TSTP Solution File: SEV089^5 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV089^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 15:58:11 EDT 2024
% Result : Theorem 71.76s 18.05s
% Output : Refutation 72.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 242 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 1062 ( 434 equ; 79 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 3817 ( 359 ~; 354 |; 89 &;3000 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 223 ( 223 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 862 ( 547 ^ 303 !; 12 ?; 862 :)
% 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 ) > a ).
thf(sk6_type,type,
sk6: ( a > a ) > a ).
thf(sk7_type,type,
sk7: a > ( a > a ) > a ).
thf(sk8_type,type,
sk8: ( a > a > a ) > a > a ).
thf(sk9_type,type,
sk9: a > ( a > a ) > a ).
thf(sk14_type,type,
sk14: a > a > a ).
thf(sk22_type,type,
sk22: a > a ).
thf(sk27_type,type,
sk27: a > 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] :
( ( ^ [F: a] :
( ( A @ F )
& ( D
= ( C @ F ) ) ) )
= ( (=) @ a @ E ) ) ) )
=> ? [C: a > a] :
( ! [D: a] :
( ( B @ D )
=> ( A @ ( C @ D ) ) )
& ! [D: a] :
( ( A @ D )
=> ? [E: a] :
( ( ^ [F: a] :
( ( B @ F )
& ( D
= ( C @ F ) ) ) )
= ( (=) @ a @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEQP_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] :
( ( ^ [F: a] :
( ( A @ F )
& ( D
= ( C @ F ) ) ) )
= ( (=) @ a @ E ) ) ) )
=> ? [C: a > a] :
( ! [D: a] :
( ( B @ D )
=> ( A @ ( C @ D ) ) )
& ! [D: a] :
( ( A @ D )
=> ? [E: a] :
( ( ^ [F: a] :
( ( B @ F )
& ( D
= ( C @ F ) ) ) )
= ( (=) @ a @ E ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o,B: a > $o] :
( ? [C: a > a] :
( ! [D: a] :
( ( A @ D )
=> ( B @ ( C @ D ) ) )
& ! [D: a] :
( ( B @ D )
=> ? [E: a] :
( ( ^ [F: a] :
( ( A @ F )
& ( D
= ( C @ F ) ) ) )
= ( (=) @ a @ E ) ) ) )
=> ? [C: a > a] :
( ! [D: a] :
( ( B @ D )
=> ( A @ ( C @ D ) ) )
& ! [D: a] :
( ( A @ D )
=> ? [E: a] :
( ( ^ [F: a] :
( ( B @ F )
& ( D
= ( C @ F ) ) ) )
= ( (=) @ a @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
! [A: a > a] :
( ( sk2 @ ( sk5 @ A ) )
| ( sk1 @ ( sk6 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(12,plain,
! [A: a > a] :
( ( sk2 @ ( sk5 @ A ) )
| ( sk1 @ ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(4,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ ( sk3 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(18,plain,
! [B: a,A: a > a] :
( ( sk2 @ ( sk5 @ A ) )
| ( sk2 @ ( sk3 @ B ) )
| ( ( sk1 @ ( sk6 @ A ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,4]) ).
thf(19,plain,
! [A: a > a] :
( ( sk2 @ ( sk5 @ A ) )
| ( sk2 @ ( sk3 @ ( sk6 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[18:[bind(A,$thf( C )),bind(B,$thf( sk6 @ C ))]]) ).
thf(20,plain,
! [A: a > a] :
( ( sk2 @ ( sk5 @ A ) )
| ( sk2 @ ( sk3 @ ( sk6 @ A ) ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(8,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( A
= ( sk3 @ B ) ) ) )
= ( (=) @ a @ ( sk4 @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(16,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( sk1 @ B )
& ( A
= ( sk3 @ B ) ) ) )
= ( (=) @ a @ ( sk4 @ A ) ) )
| ~ ( sk2 @ A ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(17,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( sk1 @ B )
& ( A
= ( sk3 @ B ) ) ) )
= ( (=) @ a @ ( sk4 @ A ) ) )
| ~ ( sk2 @ A ) ),
inference(simp,[status(thm)],[16]) ).
thf(72,plain,
! [B: a,A: a] :
( ( ( ( sk1 @ B )
& ( A
= ( sk3 @ B ) ) )
= ( ( sk4 @ A )
= B ) )
| ~ ( sk2 @ A ) ),
inference(func_ext,[status(esa)],[17]) ).
thf(2090,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A )
| ( ( sk1 @ B )
& ( A
= ( sk3 @ B ) ) )
| ( ( sk4 @ A )
!= B ) ),
inference(bool_ext,[status(thm)],[72]) ).
thf(2142,plain,
! [B: a,A: a] :
( ( ( sk4 @ A )
!= B )
| ~ ( sk2 @ A )
| ( ( sk1 @ B )
& ( A
= ( sk3 @ B ) ) ) ),
inference(lifteq,[status(thm)],[2090]) ).
thf(2174,plain,
! [B: a,A: a] :
( ( sk1 @ B )
| ~ ( sk2 @ A )
| ( ( sk4 @ A )
!= B ) ),
inference(cnf,[status(esa)],[2142]) ).
thf(2177,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ A ) )
| ~ ( sk2 @ A ) ),
inference(simp,[status(thm)],[2174]) ).
thf(2201,plain,
! [B: a,A: a > a] :
( ( sk2 @ ( sk3 @ ( sk6 @ A ) ) )
| ( sk1 @ ( sk4 @ B ) )
| ( ( sk2 @ ( sk5 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[20,2177]) ).
thf(2202,plain,
! [A: a > a] :
( ( sk2 @ ( sk3 @ ( sk6 @ A ) ) )
| ( sk1 @ ( sk4 @ ( sk5 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[2201:[bind(A,$thf( C )),bind(B,$thf( sk5 @ C ))]]) ).
thf(2298,plain,
! [A: a > a] :
( ( sk2 @ ( sk3 @ ( sk6 @ A ) ) )
| ( sk1 @ ( sk4 @ ( sk5 @ A ) ) ) ),
inference(simp,[status(thm)],[2202]) ).
thf(7,plain,
! [A: a > a] :
( ~ ( sk1 @ ( A @ ( sk5 @ A ) ) )
| ( sk1 @ ( sk6 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(15,plain,
! [A: a > a] :
( ~ ( sk1 @ ( A @ ( sk5 @ A ) ) )
| ( sk1 @ ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(24,plain,
! [B: a,A: a > a] :
( ~ ( sk1 @ ( A @ ( sk5 @ A ) ) )
| ( sk2 @ ( sk3 @ B ) )
| ( ( sk1 @ ( sk6 @ A ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[15,4]) ).
thf(25,plain,
! [A: a > a] :
( ~ ( sk1 @ ( A @ ( sk5 @ A ) ) )
| ( sk2 @ ( sk3 @ ( sk6 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( C )),bind(B,$thf( sk6 @ C ))]]) ).
thf(30,plain,
! [A: a > a] :
( ~ ( sk1 @ ( A @ ( sk5 @ A ) ) )
| ( sk2 @ ( sk3 @ ( sk6 @ A ) ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(61,plain,
! [B: a > a,A: a > a] :
( ~ ( sk1 @ ( A @ ( sk5 @ A ) ) )
| ( sk2 @ ( sk3 @ ( sk6 @ B ) ) )
| ( ( sk1 @ ( sk6 @ A ) )
!= ( sk1 @ ( B @ ( sk5 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,30]) ).
thf(64,plain,
! [A: a > a > a] :
( ~ ( sk1
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) )
| ( sk2
@ ( sk3
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[61:[bind(A,$thf( C @ ( sk5 @ ^ [D: a] : ( sk6 @ ( C @ D ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk6 @ ( C @ D ) ) ))]]) ).
thf(65,plain,
! [A: a > a > a] :
( ~ ( sk1
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) )
| ( sk2
@ ( sk3
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(3225,plain,
! [B: a > a > a,A: a > a] :
( ( sk2 @ ( sk3 @ ( sk6 @ A ) ) )
| ( sk2
@ ( sk3
@ ( sk6
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) ) ) )
| ( ( sk1 @ ( sk4 @ ( sk5 @ A ) ) )
!= ( sk1
@ ( B
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) )
@ ( sk5
@ ( B
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2298,65]) ).
thf(3273,plain,
( ( sk2
@ ( sk3
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] : ( sk4 @ A ) ) ) ) )
| ( sk2
@ ( sk3
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3225:[bind(A,$thf( ^ [C: a] : ( sk6 @ ^ [D: a] : ( sk4 @ C ) ) )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ( sk4 @ C ) ))]]) ).
thf(3362,plain,
( sk2
@ ( sk3
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ),
inference(simp,[status(thm)],[3273]) ).
thf(3678,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ A ) )
| ( ( sk2
@ ( sk3
@ ( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk4 @ B ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3362,2177]) ).
thf(3679,plain,
( sk1
@ ( sk4
@ ( sk3
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3678:[bind(A,$thf( sk3 @ ( sk6 @ ^ [B: a] : ( sk6 @ ^ [C: a] : ( sk4 @ B ) ) ) ))]]) ).
thf(3258,plain,
! [B: a > a,A: a > a] :
( ( sk2 @ ( sk3 @ ( sk6 @ A ) ) )
| ( sk2 @ ( sk3 @ ( sk6 @ B ) ) )
| ( ( sk1 @ ( sk4 @ ( sk5 @ A ) ) )
!= ( sk1 @ ( B @ ( sk5 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2298,30]) ).
thf(3299,plain,
( ( sk2 @ ( sk3 @ ( sk6 @ sk4 ) ) )
| ( sk2 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ),
inference(pre_uni,[status(thm)],[3258:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 ))]]) ).
thf(3373,plain,
sk2 @ ( sk3 @ ( sk6 @ sk4 ) ),
inference(simp,[status(thm)],[3299]) ).
thf(2251,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk3 @ B ) )
| ( ( sk1 @ ( sk4 @ A ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2177,4]) ).
thf(2252,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk3 @ ( sk4 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[2251:[bind(A,$thf( C )),bind(B,$thf( sk4 @ C ))]]) ).
thf(2309,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk3 @ ( sk4 @ A ) ) ) ),
inference(simp,[status(thm)],[2252]) ).
thf(3578,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ ( sk4 @ A ) ) )
| ( ( sk2 @ ( sk3 @ ( sk6 @ sk4 ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3373,2309]) ).
thf(3579,plain,
sk2 @ ( sk3 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[3578:[bind(A,$thf( sk3 @ ( sk6 @ sk4 ) ))]]) ).
thf(2380,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A )
| ( sk1 @ ( sk4 @ B ) )
| ( ( sk2 @ ( sk3 @ ( sk4 @ A ) ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2309,2177]) ).
thf(2381,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk1 @ ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2380:[bind(A,$thf( D )),bind(B,$thf( sk3 @ ( sk4 @ D ) ))]]) ).
thf(2430,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk1 @ ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) ) ),
inference(simp,[status(thm)],[2381]) ).
thf(3823,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) )
| ( ( sk2 @ ( sk3 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3579,2430]) ).
thf(3824,plain,
sk1 @ ( sk4 @ ( sk3 @ ( sk4 @ ( sk3 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3823:[bind(A,$thf( sk3 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ))]]) ).
thf(2173,plain,
! [B: a,A: a] :
( ( A
= ( sk3 @ B ) )
| ~ ( sk2 @ A )
| ( ( sk4 @ A )
!= B ) ),
inference(cnf,[status(esa)],[2142]) ).
thf(2175,plain,
! [B: a,A: a] :
( ( A
= ( sk3 @ B ) )
| ~ ( sk2 @ A )
| ( ( sk4 @ A )
!= B ) ),
inference(lifteq,[status(thm)],[2173]) ).
thf(2176,plain,
! [A: a] :
( ( ( sk3 @ ( sk4 @ A ) )
= A )
| ~ ( sk2 @ A ) ),
inference(simp,[status(thm)],[2175]) ).
thf(3588,plain,
! [A: a] :
( ( ( sk3 @ ( sk4 @ A ) )
= A )
| ( ( sk2 @ ( sk3 @ ( sk6 @ sk4 ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3373,2176]) ).
thf(3589,plain,
( ( sk3 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) )
= ( sk3 @ ( sk6 @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[3588:[bind(A,$thf( sk3 @ ( sk6 @ sk4 ) ))]]) ).
thf(7698,plain,
sk1 @ ( sk4 @ ( sk3 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ),
inference(rewrite,[status(thm)],[3824,3589]) ).
thf(3610,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ A ) )
| ( ( sk2 @ ( sk3 @ ( sk6 @ sk4 ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3373,2177]) ).
thf(3611,plain,
sk1 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[3610:[bind(A,$thf( sk3 @ ( sk6 @ sk4 ) ))]]) ).
thf(3724,plain,
! [A: a > a > a] :
( ( sk2
@ ( sk3
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) )
| ( ( sk1 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) )
!= ( sk1
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3611,65]) ).
thf(3755,plain,
( sk2
@ ( sk3
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3724:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ))]]) ).
thf(3749,plain,
! [A: a > a] :
( ( sk1 @ ( sk6 @ A ) )
| ( ( sk1 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) )
!= ( sk1 @ ( A @ ( sk5 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3611,15]) ).
thf(3769,plain,
( sk1
@ ( sk6
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ),
inference(pre_uni,[status(thm)],[3749:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ))]]) ).
thf(2253,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ( sk1 @ ( sk4 @ B ) )
| ( ( sk2 @ ( sk3 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4,2177]) ).
thf(2254,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk1 @ ( sk4 @ ( sk3 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[2253:[bind(A,$thf( C )),bind(B,$thf( sk3 @ C ))]]) ).
thf(2310,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk1 @ ( sk4 @ ( sk3 @ A ) ) ) ),
inference(simp,[status(thm)],[2254]) ).
thf(3943,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ ( sk3 @ A ) ) )
| ( ( sk1
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3769,2310]) ).
thf(3944,plain,
( sk1
@ ( sk4
@ ( sk3
@ ( sk6
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3943:[bind(A,$thf( sk6 @ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ))]]) ).
thf(5,plain,
! [B: a,A: a > a] :
( ( sk2 @ ( sk5 @ A ) )
| ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
! [B: a,A: a > a] :
( ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) )
| ( sk2 @ ( sk5 @ A ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(11,plain,
! [B: a,A: a > a] :
( ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) )
| ( sk2 @ ( sk5 @ A ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(82,plain,
! [C: a,B: a > a,A: a] :
( ~ ( sk2 @ A )
| ( ( (=) @ a @ ( sk4 @ A ) )
!= ( (=) @ a @ C ) )
| ( sk2 @ ( sk5 @ B ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( A
= ( sk3 @ D ) ) ) )
!= ( ^ [D: a] :
( ( sk2 @ D )
& ( ( sk6 @ B )
= ( B @ D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,11]) ).
thf(101,plain,
! [C: a,B: a > a,A: a] :
( ( sk2 @ ( sk5 @ B ) )
| ~ ( sk2 @ A )
| ( ( (=) @ a @ ( sk4 @ A ) )
!= ( (=) @ a @ C ) )
| ( sk2 != sk1 )
| ( ( ^ [D: a] :
( A
= ( sk3 @ D ) ) )
!= ( ^ [D: a] :
( ( sk6 @ B )
= ( B @ D ) ) ) ) ),
inference(simp,[status(thm)],[82]) ).
thf(9,plain,
! [B: a,A: a > a] :
( ~ ( sk1 @ ( A @ ( sk5 @ A ) ) )
| ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(13,plain,
! [B: a,A: a > a] :
( ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) )
| ~ ( sk1 @ ( A @ ( sk5 @ A ) ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(14,plain,
! [B: a,A: a > a] :
( ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) )
| ~ ( sk1 @ ( A @ ( sk5 @ A ) ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(73,plain,
! [C: a,B: a > a,A: a] :
( ~ ( sk2 @ A )
| ( ( (=) @ a @ ( sk4 @ A ) )
!= ( (=) @ a @ C ) )
| ~ ( sk1 @ ( B @ ( sk5 @ B ) ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( A
= ( sk3 @ D ) ) ) )
!= ( ^ [D: a] :
( ( sk2 @ D )
& ( ( sk6 @ B )
= ( B @ D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,14]) ).
thf(94,plain,
! [C: a,B: a > a,A: a] :
( ~ ( sk2 @ A )
| ( ( ^ [D: a] : ( sk4 @ A ) )
!= ( ^ [D: a] : C ) )
| ( ( ^ [D: a] : D )
!= ( ^ [D: a] : D ) )
| ~ ( sk1 @ ( B @ ( sk5 @ B ) ) )
| ( sk2 != sk1 )
| ( ( ^ [D: a] :
( A
= ( sk3 @ D ) ) )
!= ( ^ [D: a] :
( ( sk6 @ B )
= ( B @ D ) ) ) ) ),
inference(simp,[status(thm)],[73]) ).
thf(115,plain,
! [C: a,B: a > a,A: a] :
( ~ ( sk2 @ A )
| ( ( ^ [D: a] : ( sk4 @ A ) )
!= ( ^ [D: a] : C ) )
| ~ ( sk1 @ ( B @ ( sk5 @ B ) ) )
| ( sk2 != sk1 )
| ( ( ^ [D: a] :
( A
= ( sk3 @ D ) ) )
!= ( ^ [D: a] :
( ( sk6 @ B )
= ( B @ D ) ) ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(151,plain,
! [C: a,B: a > a,A: a] :
( ~ ( sk2 @ A )
| ( ( ^ [D: a] : ( sk4 @ A ) )
!= ( ^ [D: a] : C ) )
| ~ ( sk1 @ ( B @ ( sk5 @ B ) ) )
| ( sk2 != sk1 )
| ( ( ^ [D: a] : A )
!= ( ^ [D: a] : ( sk6 @ B ) ) )
| ( sk3 != B ) ),
inference(simp,[status(thm)],[115]) ).
thf(186,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A )
| ( ( ^ [C: a] : ( sk4 @ A ) )
!= ( ^ [C: a] : B ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ( sk2 != sk1 )
| ( ( ^ [C: a] : A )
!= ( ^ [C: a] : ( sk6 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[151]) ).
thf(3603,plain,
! [B: a,A: a] :
( ( ( ^ [C: a] : ( sk4 @ A ) )
!= ( ^ [C: a] : B ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ( sk2 != sk1 )
| ( ( ^ [C: a] : A )
!= ( ^ [C: a] : ( sk6 @ sk3 ) ) )
| ( ( sk2 @ ( sk3 @ ( sk6 @ sk4 ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3373,186]) ).
thf(3604,plain,
! [A: a] :
( ( ( ^ [B: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) )
!= ( ^ [B: a] : A ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ( sk2 != sk1 )
| ( ( ^ [B: a] : ( sk3 @ ( sk6 @ sk4 ) ) )
!= ( ^ [B: a] : ( sk6 @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[3603:[bind(A,$thf( sk3 @ ( sk6 @ sk4 ) )),bind(B,$thf( B ))]]) ).
thf(3637,plain,
! [A: a] :
( ( ( ^ [B: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) )
!= ( ^ [B: a] : A ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ( sk2 != sk1 )
| ( ( ^ [B: a] : ( sk3 @ ( sk6 @ sk4 ) ) )
!= ( ^ [B: a] : ( sk6 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[3604]) ).
thf(4071,plain,
! [A: a] :
( ( ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) )
!= A )
| ( ( sk2 @ ( sk27 @ A ) )
!= ( sk1 @ ( sk27 @ A ) ) )
| ( ( sk3 @ ( sk6 @ sk4 ) )
!= ( sk6 @ sk3 ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) ) ),
inference(func_ext,[status(esa)],[3637]) ).
thf(4110,plain,
( ( ( sk2 @ ( sk27 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) )
!= ( sk1 @ ( sk27 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) )
| ( ( sk3 @ ( sk6 @ sk4 ) )
!= ( sk6 @ sk3 ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[4071]) ).
thf(27,plain,
! [B: a > a,A: a > a] :
( ~ ( sk1 @ ( A @ ( sk5 @ A ) ) )
| ( sk1 @ ( sk6 @ B ) )
| ( ( sk1 @ ( sk6 @ A ) )
!= ( sk1 @ ( B @ ( sk5 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,15]) ).
thf(29,plain,
! [A: a > a > a] :
( ~ ( sk1
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) )
| ( sk1
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ),
inference(pre_uni,[status(thm)],[27:[bind(A,$thf( C @ ( sk5 @ ^ [D: a] : ( sk6 @ ( C @ D ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk6 @ ( C @ D ) ) ))]]) ).
thf(32,plain,
! [A: a > a > a] :
( ~ ( sk1
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) )
| ( sk1
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(3732,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) )
| ( ( sk1 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) )
!= ( sk1
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3611,32]) ).
thf(3758,plain,
( sk1
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3732:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ))]]) ).
thf(4527,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ ( sk3 @ A ) ) )
| ( ( sk1
@ ( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3758,2310]) ).
thf(4528,plain,
( sk1
@ ( sk4
@ ( sk3
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4527:[bind(A,$thf( sk6 @ ^ [B: a] : ( sk6 @ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ))]]) ).
thf(83,plain,
! [B: a,A: a > a] :
( ~ ( sk1 @ ( A @ ( sk5 @ A ) ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( B
= ( sk3 @ C ) ) ) )
= ( (=) @ a @ ( sk4 @ B ) ) )
| ( ( sk2 @ ( sk3 @ ( sk6 @ A ) ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[30,17]) ).
thf(84,plain,
! [A: a > a] :
( ~ ( sk1 @ ( A @ ( sk5 @ A ) ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3 @ ( sk6 @ A ) )
= ( sk3 @ B ) ) ) )
= ( (=) @ a @ ( sk4 @ ( sk3 @ ( sk6 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[83:[bind(A,$thf( D )),bind(B,$thf( sk3 @ ( sk6 @ D ) ))]]) ).
thf(110,plain,
! [A: a > a] :
( ~ ( sk1 @ ( A @ ( sk5 @ A ) ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3 @ ( sk6 @ A ) )
= ( sk3 @ B ) ) ) )
= ( (=) @ a @ ( sk4 @ ( sk3 @ ( sk6 @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(191,plain,
! [B: a,A: a] :
( ( ( sk4 @ A )
!= B )
| ( ( sk2 @ ( sk14 @ B @ A ) )
!= ( sk1 @ ( sk14 @ B @ A ) ) )
| ( ( sk6 @ sk3 )
!= A )
| ~ ( sk2 @ A )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) ) ),
inference(func_ext,[status(esa)],[186]) ).
thf(226,plain,
( ( ( sk2 @ ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) ) )
!= ( sk1 @ ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) ) ) )
| ~ ( sk2 @ ( sk6 @ sk3 ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[191]) ).
thf(3577,plain,
( ( ( sk2 @ ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) ) )
!= ( sk1 @ ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) ) ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ( ( sk2 @ ( sk3 @ ( sk6 @ sk4 ) ) )
!= ( sk2 @ ( sk6 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3373,226]) ).
thf(3612,plain,
( ( ( sk2 @ ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) ) )
!= ( sk1 @ ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) ) ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ( ( sk3 @ ( sk6 @ sk4 ) )
!= ( sk6 @ sk3 ) ) ),
inference(simp,[status(thm)],[3577]) ).
thf(35,plain,
! [C: a,B: a > a,A: a > a] :
( ~ ( sk1 @ ( A @ ( sk5 @ A ) ) )
| ( ( ^ [D: a] :
( ( sk2 @ D )
& ( ( sk6 @ B )
= ( B @ D ) ) ) )
!= ( (=) @ a @ C ) )
| ( ( sk1 @ ( sk6 @ A ) )
!= ( sk1 @ ( B @ ( sk5 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,14]) ).
thf(37,plain,
! [B: a > a > a,A: a] :
( ~ ( sk1
@ ( B
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) )
@ ( sk5
@ ( B
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6
@ ^ [D: a] : ( sk6 @ ( B @ D ) ) )
= ( sk6 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(pre_uni,[status(thm)],[35:[bind(A,$thf( D @ ( sk5 @ ^ [E: a] : ( sk6 @ ( D @ E ) ) ) )),bind(B,$thf( ^ [E: a] : ( sk6 @ ( D @ E ) ) ))]]) ).
thf(39,plain,
! [B: a > a > a,A: a] :
( ~ ( sk1
@ ( B
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) )
@ ( sk5
@ ( B
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6
@ ^ [D: a] : ( sk6 @ ( B @ D ) ) )
= ( sk6 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(simp,[status(thm)],[37]) ).
thf(42,plain,
! [C: a > a > a,B: a,A: a > a] :
( ~ ( sk1 @ ( A @ ( sk5 @ A ) ) )
| ( ( ^ [D: a] :
( ( sk2 @ D )
& ( ( sk6
@ ^ [E: a] : ( sk6 @ ( C @ E ) ) )
= ( sk6 @ ( C @ D ) ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1 @ ( sk6 @ A ) )
!= ( sk1
@ ( C
@ ( sk5
@ ^ [D: a] : ( sk6 @ ( C @ D ) ) )
@ ( sk5
@ ( C
@ ( sk5
@ ^ [D: a] : ( sk6 @ ( C @ D ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,39]) ).
thf(44,plain,
! [B: a > a > a > a,A: a] :
( ~ ( sk1
@ ( B
@ ( sk5
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk6 @ ( B @ C @ D ) ) ) )
@ ( sk5
@ ^ [C: a] :
( sk6
@ ( B
@ ( sk5
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk6 @ ( B @ D @ E ) ) ) )
@ C ) ) )
@ ( sk5
@ ( B
@ ( sk5
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk6 @ ( B @ C @ D ) ) ) )
@ ( sk5
@ ^ [C: a] :
( sk6
@ ( B
@ ( sk5
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk6 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk6 @ ( B @ D @ E ) ) ) )
= ( sk6
@ ^ [D: a] : ( sk6 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(pre_uni,[status(thm)],[42:[bind(A,$thf( D @ ( sk5 @ ^ [E: a] : ( sk6 @ ^ [F: a] : ( sk6 @ ( D @ E @ F ) ) ) ) @ ( sk5 @ ^ [E: a] : ( sk6 @ ( D @ ( sk5 @ ^ [F: a] : ( sk6 @ ^ [G: a] : ( sk6 @ ( D @ F @ G ) ) ) ) @ E ) ) ) )),bind(B,$thf( B )),bind(C,$thf( ^ [E: a] : ^ [F: a] : ( sk6 @ ( D @ E @ F ) ) ))]]) ).
thf(46,plain,
! [B: a > a > a > a,A: a] :
( ~ ( sk1
@ ( B
@ ( sk5
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk6 @ ( B @ C @ D ) ) ) )
@ ( sk5
@ ^ [C: a] :
( sk6
@ ( B
@ ( sk5
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk6 @ ( B @ D @ E ) ) ) )
@ C ) ) )
@ ( sk5
@ ( B
@ ( sk5
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk6 @ ( B @ C @ D ) ) ) )
@ ( sk5
@ ^ [C: a] :
( sk6
@ ( B
@ ( sk5
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk6 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk6 @ ( B @ D @ E ) ) ) )
= ( sk6
@ ^ [D: a] : ( sk6 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(simp,[status(thm)],[44]) ).
thf(26,plain,
! [B: a > a,A: a > a] :
( ( sk2 @ ( sk5 @ A ) )
| ( sk1 @ ( sk6 @ B ) )
| ( ( sk1 @ ( sk6 @ A ) )
!= ( sk1 @ ( B @ ( sk5 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,15]) ).
thf(28,plain,
! [A: a > a > a] :
( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) )
| ( sk1
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ),
inference(pre_uni,[status(thm)],[26:[bind(A,$thf( C @ ( sk5 @ ^ [D: a] : ( sk6 @ ( C @ D ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk6 @ ( C @ D ) ) ))]]) ).
thf(31,plain,
! [A: a > a > a] :
( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) )
| ( sk1
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(21,plain,
! [A: a > a] :
( ( sk2 @ ( sk5 @ A ) )
| ( ( sk2 @ ( sk3 @ ( sk6 @ A ) ) )
!= ( sk2 @ ( sk5 @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[20]) ).
thf(22,plain,
! [A: a > a] :
( ( sk2 @ ( sk5 @ A ) )
| ( ( sk2 @ ( sk3 @ ( sk6 @ A ) ) )
!= ( sk2 @ ( sk5 @ A ) ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(129,plain,
! [B: a > a,A: a > a > a] :
( ( sk1
@ ( sk6
@ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) )
| ( sk2 @ ( sk5 @ B ) )
| ~ ( sk2 @ ( sk3 @ ( sk6 @ B ) ) )
| ( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) ) ) )
!= ( sk2 @ ( sk5 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,22]) ).
thf(146,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) )
| ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) )
| ~ ( sk2
@ ( sk3
@ ( sk6
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[129:[bind(A,$thf( A )),bind(B,$thf( A @ ( sk5 @ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) ))]]) ).
thf(3605,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) )
| ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) )
| ( ( sk2
@ ( sk3
@ ( sk6
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) )
!= ( sk2 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3373,146]) ).
thf(3623,plain,
( ( sk1
@ ( sk6
@ ^ [A: a] : ( sk6 @ sk4 ) ) )
| ( sk2 @ ( sk5 @ sk4 ) ) ),
inference(pre_uni,[status(thm)],[3605:[bind(A,$thf( ^ [B: a] : sk4 ))]]) ).
thf(4269,plain,
! [A: a] :
( ( sk1
@ ( sk6
@ ^ [B: a] : ( sk6 @ sk4 ) ) )
| ( sk1 @ ( sk4 @ A ) )
| ( ( sk2 @ ( sk5 @ sk4 ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3623,2177]) ).
thf(4270,plain,
( ( sk1
@ ( sk6
@ ^ [A: a] : ( sk6 @ sk4 ) ) )
| ( sk1 @ ( sk4 @ ( sk5 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[4269:[bind(A,$thf( sk5 @ sk4 ))]]) ).
thf(48,plain,
! [C: a > a > a,B: a,A: a > a > a] :
( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [D: a] : ( sk6 @ ( A @ D ) ) ) ) ) )
| ( ( ^ [D: a] :
( ( sk2 @ D )
& ( ( sk6
@ ^ [E: a] : ( sk6 @ ( C @ E ) ) )
= ( sk6 @ ( C @ D ) ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1
@ ( sk6
@ ^ [D: a] : ( sk6 @ ( A @ D ) ) ) )
!= ( sk1
@ ( C
@ ( sk5
@ ^ [D: a] : ( sk6 @ ( C @ D ) ) )
@ ( sk5
@ ( C
@ ( sk5
@ ^ [D: a] : ( sk6 @ ( C @ D ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,39]) ).
thf(53,plain,
! [B: a > a > a > a > a,A: a] :
( ( sk2
@ ( sk5
@ ( B
@ ( sk5
@ ^ [C: a] :
( sk6
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk6 @ ( B @ C @ D @ E ) ) ) ) )
@ ( sk5
@ ^ [C: a] :
( sk6
@ ^ [D: a] :
( sk6
@ ( B
@ ( sk5
@ ^ [E: a] :
( sk6
@ ^ [F: a] :
( sk6
@ ^ [G: a] : ( sk6 @ ( B @ E @ F @ G ) ) ) ) )
@ C
@ D ) ) ) )
@ ( sk5
@ ^ [C: a] :
( sk6
@ ( B
@ ( sk5
@ ^ [D: a] :
( sk6
@ ^ [E: a] :
( sk6
@ ^ [F: a] : ( sk6 @ ( B @ D @ E @ F ) ) ) ) )
@ ( sk5
@ ^ [D: a] :
( sk6
@ ^ [E: a] :
( sk6
@ ( B
@ ( sk5
@ ^ [F: a] :
( sk6
@ ^ [G: a] :
( sk6
@ ^ [H: a] : ( sk6 @ ( B @ F @ G @ H ) ) ) ) )
@ D
@ E ) ) ) )
@ C ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6
@ ^ [D: a] :
( sk6
@ ^ [E: a] :
( sk6
@ ^ [F: a] : ( sk6 @ ( B @ D @ E @ F ) ) ) ) )
= ( sk6
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk6 @ ( B @ C @ D @ E ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(pre_uni,[status(thm)],[48:[bind(A,$thf( E @ ( sk5 @ ^ [E: a] : ( sk6 @ ^ [F: a] : ( sk6 @ ^ [G: a] : ( sk6 @ ( E @ E @ F @ G ) ) ) ) ) @ ( sk5 @ ^ [E: a] : ( sk6 @ ^ [F: a] : ( sk6 @ ( E @ ( sk5 @ ^ [G: a] : ( sk6 @ ^ [H: a] : ( sk6 @ ^ [I: a] : ( sk6 @ ( E @ G @ H @ I ) ) ) ) ) @ E @ F ) ) ) ) )),bind(B,$thf( B )),bind(C,$thf( ^ [E: a] : ^ [F: a] : ( sk6 @ ^ [G: a] : ( sk6 @ ( E @ E @ F @ G ) ) ) ))]]) ).
thf(57,plain,
! [B: a > a > a > a > a,A: a] :
( ( sk2
@ ( sk5
@ ( B
@ ( sk5
@ ^ [C: a] :
( sk6
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk6 @ ( B @ C @ D @ E ) ) ) ) )
@ ( sk5
@ ^ [C: a] :
( sk6
@ ^ [D: a] :
( sk6
@ ( B
@ ( sk5
@ ^ [E: a] :
( sk6
@ ^ [F: a] :
( sk6
@ ^ [G: a] : ( sk6 @ ( B @ E @ F @ G ) ) ) ) )
@ C
@ D ) ) ) )
@ ( sk5
@ ^ [C: a] :
( sk6
@ ( B
@ ( sk5
@ ^ [D: a] :
( sk6
@ ^ [E: a] :
( sk6
@ ^ [F: a] : ( sk6 @ ( B @ D @ E @ F ) ) ) ) )
@ ( sk5
@ ^ [D: a] :
( sk6
@ ^ [E: a] :
( sk6
@ ( B
@ ( sk5
@ ^ [F: a] :
( sk6
@ ^ [G: a] :
( sk6
@ ^ [H: a] : ( sk6 @ ( B @ F @ G @ H ) ) ) ) )
@ D
@ E ) ) ) )
@ C ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6
@ ^ [D: a] :
( sk6
@ ^ [E: a] :
( sk6
@ ^ [F: a] : ( sk6 @ ( B @ D @ E @ F ) ) ) ) )
= ( sk6
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk6 @ ( B @ C @ D @ E ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(simp,[status(thm)],[53]) ).
thf(93,plain,
! [C: a,B: a > a,A: a] :
( ~ ( sk2 @ A )
| ( ( (=) @ a @ ( sk4 @ A ) )
!= ( (=) @ a @ C ) )
| ~ ( sk1 @ ( B @ ( sk5 @ B ) ) )
| ( sk2 != sk1 )
| ( ( ^ [D: a] :
( A
= ( sk3 @ D ) ) )
!= ( ^ [D: a] :
( ( sk6 @ B )
= ( B @ D ) ) ) ) ),
inference(simp,[status(thm)],[73]) ).
thf(3880,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk4
@ ( sk3
@ ( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3679,32]) ).
thf(3919,plain,
( sk1
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk6
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3880:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk4 @ ( sk3 @ ( sk6 @ ^ [D: a] : ( sk6 @ ^ [E: a] : ( sk4 @ D ) ) ) ) ) ))]]) ).
thf(2376,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ ( sk3 @ ( sk4 @ B ) ) )
| ( ( sk2 @ ( sk3 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4,2309]) ).
thf(2377,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ ( sk3 @ ( sk4 @ ( sk3 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2376:[bind(A,$thf( C )),bind(B,$thf( sk3 @ C ))]]) ).
thf(2429,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ ( sk3 @ ( sk4 @ ( sk3 @ A ) ) ) ) ),
inference(simp,[status(thm)],[2377]) ).
thf(3886,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ ( sk4 @ ( sk3 @ A ) ) ) )
| ( ( sk1
@ ( sk4
@ ( sk3
@ ( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3679,2429]) ).
thf(3887,plain,
( sk2
@ ( sk3
@ ( sk4
@ ( sk3
@ ( sk4
@ ( sk3
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3886:[bind(A,$thf( sk4 @ ( sk3 @ ( sk6 @ ^ [B: a] : ( sk6 @ ^ [C: a] : ( sk4 @ B ) ) ) ) ))]]) ).
thf(4257,plain,
! [A: a] :
( ( sk2 @ ( sk5 @ sk4 ) )
| ( sk2 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk6
@ ^ [B: a] : ( sk6 @ sk4 ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3623,4]) ).
thf(4258,plain,
( ( sk2 @ ( sk5 @ sk4 ) )
| ( sk2
@ ( sk3
@ ( sk6
@ ^ [A: a] : ( sk6 @ sk4 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4257:[bind(A,$thf( sk6 @ ^ [B: a] : ( sk6 @ sk4 ) ))]]) ).
thf(5333,plain,
( ( ( sk3 @ ( sk6 @ sk4 ) )
!= ( sk6 @ sk3 ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ~ ( sk2 @ ( sk27 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) )
| ~ ( sk1 @ ( sk27 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) ),
inference(bool_ext,[status(thm)],[4110]) ).
thf(203,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A )
| ( ( ^ [D: a] : ( sk4 @ B ) )
!= ( ^ [D: a] : C ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ( sk2 != sk1 )
| ( ( ^ [D: a] : B )
!= ( ^ [D: a] : ( sk6 @ sk3 ) ) )
| ( ( sk2 @ ( sk3 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4,186]) ).
thf(204,plain,
! [B: a,A: a] :
( ~ ( sk1 @ B )
| ( ( ^ [C: a] : ( sk4 @ ( sk3 @ B ) ) )
!= ( ^ [C: a] : A ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ( sk2 != sk1 )
| ( ( ^ [C: a] : ( sk3 @ B ) )
!= ( ^ [C: a] : ( sk6 @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[203:[bind(A,$thf( D )),bind(B,$thf( sk3 @ D ))]]) ).
thf(221,plain,
! [B: a,A: a] :
( ~ ( sk1 @ B )
| ( ( ^ [C: a] : ( sk4 @ ( sk3 @ B ) ) )
!= ( ^ [C: a] : A ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ( sk2 != sk1 )
| ( ( ^ [C: a] : ( sk3 @ B ) )
!= ( ^ [C: a] : ( sk6 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[204]) ).
thf(3720,plain,
! [B: a > a > a > a,A: a] :
( ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk6 @ ( B @ D @ E ) ) ) )
= ( sk6
@ ^ [D: a] : ( sk6 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) )
!= ( sk1
@ ( B
@ ( sk5
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk6 @ ( B @ C @ D ) ) ) )
@ ( sk5
@ ^ [C: a] :
( sk6
@ ( B
@ ( sk5
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk6 @ ( B @ D @ E ) ) ) )
@ C ) ) )
@ ( sk5
@ ( B
@ ( sk5
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk6 @ ( B @ C @ D ) ) ) )
@ ( sk5
@ ^ [C: a] :
( sk6
@ ( B
@ ( sk5
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk6 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3611,46]) ).
thf(3756,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk2 @ B )
& ( ( sk6
@ ^ [C: a] :
( sk6
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) )
= ( sk6
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(pre_uni,[status(thm)],[3720:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ^ [E: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ))]]) ).
thf(513,plain,
( ~ ( sk2 @ ( sk6 @ sk3 ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ~ ( sk2 @ ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) ) )
| ~ ( sk1 @ ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) ) ) ),
inference(bool_ext,[status(thm)],[226]) ).
thf(601,plain,
( ~ ( sk2 @ ( sk6 @ sk3 ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ~ ( sk1 @ ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) ) )
| ( ( sk2 @ ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) ) )
!= ( sk2 @ ( sk6 @ sk3 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[513]) ).
thf(625,plain,
( ~ ( sk2 @ ( sk6 @ sk3 ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ~ ( sk1 @ ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) ) )
| ( ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) )
!= ( sk6 @ sk3 ) ) ),
inference(simp,[status(thm)],[601]) ).
thf(929,plain,
( ~ ( sk2 @ ( sk6 @ sk3 ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ( ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) )
!= ( sk6 @ sk3 ) )
| ( ( sk1 @ ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) ) )
!= ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[625]) ).
thf(957,plain,
( ~ ( sk2 @ ( sk6 @ sk3 ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ( ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) )
!= ( sk6 @ sk3 ) )
| ( ( sk1 @ ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) ) )
!= ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) ) ) ),
inference(simp,[status(thm)],[929]) ).
thf(34,plain,
! [C: a,B: a > a,A: a > a] :
( ( sk2 @ ( sk5 @ A ) )
| ( ( ^ [D: a] :
( ( sk2 @ D )
& ( ( sk6 @ B )
= ( B @ D ) ) ) )
!= ( (=) @ a @ C ) )
| ( ( sk1 @ ( sk6 @ A ) )
!= ( sk1 @ ( B @ ( sk5 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,14]) ).
thf(36,plain,
! [B: a > a > a,A: a] :
( ( sk2
@ ( sk5
@ ( B
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6
@ ^ [D: a] : ( sk6 @ ( B @ D ) ) )
= ( sk6 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(pre_uni,[status(thm)],[34:[bind(A,$thf( D @ ( sk5 @ ^ [E: a] : ( sk6 @ ( D @ E ) ) ) )),bind(B,$thf( ^ [E: a] : ( sk6 @ ( D @ E ) ) ))]]) ).
thf(38,plain,
! [B: a > a > a,A: a] :
( ( sk2
@ ( sk5
@ ( B
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6
@ ^ [D: a] : ( sk6 @ ( B @ D ) ) )
= ( sk6 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(49,plain,
! [B: a,A: a > a > a] :
( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) ) ) )
| ( sk2 @ ( sk3 @ B ) )
| ( ( sk1
@ ( sk6
@ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[31,4]) ).
thf(50,plain,
! [A: a > a > a] :
( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) )
| ( sk2
@ ( sk3
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[49:[bind(A,$thf( D )),bind(B,$thf( sk6 @ ^ [D: a] : ( sk6 @ ( D @ D ) ) ))]]) ).
thf(55,plain,
! [A: a > a > a] :
( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) )
| ( sk2
@ ( sk3
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(69,plain,
! [A: a > a > a] :
( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) )
| ( ( sk2
@ ( sk3
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) )
!= ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[55]) ).
thf(70,plain,
! [A: a > a > a] :
( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) )
| ( ( sk2
@ ( sk3
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) )
!= ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(33,plain,
! [B: a,A: a > a] :
( ( ( ( sk2 @ ( sk7 @ B @ A ) )
& ( ( sk6 @ A )
= ( A @ ( sk7 @ B @ A ) ) ) )
!= ( B
= ( sk7 @ B @ A ) ) )
| ~ ( sk1 @ ( A @ ( sk5 @ A ) ) ) ),
inference(func_ext,[status(esa)],[14]) ).
thf(80,plain,
! [C: a > a > a,B: a,A: a] :
( ~ ( sk2 @ A )
| ~ ( sk1
@ ( C
@ ( sk5
@ ^ [D: a] : ( sk6 @ ( C @ D ) ) )
@ ( sk5
@ ( C
@ ( sk5
@ ^ [D: a] : ( sk6 @ ( C @ D ) ) ) ) ) ) )
| ( ( (=) @ a @ ( sk4 @ A ) )
!= ( (=) @ a @ B ) )
| ( ( ^ [D: a] :
( ( sk2 @ D )
& ( ( sk6
@ ^ [E: a] : ( sk6 @ ( C @ E ) ) )
= ( sk6 @ ( C @ D ) ) ) ) )
!= ( ^ [D: a] :
( ( sk1 @ D )
& ( A
= ( sk3 @ D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,39]) ).
thf(97,plain,
! [C: a > a > a,B: a,A: a] :
( ~ ( sk2 @ A )
| ~ ( sk1
@ ( C
@ ( sk5
@ ^ [D: a] : ( sk6 @ ( C @ D ) ) )
@ ( sk5
@ ( C
@ ( sk5
@ ^ [D: a] : ( sk6 @ ( C @ D ) ) ) ) ) ) )
| ( ( (=) @ a @ ( sk4 @ A ) )
!= ( (=) @ a @ B ) )
| ( sk2 != sk1 )
| ( ( ^ [D: a] :
( ( sk6
@ ^ [E: a] : ( sk6 @ ( C @ E ) ) )
= ( sk6 @ ( C @ D ) ) ) )
!= ( ^ [D: a] :
( A
= ( sk3 @ D ) ) ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(2565,plain,
! [B: a,A: a] :
( ( ( ^ [C: a] : ( sk4 @ ( sk3 @ B ) ) )
!= ( ^ [C: a] : A ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ( sk2 != sk1 )
| ( ( ^ [C: a] : ( sk3 @ B ) )
!= ( ^ [C: a] : ( sk6 @ sk3 ) ) )
| ( ( sk1 @ B )
!= ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[221]) ).
thf(2567,plain,
! [A: a] :
( ( ( ^ [B: a] : ( sk4 @ ( sk3 @ ( sk3 @ ( sk5 @ sk3 ) ) ) ) )
!= ( ^ [B: a] : A ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ( sk2 != sk1 )
| ( ( ^ [B: a] : ( sk6 @ sk3 ) )
!= ( ^ [B: a] : ( sk3 @ ( sk3 @ ( sk5 @ sk3 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2565:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk5 @ sk3 ) ))]]) ).
thf(2588,plain,
! [A: a] :
( ( ( sk4 @ ( sk3 @ ( sk3 @ ( sk5 @ sk3 ) ) ) )
!= A )
| ( ( sk2 @ ( sk22 @ A ) )
!= ( sk1 @ ( sk22 @ A ) ) )
| ( ( sk6 @ sk3 )
!= ( sk3 @ ( sk3 @ ( sk5 @ sk3 ) ) ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) ) ),
inference(func_ext,[status(esa)],[2567]) ).
thf(2609,plain,
( ( ( sk2 @ ( sk22 @ ( sk4 @ ( sk3 @ ( sk3 @ ( sk5 @ sk3 ) ) ) ) ) )
!= ( sk1 @ ( sk22 @ ( sk4 @ ( sk3 @ ( sk3 @ ( sk5 @ sk3 ) ) ) ) ) ) )
| ( ( sk6 @ sk3 )
!= ( sk3 @ ( sk3 @ ( sk5 @ sk3 ) ) ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[2588]) ).
thf(3892,plain,
! [A: a > a] :
( ( sk2 @ ( sk3 @ ( sk6 @ A ) ) )
| ( ( sk1
@ ( sk4
@ ( sk3
@ ( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) )
!= ( sk1 @ ( A @ ( sk5 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3679,30]) ).
thf(3931,plain,
( sk2
@ ( sk3
@ ( sk6
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3892:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk3 @ ( sk6 @ ^ [C: a] : ( sk6 @ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ))]]) ).
thf(78,plain,
! [B: a,A: a > a] :
( ( sk1 @ ( sk6 @ A ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( B
= ( sk3 @ C ) ) ) )
= ( (=) @ a @ ( sk4 @ B ) ) )
| ( ( sk2 @ ( sk5 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,17]) ).
thf(79,plain,
! [A: a > a] :
( ( sk1 @ ( sk6 @ A ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk5 @ A )
= ( sk3 @ B ) ) ) )
= ( (=) @ a @ ( sk4 @ ( sk5 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( C )),bind(B,$thf( sk5 @ C ))]]) ).
thf(109,plain,
! [A: a > a] :
( ( sk1 @ ( sk6 @ A ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk5 @ A )
= ( sk3 @ B ) ) ) )
= ( (=) @ a @ ( sk4 @ ( sk5 @ A ) ) ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(4544,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3758,32]) ).
thf(4582,plain,
( sk1
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[4544:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk6 @ ^ [D: a] : ( sk6 @ ^ [E: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) ))]]) ).
thf(3866,plain,
! [B: a,A: a > a] :
( ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1
@ ( sk4
@ ( sk3
@ ( sk6
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) )
!= ( sk1 @ ( A @ ( sk5 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3679,14]) ).
thf(3904,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk2 @ B )
& ( ( sk6
@ ^ [C: a] :
( sk4
@ ( sk3
@ ( sk6
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk4 @ D ) ) ) ) ) )
= ( sk4
@ ( sk3
@ ( sk6
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(pre_uni,[status(thm)],[3866:[bind(A,$thf( ^ [C: a] : ( sk4 @ ( sk3 @ ( sk6 @ ^ [D: a] : ( sk6 @ ^ [E: a] : ( sk4 @ D ) ) ) ) ) )),bind(B,$thf( B ))]]) ).
thf(3935,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk2 @ B )
& ( ( sk6
@ ^ [C: a] :
( sk4
@ ( sk3
@ ( sk6
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk4 @ D ) ) ) ) ) )
= ( sk4
@ ( sk3
@ ( sk6
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(simp,[status(thm)],[3904]) ).
thf(1748,plain,
! [B: a > a > a,A: a] :
( ~ ( sk1 @ A )
| ( sk1
@ ( sk6
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) ) )
| ( sk2
@ ( sk5
@ ( B
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) ) ) ) )
| ( ( sk2
@ ( sk3
@ ( sk6
@ ( B
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) ) ) ) ) )
!= ( sk2 @ ( sk3 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[4,146]) ).
thf(1810,plain,
! [A: a > a > a] :
( ~ ( sk1
@ ( sk6
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) )
| ( sk1
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) )
| ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[1748:[bind(A,$thf( sk6 @ ( B @ ( sk5 @ ^ [C: a] : ( sk6 @ ( B @ C ) ) ) ) ))]]) ).
thf(1831,plain,
! [A: a > a > a] :
( ~ ( sk1
@ ( sk6
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) )
| ( sk1
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) )
| ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ),
inference(simp,[status(thm)],[1810]) ).
thf(3744,plain,
! [A: a > a] :
( ( sk2 @ ( sk3 @ ( sk6 @ A ) ) )
| ( ( sk1 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) )
!= ( sk1 @ ( A @ ( sk5 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3611,30]) ).
thf(3770,plain,
( sk2
@ ( sk3
@ ( sk6
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3744:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ))]]) ).
thf(3966,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ ( sk4 @ ( sk3 @ A ) ) ) )
| ( ( sk1
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3769,2429]) ).
thf(3967,plain,
( sk2
@ ( sk3
@ ( sk4
@ ( sk3
@ ( sk6
@ ^ [A: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3966:[bind(A,$thf( sk6 @ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ))]]) ).
thf(41,plain,
! [C: a > a > a,B: a,A: a > a] :
( ( sk2 @ ( sk5 @ A ) )
| ( ( ^ [D: a] :
( ( sk2 @ D )
& ( ( sk6
@ ^ [E: a] : ( sk6 @ ( C @ E ) ) )
= ( sk6 @ ( C @ D ) ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1 @ ( sk6 @ A ) )
!= ( sk1
@ ( C
@ ( sk5
@ ^ [D: a] : ( sk6 @ ( C @ D ) ) )
@ ( sk5
@ ( C
@ ( sk5
@ ^ [D: a] : ( sk6 @ ( C @ D ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,39]) ).
thf(43,plain,
! [B: a > a > a > a,A: a] :
( ( sk2
@ ( sk5
@ ( B
@ ( sk5
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk6 @ ( B @ C @ D ) ) ) )
@ ( sk5
@ ^ [C: a] :
( sk6
@ ( B
@ ( sk5
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk6 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk6 @ ( B @ D @ E ) ) ) )
= ( sk6
@ ^ [D: a] : ( sk6 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(pre_uni,[status(thm)],[41:[bind(A,$thf( D @ ( sk5 @ ^ [E: a] : ( sk6 @ ^ [F: a] : ( sk6 @ ( D @ E @ F ) ) ) ) @ ( sk5 @ ^ [E: a] : ( sk6 @ ( D @ ( sk5 @ ^ [F: a] : ( sk6 @ ^ [G: a] : ( sk6 @ ( D @ F @ G ) ) ) ) @ E ) ) ) )),bind(B,$thf( B )),bind(C,$thf( ^ [E: a] : ^ [F: a] : ( sk6 @ ( D @ E @ F ) ) ))]]) ).
thf(45,plain,
! [B: a > a > a > a,A: a] :
( ( sk2
@ ( sk5
@ ( B
@ ( sk5
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk6 @ ( B @ C @ D ) ) ) )
@ ( sk5
@ ^ [C: a] :
( sk6
@ ( B
@ ( sk5
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk6 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk6 @ ( B @ D @ E ) ) ) )
= ( sk6
@ ^ [D: a] : ( sk6 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(3673,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) )
| ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) )
| ( ( sk2
@ ( sk3
@ ( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk4 @ B ) ) ) ) )
!= ( sk2
@ ( sk3
@ ( sk6
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3362,146]) ).
thf(3696,plain,
( ( sk1
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk4 @ B ) ) ) ) )
| ( sk2
@ ( sk5
@ ^ [A: a] :
( sk6
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ),
inference(pre_uni,[status(thm)],[3673:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk6 @ ^ [D: a] : ( sk4 @ C ) ) ))]]) ).
thf(958,plain,
( ~ ( sk2 @ ( sk6 @ sk3 ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ( ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) )
!= ( sk6 @ sk3 ) )
| ( ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) )
!= ( sk3 @ ( sk5 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[929]) ).
thf(4265,plain,
! [A: a > a] :
( ( sk2 @ ( sk5 @ sk4 ) )
| ( sk1 @ ( sk6 @ A ) )
| ( ( sk1
@ ( sk6
@ ^ [B: a] : ( sk6 @ sk4 ) ) )
!= ( sk1 @ ( A @ ( sk5 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3623,15]) ).
thf(4283,plain,
( ( sk2 @ ( sk5 @ sk4 ) )
| ( sk1
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] : ( sk6 @ sk4 ) ) ) ) ),
inference(pre_uni,[status(thm)],[4265:[bind(A,$thf( ^ [B: a] : ( sk6 @ ^ [C: a] : ( sk6 @ sk4 ) ) ))]]) ).
thf(71,plain,
! [A: a > a > a] :
( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) )
| ( ( sk3
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) )
!= ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(3645,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ ( sk4 @ A ) ) )
| ( ( sk2
@ ( sk3
@ ( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk4 @ B ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3362,2309]) ).
thf(3646,plain,
( sk2
@ ( sk3
@ ( sk4
@ ( sk3
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3645:[bind(A,$thf( sk3 @ ( sk6 @ ^ [B: a] : ( sk6 @ ^ [C: a] : ( sk4 @ B ) ) ) ))]]) ).
thf(23,plain,
! [A: a > a] :
( ( sk2 @ ( sk5 @ A ) )
| ( ( sk3 @ ( sk6 @ A ) )
!= ( sk5 @ A ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(90,plain,
! [B: a,A: a > a] :
( ( ( sk3 @ ( sk6 @ A ) )
!= ( sk5 @ A ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( B
= ( sk3 @ C ) ) ) )
= ( (=) @ a @ ( sk4 @ B ) ) )
| ( ( sk2 @ ( sk5 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[23,17]) ).
thf(91,plain,
! [A: a > a] :
( ( ( sk3 @ ( sk6 @ A ) )
!= ( sk5 @ A ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk5 @ A )
= ( sk3 @ B ) ) ) )
= ( (=) @ a @ ( sk4 @ ( sk5 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( C )),bind(B,$thf( sk5 @ C ))]]) ).
thf(113,plain,
! [A: a > a] :
( ( ( sk3 @ ( sk6 @ A ) )
!= ( sk5 @ A ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk5 @ A )
= ( sk3 @ B ) ) ) )
= ( (=) @ a @ ( sk4 @ ( sk5 @ A ) ) ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(3384,plain,
( ( ( sk6 @ sk3 )
!= ( sk3 @ ( sk3 @ ( sk5 @ sk3 ) ) ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ~ ( sk2 @ ( sk22 @ ( sk4 @ ( sk3 @ ( sk3 @ ( sk5 @ sk3 ) ) ) ) ) )
| ~ ( sk1 @ ( sk22 @ ( sk4 @ ( sk3 @ ( sk3 @ ( sk5 @ sk3 ) ) ) ) ) ) ),
inference(bool_ext,[status(thm)],[2609]) ).
thf(96,plain,
! [C: a > a > a,B: a,A: a] :
( ~ ( sk2 @ A )
| ~ ( sk1
@ ( C
@ ( sk5
@ ^ [D: a] : ( sk6 @ ( C @ D ) ) )
@ ( sk5
@ ( C
@ ( sk5
@ ^ [D: a] : ( sk6 @ ( C @ D ) ) ) ) ) ) )
| ( ( ^ [D: a] : ( sk4 @ A ) )
!= ( ^ [D: a] : B ) )
| ( ( ^ [D: a] : D )
!= ( ^ [D: a] : D ) )
| ( ( ^ [D: a] :
( ( sk2 @ D )
& ( ( sk6
@ ^ [E: a] : ( sk6 @ ( C @ E ) ) )
= ( sk6 @ ( C @ D ) ) ) ) )
!= ( ^ [D: a] :
( ( sk1 @ D )
& ( A
= ( sk3 @ D ) ) ) ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(103,plain,
! [C: a > a > a,B: a,A: a] :
( ~ ( sk2 @ A )
| ~ ( sk1
@ ( C
@ ( sk5
@ ^ [D: a] : ( sk6 @ ( C @ D ) ) )
@ ( sk5
@ ( C
@ ( sk5
@ ^ [D: a] : ( sk6 @ ( C @ D ) ) ) ) ) ) )
| ( ( ^ [D: a] : ( sk4 @ A ) )
!= ( ^ [D: a] : B ) )
| ( ( ^ [D: a] :
( ( sk2 @ D )
& ( ( sk6
@ ^ [E: a] : ( sk6 @ ( C @ E ) ) )
= ( sk6 @ ( C @ D ) ) ) ) )
!= ( ^ [D: a] :
( ( sk1 @ D )
& ( A
= ( sk3 @ D ) ) ) ) ) ),
inference(simp,[status(thm)],[96]) ).
thf(3882,plain,
! [B: a > a > a,A: a] :
( ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6
@ ^ [D: a] : ( sk6 @ ( B @ D ) ) )
= ( sk6 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk4
@ ( sk3
@ ( sk6
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) )
@ ( sk5
@ ( B
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3679,39]) ).
thf(3932,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk2 @ B )
& ( ( sk6
@ ^ [C: a] :
( sk6
@ ^ [D: a] :
( sk4
@ ( sk3
@ ( sk6
@ ^ [E: a] :
( sk6
@ ^ [F: a] : ( sk4 @ E ) ) ) ) ) ) )
= ( sk6
@ ^ [C: a] :
( sk4
@ ( sk3
@ ( sk6
@ ^ [D: a] :
( sk6
@ ^ [E: a] : ( sk4 @ D ) ) ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(pre_uni,[status(thm)],[3882:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ( sk4 @ ( sk3 @ ( sk6 @ ^ [E: a] : ( sk6 @ ^ [F: a] : ( sk4 @ E ) ) ) ) ) ))]]) ).
thf(76,plain,
! [B: a,A: a > a] :
( ( sk2 @ ( sk5 @ A ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( B
= ( sk3 @ C ) ) ) )
= ( (=) @ a @ ( sk4 @ B ) ) )
| ( ( sk2 @ ( sk3 @ ( sk6 @ A ) ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[20,17]) ).
thf(77,plain,
! [A: a > a] :
( ( sk2 @ ( sk5 @ A ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3 @ ( sk6 @ A ) )
= ( sk3 @ B ) ) ) )
= ( (=) @ a @ ( sk4 @ ( sk3 @ ( sk6 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( D )),bind(B,$thf( sk3 @ ( sk6 @ D ) ))]]) ).
thf(108,plain,
! [A: a > a] :
( ( sk2 @ ( sk5 @ A ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3 @ ( sk6 @ A ) )
= ( sk3 @ B ) ) ) )
= ( (=) @ a @ ( sk4 @ ( sk3 @ ( sk6 @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(3671,plain,
! [B: a,A: a] :
( ( ( ^ [C: a] : ( sk4 @ A ) )
!= ( ^ [C: a] : B ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ( sk2 != sk1 )
| ( ( ^ [C: a] : A )
!= ( ^ [C: a] : ( sk6 @ sk3 ) ) )
| ( ( sk2
@ ( sk3
@ ( sk6
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk4 @ C ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3362,186]) ).
thf(3672,plain,
! [A: a] :
( ( ( ^ [B: a] :
( sk4
@ ( sk3
@ ( sk6
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) )
!= ( ^ [B: a] : A ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ( sk2 != sk1 )
| ( ( ^ [B: a] :
( sk3
@ ( sk6
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk4 @ C ) ) ) ) )
!= ( ^ [B: a] : ( sk6 @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[3671:[bind(A,$thf( sk3 @ ( sk6 @ ^ [C: a] : ( sk6 @ ^ [D: a] : ( sk4 @ C ) ) ) )),bind(B,$thf( B ))]]) ).
thf(3706,plain,
! [A: a] :
( ( ( ^ [B: a] :
( sk4
@ ( sk3
@ ( sk6
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) )
!= ( ^ [B: a] : A ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ( sk2 != sk1 )
| ( ( ^ [B: a] :
( sk3
@ ( sk6
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk4 @ C ) ) ) ) )
!= ( ^ [B: a] : ( sk6 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[3672]) ).
thf(3960,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3769,32]) ).
thf(4013,plain,
( sk1
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3960:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk6 @ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ))]]) ).
thf(88,plain,
! [B: a,A: a > a > a] :
( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( B
= ( sk3 @ C ) ) ) )
= ( (=) @ a @ ( sk4 @ B ) ) )
| ( ( sk2
@ ( sk3
@ ( sk6
@ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[55,17]) ).
thf(89,plain,
! [A: a > a > a] :
( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ( sk6
@ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) )
= ( sk3 @ B ) ) ) )
= ( (=) @ a
@ ( sk4
@ ( sk3
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( E )),bind(B,$thf( sk3 @ ( sk6 @ ^ [D: a] : ( sk6 @ ( E @ D ) ) ) ))]]) ).
thf(112,plain,
! [A: a > a > a] :
( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ( sk6
@ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) )
= ( sk3 @ B ) ) ) )
= ( (=) @ a
@ ( sk4
@ ( sk3
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(81,plain,
! [B: a,A: a > a > a] :
( ( sk1
@ ( sk6
@ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( B
= ( sk3 @ C ) ) ) )
= ( (=) @ a @ ( sk4 @ B ) ) )
| ( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) ) ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[31,17]) ).
thf(95,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk5
@ ( A
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) ) )
= ( sk3 @ B ) ) ) )
= ( (=) @ a
@ ( sk4
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[81:[bind(A,$thf( A )),bind(B,$thf( sk5 @ ( A @ ( sk5 @ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) ) ))]]) ).
thf(3734,plain,
! [B: a > a > a,A: a] :
( ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6
@ ^ [D: a] : ( sk6 @ ( B @ D ) ) )
= ( sk6 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) )
!= ( sk1
@ ( B
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) )
@ ( sk5
@ ( B
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3611,39]) ).
thf(3754,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk2 @ B )
& ( ( sk6
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) )
= ( sk6
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(pre_uni,[status(thm)],[3734:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ))]]) ).
thf(60,plain,
! [B: a > a,A: a > a > a] :
( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) ) ) )
| ( sk2 @ ( sk3 @ ( sk6 @ B ) ) )
| ( ( sk1
@ ( sk6
@ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) )
!= ( sk1 @ ( B @ ( sk5 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,30]) ).
thf(63,plain,
! [A: a > a > a > a] :
( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk6 @ ( A @ B @ C ) ) ) )
@ ( sk5
@ ^ [B: a] :
( sk6
@ ( A
@ ( sk5
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk6 @ ( A @ C @ D ) ) ) )
@ B ) ) ) ) ) )
| ( sk2
@ ( sk3
@ ( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk6 @ ( A @ B @ C ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[60:[bind(A,$thf( D @ ( sk5 @ ^ [D: a] : ( sk6 @ ^ [E: a] : ( sk6 @ ( D @ D @ E ) ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk6 @ ^ [E: a] : ( sk6 @ ( D @ D @ E ) ) ) ))]]) ).
thf(67,plain,
! [A: a > a > a > a] :
( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk6 @ ( A @ B @ C ) ) ) )
@ ( sk5
@ ^ [B: a] :
( sk6
@ ( A
@ ( sk5
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk6 @ ( A @ C @ D ) ) ) )
@ B ) ) ) ) ) )
| ( sk2
@ ( sk3
@ ( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk6 @ ( A @ B @ C ) ) ) ) ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(3738,plain,
! [A: a] :
( ( sk2 @ ( sk3 @ ( sk4 @ ( sk3 @ A ) ) ) )
| ( ( sk1 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3611,2429]) ).
thf(3739,plain,
sk2 @ ( sk3 @ ( sk4 @ ( sk3 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3738:[bind(A,$thf( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ))]]) ).
thf(5450,plain,
sk2 @ ( sk3 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[3739,3589]) ).
thf(4201,plain,
! [A: a] :
( ( sk2 @ ( sk5 @ sk4 ) )
| ( sk1 @ ( sk4 @ ( sk3 @ A ) ) )
| ( ( sk1
@ ( sk6
@ ^ [B: a] : ( sk6 @ sk4 ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3623,2310]) ).
thf(4202,plain,
( ( sk2 @ ( sk5 @ sk4 ) )
| ( sk1
@ ( sk4
@ ( sk3
@ ( sk6
@ ^ [A: a] : ( sk6 @ sk4 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4201:[bind(A,$thf( sk6 @ ^ [B: a] : ( sk6 @ sk4 ) ))]]) ).
thf(624,plain,
( ~ ( sk2 @ ( sk6 @ sk3 ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ~ ( sk1 @ ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) ) )
| ( ( sk2 @ ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) ) )
!= ( sk2 @ ( sk6 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[601]) ).
thf(3607,plain,
( ~ ( sk2 @ ( sk6 @ sk3 ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ~ ( sk1 @ ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) ) )
| ( ( sk2 @ ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) ) )
!= ( sk2 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3373,624]) ).
thf(3620,plain,
( ~ ( sk2 @ ( sk6 @ sk3 ) )
| ~ ( sk1 @ ( sk3 @ ( sk5 @ sk3 ) ) )
| ~ ( sk1 @ ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) ) )
| ( ( sk14 @ ( sk4 @ ( sk6 @ sk3 ) ) @ ( sk6 @ sk3 ) )
!= ( sk3 @ ( sk6 @ sk4 ) ) ) ),
inference(simp,[status(thm)],[3607]) ).
thf(87,plain,
! [B: a,A: a > a > a] :
( ( sk2
@ ( sk3
@ ( sk6
@ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( B
= ( sk3 @ C ) ) ) )
= ( (=) @ a @ ( sk4 @ B ) ) )
| ( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) ) ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[55,17]) ).
thf(99,plain,
! [A: a > a > a] :
( ( sk2
@ ( sk3
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk5
@ ( A
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) ) )
= ( sk3 @ B ) ) ) )
= ( (=) @ a
@ ( sk4
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[87:[bind(A,$thf( A )),bind(B,$thf( sk5 @ ( A @ ( sk5 @ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) ) ))]]) ).
thf(3872,plain,
! [A: a > a > a] :
( ( sk2
@ ( sk3
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) )
| ( ( sk1
@ ( sk4
@ ( sk3
@ ( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3679,65]) ).
thf(3911,plain,
( sk2
@ ( sk3
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] :
( sk4
@ ( sk3
@ ( sk6
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3872:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk4 @ ( sk3 @ ( sk6 @ ^ [D: a] : ( sk6 @ ^ [E: a] : ( sk4 @ D ) ) ) ) ) ))]]) ).
thf(3718,plain,
! [B: a,A: a > a] :
( ( ( ^ [C: a] :
( ( sk2 @ C )
& ( ( sk6 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1 @ ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) )
!= ( sk1 @ ( A @ ( sk5 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3611,14]) ).
thf(3774,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk2 @ B )
& ( ( sk6
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) )
= ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(pre_uni,[status(thm)],[3718:[bind(A,$thf( ^ [C: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) )),bind(B,$thf( B ))]]) ).
thf(3789,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk2 @ B )
& ( ( sk6
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) )
= ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(simp,[status(thm)],[3774]) ).
thf(40,plain,
! [B: a > a > a,A: a] :
( ( ( ( sk2 @ ( sk8 @ B @ A ) )
& ( ( sk6
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) )
= ( sk6 @ ( B @ ( sk8 @ B @ A ) ) ) ) )
!= ( A
= ( sk8 @ B @ A ) ) )
| ~ ( sk1
@ ( B
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) )
@ ( sk5
@ ( B
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) ) ) ) ) ) ),
inference(func_ext,[status(esa)],[39]) ).
thf(51,plain,
! [B: a > a,A: a > a > a] :
( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) ) ) )
| ( sk1 @ ( sk6 @ B ) )
| ( ( sk1
@ ( sk6
@ ^ [C: a] : ( sk6 @ ( A @ C ) ) ) )
!= ( sk1 @ ( B @ ( sk5 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,15]) ).
thf(54,plain,
! [A: a > a > a > a] :
( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk6 @ ( A @ B @ C ) ) ) )
@ ( sk5
@ ^ [B: a] :
( sk6
@ ( A
@ ( sk5
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk6 @ ( A @ C @ D ) ) ) )
@ B ) ) ) ) ) )
| ( sk1
@ ( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk6 @ ( A @ B @ C ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[51:[bind(A,$thf( D @ ( sk5 @ ^ [D: a] : ( sk6 @ ^ [E: a] : ( sk6 @ ( D @ D @ E ) ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk6 @ ^ [E: a] : ( sk6 @ ( D @ D @ E ) ) ) ))]]) ).
thf(58,plain,
! [A: a > a > a > a] :
( ( sk2
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk6 @ ( A @ B @ C ) ) ) )
@ ( sk5
@ ^ [B: a] :
( sk6
@ ( A
@ ( sk5
@ ^ [C: a] :
( sk6
@ ^ [D: a] : ( sk6 @ ( A @ C @ D ) ) ) )
@ B ) ) ) ) ) )
| ( sk1
@ ( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk6 @ ( A @ B @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(3676,plain,
! [A: a] :
( ( sk1 @ ( sk4 @ ( sk3 @ ( sk4 @ A ) ) ) )
| ( ( sk2
@ ( sk3
@ ( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk4 @ B ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3362,2430]) ).
thf(3677,plain,
( sk1
@ ( sk4
@ ( sk3
@ ( sk4
@ ( sk3
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] : ( sk4 @ A ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3676:[bind(A,$thf( sk3 @ ( sk6 @ ^ [B: a] : ( sk6 @ ^ [C: a] : ( sk4 @ B ) ) ) ))]]) ).
thf(2229,plain,
! [B: a,A: a > a] :
( ( sk1 @ ( sk6 @ A ) )
| ( sk1 @ ( sk4 @ B ) )
| ( ( sk2 @ ( sk5 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,2177]) ).
thf(2230,plain,
! [A: a > a] :
( ( sk1 @ ( sk6 @ A ) )
| ( sk1 @ ( sk4 @ ( sk5 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[2229:[bind(A,$thf( C )),bind(B,$thf( sk5 @ C ))]]) ).
thf(2302,plain,
! [A: a > a] :
( ( sk1 @ ( sk6 @ A ) )
| ( sk1 @ ( sk4 @ ( sk5 @ A ) ) ) ),
inference(simp,[status(thm)],[2230]) ).
thf(74,plain,
! [B: a,A: a > a] :
( ( sk2 @ ( sk3 @ ( sk6 @ A ) ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( B
= ( sk3 @ C ) ) ) )
= ( (=) @ a @ ( sk4 @ B ) ) )
| ( ( sk2 @ ( sk5 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[20,17]) ).
thf(75,plain,
! [A: a > a] :
( ( sk2 @ ( sk3 @ ( sk6 @ A ) ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk5 @ A )
= ( sk3 @ B ) ) ) )
= ( (=) @ a @ ( sk4 @ ( sk5 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( C )),bind(B,$thf( sk5 @ C ))]]) ).
thf(107,plain,
! [A: a > a] :
( ( sk2 @ ( sk3 @ ( sk6 @ A ) ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk5 @ A )
= ( sk3 @ B ) ) ) )
= ( (=) @ a @ ( sk4 @ ( sk5 @ A ) ) ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(3952,plain,
! [A: a > a > a] :
( ( sk2
@ ( sk3
@ ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) )
| ( ( sk1
@ ( sk6
@ ^ [B: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
@ ( sk5
@ ( A
@ ( sk5
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3769,65]) ).
thf(4007,plain,
( sk2
@ ( sk3
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3952:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk6 @ ^ [D: a] : ( sk4 @ ( sk3 @ ( sk6 @ sk4 ) ) ) ) ))]]) ).
thf(68,plain,
! [B: a,A: a > a] :
( ( ( ( sk2 @ ( sk9 @ B @ A ) )
& ( ( sk6 @ A )
= ( A @ ( sk9 @ B @ A ) ) ) )
!= ( B
= ( sk9 @ B @ A ) ) )
| ( sk2 @ ( sk5 @ A ) ) ),
inference(func_ext,[status(esa)],[11]) ).
thf(85,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( B
= ( sk3 @ C ) ) ) )
= ( (=) @ a @ ( sk4 @ B ) ) )
| ( ( sk2 @ ( sk3 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4,17]) ).
thf(86,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3 @ A )
= ( sk3 @ B ) ) ) )
= ( (=) @ a @ ( sk4 @ ( sk3 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[85:[bind(A,$thf( C )),bind(B,$thf( sk3 @ C ))]]) ).
thf(111,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3 @ A )
= ( sk3 @ B ) ) ) )
= ( (=) @ a @ ( sk4 @ ( sk3 @ A ) ) ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(3897,plain,
! [A: a > a] :
( ( sk1 @ ( sk6 @ A ) )
| ( ( sk1
@ ( sk4
@ ( sk3
@ ( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) )
!= ( sk1 @ ( A @ ( sk5 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3679,15]) ).
thf(3933,plain,
( sk1
@ ( sk6
@ ^ [A: a] :
( sk4
@ ( sk3
@ ( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : ( sk4 @ B ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3897:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk3 @ ( sk6 @ ^ [C: a] : ( sk6 @ ^ [D: a] : ( sk4 @ C ) ) ) ) ) ))]]) ).
thf(10706,plain,
$false,
inference(e,[status(thm)],[3679,7698,3755,3944,101,2309,115,4110,4528,14,110,3612,20,46,4270,57,93,3919,3887,4258,5333,221,3756,957,38,70,33,65,625,97,2609,3931,109,4582,3935,3611,1831,3770,3967,2176,513,32,45,17,3696,3758,958,22,4283,71,12,3646,113,39,3384,103,3932,108,3706,226,3,4013,112,2567,2298,95,3754,67,2429,3623,5450,3769,31,11,72,4202,3620,2310,3589,99,3911,3789,40,186,55,23,58,3677,2302,146,30,3373,107,4,4007,624,3362,2430,15,68,111,3637,3933,2177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SEV089^5 : TPTP v8.2.0. Released v4.0.0.
% 0.05/0.13 % Command : run_Leo-III %s %d THM
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 21 18:47:55 EDT 2024
% 0.14/0.35 % CPUTime :
% 1.08/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.38/1.12 % [INFO] Parsing done (142ms).
% 1.38/1.13 % [INFO] Running in sequential loop mode.
% 1.82/1.41 % [INFO] eprover registered as external prover.
% 1.82/1.42 % [INFO] Scanning for conjecture ...
% 2.07/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.20/1.54 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.20/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.20/1.55 % [INFO] Type checking passed.
% 2.20/1.55 % [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 ...
% 71.76/18.05 % External prover 'e' found a proof!
% 71.76/18.05 % [INFO] Killing All external provers ...
% 71.76/18.05 % Time passed: 17469ms (effective reasoning time: 16916ms)
% 71.76/18.05 % 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)>
% 71.76/18.05 % Axioms used in derivation (0):
% 71.76/18.05 % No. of inferences in proof: 242
% 71.76/18.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 17469 ms resp. 16916 ms w/o parsing
% 72.60/18.30 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 72.60/18.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------