TSTP Solution File: SEV106^5 by Leo-III---1.7.15
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV106^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n029.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 15:58:14 EDT 2024
% Result : Theorem 80.41s 18.20s
% Output : Refutation 81.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 1
% Syntax : Number of formulae : 470 ( 93 unt; 0 typ; 0 def)
% Number of atoms : 1461 ( 407 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 5255 ( 705 ~; 607 |; 39 &;3874 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 181 ( 181 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 14 con; 0-2 aty)
% Number of variables : 1351 ( 932 ^ 401 !; 18 ?;1351 :)
% 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 > $o ).
thf(sk4_type,type,
sk4: a > a ).
thf(sk5_type,type,
sk5: a > a ).
thf(sk6_type,type,
sk6: a > a ).
thf(sk7_type,type,
sk7: a > a ).
thf(sk8_type,type,
sk8: ( a > a ) > $o ).
thf(sk9_type,type,
sk9: ( a > a ) > a ).
thf(sk10_type,type,
sk10: ( a > a ) > a ).
thf(sk11_type,type,
sk11: a > ( a > a ) > 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(sk17_type,type,
sk17: a ).
thf(sk18_type,type,
sk18: a ).
thf(sk22_type,type,
sk22: a ).
thf(sk23_type,type,
sk23: a ).
thf(sk24_type,type,
sk24: a ).
thf(sk26_type,type,
sk26: a ).
thf(sk27_type,type,
sk27: a ).
thf(1,conjecture,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ? [D: a > a] :
( ! [E: a] :
( ( A @ E )
=> ( B @ ( D @ E ) ) )
& ! [E: a] :
( ( B @ E )
=> ? [F: a] :
( ( A @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( A @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) )
& ? [D: a > a] :
( ! [E: a] :
( ( B @ E )
=> ( C @ ( D @ E ) ) )
& ! [E: a] :
( ( C @ E )
=> ? [F: a] :
( ( B @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( B @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) ) )
=> ? [D: a > a] :
( ! [E: a] :
( ( A @ E )
=> ( C @ ( D @ E ) ) )
& ! [E: a] :
( ( C @ E )
=> ? [F: a] :
( ( A @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( A @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEQP1_1C_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o,B: a > $o,C: a > $o] :
( ( ? [D: a > a] :
( ! [E: a] :
( ( A @ E )
=> ( B @ ( D @ E ) ) )
& ! [E: a] :
( ( B @ E )
=> ? [F: a] :
( ( A @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( A @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) )
& ? [D: a > a] :
( ! [E: a] :
( ( B @ E )
=> ( C @ ( D @ E ) ) )
& ! [E: a] :
( ( C @ E )
=> ? [F: a] :
( ( B @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( B @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) ) )
=> ? [D: a > a] :
( ! [E: a] :
( ( A @ E )
=> ( C @ ( D @ E ) ) )
& ! [E: a] :
( ( C @ E )
=> ? [F: a] :
( ( A @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( A @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o,B: a > $o,C: a > $o] :
( ( ? [D: a > a] :
( ! [E: a] :
( ( A @ E )
=> ( B @ ( D @ E ) ) )
& ! [E: a] :
( ( B @ E )
=> ? [F: a] :
( ( A @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( A @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) )
& ? [D: a > a] :
( ! [E: a] :
( ( B @ E )
=> ( C @ ( D @ E ) ) )
& ! [E: a] :
( ( C @ E )
=> ? [F: a] :
( ( B @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( B @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) ) )
=> ? [D: a > a] :
( ! [E: a] :
( ( A @ E )
=> ( C @ ( D @ E ) ) )
& ! [E: a] :
( ( C @ E )
=> ? [F: a] :
( ( A @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( A @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
! [A: a > a] :
( ( sk8 @ A )
| ( sk3 @ ( sk10 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(31,plain,
! [A: a > a] :
( ( sk8 @ A )
| ( sk3 @ ( sk10 @ A ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(13,plain,
! [A: a > a] :
( ( sk1 @ ( sk9 @ A ) )
| ~ ( sk8 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(25,plain,
! [A: a > a] :
( ( sk1 @ ( sk9 @ A ) )
| ~ ( sk8 @ A ) ),
inference(simp,[status(thm)],[13]) ).
thf(8,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ ( sk4 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(47,plain,
! [B: a,A: a > a] :
( ~ ( sk8 @ A )
| ( sk2 @ ( sk4 @ B ) )
| ( ( sk1 @ ( sk9 @ A ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[25,8]) ).
thf(48,plain,
! [A: a > a] :
( ~ ( sk8 @ A )
| ( sk2 @ ( sk4 @ ( sk9 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( C )),bind(B,$thf( sk9 @ C ))]]) ).
thf(49,plain,
! [A: a > a] :
( ~ ( sk8 @ A )
| ( sk2 @ ( sk4 @ ( sk9 @ A ) ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(7,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk3 @ ( sk6 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(30,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk3 @ ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(5,plain,
! [A: a > a] :
( ~ ( sk3 @ ( A @ ( sk9 @ A ) ) )
| ~ ( sk8 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(18,plain,
! [A: a > a] :
( ~ ( sk3 @ ( A @ ( sk9 @ A ) ) )
| ~ ( sk8 @ A ) ),
inference(simp,[status(thm)],[5]) ).
thf(72,plain,
! [B: a > a,A: a] :
( ~ ( sk2 @ A )
| ~ ( sk8 @ B )
| ( ( sk3 @ ( sk6 @ A ) )
!= ( sk3 @ ( B @ ( sk9 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,18]) ).
thf(79,plain,
! [A: a > a] :
( ~ ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) )
| ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ),
inference(pre_uni,[status(thm)],[72:[bind(A,$thf( C @ ( sk9 @ ^ [D: a] : ( sk6 @ ( C @ D ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk6 @ ( C @ D ) ) ))]]) ).
thf(83,plain,
! [A: a > a] :
( ~ ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) )
| ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(195,plain,
! [B: a > a,A: a > a] :
( ~ ( sk8 @ A )
| ~ ( sk8
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) )
| ( ( sk2 @ ( sk4 @ ( sk9 @ A ) ) )
!= ( sk2
@ ( B
@ ( sk9
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,83]) ).
thf(205,plain,
( ~ ( sk8
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) )
| ~ ( sk8
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ),
inference(pre_uni,[status(thm)],[195:[bind(A,$thf( ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) )),bind(B,$thf( sk4 ))]]) ).
thf(211,plain,
~ ( sk8
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(214,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,211]) ).
thf(215,plain,
( sk3
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[214:[bind(A,$thf( ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ))]]) ).
thf(217,plain,
! [A: a > a] :
( ~ ( sk8 @ A )
| ( ( sk3
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) )
!= ( sk3 @ ( A @ ( sk9 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[215,18]) ).
thf(222,plain,
~ ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ),
inference(pre_uni,[status(thm)],[217:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ))]]) ).
thf(224,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,222]) ).
thf(225,plain,
( sk3
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[224:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ))]]) ).
thf(372,plain,
! [A: a > a] :
( ~ ( sk8 @ A )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) )
!= ( sk3 @ ( A @ ( sk9 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[225,18]) ).
thf(379,plain,
~ ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[372:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ))]]) ).
thf(384,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,379]) ).
thf(385,plain,
( sk3
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[384:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ))]]) ).
thf(626,plain,
! [A: a > a] :
( ~ ( sk8 @ A )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) )
!= ( sk3 @ ( A @ ( sk9 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[385,18]) ).
thf(639,plain,
~ ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[626:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ))]]) ).
thf(644,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,639]) ).
thf(645,plain,
( sk3
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[644:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ))]]) ).
thf(6,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk1 @ ( sk5 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(23,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk1 @ ( sk5 @ A ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(40,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ( sk1 @ ( sk5 @ B ) )
| ( ( sk2 @ ( sk4 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8,23]) ).
thf(41,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk1 @ ( sk5 @ ( sk4 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( C )),bind(B,$thf( sk4 @ C ))]]) ).
thf(43,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk1 @ ( sk5 @ ( sk4 @ A ) ) ) ),
inference(simp,[status(thm)],[41]) ).
thf(17,plain,
! [B: a,A: a > a] :
( ( sk8 @ A )
| ~ ( sk1 @ B )
| ( ( sk10 @ A )
!= ( A @ B ) )
| ( ( sk11 @ B @ A )
!= B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(26,plain,
! [B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( ( sk11 @ B @ A )
!= B )
| ( sk8 @ A )
| ~ ( sk1 @ B ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(27,plain,
! [B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( ( sk11 @ B @ A )
!= B )
| ( sk8 @ A )
| ~ ( sk1 @ B ) ),
inference(simp,[status(thm)],[26]) ).
thf(123,plain,
! [C: a,B: a > a,A: a] :
( ~ ( sk1 @ A )
| ( ( sk10 @ B )
!= ( B @ C ) )
| ( ( sk11 @ C @ B )
!= C )
| ( sk8 @ B )
| ( ( sk1 @ ( sk5 @ ( sk4 @ A ) ) )
!= ( sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[43,27]) ).
thf(124,plain,
! [B: a,A: a > a] :
( ~ ( sk1 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk5 @ ( sk4 @ B ) ) ) )
| ( ( sk11 @ ( sk5 @ ( sk4 @ B ) ) @ A )
!= ( sk5 @ ( sk4 @ B ) ) )
| ( sk8 @ A ) ),
inference(pattern_uni,[status(thm)],[123:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( sk5 @ ( sk4 @ E ) ))]]) ).
thf(138,plain,
! [B: a,A: a > a] :
( ~ ( sk1 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk5 @ ( sk4 @ B ) ) ) )
| ( ( sk11 @ ( sk5 @ ( sk4 @ B ) ) @ A )
!= ( sk5 @ ( sk4 @ B ) ) )
| ( sk8 @ A ) ),
inference(simp,[status(thm)],[124]) ).
thf(14,plain,
! [B: a,A: a > a] :
( ( sk8 @ A )
| ~ ( sk1 @ B )
| ( ( sk10 @ A )
!= ( A @ B ) )
| ( ( sk10 @ A )
= ( A @ ( sk11 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(21,plain,
! [B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( ( A @ ( sk11 @ B @ A ) )
= ( sk10 @ A ) )
| ( sk8 @ A )
| ~ ( sk1 @ B ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(22,plain,
! [B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( ( A @ ( sk11 @ B @ A ) )
= ( sk10 @ A ) )
| ( sk8 @ A )
| ~ ( sk1 @ B ) ),
inference(simp,[status(thm)],[21]) ).
thf(283,plain,
! [D: a,C: a > a,B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( sk8 @ A )
| ~ ( sk1 @ B )
| ( ( sk10 @ C )
!= ( C @ D ) )
| ( ( sk10 @ A )
!= D )
| ( sk8 @ C )
| ~ ( sk1 @ D )
| ( ( A @ ( sk11 @ B @ A ) )
!= ( sk11 @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[22,27]) ).
thf(331,plain,
! [A: a] :
( ( ( sk10
@ ^ [B: a] : B )
!= A )
| ( sk8
@ ^ [B: a] : B )
| ~ ( sk1 @ A )
| ( ( sk10
@ ^ [B: a] : B )
!= A )
| ( ( sk10
@ ^ [B: a] : B )
!= A )
| ( sk8
@ ^ [B: a] : B )
| ~ ( sk1 @ A ) ),
inference(pre_uni,[status(thm)],[283:[bind(A,$thf( ^ [E: a] : E )),bind(B,$thf( D )),bind(C,$thf( ^ [E: a] : E ))]]) ).
thf(332,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( sk8
@ ^ [A: a] : A )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( sk8
@ ^ [A: a] : A ) ),
inference(pattern_uni,[status(thm)],[331:[bind(A,$thf( sk10 @ ^ [B: a] : B ))]]) ).
thf(344,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( sk8
@ ^ [A: a] : A ) ),
inference(simp,[status(thm)],[332]) ).
thf(64,plain,
! [B: a > a,A: a > a] :
( ( sk8 @ A )
| ~ ( sk8 @ B )
| ( ( sk3 @ ( sk10 @ A ) )
!= ( sk3 @ ( B @ ( sk9 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,18]) ).
thf(69,plain,
! [A: a > a > a] :
( ( sk8
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk10 @ ( A @ B ) ) ) ) )
| ~ ( sk8
@ ^ [B: a] : ( sk10 @ ( A @ B ) ) ) ),
inference(pre_uni,[status(thm)],[64:[bind(A,$thf( C @ ( sk9 @ ^ [D: a] : ( sk10 @ ( C @ D ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk10 @ ( C @ D ) ) ))]]) ).
thf(71,plain,
! [A: a > a > a] :
( ( sk8
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk10 @ ( A @ B ) ) ) ) )
| ~ ( sk8
@ ^ [B: a] : ( sk10 @ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(484,plain,
! [A: a > a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( sk2 @ ( sk4 @ ( sk9 @ A ) ) )
| ( ( sk8
@ ^ [B: a] : B )
!= ( sk8 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[344,49]) ).
thf(485,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( sk2
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ),
inference(pattern_uni,[status(thm)],[484:[bind(A,$thf( ^ [B: a] : B ))]]) ).
thf(793,plain,
! [A: a > a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
| ( ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) )
!= ( sk2
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[485,83]) ).
thf(798,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ~ ( sk8
@ ^ [A: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) ) ),
inference(pre_uni,[status(thm)],[793:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk9 @ ^ [C: a] : C ) ) ))]]) ).
thf(1607,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [C: a] : C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,798]) ).
thf(1608,plain,
( ( sk3
@ ( sk10
@ ^ [A: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) ) )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ),
inference(pattern_uni,[status(thm)],[1607:[bind(A,$thf( ^ [B: a] : ( sk6 @ ( sk4 @ ( sk9 @ ^ [C: a] : C ) ) ) ))]]) ).
thf(2969,plain,
! [A: a > a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ~ ( sk8 @ A )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [C: a] : C ) ) ) ) )
!= ( sk3 @ ( A @ ( sk9 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1608,18]) ).
thf(2974,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ~ ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [C: a] : C ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2969:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk9 @ ^ [D: a] : D ) ) ) ) ))]]) ).
thf(3984,plain,
! [A: a > a > a] :
( ~ ( sk8
@ ^ [B: a] : ( sk10 @ ( A @ B ) ) )
| ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( ( sk8
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk10 @ ( A @ B ) ) ) ) )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [D: a] : D ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[71,2974]) ).
thf(3995,plain,
( ~ ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [D: a] : D ) ) ) ) ) )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ),
inference(pre_uni,[status(thm)],[3984:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ ( sk9 @ ^ [E: a] : E ) ) ) ) ))]]) ).
thf(6226,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [D: a] : D ) ) ) ) ) )
!= ( sk8
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[344,3995]) ).
thf(6283,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [D: a] : D ) ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[6226]) ).
thf(9,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( sk2 @ ( sk7 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(24,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( sk2 @ ( sk7 @ A ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(627,plain,
! [A: a] :
( ( sk2 @ ( sk7 @ A ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[385,24]) ).
thf(628,plain,
( sk2
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[627:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ))]]) ).
thf(12,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( A
= ( sk4 @ ( sk5 @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(28,plain,
! [A: a] :
( ( ( sk4 @ ( sk5 @ A ) )
= A )
| ~ ( sk2 @ A ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(29,plain,
! [A: a] :
( ( ( sk4 @ ( sk5 @ A ) )
= A )
| ~ ( sk2 @ A ) ),
inference(simp,[status(thm)],[28]) ).
thf(786,plain,
! [A: a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( ( sk4 @ ( sk5 @ A ) )
= A )
| ( ( sk2
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[485,29]) ).
thf(787,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk4
@ ( sk5
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) )
= ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ),
inference(pattern_uni,[status(thm)],[786:[bind(A,$thf( sk4 @ ( sk9 @ ^ [B: a] : B ) ))]]) ).
thf(38,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk4 @ B ) )
| ( ( sk1 @ ( sk5 @ A ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[23,8]) ).
thf(39,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk4 @ ( sk5 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( C )),bind(B,$thf( sk5 @ C ))]]) ).
thf(42,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk4 @ ( sk5 @ A ) ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(781,plain,
! [A: a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( sk2 @ ( sk4 @ ( sk5 @ A ) ) )
| ( ( sk2
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[485,42]) ).
thf(782,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( sk2
@ ( sk4
@ ( sk5
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[781:[bind(A,$thf( sk4 @ ( sk9 @ ^ [B: a] : B ) ))]]) ).
thf(2640,plain,
! [A: a > a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
| ( ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) )
!= ( sk2
@ ( sk4
@ ( sk5
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[782,83]) ).
thf(2648,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ~ ( sk8
@ ^ [A: a] :
( sk6
@ ( sk4
@ ( sk5
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2640:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk5 @ ( sk4 @ ( sk9 @ ^ [C: a] : C ) ) ) ) ))]]) ).
thf(5266,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk8
@ ^ [A: a] :
( sk6
@ ( sk4
@ ( sk5
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) ) ) )
!= ( sk8
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[344,2648]) ).
thf(5304,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk6
@ ( sk4
@ ( sk5
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[5266]) ).
thf(5333,plain,
( ( ( sk6
@ ( sk4
@ ( sk5
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ) )
!= sk22 )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[5304]) ).
thf(7071,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk6
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) )
!= sk22 )
| ( ( sk4
@ ( sk5
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) )
!= ( sk4
@ ( sk5
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[787,5333]) ).
thf(7072,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk6
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) )
!= sk22 ) ),
inference(pattern_uni,[status(thm)],[7071:[]]) ).
thf(486,plain,
! [A: a > a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ~ ( sk3 @ ( A @ ( sk9 @ A ) ) )
| ( ( sk8
@ ^ [B: a] : B )
!= ( sk8 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[344,18]) ).
thf(487,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ~ ( sk3
@ ( sk9
@ ^ [A: a] : A ) ) ),
inference(pattern_uni,[status(thm)],[486:[bind(A,$thf( ^ [B: a] : B ))]]) ).
thf(2968,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk3
@ ( sk10
@ ^ [A: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) ) )
!= ( sk3
@ ( sk9
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[1608,487]) ).
thf(2976,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk10
@ ^ [A: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) )
!= ( sk9
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[2968]) ).
thf(10,plain,
! [B: a,A: a > a] :
( ( sk8 @ A )
| ~ ( sk1 @ B )
| ( ( sk10 @ A )
!= ( A @ B ) )
| ( sk1 @ ( sk11 @ B @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(19,plain,
! [B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( sk8 @ A )
| ~ ( sk1 @ B )
| ( sk1 @ ( sk11 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(20,plain,
! [B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( sk8 @ A )
| ~ ( sk1 @ B )
| ( sk1 @ ( sk11 @ B @ A ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(100,plain,
! [D: a,C: a > a,B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( sk8 @ A )
| ~ ( sk1 @ B )
| ( ( sk10 @ C )
!= ( C @ D ) )
| ( sk8 @ C )
| ( sk1 @ ( sk11 @ D @ C ) )
| ( ( sk1 @ ( sk11 @ B @ A ) )
!= ( sk1 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[20,20]) ).
thf(101,plain,
! [C: a > a,B: a,A: a > a] :
( ( ( sk10 @ C )
!= ( C @ B ) )
| ( sk8 @ C )
| ~ ( sk1 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk11 @ B @ C ) ) )
| ( sk8 @ A )
| ( sk1 @ ( sk11 @ ( sk11 @ B @ C ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[100:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( sk11 @ E @ F ))]]) ).
thf(115,plain,
! [C: a > a,B: a,A: a > a] :
( ( ( sk10 @ C )
!= ( C @ B ) )
| ( sk8 @ C )
| ~ ( sk1 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk11 @ B @ C ) ) )
| ( sk8 @ A )
| ( sk1 @ ( sk11 @ ( sk11 @ B @ C ) @ A ) ) ),
inference(simp,[status(thm)],[101]) ).
thf(482,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk8
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) )
!= ( sk8
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[344,211]) ).
thf(512,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[482]) ).
thf(683,plain,
( ( ( sk6 @ ( sk4 @ sk12 ) )
!= sk12 )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[512]) ).
thf(643,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) )
!= ( sk8
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[344,639]) ).
thf(655,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[643]) ).
thf(131,plain,
! [B: a,A: a > a] :
( ~ ( sk8 @ A )
| ( sk1 @ ( sk5 @ ( sk4 @ B ) ) )
| ( ( sk1 @ ( sk9 @ A ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[25,43]) ).
thf(132,plain,
! [A: a > a] :
( ~ ( sk8 @ A )
| ( sk1 @ ( sk5 @ ( sk4 @ ( sk9 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[131:[bind(A,$thf( C )),bind(B,$thf( sk9 @ C ))]]) ).
thf(135,plain,
! [A: a > a] :
( ~ ( sk8 @ A )
| ( sk1 @ ( sk5 @ ( sk4 @ ( sk9 @ A ) ) ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(198,plain,
! [B: a > a,A: a] :
( ~ ( sk1 @ A )
| ~ ( sk8
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) )
| ( ( sk2
@ ( B
@ ( sk9
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) ) ) )
!= ( sk2 @ ( sk4 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,83]) ).
thf(202,plain,
! [A: a > a] :
( ~ ( sk1
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( A @ B ) ) ) ) ) )
| ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( A @ B ) ) ) ) ),
inference(pre_uni,[status(thm)],[198:[bind(A,$thf( C @ ( sk9 @ ^ [D: a] : ( sk6 @ ( sk4 @ ( C @ D ) ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk4 @ ( C @ D ) ) ))]]) ).
thf(208,plain,
! [A: a > a] :
( ~ ( sk1
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( A @ B ) ) ) ) ) )
| ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( A @ B ) ) ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(10715,plain,
! [B: a > a,A: a > a] :
( ~ ( sk8 @ A )
| ~ ( sk8
@ ^ [C: a] : ( sk6 @ ( sk4 @ ( B @ C ) ) ) )
| ( ( sk1 @ ( sk5 @ ( sk4 @ ( sk9 @ A ) ) ) )
!= ( sk1
@ ( B
@ ( sk9
@ ^ [C: a] : ( sk6 @ ( sk4 @ ( B @ C ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[135,208]) ).
thf(10753,plain,
( ~ ( sk8
@ ^ [A: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ A ) ) ) ) )
| ~ ( sk8
@ ^ [A: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ A ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[10715:[bind(A,$thf( ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) )),bind(B,$thf( ^ [C: a] : ( sk5 @ ( sk4 @ C ) ) ))]]) ).
thf(10805,plain,
~ ( sk8
@ ^ [A: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ A ) ) ) ) ),
inference(simp,[status(thm)],[10753]) ).
thf(529,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk3
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) )
!= ( sk3
@ ( sk9
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[215,487]) ).
thf(533,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) )
!= ( sk9
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[529]) ).
thf(3006,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [C: a] : C ) ) ) ) )
!= ( sk8
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[344,2974]) ).
thf(3044,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [C: a] : C ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[3006]) ).
thf(481,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) )
!= ( sk8
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[344,379]) ).
thf(500,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[481]) ).
thf(65,plain,
! [B: a,A: a > a] :
( ( sk8 @ A )
| ( sk2 @ ( sk7 @ B ) )
| ( ( sk3 @ ( sk10 @ A ) )
!= ( sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[31,24]) ).
thf(66,plain,
! [A: a > a] :
( ( sk8 @ A )
| ( sk2 @ ( sk7 @ ( sk10 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( C )),bind(B,$thf( sk10 @ C ))]]) ).
thf(70,plain,
! [A: a > a] :
( ( sk8 @ A )
| ( sk2 @ ( sk7 @ ( sk10 @ A ) ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(10826,plain,
! [A: a > a] :
( ( sk2 @ ( sk7 @ ( sk10 @ A ) ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[70,10805]) ).
thf(10827,plain,
( sk2
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[10826:[bind(A,$thf( ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ))]]) ).
thf(11018,plain,
! [A: a > a] :
( ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) ) )
!= ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[10827,83]) ).
thf(11020,plain,
~ ( sk8
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[11018:[bind(A,$thf( ^ [B: a] : ( sk7 @ ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) ) ) ))]]) ).
thf(10832,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,10805]) ).
thf(10833,plain,
( sk3
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[10832:[bind(A,$thf( ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ))]]) ).
thf(62,plain,
! [B: a > a,A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ~ ( sk3 @ ( B @ ( sk9 @ B ) ) )
| ( ( sk8 @ A )
!= ( sk8 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[31,18]) ).
thf(63,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ~ ( sk3 @ ( A @ ( sk9 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[62:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(10851,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) )
!= ( sk3 @ ( A @ ( sk9 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[10833,63]) ).
thf(10860,plain,
( sk3
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[10851:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) ) ))]]) ).
thf(44,plain,
! [B: a,A: a] :
( ~ ( sk3 @ A )
| ( sk1 @ ( sk5 @ B ) )
| ( ( sk2 @ ( sk7 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[24,23]) ).
thf(45,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( sk1 @ ( sk5 @ ( sk7 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[44:[bind(A,$thf( C )),bind(B,$thf( sk7 @ C ))]]) ).
thf(46,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( sk1 @ ( sk5 @ ( sk7 @ A ) ) ) ),
inference(simp,[status(thm)],[45]) ).
thf(11319,plain,
! [A: a] :
( ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10860,46]) ).
thf(11320,plain,
( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[11319:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) ) ))]]) ).
thf(778,plain,
! [A: a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( sk3 @ ( sk6 @ A ) )
| ( ( sk2
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[485,30]) ).
thf(779,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( sk3
@ ( sk6
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[778:[bind(A,$thf( sk4 @ ( sk9 @ ^ [B: a] : B ) ))]]) ).
thf(1320,plain,
! [A: a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( sk2 @ ( sk7 @ A ) )
| ( ( sk3
@ ( sk6
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[779,24]) ).
thf(1321,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( sk2
@ ( sk7
@ ( sk6
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1320:[bind(A,$thf( sk6 @ ( sk4 @ ( sk9 @ ^ [B: a] : B ) ) ))]]) ).
thf(2694,plain,
! [A: a > a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
| ( ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) )
!= ( sk2
@ ( sk7
@ ( sk6
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1321,83]) ).
thf(2711,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ~ ( sk8
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk6
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2694:[bind(A,$thf( ^ [B: a] : ( sk7 @ ( sk6 @ ( sk4 @ ( sk9 @ ^ [C: a] : C ) ) ) ) ))]]) ).
thf(5648,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk8
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk6
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) ) ) )
!= ( sk8
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[344,2711]) ).
thf(5695,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk6
@ ( sk7
@ ( sk6
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[5648]) ).
thf(5713,plain,
( ( ( sk6
@ ( sk7
@ ( sk6
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ) )
!= sk23 )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[5695]) ).
thf(220,plain,
! [A: a] :
( ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[215,46]) ).
thf(221,plain,
( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[220:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ))]]) ).
thf(684,plain,
( ( ( ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) )
!= ( ^ [A: a] : A ) )
| ( ( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) )
!= ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[221,512]) ).
thf(698,plain,
( ( ( ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) )
!= ( ^ [A: a] : A ) )
| ( ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) )
!= ( sk10
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[684]) ).
thf(1131,plain,
! [A: a > a] :
( ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) )
!= ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[628,83]) ).
thf(1135,plain,
~ ( sk8
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[1131:[bind(A,$thf( ^ [B: a] : ( sk7 @ ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ))]]) ).
thf(3413,plain,
! [A: a > a] :
( ( sk2 @ ( sk7 @ ( sk10 @ A ) ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[70,1135]) ).
thf(3414,plain,
( sk2
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3413:[bind(A,$thf( ^ [B: a] : ( sk6 @ ( sk7 @ ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ) ))]]) ).
thf(218,plain,
! [A: a] :
( ( sk2 @ ( sk7 @ A ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[215,24]) ).
thf(219,plain,
( sk2
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[218:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ))]]) ).
thf(229,plain,
! [A: a] :
( ( sk3 @ ( sk6 @ A ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[219,30]) ).
thf(230,plain,
( sk3
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[229:[bind(A,$thf( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ))]]) ).
thf(466,plain,
! [A: a] :
( ( sk2 @ ( sk7 @ A ) )
| ( ( sk3
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[230,24]) ).
thf(467,plain,
( sk2
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[466:[bind(A,$thf( sk6 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ))]]) ).
thf(945,plain,
! [A: a > a] :
( ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
| ( ( sk2
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) )
!= ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[467,83]) ).
thf(947,plain,
~ ( sk8
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[945:[bind(A,$thf( ^ [B: a] : ( sk7 @ ( sk6 @ ( sk7 @ ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ))]]) ).
thf(2186,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk6
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,947]) ).
thf(2187,plain,
( sk3
@ ( sk10
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2186:[bind(A,$thf( ^ [B: a] : ( sk6 @ ( sk7 @ ( sk6 @ ( sk7 @ ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ) ))]]) ).
thf(4,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( A
= ( sk6 @ ( sk7 @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(34,plain,
! [A: a] :
( ( ( sk6 @ ( sk7 @ A ) )
= A )
| ~ ( sk3 @ A ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(35,plain,
! [A: a] :
( ( ( sk6 @ ( sk7 @ A ) )
= A )
| ~ ( sk3 @ A ) ),
inference(simp,[status(thm)],[34]) ).
thf(1062,plain,
! [A: a] :
( ( ( sk6 @ ( sk7 @ A ) )
= A )
| ( ( sk3
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[215,35]) ).
thf(1063,plain,
( ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) )
= ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[1062:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ))]]) ).
thf(5178,plain,
( sk3
@ ( sk10
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[2187,1063]) ).
thf(77,plain,
! [B: a,A: a] :
( ~ ( sk3 @ A )
| ( sk3 @ ( sk6 @ B ) )
| ( ( sk2 @ ( sk7 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[24,30]) ).
thf(78,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( sk3 @ ( sk6 @ ( sk7 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[77:[bind(A,$thf( C )),bind(B,$thf( sk7 @ C ))]]) ).
thf(82,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( sk3 @ ( sk6 @ ( sk7 @ A ) ) ) ),
inference(simp,[status(thm)],[78]) ).
thf(11334,plain,
! [A: a] :
( ( sk3 @ ( sk6 @ ( sk7 @ A ) ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10860,82]) ).
thf(11335,plain,
( sk3
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[11334:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) ) ))]]) ).
thf(10853,plain,
! [A: a] :
( ( sk3 @ ( sk6 @ ( sk7 @ A ) ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10833,82]) ).
thf(10854,plain,
( sk3
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ A ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[10853:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ))]]) ).
thf(11,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A )
| ~ ( sk1 @ B )
| ( A
!= ( sk4 @ B ) )
| ( B
= ( sk5 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(32,plain,
! [B: a,A: a] :
( ( A
!= ( sk4 @ B ) )
| ( B
= ( sk5 @ A ) )
| ~ ( sk2 @ A )
| ~ ( sk1 @ B ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(33,plain,
! [A: a] :
( ( ( sk5 @ ( sk4 @ A ) )
= A )
| ~ ( sk2 @ ( sk4 @ A ) )
| ~ ( sk1 @ A ) ),
inference(simp,[status(thm)],[32]) ).
thf(849,plain,
! [A: a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( ( sk5 @ ( sk4 @ A ) )
= A )
| ~ ( sk1 @ A )
| ( ( sk2
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) )
!= ( sk2 @ ( sk4 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[485,33]) ).
thf(850,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk5
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) )
= ( sk9
@ ^ [A: a] : A ) )
| ~ ( sk1
@ ( sk9
@ ^ [A: a] : A ) ) ),
inference(pattern_uni,[status(thm)],[849:[bind(A,$thf( sk9 @ ^ [B: a] : B ))]]) ).
thf(7178,plain,
! [A: a > a] :
( ~ ( sk8 @ A )
| ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( ( sk5
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) )
= ( sk9
@ ^ [B: a] : B ) )
| ( ( sk1 @ ( sk9 @ A ) )
!= ( sk1
@ ( sk9
@ ^ [B: a] : B ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,850]) ).
thf(7179,plain,
( ~ ( sk8
@ ^ [A: a] : A )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk5
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) )
= ( sk9
@ ^ [A: a] : A ) ) ),
inference(pattern_uni,[status(thm)],[7178:[bind(A,$thf( ^ [B: a] : B ))]]) ).
thf(8121,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk5
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) )
= ( sk9
@ ^ [A: a] : A ) )
| ( ( sk8
@ ^ [A: a] : A )
!= ( sk8
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[344,7179]) ).
thf(8122,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk5
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) )
= ( sk9
@ ^ [A: a] : A ) ) ),
inference(pattern_uni,[status(thm)],[8121:[]]) ).
thf(15,plain,
! [B: a,A: a] :
( ~ ( sk3 @ A )
| ~ ( sk2 @ B )
| ( A
!= ( sk6 @ B ) )
| ( B
= ( sk7 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(36,plain,
! [B: a,A: a] :
( ( A
!= ( sk6 @ B ) )
| ( B
= ( sk7 @ A ) )
| ~ ( sk3 @ A )
| ~ ( sk2 @ B ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(37,plain,
! [A: a] :
( ( ( sk7 @ ( sk6 @ A ) )
= A )
| ~ ( sk3 @ ( sk6 @ A ) )
| ~ ( sk2 @ A ) ),
inference(simp,[status(thm)],[36]) ).
thf(569,plain,
! [A: a] :
( ( ( sk4 @ ( sk5 @ A ) )
= A )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[219,29]) ).
thf(570,plain,
( ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) )
= ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[569:[bind(A,$thf( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ))]]) ).
thf(1123,plain,
! [A: a] :
( ( sk2 @ ( sk4 @ ( sk5 @ A ) ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[628,42]) ).
thf(1124,plain,
( sk2
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1123:[bind(A,$thf( sk7 @ ( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ))]]) ).
thf(3652,plain,
! [A: a] :
( ( sk3 @ ( sk6 @ A ) )
| ( ( sk2
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1124,30]) ).
thf(3653,plain,
( sk3
@ ( sk6
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3652:[bind(A,$thf( sk4 @ ( sk5 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ) ))]]) ).
thf(2634,plain,
! [A: a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( sk1 @ ( sk5 @ A ) )
| ( ( sk2
@ ( sk4
@ ( sk5
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[782,23]) ).
thf(2635,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( sk1
@ ( sk5
@ ( sk4
@ ( sk5
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2634:[bind(A,$thf( sk4 @ ( sk5 @ ( sk4 @ ( sk9 @ ^ [B: a] : B ) ) ) ))]]) ).
thf(144,plain,
! [B: a,A: a] :
( ~ ( sk3 @ A )
| ( sk1 @ ( sk5 @ ( sk4 @ B ) ) )
| ( ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[46,43]) ).
thf(145,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( sk1 @ ( sk5 @ ( sk4 @ ( sk5 @ ( sk7 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[144:[bind(A,$thf( D )),bind(B,$thf( sk5 @ ( sk7 @ D ) ))]]) ).
thf(152,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( sk1 @ ( sk5 @ ( sk4 @ ( sk5 @ ( sk7 @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[145]) ).
thf(3258,plain,
( ( ( sk10
@ ^ [A: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) )
!= sk18 )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[3044]) ).
thf(2949,plain,
! [A: a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( sk2 @ ( sk7 @ A ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [C: a] : C ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1608,24]) ).
thf(2950,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( sk2
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2949:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk9 @ ^ [C: a] : C ) ) ) ))]]) ).
thf(491,plain,
! [A: a > a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( sk1 @ ( sk9 @ A ) )
| ( ( sk8
@ ^ [B: a] : B )
!= ( sk8 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[344,25]) ).
thf(492,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( sk1
@ ( sk9
@ ^ [A: a] : A ) ) ),
inference(pattern_uni,[status(thm)],[491:[bind(A,$thf( ^ [B: a] : B ))]]) ).
thf(2691,plain,
! [A: a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( sk3 @ ( sk6 @ A ) )
| ( ( sk2
@ ( sk7
@ ( sk6
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1321,30]) ).
thf(2692,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( sk3
@ ( sk6
@ ( sk7
@ ( sk6
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2691:[bind(A,$thf( sk7 @ ( sk6 @ ( sk4 @ ( sk9 @ ^ [B: a] : B ) ) ) ))]]) ).
thf(12330,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk3
@ ( sk6
@ ( sk7
@ ( sk6
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ) ) )
!= ( sk3
@ ( sk9
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[2692,487]) ).
thf(12362,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk6
@ ( sk7
@ ( sk6
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ) )
!= ( sk9
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[12330]) ).
thf(1593,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk8
@ ^ [A: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) )
!= ( sk8
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[344,798]) ).
thf(1621,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1593]) ).
thf(1632,plain,
( ( ( sk6
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) )
!= sk15 )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[1621]) ).
thf(375,plain,
! [A: a] :
( ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[225,46]) ).
thf(376,plain,
( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[375:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ))]]) ).
thf(373,plain,
! [A: a] :
( ( sk2 @ ( sk7 @ A ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[225,24]) ).
thf(374,plain,
( sk2
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[373:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ))]]) ).
thf(611,plain,
! [A: a] :
( ( sk2 @ ( sk4 @ ( sk5 @ A ) ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[374,42]) ).
thf(612,plain,
( sk2
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[611:[bind(A,$thf( sk7 @ ( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ))]]) ).
thf(1676,plain,
! [A: a] :
( ( sk2 @ ( sk4 @ ( sk5 @ A ) ) )
| ( ( sk2
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[612,42]) ).
thf(1677,plain,
( sk2
@ ( sk4
@ ( sk5
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1676:[bind(A,$thf( sk4 @ ( sk5 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ))]]) ).
thf(56,plain,
! [C: a,B: a > a,A: a > a] :
( ~ ( sk8 @ A )
| ( ( sk10 @ B )
!= ( B @ C ) )
| ( ( sk11 @ C @ B )
!= C )
| ( sk8 @ B )
| ( ( sk1 @ ( sk9 @ A ) )
!= ( sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25,27]) ).
thf(57,plain,
! [B: a > a,A: a > a] :
( ~ ( sk8 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk9 @ B ) ) )
| ( ( sk11 @ ( sk9 @ B ) @ A )
!= ( sk9 @ B ) )
| ( sk8 @ A ) ),
inference(pattern_uni,[status(thm)],[56:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( sk9 @ D ))]]) ).
thf(61,plain,
! [B: a > a,A: a > a] :
( ~ ( sk8 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk9 @ B ) ) )
| ( ( sk11 @ ( sk9 @ B ) @ A )
!= ( sk9 @ B ) )
| ( sk8 @ A ) ),
inference(simp,[status(thm)],[57]) ).
thf(738,plain,
! [A: a > a] :
( ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( A @ B ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[376,208]) ).
thf(742,plain,
~ ( sk8
@ ^ [A: a] :
( sk6
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[738:[bind(A,$thf( ^ [B: a] : ( sk5 @ ( sk7 @ ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ))]]) ).
thf(3242,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk6
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,742]) ).
thf(3243,plain,
( sk3
@ ( sk10
@ ^ [A: a] :
( sk6
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3242:[bind(A,$thf( ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk7 @ ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ) ) ))]]) ).
thf(102,plain,
! [D: a,C: a > a,B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( sk8 @ A )
| ~ ( sk1 @ B )
| ( ( sk10 @ C )
!= ( C @ D ) )
| ( ( sk11 @ D @ C )
!= D )
| ( sk8 @ C )
| ( ( sk1 @ ( sk11 @ B @ A ) )
!= ( sk1 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[20,27]) ).
thf(103,plain,
! [C: a > a,B: a,A: a > a] :
( ( ( sk10 @ C )
!= ( C @ B ) )
| ( sk8 @ C )
| ~ ( sk1 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk11 @ B @ C ) ) )
| ( ( sk11 @ ( sk11 @ B @ C ) @ A )
!= ( sk11 @ B @ C ) )
| ( sk8 @ A ) ),
inference(pattern_uni,[status(thm)],[102:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( sk11 @ E @ F ))]]) ).
thf(116,plain,
! [C: a > a,B: a,A: a > a] :
( ( ( sk10 @ C )
!= ( C @ B ) )
| ( sk8 @ C )
| ~ ( sk1 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk11 @ B @ C ) ) )
| ( ( sk11 @ ( sk11 @ B @ C ) @ A )
!= ( sk11 @ B @ C ) )
| ( sk8 @ A ) ),
inference(simp,[status(thm)],[103]) ).
thf(10831,plain,
! [A: a > a > a] :
( ~ ( sk8
@ ^ [B: a] : ( sk10 @ ( A @ B ) ) )
| ( ( sk8
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk10 @ ( A @ B ) ) ) ) )
!= ( sk8
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[71,10805]) ).
thf(10835,plain,
~ ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[10831:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) ))]]) ).
thf(10879,plain,
! [A: a > a > a] :
( ~ ( sk8
@ ^ [B: a] : ( sk10 @ ( A @ B ) ) )
| ( ( sk8
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk10 @ ( A @ B ) ) ) ) )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[71,10835]) ).
thf(10884,plain,
~ ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[10879:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ D ) ) ) ) ) ))]]) ).
thf(11364,plain,
! [A: a > a > a] :
( ~ ( sk8
@ ^ [B: a] : ( sk10 @ ( A @ B ) ) )
| ( ( sk8
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk10 @ ( A @ B ) ) ) ) )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ D ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[71,10884]) ).
thf(11367,plain,
~ ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ D ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[11364:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ E ) ) ) ) ) ) ))]]) ).
thf(7297,plain,
( ( ( sk5
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) )
= ( sk9
@ ^ [A: a] : A ) )
| ~ ( sk1
@ ( sk9
@ ^ [A: a] : A ) )
| ( ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
!= ( sk1
@ ( sk9
@ ^ [A: a] : A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[850]) ).
thf(7348,plain,
( ( ( sk5
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) )
= ( sk9
@ ^ [A: a] : A ) )
| ~ ( sk1
@ ( sk9
@ ^ [A: a] : A ) )
| ( ( sk10
@ ^ [A: a] : A )
!= ( sk9
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[7297]) ).
thf(14760,plain,
! [A: a > a] :
( ~ ( sk8 @ A )
| ( ( sk5
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) )
= ( sk9
@ ^ [B: a] : B ) )
| ( ( sk10
@ ^ [B: a] : B )
!= ( sk9
@ ^ [B: a] : B ) )
| ( ( sk1 @ ( sk9 @ A ) )
!= ( sk1
@ ( sk9
@ ^ [B: a] : B ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,7348]) ).
thf(14761,plain,
( ~ ( sk8
@ ^ [A: a] : A )
| ( ( sk5
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) )
= ( sk9
@ ^ [A: a] : A ) )
| ( ( sk10
@ ^ [A: a] : A )
!= ( sk9
@ ^ [A: a] : A ) ) ),
inference(pattern_uni,[status(thm)],[14760:[bind(A,$thf( ^ [B: a] : B ))]]) ).
thf(1144,plain,
! [A: a > a] :
( ~ ( sk8 @ A )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) )
!= ( sk3 @ ( A @ ( sk9 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[645,18]) ).
thf(1157,plain,
~ ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[1144:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk10 @ ^ [F: a] : ( sk6 @ ( sk4 @ F ) ) ) ) ) ) ))]]) ).
thf(3989,plain,
! [A: a > a > a] :
( ~ ( sk8
@ ^ [B: a] : ( sk10 @ ( A @ B ) ) )
| ( ( sk8
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk10 @ ( A @ B ) ) ) ) )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] :
( sk10
@ ^ [F: a] : ( sk6 @ ( sk4 @ F ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[71,1157]) ).
thf(4006,plain,
~ ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] :
( sk10
@ ^ [F: a] : ( sk6 @ ( sk4 @ F ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3989:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk10 @ ^ [F: a] : ( sk10 @ ^ [G: a] : ( sk6 @ ( sk4 @ G ) ) ) ) ) ) ))]]) ).
thf(4064,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] :
( sk10
@ ^ [F: a] :
( sk10
@ ^ [G: a] : ( sk6 @ ( sk4 @ G ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,4006]) ).
thf(4065,plain,
( sk3
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] :
( sk10
@ ^ [F: a] : ( sk6 @ ( sk4 @ F ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4064:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk10 @ ^ [F: a] : ( sk10 @ ^ [G: a] : ( sk6 @ ( sk4 @ G ) ) ) ) ) ) ) ))]]) ).
thf(1492,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] :
( sk10
@ ^ [F: a] : ( sk6 @ ( sk4 @ F ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,1157]) ).
thf(1493,plain,
( sk3
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1492:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk10 @ ^ [F: a] : ( sk6 @ ( sk4 @ F ) ) ) ) ) ) ))]]) ).
thf(2921,plain,
! [A: a] :
( ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] :
( sk10
@ ^ [F: a] : ( sk6 @ ( sk4 @ F ) ) ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1493,46]) ).
thf(2922,plain,
( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2921:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk10 @ ^ [F: a] : ( sk6 @ ( sk4 @ F ) ) ) ) ) ) ))]]) ).
thf(52,plain,
! [C: a,B: a > a,A: a] :
( ~ ( sk2 @ A )
| ( ( sk10 @ B )
!= ( B @ C ) )
| ( ( sk11 @ C @ B )
!= C )
| ( sk8 @ B )
| ( ( sk1 @ ( sk5 @ A ) )
!= ( sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,27]) ).
thf(53,plain,
! [B: a,A: a > a] :
( ~ ( sk2 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk5 @ B ) ) )
| ( ( sk11 @ ( sk5 @ B ) @ A )
!= ( sk5 @ B ) )
| ( sk8 @ A ) ),
inference(pattern_uni,[status(thm)],[52:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( sk5 @ D ))]]) ).
thf(60,plain,
! [B: a,A: a > a] :
( ~ ( sk2 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk5 @ B ) ) )
| ( ( sk11 @ ( sk5 @ B ) @ A )
!= ( sk5 @ B ) )
| ( sk8 @ A ) ),
inference(simp,[status(thm)],[53]) ).
thf(106,plain,
! [C: a,B: a > a,A: a] :
( ~ ( sk2 @ A )
| ( ( sk10 @ B )
!= ( B @ C ) )
| ( sk8 @ B )
| ( sk1 @ ( sk11 @ C @ B ) )
| ( ( sk1 @ ( sk5 @ A ) )
!= ( sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,20]) ).
thf(107,plain,
! [B: a,A: a > a] :
( ~ ( sk2 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk5 @ B ) ) )
| ( sk8 @ A )
| ( sk1 @ ( sk11 @ ( sk5 @ B ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[106:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( sk5 @ D ))]]) ).
thf(117,plain,
! [B: a,A: a > a] :
( ~ ( sk2 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk5 @ B ) ) )
| ( sk8 @ A )
| ( sk1 @ ( sk11 @ ( sk5 @ B ) @ A ) ) ),
inference(simp,[status(thm)],[107]) ).
thf(957,plain,
( ( ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) )
!= sk14 )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[500]) ).
thf(739,plain,
( ~ ( sk3
@ ( sk9
@ ^ [A: a] : A ) )
| ( ( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) )
!= ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[376,487]) ).
thf(746,plain,
( ~ ( sk3
@ ( sk9
@ ^ [A: a] : A ) )
| ( ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) )
!= ( sk10
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[739]) ).
thf(629,plain,
! [A: a] :
( ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[385,46]) ).
thf(630,plain,
( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[629:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ))]]) ).
thf(121,plain,
! [C: a,B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( sk8 @ A )
| ~ ( sk1 @ B )
| ( sk1 @ ( sk5 @ ( sk4 @ C ) ) )
| ( ( sk1 @ ( sk11 @ B @ A ) )
!= ( sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,43]) ).
thf(122,plain,
! [B: a > a,A: a] :
( ( ( sk10 @ B )
!= ( B @ A ) )
| ( sk8 @ B )
| ~ ( sk1 @ A )
| ( sk1 @ ( sk5 @ ( sk4 @ ( sk11 @ A @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[121:[bind(A,$thf( E )),bind(B,$thf( D )),bind(C,$thf( sk11 @ D @ E ))]]) ).
thf(137,plain,
! [B: a > a,A: a] :
( ( ( sk10 @ B )
!= ( B @ A ) )
| ( sk8 @ B )
| ~ ( sk1 @ A )
| ( sk1 @ ( sk5 @ ( sk4 @ ( sk11 @ A @ B ) ) ) ) ),
inference(simp,[status(thm)],[122]) ).
thf(935,plain,
! [A: a] :
( ( sk3 @ ( sk6 @ A ) )
| ( ( sk2
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[467,30]) ).
thf(936,plain,
( sk3
@ ( sk6
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[935:[bind(A,$thf( sk7 @ ( sk6 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ))]]) ).
thf(2141,plain,
! [A: a] :
( ( sk2 @ ( sk7 @ A ) )
| ( ( sk3
@ ( sk6
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[936,24]) ).
thf(2142,plain,
( sk2
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2141:[bind(A,$thf( sk6 @ ( sk7 @ ( sk6 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ))]]) ).
thf(4652,plain,
( sk2
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[2142,1063]) ).
thf(4681,plain,
! [A: a > a] :
( ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
| ( ( sk2
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) )
!= ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4652,83]) ).
thf(4687,plain,
~ ( sk8
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[4681:[bind(A,$thf( ^ [B: a] : ( sk7 @ ( sk6 @ ( sk7 @ ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ))]]) ).
thf(4947,plain,
~ ( sk8
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ),
inference(rewrite,[status(thm)],[4687,1063]) ).
thf(90,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk4 @ ( sk5 @ B ) ) )
| ( ( sk2 @ ( sk4 @ ( sk5 @ A ) ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[42,42]) ).
thf(91,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk4 @ ( sk5 @ ( sk4 @ ( sk5 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( D )),bind(B,$thf( sk4 @ ( sk5 @ D ) ))]]) ).
thf(97,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk4 @ ( sk5 @ ( sk4 @ ( sk5 @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(1887,plain,
! [A: a] :
( ( sk1 @ ( sk5 @ ( sk4 @ A ) ) )
| ( ( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[630,43]) ).
thf(1888,plain,
( sk1
@ ( sk5
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1887:[bind(A,$thf( sk5 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ))]]) ).
thf(429,plain,
! [A: a > a] :
( ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( A @ B ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[221,208]) ).
thf(446,plain,
~ ( sk8
@ ^ [A: a] :
( sk6
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[429:[bind(A,$thf( ^ [B: a] : ( sk5 @ ( sk7 @ ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ))]]) ).
thf(3425,plain,
! [A: a > a] :
( ( sk2 @ ( sk7 @ ( sk10 @ A ) ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk6
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[70,446]) ).
thf(3426,plain,
( sk2
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk6
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3425:[bind(A,$thf( ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk7 @ ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ) ))]]) ).
thf(14286,plain,
( sk2
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[3426,570]) ).
thf(14320,plain,
! [A: a] :
( ( sk3 @ ( sk6 @ A ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14286,30]) ).
thf(14321,plain,
( sk3
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[14320:[bind(A,$thf( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk7 @ ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ))]]) ).
thf(14338,plain,
( sk3
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[14321,1063]) ).
thf(233,plain,
! [A: a > a] :
( ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) )
!= ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[219,83]) ).
thf(234,plain,
~ ( sk8
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[233:[bind(A,$thf( ^ [B: a] : ( sk7 @ ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ))]]) ).
thf(480,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk8
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) )
!= ( sk8
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[344,234]) ).
thf(506,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[480]) ).
thf(1992,plain,
( ( ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) )
!= sk16 )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[506]) ).
thf(4979,plain,
( ( ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) )
!= sk16 )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ),
inference(rewrite,[status(thm)],[1992,1063]) ).
thf(10824,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk8
@ ^ [A: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ A ) ) ) ) )
!= ( sk8
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[344,10805]) ).
thf(10834,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ A ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[10824]) ).
thf(10887,plain,
( ( ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ sk26 ) ) ) )
!= sk26 )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[10834]) ).
thf(140,plain,
! [C: a,B: a > a,A: a] :
( ~ ( sk3 @ A )
| ( ( sk10 @ B )
!= ( B @ C ) )
| ( ( sk11 @ C @ B )
!= C )
| ( sk8 @ B )
| ( ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
!= ( sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[46,27]) ).
thf(141,plain,
! [B: a,A: a > a] :
( ~ ( sk3 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk5 @ ( sk7 @ B ) ) ) )
| ( ( sk11 @ ( sk5 @ ( sk7 @ B ) ) @ A )
!= ( sk5 @ ( sk7 @ B ) ) )
| ( sk8 @ A ) ),
inference(pattern_uni,[status(thm)],[140:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( sk5 @ ( sk7 @ E ) ))]]) ).
thf(156,plain,
! [B: a,A: a > a] :
( ~ ( sk3 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk5 @ ( sk7 @ B ) ) ) )
| ( ( sk11 @ ( sk5 @ ( sk7 @ B ) ) @ A )
!= ( sk5 @ ( sk7 @ B ) ) )
| ( sk8 @ A ) ),
inference(simp,[status(thm)],[141]) ).
thf(724,plain,
! [A: a] :
( ( sk1 @ ( sk5 @ ( sk4 @ A ) ) )
| ( ( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[376,43]) ).
thf(725,plain,
( sk1
@ ( sk5
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[724:[bind(A,$thf( sk5 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ))]]) ).
thf(10871,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) )
!= ( sk8
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[344,10835]) ).
thf(10882,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[10871]) ).
thf(2637,plain,
! [A: a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( sk3 @ ( sk6 @ A ) )
| ( ( sk2
@ ( sk4
@ ( sk5
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[782,30]) ).
thf(2638,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( sk3
@ ( sk6
@ ( sk4
@ ( sk5
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2637:[bind(A,$thf( sk4 @ ( sk5 @ ( sk4 @ ( sk9 @ ^ [B: a] : B ) ) ) ))]]) ).
thf(7132,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( A != sk22 )
| ( ( sk6 @ ( sk7 @ A ) )
!= ( sk6
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,7072]) ).
thf(7142,plain,
( ~ ( sk3 @ sk22 )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk7 @ sk22 )
!= ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ),
inference(simp,[status(thm)],[7132]) ).
thf(2839,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,1135]) ).
thf(2840,plain,
( sk3
@ ( sk10
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2839:[bind(A,$thf( ^ [B: a] : ( sk6 @ ( sk7 @ ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ) ))]]) ).
thf(1484,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) )
!= ( sk8
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[344,1157]) ).
thf(1498,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1484]) ).
thf(515,plain,
( ~ ( sk3
@ ( sk9
@ ^ [A: a] : A ) )
| ( ( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) )
!= ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[221,487]) ).
thf(537,plain,
( ~ ( sk3
@ ( sk9
@ ^ [A: a] : A ) )
| ( ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) )
!= ( sk10
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[515]) ).
thf(1153,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk3
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) )
!= ( sk3
@ ( sk9
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[645,487]) ).
thf(1155,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) )
!= ( sk9
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1153]) ).
thf(12599,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ E ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,11367]) ).
thf(12600,plain,
( sk3
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ D ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[12599:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ E ) ) ) ) ) ) ) ))]]) ).
thf(88,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A )
| ( sk3 @ ( sk6 @ B ) )
| ( ( sk2 @ ( sk4 @ ( sk5 @ A ) ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[42,30]) ).
thf(89,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk3 @ ( sk6 @ ( sk4 @ ( sk5 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( D )),bind(B,$thf( sk4 @ ( sk5 @ D ) ))]]) ).
thf(96,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk3 @ ( sk6 @ ( sk4 @ ( sk5 @ A ) ) ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(499,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) )
!= ( sk8
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[344,222]) ).
thf(502,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[499]) ).
thf(701,plain,
( ( ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) )
!= sk13 )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[502]) ).
thf(104,plain,
! [C: a > a,B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ~ ( sk1 @ B )
| ( sk1 @ ( sk11 @ B @ A ) )
| ~ ( sk3 @ ( C @ ( sk9 @ C ) ) )
| ( ( sk8 @ A )
!= ( sk8 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,18]) ).
thf(105,plain,
! [B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ~ ( sk1 @ B )
| ( sk1 @ ( sk11 @ B @ A ) )
| ~ ( sk3 @ ( A @ ( sk9 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[104:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(489,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk8
@ ^ [B: a] : B )
| ( ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
!= ( sk1 @ ( sk5 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,344]) ).
thf(508,plain,
! [A: a] :
( ( sk8
@ ^ [B: a] : B )
| ~ ( sk2 @ A )
| ( ( sk10
@ ^ [B: a] : B )
!= ( sk5 @ A ) ) ),
inference(simp,[status(thm)],[489]) ).
thf(10839,plain,
! [A: a] :
( ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10833,46]) ).
thf(10840,plain,
( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ A ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[10839:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ))]]) ).
thf(11720,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk3
@ ( sk6
@ ( sk4
@ ( sk5
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ) ) )
!= ( sk3
@ ( sk9
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[2638,487]) ).
thf(11747,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk6
@ ( sk4
@ ( sk5
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ) )
!= ( sk9
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[11720]) ).
thf(1145,plain,
! [A: a] :
( ( sk2 @ ( sk7 @ A ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[645,24]) ).
thf(1146,plain,
( sk2
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1145:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ))]]) ).
thf(722,plain,
( ( sk8
@ ^ [A: a] : A )
| ( ( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) )
!= ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[376,344]) ).
thf(745,plain,
( ( sk8
@ ^ [A: a] : A )
| ( ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) )
!= ( sk10
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[722]) ).
thf(11332,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) ) ) )
!= ( sk3 @ ( A @ ( sk9 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[10860,63]) ).
thf(11343,plain,
( sk3
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[11332:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ D ) ) ) ) ) ) ))]]) ).
thf(75,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk7 @ B ) )
| ( ( sk3 @ ( sk6 @ A ) )
!= ( sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[30,24]) ).
thf(76,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk7 @ ( sk6 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( C )),bind(B,$thf( sk6 @ C ))]]) ).
thf(81,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk7 @ ( sk6 @ A ) ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(11010,plain,
! [A: a] :
( ( sk2 @ ( sk7 @ ( sk6 @ A ) ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10827,81]) ).
thf(11011,plain,
( sk2
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ A ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[11010:[bind(A,$thf( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) ))]]) ).
thf(10873,plain,
! [A: a > a] :
( ( sk2 @ ( sk7 @ ( sk10 @ A ) ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[70,10835]) ).
thf(10874,plain,
( sk2
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[10873:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) ) ))]]) ).
thf(1506,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk8
@ ^ [A: a] :
( sk6
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) )
!= ( sk8
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[344,446]) ).
thf(1525,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk6
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1506]) ).
thf(15224,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(rewrite,[status(thm)],[1525,570]) ).
thf(58,plain,
! [B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( sk8 @ A )
| ~ ( sk1 @ B )
| ( ( sk11 @ B @ A )
!= ( A @ B ) )
| ( B
!= ( sk10 @ A ) ) ),
inference(eqfactor_ordered,[status(thm)],[27]) ).
thf(59,plain,
! [A: a > a] :
( ( sk8 @ A )
| ( ( A @ ( sk10 @ A ) )
!= ( sk10 @ A ) )
| ~ ( sk1 @ ( sk10 @ A ) )
| ( ( sk11 @ ( sk10 @ A ) @ A )
!= ( A @ ( sk10 @ A ) ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(108,plain,
! [C: a,B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( sk8 @ A )
| ~ ( sk1 @ B )
| ( sk2 @ ( sk4 @ C ) )
| ( ( sk1 @ ( sk11 @ B @ A ) )
!= ( sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,8]) ).
thf(109,plain,
! [B: a > a,A: a] :
( ( ( sk10 @ B )
!= ( B @ A ) )
| ( sk8 @ B )
| ~ ( sk1 @ A )
| ( sk2 @ ( sk4 @ ( sk11 @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[108:[bind(A,$thf( E )),bind(B,$thf( D )),bind(C,$thf( sk11 @ D @ E ))]]) ).
thf(118,plain,
! [B: a > a,A: a] :
( ( ( sk10 @ B )
!= ( B @ A ) )
| ( sk8 @ B )
| ~ ( sk1 @ A )
| ( sk2 @ ( sk4 @ ( sk11 @ A @ B ) ) ) ),
inference(simp,[status(thm)],[109]) ).
thf(231,plain,
! [A: a] :
( ( sk2 @ ( sk4 @ ( sk5 @ A ) ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[219,42]) ).
thf(232,plain,
( sk2
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ))]]) ).
thf(663,plain,
! [A: a] :
( ( sk2 @ ( sk4 @ ( sk5 @ A ) ) )
| ( ( sk2
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[232,42]) ).
thf(664,plain,
( sk2
@ ( sk4
@ ( sk5
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[663:[bind(A,$thf( sk4 @ ( sk5 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ))]]) ).
thf(3121,plain,
! [A: a] :
( ( sk3 @ ( sk6 @ A ) )
| ( ( sk2
@ ( sk4
@ ( sk5
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[664,30]) ).
thf(3122,plain,
( sk3
@ ( sk6
@ ( sk4
@ ( sk5
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3121:[bind(A,$thf( sk4 @ ( sk5 @ ( sk4 @ ( sk5 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) ))]]) ).
thf(10348,plain,
( sk3
@ ( sk6
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[3122,570]) ).
thf(10850,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk3
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ A ) ) ) ) ) )
!= ( sk3
@ ( sk9
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[10833,487]) ).
thf(10857,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ A ) ) ) ) )
!= ( sk9
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[10850]) ).
thf(1674,plain,
! [A: a] :
( ( sk3 @ ( sk6 @ A ) )
| ( ( sk2
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[612,30]) ).
thf(1675,plain,
( sk3
@ ( sk6
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1674:[bind(A,$thf( sk4 @ ( sk5 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ))]]) ).
thf(516,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk3
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) )
!= ( sk3
@ ( sk9
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[225,487]) ).
thf(540,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) )
!= ( sk9
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[516]) ).
thf(2229,plain,
( ( ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) )
!= sk17 )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[655]) ).
thf(1121,plain,
! [A: a] :
( ( sk3 @ ( sk6 @ A ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[628,30]) ).
thf(1122,plain,
( sk3
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1121:[bind(A,$thf( sk7 @ ( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ))]]) ).
thf(2801,plain,
! [A: a] :
( ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
| ( ( sk3
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1122,46]) ).
thf(2802,plain,
( sk1
@ ( sk5
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2801:[bind(A,$thf( sk6 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ))]]) ).
thf(92,plain,
! [B: a,A: a] :
( ~ ( sk3 @ A )
| ( sk2 @ ( sk4 @ ( sk5 @ B ) ) )
| ( ( sk2 @ ( sk7 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[24,42]) ).
thf(93,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( sk2 @ ( sk4 @ ( sk5 @ ( sk7 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( C )),bind(B,$thf( sk7 @ C ))]]) ).
thf(98,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( sk2 @ ( sk4 @ ( sk5 @ ( sk7 @ A ) ) ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(4677,plain,
! [A: a] :
( ( sk3 @ ( sk6 @ A ) )
| ( ( sk2
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4652,30]) ).
thf(4678,plain,
( sk3
@ ( sk6
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4677:[bind(A,$thf( sk7 @ ( sk6 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ))]]) ).
thf(4694,plain,
( sk3
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ),
inference(rewrite,[status(thm)],[4678,1063]) ).
thf(395,plain,
! [A: a] :
( ( sk1 @ ( sk5 @ ( sk4 @ A ) ) )
| ( ( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[221,43]) ).
thf(396,plain,
( sk1
@ ( sk5
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[395:[bind(A,$thf( sk5 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ))]]) ).
thf(1247,plain,
! [A: a] :
( ( sk1 @ ( sk5 @ ( sk4 @ A ) ) )
| ( ( sk1
@ ( sk5
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[396,43]) ).
thf(1248,plain,
( sk1
@ ( sk5
@ ( sk4
@ ( sk5
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1247:[bind(A,$thf( sk5 @ ( sk4 @ ( sk5 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ))]]) ).
thf(8506,plain,
( sk1
@ ( sk5
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[1248,570]) ).
thf(8584,plain,
! [A: a] :
( ( sk2 @ ( sk4 @ A ) )
| ( ( sk1
@ ( sk5
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8506,8]) ).
thf(8585,plain,
( sk2
@ ( sk4
@ ( sk5
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[8584:[bind(A,$thf( sk5 @ ( sk4 @ ( sk5 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ))]]) ).
thf(8661,plain,
( sk2
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[8585,570]) ).
thf(1324,plain,
! [A: a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
| ( ( sk3
@ ( sk6
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[779,46]) ).
thf(1325,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( sk1
@ ( sk5
@ ( sk7
@ ( sk6
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1324:[bind(A,$thf( sk6 @ ( sk4 @ ( sk9 @ ^ [B: a] : B ) ) ))]]) ).
thf(1335,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk3
@ ( sk6
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) )
!= ( sk3
@ ( sk9
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[779,487]) ).
thf(1344,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk6
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) )
!= ( sk9
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[1335]) ).
thf(754,plain,
( ( sk1
@ ( sk9
@ ^ [A: a] : A ) )
| ( ( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) )
!= ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[221,492]) ).
thf(769,plain,
( ( sk1
@ ( sk9
@ ^ [A: a] : A ) )
| ( ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) )
!= ( sk10
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[754]) ).
thf(150,plain,
! [C: a,B: a > a,A: a] :
( ~ ( sk3 @ A )
| ( ( sk10 @ B )
!= ( B @ C ) )
| ( sk8 @ B )
| ( sk1 @ ( sk11 @ C @ B ) )
| ( ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
!= ( sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[46,20]) ).
thf(151,plain,
! [B: a,A: a > a] :
( ~ ( sk3 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk5 @ ( sk7 @ B ) ) ) )
| ( sk8 @ A )
| ( sk1 @ ( sk11 @ ( sk5 @ ( sk7 @ B ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[150:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( sk5 @ ( sk7 @ E ) ))]]) ).
thf(155,plain,
! [B: a,A: a > a] :
( ~ ( sk3 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk5 @ ( sk7 @ B ) ) ) )
| ( sk8 @ A )
| ( sk1 @ ( sk11 @ ( sk5 @ ( sk7 @ B ) ) @ A ) ) ),
inference(simp,[status(thm)],[151]) ).
thf(3023,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [D: a] : D ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,2974]) ).
thf(3024,plain,
( ( sk3
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [C: a] : C ) ) ) ) ) )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ),
inference(pattern_uni,[status(thm)],[3023:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk9 @ ^ [D: a] : D ) ) ) ) ))]]) ).
thf(12962,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk3
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [C: a] : C ) ) ) ) ) )
!= ( sk3
@ ( sk9
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[3024,487]) ).
thf(13010,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [C: a] : C ) ) ) ) )
!= ( sk9
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[12962]) ).
thf(1186,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( A != sk12 )
| ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( ( sk6 @ ( sk7 @ A ) )
!= ( sk6 @ ( sk4 @ sk12 ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,683]) ).
thf(1213,plain,
( ~ ( sk3 @ sk12 )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk7 @ sk12 )
!= ( sk4 @ sk12 ) ) ),
inference(simp,[status(thm)],[1186]) ).
thf(73,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ( sk3 @ ( sk6 @ B ) )
| ( ( sk2 @ ( sk4 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8,30]) ).
thf(74,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk3 @ ( sk6 @ ( sk4 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[73:[bind(A,$thf( C )),bind(B,$thf( sk4 @ C ))]]) ).
thf(80,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk3 @ ( sk6 @ ( sk4 @ A ) ) ) ),
inference(simp,[status(thm)],[74]) ).
thf(2796,plain,
! [A: a] :
( ( sk2 @ ( sk7 @ A ) )
| ( ( sk3
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1122,24]) ).
thf(2797,plain,
( sk2
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2796:[bind(A,$thf( sk6 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ))]]) ).
thf(1033,plain,
! [A: a] :
( ( ( sk6 @ ( sk7 @ A ) )
= A )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[225,35]) ).
thf(1034,plain,
( ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) )
= ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1033:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ))]]) ).
thf(723,plain,
( ( ( ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) )
!= ( ^ [A: a] : A ) )
| ( ( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) )
!= ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[376,512]) ).
thf(749,plain,
( ( ( ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) )
!= ( ^ [A: a] : A ) )
| ( ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) )
!= ( sk10
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[723]) ).
thf(775,plain,
! [A: a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( sk1 @ ( sk5 @ A ) )
| ( ( sk2
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[485,23]) ).
thf(776,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( sk1
@ ( sk5
@ ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[775:[bind(A,$thf( sk4 @ ( sk9 @ ^ [B: a] : B ) ))]]) ).
thf(702,plain,
( ( ( ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) )
!= ( ^ [A: a] : A ) )
| ( ( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) )
!= ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[221,502]) ).
thf(712,plain,
( ( ( ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) )
!= ( ^ [A: a] : A ) )
| ( ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) )
!= ( sk10
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[702]) ).
thf(12270,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,11020]) ).
thf(12271,plain,
( sk3
@ ( sk10
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[12270:[bind(A,$thf( ^ [B: a] : ( sk6 @ ( sk7 @ ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) ) ) ) ))]]) ).
thf(86,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ ( sk4 @ ( sk5 @ B ) ) )
| ( ( sk2 @ ( sk4 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8,42]) ).
thf(87,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ ( sk4 @ ( sk5 @ ( sk4 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( C )),bind(B,$thf( sk4 @ C ))]]) ).
thf(95,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ ( sk4 @ ( sk5 @ ( sk4 @ A ) ) ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(10845,plain,
! [A: a] :
( ( sk2 @ ( sk4 @ ( sk5 @ ( sk7 @ A ) ) ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10833,98]) ).
thf(10846,plain,
( sk2
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ A ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[10845:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ B ) ) ) ) ))]]) ).
thf(148,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A )
| ( sk1 @ ( sk5 @ ( sk7 @ B ) ) )
| ( ( sk3 @ ( sk6 @ A ) )
!= ( sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[30,46]) ).
thf(149,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk1 @ ( sk5 @ ( sk7 @ ( sk6 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[148:[bind(A,$thf( C )),bind(B,$thf( sk6 @ C ))]]) ).
thf(154,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk1 @ ( sk5 @ ( sk7 @ ( sk6 @ A ) ) ) ) ),
inference(simp,[status(thm)],[149]) ).
thf(11355,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) ) ) )
!= ( sk8
@ ^ [A: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[344,10884]) ).
thf(11369,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[11355]) ).
thf(3913,plain,
! [A: a] :
( ( sk2 @ ( sk7 @ ( sk6 @ A ) ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1146,81]) ).
thf(3914,plain,
( sk2
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3913:[bind(A,$thf( sk7 @ ( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ))]]) ).
thf(661,plain,
! [A: a] :
( ( sk3 @ ( sk6 @ A ) )
| ( ( sk2
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[232,30]) ).
thf(662,plain,
( sk3
@ ( sk6
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[661:[bind(A,$thf( sk4 @ ( sk5 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ))]]) ).
thf(1926,plain,
! [A: a] :
( ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
| ( ( sk3
@ ( sk6
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[662,46]) ).
thf(1927,plain,
( sk1
@ ( sk5
@ ( sk7
@ ( sk6
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1926:[bind(A,$thf( sk6 @ ( sk4 @ ( sk5 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ))]]) ).
thf(9654,plain,
( sk1
@ ( sk5
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[1927,570]) ).
thf(2869,plain,
! [A: a] :
( ( sk3 @ ( sk6 @ A ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1146,30]) ).
thf(2870,plain,
( sk3
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2869:[bind(A,$thf( sk7 @ ( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ))]]) ).
thf(2918,plain,
! [A: a] :
( ( sk2 @ ( sk7 @ A ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] :
( sk10
@ ^ [F: a] : ( sk6 @ ( sk4 @ F ) ) ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1493,24]) ).
thf(2919,plain,
( sk2
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2918:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk10 @ ^ [F: a] : ( sk6 @ ( sk4 @ F ) ) ) ) ) ) ))]]) ).
thf(2852,plain,
! [A: a] :
( ( sk2 @ ( sk4 @ ( sk5 @ A ) ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1146,42]) ).
thf(2853,plain,
( sk2
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2852:[bind(A,$thf( sk7 @ ( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ))]]) ).
thf(125,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ( sk1 @ ( sk5 @ ( sk4 @ B ) ) )
| ( ( sk1 @ ( sk5 @ ( sk4 @ A ) ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[43,43]) ).
thf(126,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk1 @ ( sk5 @ ( sk4 @ ( sk5 @ ( sk4 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[125:[bind(A,$thf( D )),bind(B,$thf( sk5 @ ( sk4 @ D ) ))]]) ).
thf(139,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk1 @ ( sk5 @ ( sk4 @ ( sk5 @ ( sk4 @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(54,plain,
! [C: a > a,B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( ( sk11 @ B @ A )
!= B )
| ~ ( sk1 @ B )
| ( sk1 @ ( sk9 @ C ) )
| ( ( sk8 @ A )
!= ( sk8 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27,25]) ).
thf(55,plain,
! [B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( ( sk11 @ B @ A )
!= B )
| ~ ( sk1 @ B )
| ( sk1 @ ( sk9 @ A ) ) ),
inference(pattern_uni,[status(thm)],[54:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(112,plain,
! [C: a,B: a > a,A: a > a] :
( ~ ( sk8 @ A )
| ( ( sk10 @ B )
!= ( B @ C ) )
| ( sk8 @ B )
| ( sk1 @ ( sk11 @ C @ B ) )
| ( ( sk1 @ ( sk9 @ A ) )
!= ( sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25,20]) ).
thf(113,plain,
! [B: a > a,A: a > a] :
( ~ ( sk8 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk9 @ B ) ) )
| ( sk8 @ A )
| ( sk1 @ ( sk11 @ ( sk9 @ B ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[112:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( sk9 @ D ))]]) ).
thf(114,plain,
! [B: a > a,A: a > a] :
( ~ ( sk8 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk9 @ B ) ) )
| ( sk8 @ A )
| ( sk1 @ ( sk11 @ ( sk9 @ B ) @ A ) ) ),
inference(simp,[status(thm)],[113]) ).
thf(10937,plain,
( ( ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ A ) ) ) ) )
!= sk27 )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[10882]) ).
thf(6290,plain,
( ( ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk6
@ ( sk4
@ ( sk9
@ ^ [C: a] : C ) ) ) ) )
!= sk24 )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[6283]) ).
thf(483,plain,
( ( sk8
@ ^ [A: a] : A )
| ( ( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) )
!= ( sk1
@ ( sk10
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[221,344]) ).
thf(510,plain,
( ( sk8
@ ^ [A: a] : A )
| ( ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) )
!= ( sk10
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[483]) ).
thf(50,plain,
! [C: a > a,B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( ( sk11 @ B @ A )
!= B )
| ~ ( sk1 @ B )
| ~ ( sk3 @ ( C @ ( sk9 @ C ) ) )
| ( ( sk8 @ A )
!= ( sk8 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27,18]) ).
thf(51,plain,
! [B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( ( sk11 @ B @ A )
!= B )
| ~ ( sk1 @ B )
| ~ ( sk3 @ ( A @ ( sk9 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(1147,plain,
! [A: a] :
( ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[645,46]) ).
thf(1148,plain,
( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1147:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ))]]) ).
thf(119,plain,
! [C: a,B: a > a,A: a] :
( ~ ( sk1 @ A )
| ( ( sk10 @ B )
!= ( B @ C ) )
| ( sk8 @ B )
| ( sk1 @ ( sk11 @ C @ B ) )
| ( ( sk1 @ ( sk5 @ ( sk4 @ A ) ) )
!= ( sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[43,20]) ).
thf(120,plain,
! [B: a,A: a > a] :
( ~ ( sk1 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk5 @ ( sk4 @ B ) ) ) )
| ( sk8 @ A )
| ( sk1 @ ( sk11 @ ( sk5 @ ( sk4 @ B ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[119:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( sk5 @ ( sk4 @ E ) ))]]) ).
thf(136,plain,
! [B: a,A: a > a] :
( ~ ( sk1 @ B )
| ( ( sk10 @ A )
!= ( A @ ( sk5 @ ( sk4 @ B ) ) ) )
| ( sk8 @ A )
| ( sk1 @ ( sk11 @ ( sk5 @ ( sk4 @ B ) ) @ A ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(634,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk3
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) )
!= ( sk3
@ ( sk9
@ ^ [A: a] : A ) ) ) ),
inference(paramod_ordered,[status(thm)],[385,487]) ).
thf(635,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) )
!= ( sk9
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[634]) ).
thf(84,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A )
| ( sk1 @ ( sk5 @ B ) )
| ( ( sk2 @ ( sk4 @ ( sk5 @ A ) ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[42,23]) ).
thf(85,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk1 @ ( sk5 @ ( sk4 @ ( sk5 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( D )),bind(B,$thf( sk4 @ ( sk5 @ D ) ))]]) ).
thf(94,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk1 @ ( sk5 @ ( sk4 @ ( sk5 @ A ) ) ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(1953,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( A != sk15 )
| ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( ( sk6 @ ( sk7 @ A ) )
!= ( sk6
@ ( sk4
@ ( sk9
@ ^ [B: a] : B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,1632]) ).
thf(1977,plain,
( ~ ( sk3 @ sk15 )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( ( sk7 @ sk15 )
!= ( sk4
@ ( sk9
@ ^ [A: a] : A ) ) ) ),
inference(simp,[status(thm)],[1953]) ).
thf(11357,plain,
! [A: a > a] :
( ( sk2 @ ( sk7 @ ( sk10 @ A ) ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ D ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[70,10884]) ).
thf(11358,plain,
( sk2
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ C ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[11357:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ ( sk5 @ ( sk4 @ D ) ) ) ) ) ) ))]]) ).
thf(67,plain,
! [B: a > a,A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( sk1 @ ( sk9 @ B ) )
| ( ( sk8 @ A )
!= ( sk8 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[31,25]) ).
thf(68,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( sk1 @ ( sk9 @ A ) ) ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(493,plain,
! [A: a > a] :
( ~ ( sk8 @ A )
| ( sk8
@ ^ [B: a] : B )
| ( ( sk1 @ ( sk9 @ A ) )
!= ( sk1
@ ( sk10
@ ^ [B: a] : B ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,344]) ).
thf(501,plain,
! [A: a > a] :
( ( sk8
@ ^ [B: a] : B )
| ~ ( sk8 @ A )
| ( ( sk9 @ A )
!= ( sk10
@ ^ [B: a] : B ) ) ),
inference(simp,[status(thm)],[493]) ).
thf(110,plain,
! [C: a > a,B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ~ ( sk1 @ B )
| ( sk1 @ ( sk11 @ B @ A ) )
| ( sk1 @ ( sk9 @ C ) )
| ( ( sk8 @ A )
!= ( sk8 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,25]) ).
thf(111,plain,
! [B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ~ ( sk1 @ B )
| ( sk1 @ ( sk11 @ B @ A ) )
| ( sk1 @ ( sk9 @ A ) ) ),
inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(16069,plain,
$false,
inference(e,[status(thm)],[645,138,6283,628,7072,2976,115,683,379,655,10805,533,3044,500,11020,11320,1608,385,5713,698,10827,3414,5178,1063,11335,42,782,24,10854,8122,37,25,570,3653,344,20,46,2635,152,3258,29,2950,492,12362,1632,376,5333,211,485,1677,61,3243,116,11367,14761,221,10833,4065,5695,2922,512,3995,798,60,117,957,746,70,630,137,33,4947,97,1888,14338,4979,742,10887,156,725,10882,2638,7142,2840,2692,1498,1493,225,537,1155,12600,96,701,10834,779,105,508,1135,10840,11747,1146,745,11343,11011,14286,22,10874,1124,27,15224,59,118,71,787,10348,49,10857,1675,540,219,2229,81,2802,208,98,1122,4694,8661,1325,4652,1344,769,155,2974,13010,1213,3,80,35,135,2797,1034,374,487,749,776,712,63,18,10835,12271,95,502,10846,31,7348,154,2711,10860,3024,10884,43,11369,3914,9654,612,2870,4006,2919,1157,1321,2853,139,23,55,114,8,5304,2648,82,10937,8506,6290,510,30,51,1148,136,635,94,1977,11358,68,1621,501,111,83,215,639,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEV106^5 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:13:55 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.93/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.97 % [INFO] Parsing done (109ms).
% 1.31/0.98 % [INFO] Running in sequential loop mode.
% 1.64/1.20 % [INFO] eprover registered as external prover.
% 1.64/1.20 % [INFO] Scanning for conjecture ...
% 1.94/1.27 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.01/1.30 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.01/1.30 % [INFO] Problem is higher-order (TPTP THF).
% 2.01/1.30 % [INFO] Type checking passed.
% 2.01/1.30 % [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 ...
% 80.41/18.19 % External prover 'e' found a proof!
% 80.41/18.19 % [INFO] Killing All external provers ...
% 80.41/18.20 % Time passed: 17668ms (effective reasoning time: 17214ms)
% 80.41/18.20 % 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)>
% 80.41/18.20 % Axioms used in derivation (0):
% 80.41/18.20 % No. of inferences in proof: 470
% 80.41/18.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 17668 ms resp. 17214 ms w/o parsing
% 81.13/18.47 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 81.58/18.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------