ) ) )
| ~ ( sk5 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(15,plain,
! [A: a > a] :
( ~ ( sk1 @ ( A @ ( sk6 @ A ) ) )
| ~ ( sk5 @ A ) ),
inference(simp,[status(thm)],[6]) ).
thf(45,plain,
! [B: a > a,A: a > a] :
( ( sk5 @ A )
| ~ ( sk5 @ B )
| ( ( sk1 @ ( sk7 @ A ) )
!= ( sk1 @ ( B @ ( sk6 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,15]) ).
thf(47,plain,
! [A: a > a > a] :
( ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ),
inference(pre_uni,[status(thm)],[45:[bind(A,$thf( C @ ( sk6 @ ^ [D: a] : ( sk7 @ ( C @ D ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk7 @ ( C @ D ) ) ))]]) ).
thf(49,plain,
! [A: a > a > a] :
( ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(10,plain,
! [A: a > a] :
( ( sk2 @ ( sk6 @ A ) )
| ~ ( sk5 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(14,plain,
! [A: a > a] :
( ( sk2 @ ( sk6 @ A ) )
| ~ ( sk5 @ A ) ),
inference(simp,[status(thm)],[10]) ).
thf(13,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk1 @ ( sk4 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(18,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk1 @ ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(42,plain,
! [B: a > a,A: a] :
( ~ ( sk2 @ A )
| ~ ( sk5 @ B )
| ( ( sk1 @ ( sk4 @ A ) )
!= ( sk1 @ ( B @ ( sk6 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,15]) ).
thf(46,plain,
! [A: a > a] :
( ~ ( sk2
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( A @ B ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( A @ B ) ) ) ),
inference(pre_uni,[status(thm)],[42:[bind(A,$thf( C @ ( sk6 @ ^ [D: a] : ( sk4 @ ( C @ D ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk4 @ ( C @ D ) ) ))]]) ).
thf(48,plain,
! [A: a > a] :
( ~ ( sk2
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( A @ B ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(51,plain,
! [B: a > a,A: a > a] :
( ~ ( sk5 @ A )
| ~ ( sk5
@ ^ [C: a] : ( sk4 @ ( B @ C ) ) )
| ( ( sk2 @ ( sk6 @ A ) )
!= ( sk2
@ ( B
@ ( sk6
@ ^ [C: a] : ( sk4 @ ( B @ C ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,48]) ).
thf(55,plain,
! [A: a > a > a] :
( ~ ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk6 @ ( A @ B ) ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk6 @ ( A @ B ) ) ) ) ),
inference(pre_uni,[status(thm)],[51:[bind(A,$thf( C @ ( sk6 @ ^ [D: a] : ( sk4 @ ( sk6 @ ( C @ D ) ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk6 @ ( C @ D ) ) ))]]) ).
thf(59,plain,
! [A: a > a > a] :
( ~ ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk6 @ ( A @ B ) ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk6 @ ( A @ B ) ) ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(3948,plain,
! [B: a > a > a,A: a > a > a] :
( ~ ( sk5
@ ^ [C: a] : ( sk7 @ ( A @ C ) ) )
| ~ ( sk5
@ ( B
@ ( sk6
@ ^ [C: a] : ( sk4 @ ( sk6 @ ( B @ C ) ) ) ) ) )
| ( ( sk5
@ ( A
@ ( sk6
@ ^ [C: a] : ( sk7 @ ( A @ C ) ) ) ) )
!= ( sk5
@ ^ [C: a] : ( sk4 @ ( sk6 @ ( B @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,59]) ).
thf(3963,plain,
( ~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) )
| ~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) ),
inference(pre_uni,[status(thm)],[3948:[bind(A,$thf( ^ [C: a] : ^ [D: a] : ( sk4 @ C ) )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk4 @ D ) ) ))]]) ).
thf(3979,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[3963]) ).
thf(3987,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,3979]) ).
thf(3988,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[3987:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk4 @ B ) ) ))]]) ).
thf(7,plain,
! [B: a,A: a > a] :
( ( sk5 @ A )
| ~ ( sk2 @ B )
| ( ( sk7 @ A )
!= ( A @ B ) )
| ( ( sk7 @ A )
= ( A @ ( sk8 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(20,plain,
! [B: a,A: a > a] :
( ( ( sk7 @ A )
!= ( A @ B ) )
| ( ( A @ ( sk8 @ B @ A ) )
= ( sk7 @ A ) )
| ( sk5 @ A )
| ~ ( sk2 @ B ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(21,plain,
! [B: a,A: a > a] :
( ( ( sk7 @ A )
!= ( A @ B ) )
| ( ( A @ ( sk8 @ B @ A ) )
= ( sk7 @ A ) )
| ( sk5 @ A )
| ~ ( sk2 @ B ) ),
inference(simp,[status(thm)],[20]) ).
thf(4,plain,
! [B: a,A: a > a] :
( ( sk5 @ A )
| ~ ( sk2 @ B )
| ( ( sk7 @ A )
!= ( A @ B ) )
| ( ( sk8 @ B @ A )
!= B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(26,plain,
! [B: a,A: a > a] :
( ( ( sk7 @ A )
!= ( A @ B ) )
| ( ( sk8 @ B @ A )
!= B )
| ( sk5 @ A )
| ~ ( sk2 @ B ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(27,plain,
! [B: a,A: a > a] :
( ( ( sk7 @ A )
!= ( A @ B ) )
| ( ( sk8 @ B @ A )
!= B )
| ( sk5 @ A )
| ~ ( sk2 @ B ) ),
inference(simp,[status(thm)],[26]) ).
thf(1184,plain,
! [D: a,C: a > a,B: a,A: a > a] :
( ( ( sk7 @ A )
!= ( A @ B ) )
| ( sk5 @ A )
| ~ ( sk2 @ B )
| ( ( sk7 @ C )
!= ( C @ D ) )
| ( ( sk7 @ A )
!= D )
| ( sk5 @ C )
| ~ ( sk2 @ D )
| ( ( A @ ( sk8 @ B @ A ) )
!= ( sk8 @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[21,27]) ).
thf(1223,plain,
! [A: a] :
( ( ( sk7
@ ^ [B: a] : B )
!= A )
| ( sk5
@ ^ [B: a] : B )
| ~ ( sk2 @ A )
| ( ( sk7
@ ^ [B: a] : B )
!= A )
| ( ( sk7
@ ^ [B: a] : B )
!= A )
| ( sk5
@ ^ [B: a] : B )
| ~ ( sk2 @ A ) ),
inference(pre_uni,[status(thm)],[1184:[bind(A,$thf( ^ [E: a] : E )),bind(B,$thf( D )),bind(C,$thf( ^ [E: a] : E ))]]) ).
thf(1224,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( sk5
@ ^ [A: a] : A )
| ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( sk5
@ ^ [A: a] : A ) ),
inference(pattern_uni,[status(thm)],[1223:[bind(A,$thf( sk7 @ ^ [B: a] : B ))]]) ).
thf(1236,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( sk5
@ ^ [A: a] : A ) ),
inference(simp,[status(thm)],[1224]) ).
thf(1542,plain,
! [A: a > a] :
( ~ ( sk2
@ ( sk7
@ ^ [B: a] : B ) )
| ~ ( sk1 @ ( A @ ( sk6 @ A ) ) )
| ( ( sk5
@ ^ [B: a] : B )
!= ( sk5 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1236,15]) ).
thf(1543,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ~ ( sk1
@ ( sk6
@ ^ [A: a] : A ) ) ),
inference(pattern_uni,[status(thm)],[1542:[bind(A,$thf( ^ [B: a] : B ))]]) ).
thf(3999,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk1
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) )
!= ( sk1
@ ( sk6
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[3988,1543]) ).
thf(4005,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) )
!= ( sk6
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[3999]) ).
thf(32,plain,
! [B: a,A: a > a] :
( ~ ( sk5 @ A )
| ( sk1 @ ( sk4 @ B ) )
| ( ( sk2 @ ( sk6 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14,18]) ).
thf(33,plain,
! [A: a > a] :
( ~ ( sk5 @ A )
| ( sk1 @ ( sk4 @ ( sk6 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( C )),bind(B,$thf( sk6 @ C ))]]) ).
thf(34,plain,
! [A: a > a] :
( ~ ( sk5 @ A )
| ( sk1 @ ( sk4 @ ( sk6 @ A ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(1589,plain,
! [A: a > a] :
( ~ ( sk2
@ ( sk7
@ ^ [B: a] : B ) )
| ( sk1 @ ( sk4 @ ( sk6 @ A ) ) )
| ( ( sk5
@ ^ [B: a] : B )
!= ( sk5 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1236,34]) ).
thf(1590,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( sk1
@ ( sk4
@ ( sk6
@ ^ [A: a] : A ) ) ) ),
inference(pattern_uni,[status(thm)],[1589:[bind(A,$thf( ^ [B: a] : B ))]]) ).
thf(5,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ ( sk3 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(50,plain,
! [B: a > a,A: a] :
( ~ ( sk1 @ A )
| ~ ( sk5
@ ^ [C: a] : ( sk4 @ ( B @ C ) ) )
| ( ( sk2
@ ( B
@ ( sk6
@ ^ [C: a] : ( sk4 @ ( B @ C ) ) ) ) )
!= ( sk2 @ ( sk3 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[5,48]) ).
thf(54,plain,
! [A: a > a] :
( ~ ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) ),
inference(pre_uni,[status(thm)],[50:[bind(A,$thf( C @ ( sk6 @ ^ [D: a] : ( sk4 @ ( sk3 @ ( C @ D ) ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk3 @ ( C @ D ) ) ))]]) ).
thf(58,plain,
! [A: a > a] :
( ~ ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(2088,plain,
! [A: a > a] :
( ~ ( sk2
@ ( sk7
@ ^ [B: a] : B ) )
| ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( sk1
@ ( sk4
@ ( sk6
@ ^ [B: a] : B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1590,58]) ).
thf(2109,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ~ ( sk5
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk4
@ ( sk6
@ ^ [B: a] : B ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2088:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk6 @ ^ [C: a] : C ) ) ))]]) ).
thf(2093,plain,
! [A: a > a] :
( ~ ( sk2
@ ( sk7
@ ^ [B: a] : B ) )
| ~ ( sk5 @ A )
| ( ( sk1
@ ( sk4
@ ( sk6
@ ^ [B: a] : B ) ) )
!= ( sk1 @ ( A @ ( sk6 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1590,15]) ).
thf(2102,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ~ ( sk5
@ ^ [A: a] :
( sk4
@ ( sk6
@ ^ [B: a] : B ) ) ) ),
inference(pre_uni,[status(thm)],[2093:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk6 @ ^ [C: a] : C ) ) ))]]) ).
thf(2649,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ~ ( sk2
@ ( sk7
@ ^ [B: a] : B ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk4
@ ( sk6
@ ^ [C: a] : C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,2102]) ).
thf(2650,plain,
( ( sk1
@ ( sk7
@ ^ [A: a] :
( sk4
@ ( sk6
@ ^ [B: a] : B ) ) ) )
| ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ),
inference(pattern_uni,[status(thm)],[2649:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk6 @ ^ [C: a] : C ) ) ))]]) ).
thf(4690,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk1
@ ( sk7
@ ^ [A: a] :
( sk4
@ ( sk6
@ ^ [B: a] : B ) ) ) )
!= ( sk1
@ ( sk6
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[2650,1543]) ).
thf(4728,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk7
@ ^ [A: a] :
( sk4
@ ( sk6
@ ^ [B: a] : B ) ) )
!= ( sk6
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[4690]) ).
thf(56,plain,
( ~ ( sk5 @ sk4 )
| ~ ( sk5 @ sk4 ) ),
inference(pre_uni,[status(thm)],[51:[bind(A,$thf( sk4 )),bind(B,$thf( ^ [C: a] : C ))]]) ).
thf(60,plain,
~ ( sk5 @ sk4 ),
inference(simp,[status(thm)],[56]) ).
thf(74,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[19,60]) ).
thf(75,plain,
sk1 @ ( sk7 @ sk4 ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( sk4 ))]]) ).
thf(76,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ A ) )
| ( ( sk1 @ ( sk7 @ sk4 ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[75,5]) ).
thf(77,plain,
sk2 @ ( sk3 @ ( sk7 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( sk7 @ sk4 ))]]) ).
thf(102,plain,
! [A: a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( A @ B ) ) )
| ( ( sk2 @ ( sk3 @ ( sk7 @ sk4 ) ) )
!= ( sk2
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( A @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,48]) ).
thf(105,plain,
~ ( sk5
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ),
inference(pre_uni,[status(thm)],[102:[bind(A,$thf( ^ [B: a] : ( sk3 @ ( sk7 @ sk4 ) ) ))]]) ).
thf(113,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,105]) ).
thf(114,plain,
( sk1
@ ( sk7
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[113:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ))]]) ).
thf(327,plain,
! [A: a > a] :
( ~ ( sk5 @ A )
| ( ( sk1
@ ( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) )
!= ( sk1 @ ( A @ ( sk6 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[114,15]) ).
thf(333,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ),
inference(pre_uni,[status(thm)],[327:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ))]]) ).
thf(1517,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) )
!= ( sk5
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[1236,333]) ).
thf(1549,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1517]) ).
thf(78,plain,
! [A: a > a] :
( ~ ( sk5 @ A )
| ( ( sk1 @ ( sk7 @ sk4 ) )
!= ( sk1 @ ( A @ ( sk6 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[75,15]) ).
thf(79,plain,
~ ( sk5
@ ^ [A: a] : ( sk7 @ sk4 ) ),
inference(pre_uni,[status(thm)],[78:[bind(A,$thf( ^ [B: a] : ( sk7 @ sk4 ) ))]]) ).
thf(97,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] : ( sk7 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,79]) ).
thf(98,plain,
( sk1
@ ( sk7
@ ^ [A: a] : ( sk7 @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( ^ [B: a] : ( sk7 @ sk4 ) ))]]) ).
thf(108,plain,
! [A: a > a] :
( ~ ( sk5 @ A )
| ( ( sk1
@ ( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) )
!= ( sk1 @ ( A @ ( sk6 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[98,15]) ).
thf(109,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) ),
inference(pre_uni,[status(thm)],[108:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ sk4 ) ) ))]]) ).
thf(1529,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) )
!= ( sk5
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[1236,109]) ).
thf(1554,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1529]) ).
thf(43,plain,
! [B: a > a,A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ~ ( sk1 @ ( B @ ( sk6 @ B ) ) )
| ( ( sk5 @ A )
!= ( sk5 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19,15]) ).
thf(44,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ~ ( sk1 @ ( A @ ( sk6 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(3998,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) )
!= ( sk1 @ ( A @ ( sk6 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3988,44]) ).
thf(4004,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ),
inference(pre_uni,[status(thm)],[3998:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk4 @ C ) ) ) ))]]) ).
thf(30,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ( sk1 @ ( sk4 @ B ) )
| ( ( sk2 @ ( sk3 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5,18]) ).
thf(31,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk1 @ ( sk4 @ ( sk3 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( C )),bind(B,$thf( sk3 @ C ))]]) ).
thf(36,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk1 @ ( sk4 @ ( sk3 @ A ) ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(4165,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ ( sk3 @ A ) ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4004,36]) ).
thf(4166,plain,
( sk1
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4165:[bind(A,$thf( sk7 @ ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk4 @ C ) ) ) ))]]) ).
thf(364,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,333]) ).
thf(365,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[364:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ))]]) ).
thf(2654,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk5
@ ^ [A: a] :
( sk4
@ ( sk6
@ ^ [B: a] : B ) ) )
!= ( sk5
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[1236,2102]) ).
thf(2657,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk4
@ ( sk6
@ ^ [B: a] : B ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[2654]) ).
thf(2744,plain,
( ( ( sk4
@ ( sk6
@ ^ [A: a] : A ) )
!= sk16 )
| ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[2657]) ).
thf(117,plain,
! [A: a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) )
!= ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[98,58]) ).
thf(126,plain,
~ ( sk5
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) ) ) ),
inference(pre_uni,[status(thm)],[117:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ sk4 ) ) ))]]) ).
thf(346,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,126]) ).
thf(347,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[346:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [C: a] : ( sk7 @ sk4 ) ) ) ) ))]]) ).
thf(3985,plain,
! [A: a > a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,3979]) ).
thf(3990,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ),
inference(pre_uni,[status(thm)],[3985:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk4 @ C ) ) ))]]) ).
thf(4016,plain,
! [A: a > a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,3990]) ).
thf(4022,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[4016:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk4 @ D ) ) ) ))]]) ).
thf(37,plain,
! [B: a,A: a > a] :
( ( sk5 @ A )
| ( sk2 @ ( sk3 @ B ) )
| ( ( sk1 @ ( sk7 @ A ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19,5]) ).
thf(38,plain,
! [A: a > a] :
( ( sk5 @ A )
| ( sk2 @ ( sk3 @ ( sk7 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( C )),bind(B,$thf( sk7 @ C ))]]) ).
thf(41,plain,
! [A: a > a] :
( ( sk5 @ A )
| ( sk2 @ ( sk3 @ ( sk7 @ A ) ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(4013,plain,
! [A: a > a] :
( ( sk2 @ ( sk3 @ ( sk7 @ A ) ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,3990]) ).
thf(4014,plain,
( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4013:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk4 @ C ) ) ) ))]]) ).
thf(28,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk3 @ B ) )
| ( ( sk1 @ ( sk4 @ A ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[18,5]) ).
thf(29,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk3 @ ( sk4 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[28:[bind(A,$thf( C )),bind(B,$thf( sk4 @ C ))]]) ).
thf(35,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk3 @ ( sk4 @ A ) ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(4289,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ ( sk4 @ A ) ) )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4014,35]) ).
thf(4290,plain,
( sk2
@ ( sk3
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4289:[bind(A,$thf( sk3 @ ( sk7 @ ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk4 @ C ) ) ) ) ))]]) ).
thf(4001,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ ( sk3 @ A ) ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3988,36]) ).
thf(4002,plain,
( sk1
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4001:[bind(A,$thf( sk7 @ ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk4 @ B ) ) ))]]) ).
thf(4219,plain,
! [A: a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4002,58]) ).
thf(4226,plain,
~ ( sk5
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[4219:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ))]]) ).
thf(1538,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk5
@ ^ [A: a] : ( sk7 @ sk4 ) )
!= ( sk5
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[1236,79]) ).
thf(1548,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] : ( sk7 @ sk4 ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1538]) ).
thf(1796,plain,
( ( ( ^ [A: a] : ( sk7 @ sk4 ) )
!= ( ^ [A: a] : A ) )
| ( ( sk2 @ ( sk3 @ ( sk7 @ sk4 ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,1548]) ).
thf(1808,plain,
( ( ( ^ [A: a] : ( sk7 @ sk4 ) )
!= ( ^ [A: a] : A ) )
| ( ( sk3 @ ( sk7 @ sk4 ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1796]) ).
thf(1514,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk5 @ sk4 )
!= ( sk5
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[1236,60]) ).
thf(1544,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( sk4
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1514]) ).
thf(1519,plain,
! [A: a > a] :
( ~ ( sk2
@ ( sk7
@ ^ [B: a] : B ) )
| ( sk2 @ ( sk6 @ A ) )
| ( ( sk5
@ ^ [B: a] : B )
!= ( sk5 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1236,14]) ).
thf(1520,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( sk2
@ ( sk6
@ ^ [A: a] : A ) ) ),
inference(pattern_uni,[status(thm)],[1519:[bind(A,$thf( ^ [B: a] : B ))]]) ).
thf(1769,plain,
( ( sk2
@ ( sk6
@ ^ [A: a] : A ) )
| ( ( sk2 @ ( sk3 @ ( sk7 @ sk4 ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,1520]) ).
thf(1788,plain,
( ( sk2
@ ( sk6
@ ^ [A: a] : A ) )
| ( ( sk3 @ ( sk7 @ sk4 ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1769]) ).
thf(1588,plain,
! [B: a > a,A: a > a] :
( ~ ( sk5 @ A )
| ~ ( sk5
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( B @ C ) ) ) )
| ( ( sk1 @ ( sk4 @ ( sk6 @ A ) ) )
!= ( sk1
@ ( B
@ ( sk6
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( B @ C ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[34,58]) ).
thf(1595,plain,
( ~ ( sk5
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) )
| ~ ( sk5
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) ) ),
inference(pre_uni,[status(thm)],[1588:[bind(A,$thf( ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) )),bind(B,$thf( sk4 ))]]) ).
thf(1603,plain,
~ ( sk5
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) ),
inference(simp,[status(thm)],[1595]) ).
thf(1607,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ B ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,1603]) ).
thf(1608,plain,
( sk1
@ ( sk7
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1607:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ B ) ) ) ))]]) ).
thf(1613,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ B ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1608,5]) ).
thf(1614,plain,
( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1613:[bind(A,$thf( sk7 @ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ B ) ) ) ))]]) ).
thf(1652,plain,
( ( sk5
@ ^ [A: a] : A )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[1614,1236]) ).
thf(1655,plain,
( ( sk5
@ ^ [A: a] : A )
| ( ( sk3
@ ( sk7
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1652]) ).
thf(3989,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk5
@ ^ [A: a] : A )
!= ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1236,3979]) ).
thf(3991,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ),
inference(simp,[status(thm)],[3989]) ).
thf(4026,plain,
( ( ( sk7
@ ^ [A: a] : ( sk4 @ sk21 ) )
!= sk21 )
| ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[3991]) ).
thf(1710,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk1 @ ( sk7 @ sk4 ) )
!= ( sk1
@ ( sk6
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[75,1543]) ).
thf(1746,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk7 @ sk4 )
!= ( sk6
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1710]) ).
thf(4078,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] : ( sk4 @ D ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,4022]) ).
thf(4079,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4078:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk4 @ D ) ) ) ) ))]]) ).
thf(110,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,109]) ).
thf(111,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ sk4 ) ) ))]]) ).
thf(299,plain,
! [A: a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) )
!= ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[111,58]) ).
thf(301,plain,
~ ( sk5
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[299:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ sk4 ) ) ) ))]]) ).
thf(8,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A )
| ~ ( sk1 @ B )
| ( A
!= ( sk3 @ B ) )
| ( B
= ( sk4 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(24,plain,
! [B: a,A: a] :
( ( A
!= ( sk3 @ B ) )
| ( B
= ( sk4 @ A ) )
| ~ ( sk2 @ A )
| ~ ( sk1 @ B ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(25,plain,
! [A: a] :
( ( ( sk4 @ ( sk3 @ A ) )
= A )
| ~ ( sk2 @ ( sk3 @ A ) )
| ~ ( sk1 @ A ) ),
inference(simp,[status(thm)],[24]) ).
thf(1790,plain,
( ( ( sk7 @ sk4 )
!= sk12 )
| ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[1548]) ).
thf(2317,plain,
( ( ( sk7 @ sk4 )
!= sk12 )
| ( ( sk2 @ ( sk3 @ ( sk7 @ sk4 ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,1790]) ).
thf(2339,plain,
( ( ( sk7 @ sk4 )
!= sk12 )
| ( ( sk3 @ ( sk7 @ sk4 ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[2317]) ).
thf(1619,plain,
! [A: a > a] :
( ~ ( sk5 @ A )
| ( ( sk1
@ ( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ B ) ) ) ) )
!= ( sk1 @ ( A @ ( sk6 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1608,15]) ).
thf(1621,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ B ) ) ) ) ),
inference(pre_uni,[status(thm)],[1619:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ))]]) ).
thf(1625,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,1621]) ).
thf(1626,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1625:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ))]]) ).
thf(1757,plain,
! [A: a > a] :
( ~ ( sk5 @ A )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ) )
!= ( sk1 @ ( A @ ( sk6 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1626,15]) ).
thf(1762,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[1757:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk4 @ D ) ) ) ) ) ))]]) ).
thf(1894,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk4 @ D ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,1762]) ).
thf(1895,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1894:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk4 @ D ) ) ) ) ) ))]]) ).
thf(2199,plain,
! [A: a > a] :
( ~ ( sk5 @ A )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk4 @ D ) ) ) ) ) ) )
!= ( sk1 @ ( A @ ( sk6 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1895,15]) ).
thf(2200,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk4 @ D ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2199:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk4 @ ( sk3 @ ( sk4 @ E ) ) ) ) ) ) ))]]) ).
thf(2216,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] : ( sk4 @ ( sk3 @ ( sk4 @ E ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,2200]) ).
thf(2217,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk4 @ D ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2216:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk4 @ ( sk3 @ ( sk4 @ E ) ) ) ) ) ) ))]]) ).
thf(921,plain,
! [A: a > a] :
( ~ ( sk5 @ A )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) ) ) )
!= ( sk1 @ ( A @ ( sk6 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[347,15]) ).
thf(934,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[921:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) ) ))]]) ).
thf(1322,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,934]) ).
thf(1323,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1322:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) ) ))]]) ).
thf(4020,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk5
@ ^ [A: a] : A )
!= ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1236,3990]) ).
thf(4023,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[4020]) ).
thf(156,plain,
! [C: a > a,B: a,A: a > a] :
( ( ( sk7 @ A )
!= ( A @ B ) )
| ( ( A @ ( sk8 @ B @ A ) )
= ( sk7 @ A ) )
| ~ ( sk2 @ B )
| ( sk2 @ ( sk6 @ C ) )
| ( ( sk5 @ A )
!= ( sk5 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[21,14]) ).
thf(157,plain,
! [B: a,A: a > a] :
( ( ( sk7 @ A )
!= ( A @ B ) )
| ( ( A @ ( sk8 @ B @ A ) )
= ( sk7 @ A ) )
| ~ ( sk2 @ B )
| ( sk2 @ ( sk6 @ A ) ) ),
inference(pattern_uni,[status(thm)],[156:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(52,plain,
! [B: a > a,A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ~ ( sk2
@ ( B
@ ( sk6
@ ^ [C: a] : ( sk4 @ ( B @ C ) ) ) ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [C: a] : ( sk4 @ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,48]) ).
thf(53,plain,
! [A: a > a] :
( ( sk1
@ ( sk7
@ ^ [B: a] : ( sk4 @ ( A @ B ) ) ) )
| ~ ( sk2
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( A @ B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[52:[bind(A,$thf( ^ [D: a] : ( sk4 @ ( C @ D ) ) )),bind(B,$thf( C ))]]) ).
thf(57,plain,
! [A: a > a] :
( ( sk1
@ ( sk7
@ ^ [B: a] : ( sk4 @ ( A @ B ) ) ) )
| ~ ( sk2
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( A @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[53]) ).
thf(4270,plain,
! [A: a > a] :
( ( sk1
@ ( sk7
@ ^ [B: a] : ( sk4 @ ( A @ B ) ) ) )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) )
!= ( sk2
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( A @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4014,57]) ).
thf(4317,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[4270:[bind(A,$thf( ^ [B: a] : ( sk3 @ ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk4 @ D ) ) ) ) ) ))]]) ).
thf(103,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ A ) )
| ( ( sk2 @ ( sk3 @ ( sk7 @ sk4 ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[77,18]) ).
thf(104,plain,
sk1 @ ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( sk3 @ ( sk7 @ sk4 ) ))]]) ).
thf(135,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ A ) )
| ( ( sk1 @ ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[104,5]) ).
thf(136,plain,
sk2 @ ( sk3 @ ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[135:[bind(A,$thf( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ))]]) ).
thf(387,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ A ) )
| ( ( sk2 @ ( sk3 @ ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[136,18]) ).
thf(388,plain,
sk1 @ ( sk4 @ ( sk3 @ ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[387:[bind(A,$thf( sk3 @ ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ))]]) ).
thf(968,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ A ) )
| ( ( sk1 @ ( sk4 @ ( sk3 @ ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[388,5]) ).
thf(969,plain,
sk2 @ ( sk3 @ ( sk4 @ ( sk3 @ ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[968:[bind(A,$thf( sk4 @ ( sk3 @ ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ))]]) ).
thf(9,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( A
= ( sk3 @ ( sk4 @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(16,plain,
! [A: a] :
( ( ( sk3 @ ( sk4 @ A ) )
= A )
| ~ ( sk2 @ A ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(17,plain,
! [A: a] :
( ( ( sk3 @ ( sk4 @ A ) )
= A )
| ~ ( sk2 @ A ) ),
inference(simp,[status(thm)],[16]) ).
thf(99,plain,
! [A: a] :
( ( ( sk3 @ ( sk4 @ A ) )
= A )
| ( ( sk2 @ ( sk3 @ ( sk7 @ sk4 ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[77,17]) ).
thf(100,plain,
( ( sk3 @ ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) )
= ( sk3 @ ( sk7 @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( sk3 @ ( sk7 @ sk4 ) ))]]) ).
thf(2989,plain,
sk2 @ ( sk3 @ ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[969,100]) ).
thf(4000,plain,
! [A: a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) )
!= ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3988,58]) ).
thf(4006,plain,
~ ( sk5
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[4000:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk4 @ C ) ) ) ))]]) ).
thf(4247,plain,
! [A: a > a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
!= ( sk5
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,4006]) ).
thf(4253,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[4247:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk4 @ D ) ) ) ) ) ))]]) ).
thf(121,plain,
! [B: a > a,A: a > a] :
( ( sk5 @ A )
| ~ ( sk5
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( B @ C ) ) ) )
| ( ( sk1 @ ( sk7 @ A ) )
!= ( sk1
@ ( B
@ ( sk6
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( B @ C ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,58]) ).
thf(124,plain,
! [A: a > a > a] :
( ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ ( A @ B ) ) ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ ( A @ B ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[121:[bind(A,$thf( C @ ( sk6 @ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk7 @ ( C @ D ) ) ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk7 @ ( C @ D ) ) ))]]) ).
thf(132,plain,
! [A: a > a > a] :
( ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ ( A @ B ) ) ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ ( A @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(8801,plain,
! [B: a > a > a,A: a > a > a] :
( ~ ( sk5
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ ( A @ C ) ) ) ) )
| ~ ( sk5
@ ( B
@ ( sk6
@ ^ [C: a] : ( sk4 @ ( sk6 @ ( B @ C ) ) ) ) ) )
| ( ( sk5
@ ( A
@ ( sk6
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ ( A @ C ) ) ) ) ) ) )
!= ( sk5
@ ^ [C: a] : ( sk4 @ ( sk6 @ ( B @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[132,59]) ).
thf(8880,plain,
( ~ ( sk5
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) ) )
| ~ ( sk5
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[8801:[bind(A,$thf( ^ [C: a] : ^ [D: a] : ( sk4 @ C ) )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [E: a] : ( sk4 @ D ) ) ) ) ))]]) ).
thf(8894,plain,
~ ( sk5
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ),
inference(simp,[status(thm)],[8880]) ).
thf(8902,plain,
! [A: a > a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
!= ( sk5
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,8894]) ).
thf(8907,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[8902:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [D: a] : ( sk4 @ C ) ) ) ) ))]]) ).
thf(1515,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk5
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) )
!= ( sk5
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[1236,105]) ).
thf(1545,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1515]) ).
thf(84,plain,
! [B: a,A: a > a] :
( ~ ( sk5 @ A )
| ( ( sk3 @ ( sk4 @ B ) )
= B )
| ( ( sk2 @ ( sk6 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14,17]) ).
thf(85,plain,
! [A: a > a] :
( ~ ( sk5 @ A )
| ( ( sk3 @ ( sk4 @ ( sk6 @ A ) ) )
= ( sk6 @ A ) ) ),
inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( C )),bind(B,$thf( sk6 @ C ))]]) ).
thf(93,plain,
! [A: a > a] :
( ~ ( sk5 @ A )
| ( ( sk3 @ ( sk4 @ ( sk6 @ A ) ) )
= ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(4076,plain,
! [A: a > a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] : ( sk4 @ D ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,4022]) ).
thf(4082,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] : ( sk4 @ D ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[4076:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk7 @ ^ [F: a] : ( sk4 @ E ) ) ) ) ))]]) ).
thf(4621,plain,
! [A: a > a] :
( ( sk2 @ ( sk3 @ ( sk7 @ A ) ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] :
( sk7
@ ^ [F: a] : ( sk4 @ E ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,4082]) ).
thf(4622,plain,
( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] : ( sk4 @ D ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4621:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk7 @ ^ [F: a] : ( sk4 @ E ) ) ) ) ) ))]]) ).
thf(298,plain,
! [A: a > a] :
( ~ ( sk5 @ A )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) )
!= ( sk1 @ ( A @ ( sk6 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[111,15]) ).
thf(303,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) ),
inference(pre_uni,[status(thm)],[298:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ sk4 ) ) ) ))]]) ).
thf(312,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,303]) ).
thf(313,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[312:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ sk4 ) ) ) ))]]) ).
thf(573,plain,
! [A: a > a] :
( ~ ( sk5 @ A )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) )
!= ( sk1 @ ( A @ ( sk6 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[313,15]) ).
thf(578,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) ),
inference(pre_uni,[status(thm)],[573:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk7 @ sk4 ) ) ) ) ))]]) ).
thf(591,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] : ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,578]) ).
thf(592,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[591:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk7 @ sk4 ) ) ) ) ))]]) ).
thf(1289,plain,
! [A: a > a] :
( ~ ( sk5 @ A )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] : ( sk7 @ sk4 ) ) ) ) ) )
!= ( sk1 @ ( A @ ( sk6 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[592,15]) ).
thf(1302,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] : ( sk7 @ sk4 ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[1289:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk7 @ ^ [F: a] : ( sk7 @ sk4 ) ) ) ) ) ))]]) ).
thf(3982,plain,
! [A: a > a] :
( ( sk2 @ ( sk3 @ ( sk7 @ A ) ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,3979]) ).
thf(3983,plain,
( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3982:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk4 @ B ) ) ))]]) ).
thf(3158,plain,
! [A: a > a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] : ( sk4 @ ( sk3 @ ( sk4 @ E ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,2200]) ).
thf(3199,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] : ( sk4 @ ( sk3 @ ( sk4 @ E ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3158:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk7 @ ^ [F: a] : ( sk4 @ ( sk3 @ ( sk4 @ F ) ) ) ) ) ) ))]]) ).
thf(4164,plain,
! [A: a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4004,58]) ).
thf(4173,plain,
~ ( sk5
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[4164:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk4 @ D ) ) ) ) ))]]) ).
thf(1630,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ B ) ) ) ) )
!= ( sk5
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[1236,1621]) ).
thf(1632,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ B ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1630]) ).
thf(320,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[114,5]) ).
thf(321,plain,
( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[320:[bind(A,$thf( sk7 @ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ))]]) ).
thf(4098,plain,
! [A: a > a] :
( ( sk1
@ ( sk7
@ ^ [B: a] : ( sk4 @ ( A @ B ) ) ) )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) )
!= ( sk2
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( A @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3983,57]) ).
thf(4134,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[4098:[bind(A,$thf( ^ [B: a] : ( sk3 @ ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk4 @ C ) ) ) ) ))]]) ).
thf(1663,plain,
( ( ( sk4 @ sk11 )
!= sk11 )
| ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[1544]) ).
thf(2233,plain,
( ( ( sk4 @ sk11 )
!= sk11 )
| ( ( sk2 @ ( sk3 @ ( sk7 @ sk4 ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,1663]) ).
thf(2254,plain,
( ( ( sk4 @ sk11 )
!= sk11 )
| ( ( sk3 @ ( sk7 @ sk4 ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[2233]) ).
thf(948,plain,
! [A: a > a] :
( ~ ( sk5 @ A )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) )
!= ( sk1 @ ( A @ ( sk6 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[365,15]) ).
thf(956,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[948:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) ))]]) ).
thf(116,plain,
! [B: a > a,A: a] :
( ~ ( sk2 @ A )
| ~ ( sk1 @ A )
| ~ ( sk5
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( B @ C ) ) ) )
| ( ( B
@ ( sk6
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( B @ C ) ) ) ) )
!= ( sk3 @ ( sk4 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,58]) ).
thf(125,plain,
! [A: a > a] :
( ~ ( sk2
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk3 @ ( sk4 @ ( A @ B ) ) ) ) ) ) ) )
| ~ ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk3 @ ( sk4 @ ( A @ B ) ) ) ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk3 @ ( sk4 @ ( A @ B ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[116:[bind(A,$thf( D @ ( sk6 @ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk3 @ ( sk4 @ ( D @ D ) ) ) ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk3 @ ( sk4 @ ( D @ D ) ) ) ))]]) ).
thf(133,plain,
! [A: a > a] :
( ~ ( sk2
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk3 @ ( sk4 @ ( A @ B ) ) ) ) ) ) ) )
| ~ ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk3 @ ( sk4 @ ( A @ B ) ) ) ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk3 @ ( sk4 @ ( A @ B ) ) ) ) ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(941,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[365,5]) ).
thf(942,plain,
( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[941:[bind(A,$thf( sk7 @ ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ))]]) ).
thf(8904,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,8894]) ).
thf(8905,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[8904:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [C: a] : ( sk4 @ B ) ) ) ) ))]]) ).
thf(8919,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) )
!= ( sk1 @ ( A @ ( sk6 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[8905,44]) ).
thf(8927,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[8919:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ))]]) ).
thf(106,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[98,5]) ).
thf(107,plain,
( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] : ( sk7 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[106:[bind(A,$thf( sk7 @ ^ [B: a] : ( sk7 @ sk4 ) ))]]) ).
thf(1713,plain,
( ~ ( sk1
@ ( sk6
@ ^ [A: a] : A ) )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] : ( sk7 @ sk4 ) ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[107,1543]) ).
thf(1730,plain,
( ~ ( sk1
@ ( sk6
@ ^ [A: a] : A ) )
| ( ( sk3
@ ( sk7
@ ^ [A: a] : ( sk7 @ sk4 ) ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1713]) ).
thf(1668,plain,
( ( sk4
!= ( ^ [A: a] : A ) )
| ( ( sk2 @ ( sk3 @ ( sk7 @ sk4 ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,1544]) ).
thf(1681,plain,
( ( sk4
!= ( ^ [A: a] : A ) )
| ( ( sk3 @ ( sk7 @ sk4 ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1668]) ).
thf(2264,plain,
( ( ( sk4 @ sk15 )
!= sk15 )
| ( ( sk3 @ ( sk7 @ sk4 ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[1681]) ).
thf(39,plain,
! [B: a > a,A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( sk2 @ ( sk6 @ B ) )
| ( ( sk5 @ A )
!= ( sk5 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19,14]) ).
thf(40,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( sk2 @ ( sk6 @ A ) ) ),
inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(65,plain,
! [B: a,A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( sk1 @ ( sk4 @ B ) )
| ( ( sk2 @ ( sk6 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[40,18]) ).
thf(66,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( sk1 @ ( sk4 @ ( sk6 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( C )),bind(B,$thf( sk6 @ C ))]]) ).
thf(70,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( sk1 @ ( sk4 @ ( sk6 @ A ) ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(3164,plain,
! [A: a > a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,934]) ).
thf(3207,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3164:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [E: a] : ( sk7 @ sk4 ) ) ) ) ) ))]]) ).
thf(293,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[111,5]) ).
thf(294,plain,
( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( sk7 @ ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ sk4 ) ) ))]]) ).
thf(1540,plain,
( ( sk5
@ ^ [A: a] : A )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[294,1236]) ).
thf(1560,plain,
( ( sk5
@ ^ [A: a] : A )
| ( ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1540]) ).
thf(82,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ( ( sk3 @ ( sk4 @ B ) )
= B )
| ( ( sk2 @ ( sk3 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5,17]) ).
thf(83,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( ( sk3 @ ( sk4 @ ( sk3 @ A ) ) )
= ( sk3 @ A ) ) ),
inference(pattern_uni,[status(thm)],[82:[bind(A,$thf( C )),bind(B,$thf( sk3 @ C ))]]) ).
thf(92,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( ( sk3 @ ( sk4 @ ( sk3 @ A ) ) )
= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(8943,plain,
! [A: a > a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,8907]) ).
thf(8948,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[8943:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [E: a] : ( sk4 @ D ) ) ) ) ) ))]]) ).
thf(3162,plain,
! [A: a > a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
!= ( sk5
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,301]) ).
thf(3198,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3162:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk7 @ sk4 ) ) ) ) ) ))]]) ).
thf(1675,plain,
( ( sk4
!= ( ^ [A: a] : A ) )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[294,1544]) ).
thf(1687,plain,
( ( sk4
!= ( ^ [A: a] : A ) )
| ( ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1675]) ).
thf(1774,plain,
( ( sk2
@ ( sk6
@ ^ [A: a] : A ) )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] : ( sk7 @ sk4 ) ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[107,1520]) ).
thf(1787,plain,
( ( sk2
@ ( sk6
@ ^ [A: a] : A ) )
| ( ( sk3
@ ( sk7
@ ^ [A: a] : ( sk7 @ sk4 ) ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1774]) ).
thf(1716,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk1
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) ) )
!= ( sk1
@ ( sk6
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[111,1543]) ).
thf(1740,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) )
!= ( sk6
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1716]) ).
thf(1618,plain,
! [A: a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ B ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1608,58]) ).
thf(1620,plain,
~ ( sk5
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ B ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[1618:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ))]]) ).
thf(1909,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,1620]) ).
thf(1910,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ B ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1909:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ) ) ))]]) ).
thf(552,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ A ) )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[294,18]) ).
thf(553,plain,
( sk1
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[552:[bind(A,$thf( sk3 @ ( sk7 @ ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ sk4 ) ) ) ))]]) ).
thf(1088,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[553,5]) ).
thf(1089,plain,
( sk2
@ ( sk3
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1088:[bind(A,$thf( sk4 @ ( sk3 @ ( sk7 @ ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ sk4 ) ) ) ) ))]]) ).
thf(9568,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk5
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk4
@ ( sk6
@ ^ [B: a] : B ) ) ) ) )
!= ( sk5
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[1236,2109]) ).
thf(9608,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk4
@ ( sk3
@ ( sk4
@ ( sk6
@ ^ [B: a] : B ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[9568]) ).
thf(4333,plain,
( ( ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) )
!= sk22 )
| ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[4023]) ).
thf(3183,plain,
! [A: a > a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ~ ( sk2
@ ( sk7
@ ^ [B: a] : B ) )
| ( ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
!= ( sk5
@ ^ [B: a] :
( sk4
@ ( sk6
@ ^ [C: a] : C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,2102]) ).
thf(3213,plain,
( ~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk4
@ ( sk6
@ ^ [C: a] : C ) ) ) )
| ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ),
inference(pre_uni,[status(thm)],[3183:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk4 @ ( sk6 @ ^ [D: a] : D ) ) ))]]) ).
thf(4994,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk4
@ ( sk6
@ ^ [C: a] : C ) ) ) )
!= ( sk5
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[1236,3213]) ).
thf(5016,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk4
@ ( sk6
@ ^ [C: a] : C ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[4994]) ).
thf(5031,plain,
( ( ( sk7
@ ^ [A: a] :
( sk4
@ ( sk6
@ ^ [B: a] : B ) ) )
!= sk25 )
| ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[5016]) ).
thf(3172,plain,
! [A: a > a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
!= ( sk5
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,1620]) ).
thf(3210,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3172:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk4 @ D ) ) ) ) ) ) ))]]) ).
thf(4412,plain,
! [A: a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] : ( sk4 @ D ) ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4079,58]) ).
thf(4421,plain,
~ ( sk5
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] : ( sk4 @ D ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[4412:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk7 @ ^ [F: a] : ( sk4 @ E ) ) ) ) ) ))]]) ).
thf(2073,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk1
@ ( sk4
@ ( sk6
@ ^ [A: a] : A ) ) )
!= ( sk1
@ ( sk6
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[1590,1543]) ).
thf(2101,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk4
@ ( sk6
@ ^ [A: a] : A ) )
!= ( sk6
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[2073]) ).
thf(2597,plain,
( ( ( sk4
@ ( sk6
@ ^ [A: a] : A ) )
!= ( sk6
@ ^ [A: a] : A ) )
| ( ( sk2 @ ( sk3 @ ( sk7 @ sk4 ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,2101]) ).
thf(2613,plain,
( ( ( sk4
@ ( sk6
@ ^ [A: a] : A ) )
!= ( sk6
@ ^ [A: a] : A ) )
| ( ( sk3 @ ( sk7 @ sk4 ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[2597]) ).
thf(1611,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk5
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) )
!= ( sk5
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[1236,1603]) ).
thf(1612,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] : ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1611]) ).
thf(89,plain,
! [B: a > a,A: a] :
( ~ ( sk2 @ A )
| ~ ( sk5
@ ^ [C: a] : ( sk4 @ ( B @ C ) ) )
| ( ( B
@ ( sk6
@ ^ [C: a] : ( sk4 @ ( B @ C ) ) ) )
!= ( sk3 @ ( sk4 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,48]) ).
thf(91,plain,
! [A: a > a] :
( ~ ( sk2
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ ( A @ B ) ) ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ ( A @ B ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[89:[bind(A,$thf( D @ ( sk6 @ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk4 @ ( D @ D ) ) ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk3 @ ( sk4 @ ( D @ D ) ) ) ))]]) ).
thf(96,plain,
! [A: a > a] :
( ~ ( sk2
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ ( A @ B ) ) ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ ( A @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(567,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[313,5]) ).
thf(568,plain,
( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[567:[bind(A,$thf( sk7 @ ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ sk4 ) ) ) ))]]) ).
thf(1265,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ A ) )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[568,18]) ).
thf(1266,plain,
( sk1
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1265:[bind(A,$thf( sk3 @ ( sk7 @ ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) ))]]) ).
thf(4243,plain,
! [A: a > a] :
( ( sk2 @ ( sk3 @ ( sk7 @ A ) ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,4006]) ).
thf(4244,plain,
( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4243:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ))]]) ).
thf(1756,plain,
! [A: a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1626,58]) ).
thf(1759,plain,
~ ( sk5
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[1756:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk4 @ D ) ) ) ) ) ))]]) ).
thf(3155,plain,
! [A: a > a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,956]) ).
thf(3215,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3155:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) ))]]) ).
thf(118,plain,
! [B: a > a,A: a > a] :
( ( sk2 @ ( sk6 @ A ) )
| ~ ( sk5
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( B @ C ) ) ) )
| ( ( sk1 @ ( sk7 @ A ) )
!= ( sk1
@ ( B
@ ( sk6
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( B @ C ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[40,58]) ).
thf(127,plain,
! [A: a > a > a] :
( ( sk2
@ ( sk6
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ ( A @ B ) ) ) ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ ( A @ B ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[118:[bind(A,$thf( C @ ( sk6 @ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk7 @ ( C @ D ) ) ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk7 @ ( C @ D ) ) ))]]) ).
thf(134,plain,
! [A: a > a > a] :
( ( sk2
@ ( sk6
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ ( A @ B ) ) ) ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ ( A @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(61,plain,
! [B: a,A: a > a] :
( ( sk2 @ ( sk6 @ A ) )
| ( sk2 @ ( sk3 @ B ) )
| ( ( sk1 @ ( sk7 @ A ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[40,5]) ).
thf(62,plain,
! [A: a > a] :
( ( sk2 @ ( sk6 @ A ) )
| ( sk2 @ ( sk3 @ ( sk7 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[61:[bind(A,$thf( C )),bind(B,$thf( sk7 @ C ))]]) ).
thf(73,plain,
! [A: a > a] :
( ( sk2 @ ( sk6 @ A ) )
| ( sk2 @ ( sk3 @ ( sk7 @ A ) ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(632,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,301]) ).
thf(633,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[632:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) ) ))]]) ).
thf(1992,plain,
( ( ( ^ [A: a] : ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) )
!= ( ^ [A: a] : A ) )
| ( ( sk2 @ ( sk3 @ ( sk7 @ sk4 ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,1612]) ).
thf(2001,plain,
( ( ( ^ [A: a] : ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) )
!= ( ^ [A: a] : A ) )
| ( ( sk3 @ ( sk7 @ sk4 ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1992]) ).
thf(1701,plain,
( ~ ( sk1
@ ( sk6
@ ^ [A: a] : A ) )
| ( ( sk2 @ ( sk3 @ ( sk7 @ sk4 ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,1543]) ).
thf(1727,plain,
( ~ ( sk1
@ ( sk6
@ ^ [A: a] : A ) )
| ( ( sk3 @ ( sk7 @ sk4 ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1701]) ).
thf(1672,plain,
( ( sk4
!= ( ^ [A: a] : A ) )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[1614,1544]) ).
thf(1680,plain,
( ( sk4
!= ( ^ [A: a] : A ) )
| ( ( sk3
@ ( sk7
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1672]) ).
thf(148,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ A ) )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,18]) ).
thf(149,plain,
( sk1
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [A: a] : ( sk7 @ sk4 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[148:[bind(A,$thf( sk3 @ ( sk7 @ ^ [B: a] : ( sk7 @ sk4 ) ) ))]]) ).
thf(4093,plain,
( ( sk4
!= ( ^ [A: a] : A ) )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[3983,1544]) ).
thf(4144,plain,
( ( sk4
!= ( ^ [A: a] : A ) )
| ( ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[4093]) ).
thf(8899,plain,
! [A: a > a] :
( ( sk2 @ ( sk3 @ ( sk7 @ A ) ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,8894]) ).
thf(8900,plain,
( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[8899:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [C: a] : ( sk4 @ B ) ) ) ) ))]]) ).
thf(63,plain,
! [B: a > a,A: a > a] :
( ( sk2 @ ( sk6 @ A ) )
| ~ ( sk5 @ B )
| ( ( sk1 @ ( sk7 @ A ) )
!= ( sk1 @ ( B @ ( sk6 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[40,15]) ).
thf(67,plain,
! [A: a > a > a] :
( ( sk2
@ ( sk6
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ),
inference(pre_uni,[status(thm)],[63:[bind(A,$thf( C @ ( sk6 @ ^ [D: a] : ( sk7 @ ( C @ D ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk7 @ ( C @ D ) ) ))]]) ).
thf(71,plain,
! [A: a > a > a] :
( ( sk2
@ ( sk6
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(2192,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk4 @ D ) ) ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1895,5]) ).
thf(2193,plain,
( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2192:[bind(A,$thf( sk7 @ ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk4 @ D ) ) ) ) ) ))]]) ).
thf(4125,plain,
( ( sk5
@ ^ [A: a] : A )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[3983,1236]) ).
thf(4149,plain,
( ( sk5
@ ^ [A: a] : A )
| ( ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[4125]) ).
thf(1348,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,956]) ).
thf(1349,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1348:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) ))]]) ).
thf(1704,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk1
@ ( sk7
@ ^ [A: a] : ( sk7 @ sk4 ) ) )
!= ( sk1
@ ( sk6
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[98,1543]) ).
thf(1722,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk7
@ ^ [A: a] : ( sk7 @ sk4 ) )
!= ( sk6
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1704]) ).
thf(1537,plain,
( ( sk5
@ ^ [A: a] : A )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] : ( sk7 @ sk4 ) ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[107,1236]) ).
thf(1571,plain,
( ( sk5
@ ^ [A: a] : A )
| ( ( sk3
@ ( sk7
@ ^ [A: a] : ( sk7 @ sk4 ) ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1537]) ).
thf(914,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[347,5]) ).
thf(915,plain,
( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[914:[bind(A,$thf( sk7 @ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [C: a] : ( sk7 @ sk4 ) ) ) ) ))]]) ).
thf(1952,plain,
( ( ( sk7
@ ^ [A: a] : ( sk7 @ sk4 ) )
!= sk13 )
| ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[1554]) ).
thf(2074,plain,
! [A: a] :
( ~ ( sk2
@ ( sk7
@ ^ [B: a] : B ) )
| ( sk2 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk4
@ ( sk6
@ ^ [B: a] : B ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1590,5]) ).
thf(2075,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( sk2
@ ( sk3
@ ( sk4
@ ( sk6
@ ^ [A: a] : A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2074:[bind(A,$thf( sk4 @ ( sk6 @ ^ [B: a] : B ) ))]]) ).
thf(6211,plain,
! [A: a > a] :
( ~ ( sk2
@ ( sk7
@ ^ [B: a] : B ) )
| ( ( sk3 @ ( sk4 @ ( sk6 @ A ) ) )
= ( sk6 @ A ) )
| ( ( sk5
@ ^ [B: a] : B )
!= ( sk5 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1236,93]) ).
thf(6212,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk3
@ ( sk4
@ ( sk6
@ ^ [A: a] : A ) ) )
= ( sk6
@ ^ [A: a] : A ) ) ),
inference(pattern_uni,[status(thm)],[6211:[bind(A,$thf( ^ [B: a] : B ))]]) ).
thf(1530,plain,
( ( sk5
@ ^ [A: a] : A )
| ( ( sk2 @ ( sk3 @ ( sk7 @ sk4 ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,1236]) ).
thf(1562,plain,
( ( sk5
@ ^ [A: a] : A )
| ( ( sk3 @ ( sk7 @ sk4 ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1530]) ).
thf(4112,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ ( sk4 @ A ) ) )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3983,35]) ).
thf(4113,plain,
( sk2
@ ( sk3
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4112:[bind(A,$thf( sk3 @ ( sk7 @ ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk4 @ B ) ) ) ))]]) ).
thf(144,plain,
! [A: a] :
( ( ( sk3 @ ( sk4 @ A ) )
= A )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,17]) ).
thf(145,plain,
( ( sk3
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [A: a] : ( sk7 @ sk4 ) ) ) ) )
= ( sk3
@ ( sk7
@ ^ [A: a] : ( sk7 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[144:[bind(A,$thf( sk3 @ ( sk7 @ ^ [B: a] : ( sk7 @ sk4 ) ) ))]]) ).
thf(1689,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk1
@ ( sk7
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) ) )
!= ( sk1
@ ( sk6
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[1608,1543]) ).
thf(1743,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk7
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) )
!= ( sk6
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1689]) ).
thf(88,plain,
! [B: a > a,A: a] :
( ~ ( sk2 @ A )
| ~ ( sk1 @ A )
| ~ ( sk5 @ B )
| ( ( sk3 @ ( sk4 @ A ) )
!= ( B @ ( sk6 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,15]) ).
thf(90,plain,
! [A: a > a] :
( ~ ( sk2
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk3 @ ( sk4 @ ( A @ B ) ) ) ) ) )
| ~ ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk3 @ ( sk4 @ ( A @ B ) ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk3 @ ( sk4 @ ( A @ B ) ) ) ) ),
inference(pre_uni,[status(thm)],[88:[bind(A,$thf( D @ ( sk6 @ ^ [D: a] : ( sk3 @ ( sk4 @ ( D @ D ) ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk3 @ ( sk4 @ ( D @ D ) ) ) ))]]) ).
thf(95,plain,
! [A: a > a] :
( ~ ( sk2
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk3 @ ( sk4 @ ( A @ B ) ) ) ) ) )
| ~ ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk3 @ ( sk4 @ ( A @ B ) ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk3 @ ( sk4 @ ( A @ B ) ) ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(1531,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) )
!= ( sk5
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[1236,303]) ).
thf(1566,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk7 @ sk4 ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1531]) ).
thf(1752,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1626,5]) ).
thf(1753,plain,
( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ B ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1752:[bind(A,$thf( sk7 @ ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ))]]) ).
thf(1528,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) )
!= ( sk5
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[1236,578]) ).
thf(1547,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1528]) ).
thf(2285,plain,
( ( ( sk7 @ sk4 )
!= ( sk6
@ ^ [A: a] : A ) )
| ( ( sk2 @ ( sk3 @ ( sk7 @ sk4 ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,1746]) ).
thf(2298,plain,
( ( ( sk7 @ sk4 )
!= ( sk6
@ ^ [A: a] : A ) )
| ( ( sk3 @ ( sk7 @ sk4 ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[2285]) ).
thf(1801,plain,
( ( ( ^ [A: a] : ( sk7 @ sk4 ) )
!= ( ^ [A: a] : A ) )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] : ( sk7 @ sk4 ) ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[107,1548]) ).
thf(1813,plain,
( ( ( ^ [A: a] : ( sk7 @ sk4 ) )
!= ( ^ [A: a] : A ) )
| ( ( sk3
@ ( sk7
@ ^ [A: a] : ( sk7 @ sk4 ) ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1801]) ).
thf(328,plain,
! [A: a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[114,58]) ).
thf(331,plain,
~ ( sk5
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[328:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ))]]) ).
thf(3165,plain,
! [A: a > a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] :
( sk7
@ ^ [F: a] : ( sk7 @ sk4 ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,1302]) ).
thf(3202,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] :
( sk7
@ ^ [F: a] : ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3165:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk7 @ ^ [F: a] : ( sk7 @ ^ [G: a] : ( sk7 @ sk4 ) ) ) ) ) ))]]) ).
thf(1898,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ) )
!= ( sk5
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[1236,1762]) ).
thf(1901,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1898]) ).
thf(574,plain,
! [A: a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[313,58]) ).
thf(576,plain,
~ ( sk5
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[574:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk7 @ sk4 ) ) ) ) ))]]) ).
thf(1694,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk1 @ ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) )
!= ( sk1
@ ( sk6
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[104,1543]) ).
thf(1738,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) )
!= ( sk6
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1694]) ).
thf(1960,plain,
( ( ( ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) )
!= ( ^ [A: a] : A ) )
| ( ( sk2 @ ( sk3 @ ( sk7 @ sk4 ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,1554]) ).
thf(1972,plain,
( ( ( ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) )
!= ( ^ [A: a] : A ) )
| ( ( sk3 @ ( sk7 @ sk4 ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1960]) ).
thf(64,plain,
! [B: a > a,A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ~ ( sk5
@ ^ [C: a] : ( sk4 @ ( B @ C ) ) )
| ( ( sk2 @ ( sk6 @ A ) )
!= ( sk2
@ ( B
@ ( sk6
@ ^ [C: a] : ( sk4 @ ( B @ C ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[40,48]) ).
thf(68,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk7
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk6 @ ( A @ B ) ) ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk6 @ ( A @ B ) ) ) ) ),
inference(pre_uni,[status(thm)],[64:[bind(A,$thf( C @ ( sk6 @ ^ [D: a] : ( sk4 @ ( sk6 @ ( C @ D ) ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk6 @ ( C @ D ) ) ))]]) ).
thf(72,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk7
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk6 @ ( A @ B ) ) ) ) ) ) )
| ~ ( sk5
@ ^ [B: a] : ( sk4 @ ( sk6 @ ( A @ B ) ) ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(1371,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] :
( sk7
@ ^ [F: a] : ( sk7 @ sk4 ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,1302]) ).
thf(1372,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] : ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1371:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk7 @ ^ [F: a] : ( sk7 @ sk4 ) ) ) ) ) ))]]) ).
thf(4413,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ ( sk3 @ A ) ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] : ( sk4 @ D ) ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4079,36]) ).
thf(4414,plain,
( sk1
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4413:[bind(A,$thf( sk7 @ ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk4 @ D ) ) ) ) ))]]) ).
thf(1648,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ A ) )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ B ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1614,18]) ).
thf(1649,plain,
( sk1
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1648:[bind(A,$thf( sk3 @ ( sk7 @ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ B ) ) ) ) ))]]) ).
thf(1673,plain,
( ( sk4
!= ( ^ [A: a] : A ) )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] : ( sk7 @ sk4 ) ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[107,1544]) ).
thf(1685,plain,
( ( sk4
!= ( ^ [A: a] : A ) )
| ( ( sk3
@ ( sk7
@ ^ [A: a] : ( sk7 @ sk4 ) ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1673]) ).
thf(5108,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ) )
!= ( sk1 @ ( A @ ( sk6 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4134,44]) ).
thf(5115,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[5108:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk4 @ D ) ) ) ) ) ) ))]]) ).
thf(11,plain,
! [B: a,A: a > a] :
( ( sk5 @ A )
| ~ ( sk2 @ B )
| ( ( sk7 @ A )
!= ( A @ B ) )
| ( sk2 @ ( sk8 @ B @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(22,plain,
! [B: a,A: a > a] :
( ( ( sk7 @ A )
!= ( A @ B ) )
| ( sk5 @ A )
| ~ ( sk2 @ B )
| ( sk2 @ ( sk8 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(23,plain,
! [B: a,A: a > a] :
( ( ( sk7 @ A )
!= ( A @ B ) )
| ( sk5 @ A )
| ~ ( sk2 @ B )
| ( sk2 @ ( sk8 @ B @ A ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(1541,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk5
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) ) ) )
!= ( sk5
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[1236,126]) ).
thf(1558,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk7 @ sk4 ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1541]) ).
thf(2151,plain,
! [A: a] :
( ~ ( sk2
@ ( sk7
@ ^ [B: a] : B ) )
| ( sk1 @ ( sk4 @ ( sk3 @ A ) ) )
| ( ( sk1
@ ( sk4
@ ( sk6
@ ^ [B: a] : B ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1590,36]) ).
thf(2152,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( sk1
@ ( sk4
@ ( sk3
@ ( sk4
@ ( sk6
@ ^ [A: a] : A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2151:[bind(A,$thf( sk4 @ ( sk6 @ ^ [B: a] : B ) ))]]) ).
thf(2035,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ A ) )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1753,18]) ).
thf(2036,plain,
( sk1
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ B ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2035:[bind(A,$thf( sk3 @ ( sk7 @ ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk4 @ C ) ) ) ) ) ))]]) ).
thf(2082,plain,
( ( sk1
@ ( sk4
@ ( sk6
@ ^ [A: a] : A ) ) )
| ( ( sk2 @ ( sk3 @ ( sk7 @ sk4 ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,1590]) ).
thf(2095,plain,
( ( sk1
@ ( sk4
@ ( sk6
@ ^ [A: a] : A ) ) )
| ( ( sk3 @ ( sk7 @ sk4 ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[2082]) ).
thf(4073,plain,
! [A: a > a] :
( ( sk2 @ ( sk3 @ ( sk7 @ A ) ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] : ( sk4 @ D ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,4022]) ).
thf(4074,plain,
( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4073:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk4 @ D ) ) ) ) ))]]) ).
thf(8906,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk5
@ ^ [A: a] : A )
!= ( sk5
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1236,8894]) ).
thf(8908,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] :
( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ) ) ),
inference(simp,[status(thm)],[8906]) ).
thf(1986,plain,
( ( ( sk4 @ ( sk3 @ ( sk4 @ sk14 ) ) )
!= sk14 )
| ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[1612]) ).
thf(1858,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ ( sk4 @ A ) ) )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ B ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1614,35]) ).
thf(1859,plain,
( sk2
@ ( sk3
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1858:[bind(A,$thf( sk3 @ ( sk7 @ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk4 @ B ) ) ) ) ))]]) ).
thf(4080,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( sk5
@ ^ [A: a] : A )
!= ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1236,4022]) ).
thf(4083,plain,
( ~ ( sk2
@ ( sk7
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ) ),
inference(simp,[status(thm)],[4080]) ).
thf(1287,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] : ( sk7 @ sk4 ) ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[592,5]) ).
thf(1288,plain,
( sk2
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] : ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1287:[bind(A,$thf( sk7 @ ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk7 @ sk4 ) ) ) ) ))]]) ).
thf(86,plain,
! [B: a,A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk3 @ ( sk4 @ B ) )
= B )
| ( ( sk2 @ ( sk6 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[40,17]) ).
thf(87,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk3 @ ( sk4 @ ( sk6 @ A ) ) )
= ( sk6 @ A ) ) ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( C )),bind(B,$thf( sk6 @ C ))]]) ).
thf(94,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk3 @ ( sk4 @ ( sk6 @ A ) ) )
= ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(4624,plain,
! [A: a > a > a] :
( ~ ( sk5
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) )
| ( ( sk5
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk7 @ ( A @ B ) ) ) ) )
!= ( sk5
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] :
( sk7
@ ^ [F: a] : ( sk4 @ E ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,4082]) ).
thf(4631,plain,
~ ( sk5
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] :
( sk7
@ ^ [F: a] : ( sk4 @ E ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[4624:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk7 @ ^ [F: a] : ( sk7 @ ^ [G: a] : ( sk4 @ F ) ) ) ) ) ))]]) ).
thf(4035,plain,
( ( ( ^ [A: a] : A )
!= ( ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) )
| ( ( sk2 @ ( sk3 @ ( sk7 @ sk4 ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,3991]) ).
thf(4066,plain,
( ( ( ^ [A: a] : A )
!= ( ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) )
| ( ( sk3 @ ( sk7 @ sk4 ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[4035]) ).
thf(119,plain,
! [B: a > a,A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ~ ( sk1
@ ( B
@ ( sk6
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( B @ C ) ) ) ) ) )
| ( ( sk5 @ A )
!= ( sk5
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( B @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,58]) ).
thf(120,plain,
! [A: a > a] :
( ( sk1
@ ( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) )
| ~ ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[119:[bind(A,$thf( ^ [D: a] : ( sk4 @ ( sk3 @ ( D @ D ) ) ) )),bind(B,$thf( D ))]]) ).
thf(131,plain,
! [A: a > a] :
( ( sk1
@ ( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) )
| ~ ( sk1
@ ( A
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( A @ B ) ) ) ) ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(4220,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ ( sk3 @ A ) ) )
| ( ( sk1
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4002,36]) ).
thf(4221,plain,
( sk1
@ ( sk4
@ ( sk3
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4220:[bind(A,$thf( sk4 @ ( sk3 @ ( sk7 @ ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk4 @ B ) ) ) ) ))]]) ).
thf(658,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ A ) )
| ( ( sk2
@ ( sk3
@ ( sk7
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[321,18]) ).
thf(659,plain,
( sk1
@ ( sk4
@ ( sk3
@ ( sk7
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[658:[bind(A,$thf( sk3 @ ( sk7 @ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk7 @ sk4 ) ) ) ) ))]]) ).
thf(4410,plain,
! [A: a > a] :
( ( sk1 @ ( sk7 @ A ) )
| ( ( sk1
@ ( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] : ( sk4 @ D ) ) ) ) ) )
!= ( sk1 @ ( A @ ( sk6 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4079,44]) ).
thf(4423,plain,
( sk1
@ ( sk7
@ ^ [A: a] :
( sk7
@ ^ [B: a] :
( sk7
@ ^ [C: a] :
( sk7
@ ^ [D: a] :
( sk7
@ ^ [E: a] : ( sk4 @ D ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[4410:[bind(A,$thf( ^ [B: a] : ( sk7 @ ^ [C: a] : ( sk7 @ ^ [D: a] : ( sk7 @ ^ [E: a] : ( sk7 @ ^ [F: a] : ( sk4 @ E ) ) ) ) ) ))]]) ).
thf(2754,plain,
( ( ( ^ [A: a] :
( sk4
@ ( sk6
@ ^ [B: a] : B ) ) )
!= ( ^ [A: a] : A ) )
| ( ( sk2 @ ( sk3 @ ( sk7 @ sk4 ) ) )
!= ( sk2
@ ( sk7
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,2657]) ).
thf(2771,plain,
( ( ( ^ [A: a] :
( sk4
@ ( sk6
@ ^ [B: a] : B ) ) )
!= ( ^ [A: a] : A ) )
| ( ( sk3 @ ( sk7 @ sk4 ) )
!= ( sk7
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[2754]) ).
thf(18332,plain,
$false,
inference(e,[status(thm)],[4005,2109,4728,1549,1554,4166,365,2744,347,4022,4290,333,3979,3990,4226,1808,1544,5,1788,1608,1655,4026,1746,4079,301,25,14,2339,2217,1323,4023,934,157,4317,57,2989,4253,8907,1545,93,4622,1302,2650,3983,3199,4173,1632,321,4134,2254,956,132,133,4082,60,942,8927,1730,2264,70,21,3207,1560,92,8948,3198,1687,2200,1787,1740,1910,578,1089,1762,9608,109,4333,5031,77,3210,4421,2613,1612,96,1266,4244,41,1759,3215,134,73,105,633,1663,1895,4004,2001,1727,1680,34,1548,5016,17,149,4144,2657,1620,8894,59,1520,27,3213,44,8900,71,2193,313,4149,49,1349,1603,1722,1571,98,303,915,1952,2075,2101,3,6212,35,1562,1626,4113,553,145,3988,18,1743,95,1566,1753,8905,1547,2298,48,1790,1813,331,3202,1901,576,1738,1543,1972,72,1372,4414,1649,1685,5115,104,4006,1590,40,3991,114,23,1558,2152,75,568,58,2036,1614,2095,4074,2102,4014,36,8908,1986,19,1859,107,4083,1288,94,294,126,4631,79,1236,4066,131,15,1621,4221,111,1681,659,4423,592,2771,100,4002]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV094^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 18:14:40 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.95/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.00 % [INFO] Parsing done (109ms).
% 1.29/1.01 % [INFO] Running in sequential loop mode.
% 1.75/1.26 % [INFO] eprover registered as external prover.
% 1.75/1.26 % [INFO] Scanning for conjecture ...
% 1.87/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.10/1.36 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.10/1.36 % [INFO] Problem is higher-order (TPTP THF).
% 2.10/1.37 % [INFO] Type checking passed.
% 2.10/1.37 % [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 ...
% 77.55/18.55 % External prover 'e' found a proof!
% 77.55/18.55 % [INFO] Killing All external provers ...
% 77.55/18.55 % Time passed: 18008ms (effective reasoning time: 17534ms)
% 77.55/18.55 % 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)>
% 77.55/18.55 % Axioms used in derivation (0):
% 77.55/18.55 % No. of inferences in proof: 443
% 77.55/18.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 18008 ms resp. 17534 ms w/o parsing
% 77.88/18.75 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 77.88/18.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------