TSTP Solution File: SEV108^5 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV108^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n026.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 67.56s 17.77s
% Output : Refutation 67.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 1
% Syntax : Number of formulae : 422 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 2157 ( 688 equ; 0 cnn)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 4933 ( 636 ~;1335 |; 88 &;2866 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 8 con; 0-2 aty)
% Number of variables : 370 ( 0 ^ 352 !; 18 ?; 370 :)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_type,type,
sk1: $i > $i > $o ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(1,conjecture,
! [A: $i > $i > $o,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ! [H: $i,I: $i] :
( ( A @ H @ I )
=> ( A @ I @ H ) )
& ( B != C )
& ( B != D )
& ( B != E )
& ( B != F )
& ( B != G )
& ( C != D )
& ( C != E )
& ( C != F )
& ( C != G )
& ( D != E )
& ( D != F )
& ( D != G )
& ( E != F )
& ( E != G )
& ( F != G ) )
=> ? [H: $i,I: $i,J: $i] :
( ( H != I )
& ( H != J )
& ( I != J )
& ( ( ( A @ H @ I )
& ( A @ H @ J )
& ( A @ I @ J ) )
| ( ~ ( A @ H @ I )
& ~ ( A @ H @ J )
& ~ ( A @ I @ J ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSIX_THEOREM_pme) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ! [H: $i,I: $i] :
( ( A @ H @ I )
=> ( A @ I @ H ) )
& ( B != C )
& ( B != D )
& ( B != E )
& ( B != F )
& ( B != G )
& ( C != D )
& ( C != E )
& ( C != F )
& ( C != G )
& ( D != E )
& ( D != F )
& ( D != G )
& ( E != F )
& ( E != G )
& ( F != G ) )
=> ? [H: $i,I: $i,J: $i] :
( ( H != I )
& ( H != J )
& ( I != J )
& ( ( ( A @ H @ I )
& ( A @ H @ J )
& ( A @ I @ J ) )
| ( ~ ( A @ H @ I )
& ~ ( A @ H @ J )
& ~ ( A @ I @ J ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ! [H: $i,I: $i] :
( ( A @ H @ I )
=> ( A @ I @ H ) )
& ( B != C )
& ( B != D )
& ( B != E )
& ( B != F )
& ( B != G )
& ( C != D )
& ( C != E )
& ( C != F )
& ( C != G )
& ( D != E )
& ( D != F )
& ( D != G )
& ( E != F )
& ( E != G )
& ( F != G ) )
=> ? [H: $i,I: $i,J: $i] :
( ( H != I )
& ( H != J )
& ( I != J )
& ( ( ( A @ H @ I )
& ( A @ H @ J )
& ( A @ I @ J ) )
| ( ~ ( A @ H @ I )
& ~ ( A @ H @ J )
& ~ ( A @ I @ J ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ! [A: $i > $i > $o] :
( ( ! [B: $i,C: $i] :
( ( A @ B @ C )
=> ( A @ C @ B ) )
& ? [B: $i,C: $i] :
( ( B != C )
& ? [D: $i] :
( ( B != D )
& ? [E: $i] :
( ( B != E )
& ? [F: $i] :
( ( B != F )
& ? [G: $i] :
( ( B != G )
& ( C != D )
& ( C != E )
& ( C != F )
& ( C != G )
& ( D != E )
& ( D != F )
& ( D != G )
& ( E != F )
& ( E != G )
& ( F != G ) ) ) ) ) ) )
=> ? [B: $i,C: $i] :
( ( B != C )
& ? [D: $i] :
( ( B != D )
& ( C != D )
& ( ( ( A @ B @ C )
& ( A @ B @ D )
& ( A @ C @ D ) )
| ( ~ ( A @ B @ C )
& ~ ( A @ B @ D )
& ~ ( A @ C @ D ) ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C ) ),
inference(cnf,[status(esa)],[4]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C ) ),
inference(simp,[status(thm)],[25]) ).
thf(20,plain,
sk2 != sk7,
inference(cnf,[status(esa)],[4]) ).
thf(27,plain,
sk7 != sk2,
inference(lifteq,[status(thm)],[20]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( B != sk2 )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[26,27]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( sk7 = B )
| ( A = B )
| ( sk1 @ sk7 @ A )
| ( sk1 @ sk7 @ B )
| ( sk1 @ A @ B )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( sk7 ))]]) ).
thf(133,plain,
! [A: $i] :
( ( sk7 = A )
| ( sk2 = A )
| ( sk1 @ sk7 @ sk2 )
| ( sk1 @ sk7 @ A )
| ( sk1 @ sk2 @ A ) ),
inference(simp,[status(thm)],[79]) ).
thf(7,plain,
sk5 != sk7,
inference(cnf,[status(esa)],[4]) ).
thf(35,plain,
sk7 != sk5,
inference(lifteq,[status(thm)],[7]) ).
thf(9316,plain,
! [A: $i] :
( ( sk2 = A )
| ( sk1 @ sk7 @ sk2 )
| ( sk1 @ sk7 @ A )
| ( sk1 @ sk2 @ A )
| ( A != sk5 )
| ( sk7 != sk7 ) ),
inference(paramod_ordered,[status(thm)],[133,35]) ).
thf(9317,plain,
! [A: $i] :
( ( sk2 = A )
| ( sk1 @ sk7 @ sk2 )
| ( sk1 @ sk7 @ A )
| ( sk1 @ sk2 @ A )
| ( A != sk5 ) ),
inference(pattern_uni,[status(thm)],[9316:[]]) ).
thf(9515,plain,
( ( sk5 = sk2 )
| ( sk1 @ sk7 @ sk2 )
| ( sk1 @ sk7 @ sk5 )
| ( sk1 @ sk2 @ sk5 ) ),
inference(simp,[status(thm)],[9317]) ).
thf(15,plain,
sk2 != sk5,
inference(cnf,[status(esa)],[4]) ).
thf(41,plain,
sk5 != sk2,
inference(lifteq,[status(thm)],[15]) ).
thf(76648,plain,
( ( sk1 @ sk7 @ sk2 )
| ( sk1 @ sk7 @ sk5 )
| ( sk1 @ sk2 @ sk5 ) ),
inference(simplifyReflect,[status(thm)],[9515,41]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ( sk1 @ B @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(76826,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk7 @ sk2 )
| ( sk1 @ sk2 @ sk5 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[76648,22]) ).
thf(76827,plain,
( ( sk1 @ sk7 @ sk2 )
| ( sk1 @ sk2 @ sk5 )
| ( sk1 @ sk5 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[76826:[bind(A,$thf( sk7 )),bind(B,$thf( sk5 ))]]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( B != sk2 )
| ( C != sk7 ) ),
inference(paramod_ordered,[status(thm)],[26,27]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( A = sk7 )
| ( sk1 @ A @ B )
| ( sk1 @ A @ sk7 )
| ( sk1 @ B @ sk7 )
| ( B != sk2 ) ),
inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk7 ))]]) ).
thf(138,plain,
! [A: $i] :
( ( A = sk2 )
| ( A = sk7 )
| ( sk1 @ A @ sk2 )
| ( sk1 @ A @ sk7 )
| ( sk1 @ sk2 @ sk7 ) ),
inference(simp,[status(thm)],[89]) ).
thf(21,plain,
sk4 != sk5,
inference(cnf,[status(esa)],[4]) ).
thf(29,plain,
sk5 != sk4,
inference(lifteq,[status(thm)],[21]) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( B != sk4 )
| ( C != sk5 ) ),
inference(paramod_ordered,[status(thm)],[26,29]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( A = sk5 )
| ( sk1 @ A @ B )
| ( sk1 @ A @ sk5 )
| ( sk1 @ B @ sk5 )
| ( B != sk4 ) ),
inference(pattern_uni,[status(thm)],[64:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk5 ))]]) ).
thf(126,plain,
! [A: $i] :
( ( A = sk4 )
| ( A = sk5 )
| ( sk1 @ A @ sk4 )
| ( sk1 @ A @ sk5 )
| ( sk1 @ sk4 @ sk5 ) ),
inference(simp,[status(thm)],[65]) ).
thf(324,plain,
! [A: $i] :
( ( A = sk4 )
| ( sk1 @ A @ sk4 )
| ( sk1 @ A @ sk5 )
| ( sk1 @ sk4 @ sk5 )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[126,35]) ).
thf(325,plain,
( ( sk7 = sk4 )
| ( sk1 @ sk7 @ sk4 )
| ( sk1 @ sk7 @ sk5 )
| ( sk1 @ sk4 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[324:[bind(A,$thf( sk7 ))]]) ).
thf(13,plain,
sk4 != sk7,
inference(cnf,[status(esa)],[4]) ).
thf(31,plain,
sk7 != sk4,
inference(lifteq,[status(thm)],[13]) ).
thf(469,plain,
( ( sk1 @ sk7 @ sk4 )
| ( sk1 @ sk7 @ sk5 )
| ( sk1 @ sk4 @ sk5 ) ),
inference(simplifyReflect,[status(thm)],[325,31]) ).
thf(476,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk7 @ sk4 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[469,22]) ).
thf(477,plain,
( ( sk1 @ sk7 @ sk4 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk5 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[476:[bind(A,$thf( sk7 )),bind(B,$thf( sk5 ))]]) ).
thf(1028,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk5 @ sk7 )
| ( ( sk1 @ sk7 @ sk4 )
!= ( sk1 @ sk5 @ sk7 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[477]) ).
thf(1031,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk5 @ sk7 )
| ( ( sk1 @ sk7 @ sk4 )
!= ( sk1 @ sk5 @ sk7 ) ) ),
inference(simp,[status(thm)],[1028]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ( B = C )
| ~ ( sk1 @ A @ B )
| ~ ( sk1 @ A @ C )
| ~ ( sk1 @ B @ C ) ),
inference(cnf,[status(esa)],[4]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ( B = C )
| ~ ( sk1 @ A @ B )
| ~ ( sk1 @ A @ C )
| ~ ( sk1 @ B @ C ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ( B = C )
| ~ ( sk1 @ A @ B )
| ~ ( sk1 @ A @ C )
| ~ ( sk1 @ B @ C ) ),
inference(simp,[status(thm)],[32]) ).
thf(519,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = C )
| ~ ( sk1 @ A @ B )
| ~ ( sk1 @ A @ C )
| ~ ( sk1 @ B @ C )
| ( B != sk4 )
| ( A != sk5 ) ),
inference(paramod_ordered,[status(thm)],[33,29]) ).
thf(520,plain,
! [B: $i,A: $i] :
( ( sk5 = B )
| ( A = B )
| ~ ( sk1 @ sk5 @ A )
| ~ ( sk1 @ sk5 @ B )
| ~ ( sk1 @ A @ B )
| ( A != sk4 ) ),
inference(pattern_uni,[status(thm)],[519:[bind(A,$thf( sk5 ))]]) ).
thf(829,plain,
! [A: $i] :
( ( sk5 = A )
| ( sk4 = A )
| ~ ( sk1 @ sk5 @ sk4 )
| ~ ( sk1 @ sk5 @ A )
| ~ ( sk1 @ sk4 @ A ) ),
inference(simp,[status(thm)],[520]) ).
thf(1151,plain,
! [A: $i] :
( ( sk4 = A )
| ~ ( sk1 @ sk5 @ sk4 )
| ~ ( sk1 @ sk5 @ A )
| ~ ( sk1 @ sk4 @ A )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[829,35]) ).
thf(1152,plain,
( ( sk7 = sk4 )
| ~ ( sk1 @ sk5 @ sk4 )
| ~ ( sk1 @ sk5 @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[1151:[bind(A,$thf( sk7 ))]]) ).
thf(6054,plain,
( ~ ( sk1 @ sk5 @ sk4 )
| ~ ( sk1 @ sk5 @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 ) ),
inference(simplifyReflect,[status(thm)],[1152,31]) ).
thf(6208,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ sk5 @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ B @ A )
!= ( sk1 @ sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[22,6054]) ).
thf(6209,plain,
( ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk5 @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[6208:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(7747,plain,
( ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk4 @ sk7 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6209]) ).
thf(7798,plain,
( ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk4 @ sk7 ) ) ),
inference(simp,[status(thm)],[7747]) ).
thf(6,plain,
sk3 != sk5,
inference(cnf,[status(esa)],[4]) ).
thf(28,plain,
sk5 != sk3,
inference(lifteq,[status(thm)],[6]) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( C != sk3 )
| ( A != sk5 ) ),
inference(paramod_ordered,[status(thm)],[26,28]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( sk5 = A )
| ( A = B )
| ( sk1 @ sk5 @ A )
| ( sk1 @ sk5 @ B )
| ( sk1 @ A @ B )
| ( B != sk3 ) ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$thf( sk5 ))]]) ).
thf(129,plain,
! [A: $i] :
( ( sk5 = A )
| ( A = sk3 )
| ( sk1 @ sk5 @ A )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ A @ sk3 ) ),
inference(simp,[status(thm)],[71]) ).
thf(3175,plain,
! [A: $i] :
( ( A = sk3 )
| ( sk1 @ sk5 @ A )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ A @ sk3 )
| ( A != sk2 )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[129,41]) ).
thf(3176,plain,
! [A: $i] :
( ( A = sk3 )
| ( sk1 @ sk5 @ A )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ A @ sk3 )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[3175:[]]) ).
thf(3404,plain,
( ( sk3 = sk2 )
| ( sk1 @ sk5 @ sk2 )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk2 @ sk3 ) ),
inference(simp,[status(thm)],[3176]) ).
thf(12,plain,
sk2 != sk3,
inference(cnf,[status(esa)],[4]) ).
thf(34,plain,
sk3 != sk2,
inference(lifteq,[status(thm)],[12]) ).
thf(28981,plain,
( ( sk1 @ sk5 @ sk2 )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk2 @ sk3 ) ),
inference(simplifyReflect,[status(thm)],[3404,34]) ).
thf(7395,plain,
! [A: $i] :
( ( sk4 = A )
| ~ ( sk1 @ sk5 @ sk4 )
| ~ ( sk1 @ sk5 @ A )
| ~ ( sk1 @ sk4 @ A )
| ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ A @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[829,6209]) ).
thf(7396,plain,
! [A: $i] :
( ( sk4 = A )
| ~ ( sk1 @ sk5 @ sk4 )
| ~ ( sk1 @ sk5 @ A )
| ~ ( sk1 @ sk4 @ A )
| ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ A @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[7395:[]]) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( B != sk3 )
| ( C != sk5 ) ),
inference(paramod_ordered,[status(thm)],[26,28]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( A = sk5 )
| ( sk1 @ A @ B )
| ( sk1 @ A @ sk5 )
| ( sk1 @ B @ sk5 )
| ( B != sk3 ) ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk5 ))]]) ).
thf(132,plain,
! [A: $i] :
( ( A = sk3 )
| ( A = sk5 )
| ( sk1 @ A @ sk3 )
| ( sk1 @ A @ sk5 )
| ( sk1 @ sk3 @ sk5 ) ),
inference(simp,[status(thm)],[77]) ).
thf(11,plain,
sk5 != sk6,
inference(cnf,[status(esa)],[4]) ).
thf(38,plain,
sk6 != sk5,
inference(lifteq,[status(thm)],[11]) ).
thf(6942,plain,
! [A: $i] :
( ( A = sk3 )
| ( sk1 @ A @ sk3 )
| ( sk1 @ A @ sk5 )
| ( sk1 @ sk3 @ sk5 )
| ( A != sk6 ) ),
inference(paramod_ordered,[status(thm)],[132,38]) ).
thf(6943,plain,
( ( sk6 = sk3 )
| ( sk1 @ sk6 @ sk3 )
| ( sk1 @ sk6 @ sk5 )
| ( sk1 @ sk3 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[6942:[bind(A,$thf( sk6 ))]]) ).
thf(9,plain,
sk3 != sk6,
inference(cnf,[status(esa)],[4]) ).
thf(30,plain,
sk6 != sk3,
inference(lifteq,[status(thm)],[9]) ).
thf(58460,plain,
( ( sk1 @ sk6 @ sk3 )
| ( sk1 @ sk6 @ sk5 )
| ( sk1 @ sk3 @ sk5 ) ),
inference(simplifyReflect,[status(thm)],[6943,30]) ).
thf(58614,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk6 @ sk3 )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[58460,22]) ).
thf(58615,plain,
( ( sk1 @ sk6 @ sk3 )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk5 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[58614:[bind(A,$thf( sk6 )),bind(B,$thf( sk5 ))]]) ).
thf(448,plain,
! [A: $i] :
( ( A = sk4 )
| ( sk1 @ A @ sk4 )
| ( sk1 @ A @ sk5 )
| ( sk1 @ sk4 @ sk5 )
| ( A != sk2 )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[126,41]) ).
thf(449,plain,
! [A: $i] :
( ( A = sk4 )
| ( sk1 @ A @ sk4 )
| ( sk1 @ A @ sk5 )
| ( sk1 @ sk4 @ sk5 )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[448:[]]) ).
thf(462,plain,
( ( sk4 = sk2 )
| ( sk1 @ sk2 @ sk4 )
| ( sk1 @ sk2 @ sk5 )
| ( sk1 @ sk4 @ sk5 ) ),
inference(simp,[status(thm)],[449]) ).
thf(5,plain,
sk2 != sk4,
inference(cnf,[status(esa)],[4]) ).
thf(23,plain,
sk4 != sk2,
inference(lifteq,[status(thm)],[5]) ).
thf(3817,plain,
( ( sk1 @ sk2 @ sk4 )
| ( sk1 @ sk2 @ sk5 )
| ( sk1 @ sk4 @ sk5 ) ),
inference(simplifyReflect,[status(thm)],[462,23]) ).
thf(3908,plain,
( ( sk1 @ sk2 @ sk4 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk4 @ sk5 )
!= ( sk1 @ sk2 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3817]) ).
thf(3910,plain,
( ( sk1 @ sk2 @ sk4 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk4 @ sk5 )
!= ( sk1 @ sk2 @ sk5 ) ) ),
inference(simp,[status(thm)],[3908]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( B != sk3 )
| ( A != sk5 ) ),
inference(paramod_ordered,[status(thm)],[26,28]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( sk5 = B )
| ( A = B )
| ( sk1 @ sk5 @ A )
| ( sk1 @ sk5 @ B )
| ( sk1 @ A @ B )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[66:[bind(A,$thf( sk5 ))]]) ).
thf(127,plain,
! [A: $i] :
( ( sk5 = A )
| ( sk3 = A )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk5 @ A )
| ( sk1 @ sk3 @ A ) ),
inference(simp,[status(thm)],[67]) ).
thf(1605,plain,
! [A: $i] :
( ( sk3 = A )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk5 @ A )
| ( sk1 @ sk3 @ A )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[127,35]) ).
thf(1606,plain,
( ( sk7 = sk3 )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk5 @ sk7 )
| ( sk1 @ sk3 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[1605:[bind(A,$thf( sk7 ))]]) ).
thf(10,plain,
sk3 != sk7,
inference(cnf,[status(esa)],[4]) ).
thf(24,plain,
sk7 != sk3,
inference(lifteq,[status(thm)],[10]) ).
thf(4902,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk5 @ sk7 )
| ( sk1 @ sk3 @ sk7 ) ),
inference(simplifyReflect,[status(thm)],[1606,24]) ).
thf(4959,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk7 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4902,22]) ).
thf(4960,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk7 )
| ( sk1 @ sk7 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[4959:[bind(A,$thf( sk5 )),bind(B,$thf( sk7 ))]]) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( A != sk3 )
| ( C != sk6 ) ),
inference(paramod_ordered,[status(thm)],[26,30]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B = sk6 )
| ( sk1 @ A @ B )
| ( sk1 @ A @ sk6 )
| ( sk1 @ B @ sk6 )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[96:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk6 ))]]) ).
thf(142,plain,
! [A: $i] :
( ( sk3 = A )
| ( A = sk6 )
| ( sk1 @ sk3 @ A )
| ( sk1 @ sk3 @ sk6 )
| ( sk1 @ A @ sk6 ) ),
inference(simp,[status(thm)],[97]) ).
thf(343,plain,
! [A: $i] :
( ( A = sk4 )
| ( sk1 @ A @ sk4 )
| ( sk1 @ A @ sk5 )
| ( sk1 @ sk4 @ sk5 )
| ( A != sk3 )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[126,28]) ).
thf(344,plain,
! [A: $i] :
( ( A = sk4 )
| ( sk1 @ A @ sk4 )
| ( sk1 @ A @ sk5 )
| ( sk1 @ sk4 @ sk5 )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[343:[]]) ).
thf(428,plain,
( ( sk4 = sk3 )
| ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk4 @ sk5 ) ),
inference(simp,[status(thm)],[344]) ).
thf(18,plain,
sk3 != sk4,
inference(cnf,[status(esa)],[4]) ).
thf(36,plain,
sk4 != sk3,
inference(lifteq,[status(thm)],[18]) ).
thf(2859,plain,
( ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk4 @ sk5 ) ),
inference(simplifyReflect,[status(thm)],[428,36]) ).
thf(2905,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk4 @ sk5 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2859,22]) ).
thf(2906,plain,
( ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk5 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2905:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(3559,plain,
( ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk3 @ sk5 )
| ( ( sk1 @ sk5 @ sk4 )
!= ( sk1 @ sk3 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2906]) ).
thf(3562,plain,
( ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk3 @ sk5 )
| ( ( sk1 @ sk5 @ sk4 )
!= ( sk1 @ sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[3559]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( A != sk3 )
| ( C != sk7 ) ),
inference(paramod_ordered,[status(thm)],[26,24]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B = sk7 )
| ( sk1 @ A @ B )
| ( sk1 @ A @ sk7 )
| ( sk1 @ B @ sk7 )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk7 ))]]) ).
thf(153,plain,
! [A: $i] :
( ( sk3 = A )
| ( A = sk7 )
| ( sk1 @ sk3 @ A )
| ( sk1 @ sk3 @ sk7 )
| ( sk1 @ A @ sk7 ) ),
inference(simp,[status(thm)],[49]) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( A != sk3 )
| ( B != sk5 ) ),
inference(paramod_ordered,[status(thm)],[26,28]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( sk5 = B )
| ( sk1 @ A @ sk5 )
| ( sk1 @ A @ B )
| ( sk1 @ sk5 @ B )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[68:[bind(A,$thf( A )),bind(B,$thf( sk5 ))]]) ).
thf(128,plain,
! [A: $i] :
( ( sk3 = A )
| ( sk5 = A )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ A )
| ( sk1 @ sk5 @ A ) ),
inference(simp,[status(thm)],[69]) ).
thf(2271,plain,
! [A: $i] :
( ( sk3 = A )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ A )
| ( sk1 @ sk5 @ A )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[128,35]) ).
thf(2272,plain,
( ( sk7 = sk3 )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk7 )
| ( sk1 @ sk5 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[2271:[bind(A,$thf( sk7 ))]]) ).
thf(15188,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk7 )
| ( sk1 @ sk5 @ sk7 ) ),
inference(simplifyReflect,[status(thm)],[2272,24]) ).
thf(15351,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk3 @ sk7 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[15188]) ).
thf(15384,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk3 @ sk7 ) ) ),
inference(simp,[status(thm)],[15351]) ).
thf(3157,plain,
! [A: $i] :
( ( A = sk3 )
| ( sk1 @ sk5 @ A )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ A @ sk3 )
| ( A != sk6 ) ),
inference(paramod_ordered,[status(thm)],[129,38]) ).
thf(3158,plain,
( ( sk6 = sk3 )
| ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk6 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[3157:[bind(A,$thf( sk6 ))]]) ).
thf(26714,plain,
( ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk6 @ sk3 ) ),
inference(simplifyReflect,[status(thm)],[3158,30]) ).
thf(15280,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk7 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[15188,22]) ).
thf(15281,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk7 )
| ( sk1 @ sk7 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[15280:[bind(A,$thf( sk5 )),bind(B,$thf( sk7 ))]]) ).
thf(15597,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk7 )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ sk3 @ sk7 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[15281]) ).
thf(15637,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk7 )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ sk3 @ sk7 ) ) ),
inference(simp,[status(thm)],[15597]) ).
thf(1737,plain,
! [A: $i] :
( ( sk3 = A )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk5 @ A )
| ( sk1 @ sk3 @ A )
| ( A != sk6 ) ),
inference(paramod_ordered,[status(thm)],[127,38]) ).
thf(1738,plain,
( ( sk6 = sk3 )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk3 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[1737:[bind(A,$thf( sk6 ))]]) ).
thf(6583,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk3 @ sk6 ) ),
inference(simplifyReflect,[status(thm)],[1738,30]) ).
thf(6407,plain,
( ~ ( sk1 @ sk5 @ sk4 )
| ~ ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk5 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6054]) ).
thf(6444,plain,
( ~ ( sk1 @ sk5 @ sk4 )
| ~ ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk5 @ sk4 ) ) ),
inference(simp,[status(thm)],[6407]) ).
thf(8255,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk5 @ sk4 ) )
| ( ( sk1 @ B @ A )
!= ( sk1 @ sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[22,6444]) ).
thf(8256,plain,
( ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk5 @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[8255:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(3869,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk2 @ sk4 )
| ( sk1 @ sk2 @ sk5 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk4 @ sk5 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3817,22]) ).
thf(3870,plain,
( ( sk1 @ sk2 @ sk4 )
| ( sk1 @ sk2 @ sk5 )
| ( sk1 @ sk5 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[3869:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(4028,plain,
( ( sk1 @ sk2 @ sk4 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk5 @ sk4 )
!= ( sk1 @ sk2 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3870]) ).
thf(4030,plain,
( ( sk1 @ sk2 @ sk4 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk5 @ sk4 )
!= ( sk1 @ sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[4028]) ).
thf(16,plain,
sk6 != sk7,
inference(cnf,[status(esa)],[4]) ).
thf(37,plain,
sk7 != sk6,
inference(lifteq,[status(thm)],[16]) ).
thf(503,plain,
( ( sk1 @ sk7 @ sk4 )
| ( sk1 @ sk4 @ sk5 )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ sk4 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[469]) ).
thf(504,plain,
( ( sk1 @ sk7 @ sk4 )
| ( sk1 @ sk4 @ sk5 )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ sk4 @ sk5 ) ) ),
inference(simp,[status(thm)],[503]) ).
thf(1745,plain,
! [A: $i] :
( ( sk3 = A )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk5 @ A )
| ( sk1 @ sk3 @ A )
| ( A != sk2 )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[127,41]) ).
thf(1746,plain,
! [A: $i] :
( ( sk3 = A )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk5 @ A )
| ( sk1 @ sk3 @ A )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[1745:[]]) ).
thf(1907,plain,
( ( sk3 = sk2 )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk5 @ sk2 )
| ( sk1 @ sk3 @ sk2 ) ),
inference(simp,[status(thm)],[1746]) ).
thf(10806,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk5 @ sk2 )
| ( sk1 @ sk3 @ sk2 ) ),
inference(simplifyReflect,[status(thm)],[1907,34]) ).
thf(10877,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk5 @ sk2 )
| ( sk1 @ sk3 @ sk2 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10806,22]) ).
thf(10878,plain,
( ( sk1 @ sk5 @ sk2 )
| ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk3 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[10877:[bind(A,$thf( sk5 )),bind(B,$thf( sk3 ))]]) ).
thf(11069,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk5 @ sk2 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10878,22]) ).
thf(11070,plain,
( ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[11069:[bind(A,$thf( sk5 )),bind(B,$thf( sk2 ))]]) ).
thf(11750,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk2 @ sk5 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk3 @ sk5 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11070,22]) ).
thf(11751,plain,
( ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk2 @ sk5 )
| ( sk1 @ sk5 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[11750:[bind(A,$thf( sk3 )),bind(B,$thf( sk5 ))]]) ).
thf(12797,plain,
( ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ sk3 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11751]) ).
thf(12819,plain,
( ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[12797]) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( B != sk4 )
| ( A != sk5 ) ),
inference(paramod_ordered,[status(thm)],[26,29]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( sk5 = B )
| ( A = B )
| ( sk1 @ sk5 @ A )
| ( sk1 @ sk5 @ B )
| ( sk1 @ A @ B )
| ( A != sk4 ) ),
inference(pattern_uni,[status(thm)],[54:[bind(A,$thf( sk5 ))]]) ).
thf(157,plain,
! [A: $i] :
( ( sk5 = A )
| ( sk4 = A )
| ( sk1 @ sk5 @ sk4 )
| ( sk1 @ sk5 @ A )
| ( sk1 @ sk4 @ A ) ),
inference(simp,[status(thm)],[55]) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( C != sk2 )
| ( B != sk4 ) ),
inference(paramod_ordered,[status(thm)],[26,23]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( A = sk4 )
| ( A = B )
| ( sk1 @ A @ sk4 )
| ( sk1 @ A @ B )
| ( sk1 @ sk4 @ B )
| ( B != sk2 ) ),
inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(152,plain,
! [A: $i] :
( ( A = sk4 )
| ( A = sk2 )
| ( sk1 @ A @ sk4 )
| ( sk1 @ A @ sk2 )
| ( sk1 @ sk4 @ sk2 ) ),
inference(simp,[status(thm)],[111]) ).
thf(2344,plain,
! [A: $i] :
( ( sk3 = A )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ A )
| ( sk1 @ sk5 @ A )
| ( A != sk6 ) ),
inference(paramod_ordered,[status(thm)],[128,38]) ).
thf(2345,plain,
( ( sk6 = sk3 )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk6 )
| ( sk1 @ sk5 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[2344:[bind(A,$thf( sk6 ))]]) ).
thf(18085,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk6 )
| ( sk1 @ sk5 @ sk6 ) ),
inference(simplifyReflect,[status(thm)],[2345,30]) ).
thf(18173,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk6 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[18085,22]) ).
thf(18174,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk6 )
| ( sk1 @ sk6 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[18173:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(18498,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk6 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk3 @ sk6 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[18174]) ).
thf(18511,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk6 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk3 @ sk6 ) ) ),
inference(simp,[status(thm)],[18498]) ).
thf(6643,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk6 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6583,22]) ).
thf(6644,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk6 )
| ( sk1 @ sk6 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[6643:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(8033,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk6 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk3 @ sk6 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6644]) ).
thf(8037,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk6 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk3 @ sk6 ) ) ),
inference(simp,[status(thm)],[8033]) ).
thf(15596,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk7 )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ sk3 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[15281]) ).
thf(15601,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk7 )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[15596]) ).
thf(345,plain,
! [A: $i] :
( ( A = sk4 )
| ( sk1 @ A @ sk4 )
| ( sk1 @ A @ sk5 )
| ( sk1 @ sk4 @ sk5 )
| ( A != sk6 ) ),
inference(paramod_ordered,[status(thm)],[126,38]) ).
thf(346,plain,
( ( sk6 = sk4 )
| ( sk1 @ sk6 @ sk4 )
| ( sk1 @ sk6 @ sk5 )
| ( sk1 @ sk4 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[345:[bind(A,$thf( sk6 ))]]) ).
thf(19,plain,
sk4 != sk6,
inference(cnf,[status(esa)],[4]) ).
thf(40,plain,
sk6 != sk4,
inference(lifteq,[status(thm)],[19]) ).
thf(2138,plain,
( ( sk1 @ sk6 @ sk4 )
| ( sk1 @ sk6 @ sk5 )
| ( sk1 @ sk4 @ sk5 ) ),
inference(simplifyReflect,[status(thm)],[346,40]) ).
thf(2179,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk6 @ sk4 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2138,22]) ).
thf(2180,plain,
( ( sk1 @ sk6 @ sk4 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk5 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[2179:[bind(A,$thf( sk6 )),bind(B,$thf( sk5 ))]]) ).
thf(2560,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk5 @ sk6 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk6 @ sk4 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2180,22]) ).
thf(2561,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk4 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[2560:[bind(A,$thf( sk6 )),bind(B,$thf( sk4 ))]]) ).
thf(2712,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk6 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk4 @ sk6 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2561]) ).
thf(2713,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk6 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk4 @ sk6 ) ) ),
inference(simp,[status(thm)],[2712]) ).
thf(1001,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk5 @ sk7 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk7 @ sk4 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[477,22]) ).
thf(1002,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk5 @ sk7 )
| ( sk1 @ sk4 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[1001:[bind(A,$thf( sk7 )),bind(B,$thf( sk4 ))]]) ).
thf(1114,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk4 @ sk7 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1002]) ).
thf(1115,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk4 @ sk7 ) ) ),
inference(simp,[status(thm)],[1114]) ).
thf(3017,plain,
! [A: $i] :
( ( A = sk3 )
| ( sk1 @ sk5 @ A )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ A @ sk3 )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[129,35]) ).
thf(3018,plain,
( ( sk7 = sk3 )
| ( sk1 @ sk5 @ sk7 )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk7 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[3017:[bind(A,$thf( sk7 ))]]) ).
thf(25058,plain,
( ( sk1 @ sk5 @ sk7 )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk7 @ sk3 ) ),
inference(simplifyReflect,[status(thm)],[3018,24]) ).
thf(25228,plain,
( ( sk1 @ sk5 @ sk7 )
| ( sk1 @ sk5 @ sk3 )
| ( ( sk1 @ sk7 @ sk3 )
!= ( sk1 @ sk5 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[25058]) ).
thf(25247,plain,
( ( sk1 @ sk5 @ sk7 )
| ( sk1 @ sk5 @ sk3 )
| ( ( sk1 @ sk7 @ sk3 )
!= ( sk1 @ sk5 @ sk3 ) ) ),
inference(simp,[status(thm)],[25228]) ).
thf(2672,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2561,22]) ).
thf(2673,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk6 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[2672:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(2826,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk6 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk4 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2673]) ).
thf(2829,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk6 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk4 @ sk5 ) ) ),
inference(simp,[status(thm)],[2826]) ).
thf(11804,plain,
( ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk3 @ sk5 )
!= ( sk1 @ sk2 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11070]) ).
thf(11821,plain,
( ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk3 @ sk5 )
!= ( sk1 @ sk2 @ sk5 ) ) ),
inference(simp,[status(thm)],[11804]) ).
thf(29160,plain,
( ( sk1 @ sk5 @ sk2 )
| ( sk1 @ sk2 @ sk3 )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ sk2 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[28981]) ).
thf(29167,plain,
( ( sk1 @ sk5 @ sk2 )
| ( sk1 @ sk2 @ sk3 )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[29160]) ).
thf(5008,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk3 @ sk7 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[4902]) ).
thf(5013,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk3 @ sk7 ) ) ),
inference(simp,[status(thm)],[5008]) ).
thf(26876,plain,
( ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk5 @ sk3 )
| ( ( sk1 @ sk6 @ sk3 )
!= ( sk1 @ sk5 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[26714]) ).
thf(26916,plain,
( ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk5 @ sk3 )
| ( ( sk1 @ sk6 @ sk3 )
!= ( sk1 @ sk5 @ sk3 ) ) ),
inference(simp,[status(thm)],[26876]) ).
thf(29088,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk5 @ sk2 )
| ( sk1 @ sk2 @ sk3 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[28981,22]) ).
thf(29089,plain,
( ( sk1 @ sk5 @ sk2 )
| ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk3 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[29088:[bind(A,$thf( sk5 )),bind(B,$thf( sk3 ))]]) ).
thf(30688,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk5 @ sk2 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29089,22]) ).
thf(30689,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[30688:[bind(A,$thf( sk5 )),bind(B,$thf( sk2 ))]]) ).
thf(30976,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk2 @ sk5 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk3 @ sk5 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[30689,22]) ).
thf(30977,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk2 @ sk5 )
| ( sk1 @ sk5 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[30976:[bind(A,$thf( sk3 )),bind(B,$thf( sk5 ))]]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( B != sk3 )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[26,24]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( sk7 = B )
| ( A = B )
| ( sk1 @ sk7 @ A )
| ( sk1 @ sk7 @ B )
| ( sk1 @ A @ B )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( sk7 ))]]) ).
thf(147,plain,
! [A: $i] :
( ( sk7 = A )
| ( sk3 = A )
| ( sk1 @ sk7 @ sk3 )
| ( sk1 @ sk7 @ A )
| ( sk1 @ sk3 @ A ) ),
inference(simp,[status(thm)],[43]) ).
thf(31048,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk3 @ sk5 )
!= ( sk1 @ sk2 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[30689]) ).
thf(31071,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk3 @ sk5 )
!= ( sk1 @ sk2 @ sk5 ) ) ),
inference(simp,[status(thm)],[31048]) ).
thf(4029,plain,
( ( sk1 @ sk2 @ sk4 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk5 @ sk4 )
!= ( sk1 @ sk2 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3870]) ).
thf(4033,plain,
( ( sk1 @ sk2 @ sk4 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk5 @ sk4 )
!= ( sk1 @ sk2 @ sk5 ) ) ),
inference(simp,[status(thm)],[4029]) ).
thf(2827,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk6 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk4 @ sk6 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2673]) ).
thf(2833,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk6 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk4 @ sk6 ) ) ),
inference(simp,[status(thm)],[2827]) ).
thf(1595,plain,
! [A: $i] :
( ( sk3 = A )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk5 @ A )
| ( sk1 @ sk3 @ A )
| ( A != sk4 )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[127,29]) ).
thf(1596,plain,
! [A: $i] :
( ( sk3 = A )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk5 @ A )
| ( sk1 @ sk3 @ A )
| ( A != sk4 ) ),
inference(pattern_uni,[status(thm)],[1595:[]]) ).
thf(1862,plain,
( ( sk4 = sk3 )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk5 @ sk4 )
| ( sk1 @ sk3 @ sk4 ) ),
inference(simp,[status(thm)],[1596]) ).
thf(8867,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk5 @ sk4 )
| ( sk1 @ sk3 @ sk4 ) ),
inference(simplifyReflect,[status(thm)],[1862,36]) ).
thf(8989,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk4 )
| ( ( sk1 @ sk5 @ sk4 )
!= ( sk1 @ sk3 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8867]) ).
thf(8999,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk4 )
| ( ( sk1 @ sk5 @ sk4 )
!= ( sk1 @ sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[8989]) ).
thf(15350,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk3 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[15188]) ).
thf(15364,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[15350]) ).
thf(25227,plain,
( ( sk1 @ sk5 @ sk7 )
| ( sk1 @ sk5 @ sk3 )
| ( ( sk1 @ sk7 @ sk3 )
!= ( sk1 @ sk5 @ sk7 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[25058]) ).
thf(25267,plain,
( ( sk1 @ sk5 @ sk7 )
| ( sk1 @ sk5 @ sk3 )
| ( ( sk1 @ sk7 @ sk3 )
!= ( sk1 @ sk5 @ sk7 ) ) ),
inference(simp,[status(thm)],[25227]) ).
thf(22390,plain,
! [A: $i] :
( ~ ( sk1 @ sk5 @ sk4 )
| ~ ( sk1 @ sk5 @ A )
| ~ ( sk1 @ sk4 @ A )
| ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ A @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 )
| ( A != sk6 ) ),
inference(paramod_ordered,[status(thm)],[7396,40]) ).
thf(22391,plain,
( ~ ( sk1 @ sk5 @ sk4 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk4 @ sk6 )
| ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk6 @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[22390:[bind(A,$thf( sk6 ))]]) ).
thf(49443,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk4 @ sk6 )
| ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk6 @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ B @ A )
!= ( sk1 @ sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[22,22391]) ).
thf(49444,plain,
( ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk4 @ sk6 )
| ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk6 @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[49443:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(50747,plain,
( ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk4 @ sk6 )
| ~ ( sk1 @ sk6 @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 ) ),
inference(simp,[status(thm)],[49444]) ).
thf(30759,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk3 @ sk5 )
| ( ( sk1 @ sk5 @ sk2 )
!= ( sk1 @ sk2 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[29089]) ).
thf(30776,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk3 @ sk5 )
| ( ( sk1 @ sk5 @ sk2 )
!= ( sk1 @ sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[30759]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( C != sk2 )
| ( B != sk7 ) ),
inference(paramod_ordered,[status(thm)],[26,27]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( A = sk7 )
| ( A = B )
| ( sk1 @ A @ sk7 )
| ( sk1 @ A @ B )
| ( sk1 @ sk7 @ B )
| ( B != sk2 ) ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( A )),bind(B,$thf( sk7 ))]]) ).
thf(137,plain,
! [A: $i] :
( ( A = sk7 )
| ( A = sk2 )
| ( sk1 @ A @ sk7 )
| ( sk1 @ A @ sk2 )
| ( sk1 @ sk7 @ sk2 ) ),
inference(simp,[status(thm)],[87]) ).
thf(5707,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk7 )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ sk5 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[4960]) ).
thf(5714,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk7 )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ sk5 @ sk3 ) ) ),
inference(simp,[status(thm)],[5707]) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( B != sk3 )
| ( C != sk7 ) ),
inference(paramod_ordered,[status(thm)],[26,24]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( A = sk7 )
| ( sk1 @ A @ B )
| ( sk1 @ A @ sk7 )
| ( sk1 @ B @ sk7 )
| ( B != sk3 ) ),
inference(pattern_uni,[status(thm)],[52:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk7 ))]]) ).
thf(156,plain,
! [A: $i] :
( ( A = sk3 )
| ( A = sk7 )
| ( sk1 @ A @ sk3 )
| ( sk1 @ A @ sk7 )
| ( sk1 @ sk3 @ sk7 ) ),
inference(simp,[status(thm)],[53]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( C != sk3 )
| ( B != sk5 ) ),
inference(paramod_ordered,[status(thm)],[26,28]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( A = sk5 )
| ( A = B )
| ( sk1 @ A @ sk5 )
| ( sk1 @ A @ B )
| ( sk1 @ sk5 @ B )
| ( B != sk3 ) ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( A )),bind(B,$thf( sk5 ))]]) ).
thf(131,plain,
! [A: $i] :
( ( A = sk5 )
| ( A = sk3 )
| ( sk1 @ A @ sk5 )
| ( sk1 @ A @ sk3 )
| ( sk1 @ sk5 @ sk3 ) ),
inference(simp,[status(thm)],[75]) ).
thf(5211,plain,
! [A: $i] :
( ( A = sk3 )
| ( sk1 @ A @ sk5 )
| ( sk1 @ A @ sk3 )
| ( sk1 @ sk5 @ sk3 )
| ( A != sk6 ) ),
inference(paramod_ordered,[status(thm)],[131,38]) ).
thf(5212,plain,
( ( sk6 = sk3 )
| ( sk1 @ sk6 @ sk5 )
| ( sk1 @ sk6 @ sk3 )
| ( sk1 @ sk5 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[5211:[bind(A,$thf( sk6 ))]]) ).
thf(43449,plain,
( ( sk1 @ sk6 @ sk5 )
| ( sk1 @ sk6 @ sk3 )
| ( sk1 @ sk5 @ sk3 ) ),
inference(simplifyReflect,[status(thm)],[5212,30]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( C != sk3 )
| ( A != sk6 ) ),
inference(paramod_ordered,[status(thm)],[26,30]) ).
thf(95,plain,
! [B: $i,A: $i] :
( ( sk6 = A )
| ( A = B )
| ( sk1 @ sk6 @ A )
| ( sk1 @ sk6 @ B )
| ( sk1 @ A @ B )
| ( B != sk3 ) ),
inference(pattern_uni,[status(thm)],[94:[bind(A,$thf( sk6 ))]]) ).
thf(141,plain,
! [A: $i] :
( ( sk6 = A )
| ( A = sk3 )
| ( sk1 @ sk6 @ A )
| ( sk1 @ sk6 @ sk3 )
| ( sk1 @ A @ sk3 ) ),
inference(simp,[status(thm)],[95]) ).
thf(1087,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk7 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1002,22]) ).
thf(1088,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk7 )
| ( sk1 @ sk7 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[1087:[bind(A,$thf( sk5 )),bind(B,$thf( sk7 ))]]) ).
thf(1565,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ sk4 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1088]) ).
thf(1567,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ sk4 @ sk5 ) ) ),
inference(simp,[status(thm)],[1565]) ).
thf(18497,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk6 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk3 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[18174]) ).
thf(18521,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk6 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[18497]) ).
thf(9331,plain,
! [A: $i] :
( ( sk2 = A )
| ( sk1 @ sk7 @ sk2 )
| ( sk1 @ sk7 @ A )
| ( sk1 @ sk2 @ A )
| ( A != sk4 )
| ( sk7 != sk7 ) ),
inference(paramod_ordered,[status(thm)],[133,31]) ).
thf(9332,plain,
! [A: $i] :
( ( sk2 = A )
| ( sk1 @ sk7 @ sk2 )
| ( sk1 @ sk7 @ A )
| ( sk1 @ sk2 @ A )
| ( A != sk4 ) ),
inference(pattern_uni,[status(thm)],[9331:[]]) ).
thf(9519,plain,
( ( sk4 = sk2 )
| ( sk1 @ sk7 @ sk2 )
| ( sk1 @ sk7 @ sk4 )
| ( sk1 @ sk2 @ sk4 ) ),
inference(simp,[status(thm)],[9332]) ).
thf(80492,plain,
( ( sk1 @ sk7 @ sk2 )
| ( sk1 @ sk7 @ sk4 )
| ( sk1 @ sk2 @ sk4 ) ),
inference(simplifyReflect,[status(thm)],[9519,23]) ).
thf(11123,plain,
( ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk3 @ sk5 )
| ( ( sk1 @ sk5 @ sk2 )
!= ( sk1 @ sk3 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[10878]) ).
thf(11129,plain,
( ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk3 @ sk5 )
| ( ( sk1 @ sk5 @ sk2 )
!= ( sk1 @ sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[11123]) ).
thf(18240,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk6 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk3 @ sk6 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[18085]) ).
thf(18248,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk6 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk3 @ sk6 ) ) ),
inference(simp,[status(thm)],[18240]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( A != sk2 )
| ( B != sk7 ) ),
inference(paramod_ordered,[status(thm)],[26,27]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( sk7 = B )
| ( sk1 @ A @ sk7 )
| ( sk1 @ A @ B )
| ( sk1 @ sk7 @ B )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[80:[bind(A,$thf( A )),bind(B,$thf( sk7 ))]]) ).
thf(134,plain,
! [A: $i] :
( ( sk2 = A )
| ( sk7 = A )
| ( sk1 @ sk2 @ sk7 )
| ( sk1 @ sk2 @ A )
| ( sk1 @ sk7 @ A ) ),
inference(simp,[status(thm)],[81]) ).
thf(2219,plain,
( ( sk1 @ sk6 @ sk4 )
| ( sk1 @ sk4 @ sk5 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk4 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2138]) ).
thf(2221,plain,
( ( sk1 @ sk6 @ sk4 )
| ( sk1 @ sk4 @ sk5 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk4 @ sk5 ) ) ),
inference(simp,[status(thm)],[2219]) ).
thf(7075,plain,
! [A: $i] :
( ( A = sk3 )
| ( sk1 @ A @ sk3 )
| ( sk1 @ A @ sk5 )
| ( sk1 @ sk3 @ sk5 )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[132,35]) ).
thf(7076,plain,
( ( sk7 = sk3 )
| ( sk1 @ sk7 @ sk3 )
| ( sk1 @ sk7 @ sk5 )
| ( sk1 @ sk3 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[7075:[bind(A,$thf( sk7 ))]]) ).
thf(61618,plain,
( ( sk1 @ sk7 @ sk3 )
| ( sk1 @ sk7 @ sk5 )
| ( sk1 @ sk3 @ sk5 ) ),
inference(simplifyReflect,[status(thm)],[7076,24]) ).
thf(2711,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk6 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk4 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2561]) ).
thf(2717,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk6 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk4 @ sk5 ) ) ),
inference(simp,[status(thm)],[2711]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( C != sk2 )
| ( A != sk4 ) ),
inference(paramod_ordered,[status(thm)],[26,23]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( sk4 = A )
| ( A = B )
| ( sk1 @ sk4 @ A )
| ( sk1 @ sk4 @ B )
| ( sk1 @ A @ B )
| ( B != sk2 ) ),
inference(pattern_uni,[status(thm)],[106:[bind(A,$thf( sk4 ))]]) ).
thf(148,plain,
! [A: $i] :
( ( sk4 = A )
| ( A = sk2 )
| ( sk1 @ sk4 @ A )
| ( sk1 @ sk4 @ sk2 )
| ( sk1 @ A @ sk2 ) ),
inference(simp,[status(thm)],[107]) ).
thf(2982,plain,
! [A: $i] :
( ( A = sk3 )
| ( sk1 @ sk5 @ A )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ A @ sk3 )
| ( A != sk4 )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[129,29]) ).
thf(2983,plain,
! [A: $i] :
( ( A = sk3 )
| ( sk1 @ sk5 @ A )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ A @ sk3 )
| ( A != sk4 ) ),
inference(pattern_uni,[status(thm)],[2982:[]]) ).
thf(3421,plain,
( ( sk4 = sk3 )
| ( sk1 @ sk5 @ sk4 )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk4 @ sk3 ) ),
inference(simp,[status(thm)],[2983]) ).
thf(31447,plain,
( ( sk1 @ sk5 @ sk4 )
| ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk4 @ sk3 ) ),
inference(simplifyReflect,[status(thm)],[3421,36]) ).
thf(31567,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk4 @ sk3 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk5 @ sk4 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[31447,22]) ).
thf(31568,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk4 @ sk3 )
| ( sk1 @ sk4 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[31567:[bind(A,$thf( sk5 )),bind(B,$thf( sk4 ))]]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( A != sk3 )
| ( B != sk7 ) ),
inference(paramod_ordered,[status(thm)],[26,24]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( sk7 = B )
| ( sk1 @ A @ sk7 )
| ( sk1 @ A @ B )
| ( sk1 @ sk7 @ B )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[44:[bind(A,$thf( A )),bind(B,$thf( sk7 ))]]) ).
thf(149,plain,
! [A: $i] :
( ( sk3 = A )
| ( sk7 = A )
| ( sk1 @ sk3 @ sk7 )
| ( sk1 @ sk3 @ A )
| ( sk1 @ sk7 @ A ) ),
inference(simp,[status(thm)],[45]) ).
thf(6408,plain,
( ~ ( sk1 @ sk5 @ sk4 )
| ~ ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk4 @ sk7 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6054]) ).
thf(6468,plain,
( ~ ( sk1 @ sk5 @ sk4 )
| ~ ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk4 @ sk7 ) ) ),
inference(simp,[status(thm)],[6408]) ).
thf(2218,plain,
( ( sk1 @ sk6 @ sk4 )
| ( sk1 @ sk4 @ sk5 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk6 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2138]) ).
thf(2225,plain,
( ( sk1 @ sk6 @ sk4 )
| ( sk1 @ sk4 @ sk5 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk6 @ sk4 ) ) ),
inference(simp,[status(thm)],[2218]) ).
thf(18239,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk6 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk3 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[18085]) ).
thf(18262,plain,
( ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk3 @ sk6 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[18239]) ).
thf(8988,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk4 )
| ( ( sk1 @ sk5 @ sk4 )
!= ( sk1 @ sk5 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8867]) ).
thf(8993,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk4 )
| ( ( sk1 @ sk5 @ sk4 )
!= ( sk1 @ sk5 @ sk3 ) ) ),
inference(simp,[status(thm)],[8988]) ).
thf(6697,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk6 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk5 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6583]) ).
thf(6705,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk6 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk5 @ sk3 ) ) ),
inference(simp,[status(thm)],[6697]) ).
thf(5007,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk5 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[4902]) ).
thf(5011,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk5 @ sk3 ) ) ),
inference(simp,[status(thm)],[5007]) ).
thf(10930,plain,
( ( sk1 @ sk5 @ sk2 )
| ( sk1 @ sk3 @ sk2 )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ sk5 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[10806]) ).
thf(10948,plain,
( ( sk1 @ sk5 @ sk2 )
| ( sk1 @ sk3 @ sk2 )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ sk5 @ sk2 ) ) ),
inference(simp,[status(thm)],[10930]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( B != sk3 )
| ( C != sk6 ) ),
inference(paramod_ordered,[status(thm)],[26,30]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( A = sk6 )
| ( sk1 @ A @ B )
| ( sk1 @ A @ sk6 )
| ( sk1 @ B @ sk6 )
| ( B != sk3 ) ),
inference(pattern_uni,[status(thm)],[100:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk6 ))]]) ).
thf(144,plain,
! [A: $i] :
( ( A = sk3 )
| ( A = sk6 )
| ( sk1 @ A @ sk3 )
| ( sk1 @ A @ sk6 )
| ( sk1 @ sk3 @ sk6 ) ),
inference(simp,[status(thm)],[101]) ).
thf(12798,plain,
( ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ sk2 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11751]) ).
thf(12830,plain,
( ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ sk2 @ sk5 ) ) ),
inference(simp,[status(thm)],[12798]) ).
thf(22546,plain,
! [A: $i] :
( ~ ( sk1 @ sk5 @ sk4 )
| ~ ( sk1 @ sk5 @ A )
| ~ ( sk1 @ sk4 @ A )
| ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ A @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 )
| ( A != sk2 )
| ( sk4 != sk4 ) ),
inference(paramod_ordered,[status(thm)],[7396,23]) ).
thf(22547,plain,
! [A: $i] :
( ~ ( sk1 @ sk5 @ sk4 )
| ~ ( sk1 @ sk5 @ A )
| ~ ( sk1 @ sk4 @ A )
| ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ A @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[22546:[]]) ).
thf(23034,plain,
( ~ ( sk1 @ sk5 @ sk4 )
| ~ ( sk1 @ sk5 @ sk2 )
| ~ ( sk1 @ sk4 @ sk2 )
| ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk2 @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 ) ),
inference(simp,[status(thm)],[22547]) ).
thf(65481,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ sk5 @ sk2 )
| ~ ( sk1 @ sk4 @ sk2 )
| ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk2 @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ B @ A )
!= ( sk1 @ sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[22,23034]) ).
thf(65482,plain,
( ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk5 @ sk2 )
| ~ ( sk1 @ sk4 @ sk2 )
| ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk2 @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[65481:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(67242,plain,
( ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk5 @ sk2 )
| ~ ( sk1 @ sk4 @ sk2 )
| ~ ( sk1 @ sk2 @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 ) ),
inference(simp,[status(thm)],[65482]) ).
thf(10931,plain,
( ( sk1 @ sk5 @ sk2 )
| ( sk1 @ sk3 @ sk2 )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ sk3 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[10806]) ).
thf(10953,plain,
( ( sk1 @ sk5 @ sk2 )
| ( sk1 @ sk3 @ sk2 )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[10931]) ).
thf(5320,plain,
! [A: $i] :
( ( A = sk3 )
| ( sk1 @ A @ sk5 )
| ( sk1 @ A @ sk3 )
| ( sk1 @ sk5 @ sk3 )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[131,35]) ).
thf(5321,plain,
( ( sk7 = sk3 )
| ( sk1 @ sk7 @ sk5 )
| ( sk1 @ sk7 @ sk3 )
| ( sk1 @ sk5 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[5320:[bind(A,$thf( sk7 ))]]) ).
thf(45608,plain,
( ( sk1 @ sk7 @ sk5 )
| ( sk1 @ sk7 @ sk3 )
| ( sk1 @ sk5 @ sk3 ) ),
inference(simplifyReflect,[status(thm)],[5321,24]) ).
thf(8032,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk6 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk5 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6644]) ).
thf(8042,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk6 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk5 @ sk3 ) ) ),
inference(simp,[status(thm)],[8032]) ).
thf(1113,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk4 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1002]) ).
thf(1117,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk4 @ sk5 ) ) ),
inference(simp,[status(thm)],[1113]) ).
thf(2943,plain,
( ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk3 @ sk5 )
| ( ( sk1 @ sk4 @ sk5 )
!= ( sk1 @ sk3 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2859]) ).
thf(2945,plain,
( ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk3 @ sk5 )
| ( ( sk1 @ sk4 @ sk5 )
!= ( sk1 @ sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[2943]) ).
thf(8,plain,
sk2 != sk6,
inference(cnf,[status(esa)],[4]) ).
thf(39,plain,
sk6 != sk2,
inference(lifteq,[status(thm)],[8]) ).
thf(1566,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ sk4 @ sk7 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1088]) ).
thf(1571,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ sk4 @ sk7 ) ) ),
inference(simp,[status(thm)],[1566]) ).
thf(79306,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk2 @ sk5 )
| ( sk1 @ sk5 @ sk7 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk7 @ sk2 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[76827,22]) ).
thf(79307,plain,
( ( sk1 @ sk2 @ sk5 )
| ( sk1 @ sk5 @ sk7 )
| ( sk1 @ sk2 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[79306:[bind(A,$thf( sk7 )),bind(B,$thf( sk2 ))]]) ).
thf(79743,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk2 @ sk5 )
| ( sk1 @ sk2 @ sk7 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[79307,22]) ).
thf(79744,plain,
( ( sk1 @ sk2 @ sk5 )
| ( sk1 @ sk2 @ sk7 )
| ( sk1 @ sk7 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[79743:[bind(A,$thf( sk5 )),bind(B,$thf( sk7 ))]]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( A != sk3 )
| ( B != sk6 ) ),
inference(paramod_ordered,[status(thm)],[26,30]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( sk6 = B )
| ( sk1 @ A @ sk6 )
| ( sk1 @ A @ B )
| ( sk1 @ sk6 @ B )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( A )),bind(B,$thf( sk6 ))]]) ).
thf(140,plain,
! [A: $i] :
( ( sk3 = A )
| ( sk6 = A )
| ( sk1 @ sk3 @ sk6 )
| ( sk1 @ sk3 @ A )
| ( sk1 @ sk6 @ A ) ),
inference(simp,[status(thm)],[93]) ).
thf(70408,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk4 @ sk2 )
| ~ ( sk1 @ sk2 @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ B @ A )
!= ( sk1 @ sk5 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[22,67242]) ).
thf(70409,plain,
( ~ ( sk1 @ sk2 @ sk5 )
| ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk4 @ sk2 )
| ~ ( sk1 @ sk2 @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[70408:[bind(A,$thf( sk2 )),bind(B,$thf( sk5 ))]]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( C != sk3 )
| ( B != sk7 ) ),
inference(paramod_ordered,[status(thm)],[26,24]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( A = sk7 )
| ( A = B )
| ( sk1 @ A @ sk7 )
| ( sk1 @ A @ B )
| ( sk1 @ sk7 @ B )
| ( B != sk3 ) ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( A )),bind(B,$thf( sk7 ))]]) ).
thf(155,plain,
! [A: $i] :
( ( A = sk7 )
| ( A = sk3 )
| ( sk1 @ A @ sk7 )
| ( sk1 @ A @ sk3 )
| ( sk1 @ sk7 @ sk3 ) ),
inference(simp,[status(thm)],[51]) ).
thf(7746,plain,
( ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk4 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6209]) ).
thf(7778,plain,
( ~ ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk4 @ sk7 )
| ( ( sk1 @ sk5 @ sk7 )
!= ( sk1 @ sk4 @ sk5 ) ) ),
inference(simp,[status(thm)],[7746]) ).
thf(1027,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk5 @ sk7 )
| ( ( sk1 @ sk7 @ sk4 )
!= ( sk1 @ sk4 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[477]) ).
thf(1029,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk5 @ sk7 )
| ( ( sk1 @ sk7 @ sk4 )
!= ( sk1 @ sk4 @ sk5 ) ) ),
inference(simp,[status(thm)],[1027]) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( A != sk3 )
| ( C != sk5 ) ),
inference(paramod_ordered,[status(thm)],[26,28]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B = sk5 )
| ( sk1 @ A @ B )
| ( sk1 @ A @ sk5 )
| ( sk1 @ B @ sk5 )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[72:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk5 ))]]) ).
thf(130,plain,
! [A: $i] :
( ( sk3 = A )
| ( A = sk5 )
| ( sk1 @ sk3 @ A )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ A @ sk5 ) ),
inference(simp,[status(thm)],[73]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( C != sk2 )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[26,27]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( sk7 = A )
| ( A = B )
| ( sk1 @ sk7 @ A )
| ( sk1 @ sk7 @ B )
| ( sk1 @ A @ B )
| ( B != sk2 ) ),
inference(pattern_uni,[status(thm)],[82:[bind(A,$thf( sk7 ))]]) ).
thf(135,plain,
! [A: $i] :
( ( sk7 = A )
| ( A = sk2 )
| ( sk1 @ sk7 @ A )
| ( sk1 @ sk7 @ sk2 )
| ( sk1 @ A @ sk2 ) ),
inference(simp,[status(thm)],[83]) ).
thf(26875,plain,
( ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk5 @ sk3 )
| ( ( sk1 @ sk6 @ sk3 )
!= ( sk1 @ sk5 @ sk6 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[26714]) ).
thf(26899,plain,
( ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk5 @ sk3 )
| ( ( sk1 @ sk6 @ sk3 )
!= ( sk1 @ sk5 @ sk6 ) ) ),
inference(simp,[status(thm)],[26875]) ).
thf(8935,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk4 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk5 @ sk4 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8867,22]) ).
thf(8936,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk4 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[8935:[bind(A,$thf( sk5 )),bind(B,$thf( sk4 ))]]) ).
thf(9720,plain,
( ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk4 @ sk5 )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ sk4 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8936]) ).
thf(9727,plain,
( ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk4 @ sk5 )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ sk4 @ sk5 ) ) ),
inference(simp,[status(thm)],[9720]) ).
thf(29159,plain,
( ( sk1 @ sk5 @ sk2 )
| ( sk1 @ sk2 @ sk3 )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ sk5 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[28981]) ).
thf(29162,plain,
( ( sk1 @ sk5 @ sk2 )
| ( sk1 @ sk2 @ sk3 )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ sk5 @ sk2 ) ) ),
inference(simp,[status(thm)],[29159]) ).
thf(2593,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk5 @ sk6 )
| ( ( sk1 @ sk6 @ sk4 )
!= ( sk1 @ sk4 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2180]) ).
thf(2597,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk5 @ sk6 )
| ( ( sk1 @ sk6 @ sk4 )
!= ( sk1 @ sk4 @ sk5 ) ) ),
inference(simp,[status(thm)],[2593]) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( B != sk2 )
| ( A != sk4 ) ),
inference(paramod_ordered,[status(thm)],[26,23]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( sk4 = B )
| ( A = B )
| ( sk1 @ sk4 @ A )
| ( sk1 @ sk4 @ B )
| ( sk1 @ A @ B )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[102:[bind(A,$thf( sk4 ))]]) ).
thf(145,plain,
! [A: $i] :
( ( sk4 = A )
| ( sk2 = A )
| ( sk1 @ sk4 @ sk2 )
| ( sk1 @ sk4 @ A )
| ( sk1 @ sk2 @ A ) ),
inference(simp,[status(thm)],[103]) ).
thf(3907,plain,
( ( sk1 @ sk2 @ sk4 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk4 @ sk5 )
!= ( sk1 @ sk2 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3817]) ).
thf(3913,plain,
( ( sk1 @ sk2 @ sk4 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk4 @ sk5 )
!= ( sk1 @ sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[3907]) ).
thf(30760,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk3 @ sk5 )
| ( ( sk1 @ sk5 @ sk2 )
!= ( sk1 @ sk3 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[29089]) ).
thf(30791,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk3 @ sk5 )
| ( ( sk1 @ sk5 @ sk2 )
!= ( sk1 @ sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[30760]) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( A != sk2 )
| ( C != sk4 ) ),
inference(paramod_ordered,[status(thm)],[26,23]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B = sk4 )
| ( sk1 @ A @ B )
| ( sk1 @ A @ sk4 )
| ( sk1 @ B @ sk4 )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[108:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(150,plain,
! [A: $i] :
( ( sk2 = A )
| ( A = sk4 )
| ( sk1 @ sk2 @ A )
| ( sk1 @ sk2 @ sk4 )
| ( sk1 @ A @ sk4 ) ),
inference(simp,[status(thm)],[109]) ).
thf(32959,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk4 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[31568,22]) ).
thf(32960,plain,
( ( sk1 @ sk4 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk3 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[32959:[bind(A,$thf( sk5 )),bind(B,$thf( sk3 ))]]) ).
thf(33228,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk4 @ sk3 )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk4 @ sk5 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[32960,22]) ).
thf(33229,plain,
( ( sk1 @ sk4 @ sk3 )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk5 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[33228:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(2594,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk5 @ sk6 )
| ( ( sk1 @ sk6 @ sk4 )
!= ( sk1 @ sk5 @ sk6 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2180]) ).
thf(2599,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk5 @ sk6 )
| ( ( sk1 @ sk6 @ sk4 )
!= ( sk1 @ sk5 @ sk6 ) ) ),
inference(simp,[status(thm)],[2594]) ).
thf(2942,plain,
( ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk3 @ sk5 )
| ( ( sk1 @ sk4 @ sk5 )
!= ( sk1 @ sk3 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2859]) ).
thf(2948,plain,
( ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk3 @ sk5 )
| ( ( sk1 @ sk4 @ sk5 )
!= ( sk1 @ sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[2942]) ).
thf(11803,plain,
( ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk3 @ sk5 )
!= ( sk1 @ sk3 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11070]) ).
thf(11830,plain,
( ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk3 @ sk5 )
!= ( sk1 @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[11803]) ).
thf(112,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( B != sk2 )
| ( C != sk4 ) ),
inference(paramod_ordered,[status(thm)],[26,23]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( A = sk4 )
| ( sk1 @ A @ B )
| ( sk1 @ A @ sk4 )
| ( sk1 @ B @ sk4 )
| ( B != sk2 ) ),
inference(pattern_uni,[status(thm)],[112:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(154,plain,
! [A: $i] :
( ( A = sk2 )
| ( A = sk4 )
| ( sk1 @ A @ sk2 )
| ( sk1 @ A @ sk4 )
| ( sk1 @ sk2 @ sk4 ) ),
inference(simp,[status(thm)],[113]) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( C != sk3 )
| ( B != sk6 ) ),
inference(paramod_ordered,[status(thm)],[26,30]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( A = sk6 )
| ( A = B )
| ( sk1 @ A @ sk6 )
| ( sk1 @ A @ B )
| ( sk1 @ sk6 @ B )
| ( B != sk3 ) ),
inference(pattern_uni,[status(thm)],[98:[bind(A,$thf( A )),bind(B,$thf( sk6 ))]]) ).
thf(143,plain,
! [A: $i] :
( ( A = sk6 )
| ( A = sk3 )
| ( sk1 @ A @ sk6 )
| ( sk1 @ A @ sk3 )
| ( sk1 @ sk6 @ sk3 ) ),
inference(simp,[status(thm)],[99]) ).
thf(9719,plain,
( ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk4 @ sk5 )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ sk3 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8936]) ).
thf(9732,plain,
( ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk4 @ sk5 )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[9719]) ).
thf(61790,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk7 @ sk3 )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[61618,22]) ).
thf(61791,plain,
( ( sk1 @ sk7 @ sk3 )
| ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk5 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[61790:[bind(A,$thf( sk7 )),bind(B,$thf( sk5 ))]]) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( A != sk4 )
| ( B != sk5 ) ),
inference(paramod_ordered,[status(thm)],[26,29]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( sk5 = B )
| ( sk1 @ A @ sk5 )
| ( sk1 @ A @ B )
| ( sk1 @ sk5 @ B )
| ( A != sk4 ) ),
inference(pattern_uni,[status(thm)],[56:[bind(A,$thf( A )),bind(B,$thf( sk5 ))]]) ).
thf(158,plain,
! [A: $i] :
( ( sk4 = A )
| ( sk5 = A )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk4 @ A )
| ( sk1 @ sk5 @ A ) ),
inference(simp,[status(thm)],[57]) ).
thf(90,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( B != sk3 )
| ( A != sk6 ) ),
inference(paramod_ordered,[status(thm)],[26,30]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ( sk6 = B )
| ( A = B )
| ( sk1 @ sk6 @ A )
| ( sk1 @ sk6 @ B )
| ( sk1 @ A @ B )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( sk6 ))]]) ).
thf(139,plain,
! [A: $i] :
( ( sk6 = A )
| ( sk3 = A )
| ( sk1 @ sk6 @ sk3 )
| ( sk1 @ sk6 @ A )
| ( sk1 @ sk3 @ A ) ),
inference(simp,[status(thm)],[91]) ).
thf(31047,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk3 @ sk5 )
!= ( sk1 @ sk2 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[30689]) ).
thf(31049,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk3 @ sk5 )
!= ( sk1 @ sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[31047]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( C != sk3 )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[26,24]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( sk7 = A )
| ( A = B )
| ( sk1 @ sk7 @ A )
| ( sk1 @ sk7 @ B )
| ( sk1 @ A @ B )
| ( B != sk3 ) ),
inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( sk7 ))]]) ).
thf(151,plain,
! [A: $i] :
( ( sk7 = A )
| ( A = sk3 )
| ( sk1 @ sk7 @ A )
| ( sk1 @ sk7 @ sk3 )
| ( sk1 @ A @ sk3 ) ),
inference(simp,[status(thm)],[47]) ).
thf(11122,plain,
( ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk3 @ sk5 )
| ( ( sk1 @ sk5 @ sk2 )
!= ( sk1 @ sk3 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[10878]) ).
thf(11131,plain,
( ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk3 @ sk5 )
| ( ( sk1 @ sk5 @ sk2 )
!= ( sk1 @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[11122]) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( A != sk2 )
| ( B != sk4 ) ),
inference(paramod_ordered,[status(thm)],[26,23]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( sk4 = B )
| ( sk1 @ A @ sk4 )
| ( sk1 @ A @ B )
| ( sk1 @ sk4 @ B )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[104:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(146,plain,
! [A: $i] :
( ( sk2 = A )
| ( sk4 = A )
| ( sk1 @ sk2 @ sk4 )
| ( sk1 @ sk2 @ A )
| ( sk1 @ sk4 @ A ) ),
inference(simp,[status(thm)],[105]) ).
thf(6698,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk6 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk3 @ sk6 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6583]) ).
thf(6703,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk6 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk3 @ sk6 ) ) ),
inference(simp,[status(thm)],[6698]) ).
thf(3558,plain,
( ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk3 @ sk5 )
| ( ( sk1 @ sk5 @ sk4 )
!= ( sk1 @ sk3 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2906]) ).
thf(3560,plain,
( ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk3 @ sk5 )
| ( ( sk1 @ sk5 @ sk4 )
!= ( sk1 @ sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[3558]) ).
thf(5708,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk7 )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ sk3 @ sk7 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[4960]) ).
thf(5709,plain,
( ( sk1 @ sk5 @ sk3 )
| ( sk1 @ sk3 @ sk7 )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ sk3 @ sk7 ) ) ),
inference(simp,[status(thm)],[5708]) ).
thf(502,plain,
( ( sk1 @ sk7 @ sk4 )
| ( sk1 @ sk4 @ sk5 )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ sk7 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[469]) ).
thf(506,plain,
( ( sk1 @ sk7 @ sk4 )
| ( sk1 @ sk4 @ sk5 )
| ( ( sk1 @ sk7 @ sk5 )
!= ( sk1 @ sk7 @ sk4 ) ) ),
inference(simp,[status(thm)],[502]) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = C )
| ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ( A != sk2 )
| ( C != sk7 ) ),
inference(paramod_ordered,[status(thm)],[26,27]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B = sk7 )
| ( sk1 @ A @ B )
| ( sk1 @ A @ sk7 )
| ( sk1 @ B @ sk7 )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk7 ))]]) ).
thf(136,plain,
! [A: $i] :
( ( sk2 = A )
| ( A = sk7 )
| ( sk1 @ sk2 @ A )
| ( sk1 @ sk2 @ sk7 )
| ( sk1 @ A @ sk7 ) ),
inference(simp,[status(thm)],[85]) ).
thf(31336,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ sk2 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[30977]) ).
thf(31371,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk2 @ sk5 )
| ( ( sk1 @ sk5 @ sk3 )
!= ( sk1 @ sk2 @ sk5 ) ) ),
inference(simp,[status(thm)],[31336]) ).
thf(99387,plain,
$false,
inference(e,[status(thm)],[76827,138,1031,7798,28981,7396,58615,3910,4960,142,3562,153,15384,26714,829,15637,24,6583,58460,8256,4030,37,504,12819,157,152,18511,8037,15601,2713,1115,25247,29,2829,11821,29167,5013,26916,6054,30977,147,31071,132,133,3870,4033,2833,8867,8999,15364,25267,11751,33,50747,2673,28,38,30776,137,5714,156,43449,141,15281,1567,2561,18521,76648,80492,11129,129,1002,4902,18248,41,134,128,2221,61618,2717,34,148,31568,149,6468,2859,2225,22,18262,29089,8993,6705,27,11070,5011,10948,144,12830,67242,10953,45608,8042,1117,2906,2945,39,1571,79744,2180,477,140,70409,155,7778,1029,130,15188,135,3,35,26899,9727,8936,29162,2597,145,10878,3913,30791,150,33229,127,2599,31,2948,32960,11830,154,143,9732,18085,10806,61791,40,26,158,30689,139,23,31049,6444,151,11131,36,146,30,79307,6703,3560,5709,506,6644,31447,126,136,18174,6209,3817,131,2138,469,1088,25058,31371]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEV108^5 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.12 % Command : run_Leo-III %s %d THM
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Jun 21 18:35:40 EDT 2024
% 0.14/0.34 % CPUTime :
% 1.00/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.99 % [INFO] Parsing done (103ms).
% 1.20/0.99 % [INFO] Running in sequential loop mode.
% 1.59/1.20 % [INFO] eprover registered as external prover.
% 1.69/1.20 % [INFO] Scanning for conjecture ...
% 1.81/1.27 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.81/1.29 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.81/1.30 % [INFO] Problem is higher-order (TPTP THF).
% 1.81/1.30 % [INFO] Type checking passed.
% 1.81/1.30 % [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 ...
% 67.56/17.77 % External prover 'e' found a proof!
% 67.56/17.77 % [INFO] Killing All external provers ...
% 67.56/17.77 % Time passed: 17232ms (effective reasoning time: 16772ms)
% 67.56/17.77 % 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)>
% 67.56/17.77 % Axioms used in derivation (0):
% 67.56/17.77 % No. of inferences in proof: 422
% 67.56/17.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 17232 ms resp. 16772 ms w/o parsing
% 67.56/17.88 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 67.56/17.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------