TSTP Solution File: GEO169+1 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GEO169+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.j1xAtovNfz true
% 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 : Wed Aug 30 23:57:02 EDT 2023
% Result : Theorem 59.45s 9.16s
% Output : Refutation 59.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 73
% Syntax : Number of formulae : 1695 ( 413 unt; 23 typ; 0 def)
% Number of atoms : 4438 ( 0 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 13342 (1780 ~;1848 |; 190 &;8796 @)
% ( 0 <=>; 19 =>; 709 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 23 usr; 21 con; 0-2 aty)
% Number of variables : 918 ( 0 ^; 918 !; 0 ?; 918 :)
% Comments :
%------------------------------------------------------------------------------
thf(ac_type,type,
ac: $i ).
thf(b1_type,type,
b1: $i ).
thf(a2b2_type,type,
a2b2: $i ).
thf(bc_type,type,
bc: $i ).
thf(a1b1_type,type,
a1b1: $i ).
thf(ob_type,type,
ob: $i ).
thf(ab_type,type,
ab: $i ).
thf(b1c1_type,type,
b1c1: $i ).
thf(incident_type,type,
incident: $i > $i > $o ).
thf(b2c2_type,type,
b2c2: $i ).
thf(point_equal_type,type,
point_equal: $i > $i > $o ).
thf(a1_type,type,
a1: $i ).
thf(line_equal_type,type,
line_equal: $i > $i > $o ).
thf(oa_type,type,
oa: $i ).
thf(oc_type,type,
oc: $i ).
thf(o_type,type,
o: $i ).
thf(a1c1_type,type,
a1c1: $i ).
thf(c1_type,type,
c1: $i ).
thf(a2c2_type,type,
a2c2: $i ).
thf(goal_type,type,
goal: $o ).
thf(b2_type,type,
b2: $i ).
thf(c2_type,type,
c2: $i ).
thf(a2_type,type,
a2: $i ).
thf(ib2c2,axiom,
incident @ b2 @ b2c2 ).
thf(zip_derived_cl17,plain,
incident @ b2 @ b2c2,
inference(cnf,[status(esa)],[ib2c2]) ).
thf(ia1oa,axiom,
incident @ a1 @ oa ).
thf(zip_derived_cl21,plain,
incident @ a1 @ oa,
inference(cnf,[status(esa)],[ia1oa]) ).
thf(unique,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( incident @ A @ C )
& ( incident @ A @ D )
& ( incident @ B @ C )
& ( incident @ B @ D ) )
=> ( ( point_equal @ A @ B )
| ( line_equal @ C @ D ) ) ) ).
thf(zip_derived_cl49,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl322,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ oa )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ oa @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl49]) ).
thf(zip_derived_cl1561,plain,
( ( point_equal @ b2 @ a1 )
| ~ ( incident @ b2 @ oa )
| ~ ( incident @ a1 @ b2c2 )
| ( line_equal @ oa @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl322]) ).
thf('0',plain,
( ~ ( incident @ b2 @ oa )
| ( point_equal @ b2 @ a1 )
| ( line_equal @ oa @ b2c2 )
| ~ ( incident @ a1 @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl1561]) ).
thf(gap_b,axiom,
( ( incident @ b1 @ a2c2 )
| ( incident @ c2 @ a1b1 ) ) ).
thf(zip_derived_cl4,plain,
( ( incident @ b1 @ a2c2 )
| ( incident @ c2 @ a1b1 ) ),
inference(cnf,[status(esa)],[gap_b]) ).
thf(zip_derived_cl63,plain,
( ( incident @ c2 @ a1b1 )
<= ( incident @ c2 @ a1b1 ) ),
inference(split,[status(esa)],[zip_derived_cl4]) ).
thf(gap_a,axiom,
( ( incident @ a1 @ b2c2 )
| ( incident @ b2 @ a1c1 ) ) ).
thf(zip_derived_cl3,plain,
( ( incident @ a1 @ b2c2 )
| ( incident @ b2 @ a1c1 ) ),
inference(cnf,[status(esa)],[gap_a]) ).
thf(zip_derived_cl62,plain,
( ( incident @ a1 @ b2c2 )
<= ( incident @ a1 @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl3]) ).
thf(zip_derived_cl49_001,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl319,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ b2c2 @ X1 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl49]) ).
thf(zip_derived_cl380,plain,
( ( ( point_equal @ c2 @ a1 )
| ~ ( incident @ c2 @ b2c2 )
| ~ ( incident @ a1 @ a1b1 )
| ( line_equal @ b2c2 @ a1b1 ) )
<= ( ( incident @ a1 @ b2c2 )
& ( incident @ c2 @ a1b1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl63,zip_derived_cl319]) ).
thf(ic2b2,axiom,
incident @ c2 @ b2c2 ).
thf(zip_derived_cl16,plain,
incident @ c2 @ b2c2,
inference(cnf,[status(esa)],[ic2b2]) ).
thf(ia1b1,axiom,
incident @ a1 @ a1b1 ).
thf(zip_derived_cl6,plain,
incident @ a1 @ a1b1,
inference(cnf,[status(esa)],[ia1b1]) ).
thf(zip_derived_cl408,plain,
( ( ( point_equal @ c2 @ a1 )
| ( line_equal @ b2c2 @ a1b1 ) )
<= ( ( incident @ a1 @ b2c2 )
& ( incident @ c2 @ a1b1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl380,zip_derived_cl16,zip_derived_cl6]) ).
thf(zip_derived_cl417,plain,
( ( line_equal @ b2c2 @ a1b1 )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference(split,[status(esa)],[zip_derived_cl408]) ).
thf(symmetry_of_line_equal,axiom,
! [A: $i,B: $i] :
( ( line_equal @ A @ B )
=> ( line_equal @ B @ A ) ) ).
thf(zip_derived_cl45,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl432,plain,
( ( line_equal @ a1b1 @ b2c2 )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl417,zip_derived_cl45]) ).
thf(lcon,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( incident @ A @ B )
& ( line_equal @ B @ C ) )
=> ( incident @ A @ C ) ) ).
thf(zip_derived_cl48,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl464,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ a1b1 )
| ( incident @ X0 @ b2c2 ) )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl432,zip_derived_cl48]) ).
thf(ib1a1,axiom,
incident @ b1 @ a1b1 ).
thf(zip_derived_cl7,plain,
incident @ b1 @ a1b1,
inference(cnf,[status(esa)],[ib1a1]) ).
thf(zip_derived_cl624,plain,
( ( incident @ b1 @ b2c2 )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl464,zip_derived_cl7]) ).
thf(ibc1,axiom,
incident @ bc @ b1c1 ).
thf(zip_derived_cl27,plain,
incident @ bc @ b1c1,
inference(cnf,[status(esa)],[ibc1]) ).
thf(zip_derived_cl49_002,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl314,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl49]) ).
thf(zip_derived_cl878,plain,
( ( ( point_equal @ b1 @ bc )
| ~ ( incident @ b1 @ b1c1 )
| ~ ( incident @ bc @ b2c2 )
| ( line_equal @ b1c1 @ b2c2 ) )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl624,zip_derived_cl314]) ).
thf(ib1c1,axiom,
incident @ b1 @ b1c1 ).
thf(zip_derived_cl15,plain,
incident @ b1 @ b1c1,
inference(cnf,[status(esa)],[ib1c1]) ).
thf(ibc2,axiom,
incident @ bc @ b2c2 ).
thf(zip_derived_cl28,plain,
incident @ bc @ b2c2,
inference(cnf,[status(esa)],[ibc2]) ).
thf(notbc,axiom,
( ( line_equal @ b1c1 @ b2c2 )
=> goal ) ).
thf(zip_derived_cl38,plain,
( goal
| ~ ( line_equal @ b1c1 @ b2c2 ) ),
inference(cnf,[status(esa)],[notbc]) ).
thf(zip_derived_cl77,plain,
( ~ ( line_equal @ b1c1 @ b2c2 )
<= ~ ( line_equal @ b1c1 @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl38]) ).
thf(goal_normal,axiom,
! [A: $i] :
( ( ( line_equal @ A @ A )
& ( incident @ bc @ A )
& ( incident @ ac @ A )
& ( incident @ ab @ A ) )
=> goal ) ).
thf(zip_derived_cl0,plain,
! [X0: $i] :
( goal
| ~ ( line_equal @ X0 @ X0 )
| ~ ( incident @ bc @ X0 )
| ~ ( incident @ ac @ X0 )
| ~ ( incident @ ab @ X0 ) ),
inference(cnf,[status(esa)],[goal_normal]) ).
thf(zip_derived_cl52,plain,
( goal
<= goal ),
inference(split,[status(esa)],[zip_derived_cl0]) ).
thf(goal_to_be_proved,conjecture,
goal ).
thf(zf_stmt_0,negated_conjecture,
~ goal,
inference('cnf.neg',[status(esa)],[goal_to_be_proved]) ).
thf(zip_derived_cl50,plain,
~ goal,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf('1',plain,
~ goal,
inference('s_sup-',[status(thm)],[zip_derived_cl52,zip_derived_cl50]) ).
thf('2',plain,
( ~ ( line_equal @ b1c1 @ b2c2 )
| goal ),
inference(split,[status(esa)],[zip_derived_cl38]) ).
thf('3',plain,
~ ( line_equal @ b1c1 @ b2c2 ),
inference('sat_resolution*',[status(thm)],['1','2']) ).
thf(zip_derived_cl87,plain,
~ ( line_equal @ b1c1 @ b2c2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl77,'3']) ).
thf(zip_derived_cl919,plain,
( ( point_equal @ b1 @ bc )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference(demod,[status(thm)],[zip_derived_cl878,zip_derived_cl15,zip_derived_cl28,zip_derived_cl87]) ).
thf(symmetry_of_point_equal,axiom,
! [A: $i,B: $i] :
( ( point_equal @ A @ B )
=> ( point_equal @ B @ A ) ) ).
thf(zip_derived_cl42,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl934,plain,
( ( point_equal @ bc @ b1 )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl919,zip_derived_cl42]) ).
thf(pcon,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( point_equal @ A @ B )
& ( incident @ B @ C ) )
=> ( incident @ A @ C ) ) ).
thf(zip_derived_cl47,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl939,plain,
( ! [X0: $i] :
( ~ ( incident @ b1 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl934,zip_derived_cl47]) ).
thf(zip_derived_cl64,plain,
( ( incident @ b1 @ a2c2 )
<= ( incident @ b1 @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl4]) ).
thf(zip_derived_cl1175,plain,
( ( incident @ bc @ a2c2 )
<= ( ( incident @ b1 @ a2c2 )
& ( line_equal @ b2c2 @ a1b1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl939,zip_derived_cl64]) ).
thf(gap_c,axiom,
( ( incident @ c1 @ a2b2 )
| ( incident @ a2 @ b1c1 ) ) ).
thf(zip_derived_cl5,plain,
( ( incident @ c1 @ a2b2 )
| ( incident @ a2 @ b1c1 ) ),
inference(cnf,[status(esa)],[gap_c]) ).
thf(zip_derived_cl65,plain,
( ( incident @ a2 @ b1c1 )
<= ( incident @ a2 @ b1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl5]) ).
thf(zip_derived_cl49_003,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl333,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a2 )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a2 @ X1 )
| ( line_equal @ b1c1 @ X1 ) )
<= ( incident @ a2 @ b1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl65,zip_derived_cl49]) ).
thf(zip_derived_cl2849,plain,
( ( ( point_equal @ bc @ a2 )
| ~ ( incident @ bc @ b1c1 )
| ~ ( incident @ a2 @ a2c2 )
| ( line_equal @ b1c1 @ a2c2 ) )
<= ( ( incident @ b1 @ a2c2 )
& ( incident @ a2 @ b1c1 )
& ( line_equal @ b2c2 @ a1b1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1175,zip_derived_cl333]) ).
thf(zip_derived_cl27_004,plain,
incident @ bc @ b1c1,
inference(cnf,[status(esa)],[ibc1]) ).
thf(ia2c2,axiom,
incident @ a2 @ a2c2 ).
thf(zip_derived_cl12,plain,
incident @ a2 @ a2c2,
inference(cnf,[status(esa)],[ia2c2]) ).
thf(zip_derived_cl2903,plain,
( ( ( point_equal @ bc @ a2 )
| ( line_equal @ b1c1 @ a2c2 ) )
<= ( ( incident @ b1 @ a2c2 )
& ( incident @ a2 @ b1c1 )
& ( line_equal @ b2c2 @ a1b1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2849,zip_derived_cl27,zip_derived_cl12]) ).
thf(zip_derived_cl2970,plain,
( ( line_equal @ b1c1 @ a2c2 )
<= ( line_equal @ b1c1 @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl2903]) ).
thf(zip_derived_cl48_005,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl2973,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ b1c1 )
| ( incident @ X0 @ a2c2 ) )
<= ( line_equal @ b1c1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2970,zip_derived_cl48]) ).
thf(ic1b1,axiom,
incident @ c1 @ b1c1 ).
thf(zip_derived_cl14,plain,
incident @ c1 @ b1c1,
inference(cnf,[status(esa)],[ic1b1]) ).
thf(zip_derived_cl11136,plain,
( ( incident @ c1 @ a2c2 )
<= ( line_equal @ b1c1 @ a2c2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2973,zip_derived_cl14]) ).
thf(zip_derived_cl1175_006,plain,
( ( incident @ bc @ a2c2 )
<= ( ( incident @ b1 @ a2c2 )
& ( line_equal @ b2c2 @ a1b1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl939,zip_derived_cl64]) ).
thf(zip_derived_cl66,plain,
( ( incident @ c1 @ a2b2 )
<= ( incident @ c1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl5]) ).
thf(zip_derived_cl49_007,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl327,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ a2b2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ a2b2 @ X1 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl49]) ).
thf(zip_derived_cl2121,plain,
( ( ( point_equal @ bc @ c1 )
| ~ ( incident @ bc @ a2b2 )
| ~ ( incident @ c1 @ a2c2 )
| ( line_equal @ a2b2 @ a2c2 ) )
<= ( ( incident @ b1 @ a2c2 )
& ( incident @ c1 @ a2b2 )
& ( line_equal @ b2c2 @ a1b1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1175,zip_derived_cl327]) ).
thf(zip_derived_cl2213,plain,
( ~ ( incident @ c1 @ a2c2 )
<= ~ ( incident @ c1 @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl2121]) ).
thf('4',plain,
( ~ ( line_equal @ b1c1 @ a2c2 )
| ( incident @ c1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11136,zip_derived_cl2213]) ).
thf(zip_derived_cl16_008,plain,
incident @ c2 @ b2c2,
inference(cnf,[status(esa)],[ic2b2]) ).
thf(zip_derived_cl64_009,plain,
( ( incident @ b1 @ a2c2 )
<= ( incident @ b1 @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl4]) ).
thf(zip_derived_cl49_010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl323,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ b1 )
| ~ ( incident @ X0 @ a2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ b1 @ X1 )
| ( line_equal @ a2c2 @ X1 ) )
<= ( incident @ b1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl49]) ).
thf(zip_derived_cl1672,plain,
( ( ( point_equal @ c2 @ b1 )
| ~ ( incident @ c2 @ a2c2 )
| ~ ( incident @ b1 @ b2c2 )
| ( line_equal @ a2c2 @ b2c2 ) )
<= ( incident @ b1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl323]) ).
thf(ic2a2,axiom,
incident @ c2 @ a2c2 ).
thf(zip_derived_cl13,plain,
incident @ c2 @ a2c2,
inference(cnf,[status(esa)],[ic2a2]) ).
thf(zip_derived_cl1714,plain,
( ( ( point_equal @ c2 @ b1 )
| ~ ( incident @ b1 @ b2c2 )
| ( line_equal @ a2c2 @ b2c2 ) )
<= ( incident @ b1 @ a2c2 ) ),
inference(demod,[status(thm)],[zip_derived_cl1672,zip_derived_cl13]) ).
thf(zip_derived_cl37505,plain,
( ( point_equal @ c2 @ b1 )
<= ( point_equal @ c2 @ b1 ) ),
inference(split,[status(esa)],[zip_derived_cl1714]) ).
thf(zip_derived_cl42_011,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl37510,plain,
( ( point_equal @ b1 @ c2 )
<= ( point_equal @ c2 @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl37505,zip_derived_cl42]) ).
thf(zip_derived_cl47_012,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl37520,plain,
( ! [X0: $i] :
( ~ ( incident @ c2 @ X0 )
| ( incident @ b1 @ X0 ) )
<= ( point_equal @ c2 @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl37510,zip_derived_cl47]) ).
thf(zip_derived_cl16_013,plain,
incident @ c2 @ b2c2,
inference(cnf,[status(esa)],[ic2b2]) ).
thf(zip_derived_cl45666,plain,
( ( incident @ b1 @ b2c2 )
<= ( point_equal @ c2 @ b1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl37520,zip_derived_cl16]) ).
thf(zip_derived_cl314_014,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl49]) ).
thf(zip_derived_cl45690,plain,
( ( ( point_equal @ b1 @ bc )
| ~ ( incident @ b1 @ b1c1 )
| ~ ( incident @ bc @ b2c2 )
| ( line_equal @ b1c1 @ b2c2 ) )
<= ( point_equal @ c2 @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl45666,zip_derived_cl314]) ).
thf(zip_derived_cl15_015,plain,
incident @ b1 @ b1c1,
inference(cnf,[status(esa)],[ib1c1]) ).
thf(zip_derived_cl28_016,plain,
incident @ bc @ b2c2,
inference(cnf,[status(esa)],[ibc2]) ).
thf(zip_derived_cl87_017,plain,
~ ( line_equal @ b1c1 @ b2c2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl77,'3']) ).
thf(zip_derived_cl45755,plain,
( ( point_equal @ b1 @ bc )
<= ( point_equal @ c2 @ b1 ) ),
inference(demod,[status(thm)],[zip_derived_cl45690,zip_derived_cl15,zip_derived_cl28,zip_derived_cl87]) ).
thf(zip_derived_cl42_018,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl46038,plain,
( ( point_equal @ bc @ b1 )
<= ( point_equal @ c2 @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl45755,zip_derived_cl42]) ).
thf(zip_derived_cl47_019,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl46066,plain,
( ! [X0: $i] :
( ~ ( incident @ b1 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( point_equal @ c2 @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl46038,zip_derived_cl47]) ).
thf(ib1ob,axiom,
incident @ b1 @ ob ).
thf(zip_derived_cl23,plain,
incident @ b1 @ ob,
inference(cnf,[status(esa)],[ib1ob]) ).
thf(zip_derived_cl52688,plain,
( ( incident @ bc @ ob )
<= ( point_equal @ c2 @ b1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl46066,zip_derived_cl23]) ).
thf(ioob,axiom,
incident @ o @ ob ).
thf(zip_derived_cl19,plain,
incident @ o @ ob,
inference(cnf,[status(esa)],[ioob]) ).
thf(reflexivity_of_line_equal,axiom,
! [A: $i,B: $i] :
( ( incident @ A @ B )
=> ( line_equal @ B @ B ) ) ).
thf(zip_derived_cl44,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X0 )
| ~ ( incident @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[reflexivity_of_line_equal]) ).
thf(zip_derived_cl187,plain,
line_equal @ ob @ ob,
inference('s_sup-',[status(thm)],[zip_derived_cl19,zip_derived_cl44]) ).
thf(zip_derived_cl51,plain,
( ! [X0: $i] :
( ~ ( line_equal @ X0 @ X0 )
| ~ ( incident @ bc @ X0 )
| ~ ( incident @ ac @ X0 )
| ~ ( incident @ ab @ X0 ) )
<= ! [X0: $i] :
( ~ ( line_equal @ X0 @ X0 )
| ~ ( incident @ bc @ X0 )
| ~ ( incident @ ac @ X0 )
| ~ ( incident @ ab @ X0 ) ) ),
inference(split,[status(esa)],[zip_derived_cl0]) ).
thf('5',plain,
( ! [X0: $i] :
( ~ ( line_equal @ X0 @ X0 )
| ~ ( incident @ bc @ X0 )
| ~ ( incident @ ac @ X0 )
| ~ ( incident @ ab @ X0 ) )
| goal ),
inference(split,[status(esa)],[zip_derived_cl0]) ).
thf('6',plain,
! [X0: $i] :
( ~ ( line_equal @ X0 @ X0 )
| ~ ( incident @ bc @ X0 )
| ~ ( incident @ ac @ X0 )
| ~ ( incident @ ab @ X0 ) ),
inference('sat_resolution*',[status(thm)],['1','5']) ).
thf(zip_derived_cl114,plain,
! [X0: $i] :
( ~ ( line_equal @ X0 @ X0 )
| ~ ( incident @ bc @ X0 )
| ~ ( incident @ ac @ X0 )
| ~ ( incident @ ab @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl51,'6']) ).
thf(zip_derived_cl536,plain,
( ~ ( incident @ bc @ ob )
| ~ ( incident @ ac @ ob )
| ~ ( incident @ ab @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl187,zip_derived_cl114]) ).
thf(zip_derived_cl542,plain,
( ~ ( incident @ bc @ ob )
<= ~ ( incident @ bc @ ob ) ),
inference(split,[status(esa)],[zip_derived_cl536]) ).
thf('7',plain,
( ~ ( point_equal @ c2 @ b1 )
| ( incident @ bc @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl52688,zip_derived_cl542]) ).
thf(zip_derived_cl64_020,plain,
( ( incident @ b1 @ a2c2 )
<= ( incident @ b1 @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl4]) ).
thf(zip_derived_cl319_021,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ b2c2 @ X1 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl49]) ).
thf(zip_derived_cl362,plain,
( ( ( point_equal @ b1 @ a1 )
| ~ ( incident @ b1 @ b2c2 )
| ~ ( incident @ a1 @ a2c2 )
| ( line_equal @ b2c2 @ a2c2 ) )
<= ( ( incident @ a1 @ b2c2 )
& ( incident @ b1 @ a2c2 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl319]) ).
thf(zip_derived_cl423,plain,
( ( line_equal @ b2c2 @ a2c2 )
<= ( line_equal @ b2c2 @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl362]) ).
thf(zip_derived_cl45_022,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl450,plain,
( ( line_equal @ a2c2 @ b2c2 )
<= ( line_equal @ b2c2 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl423,zip_derived_cl45]) ).
thf(zip_derived_cl48_023,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl478,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ a2c2 )
| ( incident @ X0 @ b2c2 ) )
<= ( line_equal @ b2c2 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl450,zip_derived_cl48]) ).
thf(zip_derived_cl12_024,plain,
incident @ a2 @ a2c2,
inference(cnf,[status(esa)],[ia2c2]) ).
thf(zip_derived_cl683,plain,
( ( incident @ a2 @ b2c2 )
<= ( line_equal @ b2c2 @ a2c2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl478,zip_derived_cl12]) ).
thf(zip_derived_cl16_025,plain,
incident @ c2 @ b2c2,
inference(cnf,[status(esa)],[ic2b2]) ).
thf(triangle2,axiom,
! [A: $i] :
( ( ( incident @ a2 @ A )
& ( incident @ b2 @ A )
& ( incident @ c2 @ A ) )
=> goal ) ).
thf(zip_derived_cl34,plain,
! [X0: $i] :
( goal
| ~ ( incident @ a2 @ X0 )
| ~ ( incident @ b2 @ X0 )
| ~ ( incident @ c2 @ X0 ) ),
inference(cnf,[status(esa)],[triangle2]) ).
thf(zip_derived_cl69,plain,
( ! [X0: $i] :
( ~ ( incident @ a2 @ X0 )
| ~ ( incident @ b2 @ X0 )
| ~ ( incident @ c2 @ X0 ) )
<= ! [X0: $i] :
( ~ ( incident @ a2 @ X0 )
| ~ ( incident @ b2 @ X0 )
| ~ ( incident @ c2 @ X0 ) ) ),
inference(split,[status(esa)],[zip_derived_cl34]) ).
thf('8',plain,
( ! [X0: $i] :
( ~ ( incident @ a2 @ X0 )
| ~ ( incident @ b2 @ X0 )
| ~ ( incident @ c2 @ X0 ) )
| goal ),
inference(split,[status(esa)],[zip_derived_cl34]) ).
thf('9',plain,
! [X0: $i] :
( ~ ( incident @ a2 @ X0 )
| ~ ( incident @ b2 @ X0 )
| ~ ( incident @ c2 @ X0 ) ),
inference('sat_resolution*',[status(thm)],['1','8']) ).
thf(zip_derived_cl107,plain,
! [X0: $i] :
( ~ ( incident @ a2 @ X0 )
| ~ ( incident @ b2 @ X0 )
| ~ ( incident @ c2 @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl69,'9']) ).
thf(zip_derived_cl165,plain,
( ~ ( incident @ a2 @ b2c2 )
| ~ ( incident @ b2 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl107]) ).
thf(zip_derived_cl17_026,plain,
incident @ b2 @ b2c2,
inference(cnf,[status(esa)],[ib2c2]) ).
thf(zip_derived_cl173,plain,
~ ( incident @ a2 @ b2c2 ),
inference(demod,[status(thm)],[zip_derived_cl165,zip_derived_cl17]) ).
thf('10',plain,
~ ( line_equal @ b2c2 @ a2c2 ),
inference('s_sup-',[status(thm)],[zip_derived_cl683,zip_derived_cl173]) ).
thf(iac2,axiom,
incident @ ac @ a2c2 ).
thf(zip_derived_cl30,plain,
incident @ ac @ a2c2,
inference(cnf,[status(esa)],[iac2]) ).
thf(zip_derived_cl28_027,plain,
incident @ bc @ b2c2,
inference(cnf,[status(esa)],[ibc2]) ).
thf(zip_derived_cl49_028,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl313,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b2c2 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl28,zip_derived_cl49]) ).
thf(zip_derived_cl754,plain,
( ( point_equal @ ac @ bc )
| ~ ( incident @ ac @ b2c2 )
| ~ ( incident @ bc @ a2c2 )
| ( line_equal @ b2c2 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl313]) ).
thf('11',plain,
( ( point_equal @ ac @ bc )
| ( line_equal @ b2c2 @ a2c2 )
| ~ ( incident @ ac @ b2c2 )
| ~ ( incident @ bc @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl754]) ).
thf(zip_derived_cl16_029,plain,
incident @ c2 @ b2c2,
inference(cnf,[status(esa)],[ic2b2]) ).
thf(zip_derived_cl1175_030,plain,
( ( incident @ bc @ a2c2 )
<= ( ( incident @ b1 @ a2c2 )
& ( line_equal @ b2c2 @ a1b1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl939,zip_derived_cl64]) ).
thf(zip_derived_cl319_031,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ b2c2 @ X1 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl49]) ).
thf(zip_derived_cl1205,plain,
( ( ( point_equal @ bc @ a1 )
| ~ ( incident @ bc @ b2c2 )
| ~ ( incident @ a1 @ a2c2 )
| ( line_equal @ b2c2 @ a2c2 ) )
<= ( ( incident @ a1 @ b2c2 )
& ( incident @ b1 @ a2c2 )
& ( line_equal @ b2c2 @ a1b1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1175,zip_derived_cl319]) ).
thf(zip_derived_cl28_032,plain,
incident @ bc @ b2c2,
inference(cnf,[status(esa)],[ibc2]) ).
thf(zip_derived_cl1213,plain,
( ( ( point_equal @ bc @ a1 )
| ~ ( incident @ a1 @ a2c2 )
| ( line_equal @ b2c2 @ a2c2 ) )
<= ( ( incident @ a1 @ b2c2 )
& ( incident @ b1 @ a2c2 )
& ( line_equal @ b2c2 @ a1b1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1205,zip_derived_cl28]) ).
thf(zip_derived_cl1214,plain,
( ( point_equal @ bc @ a1 )
<= ( point_equal @ bc @ a1 ) ),
inference(split,[status(esa)],[zip_derived_cl1213]) ).
thf(zip_derived_cl42_033,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl1219,plain,
( ( point_equal @ a1 @ bc )
<= ( point_equal @ bc @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1214,zip_derived_cl42]) ).
thf(zip_derived_cl61,plain,
( ( incident @ b2 @ a1c1 )
<= ( incident @ b2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl3]) ).
thf(zip_derived_cl319_034,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ b2c2 @ X1 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl49]) ).
thf(zip_derived_cl376,plain,
( ( ( point_equal @ b2 @ a1 )
| ~ ( incident @ b2 @ b2c2 )
| ~ ( incident @ a1 @ a1c1 )
| ( line_equal @ b2c2 @ a1c1 ) )
<= ( ( incident @ a1 @ b2c2 )
& ( incident @ b2 @ a1c1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl319]) ).
thf(zip_derived_cl17_035,plain,
incident @ b2 @ b2c2,
inference(cnf,[status(esa)],[ib2c2]) ).
thf(ia1c1,axiom,
incident @ a1 @ a1c1 ).
thf(zip_derived_cl10,plain,
incident @ a1 @ a1c1,
inference(cnf,[status(esa)],[ia1c1]) ).
thf(zip_derived_cl404,plain,
( ( ( point_equal @ b2 @ a1 )
| ( line_equal @ b2c2 @ a1c1 ) )
<= ( ( incident @ a1 @ b2c2 )
& ( incident @ b2 @ a1c1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl376,zip_derived_cl17,zip_derived_cl10]) ).
thf(zip_derived_cl411,plain,
( ( point_equal @ b2 @ a1 )
<= ( point_equal @ b2 @ a1 ) ),
inference(split,[status(esa)],[zip_derived_cl404]) ).
thf(transitivity_of_point_equal,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( point_equal @ A @ B )
& ( point_equal @ B @ C ) )
=> ( point_equal @ A @ C ) ) ).
thf(zip_derived_cl43,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X2 )
| ( point_equal @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[transitivity_of_point_equal]) ).
thf(zip_derived_cl413,plain,
( ! [X0: $i] :
( ~ ( point_equal @ a1 @ X0 )
| ( point_equal @ b2 @ X0 ) )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl411,zip_derived_cl43]) ).
thf(zip_derived_cl42_036,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl841,plain,
( ! [X0: $i] :
( ~ ( point_equal @ a1 @ X0 )
| ( point_equal @ X0 @ b2 ) )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl413,zip_derived_cl42]) ).
thf(zip_derived_cl1405,plain,
( ( point_equal @ bc @ b2 )
<= ( ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1219,zip_derived_cl841]) ).
thf(zip_derived_cl47_037,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl1522,plain,
( ! [X0: $i] :
( ~ ( incident @ b2 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1405,zip_derived_cl47]) ).
thf(zip_derived_cl61_038,plain,
( ( incident @ b2 @ a1c1 )
<= ( incident @ b2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl3]) ).
thf(zip_derived_cl2317,plain,
( ( incident @ bc @ a1c1 )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1522,zip_derived_cl61]) ).
thf(zip_derived_cl49_039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl2341,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ a1c1 @ X1 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2317,zip_derived_cl49]) ).
thf(zip_derived_cl3355,plain,
( ( ( point_equal @ c2 @ bc )
| ~ ( incident @ c2 @ a1c1 )
| ~ ( incident @ bc @ b2c2 )
| ( line_equal @ a1c1 @ b2c2 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl2341]) ).
thf(zip_derived_cl28_040,plain,
incident @ bc @ b2c2,
inference(cnf,[status(esa)],[ibc2]) ).
thf(zip_derived_cl3407,plain,
( ( ( point_equal @ c2 @ bc )
| ~ ( incident @ c2 @ a1c1 )
| ( line_equal @ a1c1 @ b2c2 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3355,zip_derived_cl28]) ).
thf(zip_derived_cl4512,plain,
( ( line_equal @ a1c1 @ b2c2 )
<= ( line_equal @ a1c1 @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl3407]) ).
thf(zip_derived_cl48_041,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl4515,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ a1c1 )
| ( incident @ X0 @ b2c2 ) )
<= ( line_equal @ a1c1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4512,zip_derived_cl48]) ).
thf(ic1a1,axiom,
incident @ c1 @ a1c1 ).
thf(zip_derived_cl11,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl16569,plain,
( ( incident @ c1 @ b2c2 )
<= ( line_equal @ a1c1 @ b2c2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4515,zip_derived_cl11]) ).
thf(zip_derived_cl66_042,plain,
( ( incident @ c1 @ a2b2 )
<= ( incident @ c1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl5]) ).
thf(zip_derived_cl319_043,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ b2c2 @ X1 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl49]) ).
thf(zip_derived_cl366,plain,
( ( ( point_equal @ c1 @ a1 )
| ~ ( incident @ c1 @ b2c2 )
| ~ ( incident @ a1 @ a2b2 )
| ( line_equal @ b2c2 @ a2b2 ) )
<= ( ( incident @ a1 @ b2c2 )
& ( incident @ c1 @ a2b2 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl319]) ).
thf(zip_derived_cl442,plain,
( ~ ( incident @ c1 @ b2c2 )
<= ~ ( incident @ c1 @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl366]) ).
thf('12',plain,
( ~ ( line_equal @ a1c1 @ b2c2 )
| ( incident @ c1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl16569,zip_derived_cl442]) ).
thf(zip_derived_cl28_044,plain,
incident @ bc @ b2c2,
inference(cnf,[status(esa)],[ibc2]) ).
thf(zip_derived_cl10_045,plain,
incident @ a1 @ a1c1,
inference(cnf,[status(esa)],[ia1c1]) ).
thf(zip_derived_cl49_046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl320,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ a1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl49]) ).
thf(zip_derived_cl1316,plain,
( ( point_equal @ bc @ a1 )
| ~ ( incident @ bc @ a1c1 )
| ~ ( incident @ a1 @ b2c2 )
| ( line_equal @ a1c1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl28,zip_derived_cl320]) ).
thf('13',plain,
( ~ ( incident @ bc @ a1c1 )
| ( line_equal @ a1c1 @ b2c2 )
| ( point_equal @ bc @ a1 )
| ~ ( incident @ a1 @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl1316]) ).
thf(zip_derived_cl30_047,plain,
incident @ ac @ a2c2,
inference(cnf,[status(esa)],[iac2]) ).
thf(zip_derived_cl2341_048,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ a1c1 @ X1 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2317,zip_derived_cl49]) ).
thf(zip_derived_cl3320,plain,
( ( ( point_equal @ ac @ bc )
| ~ ( incident @ ac @ a1c1 )
| ~ ( incident @ bc @ a2c2 )
| ( line_equal @ a1c1 @ a2c2 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl2341]) ).
thf(iac1,axiom,
incident @ ac @ a1c1 ).
thf(zip_derived_cl29,plain,
incident @ ac @ a1c1,
inference(cnf,[status(esa)],[iac1]) ).
thf(notac,axiom,
( ( line_equal @ a1c1 @ a2c2 )
=> goal ) ).
thf(zip_derived_cl39,plain,
( goal
| ~ ( line_equal @ a1c1 @ a2c2 ) ),
inference(cnf,[status(esa)],[notac]) ).
thf(zip_derived_cl79,plain,
( ~ ( line_equal @ a1c1 @ a2c2 )
<= ~ ( line_equal @ a1c1 @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl39]) ).
thf('14',plain,
( ~ ( line_equal @ a1c1 @ a2c2 )
| goal ),
inference(split,[status(esa)],[zip_derived_cl39]) ).
thf('15',plain,
~ ( line_equal @ a1c1 @ a2c2 ),
inference('sat_resolution*',[status(thm)],['1','14']) ).
thf(zip_derived_cl88,plain,
~ ( line_equal @ a1c1 @ a2c2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl79,'15']) ).
thf(zip_derived_cl3374,plain,
( ( ( point_equal @ ac @ bc )
| ~ ( incident @ bc @ a2c2 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3320,zip_derived_cl29,zip_derived_cl88]) ).
thf(zip_derived_cl3856,plain,
( ( point_equal @ ac @ bc )
<= ( point_equal @ ac @ bc ) ),
inference(split,[status(esa)],[zip_derived_cl3374]) ).
thf(zip_derived_cl42_049,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl3860,plain,
( ( point_equal @ bc @ ac )
<= ( point_equal @ ac @ bc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl3856,zip_derived_cl42]) ).
thf(zip_derived_cl47_050,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl4073,plain,
( ! [X0: $i] :
( ~ ( incident @ ac @ X0 )
| ( incident @ bc @ X0 ) )
<= ( point_equal @ ac @ bc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl3860,zip_derived_cl47]) ).
thf(zip_derived_cl29_051,plain,
incident @ ac @ a1c1,
inference(cnf,[status(esa)],[iac1]) ).
thf(zip_derived_cl14378,plain,
( ( incident @ bc @ a1c1 )
<= ( point_equal @ ac @ bc ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4073,zip_derived_cl29]) ).
thf(zip_derived_cl61_052,plain,
( ( incident @ b2 @ a1c1 )
<= ( incident @ b2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl3]) ).
thf(zip_derived_cl44_053,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X0 )
| ~ ( incident @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[reflexivity_of_line_equal]) ).
thf(zip_derived_cl159,plain,
( ( line_equal @ a1c1 @ a1c1 )
<= ( incident @ b2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl44]) ).
thf(zip_derived_cl114_054,plain,
! [X0: $i] :
( ~ ( line_equal @ X0 @ X0 )
| ~ ( incident @ bc @ X0 )
| ~ ( incident @ ac @ X0 )
| ~ ( incident @ ab @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl51,'6']) ).
thf(zip_derived_cl170,plain,
( ( ~ ( incident @ bc @ a1c1 )
| ~ ( incident @ ac @ a1c1 )
| ~ ( incident @ ab @ a1c1 ) )
<= ( incident @ b2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl159,zip_derived_cl114]) ).
thf(zip_derived_cl194,plain,
( ~ ( incident @ bc @ a1c1 )
<= ~ ( incident @ bc @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl170]) ).
thf('16',plain,
( ~ ( point_equal @ ac @ bc )
| ( incident @ bc @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl14378,zip_derived_cl194]) ).
thf(zip_derived_cl28_055,plain,
incident @ bc @ b2c2,
inference(cnf,[status(esa)],[ibc2]) ).
thf(zip_derived_cl322_056,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ oa )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ oa @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl49]) ).
thf(zip_derived_cl1524,plain,
( ( point_equal @ bc @ a1 )
| ~ ( incident @ bc @ oa )
| ~ ( incident @ a1 @ b2c2 )
| ( line_equal @ oa @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl28,zip_derived_cl322]) ).
thf(zip_derived_cl31031,plain,
( ( line_equal @ oa @ b2c2 )
<= ( line_equal @ oa @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl1524]) ).
thf(zip_derived_cl48_057,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl31037,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ oa )
| ( incident @ X0 @ b2c2 ) )
<= ( line_equal @ oa @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl31031,zip_derived_cl48]) ).
thf(ia2oa,axiom,
incident @ a2 @ oa ).
thf(zip_derived_cl22,plain,
incident @ a2 @ oa,
inference(cnf,[status(esa)],[ia2oa]) ).
thf(zip_derived_cl40788,plain,
( ( incident @ a2 @ b2c2 )
<= ( line_equal @ oa @ b2c2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl31037,zip_derived_cl22]) ).
thf(zip_derived_cl173_058,plain,
~ ( incident @ a2 @ b2c2 ),
inference(demod,[status(thm)],[zip_derived_cl165,zip_derived_cl17]) ).
thf('17',plain,
~ ( line_equal @ oa @ b2c2 ),
inference('s_sup-',[status(thm)],[zip_derived_cl40788,zip_derived_cl173]) ).
thf(zip_derived_cl1219_059,plain,
( ( point_equal @ a1 @ bc )
<= ( point_equal @ bc @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1214,zip_derived_cl42]) ).
thf(zip_derived_cl47_060,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl1403,plain,
( ! [X0: $i] :
( ~ ( incident @ bc @ X0 )
| ( incident @ a1 @ X0 ) )
<= ( point_equal @ bc @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1219,zip_derived_cl47]) ).
thf(zip_derived_cl14_061,plain,
incident @ c1 @ b1c1,
inference(cnf,[status(esa)],[ic1b1]) ).
thf(triangle1,axiom,
! [A: $i] :
( ( ( incident @ a1 @ A )
& ( incident @ b1 @ A )
& ( incident @ c1 @ A ) )
=> goal ) ).
thf(zip_derived_cl33,plain,
! [X0: $i] :
( goal
| ~ ( incident @ a1 @ X0 )
| ~ ( incident @ b1 @ X0 )
| ~ ( incident @ c1 @ X0 ) ),
inference(cnf,[status(esa)],[triangle1]) ).
thf(zip_derived_cl67,plain,
( ! [X0: $i] :
( ~ ( incident @ a1 @ X0 )
| ~ ( incident @ b1 @ X0 )
| ~ ( incident @ c1 @ X0 ) )
<= ! [X0: $i] :
( ~ ( incident @ a1 @ X0 )
| ~ ( incident @ b1 @ X0 )
| ~ ( incident @ c1 @ X0 ) ) ),
inference(split,[status(esa)],[zip_derived_cl33]) ).
thf('18',plain,
( ! [X0: $i] :
( ~ ( incident @ a1 @ X0 )
| ~ ( incident @ b1 @ X0 )
| ~ ( incident @ c1 @ X0 ) )
| goal ),
inference(split,[status(esa)],[zip_derived_cl33]) ).
thf('19',plain,
! [X0: $i] :
( ~ ( incident @ a1 @ X0 )
| ~ ( incident @ b1 @ X0 )
| ~ ( incident @ c1 @ X0 ) ),
inference('sat_resolution*',[status(thm)],['1','18']) ).
thf(zip_derived_cl96,plain,
! [X0: $i] :
( ~ ( incident @ a1 @ X0 )
| ~ ( incident @ b1 @ X0 )
| ~ ( incident @ c1 @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl67,'19']) ).
thf(zip_derived_cl134,plain,
( ~ ( incident @ a1 @ b1c1 )
| ~ ( incident @ b1 @ b1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl96]) ).
thf(zip_derived_cl15_062,plain,
incident @ b1 @ b1c1,
inference(cnf,[status(esa)],[ib1c1]) ).
thf(zip_derived_cl137,plain,
~ ( incident @ a1 @ b1c1 ),
inference(demod,[status(thm)],[zip_derived_cl134,zip_derived_cl15]) ).
thf(zip_derived_cl28176,plain,
( ~ ( incident @ bc @ b1c1 )
<= ( point_equal @ bc @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1403,zip_derived_cl137]) ).
thf(zip_derived_cl27_063,plain,
incident @ bc @ b1c1,
inference(cnf,[status(esa)],[ibc1]) ).
thf('20',plain,
~ ( point_equal @ bc @ a1 ),
inference(demod,[status(thm)],[zip_derived_cl28176,zip_derived_cl27]) ).
thf('21',plain,
( ( line_equal @ oa @ b2c2 )
| ( point_equal @ bc @ a1 )
| ~ ( incident @ a1 @ b2c2 )
| ~ ( incident @ bc @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl1524]) ).
thf(zip_derived_cl65_064,plain,
( ( incident @ a2 @ b1c1 )
<= ( incident @ a2 @ b1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl5]) ).
thf(zip_derived_cl2341_065,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ a1c1 @ X1 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2317,zip_derived_cl49]) ).
thf(zip_derived_cl3349,plain,
( ( ( point_equal @ a2 @ bc )
| ~ ( incident @ a2 @ a1c1 )
| ~ ( incident @ bc @ b1c1 )
| ( line_equal @ a1c1 @ b1c1 ) )
<= ( ( incident @ a2 @ b1c1 )
& ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl65,zip_derived_cl2341]) ).
thf(zip_derived_cl27_066,plain,
incident @ bc @ b1c1,
inference(cnf,[status(esa)],[ibc1]) ).
thf(zip_derived_cl3402,plain,
( ( ( point_equal @ a2 @ bc )
| ~ ( incident @ a2 @ a1c1 )
| ( line_equal @ a1c1 @ b1c1 ) )
<= ( ( incident @ a2 @ b1c1 )
& ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3349,zip_derived_cl27]) ).
thf(zip_derived_cl3753,plain,
( ( point_equal @ a2 @ bc )
<= ( point_equal @ a2 @ bc ) ),
inference(split,[status(esa)],[zip_derived_cl3402]) ).
thf(zip_derived_cl42_067,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl3961,plain,
( ( point_equal @ bc @ a2 )
<= ( point_equal @ a2 @ bc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl3753,zip_derived_cl42]) ).
thf(zip_derived_cl47_068,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl4076,plain,
( ! [X0: $i] :
( ~ ( incident @ a2 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( point_equal @ a2 @ bc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl3961,zip_derived_cl47]) ).
thf(zip_derived_cl22_069,plain,
incident @ a2 @ oa,
inference(cnf,[status(esa)],[ia2oa]) ).
thf(zip_derived_cl14626,plain,
( ( incident @ bc @ oa )
<= ( point_equal @ a2 @ bc ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4076,zip_derived_cl22]) ).
thf(iooa,axiom,
incident @ o @ oa ).
thf(zip_derived_cl18,plain,
incident @ o @ oa,
inference(cnf,[status(esa)],[iooa]) ).
thf(zip_derived_cl44_070,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X0 )
| ~ ( incident @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[reflexivity_of_line_equal]) ).
thf(zip_derived_cl179,plain,
line_equal @ oa @ oa,
inference('s_sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl44]) ).
thf(zip_derived_cl114_071,plain,
! [X0: $i] :
( ~ ( line_equal @ X0 @ X0 )
| ~ ( incident @ bc @ X0 )
| ~ ( incident @ ac @ X0 )
| ~ ( incident @ ab @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl51,'6']) ).
thf(zip_derived_cl528,plain,
( ~ ( incident @ bc @ oa )
| ~ ( incident @ ac @ oa )
| ~ ( incident @ ab @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl179,zip_derived_cl114]) ).
thf(zip_derived_cl534,plain,
( ~ ( incident @ bc @ oa )
<= ~ ( incident @ bc @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl528]) ).
thf('22',plain,
( ~ ( point_equal @ a2 @ bc )
| ( incident @ bc @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl14626,zip_derived_cl534]) ).
thf(zip_derived_cl412,plain,
( ( line_equal @ b2c2 @ a1c1 )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl404]) ).
thf(zip_derived_cl45_072,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl426,plain,
( ( line_equal @ a1c1 @ b2c2 )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl412,zip_derived_cl45]) ).
thf(zip_derived_cl48_073,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl454,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ a1c1 )
| ( incident @ X0 @ b2c2 ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl426,zip_derived_cl48]) ).
thf(zip_derived_cl11_074,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl590,plain,
( ( incident @ c1 @ b2c2 )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl454,zip_derived_cl11]) ).
thf(zip_derived_cl314_075,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl49]) ).
thf(zip_derived_cl883,plain,
( ( ( point_equal @ c1 @ bc )
| ~ ( incident @ c1 @ b1c1 )
| ~ ( incident @ bc @ b2c2 )
| ( line_equal @ b1c1 @ b2c2 ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl590,zip_derived_cl314]) ).
thf(zip_derived_cl14_076,plain,
incident @ c1 @ b1c1,
inference(cnf,[status(esa)],[ic1b1]) ).
thf(zip_derived_cl28_077,plain,
incident @ bc @ b2c2,
inference(cnf,[status(esa)],[ibc2]) ).
thf(zip_derived_cl87_078,plain,
~ ( line_equal @ b1c1 @ b2c2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl77,'3']) ).
thf(zip_derived_cl924,plain,
( ( point_equal @ c1 @ bc )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl883,zip_derived_cl14,zip_derived_cl28,zip_derived_cl87]) ).
thf(zip_derived_cl42_079,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl937,plain,
( ( point_equal @ bc @ c1 )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl924,zip_derived_cl42]) ).
thf(zip_derived_cl47_080,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl1016,plain,
( ! [X0: $i] :
( ~ ( incident @ c1 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl937,zip_derived_cl47]) ).
thf(zip_derived_cl66_081,plain,
( ( incident @ c1 @ a2b2 )
<= ( incident @ c1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl5]) ).
thf(zip_derived_cl1942,plain,
( ( incident @ bc @ a2b2 )
<= ( ( incident @ c1 @ a2b2 )
& ( line_equal @ b2c2 @ a1c1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1016,zip_derived_cl66]) ).
thf(zip_derived_cl333_082,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a2 )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a2 @ X1 )
| ( line_equal @ b1c1 @ X1 ) )
<= ( incident @ a2 @ b1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl65,zip_derived_cl49]) ).
thf(zip_derived_cl2850,plain,
( ( ( point_equal @ bc @ a2 )
| ~ ( incident @ bc @ b1c1 )
| ~ ( incident @ a2 @ a2b2 )
| ( line_equal @ b1c1 @ a2b2 ) )
<= ( ( incident @ c1 @ a2b2 )
& ( incident @ a2 @ b1c1 )
& ( line_equal @ b2c2 @ a1c1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1942,zip_derived_cl333]) ).
thf(zip_derived_cl27_083,plain,
incident @ bc @ b1c1,
inference(cnf,[status(esa)],[ibc1]) ).
thf(ia2b2,axiom,
incident @ a2 @ a2b2 ).
thf(zip_derived_cl8,plain,
incident @ a2 @ a2b2,
inference(cnf,[status(esa)],[ia2b2]) ).
thf(zip_derived_cl2904,plain,
( ( ( point_equal @ bc @ a2 )
| ( line_equal @ b1c1 @ a2b2 ) )
<= ( ( incident @ c1 @ a2b2 )
& ( incident @ a2 @ b1c1 )
& ( line_equal @ b2c2 @ a1c1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2850,zip_derived_cl27,zip_derived_cl8]) ).
thf(zip_derived_cl2975,plain,
( ( line_equal @ b1c1 @ a2b2 )
<= ( line_equal @ b1c1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl2904]) ).
thf(zip_derived_cl48_084,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl2978,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ b1c1 )
| ( incident @ X0 @ a2b2 ) )
<= ( line_equal @ b1c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2975,zip_derived_cl48]) ).
thf(zip_derived_cl14_085,plain,
incident @ c1 @ b1c1,
inference(cnf,[status(esa)],[ic1b1]) ).
thf(zip_derived_cl11478,plain,
( ( incident @ c1 @ a2b2 )
<= ( line_equal @ b1c1 @ a2b2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2978,zip_derived_cl14]) ).
thf(t1in2,axiom,
( ( ( incident @ a1 @ b2c2 )
& ( incident @ b1 @ a2c2 )
& ( incident @ c1 @ a2b2 ) )
=> goal ) ).
thf(zip_derived_cl1,plain,
( goal
| ~ ( incident @ c1 @ a2b2 )
| ~ ( incident @ b1 @ a2c2 )
| ~ ( incident @ a1 @ b2c2 ) ),
inference(cnf,[status(esa)],[t1in2]) ).
thf(zip_derived_cl55,plain,
( ~ ( incident @ c1 @ a2b2 )
<= ~ ( incident @ c1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl1]) ).
thf('23',plain,
( ~ ( line_equal @ b1c1 @ a2b2 )
| ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11478,zip_derived_cl55]) ).
thf(zip_derived_cl8_086,plain,
incident @ a2 @ a2b2,
inference(cnf,[status(esa)],[ia2b2]) ).
thf(zip_derived_cl314_087,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl49]) ).
thf(zip_derived_cl889,plain,
( ( point_equal @ a2 @ bc )
| ~ ( incident @ a2 @ b1c1 )
| ~ ( incident @ bc @ a2b2 )
| ( line_equal @ b1c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl8,zip_derived_cl314]) ).
thf('24',plain,
( ~ ( incident @ bc @ a2b2 )
| ~ ( incident @ a2 @ b1c1 )
| ( point_equal @ a2 @ bc )
| ( line_equal @ b1c1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl889]) ).
thf(zip_derived_cl416,plain,
( ( point_equal @ c2 @ a1 )
<= ( point_equal @ c2 @ a1 ) ),
inference(split,[status(esa)],[zip_derived_cl408]) ).
thf(zip_derived_cl42_088,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl420,plain,
( ( point_equal @ a1 @ c2 )
<= ( point_equal @ c2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl416,zip_derived_cl42]) ).
thf(zip_derived_cl841_089,plain,
( ! [X0: $i] :
( ~ ( point_equal @ a1 @ X0 )
| ( point_equal @ X0 @ b2 ) )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl413,zip_derived_cl42]) ).
thf(zip_derived_cl849,plain,
( ( point_equal @ c2 @ b2 )
<= ( ( point_equal @ b2 @ a1 )
& ( point_equal @ c2 @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl420,zip_derived_cl841]) ).
thf(zip_derived_cl42_090,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl852,plain,
( ( point_equal @ b2 @ c2 )
<= ( ( point_equal @ b2 @ a1 )
& ( point_equal @ c2 @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl849,zip_derived_cl42]) ).
thf(zip_derived_cl47_091,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl855,plain,
( ! [X0: $i] :
( ~ ( incident @ c2 @ X0 )
| ( incident @ b2 @ X0 ) )
<= ( ( point_equal @ b2 @ a1 )
& ( point_equal @ c2 @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl852,zip_derived_cl47]) ).
thf(zip_derived_cl63_092,plain,
( ( incident @ c2 @ a1b1 )
<= ( incident @ c2 @ a1b1 ) ),
inference(split,[status(esa)],[zip_derived_cl4]) ).
thf(zip_derived_cl1310,plain,
( ( incident @ b2 @ a1b1 )
<= ( ( incident @ c2 @ a1b1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ c2 @ a1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl855,zip_derived_cl63]) ).
thf(zip_derived_cl313_093,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b2c2 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl28,zip_derived_cl49]) ).
thf(zip_derived_cl1411,plain,
( ( ( point_equal @ b2 @ bc )
| ~ ( incident @ b2 @ b2c2 )
| ~ ( incident @ bc @ a1b1 )
| ( line_equal @ b2c2 @ a1b1 ) )
<= ( ( incident @ c2 @ a1b1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ c2 @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1310,zip_derived_cl313]) ).
thf(zip_derived_cl17_094,plain,
incident @ b2 @ b2c2,
inference(cnf,[status(esa)],[ib2c2]) ).
thf(zip_derived_cl1424,plain,
( ( ( point_equal @ b2 @ bc )
| ~ ( incident @ bc @ a1b1 )
| ( line_equal @ b2c2 @ a1b1 ) )
<= ( ( incident @ c2 @ a1b1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ c2 @ a1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1411,zip_derived_cl17]) ).
thf(zip_derived_cl1619,plain,
( ( point_equal @ b2 @ bc )
<= ( point_equal @ b2 @ bc ) ),
inference(split,[status(esa)],[zip_derived_cl1424]) ).
thf(zip_derived_cl42_095,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl1624,plain,
( ( point_equal @ bc @ b2 )
<= ( point_equal @ b2 @ bc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1619,zip_derived_cl42]) ).
thf(zip_derived_cl47_096,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl1745,plain,
( ! [X0: $i] :
( ~ ( incident @ b2 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( point_equal @ b2 @ bc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1624,zip_derived_cl47]) ).
thf(ib2a2,axiom,
incident @ b2 @ a2b2 ).
thf(zip_derived_cl9,plain,
incident @ b2 @ a2b2,
inference(cnf,[status(esa)],[ib2a2]) ).
thf(zip_derived_cl7409,plain,
( ( incident @ bc @ a2b2 )
<= ( point_equal @ b2 @ bc ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1745,zip_derived_cl9]) ).
thf(zip_derived_cl66_097,plain,
( ( incident @ c1 @ a2b2 )
<= ( incident @ c1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl5]) ).
thf(zip_derived_cl44_098,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X0 )
| ~ ( incident @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[reflexivity_of_line_equal]) ).
thf(zip_derived_cl152,plain,
( ( line_equal @ a2b2 @ a2b2 )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl44]) ).
thf(zip_derived_cl114_099,plain,
! [X0: $i] :
( ~ ( line_equal @ X0 @ X0 )
| ~ ( incident @ bc @ X0 )
| ~ ( incident @ ac @ X0 )
| ~ ( incident @ ab @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl51,'6']) ).
thf(zip_derived_cl168,plain,
( ( ~ ( incident @ bc @ a2b2 )
| ~ ( incident @ ac @ a2b2 )
| ~ ( incident @ ab @ a2b2 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl152,zip_derived_cl114]) ).
thf(zip_derived_cl184,plain,
( ~ ( incident @ bc @ a2b2 )
<= ~ ( incident @ bc @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl168]) ).
thf('25',plain,
( ~ ( point_equal @ b2 @ bc )
| ( incident @ bc @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl7409,zip_derived_cl184]) ).
thf(zip_derived_cl18_100,plain,
incident @ o @ oa,
inference(cnf,[status(esa)],[iooa]) ).
thf(zip_derived_cl319_101,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ b2c2 @ X1 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl49]) ).
thf(zip_derived_cl382,plain,
( ( ( point_equal @ o @ a1 )
| ~ ( incident @ o @ b2c2 )
| ~ ( incident @ a1 @ oa )
| ( line_equal @ b2c2 @ oa ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl319]) ).
thf(zip_derived_cl21_102,plain,
incident @ a1 @ oa,
inference(cnf,[status(esa)],[ia1oa]) ).
thf(zip_derived_cl410,plain,
( ( ( point_equal @ o @ a1 )
| ~ ( incident @ o @ b2c2 )
| ( line_equal @ b2c2 @ oa ) )
<= ( incident @ a1 @ b2c2 ) ),
inference(demod,[status(thm)],[zip_derived_cl382,zip_derived_cl21]) ).
thf(zip_derived_cl5221,plain,
( ( line_equal @ b2c2 @ oa )
<= ( line_equal @ b2c2 @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl410]) ).
thf(zip_derived_cl45_103,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl5223,plain,
( ( line_equal @ oa @ b2c2 )
<= ( line_equal @ b2c2 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl5221,zip_derived_cl45]) ).
thf(zip_derived_cl48_104,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl5227,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ oa )
| ( incident @ X0 @ b2c2 ) )
<= ( line_equal @ b2c2 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl5223,zip_derived_cl48]) ).
thf(zip_derived_cl22_105,plain,
incident @ a2 @ oa,
inference(cnf,[status(esa)],[ia2oa]) ).
thf(zip_derived_cl20993,plain,
( ( incident @ a2 @ b2c2 )
<= ( line_equal @ b2c2 @ oa ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl5227,zip_derived_cl22]) ).
thf(zip_derived_cl173_106,plain,
~ ( incident @ a2 @ b2c2 ),
inference(demod,[status(thm)],[zip_derived_cl165,zip_derived_cl17]) ).
thf('26',plain,
~ ( line_equal @ b2c2 @ oa ),
inference('s_sup-',[status(thm)],[zip_derived_cl20993,zip_derived_cl173]) ).
thf(zip_derived_cl17_107,plain,
incident @ b2 @ b2c2,
inference(cnf,[status(esa)],[ib2c2]) ).
thf(zip_derived_cl23_108,plain,
incident @ b1 @ ob,
inference(cnf,[status(esa)],[ib1ob]) ).
thf(zip_derived_cl49_109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl326,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ b1 )
| ~ ( incident @ X0 @ ob )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ b1 @ X1 )
| ( line_equal @ ob @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl49]) ).
thf(zip_derived_cl2021,plain,
( ( point_equal @ b2 @ b1 )
| ~ ( incident @ b2 @ ob )
| ~ ( incident @ b1 @ b2c2 )
| ( line_equal @ ob @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl326]) ).
thf(ib2ob,axiom,
incident @ b2 @ ob ).
thf(zip_derived_cl24,plain,
incident @ b2 @ ob,
inference(cnf,[status(esa)],[ib2ob]) ).
thf(zip_derived_cl2057,plain,
( ( point_equal @ b2 @ b1 )
| ~ ( incident @ b1 @ b2c2 )
| ( line_equal @ ob @ b2c2 ) ),
inference(demod,[status(thm)],[zip_derived_cl2021,zip_derived_cl24]) ).
thf(notbb,axiom,
( ( point_equal @ b2 @ b1 )
=> goal ) ).
thf(zip_derived_cl36,plain,
( goal
| ~ ( point_equal @ b2 @ b1 ) ),
inference(cnf,[status(esa)],[notbb]) ).
thf(zip_derived_cl73,plain,
( ~ ( point_equal @ b2 @ b1 )
<= ~ ( point_equal @ b2 @ b1 ) ),
inference(split,[status(esa)],[zip_derived_cl36]) ).
thf('27',plain,
( ~ ( point_equal @ b2 @ b1 )
| goal ),
inference(split,[status(esa)],[zip_derived_cl36]) ).
thf('28',plain,
~ ( point_equal @ b2 @ b1 ),
inference('sat_resolution*',[status(thm)],['1','27']) ).
thf(zip_derived_cl85,plain,
~ ( point_equal @ b2 @ b1 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl73,'28']) ).
thf(zip_derived_cl46589,plain,
( ( line_equal @ ob @ b2c2 )
| ~ ( incident @ b1 @ b2c2 ) ),
inference(clc,[status(thm)],[zip_derived_cl2057,zip_derived_cl85]) ).
thf('29',plain,
( ~ ( incident @ b1 @ b2c2 )
| ( line_equal @ ob @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl46589]) ).
thf(zip_derived_cl624_110,plain,
( ( incident @ b1 @ b2c2 )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl464,zip_derived_cl7]) ).
thf(zip_derived_cl421,plain,
( ~ ( incident @ b1 @ b2c2 )
<= ~ ( incident @ b1 @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl362]) ).
thf('30',plain,
( ~ ( line_equal @ b2c2 @ a1b1 )
| ( incident @ b1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl624,zip_derived_cl421]) ).
thf(zip_derived_cl443,plain,
( ( point_equal @ c1 @ a1 )
<= ( point_equal @ c1 @ a1 ) ),
inference(split,[status(esa)],[zip_derived_cl366]) ).
thf(zip_derived_cl42_111,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl467,plain,
( ( point_equal @ a1 @ c1 )
<= ( point_equal @ c1 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl443,zip_derived_cl42]) ).
thf(zip_derived_cl47_112,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl480,plain,
( ! [X0: $i] :
( ~ ( incident @ c1 @ X0 )
| ( incident @ a1 @ X0 ) )
<= ( point_equal @ c1 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl467,zip_derived_cl47]) ).
thf(zip_derived_cl14_113,plain,
incident @ c1 @ b1c1,
inference(cnf,[status(esa)],[ic1b1]) ).
thf(zip_derived_cl715,plain,
( ( incident @ a1 @ b1c1 )
<= ( point_equal @ c1 @ a1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl480,zip_derived_cl14]) ).
thf(zip_derived_cl137_114,plain,
~ ( incident @ a1 @ b1c1 ),
inference(demod,[status(thm)],[zip_derived_cl134,zip_derived_cl15]) ).
thf('31',plain,
~ ( point_equal @ c1 @ a1 ),
inference('s_sup-',[status(thm)],[zip_derived_cl715,zip_derived_cl137]) ).
thf(zip_derived_cl11_115,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl319_116,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ b2c2 @ X1 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl49]) ).
thf(zip_derived_cl368,plain,
( ( ( point_equal @ c1 @ a1 )
| ~ ( incident @ c1 @ b2c2 )
| ~ ( incident @ a1 @ a1c1 )
| ( line_equal @ b2c2 @ a1c1 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl319]) ).
thf(zip_derived_cl10_117,plain,
incident @ a1 @ a1c1,
inference(cnf,[status(esa)],[ia1c1]) ).
thf(zip_derived_cl396,plain,
( ( ( point_equal @ c1 @ a1 )
| ~ ( incident @ c1 @ b2c2 )
| ( line_equal @ b2c2 @ a1c1 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference(demod,[status(thm)],[zip_derived_cl368,zip_derived_cl10]) ).
thf('32',plain,
( ( point_equal @ c1 @ a1 )
| ( line_equal @ b2c2 @ a1c1 )
| ~ ( incident @ a1 @ b2c2 )
| ~ ( incident @ c1 @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl396]) ).
thf(ic1oc,axiom,
incident @ c1 @ oc ).
thf(zip_derived_cl25,plain,
incident @ c1 @ oc,
inference(cnf,[status(esa)],[ic1oc]) ).
thf(zip_derived_cl319_118,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ b2c2 @ X1 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl49]) ).
thf(zip_derived_cl369,plain,
( ( ( point_equal @ c1 @ a1 )
| ~ ( incident @ c1 @ b2c2 )
| ~ ( incident @ a1 @ oc )
| ( line_equal @ b2c2 @ oc ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl25,zip_derived_cl319]) ).
thf(zip_derived_cl4808,plain,
( ( line_equal @ b2c2 @ oc )
<= ( line_equal @ b2c2 @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl369]) ).
thf(zip_derived_cl45_119,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl4813,plain,
( ( line_equal @ oc @ b2c2 )
<= ( line_equal @ b2c2 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4808,zip_derived_cl45]) ).
thf(zip_derived_cl48_120,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl4899,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ oc )
| ( incident @ X0 @ b2c2 ) )
<= ( line_equal @ b2c2 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4813,zip_derived_cl48]) ).
thf(zip_derived_cl25_121,plain,
incident @ c1 @ oc,
inference(cnf,[status(esa)],[ic1oc]) ).
thf(zip_derived_cl19876,plain,
( ( incident @ c1 @ b2c2 )
<= ( line_equal @ b2c2 @ oc ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4899,zip_derived_cl25]) ).
thf(zip_derived_cl442_122,plain,
( ~ ( incident @ c1 @ b2c2 )
<= ~ ( incident @ c1 @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl366]) ).
thf('33',plain,
( ~ ( line_equal @ b2c2 @ oc )
| ( incident @ c1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl19876,zip_derived_cl442]) ).
thf(zip_derived_cl9_123,plain,
incident @ b2 @ a2b2,
inference(cnf,[status(esa)],[ib2a2]) ).
thf(zip_derived_cl319_124,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ b2c2 @ X1 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl49]) ).
thf(zip_derived_cl375,plain,
( ( ( point_equal @ b2 @ a1 )
| ~ ( incident @ b2 @ b2c2 )
| ~ ( incident @ a1 @ a2b2 )
| ( line_equal @ b2c2 @ a2b2 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl9,zip_derived_cl319]) ).
thf(zip_derived_cl17_125,plain,
incident @ b2 @ b2c2,
inference(cnf,[status(esa)],[ib2c2]) ).
thf(zip_derived_cl403,plain,
( ( ( point_equal @ b2 @ a1 )
| ~ ( incident @ a1 @ a2b2 )
| ( line_equal @ b2c2 @ a2b2 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference(demod,[status(thm)],[zip_derived_cl375,zip_derived_cl17]) ).
thf('34',plain,
( ( line_equal @ b2c2 @ a2b2 )
| ( point_equal @ b2 @ a1 )
| ~ ( incident @ a1 @ b2c2 )
| ~ ( incident @ a1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl403]) ).
thf('35',plain,
( ~ ( incident @ ac @ ob )
| ~ ( incident @ ab @ ob )
| ~ ( incident @ bc @ ob ) ),
inference(split,[status(esa)],[zip_derived_cl536]) ).
thf(iooc,axiom,
incident @ o @ oc ).
thf(zip_derived_cl20,plain,
incident @ o @ oc,
inference(cnf,[status(esa)],[iooc]) ).
thf(zip_derived_cl29_126,plain,
incident @ ac @ a1c1,
inference(cnf,[status(esa)],[iac1]) ).
thf(zip_derived_cl49_127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl316,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ac )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ac @ X1 )
| ( line_equal @ a1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl29,zip_derived_cl49]) ).
thf(zip_derived_cl1066,plain,
( ( point_equal @ o @ ac )
| ~ ( incident @ o @ a1c1 )
| ~ ( incident @ ac @ oc )
| ( line_equal @ a1c1 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl316]) ).
thf('36',plain,
( ~ ( incident @ o @ a1c1 )
| ( point_equal @ o @ ac )
| ~ ( incident @ ac @ oc )
| ( line_equal @ a1c1 @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl1066]) ).
thf(zip_derived_cl9_128,plain,
incident @ b2 @ a2b2,
inference(cnf,[status(esa)],[ib2a2]) ).
thf(zip_derived_cl464_129,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ a1b1 )
| ( incident @ X0 @ b2c2 ) )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl432,zip_derived_cl48]) ).
thf(iab1,axiom,
incident @ ab @ a1b1 ).
thf(zip_derived_cl31,plain,
incident @ ab @ a1b1,
inference(cnf,[status(esa)],[iab1]) ).
thf(zip_derived_cl622,plain,
( ( incident @ ab @ b2c2 )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl464,zip_derived_cl31]) ).
thf(zip_derived_cl49_130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl633,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ab )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ab @ X1 )
| ( line_equal @ b2c2 @ X1 ) )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl622,zip_derived_cl49]) ).
thf(zip_derived_cl7482,plain,
( ( ( point_equal @ b2 @ ab )
| ~ ( incident @ b2 @ b2c2 )
| ~ ( incident @ ab @ a2b2 )
| ( line_equal @ b2c2 @ a2b2 ) )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl9,zip_derived_cl633]) ).
thf(zip_derived_cl17_131,plain,
incident @ b2 @ b2c2,
inference(cnf,[status(esa)],[ib2c2]) ).
thf(iab2,axiom,
incident @ ab @ a2b2 ).
thf(zip_derived_cl32,plain,
incident @ ab @ a2b2,
inference(cnf,[status(esa)],[iab2]) ).
thf(zip_derived_cl432_132,plain,
( ( line_equal @ a1b1 @ b2c2 )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl417,zip_derived_cl45]) ).
thf(transitivity_of_line_equal,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( line_equal @ A @ B )
& ( line_equal @ B @ C ) )
=> ( line_equal @ A @ C ) ) ).
thf(zip_derived_cl46,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( line_equal @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[transitivity_of_line_equal]) ).
thf(zip_derived_cl462,plain,
( ! [X0: $i] :
( ~ ( line_equal @ b2c2 @ X0 )
| ( line_equal @ a1b1 @ X0 ) )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl432,zip_derived_cl46]) ).
thf(notab,axiom,
( ( line_equal @ a1b1 @ a2b2 )
=> goal ) ).
thf(zip_derived_cl40,plain,
( goal
| ~ ( line_equal @ a1b1 @ a2b2 ) ),
inference(cnf,[status(esa)],[notab]) ).
thf(zip_derived_cl81,plain,
( ~ ( line_equal @ a1b1 @ a2b2 )
<= ~ ( line_equal @ a1b1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl40]) ).
thf('37',plain,
( ~ ( line_equal @ a1b1 @ a2b2 )
| goal ),
inference(split,[status(esa)],[zip_derived_cl40]) ).
thf('38',plain,
~ ( line_equal @ a1b1 @ a2b2 ),
inference('sat_resolution*',[status(thm)],['1','37']) ).
thf(zip_derived_cl89,plain,
~ ( line_equal @ a1b1 @ a2b2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl81,'38']) ).
thf(zip_derived_cl5989,plain,
( ~ ( line_equal @ b2c2 @ a2b2 )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl462,zip_derived_cl89]) ).
thf(zip_derived_cl7558,plain,
( ( point_equal @ b2 @ ab )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference(demod,[status(thm)],[zip_derived_cl7482,zip_derived_cl17,zip_derived_cl32,zip_derived_cl5989]) ).
thf(zip_derived_cl42_133,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl7873,plain,
( ( point_equal @ ab @ b2 )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl7558,zip_derived_cl42]) ).
thf(zip_derived_cl47_134,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl8038,plain,
( ! [X0: $i] :
( ~ ( incident @ b2 @ X0 )
| ( incident @ ab @ X0 ) )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl7873,zip_derived_cl47]) ).
thf(zip_derived_cl24_135,plain,
incident @ b2 @ ob,
inference(cnf,[status(esa)],[ib2ob]) ).
thf(zip_derived_cl21825,plain,
( ( incident @ ab @ ob )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl8038,zip_derived_cl24]) ).
thf(zip_derived_cl540,plain,
( ~ ( incident @ ab @ ob )
<= ~ ( incident @ ab @ ob ) ),
inference(split,[status(esa)],[zip_derived_cl536]) ).
thf('39',plain,
( ( incident @ ab @ ob )
| ~ ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl21825,zip_derived_cl540]) ).
thf(zip_derived_cl22_136,plain,
incident @ a2 @ oa,
inference(cnf,[status(esa)],[ia2oa]) ).
thf(zip_derived_cl2341_137,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ a1c1 @ X1 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2317,zip_derived_cl49]) ).
thf(zip_derived_cl3350,plain,
( ( ( point_equal @ a2 @ bc )
| ~ ( incident @ a2 @ a1c1 )
| ~ ( incident @ bc @ oa )
| ( line_equal @ a1c1 @ oa ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl2341]) ).
thf(zip_derived_cl4734,plain,
( ( line_equal @ a1c1 @ oa )
<= ( line_equal @ a1c1 @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl3350]) ).
thf(zip_derived_cl45_138,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl4738,plain,
( ( line_equal @ oa @ a1c1 )
<= ( line_equal @ a1c1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4734,zip_derived_cl45]) ).
thf(zip_derived_cl48_139,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl4866,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ oa )
| ( incident @ X0 @ a1c1 ) )
<= ( line_equal @ a1c1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4738,zip_derived_cl48]) ).
thf(zip_derived_cl18_140,plain,
incident @ o @ oa,
inference(cnf,[status(esa)],[iooa]) ).
thf(zip_derived_cl18522,plain,
( ( incident @ o @ a1c1 )
<= ( line_equal @ a1c1 @ oa ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4866,zip_derived_cl18]) ).
thf(zip_derived_cl19_141,plain,
incident @ o @ ob,
inference(cnf,[status(esa)],[ioob]) ).
thf(zip_derived_cl2341_142,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ a1c1 @ X1 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2317,zip_derived_cl49]) ).
thf(zip_derived_cl3360,plain,
( ( ( point_equal @ o @ bc )
| ~ ( incident @ o @ a1c1 )
| ~ ( incident @ bc @ ob )
| ( line_equal @ a1c1 @ ob ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl19,zip_derived_cl2341]) ).
thf(zip_derived_cl1522_143,plain,
( ! [X0: $i] :
( ~ ( incident @ b2 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1405,zip_derived_cl47]) ).
thf(zip_derived_cl24_144,plain,
incident @ b2 @ ob,
inference(cnf,[status(esa)],[ib2ob]) ).
thf(zip_derived_cl2318,plain,
( ( incident @ bc @ ob )
<= ( ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1522,zip_derived_cl24]) ).
thf(zip_derived_cl3409,plain,
( ( ( point_equal @ o @ bc )
| ~ ( incident @ o @ a1c1 )
| ( line_equal @ a1c1 @ ob ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3360,zip_derived_cl2318]) ).
thf(zip_derived_cl4517,plain,
( ~ ( incident @ o @ a1c1 )
<= ~ ( incident @ o @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl3409]) ).
thf('40',plain,
( ~ ( line_equal @ a1c1 @ oa )
| ( incident @ o @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl18522,zip_derived_cl4517]) ).
thf(zip_derived_cl25_145,plain,
incident @ c1 @ oc,
inference(cnf,[status(esa)],[ic1oc]) ).
thf(zip_derived_cl2341_146,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ a1c1 @ X1 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2317,zip_derived_cl49]) ).
thf(zip_derived_cl3346,plain,
( ( ( point_equal @ c1 @ bc )
| ~ ( incident @ c1 @ a1c1 )
| ~ ( incident @ bc @ oc )
| ( line_equal @ a1c1 @ oc ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl25,zip_derived_cl2341]) ).
thf(zip_derived_cl11_147,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl3399,plain,
( ( ( point_equal @ c1 @ bc )
| ~ ( incident @ bc @ oc )
| ( line_equal @ a1c1 @ oc ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3346,zip_derived_cl11]) ).
thf(zip_derived_cl4403,plain,
( ( line_equal @ a1c1 @ oc )
<= ( line_equal @ a1c1 @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl3399]) ).
thf(zip_derived_cl45_148,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl4407,plain,
( ( line_equal @ oc @ a1c1 )
<= ( line_equal @ a1c1 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4403,zip_derived_cl45]) ).
thf(zip_derived_cl48_149,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl4421,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ oc )
| ( incident @ X0 @ a1c1 ) )
<= ( line_equal @ a1c1 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4407,zip_derived_cl48]) ).
thf(ic2oc,axiom,
incident @ c2 @ oc ).
thf(zip_derived_cl26,plain,
incident @ c2 @ oc,
inference(cnf,[status(esa)],[ic2oc]) ).
thf(zip_derived_cl16326,plain,
( ( incident @ c2 @ a1c1 )
<= ( line_equal @ a1c1 @ oc ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4421,zip_derived_cl26]) ).
thf(zip_derived_cl63_150,plain,
( ( incident @ c2 @ a1b1 )
<= ( incident @ c2 @ a1b1 ) ),
inference(split,[status(esa)],[zip_derived_cl4]) ).
thf(zip_derived_cl2341_151,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ a1c1 @ X1 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2317,zip_derived_cl49]) ).
thf(zip_derived_cl3357,plain,
( ( ( point_equal @ c2 @ bc )
| ~ ( incident @ c2 @ a1c1 )
| ~ ( incident @ bc @ a1b1 )
| ( line_equal @ a1c1 @ a1b1 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( incident @ c2 @ a1b1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl63,zip_derived_cl2341]) ).
thf(zip_derived_cl3758,plain,
( ~ ( incident @ c2 @ a1c1 )
<= ~ ( incident @ c2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl3357]) ).
thf('41',plain,
( ~ ( line_equal @ a1c1 @ oc )
| ( incident @ c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl16326,zip_derived_cl3758]) ).
thf(zip_derived_cl21_152,plain,
incident @ a1 @ oa,
inference(cnf,[status(esa)],[ia1oa]) ).
thf(zip_derived_cl11_153,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl49_154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl329,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ a1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl49]) ).
thf(zip_derived_cl2382,plain,
( ( point_equal @ a1 @ c1 )
| ~ ( incident @ a1 @ a1c1 )
| ~ ( incident @ c1 @ oa )
| ( line_equal @ a1c1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl329]) ).
thf(zip_derived_cl10_155,plain,
incident @ a1 @ a1c1,
inference(cnf,[status(esa)],[ia1c1]) ).
thf(zip_derived_cl2428,plain,
( ( point_equal @ a1 @ c1 )
| ~ ( incident @ c1 @ oa )
| ( line_equal @ a1c1 @ oa ) ),
inference(demod,[status(thm)],[zip_derived_cl2382,zip_derived_cl10]) ).
thf('42',plain,
( ( point_equal @ a1 @ c1 )
| ( line_equal @ a1c1 @ oa )
| ~ ( incident @ c1 @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl2428]) ).
thf(zip_derived_cl12_156,plain,
incident @ a2 @ a2c2,
inference(cnf,[status(esa)],[ia2c2]) ).
thf(zip_derived_cl327_157,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ a2b2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ a2b2 @ X1 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl49]) ).
thf(zip_derived_cl2156,plain,
( ( ( point_equal @ a2 @ c1 )
| ~ ( incident @ a2 @ a2b2 )
| ~ ( incident @ c1 @ a2c2 )
| ( line_equal @ a2b2 @ a2c2 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl327]) ).
thf(zip_derived_cl8_158,plain,
incident @ a2 @ a2b2,
inference(cnf,[status(esa)],[ia2b2]) ).
thf(zip_derived_cl2192,plain,
( ( ( point_equal @ a2 @ c1 )
| ~ ( incident @ c1 @ a2c2 )
| ( line_equal @ a2b2 @ a2c2 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference(demod,[status(thm)],[zip_derived_cl2156,zip_derived_cl8]) ).
thf(zip_derived_cl53638,plain,
( ( point_equal @ a2 @ c1 )
<= ( point_equal @ a2 @ c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2192]) ).
thf(zip_derived_cl42_159,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl53643,plain,
( ( point_equal @ c1 @ a2 )
<= ( point_equal @ a2 @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl53638,zip_derived_cl42]) ).
thf(zip_derived_cl47_160,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl53659,plain,
( ! [X0: $i] :
( ~ ( incident @ a2 @ X0 )
| ( incident @ c1 @ X0 ) )
<= ( point_equal @ a2 @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl53643,zip_derived_cl47]) ).
thf(zip_derived_cl12_161,plain,
incident @ a2 @ a2c2,
inference(cnf,[status(esa)],[ia2c2]) ).
thf(zip_derived_cl55360,plain,
( ( incident @ c1 @ a2c2 )
<= ( point_equal @ a2 @ c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl53659,zip_derived_cl12]) ).
thf(zip_derived_cl316_162,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ac )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ac @ X1 )
| ( line_equal @ a1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl29,zip_derived_cl49]) ).
thf(zip_derived_cl55386,plain,
( ( ( point_equal @ c1 @ ac )
| ~ ( incident @ c1 @ a1c1 )
| ~ ( incident @ ac @ a2c2 )
| ( line_equal @ a1c1 @ a2c2 ) )
<= ( point_equal @ a2 @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl55360,zip_derived_cl316]) ).
thf(zip_derived_cl11_163,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl30_164,plain,
incident @ ac @ a2c2,
inference(cnf,[status(esa)],[iac2]) ).
thf(zip_derived_cl88_165,plain,
~ ( line_equal @ a1c1 @ a2c2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl79,'15']) ).
thf(zip_derived_cl55452,plain,
( ( point_equal @ c1 @ ac )
<= ( point_equal @ a2 @ c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl55386,zip_derived_cl11,zip_derived_cl30,zip_derived_cl88]) ).
thf(zip_derived_cl42_166,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl55747,plain,
( ( point_equal @ ac @ c1 )
<= ( point_equal @ a2 @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl55452,zip_derived_cl42]) ).
thf(zip_derived_cl420_167,plain,
( ( point_equal @ a1 @ c2 )
<= ( point_equal @ c2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl416,zip_derived_cl42]) ).
thf(zip_derived_cl47_168,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl435,plain,
( ! [X0: $i] :
( ~ ( incident @ c2 @ X0 )
| ( incident @ a1 @ X0 ) )
<= ( point_equal @ c2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl420,zip_derived_cl47]) ).
thf(zip_derived_cl13_169,plain,
incident @ c2 @ a2c2,
inference(cnf,[status(esa)],[ic2a2]) ).
thf(zip_derived_cl558,plain,
( ( incident @ a1 @ a2c2 )
<= ( point_equal @ c2 @ a1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl435,zip_derived_cl13]) ).
thf(zip_derived_cl316_170,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ac )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ac @ X1 )
| ( line_equal @ a1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl29,zip_derived_cl49]) ).
thf(zip_derived_cl1035,plain,
( ( ( point_equal @ a1 @ ac )
| ~ ( incident @ a1 @ a1c1 )
| ~ ( incident @ ac @ a2c2 )
| ( line_equal @ a1c1 @ a2c2 ) )
<= ( point_equal @ c2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl558,zip_derived_cl316]) ).
thf(zip_derived_cl10_171,plain,
incident @ a1 @ a1c1,
inference(cnf,[status(esa)],[ia1c1]) ).
thf(zip_derived_cl30_172,plain,
incident @ ac @ a2c2,
inference(cnf,[status(esa)],[iac2]) ).
thf(zip_derived_cl88_173,plain,
~ ( line_equal @ a1c1 @ a2c2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl79,'15']) ).
thf(zip_derived_cl1075,plain,
( ( point_equal @ a1 @ ac )
<= ( point_equal @ c2 @ a1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1035,zip_derived_cl10,zip_derived_cl30,zip_derived_cl88]) ).
thf(zip_derived_cl43_174,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X2 )
| ( point_equal @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[transitivity_of_point_equal]) ).
thf(zip_derived_cl1095,plain,
( ! [X0: $i] :
( ~ ( point_equal @ ac @ X0 )
| ( point_equal @ a1 @ X0 ) )
<= ( point_equal @ c2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1075,zip_derived_cl43]) ).
thf(zip_derived_cl416_175,plain,
( ( point_equal @ c2 @ a1 )
<= ( point_equal @ c2 @ a1 ) ),
inference(split,[status(esa)],[zip_derived_cl408]) ).
thf(zip_derived_cl43_176,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X2 )
| ( point_equal @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[transitivity_of_point_equal]) ).
thf(zip_derived_cl418,plain,
( ! [X0: $i] :
( ~ ( point_equal @ a1 @ X0 )
| ( point_equal @ c2 @ X0 ) )
<= ( point_equal @ c2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl416,zip_derived_cl43]) ).
thf(notcc,axiom,
( ( point_equal @ c2 @ c1 )
=> goal ) ).
thf(zip_derived_cl37,plain,
( goal
| ~ ( point_equal @ c2 @ c1 ) ),
inference(cnf,[status(esa)],[notcc]) ).
thf(zip_derived_cl75,plain,
( ~ ( point_equal @ c2 @ c1 )
<= ~ ( point_equal @ c2 @ c1 ) ),
inference(split,[status(esa)],[zip_derived_cl37]) ).
thf('43',plain,
( ~ ( point_equal @ c2 @ c1 )
| goal ),
inference(split,[status(esa)],[zip_derived_cl37]) ).
thf('44',plain,
~ ( point_equal @ c2 @ c1 ),
inference('sat_resolution*',[status(thm)],['1','43']) ).
thf(zip_derived_cl86,plain,
~ ( point_equal @ c2 @ c1 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl75,'44']) ).
thf(zip_derived_cl5365,plain,
( ~ ( point_equal @ a1 @ c1 )
<= ( point_equal @ c2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl418,zip_derived_cl86]) ).
thf(zip_derived_cl17580,plain,
( ~ ( point_equal @ ac @ c1 )
<= ( point_equal @ c2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1095,zip_derived_cl5365]) ).
thf('45',plain,
( ~ ( point_equal @ a2 @ c1 )
| ~ ( point_equal @ c2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl55747,zip_derived_cl17580]) ).
thf(zip_derived_cl55747_177,plain,
( ( point_equal @ ac @ c1 )
<= ( point_equal @ a2 @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl55452,zip_derived_cl42]) ).
thf(zip_derived_cl47_178,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl55764,plain,
( ! [X0: $i] :
( ~ ( incident @ c1 @ X0 )
| ( incident @ ac @ X0 ) )
<= ( point_equal @ a2 @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl55747,zip_derived_cl47]) ).
thf(zip_derived_cl25_179,plain,
incident @ c1 @ oc,
inference(cnf,[status(esa)],[ic1oc]) ).
thf(zip_derived_cl56354,plain,
( ( incident @ ac @ oc )
<= ( point_equal @ a2 @ c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl55764,zip_derived_cl25]) ).
thf(zip_derived_cl20_180,plain,
incident @ o @ oc,
inference(cnf,[status(esa)],[iooc]) ).
thf(zip_derived_cl44_181,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X0 )
| ~ ( incident @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[reflexivity_of_line_equal]) ).
thf(zip_derived_cl192,plain,
line_equal @ oc @ oc,
inference('s_sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl44]) ).
thf(zip_derived_cl114_182,plain,
! [X0: $i] :
( ~ ( line_equal @ X0 @ X0 )
| ~ ( incident @ bc @ X0 )
| ~ ( incident @ ac @ X0 )
| ~ ( incident @ ab @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl51,'6']) ).
thf(zip_derived_cl546,plain,
( ~ ( incident @ bc @ oc )
| ~ ( incident @ ac @ oc )
| ~ ( incident @ ab @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl192,zip_derived_cl114]) ).
thf(zip_derived_cl551,plain,
( ~ ( incident @ ac @ oc )
<= ~ ( incident @ ac @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl546]) ).
thf('46',plain,
( ~ ( point_equal @ a2 @ c1 )
| ( incident @ ac @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl56354,zip_derived_cl551]) ).
thf(zip_derived_cl55360_183,plain,
( ( incident @ c1 @ a2c2 )
<= ( point_equal @ a2 @ c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl53659,zip_derived_cl12]) ).
thf(zip_derived_cl2213_184,plain,
( ~ ( incident @ c1 @ a2c2 )
<= ~ ( incident @ c1 @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl2121]) ).
thf('47',plain,
( ~ ( point_equal @ a2 @ c1 )
| ( incident @ c1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl55360,zip_derived_cl2213]) ).
thf(zip_derived_cl19_185,plain,
incident @ o @ ob,
inference(cnf,[status(esa)],[ioob]) ).
thf(zip_derived_cl30_186,plain,
incident @ ac @ a2c2,
inference(cnf,[status(esa)],[iac2]) ).
thf(zip_derived_cl49_187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl315,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ac )
| ~ ( incident @ X0 @ a2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ac @ X1 )
| ( line_equal @ a2c2 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl49]) ).
thf(zip_derived_cl990,plain,
( ( point_equal @ o @ ac )
| ~ ( incident @ o @ a2c2 )
| ~ ( incident @ ac @ ob )
| ( line_equal @ a2c2 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl19,zip_derived_cl315]) ).
thf(zip_derived_cl14057,plain,
( ( point_equal @ o @ ac )
<= ( point_equal @ o @ ac ) ),
inference(split,[status(esa)],[zip_derived_cl990]) ).
thf(zip_derived_cl42_188,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl14062,plain,
( ( point_equal @ ac @ o )
<= ( point_equal @ o @ ac ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl14057,zip_derived_cl42]) ).
thf(zip_derived_cl47_189,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl14064,plain,
( ! [X0: $i] :
( ~ ( incident @ o @ X0 )
| ( incident @ ac @ X0 ) )
<= ( point_equal @ o @ ac ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl14062,zip_derived_cl47]) ).
thf(zip_derived_cl19_190,plain,
incident @ o @ ob,
inference(cnf,[status(esa)],[ioob]) ).
thf(zip_derived_cl29774,plain,
( ( incident @ ac @ ob )
<= ( point_equal @ o @ ac ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl14064,zip_derived_cl19]) ).
thf(zip_derived_cl541,plain,
( ~ ( incident @ ac @ ob )
<= ~ ( incident @ ac @ ob ) ),
inference(split,[status(esa)],[zip_derived_cl536]) ).
thf('48',plain,
( ~ ( point_equal @ o @ ac )
| ( incident @ ac @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl29774,zip_derived_cl541]) ).
thf('49',plain,
( ~ ( incident @ c1 @ a2b2 )
| ~ ( incident @ b1 @ a2c2 )
| goal
| ~ ( incident @ a1 @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl1]) ).
thf(zip_derived_cl28_191,plain,
incident @ bc @ b2c2,
inference(cnf,[status(esa)],[ibc2]) ).
thf(zip_derived_cl326_192,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ b1 )
| ~ ( incident @ X0 @ ob )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ b1 @ X1 )
| ( line_equal @ ob @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl49]) ).
thf(zip_derived_cl1983,plain,
( ( point_equal @ bc @ b1 )
| ~ ( incident @ bc @ ob )
| ~ ( incident @ b1 @ b2c2 )
| ( line_equal @ ob @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl28,zip_derived_cl326]) ).
thf(zip_derived_cl43984,plain,
( ( line_equal @ ob @ b2c2 )
<= ( line_equal @ ob @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl1983]) ).
thf(zip_derived_cl48_193,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl43990,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ ob )
| ( incident @ X0 @ b2c2 ) )
<= ( line_equal @ ob @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl43984,zip_derived_cl48]) ).
thf(zip_derived_cl19_194,plain,
incident @ o @ ob,
inference(cnf,[status(esa)],[ioob]) ).
thf(zip_derived_cl48470,plain,
( ( incident @ o @ b2c2 )
<= ( line_equal @ ob @ b2c2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl43990,zip_derived_cl19]) ).
thf(zip_derived_cl19_195,plain,
incident @ o @ ob,
inference(cnf,[status(esa)],[ioob]) ).
thf(zip_derived_cl319_196,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ b2c2 @ X1 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl49]) ).
thf(zip_derived_cl383,plain,
( ( ( point_equal @ o @ a1 )
| ~ ( incident @ o @ b2c2 )
| ~ ( incident @ a1 @ ob )
| ( line_equal @ b2c2 @ ob ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl19,zip_derived_cl319]) ).
thf(zip_derived_cl4826,plain,
( ~ ( incident @ o @ b2c2 )
<= ~ ( incident @ o @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl383]) ).
thf('50',plain,
( ~ ( line_equal @ ob @ b2c2 )
| ( incident @ o @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl48470,zip_derived_cl4826]) ).
thf(zip_derived_cl22_197,plain,
incident @ a2 @ oa,
inference(cnf,[status(esa)],[ia2oa]) ).
thf(zip_derived_cl14_198,plain,
incident @ c1 @ b1c1,
inference(cnf,[status(esa)],[ic1b1]) ).
thf(zip_derived_cl49_199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl328,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl49]) ).
thf(zip_derived_cl2258,plain,
( ( point_equal @ a2 @ c1 )
| ~ ( incident @ a2 @ b1c1 )
| ~ ( incident @ c1 @ oa )
| ( line_equal @ b1c1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl328]) ).
thf('51',plain,
( ( point_equal @ a2 @ c1 )
| ( line_equal @ b1c1 @ oa )
| ~ ( incident @ a2 @ b1c1 )
| ~ ( incident @ c1 @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl2258]) ).
thf(zip_derived_cl25_200,plain,
incident @ c1 @ oc,
inference(cnf,[status(esa)],[ic1oc]) ).
thf(zip_derived_cl322_201,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ oa )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ oa @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl49]) ).
thf(zip_derived_cl1556,plain,
( ( point_equal @ c1 @ a1 )
| ~ ( incident @ c1 @ oa )
| ~ ( incident @ a1 @ oc )
| ( line_equal @ oa @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl25,zip_derived_cl322]) ).
thf(zip_derived_cl31588,plain,
( ( line_equal @ oa @ oc )
<= ( line_equal @ oa @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl1556]) ).
thf(zip_derived_cl45_202,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl31592,plain,
( ( line_equal @ oc @ oa )
<= ( line_equal @ oa @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl31588,zip_derived_cl45]) ).
thf(zip_derived_cl48_203,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl31607,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ oc )
| ( incident @ X0 @ oa ) )
<= ( line_equal @ oa @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl31592,zip_derived_cl48]) ).
thf(zip_derived_cl25_204,plain,
incident @ c1 @ oc,
inference(cnf,[status(esa)],[ic1oc]) ).
thf(zip_derived_cl42148,plain,
( ( incident @ c1 @ oa )
<= ( line_equal @ oa @ oc ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl31607,zip_derived_cl25]) ).
thf(zip_derived_cl66_205,plain,
( ( incident @ c1 @ a2b2 )
<= ( incident @ c1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl5]) ).
thf(zip_derived_cl322_206,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ oa )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ oa @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl49]) ).
thf(zip_derived_cl1553,plain,
( ( ( point_equal @ c1 @ a1 )
| ~ ( incident @ c1 @ oa )
| ~ ( incident @ a1 @ a2b2 )
| ( line_equal @ oa @ a2b2 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl322]) ).
thf(zip_derived_cl31485,plain,
( ~ ( incident @ c1 @ oa )
<= ~ ( incident @ c1 @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl1553]) ).
thf('52',plain,
( ~ ( line_equal @ oa @ oc )
| ( incident @ c1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl42148,zip_derived_cl31485]) ).
thf(zip_derived_cl411_207,plain,
( ( point_equal @ b2 @ a1 )
<= ( point_equal @ b2 @ a1 ) ),
inference(split,[status(esa)],[zip_derived_cl404]) ).
thf(zip_derived_cl47_208,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl414,plain,
( ! [X0: $i] :
( ~ ( incident @ a1 @ X0 )
| ( incident @ b2 @ X0 ) )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl411,zip_derived_cl47]) ).
thf(t2in1,axiom,
( ( ( incident @ a2 @ b1c1 )
& ( incident @ b2 @ a1c1 )
& ( incident @ c2 @ a1b1 ) )
=> goal ) ).
thf(zip_derived_cl2,plain,
( goal
| ~ ( incident @ c2 @ a1b1 )
| ~ ( incident @ b2 @ a1c1 )
| ~ ( incident @ a2 @ b1c1 ) ),
inference(cnf,[status(esa)],[t2in1]) ).
thf(zip_derived_cl58,plain,
( ~ ( incident @ b2 @ a1c1 )
<= ~ ( incident @ b2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2]) ).
thf(zip_derived_cl5297,plain,
( ~ ( incident @ a1 @ a1c1 )
<= ( ~ ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl414,zip_derived_cl58]) ).
thf(zip_derived_cl10_209,plain,
incident @ a1 @ a1c1,
inference(cnf,[status(esa)],[ia1c1]) ).
thf('53',plain,
( ~ ( point_equal @ b2 @ a1 )
| ( incident @ b2 @ a1c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl5297,zip_derived_cl10]) ).
thf(zip_derived_cl8_210,plain,
incident @ a2 @ a2b2,
inference(cnf,[status(esa)],[ia2b2]) ).
thf(zip_derived_cl323_211,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ b1 )
| ~ ( incident @ X0 @ a2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ b1 @ X1 )
| ( line_equal @ a2c2 @ X1 ) )
<= ( incident @ b1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl49]) ).
thf(zip_derived_cl1664,plain,
( ( ( point_equal @ a2 @ b1 )
| ~ ( incident @ a2 @ a2c2 )
| ~ ( incident @ b1 @ a2b2 )
| ( line_equal @ a2c2 @ a2b2 ) )
<= ( incident @ b1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl8,zip_derived_cl323]) ).
thf(zip_derived_cl12_212,plain,
incident @ a2 @ a2c2,
inference(cnf,[status(esa)],[ia2c2]) ).
thf(zip_derived_cl1705,plain,
( ( ( point_equal @ a2 @ b1 )
| ~ ( incident @ b1 @ a2b2 )
| ( line_equal @ a2c2 @ a2b2 ) )
<= ( incident @ b1 @ a2c2 ) ),
inference(demod,[status(thm)],[zip_derived_cl1664,zip_derived_cl12]) ).
thf(zip_derived_cl37435,plain,
( ( point_equal @ a2 @ b1 )
<= ( point_equal @ a2 @ b1 ) ),
inference(split,[status(esa)],[zip_derived_cl1705]) ).
thf(zip_derived_cl42_213,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl37440,plain,
( ( point_equal @ b1 @ a2 )
<= ( point_equal @ a2 @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl37435,zip_derived_cl42]) ).
thf(zip_derived_cl47_214,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl37456,plain,
( ! [X0: $i] :
( ~ ( incident @ a2 @ X0 )
| ( incident @ b1 @ X0 ) )
<= ( point_equal @ a2 @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl37440,zip_derived_cl47]) ).
thf(zip_derived_cl22_215,plain,
incident @ a2 @ oa,
inference(cnf,[status(esa)],[ia2oa]) ).
thf(zip_derived_cl45198,plain,
( ( incident @ b1 @ oa )
<= ( point_equal @ a2 @ b1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl37456,zip_derived_cl22]) ).
thf(zip_derived_cl64_216,plain,
( ( incident @ b1 @ a2c2 )
<= ( incident @ b1 @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl4]) ).
thf(zip_derived_cl322_217,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ oa )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ oa @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl49]) ).
thf(zip_derived_cl1548,plain,
( ( ( point_equal @ b1 @ a1 )
| ~ ( incident @ b1 @ oa )
| ~ ( incident @ a1 @ a2c2 )
| ( line_equal @ oa @ a2c2 ) )
<= ( incident @ b1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl322]) ).
thf(zip_derived_cl31324,plain,
( ~ ( incident @ b1 @ oa )
<= ~ ( incident @ b1 @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl1548]) ).
thf('54',plain,
( ( incident @ b1 @ oa )
| ~ ( point_equal @ a2 @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl45198,zip_derived_cl31324]) ).
thf(zip_derived_cl46066_218,plain,
( ! [X0: $i] :
( ~ ( incident @ b1 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( point_equal @ c2 @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl46038,zip_derived_cl47]) ).
thf(zip_derived_cl37520_219,plain,
( ! [X0: $i] :
( ~ ( incident @ c2 @ X0 )
| ( incident @ b1 @ X0 ) )
<= ( point_equal @ c2 @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl37510,zip_derived_cl47]) ).
thf(zip_derived_cl13_220,plain,
incident @ c2 @ a2c2,
inference(cnf,[status(esa)],[ic2a2]) ).
thf(zip_derived_cl45667,plain,
( ( incident @ b1 @ a2c2 )
<= ( point_equal @ c2 @ b1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl37520,zip_derived_cl13]) ).
thf(zip_derived_cl52678,plain,
( ( incident @ bc @ a2c2 )
<= ( point_equal @ c2 @ b1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl46066,zip_derived_cl45667]) ).
thf(zip_derived_cl64_221,plain,
( ( incident @ b1 @ a2c2 )
<= ( incident @ b1 @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl4]) ).
thf(zip_derived_cl44_222,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X0 )
| ~ ( incident @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[reflexivity_of_line_equal]) ).
thf(zip_derived_cl149,plain,
( ( line_equal @ a2c2 @ a2c2 )
<= ( incident @ b1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl44]) ).
thf(zip_derived_cl114_223,plain,
! [X0: $i] :
( ~ ( line_equal @ X0 @ X0 )
| ~ ( incident @ bc @ X0 )
| ~ ( incident @ ac @ X0 )
| ~ ( incident @ ab @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl51,'6']) ).
thf(zip_derived_cl167,plain,
( ( ~ ( incident @ bc @ a2c2 )
| ~ ( incident @ ac @ a2c2 )
| ~ ( incident @ ab @ a2c2 ) )
<= ( incident @ b1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl149,zip_derived_cl114]) ).
thf(zip_derived_cl181,plain,
( ~ ( incident @ bc @ a2c2 )
<= ~ ( incident @ bc @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl167]) ).
thf('55',plain,
( ~ ( point_equal @ c2 @ b1 )
| ( incident @ bc @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl52678,zip_derived_cl181]) ).
thf(zip_derived_cl12_224,plain,
incident @ a2 @ a2c2,
inference(cnf,[status(esa)],[ia2c2]) ).
thf(zip_derived_cl314_225,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl49]) ).
thf(zip_derived_cl888,plain,
( ( point_equal @ a2 @ bc )
| ~ ( incident @ a2 @ b1c1 )
| ~ ( incident @ bc @ a2c2 )
| ( line_equal @ b1c1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl314]) ).
thf('56',plain,
( ~ ( incident @ bc @ a2c2 )
| ( line_equal @ b1c1 @ a2c2 )
| ~ ( incident @ a2 @ b1c1 )
| ( point_equal @ a2 @ bc ) ),
inference(split,[status(esa)],[zip_derived_cl888]) ).
thf(zip_derived_cl11136_226,plain,
( ( incident @ c1 @ a2c2 )
<= ( line_equal @ b1c1 @ a2c2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2973,zip_derived_cl14]) ).
thf(zip_derived_cl2341_227,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ a1c1 @ X1 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2317,zip_derived_cl49]) ).
thf(zip_derived_cl11378,plain,
( ( ( point_equal @ c1 @ bc )
| ~ ( incident @ c1 @ a1c1 )
| ~ ( incident @ bc @ a2c2 )
| ( line_equal @ a1c1 @ a2c2 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 )
& ( line_equal @ b1c1 @ a2c2 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11136,zip_derived_cl2341]) ).
thf(zip_derived_cl11_228,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl2973_229,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ b1c1 )
| ( incident @ X0 @ a2c2 ) )
<= ( line_equal @ b1c1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2970,zip_derived_cl48]) ).
thf(zip_derived_cl27_230,plain,
incident @ bc @ b1c1,
inference(cnf,[status(esa)],[ibc1]) ).
thf(zip_derived_cl11134,plain,
( ( incident @ bc @ a2c2 )
<= ( line_equal @ b1c1 @ a2c2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2973,zip_derived_cl27]) ).
thf(zip_derived_cl88_231,plain,
~ ( line_equal @ a1c1 @ a2c2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl79,'15']) ).
thf(zip_derived_cl11423,plain,
( ( point_equal @ c1 @ bc )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 )
& ( line_equal @ b1c1 @ a2c2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl11378,zip_derived_cl11,zip_derived_cl11134,zip_derived_cl88]) ).
thf(zip_derived_cl42_232,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl11429,plain,
( ( point_equal @ bc @ c1 )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 )
& ( line_equal @ b1c1 @ a2c2 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11423,zip_derived_cl42]) ).
thf(zip_derived_cl47_233,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl11433,plain,
( ! [X0: $i] :
( ~ ( incident @ c1 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 )
& ( line_equal @ b1c1 @ a2c2 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11429,zip_derived_cl47]) ).
thf(zip_derived_cl25_234,plain,
incident @ c1 @ oc,
inference(cnf,[status(esa)],[ic1oc]) ).
thf(zip_derived_cl12038,plain,
( ( incident @ bc @ oc )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 )
& ( line_equal @ b1c1 @ a2c2 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl11433,zip_derived_cl25]) ).
thf(zip_derived_cl323_235,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ b1 )
| ~ ( incident @ X0 @ a2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ b1 @ X1 )
| ( line_equal @ a2c2 @ X1 ) )
<= ( incident @ b1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl49]) ).
thf(zip_derived_cl12106,plain,
( ( ( point_equal @ bc @ b1 )
| ~ ( incident @ bc @ a2c2 )
| ~ ( incident @ b1 @ oc )
| ( line_equal @ a2c2 @ oc ) )
<= ( ( incident @ b1 @ a2c2 )
& ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 )
& ( line_equal @ b1c1 @ a2c2 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl12038,zip_derived_cl323]) ).
thf(zip_derived_cl11134_236,plain,
( ( incident @ bc @ a2c2 )
<= ( line_equal @ b1c1 @ a2c2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2973,zip_derived_cl27]) ).
thf(zip_derived_cl12156,plain,
( ( ( point_equal @ bc @ b1 )
| ~ ( incident @ b1 @ oc )
| ( line_equal @ a2c2 @ oc ) )
<= ( ( incident @ b1 @ a2c2 )
& ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 )
& ( line_equal @ b1c1 @ a2c2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl12106,zip_derived_cl11134]) ).
thf(zip_derived_cl12243,plain,
( ( line_equal @ a2c2 @ oc )
<= ( line_equal @ a2c2 @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl12156]) ).
thf(zip_derived_cl45_237,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl12247,plain,
( ( line_equal @ oc @ a2c2 )
<= ( line_equal @ a2c2 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl12243,zip_derived_cl45]) ).
thf(zip_derived_cl48_238,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl12459,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ oc )
| ( incident @ X0 @ a2c2 ) )
<= ( line_equal @ a2c2 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl12247,zip_derived_cl48]) ).
thf(zip_derived_cl25_239,plain,
incident @ c1 @ oc,
inference(cnf,[status(esa)],[ic1oc]) ).
thf(zip_derived_cl25675,plain,
( ( incident @ c1 @ a2c2 )
<= ( line_equal @ a2c2 @ oc ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl12459,zip_derived_cl25]) ).
thf(zip_derived_cl316_240,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ac )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ac @ X1 )
| ( line_equal @ a1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl29,zip_derived_cl49]) ).
thf(zip_derived_cl25713,plain,
( ( ( point_equal @ c1 @ ac )
| ~ ( incident @ c1 @ a1c1 )
| ~ ( incident @ ac @ a2c2 )
| ( line_equal @ a1c1 @ a2c2 ) )
<= ( line_equal @ a2c2 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl25675,zip_derived_cl316]) ).
thf(zip_derived_cl11_241,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl30_242,plain,
incident @ ac @ a2c2,
inference(cnf,[status(esa)],[iac2]) ).
thf(zip_derived_cl88_243,plain,
~ ( line_equal @ a1c1 @ a2c2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl79,'15']) ).
thf(zip_derived_cl25771,plain,
( ( point_equal @ c1 @ ac )
<= ( line_equal @ a2c2 @ oc ) ),
inference(demod,[status(thm)],[zip_derived_cl25713,zip_derived_cl11,zip_derived_cl30,zip_derived_cl88]) ).
thf(zip_derived_cl42_244,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl25945,plain,
( ( point_equal @ ac @ c1 )
<= ( line_equal @ a2c2 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl25771,zip_derived_cl42]) ).
thf(zip_derived_cl47_245,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl25961,plain,
( ! [X0: $i] :
( ~ ( incident @ c1 @ X0 )
| ( incident @ ac @ X0 ) )
<= ( line_equal @ a2c2 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl25945,zip_derived_cl47]) ).
thf(zip_derived_cl25_246,plain,
incident @ c1 @ oc,
inference(cnf,[status(esa)],[ic1oc]) ).
thf(zip_derived_cl39468,plain,
( ( incident @ ac @ oc )
<= ( line_equal @ a2c2 @ oc ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl25961,zip_derived_cl25]) ).
thf(zip_derived_cl551_247,plain,
( ~ ( incident @ ac @ oc )
<= ~ ( incident @ ac @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl546]) ).
thf('57',plain,
( ~ ( line_equal @ a2c2 @ oc )
| ( incident @ ac @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl39468,zip_derived_cl551]) ).
thf(zip_derived_cl11136_248,plain,
( ( incident @ c1 @ a2c2 )
<= ( line_equal @ b1c1 @ a2c2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2973,zip_derived_cl14]) ).
thf(zip_derived_cl316_249,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ac )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ac @ X1 )
| ( line_equal @ a1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl29,zip_derived_cl49]) ).
thf(zip_derived_cl11336,plain,
( ( ( point_equal @ c1 @ ac )
| ~ ( incident @ c1 @ a1c1 )
| ~ ( incident @ ac @ a2c2 )
| ( line_equal @ a1c1 @ a2c2 ) )
<= ( line_equal @ b1c1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11136,zip_derived_cl316]) ).
thf(zip_derived_cl11_250,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl30_251,plain,
incident @ ac @ a2c2,
inference(cnf,[status(esa)],[iac2]) ).
thf(zip_derived_cl88_252,plain,
~ ( line_equal @ a1c1 @ a2c2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl79,'15']) ).
thf(zip_derived_cl11388,plain,
( ( point_equal @ c1 @ ac )
<= ( line_equal @ b1c1 @ a2c2 ) ),
inference(demod,[status(thm)],[zip_derived_cl11336,zip_derived_cl11,zip_derived_cl30,zip_derived_cl88]) ).
thf(zip_derived_cl42_253,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl11461,plain,
( ( point_equal @ ac @ c1 )
<= ( line_equal @ b1c1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11388,zip_derived_cl42]) ).
thf(zip_derived_cl47_254,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl11471,plain,
( ! [X0: $i] :
( ~ ( incident @ c1 @ X0 )
| ( incident @ ac @ X0 ) )
<= ( line_equal @ b1c1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11461,zip_derived_cl47]) ).
thf(zip_derived_cl25_255,plain,
incident @ c1 @ oc,
inference(cnf,[status(esa)],[ic1oc]) ).
thf(zip_derived_cl24095,plain,
( ( incident @ ac @ oc )
<= ( line_equal @ b1c1 @ a2c2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl11471,zip_derived_cl25]) ).
thf(zip_derived_cl551_256,plain,
( ~ ( incident @ ac @ oc )
<= ~ ( incident @ ac @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl546]) ).
thf('58',plain,
( ~ ( line_equal @ b1c1 @ a2c2 )
| ( incident @ ac @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl24095,zip_derived_cl551]) ).
thf(zip_derived_cl25_257,plain,
incident @ c1 @ oc,
inference(cnf,[status(esa)],[ic1oc]) ).
thf(zip_derived_cl316_258,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ac )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ac @ X1 )
| ( line_equal @ a1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl29,zip_derived_cl49]) ).
thf(zip_derived_cl1051,plain,
( ( point_equal @ c1 @ ac )
| ~ ( incident @ c1 @ a1c1 )
| ~ ( incident @ ac @ oc )
| ( line_equal @ a1c1 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl25,zip_derived_cl316]) ).
thf(zip_derived_cl11_259,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl1091,plain,
( ( point_equal @ c1 @ ac )
| ~ ( incident @ ac @ oc )
| ( line_equal @ a1c1 @ oc ) ),
inference(demod,[status(thm)],[zip_derived_cl1051,zip_derived_cl11]) ).
thf('59',plain,
( ~ ( incident @ ac @ oc )
| ( point_equal @ c1 @ ac )
| ( line_equal @ a1c1 @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl1091]) ).
thf(zip_derived_cl2318_260,plain,
( ( incident @ bc @ ob )
<= ( ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1522,zip_derived_cl24]) ).
thf(zip_derived_cl323_261,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ b1 )
| ~ ( incident @ X0 @ a2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ b1 @ X1 )
| ( line_equal @ a2c2 @ X1 ) )
<= ( incident @ b1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl49]) ).
thf(zip_derived_cl2692,plain,
( ( ( point_equal @ bc @ b1 )
| ~ ( incident @ bc @ a2c2 )
| ~ ( incident @ b1 @ ob )
| ( line_equal @ a2c2 @ ob ) )
<= ( ( incident @ b1 @ a2c2 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2318,zip_derived_cl323]) ).
thf(zip_derived_cl23_262,plain,
incident @ b1 @ ob,
inference(cnf,[status(esa)],[ib1ob]) ).
thf(zip_derived_cl2711,plain,
( ( ( point_equal @ bc @ b1 )
| ~ ( incident @ bc @ a2c2 )
| ( line_equal @ a2c2 @ ob ) )
<= ( ( incident @ b1 @ a2c2 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2692,zip_derived_cl23]) ).
thf(zip_derived_cl2839,plain,
( ( line_equal @ a2c2 @ ob )
<= ( line_equal @ a2c2 @ ob ) ),
inference(split,[status(esa)],[zip_derived_cl2711]) ).
thf(zip_derived_cl45_263,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl2843,plain,
( ( line_equal @ ob @ a2c2 )
<= ( line_equal @ a2c2 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2839,zip_derived_cl45]) ).
thf(zip_derived_cl48_264,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl2959,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ ob )
| ( incident @ X0 @ a2c2 ) )
<= ( line_equal @ a2c2 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2843,zip_derived_cl48]) ).
thf(zip_derived_cl24_265,plain,
incident @ b2 @ ob,
inference(cnf,[status(esa)],[ib2ob]) ).
thf(zip_derived_cl10467,plain,
( ( incident @ b2 @ a2c2 )
<= ( line_equal @ a2c2 @ ob ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2959,zip_derived_cl24]) ).
thf(zip_derived_cl107_266,plain,
! [X0: $i] :
( ~ ( incident @ a2 @ X0 )
| ~ ( incident @ b2 @ X0 )
| ~ ( incident @ c2 @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl69,'9']) ).
thf(zip_derived_cl13_267,plain,
incident @ c2 @ a2c2,
inference(cnf,[status(esa)],[ic2a2]) ).
thf(zip_derived_cl116,plain,
( ~ ( incident @ b2 @ a2c2 )
| ~ ( incident @ a2 @ a2c2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl107,zip_derived_cl13]) ).
thf(zip_derived_cl12_268,plain,
incident @ a2 @ a2c2,
inference(cnf,[status(esa)],[ia2c2]) ).
thf(zip_derived_cl117,plain,
~ ( incident @ b2 @ a2c2 ),
inference(demod,[status(thm)],[zip_derived_cl116,zip_derived_cl12]) ).
thf('60',plain,
~ ( line_equal @ a2c2 @ ob ),
inference('s_sup-',[status(thm)],[zip_derived_cl10467,zip_derived_cl117]) ).
thf(zip_derived_cl19_269,plain,
incident @ o @ ob,
inference(cnf,[status(esa)],[ioob]) ).
thf(zip_derived_cl323_270,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ b1 )
| ~ ( incident @ X0 @ a2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ b1 @ X1 )
| ( line_equal @ a2c2 @ X1 ) )
<= ( incident @ b1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl49]) ).
thf(zip_derived_cl1677,plain,
( ( ( point_equal @ o @ b1 )
| ~ ( incident @ o @ a2c2 )
| ~ ( incident @ b1 @ ob )
| ( line_equal @ a2c2 @ ob ) )
<= ( incident @ b1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl19,zip_derived_cl323]) ).
thf(zip_derived_cl23_271,plain,
incident @ b1 @ ob,
inference(cnf,[status(esa)],[ib1ob]) ).
thf(zip_derived_cl1718,plain,
( ( ( point_equal @ o @ b1 )
| ~ ( incident @ o @ a2c2 )
| ( line_equal @ a2c2 @ ob ) )
<= ( incident @ b1 @ a2c2 ) ),
inference(demod,[status(thm)],[zip_derived_cl1677,zip_derived_cl23]) ).
thf('61',plain,
( ( point_equal @ o @ b1 )
| ( line_equal @ a2c2 @ ob )
| ~ ( incident @ b1 @ a2c2 )
| ~ ( incident @ o @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl1718]) ).
thf(zip_derived_cl22_272,plain,
incident @ a2 @ oa,
inference(cnf,[status(esa)],[ia2oa]) ).
thf(zip_derived_cl314_273,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl49]) ).
thf(zip_derived_cl891,plain,
( ( point_equal @ a2 @ bc )
| ~ ( incident @ a2 @ b1c1 )
| ~ ( incident @ bc @ oa )
| ( line_equal @ b1c1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl314]) ).
thf(zip_derived_cl11118,plain,
( ( line_equal @ b1c1 @ oa )
<= ( line_equal @ b1c1 @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl891]) ).
thf(zip_derived_cl45_274,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl11123,plain,
( ( line_equal @ oa @ b1c1 )
<= ( line_equal @ b1c1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11118,zip_derived_cl45]) ).
thf(zip_derived_cl48_275,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl11127,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ oa )
| ( incident @ X0 @ b1c1 ) )
<= ( line_equal @ b1c1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11123,zip_derived_cl48]) ).
thf(zip_derived_cl21_276,plain,
incident @ a1 @ oa,
inference(cnf,[status(esa)],[ia1oa]) ).
thf(zip_derived_cl23892,plain,
( ( incident @ a1 @ b1c1 )
<= ( line_equal @ b1c1 @ oa ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl11127,zip_derived_cl21]) ).
thf(zip_derived_cl137_277,plain,
~ ( incident @ a1 @ b1c1 ),
inference(demod,[status(thm)],[zip_derived_cl134,zip_derived_cl15]) ).
thf('62',plain,
~ ( line_equal @ b1c1 @ oa ),
inference('s_sup-',[status(thm)],[zip_derived_cl23892,zip_derived_cl137]) ).
thf(zip_derived_cl22_278,plain,
incident @ a2 @ oa,
inference(cnf,[status(esa)],[ia2oa]) ).
thf(zip_derived_cl15_279,plain,
incident @ b1 @ b1c1,
inference(cnf,[status(esa)],[ib1c1]) ).
thf(zip_derived_cl49_280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl324,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ b1 )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ b1 @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl15,zip_derived_cl49]) ).
thf(zip_derived_cl1788,plain,
( ( point_equal @ a2 @ b1 )
| ~ ( incident @ a2 @ b1c1 )
| ~ ( incident @ b1 @ oa )
| ( line_equal @ b1c1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl324]) ).
thf('63',plain,
( ( point_equal @ a2 @ b1 )
| ( line_equal @ b1c1 @ oa )
| ~ ( incident @ a2 @ b1c1 )
| ~ ( incident @ b1 @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl1788]) ).
thf(zip_derived_cl12459_281,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ oc )
| ( incident @ X0 @ a2c2 ) )
<= ( line_equal @ a2c2 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl12247,zip_derived_cl48]) ).
thf(zip_derived_cl20_282,plain,
incident @ o @ oc,
inference(cnf,[status(esa)],[iooc]) ).
thf(zip_derived_cl25679,plain,
( ( incident @ o @ a2c2 )
<= ( line_equal @ a2c2 @ oc ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl12459,zip_derived_cl20]) ).
thf(zip_derived_cl18_283,plain,
incident @ o @ oa,
inference(cnf,[status(esa)],[iooa]) ).
thf(zip_derived_cl315_284,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ac )
| ~ ( incident @ X0 @ a2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ac @ X1 )
| ( line_equal @ a2c2 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl49]) ).
thf(zip_derived_cl989,plain,
( ( point_equal @ o @ ac )
| ~ ( incident @ o @ a2c2 )
| ~ ( incident @ ac @ oa )
| ( line_equal @ a2c2 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl315]) ).
thf(zip_derived_cl14052,plain,
( ~ ( incident @ o @ a2c2 )
<= ~ ( incident @ o @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl989]) ).
thf('64',plain,
( ( incident @ o @ a2c2 )
| ~ ( line_equal @ a2c2 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl25679,zip_derived_cl14052]) ).
thf(zip_derived_cl26_285,plain,
incident @ c2 @ oc,
inference(cnf,[status(esa)],[ic2oc]) ).
thf(zip_derived_cl315_286,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ac )
| ~ ( incident @ X0 @ a2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ac @ X1 )
| ( line_equal @ a2c2 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl49]) ).
thf(zip_derived_cl988,plain,
( ( point_equal @ c2 @ ac )
| ~ ( incident @ c2 @ a2c2 )
| ~ ( incident @ ac @ oc )
| ( line_equal @ a2c2 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl315]) ).
thf(zip_derived_cl13_287,plain,
incident @ c2 @ a2c2,
inference(cnf,[status(esa)],[ic2a2]) ).
thf(zip_derived_cl1014,plain,
( ( point_equal @ c2 @ ac )
| ~ ( incident @ ac @ oc )
| ( line_equal @ a2c2 @ oc ) ),
inference(demod,[status(thm)],[zip_derived_cl988,zip_derived_cl13]) ).
thf('65',plain,
( ~ ( incident @ ac @ oc )
| ( point_equal @ c2 @ ac )
| ( line_equal @ a2c2 @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl1014]) ).
thf(zip_derived_cl66_288,plain,
( ( incident @ c1 @ a2b2 )
<= ( incident @ c1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl5]) ).
thf(zip_derived_cl315_289,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ac )
| ~ ( incident @ X0 @ a2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ac @ X1 )
| ( line_equal @ a2c2 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl49]) ).
thf(zip_derived_cl973,plain,
( ( ( point_equal @ c1 @ ac )
| ~ ( incident @ c1 @ a2c2 )
| ~ ( incident @ ac @ a2b2 )
| ( line_equal @ a2c2 @ a2b2 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl315]) ).
thf(zip_derived_cl13775,plain,
( ( point_equal @ c1 @ ac )
<= ( point_equal @ c1 @ ac ) ),
inference(split,[status(esa)],[zip_derived_cl973]) ).
thf(zip_derived_cl42_290,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl13780,plain,
( ( point_equal @ ac @ c1 )
<= ( point_equal @ c1 @ ac ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl13775,zip_derived_cl42]) ).
thf(zip_derived_cl47_291,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl13795,plain,
( ! [X0: $i] :
( ~ ( incident @ c1 @ X0 )
| ( incident @ ac @ X0 ) )
<= ( point_equal @ c1 @ ac ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl13780,zip_derived_cl47]) ).
thf(zip_derived_cl25_292,plain,
incident @ c1 @ oc,
inference(cnf,[status(esa)],[ic1oc]) ).
thf(zip_derived_cl29522,plain,
( ( incident @ ac @ oc )
<= ( point_equal @ c1 @ ac ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl13795,zip_derived_cl25]) ).
thf(zip_derived_cl551_293,plain,
( ~ ( incident @ ac @ oc )
<= ~ ( incident @ ac @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl546]) ).
thf('66',plain,
( ~ ( point_equal @ c1 @ ac )
| ( incident @ ac @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl29522,zip_derived_cl551]) ).
thf(zip_derived_cl18_294,plain,
incident @ o @ oa,
inference(cnf,[status(esa)],[iooa]) ).
thf(zip_derived_cl323_295,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ b1 )
| ~ ( incident @ X0 @ a2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ b1 @ X1 )
| ( line_equal @ a2c2 @ X1 ) )
<= ( incident @ b1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl49]) ).
thf(zip_derived_cl1676,plain,
( ( ( point_equal @ o @ b1 )
| ~ ( incident @ o @ a2c2 )
| ~ ( incident @ b1 @ oa )
| ( line_equal @ a2c2 @ oa ) )
<= ( incident @ b1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl323]) ).
thf(zip_derived_cl35937,plain,
( ( point_equal @ o @ b1 )
<= ( point_equal @ o @ b1 ) ),
inference(split,[status(esa)],[zip_derived_cl1676]) ).
thf(zip_derived_cl42_296,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl35943,plain,
( ( point_equal @ b1 @ o )
<= ( point_equal @ o @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl35937,zip_derived_cl42]) ).
thf(zip_derived_cl47_297,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl36150,plain,
( ! [X0: $i] :
( ~ ( incident @ o @ X0 )
| ( incident @ b1 @ X0 ) )
<= ( point_equal @ o @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl35943,zip_derived_cl47]) ).
thf(zip_derived_cl18_298,plain,
incident @ o @ oa,
inference(cnf,[status(esa)],[iooa]) ).
thf(zip_derived_cl44888,plain,
( ( incident @ b1 @ oa )
<= ( point_equal @ o @ b1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl36150,zip_derived_cl18]) ).
thf(zip_derived_cl31324_299,plain,
( ~ ( incident @ b1 @ oa )
<= ~ ( incident @ b1 @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl1548]) ).
thf('67',plain,
( ~ ( point_equal @ o @ b1 )
| ( incident @ b1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl44888,zip_derived_cl31324]) ).
thf(zip_derived_cl16_300,plain,
incident @ c2 @ b2c2,
inference(cnf,[status(esa)],[ic2b2]) ).
thf(zip_derived_cl315_301,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ac )
| ~ ( incident @ X0 @ a2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ac @ X1 )
| ( line_equal @ a2c2 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl49]) ).
thf(zip_derived_cl985,plain,
( ( point_equal @ c2 @ ac )
| ~ ( incident @ c2 @ a2c2 )
| ~ ( incident @ ac @ b2c2 )
| ( line_equal @ a2c2 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl315]) ).
thf(zip_derived_cl13_302,plain,
incident @ c2 @ a2c2,
inference(cnf,[status(esa)],[ic2a2]) ).
thf(zip_derived_cl1011,plain,
( ( point_equal @ c2 @ ac )
| ~ ( incident @ ac @ b2c2 )
| ( line_equal @ a2c2 @ b2c2 ) ),
inference(demod,[status(thm)],[zip_derived_cl985,zip_derived_cl13]) ).
thf(zip_derived_cl14906,plain,
( ( point_equal @ c2 @ ac )
<= ( point_equal @ c2 @ ac ) ),
inference(split,[status(esa)],[zip_derived_cl1011]) ).
thf(zip_derived_cl42_303,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl14911,plain,
( ( point_equal @ ac @ c2 )
<= ( point_equal @ c2 @ ac ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl14906,zip_derived_cl42]) ).
thf(zip_derived_cl47_304,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl14922,plain,
( ! [X0: $i] :
( ~ ( incident @ c2 @ X0 )
| ( incident @ ac @ X0 ) )
<= ( point_equal @ c2 @ ac ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl14911,zip_derived_cl47]) ).
thf(zip_derived_cl16_305,plain,
incident @ c2 @ b2c2,
inference(cnf,[status(esa)],[ic2b2]) ).
thf(zip_derived_cl30351,plain,
( ( incident @ ac @ b2c2 )
<= ( point_equal @ c2 @ ac ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl14922,zip_derived_cl16]) ).
thf(zip_derived_cl62_306,plain,
( ( incident @ a1 @ b2c2 )
<= ( incident @ a1 @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl3]) ).
thf(zip_derived_cl44_307,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X0 )
| ~ ( incident @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[reflexivity_of_line_equal]) ).
thf(zip_derived_cl146,plain,
( ( line_equal @ b2c2 @ b2c2 )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl44]) ).
thf(zip_derived_cl114_308,plain,
! [X0: $i] :
( ~ ( line_equal @ X0 @ X0 )
| ~ ( incident @ bc @ X0 )
| ~ ( incident @ ac @ X0 )
| ~ ( incident @ ab @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl51,'6']) ).
thf(zip_derived_cl162,plain,
( ( ~ ( incident @ bc @ b2c2 )
| ~ ( incident @ ac @ b2c2 )
| ~ ( incident @ ab @ b2c2 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl146,zip_derived_cl114]) ).
thf(zip_derived_cl176,plain,
( ~ ( incident @ ac @ b2c2 )
<= ~ ( incident @ ac @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl162]) ).
thf('68',plain,
( ~ ( point_equal @ c2 @ ac )
| ( incident @ ac @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl30351,zip_derived_cl176]) ).
thf(zip_derived_cl17_309,plain,
incident @ b2 @ b2c2,
inference(cnf,[status(esa)],[ib2c2]) ).
thf(zip_derived_cl316_310,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ac )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ac @ X1 )
| ( line_equal @ a1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl29,zip_derived_cl49]) ).
thf(zip_derived_cl1056,plain,
( ( point_equal @ b2 @ ac )
| ~ ( incident @ b2 @ a1c1 )
| ~ ( incident @ ac @ b2c2 )
| ( line_equal @ a1c1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl316]) ).
thf('69',plain,
( ~ ( incident @ b2 @ a1c1 )
| ( point_equal @ b2 @ ac )
| ( line_equal @ a1c1 @ b2c2 )
| ~ ( incident @ ac @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl1056]) ).
thf(zip_derived_cl15_311,plain,
incident @ b1 @ b1c1,
inference(cnf,[status(esa)],[ib1c1]) ).
thf(zip_derived_cl44_312,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X0 )
| ~ ( incident @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[reflexivity_of_line_equal]) ).
thf(zip_derived_cl150,plain,
line_equal @ b1c1 @ b1c1,
inference('s_sup-',[status(thm)],[zip_derived_cl15,zip_derived_cl44]) ).
thf(zip_derived_cl114_313,plain,
! [X0: $i] :
( ~ ( line_equal @ X0 @ X0 )
| ~ ( incident @ bc @ X0 )
| ~ ( incident @ ac @ X0 )
| ~ ( incident @ ab @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl51,'6']) ).
thf(zip_derived_cl297,plain,
( ~ ( incident @ bc @ b1c1 )
| ~ ( incident @ ac @ b1c1 )
| ~ ( incident @ ab @ b1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl150,zip_derived_cl114]) ).
thf(zip_derived_cl27_314,plain,
incident @ bc @ b1c1,
inference(cnf,[status(esa)],[ibc1]) ).
thf(zip_derived_cl300,plain,
( ~ ( incident @ ac @ b1c1 )
| ~ ( incident @ ab @ b1c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl297,zip_derived_cl27]) ).
thf('70',plain,
( ~ ( incident @ ab @ b1c1 )
| ~ ( incident @ ac @ b1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl300]) ).
thf(zip_derived_cl12_315,plain,
incident @ a2 @ a2c2,
inference(cnf,[status(esa)],[ia2c2]) ).
thf(zip_derived_cl324_316,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ b1 )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ b1 @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl15,zip_derived_cl49]) ).
thf(zip_derived_cl1785,plain,
( ( point_equal @ a2 @ b1 )
| ~ ( incident @ a2 @ b1c1 )
| ~ ( incident @ b1 @ a2c2 )
| ( line_equal @ b1c1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl324]) ).
thf('71',plain,
( ( point_equal @ a2 @ b1 )
| ( line_equal @ b1c1 @ a2c2 )
| ~ ( incident @ a2 @ b1c1 )
| ~ ( incident @ b1 @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl1785]) ).
thf(zip_derived_cl30_317,plain,
incident @ ac @ a2c2,
inference(cnf,[status(esa)],[iac2]) ).
thf(zip_derived_cl324_318,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ b1 )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ b1 @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl15,zip_derived_cl49]) ).
thf(zip_derived_cl1758,plain,
( ( point_equal @ ac @ b1 )
| ~ ( incident @ ac @ b1c1 )
| ~ ( incident @ b1 @ a2c2 )
| ( line_equal @ b1c1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl324]) ).
thf(zip_derived_cl38615,plain,
( ( point_equal @ ac @ b1 )
<= ( point_equal @ ac @ b1 ) ),
inference(split,[status(esa)],[zip_derived_cl1758]) ).
thf(zip_derived_cl47_319,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl38620,plain,
( ! [X0: $i] :
( ~ ( incident @ b1 @ X0 )
| ( incident @ ac @ X0 ) )
<= ( point_equal @ ac @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl38615,zip_derived_cl47]) ).
thf(zip_derived_cl15_320,plain,
incident @ b1 @ b1c1,
inference(cnf,[status(esa)],[ib1c1]) ).
thf(zip_derived_cl46169,plain,
( ( incident @ ac @ b1c1 )
<= ( point_equal @ ac @ b1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl38620,zip_derived_cl15]) ).
thf(zip_derived_cl65_321,plain,
( ( incident @ a2 @ b1c1 )
<= ( incident @ a2 @ b1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl5]) ).
thf(zip_derived_cl44_322,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X0 )
| ~ ( incident @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[reflexivity_of_line_equal]) ).
thf(zip_derived_cl157,plain,
( ( line_equal @ b1c1 @ b1c1 )
<= ( incident @ a2 @ b1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl65,zip_derived_cl44]) ).
thf(zip_derived_cl114_323,plain,
! [X0: $i] :
( ~ ( line_equal @ X0 @ X0 )
| ~ ( incident @ bc @ X0 )
| ~ ( incident @ ac @ X0 )
| ~ ( incident @ ab @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl51,'6']) ).
thf(zip_derived_cl169,plain,
( ( ~ ( incident @ bc @ b1c1 )
| ~ ( incident @ ac @ b1c1 )
| ~ ( incident @ ab @ b1c1 ) )
<= ( incident @ a2 @ b1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl157,zip_derived_cl114]) ).
thf(zip_derived_cl189,plain,
( ~ ( incident @ ac @ b1c1 )
<= ~ ( incident @ ac @ b1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl169]) ).
thf('72',plain,
( ~ ( point_equal @ ac @ b1 )
| ( incident @ ac @ b1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl46169,zip_derived_cl189]) ).
thf(zip_derived_cl30_324,plain,
incident @ ac @ a2c2,
inference(cnf,[status(esa)],[iac2]) ).
thf(zip_derived_cl326_325,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ b1 )
| ~ ( incident @ X0 @ ob )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ b1 @ X1 )
| ( line_equal @ ob @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl49]) ).
thf(zip_derived_cl1990,plain,
( ( point_equal @ ac @ b1 )
| ~ ( incident @ ac @ ob )
| ~ ( incident @ b1 @ a2c2 )
| ( line_equal @ ob @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl326]) ).
thf('73',plain,
( ~ ( incident @ ac @ ob )
| ( point_equal @ ac @ b1 )
| ( line_equal @ ob @ a2c2 )
| ~ ( incident @ b1 @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl1990]) ).
thf(zip_derived_cl44049,plain,
( ( line_equal @ ob @ a2c2 )
<= ( line_equal @ ob @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl1990]) ).
thf(zip_derived_cl48_326,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl44055,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ ob )
| ( incident @ X0 @ a2c2 ) )
<= ( line_equal @ ob @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl44049,zip_derived_cl48]) ).
thf(zip_derived_cl24_327,plain,
incident @ b2 @ ob,
inference(cnf,[status(esa)],[ib2ob]) ).
thf(zip_derived_cl49376,plain,
( ( incident @ b2 @ a2c2 )
<= ( line_equal @ ob @ a2c2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl44055,zip_derived_cl24]) ).
thf(zip_derived_cl117_328,plain,
~ ( incident @ b2 @ a2c2 ),
inference(demod,[status(thm)],[zip_derived_cl116,zip_derived_cl12]) ).
thf('74',plain,
~ ( line_equal @ ob @ a2c2 ),
inference('s_sup-',[status(thm)],[zip_derived_cl49376,zip_derived_cl117]) ).
thf(zip_derived_cl28_329,plain,
incident @ bc @ b2c2,
inference(cnf,[status(esa)],[ibc2]) ).
thf(zip_derived_cl315_330,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ac )
| ~ ( incident @ X0 @ a2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ac @ X1 )
| ( line_equal @ a2c2 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl49]) ).
thf(zip_derived_cl947,plain,
( ( point_equal @ bc @ ac )
| ~ ( incident @ bc @ a2c2 )
| ~ ( incident @ ac @ b2c2 )
| ( line_equal @ a2c2 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl28,zip_derived_cl315]) ).
thf('75',plain,
( ~ ( incident @ bc @ a2c2 )
| ~ ( incident @ ac @ b2c2 )
| ( point_equal @ bc @ ac )
| ( line_equal @ a2c2 @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl947]) ).
thf(zip_derived_cl12825,plain,
( ( line_equal @ a2c2 @ b2c2 )
<= ( line_equal @ a2c2 @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl947]) ).
thf(zip_derived_cl48_331,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl12830,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ a2c2 )
| ( incident @ X0 @ b2c2 ) )
<= ( line_equal @ a2c2 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl12825,zip_derived_cl48]) ).
thf(zip_derived_cl12_332,plain,
incident @ a2 @ a2c2,
inference(cnf,[status(esa)],[ia2c2]) ).
thf(zip_derived_cl26120,plain,
( ( incident @ a2 @ b2c2 )
<= ( line_equal @ a2c2 @ b2c2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl12830,zip_derived_cl12]) ).
thf(zip_derived_cl173_333,plain,
~ ( incident @ a2 @ b2c2 ),
inference(demod,[status(thm)],[zip_derived_cl165,zip_derived_cl17]) ).
thf('76',plain,
~ ( line_equal @ a2c2 @ b2c2 ),
inference('s_sup-',[status(thm)],[zip_derived_cl26120,zip_derived_cl173]) ).
thf(zip_derived_cl15879,plain,
( ( point_equal @ b2 @ ac )
<= ( point_equal @ b2 @ ac ) ),
inference(split,[status(esa)],[zip_derived_cl1056]) ).
thf(zip_derived_cl42_334,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl15885,plain,
( ( point_equal @ ac @ b2 )
<= ( point_equal @ b2 @ ac ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl15879,zip_derived_cl42]) ).
thf(zip_derived_cl47_335,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl15914,plain,
( ! [X0: $i] :
( ~ ( incident @ b2 @ X0 )
| ( incident @ ac @ X0 ) )
<= ( point_equal @ b2 @ ac ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl15885,zip_derived_cl47]) ).
thf(zip_derived_cl24_336,plain,
incident @ b2 @ ob,
inference(cnf,[status(esa)],[ib2ob]) ).
thf(zip_derived_cl30621,plain,
( ( incident @ ac @ ob )
<= ( point_equal @ b2 @ ac ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl15914,zip_derived_cl24]) ).
thf(zip_derived_cl541_337,plain,
( ~ ( incident @ ac @ ob )
<= ~ ( incident @ ac @ ob ) ),
inference(split,[status(esa)],[zip_derived_cl536]) ).
thf('77',plain,
( ~ ( point_equal @ b2 @ ac )
| ( incident @ ac @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl30621,zip_derived_cl541]) ).
thf(zip_derived_cl15914_338,plain,
( ! [X0: $i] :
( ~ ( incident @ b2 @ X0 )
| ( incident @ ac @ X0 ) )
<= ( point_equal @ b2 @ ac ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl15885,zip_derived_cl47]) ).
thf(zip_derived_cl17_339,plain,
incident @ b2 @ b2c2,
inference(cnf,[status(esa)],[ib2c2]) ).
thf(zip_derived_cl30617,plain,
( ( incident @ ac @ b2c2 )
<= ( point_equal @ b2 @ ac ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl15914,zip_derived_cl17]) ).
thf(zip_derived_cl176_340,plain,
( ~ ( incident @ ac @ b2c2 )
<= ~ ( incident @ ac @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl162]) ).
thf('78',plain,
( ~ ( point_equal @ b2 @ ac )
| ( incident @ ac @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl30617,zip_derived_cl176]) ).
thf(zip_derived_cl37456_341,plain,
( ! [X0: $i] :
( ~ ( incident @ a2 @ X0 )
| ( incident @ b1 @ X0 ) )
<= ( point_equal @ a2 @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl37440,zip_derived_cl47]) ).
thf(zip_derived_cl8_342,plain,
incident @ a2 @ a2b2,
inference(cnf,[status(esa)],[ia2b2]) ).
thf(zip_derived_cl45194,plain,
( ( incident @ b1 @ a2b2 )
<= ( point_equal @ a2 @ b1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl37456,zip_derived_cl8]) ).
thf(zip_derived_cl31_343,plain,
incident @ ab @ a1b1,
inference(cnf,[status(esa)],[iab1]) ).
thf(zip_derived_cl49_344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl318,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ab )
| ~ ( incident @ X0 @ a1b1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ab @ X1 )
| ( line_equal @ a1b1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl31,zip_derived_cl49]) ).
thf(zip_derived_cl45327,plain,
( ( ( point_equal @ b1 @ ab )
| ~ ( incident @ b1 @ a1b1 )
| ~ ( incident @ ab @ a2b2 )
| ( line_equal @ a1b1 @ a2b2 ) )
<= ( point_equal @ a2 @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl45194,zip_derived_cl318]) ).
thf(zip_derived_cl7_345,plain,
incident @ b1 @ a1b1,
inference(cnf,[status(esa)],[ib1a1]) ).
thf(zip_derived_cl32_346,plain,
incident @ ab @ a2b2,
inference(cnf,[status(esa)],[iab2]) ).
thf(zip_derived_cl89_347,plain,
~ ( line_equal @ a1b1 @ a2b2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl81,'38']) ).
thf(zip_derived_cl45392,plain,
( ( point_equal @ b1 @ ab )
<= ( point_equal @ a2 @ b1 ) ),
inference(demod,[status(thm)],[zip_derived_cl45327,zip_derived_cl7,zip_derived_cl32,zip_derived_cl89]) ).
thf(zip_derived_cl42_348,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl45561,plain,
( ( point_equal @ ab @ b1 )
<= ( point_equal @ a2 @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl45392,zip_derived_cl42]) ).
thf(zip_derived_cl47_349,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl45584,plain,
( ! [X0: $i] :
( ~ ( incident @ b1 @ X0 )
| ( incident @ ab @ X0 ) )
<= ( point_equal @ a2 @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl45561,zip_derived_cl47]) ).
thf(zip_derived_cl15_350,plain,
incident @ b1 @ b1c1,
inference(cnf,[status(esa)],[ib1c1]) ).
thf(zip_derived_cl51657,plain,
( ( incident @ ab @ b1c1 )
<= ( point_equal @ a2 @ b1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl45584,zip_derived_cl15]) ).
thf(zip_derived_cl188,plain,
( ~ ( incident @ ab @ b1c1 )
<= ~ ( incident @ ab @ b1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl169]) ).
thf('79',plain,
( ( incident @ ab @ b1c1 )
| ~ ( point_equal @ a2 @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl51657,zip_derived_cl188]) ).
thf(zip_derived_cl21_351,plain,
incident @ a1 @ oa,
inference(cnf,[status(esa)],[ia1oa]) ).
thf(zip_derived_cl326_352,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ b1 )
| ~ ( incident @ X0 @ ob )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ b1 @ X1 )
| ( line_equal @ ob @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl49]) ).
thf(zip_derived_cl2004,plain,
( ( point_equal @ a1 @ b1 )
| ~ ( incident @ a1 @ ob )
| ~ ( incident @ b1 @ oa )
| ( line_equal @ ob @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl326]) ).
thf(zip_derived_cl44402,plain,
( ( line_equal @ ob @ oa )
<= ( line_equal @ ob @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl2004]) ).
thf(zip_derived_cl48_353,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl44408,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ ob )
| ( incident @ X0 @ oa ) )
<= ( line_equal @ ob @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl44402,zip_derived_cl48]) ).
thf(zip_derived_cl24_354,plain,
incident @ b2 @ ob,
inference(cnf,[status(esa)],[ib2ob]) ).
thf(zip_derived_cl50036,plain,
( ( incident @ b2 @ oa )
<= ( line_equal @ ob @ oa ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl44408,zip_derived_cl24]) ).
thf(zip_derived_cl31597,plain,
( ~ ( incident @ b2 @ oa )
<= ~ ( incident @ b2 @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl1561]) ).
thf('80',plain,
( ~ ( line_equal @ ob @ oa )
| ( incident @ b2 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl50036,zip_derived_cl31597]) ).
thf(zip_derived_cl61_355,plain,
( ( incident @ b2 @ a1c1 )
<= ( incident @ b2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl3]) ).
thf(zip_derived_cl322_356,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ oa )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ oa @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl49]) ).
thf(zip_derived_cl1563,plain,
( ( ( point_equal @ b2 @ a1 )
| ~ ( incident @ b2 @ oa )
| ~ ( incident @ a1 @ a1c1 )
| ( line_equal @ oa @ a1c1 ) )
<= ( incident @ b2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl322]) ).
thf(zip_derived_cl10_357,plain,
incident @ a1 @ a1c1,
inference(cnf,[status(esa)],[ia1c1]) ).
thf(zip_derived_cl1601,plain,
( ( ( point_equal @ b2 @ a1 )
| ~ ( incident @ b2 @ oa )
| ( line_equal @ oa @ a1c1 ) )
<= ( incident @ b2 @ a1c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1563,zip_derived_cl10]) ).
thf('81',plain,
( ~ ( incident @ b2 @ oa )
| ( point_equal @ b2 @ a1 )
| ~ ( incident @ b2 @ a1c1 )
| ( line_equal @ oa @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl1601]) ).
thf(zip_derived_cl411_358,plain,
( ( point_equal @ b2 @ a1 )
<= ( point_equal @ b2 @ a1 ) ),
inference(split,[status(esa)],[zip_derived_cl404]) ).
thf(zip_derived_cl42_359,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl415,plain,
( ( point_equal @ a1 @ b2 )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl411,zip_derived_cl42]) ).
thf(zip_derived_cl47_360,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl429,plain,
( ! [X0: $i] :
( ~ ( incident @ b2 @ X0 )
| ( incident @ a1 @ X0 ) )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl415,zip_derived_cl47]) ).
thf(zip_derived_cl9_361,plain,
incident @ b2 @ a2b2,
inference(cnf,[status(esa)],[ib2a2]) ).
thf(zip_derived_cl503,plain,
( ( incident @ a1 @ a2b2 )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl429,zip_derived_cl9]) ).
thf(zip_derived_cl96_362,plain,
! [X0: $i] :
( ~ ( incident @ a1 @ X0 )
| ~ ( incident @ b1 @ X0 )
| ~ ( incident @ c1 @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl67,'19']) ).
thf(zip_derived_cl66_363,plain,
( ( incident @ c1 @ a2b2 )
<= ( incident @ c1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl5]) ).
thf(zip_derived_cl97,plain,
( ( ~ ( incident @ b1 @ a2b2 )
| ~ ( incident @ a1 @ a2b2 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl96,zip_derived_cl66]) ).
thf(zip_derived_cl100,plain,
( ~ ( incident @ a1 @ a2b2 )
<= ~ ( incident @ a1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl97]) ).
thf('82',plain,
( ~ ( point_equal @ b2 @ a1 )
| ( incident @ a1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl503,zip_derived_cl100]) ).
thf(zip_derived_cl18_364,plain,
incident @ o @ oa,
inference(cnf,[status(esa)],[iooa]) ).
thf(zip_derived_cl6_365,plain,
incident @ a1 @ a1b1,
inference(cnf,[status(esa)],[ia1b1]) ).
thf(zip_derived_cl49_366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl321,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ a1b1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ a1b1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl49]) ).
thf(zip_derived_cl1477,plain,
( ( point_equal @ o @ a1 )
| ~ ( incident @ o @ a1b1 )
| ~ ( incident @ a1 @ oa )
| ( line_equal @ a1b1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl321]) ).
thf(zip_derived_cl21_367,plain,
incident @ a1 @ oa,
inference(cnf,[status(esa)],[ia1oa]) ).
thf(zip_derived_cl1517,plain,
( ( point_equal @ o @ a1 )
| ~ ( incident @ o @ a1b1 )
| ( line_equal @ a1b1 @ oa ) ),
inference(demod,[status(thm)],[zip_derived_cl1477,zip_derived_cl21]) ).
thf('83',plain,
( ~ ( incident @ o @ a1b1 )
| ( line_equal @ a1b1 @ oa )
| ( point_equal @ o @ a1 ) ),
inference(split,[status(esa)],[zip_derived_cl1517]) ).
thf(zip_derived_cl429_368,plain,
( ! [X0: $i] :
( ~ ( incident @ b2 @ X0 )
| ( incident @ a1 @ X0 ) )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl415,zip_derived_cl47]) ).
thf(zip_derived_cl24_369,plain,
incident @ b2 @ ob,
inference(cnf,[status(esa)],[ib2ob]) ).
thf(zip_derived_cl505,plain,
( ( incident @ a1 @ ob )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl429,zip_derived_cl24]) ).
thf(zip_derived_cl7_370,plain,
incident @ b1 @ a1b1,
inference(cnf,[status(esa)],[ib1a1]) ).
thf(zip_derived_cl49_371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl325,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ b1 )
| ~ ( incident @ X0 @ a1b1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ b1 @ X1 )
| ( line_equal @ a1b1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl49]) ).
thf(zip_derived_cl1877,plain,
( ( ( point_equal @ a1 @ b1 )
| ~ ( incident @ a1 @ a1b1 )
| ~ ( incident @ b1 @ ob )
| ( line_equal @ a1b1 @ ob ) )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl505,zip_derived_cl325]) ).
thf(zip_derived_cl6_372,plain,
incident @ a1 @ a1b1,
inference(cnf,[status(esa)],[ia1b1]) ).
thf(zip_derived_cl23_373,plain,
incident @ b1 @ ob,
inference(cnf,[status(esa)],[ib1ob]) ).
thf(zip_derived_cl1923,plain,
( ( ( point_equal @ a1 @ b1 )
| ( line_equal @ a1b1 @ ob ) )
<= ( point_equal @ b2 @ a1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1877,zip_derived_cl6,zip_derived_cl23]) ).
thf(zip_derived_cl413_374,plain,
( ! [X0: $i] :
( ~ ( point_equal @ a1 @ X0 )
| ( point_equal @ b2 @ X0 ) )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl411,zip_derived_cl43]) ).
thf(zip_derived_cl85_375,plain,
~ ( point_equal @ b2 @ b1 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl73,'28']) ).
thf(zip_derived_cl843,plain,
( ~ ( point_equal @ a1 @ b1 )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl413,zip_derived_cl85]) ).
thf(zip_derived_cl42109,plain,
( ( line_equal @ a1b1 @ ob )
<= ( point_equal @ b2 @ a1 ) ),
inference(clc,[status(thm)],[zip_derived_cl1923,zip_derived_cl843]) ).
thf(zip_derived_cl45_376,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl42111,plain,
( ( line_equal @ ob @ a1b1 )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl42109,zip_derived_cl45]) ).
thf(zip_derived_cl48_377,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl42119,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ ob )
| ( incident @ X0 @ a1b1 ) )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl42111,zip_derived_cl48]) ).
thf(zip_derived_cl19_378,plain,
incident @ o @ ob,
inference(cnf,[status(esa)],[ioob]) ).
thf(zip_derived_cl48119,plain,
( ( incident @ o @ a1b1 )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl42119,zip_derived_cl19]) ).
thf(zip_derived_cl18_379,plain,
incident @ o @ oa,
inference(cnf,[status(esa)],[iooa]) ).
thf(zip_derived_cl318_380,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ab )
| ~ ( incident @ X0 @ a1b1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ab @ X1 )
| ( line_equal @ a1b1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl31,zip_derived_cl49]) ).
thf(zip_derived_cl1264,plain,
( ( point_equal @ o @ ab )
| ~ ( incident @ o @ a1b1 )
| ~ ( incident @ ab @ oa )
| ( line_equal @ a1b1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl318]) ).
thf(zip_derived_cl22972,plain,
( ~ ( incident @ o @ a1b1 )
<= ~ ( incident @ o @ a1b1 ) ),
inference(split,[status(esa)],[zip_derived_cl1264]) ).
thf('84',plain,
( ( incident @ o @ a1b1 )
| ~ ( point_equal @ b2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl48119,zip_derived_cl22972]) ).
thf(zip_derived_cl429_381,plain,
( ! [X0: $i] :
( ~ ( incident @ b2 @ X0 )
| ( incident @ a1 @ X0 ) )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl415,zip_derived_cl47]) ).
thf(zip_derived_cl17_382,plain,
incident @ b2 @ b2c2,
inference(cnf,[status(esa)],[ib2c2]) ).
thf(zip_derived_cl502,plain,
( ( incident @ a1 @ b2c2 )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl429,zip_derived_cl17]) ).
thf(zip_derived_cl53,plain,
( ~ ( incident @ a1 @ b2c2 )
<= ~ ( incident @ a1 @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl1]) ).
thf('85',plain,
( ~ ( point_equal @ b2 @ a1 )
| ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl502,zip_derived_cl53]) ).
thf(zip_derived_cl22_383,plain,
incident @ a2 @ oa,
inference(cnf,[status(esa)],[ia2oa]) ).
thf(zip_derived_cl318_384,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ab )
| ~ ( incident @ X0 @ a1b1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ab @ X1 )
| ( line_equal @ a1b1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl31,zip_derived_cl49]) ).
thf(zip_derived_cl1255,plain,
( ( point_equal @ a2 @ ab )
| ~ ( incident @ a2 @ a1b1 )
| ~ ( incident @ ab @ oa )
| ( line_equal @ a1b1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl318]) ).
thf(zip_derived_cl22348,plain,
( ( line_equal @ a1b1 @ oa )
<= ( line_equal @ a1b1 @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl1255]) ).
thf(zip_derived_cl45_385,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl22353,plain,
( ( line_equal @ oa @ a1b1 )
<= ( line_equal @ a1b1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl22348,zip_derived_cl45]) ).
thf(zip_derived_cl48_386,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl22359,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ oa )
| ( incident @ X0 @ a1b1 ) )
<= ( line_equal @ a1b1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl22353,zip_derived_cl48]) ).
thf(zip_derived_cl22_387,plain,
incident @ a2 @ oa,
inference(cnf,[status(esa)],[ia2oa]) ).
thf(zip_derived_cl39140,plain,
( ( incident @ a2 @ a1b1 )
<= ( line_equal @ a1b1 @ oa ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl22359,zip_derived_cl22]) ).
thf(zip_derived_cl107_388,plain,
! [X0: $i] :
( ~ ( incident @ a2 @ X0 )
| ~ ( incident @ b2 @ X0 )
| ~ ( incident @ c2 @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl69,'9']) ).
thf(zip_derived_cl63_389,plain,
( ( incident @ c2 @ a1b1 )
<= ( incident @ c2 @ a1b1 ) ),
inference(split,[status(esa)],[zip_derived_cl4]) ).
thf(zip_derived_cl108,plain,
( ( ~ ( incident @ b2 @ a1b1 )
| ~ ( incident @ a2 @ a1b1 ) )
<= ( incident @ c2 @ a1b1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl107,zip_derived_cl63]) ).
thf(zip_derived_cl111,plain,
( ~ ( incident @ a2 @ a1b1 )
<= ~ ( incident @ a2 @ a1b1 ) ),
inference(split,[status(esa)],[zip_derived_cl108]) ).
thf('86',plain,
( ~ ( line_equal @ a1b1 @ oa )
| ( incident @ a2 @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl39140,zip_derived_cl111]) ).
thf(zip_derived_cl9_390,plain,
incident @ b2 @ a2b2,
inference(cnf,[status(esa)],[ib2a2]) ).
thf(zip_derived_cl320_391,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ a1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl49]) ).
thf(zip_derived_cl1354,plain,
( ( point_equal @ b2 @ a1 )
| ~ ( incident @ b2 @ a1c1 )
| ~ ( incident @ a1 @ a2b2 )
| ( line_equal @ a1c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl9,zip_derived_cl320]) ).
thf('87',plain,
( ~ ( incident @ a1 @ a2b2 )
| ( point_equal @ b2 @ a1 )
| ~ ( incident @ b2 @ a1c1 )
| ( line_equal @ a1c1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl1354]) ).
thf(zip_derived_cl8_392,plain,
incident @ a2 @ a2b2,
inference(cnf,[status(esa)],[ia2b2]) ).
thf(zip_derived_cl321_393,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ a1b1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ a1b1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl49]) ).
thf(zip_derived_cl1465,plain,
( ( point_equal @ a2 @ a1 )
| ~ ( incident @ a2 @ a1b1 )
| ~ ( incident @ a1 @ a2b2 )
| ( line_equal @ a1b1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl8,zip_derived_cl321]) ).
thf(zip_derived_cl89_394,plain,
~ ( line_equal @ a1b1 @ a2b2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl81,'38']) ).
thf(zip_derived_cl1510,plain,
( ( point_equal @ a2 @ a1 )
| ~ ( incident @ a2 @ a1b1 )
| ~ ( incident @ a1 @ a2b2 ) ),
inference(demod,[status(thm)],[zip_derived_cl1465,zip_derived_cl89]) ).
thf(notaa,axiom,
( ( point_equal @ a2 @ a1 )
=> goal ) ).
thf(zip_derived_cl35,plain,
( goal
| ~ ( point_equal @ a2 @ a1 ) ),
inference(cnf,[status(esa)],[notaa]) ).
thf(zip_derived_cl71,plain,
( ~ ( point_equal @ a2 @ a1 )
<= ~ ( point_equal @ a2 @ a1 ) ),
inference(split,[status(esa)],[zip_derived_cl35]) ).
thf('88',plain,
( ~ ( point_equal @ a2 @ a1 )
| goal ),
inference(split,[status(esa)],[zip_derived_cl35]) ).
thf('89',plain,
~ ( point_equal @ a2 @ a1 ),
inference('sat_resolution*',[status(thm)],['1','88']) ).
thf(zip_derived_cl84,plain,
~ ( point_equal @ a2 @ a1 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl71,'89']) ).
thf(zip_derived_cl30636,plain,
( ~ ( incident @ a1 @ a2b2 )
| ~ ( incident @ a2 @ a1b1 ) ),
inference(clc,[status(thm)],[zip_derived_cl1510,zip_derived_cl84]) ).
thf('90',plain,
( ~ ( incident @ a2 @ a1b1 )
| ~ ( incident @ a1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl30636]) ).
thf(zip_derived_cl19876_395,plain,
( ( incident @ c1 @ b2c2 )
<= ( line_equal @ b2c2 @ oc ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4899,zip_derived_cl25]) ).
thf(zip_derived_cl314_396,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl49]) ).
thf(zip_derived_cl19909,plain,
( ( ( point_equal @ c1 @ bc )
| ~ ( incident @ c1 @ b1c1 )
| ~ ( incident @ bc @ b2c2 )
| ( line_equal @ b1c1 @ b2c2 ) )
<= ( line_equal @ b2c2 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl19876,zip_derived_cl314]) ).
thf(zip_derived_cl14_397,plain,
incident @ c1 @ b1c1,
inference(cnf,[status(esa)],[ic1b1]) ).
thf(zip_derived_cl28_398,plain,
incident @ bc @ b2c2,
inference(cnf,[status(esa)],[ibc2]) ).
thf(zip_derived_cl87_399,plain,
~ ( line_equal @ b1c1 @ b2c2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl77,'3']) ).
thf(zip_derived_cl19965,plain,
( ( point_equal @ c1 @ bc )
<= ( line_equal @ b2c2 @ oc ) ),
inference(demod,[status(thm)],[zip_derived_cl19909,zip_derived_cl14,zip_derived_cl28,zip_derived_cl87]) ).
thf(zip_derived_cl42_400,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl20114,plain,
( ( point_equal @ bc @ c1 )
<= ( line_equal @ b2c2 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl19965,zip_derived_cl42]) ).
thf(zip_derived_cl47_401,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl20134,plain,
( ! [X0: $i] :
( ~ ( incident @ c1 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( line_equal @ b2c2 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl20114,zip_derived_cl47]) ).
thf(zip_derived_cl11_402,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl37552,plain,
( ( incident @ bc @ a1c1 )
<= ( line_equal @ b2c2 @ oc ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl20134,zip_derived_cl11]) ).
thf(zip_derived_cl194_403,plain,
( ~ ( incident @ bc @ a1c1 )
<= ~ ( incident @ bc @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl170]) ).
thf('91',plain,
( ~ ( line_equal @ b2c2 @ oc )
| ( incident @ bc @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl37552,zip_derived_cl194]) ).
thf(zip_derived_cl16569_404,plain,
( ( incident @ c1 @ b2c2 )
<= ( line_equal @ a1c1 @ b2c2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4515,zip_derived_cl11]) ).
thf(zip_derived_cl314_405,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl49]) ).
thf(zip_derived_cl16793,plain,
( ( ( point_equal @ c1 @ bc )
| ~ ( incident @ c1 @ b1c1 )
| ~ ( incident @ bc @ b2c2 )
| ( line_equal @ b1c1 @ b2c2 ) )
<= ( line_equal @ a1c1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl16569,zip_derived_cl314]) ).
thf(zip_derived_cl14_406,plain,
incident @ c1 @ b1c1,
inference(cnf,[status(esa)],[ic1b1]) ).
thf(zip_derived_cl28_407,plain,
incident @ bc @ b2c2,
inference(cnf,[status(esa)],[ibc2]) ).
thf(zip_derived_cl87_408,plain,
~ ( line_equal @ b1c1 @ b2c2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl77,'3']) ).
thf(zip_derived_cl16848,plain,
( ( point_equal @ c1 @ bc )
<= ( line_equal @ a1c1 @ b2c2 ) ),
inference(demod,[status(thm)],[zip_derived_cl16793,zip_derived_cl14,zip_derived_cl28,zip_derived_cl87]) ).
thf(zip_derived_cl42_409,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl16907,plain,
( ( point_equal @ bc @ c1 )
<= ( line_equal @ a1c1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl16848,zip_derived_cl42]) ).
thf(zip_derived_cl47_410,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl16969,plain,
( ! [X0: $i] :
( ~ ( incident @ c1 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( line_equal @ a1c1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl16907,zip_derived_cl47]) ).
thf(zip_derived_cl11_411,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl31365,plain,
( ( incident @ bc @ a1c1 )
<= ( line_equal @ a1c1 @ b2c2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl16969,zip_derived_cl11]) ).
thf(zip_derived_cl194_412,plain,
( ~ ( incident @ bc @ a1c1 )
<= ~ ( incident @ bc @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl170]) ).
thf('92',plain,
( ~ ( line_equal @ a1c1 @ b2c2 )
| ( incident @ bc @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl31365,zip_derived_cl194]) ).
thf(zip_derived_cl2317_413,plain,
( ( incident @ bc @ a1c1 )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1522,zip_derived_cl61]) ).
thf(zip_derived_cl315_414,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ac )
| ~ ( incident @ X0 @ a2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ac @ X1 )
| ( line_equal @ a2c2 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl49]) ).
thf(zip_derived_cl2326,plain,
( ( ( point_equal @ bc @ ac )
| ~ ( incident @ bc @ a2c2 )
| ~ ( incident @ ac @ a1c1 )
| ( line_equal @ a2c2 @ a1c1 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2317,zip_derived_cl315]) ).
thf(zip_derived_cl29_415,plain,
incident @ ac @ a1c1,
inference(cnf,[status(esa)],[iac1]) ).
thf(zip_derived_cl2346,plain,
( ( ( point_equal @ bc @ ac )
| ~ ( incident @ bc @ a2c2 )
| ( line_equal @ a2c2 @ a1c1 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2326,zip_derived_cl29]) ).
thf(zip_derived_cl2724,plain,
( ( point_equal @ bc @ ac )
<= ( point_equal @ bc @ ac ) ),
inference(split,[status(esa)],[zip_derived_cl2346]) ).
thf(zip_derived_cl47_416,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl2821,plain,
( ! [X0: $i] :
( ~ ( incident @ ac @ X0 )
| ( incident @ bc @ X0 ) )
<= ( point_equal @ bc @ ac ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2724,zip_derived_cl47]) ).
thf(zip_derived_cl29_417,plain,
incident @ ac @ a1c1,
inference(cnf,[status(esa)],[iac1]) ).
thf(zip_derived_cl9871,plain,
( ( incident @ bc @ a1c1 )
<= ( point_equal @ bc @ ac ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2821,zip_derived_cl29]) ).
thf(zip_derived_cl194_418,plain,
( ~ ( incident @ bc @ a1c1 )
<= ~ ( incident @ bc @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl170]) ).
thf('93',plain,
( ~ ( point_equal @ bc @ ac )
| ( incident @ bc @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl9871,zip_derived_cl194]) ).
thf(zip_derived_cl4076_419,plain,
( ! [X0: $i] :
( ~ ( incident @ a2 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( point_equal @ a2 @ bc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl3961,zip_derived_cl47]) ).
thf(zip_derived_cl8_420,plain,
incident @ a2 @ a2b2,
inference(cnf,[status(esa)],[ia2b2]) ).
thf(zip_derived_cl14624,plain,
( ( incident @ bc @ a2b2 )
<= ( point_equal @ a2 @ bc ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4076,zip_derived_cl8]) ).
thf(zip_derived_cl184_421,plain,
( ~ ( incident @ bc @ a2b2 )
<= ~ ( incident @ bc @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl168]) ).
thf('94',plain,
( ~ ( point_equal @ a2 @ bc )
| ( incident @ bc @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl14624,zip_derived_cl184]) ).
thf(zip_derived_cl61_422,plain,
( ( incident @ b2 @ a1c1 )
<= ( incident @ b2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl3]) ).
thf(zip_derived_cl313_423,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b2c2 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl28,zip_derived_cl49]) ).
thf(zip_derived_cl789,plain,
( ( ( point_equal @ b2 @ bc )
| ~ ( incident @ b2 @ b2c2 )
| ~ ( incident @ bc @ a1c1 )
| ( line_equal @ b2c2 @ a1c1 ) )
<= ( incident @ b2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl313]) ).
thf(zip_derived_cl17_424,plain,
incident @ b2 @ b2c2,
inference(cnf,[status(esa)],[ib2c2]) ).
thf(zip_derived_cl823,plain,
( ( ( point_equal @ b2 @ bc )
| ~ ( incident @ bc @ a1c1 )
| ( line_equal @ b2c2 @ a1c1 ) )
<= ( incident @ b2 @ a1c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl789,zip_derived_cl17]) ).
thf('95',plain,
( ~ ( incident @ bc @ a1c1 )
| ( point_equal @ b2 @ bc )
| ( line_equal @ b2c2 @ a1c1 )
| ~ ( incident @ b2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl823]) ).
thf(zip_derived_cl18_425,plain,
incident @ o @ oa,
inference(cnf,[status(esa)],[iooa]) ).
thf(zip_derived_cl320_426,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ a1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl49]) ).
thf(zip_derived_cl1361,plain,
( ( point_equal @ o @ a1 )
| ~ ( incident @ o @ a1c1 )
| ~ ( incident @ a1 @ oa )
| ( line_equal @ a1c1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl320]) ).
thf(zip_derived_cl21_427,plain,
incident @ a1 @ oa,
inference(cnf,[status(esa)],[ia1oa]) ).
thf(zip_derived_cl1401,plain,
( ( point_equal @ o @ a1 )
| ~ ( incident @ o @ a1c1 )
| ( line_equal @ a1c1 @ oa ) ),
inference(demod,[status(thm)],[zip_derived_cl1361,zip_derived_cl21]) ).
thf('96',plain,
( ~ ( incident @ o @ a1c1 )
| ( point_equal @ o @ a1 )
| ( line_equal @ a1c1 @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl1401]) ).
thf(zip_derived_cl1016_428,plain,
( ! [X0: $i] :
( ~ ( incident @ c1 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl937,zip_derived_cl47]) ).
thf(zip_derived_cl25_429,plain,
incident @ c1 @ oc,
inference(cnf,[status(esa)],[ic1oc]) ).
thf(zip_derived_cl1945,plain,
( ( incident @ bc @ oc )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1016,zip_derived_cl25]) ).
thf(zip_derived_cl316_430,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ac )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ac @ X1 )
| ( line_equal @ a1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl29,zip_derived_cl49]) ).
thf(zip_derived_cl2069,plain,
( ( ( point_equal @ bc @ ac )
| ~ ( incident @ bc @ a1c1 )
| ~ ( incident @ ac @ oc )
| ( line_equal @ a1c1 @ oc ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1945,zip_derived_cl316]) ).
thf(zip_derived_cl1016_431,plain,
( ! [X0: $i] :
( ~ ( incident @ c1 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl937,zip_derived_cl47]) ).
thf(zip_derived_cl11_432,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl1944,plain,
( ( incident @ bc @ a1c1 )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1016,zip_derived_cl11]) ).
thf(zip_derived_cl2085,plain,
( ( ( point_equal @ bc @ ac )
| ~ ( incident @ ac @ oc )
| ( line_equal @ a1c1 @ oc ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl2069,zip_derived_cl1944]) ).
thf(zip_derived_cl13_433,plain,
incident @ c2 @ a2c2,
inference(cnf,[status(esa)],[ic2a2]) ).
thf(zip_derived_cl454_434,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ a1c1 )
| ( incident @ X0 @ b2c2 ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl426,zip_derived_cl48]) ).
thf(zip_derived_cl29_435,plain,
incident @ ac @ a1c1,
inference(cnf,[status(esa)],[iac1]) ).
thf(zip_derived_cl588,plain,
( ( incident @ ac @ b2c2 )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl454,zip_derived_cl29]) ).
thf(zip_derived_cl49_436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl599,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ac )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ac @ X1 )
| ( line_equal @ b2c2 @ X1 ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl588,zip_derived_cl49]) ).
thf(zip_derived_cl7012,plain,
( ( ( point_equal @ c2 @ ac )
| ~ ( incident @ c2 @ b2c2 )
| ~ ( incident @ ac @ a2c2 )
| ( line_equal @ b2c2 @ a2c2 ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl599]) ).
thf(zip_derived_cl16_437,plain,
incident @ c2 @ b2c2,
inference(cnf,[status(esa)],[ic2b2]) ).
thf(zip_derived_cl30_438,plain,
incident @ ac @ a2c2,
inference(cnf,[status(esa)],[iac2]) ).
thf(zip_derived_cl426_439,plain,
( ( line_equal @ a1c1 @ b2c2 )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl412,zip_derived_cl45]) ).
thf(zip_derived_cl46_440,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( line_equal @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[transitivity_of_line_equal]) ).
thf(zip_derived_cl452,plain,
( ! [X0: $i] :
( ~ ( line_equal @ b2c2 @ X0 )
| ( line_equal @ a1c1 @ X0 ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl426,zip_derived_cl46]) ).
thf(zip_derived_cl88_441,plain,
~ ( line_equal @ a1c1 @ a2c2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl79,'15']) ).
thf(zip_derived_cl5942,plain,
( ~ ( line_equal @ b2c2 @ a2c2 )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl452,zip_derived_cl88]) ).
thf(zip_derived_cl7088,plain,
( ( point_equal @ c2 @ ac )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl7012,zip_derived_cl16,zip_derived_cl30,zip_derived_cl5942]) ).
thf(zip_derived_cl42_442,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl7093,plain,
( ( point_equal @ ac @ c2 )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl7088,zip_derived_cl42]) ).
thf(zip_derived_cl47_443,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl7244,plain,
( ! [X0: $i] :
( ~ ( incident @ c2 @ X0 )
| ( incident @ ac @ X0 ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl7093,zip_derived_cl47]) ).
thf(zip_derived_cl26_444,plain,
incident @ c2 @ oc,
inference(cnf,[status(esa)],[ic2oc]) ).
thf(zip_derived_cl21644,plain,
( ( incident @ ac @ oc )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl7244,zip_derived_cl26]) ).
thf(zip_derived_cl48278,plain,
( ( ( point_equal @ bc @ ac )
| ( line_equal @ a1c1 @ oc ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl2085,zip_derived_cl21644]) ).
thf('97',plain,
( ~ ( line_equal @ b2c2 @ a1c1 )
| ( point_equal @ bc @ ac )
| ( line_equal @ a1c1 @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl48278]) ).
thf(zip_derived_cl924_445,plain,
( ( point_equal @ c1 @ bc )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl883,zip_derived_cl14,zip_derived_cl28,zip_derived_cl87]) ).
thf(zip_derived_cl47_446,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl936,plain,
( ! [X0: $i] :
( ~ ( incident @ bc @ X0 )
| ( incident @ c1 @ X0 ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl924,zip_derived_cl47]) ).
thf(zip_derived_cl2213_447,plain,
( ~ ( incident @ c1 @ a2c2 )
<= ~ ( incident @ c1 @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl2121]) ).
thf(zip_derived_cl12740,plain,
( ~ ( incident @ bc @ a2c2 )
<= ( ~ ( incident @ c1 @ a2c2 )
& ( line_equal @ b2c2 @ a1c1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl936,zip_derived_cl2213]) ).
thf(zip_derived_cl2821_448,plain,
( ! [X0: $i] :
( ~ ( incident @ ac @ X0 )
| ( incident @ bc @ X0 ) )
<= ( point_equal @ bc @ ac ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2724,zip_derived_cl47]) ).
thf(zip_derived_cl30_449,plain,
incident @ ac @ a2c2,
inference(cnf,[status(esa)],[iac2]) ).
thf(zip_derived_cl9870,plain,
( ( incident @ bc @ a2c2 )
<= ( point_equal @ bc @ ac ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2821,zip_derived_cl30]) ).
thf('98',plain,
( ~ ( point_equal @ bc @ ac )
| ~ ( line_equal @ b2c2 @ a1c1 )
| ( incident @ c1 @ a2c2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl12740,zip_derived_cl9870]) ).
thf(zip_derived_cl24_450,plain,
incident @ b2 @ ob,
inference(cnf,[status(esa)],[ib2ob]) ).
thf(zip_derived_cl320_451,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ a1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl49]) ).
thf(zip_derived_cl1356,plain,
( ( point_equal @ b2 @ a1 )
| ~ ( incident @ b2 @ a1c1 )
| ~ ( incident @ a1 @ ob )
| ( line_equal @ a1c1 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl320]) ).
thf('99',plain,
( ( line_equal @ a1c1 @ ob )
| ( point_equal @ b2 @ a1 )
| ~ ( incident @ b2 @ a1c1 )
| ~ ( incident @ a1 @ ob ) ),
inference(split,[status(esa)],[zip_derived_cl1356]) ).
thf(zip_derived_cl13_452,plain,
incident @ c2 @ a2c2,
inference(cnf,[status(esa)],[ic2a2]) ).
thf(zip_derived_cl329_453,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ a1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl49]) ).
thf(zip_derived_cl2404,plain,
( ( point_equal @ c2 @ c1 )
| ~ ( incident @ c2 @ a1c1 )
| ~ ( incident @ c1 @ a2c2 )
| ( line_equal @ a1c1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl329]) ).
thf(zip_derived_cl88_454,plain,
~ ( line_equal @ a1c1 @ a2c2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl79,'15']) ).
thf(zip_derived_cl2444,plain,
( ( point_equal @ c2 @ c1 )
| ~ ( incident @ c2 @ a1c1 )
| ~ ( incident @ c1 @ a2c2 ) ),
inference(demod,[status(thm)],[zip_derived_cl2404,zip_derived_cl88]) ).
thf(zip_derived_cl86_455,plain,
~ ( point_equal @ c2 @ c1 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl75,'44']) ).
thf(zip_derived_cl59679,plain,
( ~ ( incident @ c1 @ a2c2 )
| ~ ( incident @ c2 @ a1c1 ) ),
inference(clc,[status(thm)],[zip_derived_cl2444,zip_derived_cl86]) ).
thf('100',plain,
( ~ ( incident @ c1 @ a2c2 )
| ~ ( incident @ c2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl59679]) ).
thf(zip_derived_cl452_456,plain,
( ! [X0: $i] :
( ~ ( line_equal @ b2c2 @ X0 )
| ( line_equal @ a1c1 @ X0 ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl426,zip_derived_cl46]) ).
thf(zip_derived_cl114_457,plain,
! [X0: $i] :
( ~ ( line_equal @ X0 @ X0 )
| ~ ( incident @ bc @ X0 )
| ~ ( incident @ ac @ X0 )
| ~ ( incident @ ab @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl51,'6']) ).
thf(zip_derived_cl5937,plain,
( ( ~ ( line_equal @ b2c2 @ a1c1 )
| ~ ( incident @ bc @ a1c1 )
| ~ ( incident @ ac @ a1c1 )
| ~ ( incident @ ab @ a1c1 ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl452,zip_derived_cl114]) ).
thf(zip_derived_cl412_458,plain,
( ( line_equal @ b2c2 @ a1c1 )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl404]) ).
thf(zip_derived_cl1944_459,plain,
( ( incident @ bc @ a1c1 )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1016,zip_derived_cl11]) ).
thf(zip_derived_cl29_460,plain,
incident @ ac @ a1c1,
inference(cnf,[status(esa)],[iac1]) ).
thf(zip_derived_cl5943,plain,
( ~ ( incident @ ab @ a1c1 )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl5937,zip_derived_cl412,zip_derived_cl1944,zip_derived_cl29]) ).
thf(zip_derived_cl503_461,plain,
( ( incident @ a1 @ a2b2 )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl429,zip_derived_cl9]) ).
thf(zip_derived_cl318_462,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ab )
| ~ ( incident @ X0 @ a1b1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ab @ X1 )
| ( line_equal @ a1b1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl31,zip_derived_cl49]) ).
thf(zip_derived_cl1236,plain,
( ( ( point_equal @ a1 @ ab )
| ~ ( incident @ a1 @ a1b1 )
| ~ ( incident @ ab @ a2b2 )
| ( line_equal @ a1b1 @ a2b2 ) )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl503,zip_derived_cl318]) ).
thf(zip_derived_cl6_463,plain,
incident @ a1 @ a1b1,
inference(cnf,[status(esa)],[ia1b1]) ).
thf(zip_derived_cl32_464,plain,
incident @ ab @ a2b2,
inference(cnf,[status(esa)],[iab2]) ).
thf(zip_derived_cl89_465,plain,
~ ( line_equal @ a1b1 @ a2b2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl81,'38']) ).
thf(zip_derived_cl1278,plain,
( ( point_equal @ a1 @ ab )
<= ( point_equal @ b2 @ a1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1236,zip_derived_cl6,zip_derived_cl32,zip_derived_cl89]) ).
thf(zip_derived_cl42_466,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl1408,plain,
( ( point_equal @ ab @ a1 )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1278,zip_derived_cl42]) ).
thf(zip_derived_cl47_467,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl1519,plain,
( ! [X0: $i] :
( ~ ( incident @ a1 @ X0 )
| ( incident @ ab @ X0 ) )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1408,zip_derived_cl47]) ).
thf(zip_derived_cl10_468,plain,
incident @ a1 @ a1c1,
inference(cnf,[status(esa)],[ia1c1]) ).
thf(zip_derived_cl5448,plain,
( ( incident @ ab @ a1c1 )
<= ( point_equal @ b2 @ a1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1519,zip_derived_cl10]) ).
thf('101',plain,
( ~ ( line_equal @ b2c2 @ a1c1 )
| ~ ( point_equal @ b2 @ a1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl5943,zip_derived_cl5448]) ).
thf(zip_derived_cl3758_469,plain,
( ~ ( incident @ c2 @ a1c1 )
<= ~ ( incident @ c2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl3357]) ).
thf(zip_derived_cl412_470,plain,
( ( line_equal @ b2c2 @ a1c1 )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl404]) ).
thf(zip_derived_cl48_471,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl427,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ b2c2 )
| ( incident @ X0 @ a1c1 ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl412,zip_derived_cl48]) ).
thf(zip_derived_cl5656,plain,
( ~ ( incident @ c2 @ b2c2 )
<= ( ~ ( incident @ c2 @ a1c1 )
& ( line_equal @ b2c2 @ a1c1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3758,zip_derived_cl427]) ).
thf(zip_derived_cl16_472,plain,
incident @ c2 @ b2c2,
inference(cnf,[status(esa)],[ic2b2]) ).
thf('102',plain,
( ~ ( line_equal @ b2c2 @ a1c1 )
| ( incident @ c2 @ a1c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl5656,zip_derived_cl16]) ).
thf(zip_derived_cl427_473,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ b2c2 )
| ( incident @ X0 @ a1c1 ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl412,zip_derived_cl48]) ).
thf(zip_derived_cl58_474,plain,
( ~ ( incident @ b2 @ a1c1 )
<= ~ ( incident @ b2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2]) ).
thf(zip_derived_cl5641,plain,
( ~ ( incident @ b2 @ b2c2 )
<= ( ~ ( incident @ b2 @ a1c1 )
& ( line_equal @ b2c2 @ a1c1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl427,zip_derived_cl58]) ).
thf(zip_derived_cl17_475,plain,
incident @ b2 @ b2c2,
inference(cnf,[status(esa)],[ib2c2]) ).
thf('103',plain,
( ~ ( line_equal @ b2c2 @ a1c1 )
| ( incident @ b2 @ a1c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl5641,zip_derived_cl17]) ).
thf(zip_derived_cl427_476,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ b2c2 )
| ( incident @ X0 @ a1c1 ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl412,zip_derived_cl48]) ).
thf(zip_derived_cl107_477,plain,
! [X0: $i] :
( ~ ( incident @ a2 @ X0 )
| ~ ( incident @ b2 @ X0 )
| ~ ( incident @ c2 @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl69,'9']) ).
thf(zip_derived_cl5642,plain,
( ( ~ ( incident @ c2 @ b2c2 )
| ~ ( incident @ a2 @ a1c1 )
| ~ ( incident @ b2 @ a1c1 ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl427,zip_derived_cl107]) ).
thf(zip_derived_cl16_478,plain,
incident @ c2 @ b2c2,
inference(cnf,[status(esa)],[ic2b2]) ).
thf(zip_derived_cl5701,plain,
( ( ~ ( incident @ a2 @ a1c1 )
| ~ ( incident @ b2 @ a1c1 ) )
<= ( line_equal @ b2c2 @ a1c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl5642,zip_derived_cl16]) ).
thf('104',plain,
( ~ ( line_equal @ b2c2 @ a1c1 )
| ~ ( incident @ a2 @ a1c1 )
| ~ ( incident @ b2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl5701]) ).
thf(zip_derived_cl4421_479,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ oc )
| ( incident @ X0 @ a1c1 ) )
<= ( line_equal @ a1c1 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4407,zip_derived_cl48]) ).
thf(zip_derived_cl20_480,plain,
incident @ o @ oc,
inference(cnf,[status(esa)],[iooc]) ).
thf(zip_derived_cl16327,plain,
( ( incident @ o @ a1c1 )
<= ( line_equal @ a1c1 @ oc ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4421,zip_derived_cl20]) ).
thf(zip_derived_cl4517_481,plain,
( ~ ( incident @ o @ a1c1 )
<= ~ ( incident @ o @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl3409]) ).
thf('105',plain,
( ~ ( line_equal @ a1c1 @ oc )
| ( incident @ o @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl16327,zip_derived_cl4517]) ).
thf(zip_derived_cl4866_482,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ oa )
| ( incident @ X0 @ a1c1 ) )
<= ( line_equal @ a1c1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4738,zip_derived_cl48]) ).
thf(zip_derived_cl22_483,plain,
incident @ a2 @ oa,
inference(cnf,[status(esa)],[ia2oa]) ).
thf(zip_derived_cl18519,plain,
( ( incident @ a2 @ a1c1 )
<= ( line_equal @ a1c1 @ oa ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4866,zip_derived_cl22]) ).
thf(zip_derived_cl2317_484,plain,
( ( incident @ bc @ a1c1 )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1522,zip_derived_cl61]) ).
thf(zip_derived_cl333_485,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a2 )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a2 @ X1 )
| ( line_equal @ b1c1 @ X1 ) )
<= ( incident @ a2 @ b1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl65,zip_derived_cl49]) ).
thf(zip_derived_cl2854,plain,
( ( ( point_equal @ bc @ a2 )
| ~ ( incident @ bc @ b1c1 )
| ~ ( incident @ a2 @ a1c1 )
| ( line_equal @ b1c1 @ a1c1 ) )
<= ( ( incident @ a2 @ b1c1 )
& ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2317,zip_derived_cl333]) ).
thf(zip_derived_cl27_486,plain,
incident @ bc @ b1c1,
inference(cnf,[status(esa)],[ibc1]) ).
thf(zip_derived_cl2908,plain,
( ( ( point_equal @ bc @ a2 )
| ~ ( incident @ a2 @ a1c1 )
| ( line_equal @ b1c1 @ a1c1 ) )
<= ( ( incident @ a2 @ b1c1 )
& ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2854,zip_derived_cl27]) ).
thf(zip_derived_cl2964,plain,
( ~ ( incident @ a2 @ a1c1 )
<= ~ ( incident @ a2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2908]) ).
thf('106',plain,
( ~ ( line_equal @ a1c1 @ oa )
| ( incident @ a2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl18519,zip_derived_cl2964]) ).
thf(zip_derived_cl2317_487,plain,
( ( incident @ bc @ a1c1 )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1522,zip_derived_cl61]) ).
thf(zip_derived_cl22_488,plain,
incident @ a2 @ oa,
inference(cnf,[status(esa)],[ia2oa]) ).
thf(zip_derived_cl49_489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl334,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a2 )
| ~ ( incident @ X0 @ oa )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a2 @ X1 )
| ( line_equal @ oa @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl49]) ).
thf(zip_derived_cl2987,plain,
( ( ( point_equal @ bc @ a2 )
| ~ ( incident @ bc @ oa )
| ~ ( incident @ a2 @ a1c1 )
| ( line_equal @ oa @ a1c1 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2317,zip_derived_cl334]) ).
thf(zip_derived_cl3201,plain,
( ( line_equal @ oa @ a1c1 )
<= ( line_equal @ oa @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2987]) ).
thf(zip_derived_cl48_490,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl3206,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ oa )
| ( incident @ X0 @ a1c1 ) )
<= ( line_equal @ oa @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl3201,zip_derived_cl48]) ).
thf(zip_derived_cl22_491,plain,
incident @ a2 @ oa,
inference(cnf,[status(esa)],[ia2oa]) ).
thf(zip_derived_cl12220,plain,
( ( incident @ a2 @ a1c1 )
<= ( line_equal @ oa @ a1c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3206,zip_derived_cl22]) ).
thf(zip_derived_cl2964_492,plain,
( ~ ( incident @ a2 @ a1c1 )
<= ~ ( incident @ a2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2908]) ).
thf('107',plain,
( ~ ( line_equal @ oa @ a1c1 )
| ( incident @ a2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl12220,zip_derived_cl2964]) ).
thf(zip_derived_cl416_493,plain,
( ( point_equal @ c2 @ a1 )
<= ( point_equal @ c2 @ a1 ) ),
inference(split,[status(esa)],[zip_derived_cl408]) ).
thf(zip_derived_cl47_494,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl419,plain,
( ! [X0: $i] :
( ~ ( incident @ a1 @ X0 )
| ( incident @ c2 @ X0 ) )
<= ( point_equal @ c2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl416,zip_derived_cl47]) ).
thf(zip_derived_cl59,plain,
( ~ ( incident @ c2 @ a1b1 )
<= ~ ( incident @ c2 @ a1b1 ) ),
inference(split,[status(esa)],[zip_derived_cl2]) ).
thf(zip_derived_cl5410,plain,
( ~ ( incident @ a1 @ a1b1 )
<= ( ~ ( incident @ c2 @ a1b1 )
& ( point_equal @ c2 @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl419,zip_derived_cl59]) ).
thf(zip_derived_cl6_495,plain,
incident @ a1 @ a1b1,
inference(cnf,[status(esa)],[ia1b1]) ).
thf('108',plain,
( ~ ( point_equal @ c2 @ a1 )
| ( incident @ c2 @ a1b1 ) ),
inference(demod,[status(thm)],[zip_derived_cl5410,zip_derived_cl6]) ).
thf(zip_derived_cl2317_496,plain,
( ( incident @ bc @ a1c1 )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1522,zip_derived_cl61]) ).
thf(zip_derived_cl328_497,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl49]) ).
thf(zip_derived_cl2339,plain,
( ( ( point_equal @ bc @ c1 )
| ~ ( incident @ bc @ b1c1 )
| ~ ( incident @ c1 @ a1c1 )
| ( line_equal @ b1c1 @ a1c1 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2317,zip_derived_cl328]) ).
thf(zip_derived_cl27_498,plain,
incident @ bc @ b1c1,
inference(cnf,[status(esa)],[ibc1]) ).
thf(zip_derived_cl11_499,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl2357,plain,
( ( ( point_equal @ bc @ c1 )
| ( line_equal @ b1c1 @ a1c1 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2339,zip_derived_cl27,zip_derived_cl11]) ).
thf(zip_derived_cl2588,plain,
( ( line_equal @ b1c1 @ a1c1 )
<= ( line_equal @ b1c1 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2357]) ).
thf(zip_derived_cl45_500,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl2590,plain,
( ( line_equal @ a1c1 @ b1c1 )
<= ( line_equal @ b1c1 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2588,zip_derived_cl45]) ).
thf(zip_derived_cl48_501,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl2719,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ a1c1 )
| ( incident @ X0 @ b1c1 ) )
<= ( line_equal @ b1c1 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2590,zip_derived_cl48]) ).
thf(zip_derived_cl10_502,plain,
incident @ a1 @ a1c1,
inference(cnf,[status(esa)],[ia1c1]) ).
thf(zip_derived_cl9493,plain,
( ( incident @ a1 @ b1c1 )
<= ( line_equal @ b1c1 @ a1c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2719,zip_derived_cl10]) ).
thf(zip_derived_cl137_503,plain,
~ ( incident @ a1 @ b1c1 ),
inference(demod,[status(thm)],[zip_derived_cl134,zip_derived_cl15]) ).
thf('109',plain,
~ ( line_equal @ b1c1 @ a1c1 ),
inference('s_sup-',[status(thm)],[zip_derived_cl9493,zip_derived_cl137]) ).
thf(zip_derived_cl61_504,plain,
( ( incident @ b2 @ a1c1 )
<= ( incident @ b2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl3]) ).
thf(zip_derived_cl328_505,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl49]) ).
thf(zip_derived_cl2261,plain,
( ( ( point_equal @ b2 @ c1 )
| ~ ( incident @ b2 @ b1c1 )
| ~ ( incident @ c1 @ a1c1 )
| ( line_equal @ b1c1 @ a1c1 ) )
<= ( incident @ b2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl328]) ).
thf(zip_derived_cl11_506,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl2305,plain,
( ( ( point_equal @ b2 @ c1 )
| ~ ( incident @ b2 @ b1c1 )
| ( line_equal @ b1c1 @ a1c1 ) )
<= ( incident @ b2 @ a1c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl2261,zip_derived_cl11]) ).
thf('110',plain,
( ( point_equal @ b2 @ c1 )
| ( line_equal @ b1c1 @ a1c1 )
| ~ ( incident @ b2 @ a1c1 )
| ~ ( incident @ b2 @ b1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2305]) ).
thf(zip_derived_cl3752,plain,
( ( line_equal @ a1c1 @ b1c1 )
<= ( line_equal @ a1c1 @ b1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl3402]) ).
thf(zip_derived_cl48_507,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl3756,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ a1c1 )
| ( incident @ X0 @ b1c1 ) )
<= ( line_equal @ a1c1 @ b1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl3752,zip_derived_cl48]) ).
thf(zip_derived_cl10_508,plain,
incident @ a1 @ a1c1,
inference(cnf,[status(esa)],[ia1c1]) ).
thf(zip_derived_cl13527,plain,
( ( incident @ a1 @ b1c1 )
<= ( line_equal @ a1c1 @ b1c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3756,zip_derived_cl10]) ).
thf(zip_derived_cl137_509,plain,
~ ( incident @ a1 @ b1c1 ),
inference(demod,[status(thm)],[zip_derived_cl134,zip_derived_cl15]) ).
thf('111',plain,
~ ( line_equal @ a1c1 @ b1c1 ),
inference('s_sup-',[status(thm)],[zip_derived_cl13527,zip_derived_cl137]) ).
thf(zip_derived_cl65_510,plain,
( ( incident @ a2 @ b1c1 )
<= ( incident @ a2 @ b1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl5]) ).
thf(zip_derived_cl329_511,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ a1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl49]) ).
thf(zip_derived_cl2397,plain,
( ( ( point_equal @ a2 @ c1 )
| ~ ( incident @ a2 @ a1c1 )
| ~ ( incident @ c1 @ b1c1 )
| ( line_equal @ a1c1 @ b1c1 ) )
<= ( incident @ a2 @ b1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl65,zip_derived_cl329]) ).
thf(zip_derived_cl14_512,plain,
incident @ c1 @ b1c1,
inference(cnf,[status(esa)],[ic1b1]) ).
thf(zip_derived_cl2442,plain,
( ( ( point_equal @ a2 @ c1 )
| ~ ( incident @ a2 @ a1c1 )
| ( line_equal @ a1c1 @ b1c1 ) )
<= ( incident @ a2 @ b1c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl2397,zip_derived_cl14]) ).
thf('112',plain,
( ( point_equal @ a2 @ c1 )
| ( line_equal @ a1c1 @ b1c1 )
| ~ ( incident @ a2 @ b1c1 )
| ~ ( incident @ a2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2442]) ).
thf('113',plain,
( ~ ( incident @ b2 @ a1c1 )
| ~ ( incident @ a2 @ b1c1 )
| goal
| ~ ( incident @ c2 @ a1b1 ) ),
inference(split,[status(esa)],[zip_derived_cl2]) ).
thf(zip_derived_cl17_513,plain,
incident @ b2 @ b2c2,
inference(cnf,[status(esa)],[ib2c2]) ).
thf(zip_derived_cl327_514,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ a2b2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ a2b2 @ X1 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl49]) ).
thf(zip_derived_cl2160,plain,
( ( ( point_equal @ b2 @ c1 )
| ~ ( incident @ b2 @ a2b2 )
| ~ ( incident @ c1 @ b2c2 )
| ( line_equal @ a2b2 @ b2c2 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl327]) ).
thf(zip_derived_cl9_515,plain,
incident @ b2 @ a2b2,
inference(cnf,[status(esa)],[ib2a2]) ).
thf(zip_derived_cl2196,plain,
( ( ( point_equal @ b2 @ c1 )
| ~ ( incident @ c1 @ b2c2 )
| ( line_equal @ a2b2 @ b2c2 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference(demod,[status(thm)],[zip_derived_cl2160,zip_derived_cl9]) ).
thf(zip_derived_cl53751,plain,
( ( point_equal @ b2 @ c1 )
<= ( point_equal @ b2 @ c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2196]) ).
thf(zip_derived_cl42_516,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl53756,plain,
( ( point_equal @ c1 @ b2 )
<= ( point_equal @ b2 @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl53751,zip_derived_cl42]) ).
thf(zip_derived_cl47_517,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl53765,plain,
( ! [X0: $i] :
( ~ ( incident @ b2 @ X0 )
| ( incident @ c1 @ X0 ) )
<= ( point_equal @ b2 @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl53756,zip_derived_cl47]) ).
thf(zip_derived_cl9_518,plain,
incident @ b2 @ a2b2,
inference(cnf,[status(esa)],[ib2a2]) ).
thf(zip_derived_cl55815,plain,
( ( incident @ c1 @ a2b2 )
<= ( point_equal @ b2 @ c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl53765,zip_derived_cl9]) ).
thf(zip_derived_cl55_519,plain,
( ~ ( incident @ c1 @ a2b2 )
<= ~ ( incident @ c1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl1]) ).
thf('114',plain,
( ~ ( point_equal @ b2 @ c1 )
| ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl55815,zip_derived_cl55]) ).
thf(zip_derived_cl66_520,plain,
( ( incident @ c1 @ a2b2 )
<= ( incident @ c1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl5]) ).
thf(zip_derived_cl2341_521,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ a1c1 @ X1 ) )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2317,zip_derived_cl49]) ).
thf(zip_derived_cl3343,plain,
( ( ( point_equal @ c1 @ bc )
| ~ ( incident @ c1 @ a1c1 )
| ~ ( incident @ bc @ a2b2 )
| ( line_equal @ a1c1 @ a2b2 ) )
<= ( ( incident @ c1 @ a2b2 )
& ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl2341]) ).
thf(zip_derived_cl11_522,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl1522_523,plain,
( ! [X0: $i] :
( ~ ( incident @ b2 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1405,zip_derived_cl47]) ).
thf(zip_derived_cl9_524,plain,
incident @ b2 @ a2b2,
inference(cnf,[status(esa)],[ib2a2]) ).
thf(zip_derived_cl2316,plain,
( ( incident @ bc @ a2b2 )
<= ( ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1522,zip_derived_cl9]) ).
thf(zip_derived_cl3396,plain,
( ( ( point_equal @ c1 @ bc )
| ( line_equal @ a1c1 @ a2b2 ) )
<= ( ( incident @ c1 @ a2b2 )
& ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3343,zip_derived_cl11,zip_derived_cl2316]) ).
thf(zip_derived_cl3636,plain,
( ( line_equal @ a1c1 @ a2b2 )
<= ( line_equal @ a1c1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl3396]) ).
thf(zip_derived_cl48_525,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl3640,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ a1c1 )
| ( incident @ X0 @ a2b2 ) )
<= ( line_equal @ a1c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl3636,zip_derived_cl48]) ).
thf(zip_derived_cl11_526,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl13137,plain,
( ( incident @ c1 @ a2b2 )
<= ( line_equal @ a1c1 @ a2b2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3640,zip_derived_cl11]) ).
thf(zip_derived_cl55_527,plain,
( ~ ( incident @ c1 @ a2b2 )
<= ~ ( incident @ c1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl1]) ).
thf('115',plain,
( ~ ( line_equal @ a1c1 @ a2b2 )
| ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl13137,zip_derived_cl55]) ).
thf('116',plain,
( ( incident @ a2 @ b1c1 )
| ( incident @ c1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl5]) ).
thf(zip_derived_cl8_528,plain,
incident @ a2 @ a2b2,
inference(cnf,[status(esa)],[ia2b2]) ).
thf(zip_derived_cl322_529,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ oa )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ oa @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl49]) ).
thf(zip_derived_cl1558,plain,
( ( point_equal @ a2 @ a1 )
| ~ ( incident @ a2 @ oa )
| ~ ( incident @ a1 @ a2b2 )
| ( line_equal @ oa @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl8,zip_derived_cl322]) ).
thf(zip_derived_cl22_530,plain,
incident @ a2 @ oa,
inference(cnf,[status(esa)],[ia2oa]) ).
thf(zip_derived_cl1598,plain,
( ( point_equal @ a2 @ a1 )
| ~ ( incident @ a1 @ a2b2 )
| ( line_equal @ oa @ a2b2 ) ),
inference(demod,[status(thm)],[zip_derived_cl1558,zip_derived_cl22]) ).
thf(zip_derived_cl84_531,plain,
~ ( point_equal @ a2 @ a1 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl71,'89']) ).
thf(zip_derived_cl34084,plain,
( ( line_equal @ oa @ a2b2 )
| ~ ( incident @ a1 @ a2b2 ) ),
inference(clc,[status(thm)],[zip_derived_cl1598,zip_derived_cl84]) ).
thf('117',plain,
( ~ ( incident @ a1 @ a2b2 )
| ( line_equal @ oa @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl34084]) ).
thf(zip_derived_cl20_532,plain,
incident @ o @ oc,
inference(cnf,[status(esa)],[iooc]) ).
thf(zip_derived_cl328_533,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl49]) ).
thf(zip_derived_cl2269,plain,
( ( point_equal @ o @ c1 )
| ~ ( incident @ o @ b1c1 )
| ~ ( incident @ c1 @ oc )
| ( line_equal @ b1c1 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl328]) ).
thf(zip_derived_cl25_534,plain,
incident @ c1 @ oc,
inference(cnf,[status(esa)],[ic1oc]) ).
thf(zip_derived_cl2308,plain,
( ( point_equal @ o @ c1 )
| ~ ( incident @ o @ b1c1 )
| ( line_equal @ b1c1 @ oc ) ),
inference(demod,[status(thm)],[zip_derived_cl2269,zip_derived_cl25]) ).
thf('118',plain,
( ~ ( incident @ o @ b1c1 )
| ( line_equal @ b1c1 @ oc )
| ( point_equal @ o @ c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2308]) ).
thf(zip_derived_cl22_535,plain,
incident @ a2 @ oa,
inference(cnf,[status(esa)],[ia2oa]) ).
thf(zip_derived_cl327_536,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ a2b2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ a2b2 @ X1 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl49]) ).
thf(zip_derived_cl2159,plain,
( ( ( point_equal @ a2 @ c1 )
| ~ ( incident @ a2 @ a2b2 )
| ~ ( incident @ c1 @ oa )
| ( line_equal @ a2b2 @ oa ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl327]) ).
thf(zip_derived_cl8_537,plain,
incident @ a2 @ a2b2,
inference(cnf,[status(esa)],[ia2b2]) ).
thf(zip_derived_cl2195,plain,
( ( ( point_equal @ a2 @ c1 )
| ~ ( incident @ c1 @ oa )
| ( line_equal @ a2b2 @ oa ) )
<= ( incident @ c1 @ a2b2 ) ),
inference(demod,[status(thm)],[zip_derived_cl2159,zip_derived_cl8]) ).
thf('119',plain,
( ~ ( incident @ c1 @ oa )
| ~ ( incident @ c1 @ a2b2 )
| ( line_equal @ a2b2 @ oa )
| ( point_equal @ a2 @ c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2195]) ).
thf(zip_derived_cl2318_538,plain,
( ( incident @ bc @ ob )
<= ( ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1522,zip_derived_cl24]) ).
thf(zip_derived_cl333_539,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a2 )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a2 @ X1 )
| ( line_equal @ b1c1 @ X1 ) )
<= ( incident @ a2 @ b1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl65,zip_derived_cl49]) ).
thf(zip_derived_cl2857,plain,
( ( ( point_equal @ bc @ a2 )
| ~ ( incident @ bc @ b1c1 )
| ~ ( incident @ a2 @ ob )
| ( line_equal @ b1c1 @ ob ) )
<= ( ( incident @ a2 @ b1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2318,zip_derived_cl333]) ).
thf(zip_derived_cl27_540,plain,
incident @ bc @ b1c1,
inference(cnf,[status(esa)],[ibc1]) ).
thf(zip_derived_cl2911,plain,
( ( ( point_equal @ bc @ a2 )
| ~ ( incident @ a2 @ ob )
| ( line_equal @ b1c1 @ ob ) )
<= ( ( incident @ a2 @ b1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2857,zip_derived_cl27]) ).
thf(zip_derived_cl3081,plain,
( ( line_equal @ b1c1 @ ob )
<= ( line_equal @ b1c1 @ ob ) ),
inference(split,[status(esa)],[zip_derived_cl2911]) ).
thf(zip_derived_cl45_541,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl3301,plain,
( ( line_equal @ ob @ b1c1 )
<= ( line_equal @ b1c1 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl3081,zip_derived_cl45]) ).
thf(zip_derived_cl48_542,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl3513,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ ob )
| ( incident @ X0 @ b1c1 ) )
<= ( line_equal @ b1c1 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl3301,zip_derived_cl48]) ).
thf(zip_derived_cl19_543,plain,
incident @ o @ ob,
inference(cnf,[status(esa)],[ioob]) ).
thf(zip_derived_cl12806,plain,
( ( incident @ o @ b1c1 )
<= ( line_equal @ b1c1 @ ob ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl3513,zip_derived_cl19]) ).
thf(zip_derived_cl18_544,plain,
incident @ o @ oa,
inference(cnf,[status(esa)],[iooa]) ).
thf(zip_derived_cl314_545,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl49]) ).
thf(zip_derived_cl900,plain,
( ( point_equal @ o @ bc )
| ~ ( incident @ o @ b1c1 )
| ~ ( incident @ bc @ oa )
| ( line_equal @ b1c1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl314]) ).
thf(zip_derived_cl11774,plain,
( ~ ( incident @ o @ b1c1 )
<= ~ ( incident @ o @ b1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl900]) ).
thf('120',plain,
( ~ ( line_equal @ b1c1 @ ob )
| ( incident @ o @ b1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl12806,zip_derived_cl11774]) ).
thf(zip_derived_cl26_546,plain,
incident @ c2 @ oc,
inference(cnf,[status(esa)],[ic2oc]) ).
thf(zip_derived_cl314_547,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl49]) ).
thf(zip_derived_cl899,plain,
( ( point_equal @ c2 @ bc )
| ~ ( incident @ c2 @ b1c1 )
| ~ ( incident @ bc @ oc )
| ( line_equal @ b1c1 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl314]) ).
thf(zip_derived_cl11495,plain,
( ( line_equal @ b1c1 @ oc )
<= ( line_equal @ b1c1 @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl899]) ).
thf(zip_derived_cl45_548,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl11499,plain,
( ( line_equal @ oc @ b1c1 )
<= ( line_equal @ b1c1 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11495,zip_derived_cl45]) ).
thf(zip_derived_cl48_549,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl11780,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ oc )
| ( incident @ X0 @ b1c1 ) )
<= ( line_equal @ b1c1 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11499,zip_derived_cl48]) ).
thf(zip_derived_cl26_550,plain,
incident @ c2 @ oc,
inference(cnf,[status(esa)],[ic2oc]) ).
thf(zip_derived_cl24344,plain,
( ( incident @ c2 @ b1c1 )
<= ( line_equal @ b1c1 @ oc ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl11780,zip_derived_cl26]) ).
thf(zip_derived_cl13_551,plain,
incident @ c2 @ a2c2,
inference(cnf,[status(esa)],[ic2a2]) ).
thf(zip_derived_cl314_552,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl49]) ).
thf(zip_derived_cl897,plain,
( ( point_equal @ c2 @ bc )
| ~ ( incident @ c2 @ b1c1 )
| ~ ( incident @ bc @ a2c2 )
| ( line_equal @ b1c1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl314]) ).
thf(zip_derived_cl11453,plain,
( ~ ( incident @ c2 @ b1c1 )
<= ~ ( incident @ c2 @ b1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl897]) ).
thf('121',plain,
( ~ ( line_equal @ b1c1 @ oc )
| ( incident @ c2 @ b1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl24344,zip_derived_cl11453]) ).
thf(zip_derived_cl21_553,plain,
incident @ a1 @ oa,
inference(cnf,[status(esa)],[ia1oa]) ).
thf(zip_derived_cl32_554,plain,
incident @ ab @ a2b2,
inference(cnf,[status(esa)],[iab2]) ).
thf(zip_derived_cl49_555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ~ ( incident @ X0 @ X2 )
| ~ ( incident @ X0 @ X3 )
| ~ ( incident @ X1 @ X3 )
| ( line_equal @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[unique]) ).
thf(zip_derived_cl317,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ab )
| ~ ( incident @ X0 @ a2b2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ab @ X1 )
| ( line_equal @ a2b2 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl32,zip_derived_cl49]) ).
thf(zip_derived_cl1126,plain,
( ( point_equal @ a1 @ ab )
| ~ ( incident @ a1 @ a2b2 )
| ~ ( incident @ ab @ oa )
| ( line_equal @ a2b2 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl317]) ).
thf(zip_derived_cl18328,plain,
( ( line_equal @ a2b2 @ oa )
<= ( line_equal @ a2b2 @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl1126]) ).
thf(zip_derived_cl45_556,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl18333,plain,
( ( line_equal @ oa @ a2b2 )
<= ( line_equal @ a2b2 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl18328,zip_derived_cl45]) ).
thf(zip_derived_cl48_557,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl18337,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ oa )
| ( incident @ X0 @ a2b2 ) )
<= ( line_equal @ a2b2 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl18333,zip_derived_cl48]) ).
thf(zip_derived_cl21_558,plain,
incident @ a1 @ oa,
inference(cnf,[status(esa)],[ia1oa]) ).
thf(zip_derived_cl33844,plain,
( ( incident @ a1 @ a2b2 )
<= ( line_equal @ a2b2 @ oa ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl18337,zip_derived_cl21]) ).
thf(zip_derived_cl100_559,plain,
( ~ ( incident @ a1 @ a2b2 )
<= ~ ( incident @ a1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl97]) ).
thf('122',plain,
( ~ ( line_equal @ a2b2 @ oa )
| ( incident @ a1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl33844,zip_derived_cl100]) ).
thf(zip_derived_cl24_560,plain,
incident @ b2 @ ob,
inference(cnf,[status(esa)],[ib2ob]) ).
thf(zip_derived_cl324_561,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ b1 )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ b1 @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl15,zip_derived_cl49]) ).
thf(zip_derived_cl1792,plain,
( ( point_equal @ b2 @ b1 )
| ~ ( incident @ b2 @ b1c1 )
| ~ ( incident @ b1 @ ob )
| ( line_equal @ b1c1 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl324]) ).
thf(zip_derived_cl23_562,plain,
incident @ b1 @ ob,
inference(cnf,[status(esa)],[ib1ob]) ).
thf(zip_derived_cl1836,plain,
( ( point_equal @ b2 @ b1 )
| ~ ( incident @ b2 @ b1c1 )
| ( line_equal @ b1c1 @ ob ) ),
inference(demod,[status(thm)],[zip_derived_cl1792,zip_derived_cl23]) ).
thf(zip_derived_cl85_563,plain,
~ ( point_equal @ b2 @ b1 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl73,'28']) ).
thf(zip_derived_cl40064,plain,
( ( line_equal @ b1c1 @ ob )
| ~ ( incident @ b2 @ b1c1 ) ),
inference(clc,[status(thm)],[zip_derived_cl1836,zip_derived_cl85]) ).
thf('123',plain,
( ~ ( incident @ b2 @ b1c1 )
| ( line_equal @ b1c1 @ ob ) ),
inference(split,[status(esa)],[zip_derived_cl40064]) ).
thf(zip_derived_cl16_564,plain,
incident @ c2 @ b2c2,
inference(cnf,[status(esa)],[ic2b2]) ).
thf(zip_derived_cl314_565,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl49]) ).
thf(zip_derived_cl896,plain,
( ( point_equal @ c2 @ bc )
| ~ ( incident @ c2 @ b1c1 )
| ~ ( incident @ bc @ b2c2 )
| ( line_equal @ b1c1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl314]) ).
thf(zip_derived_cl28_566,plain,
incident @ bc @ b2c2,
inference(cnf,[status(esa)],[ibc2]) ).
thf(zip_derived_cl87_567,plain,
~ ( line_equal @ b1c1 @ b2c2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl77,'3']) ).
thf(zip_derived_cl931,plain,
( ( point_equal @ c2 @ bc )
| ~ ( incident @ c2 @ b1c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl896,zip_derived_cl28,zip_derived_cl87]) ).
thf('124',plain,
( ~ ( incident @ c2 @ b1c1 )
| ( point_equal @ c2 @ bc ) ),
inference(split,[status(esa)],[zip_derived_cl931]) ).
thf(zip_derived_cl10_568,plain,
incident @ a1 @ a1c1,
inference(cnf,[status(esa)],[ia1c1]) ).
thf(zip_derived_cl327_569,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ a2b2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ a2b2 @ X1 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl49]) ).
thf(zip_derived_cl2141,plain,
( ( ( point_equal @ a1 @ c1 )
| ~ ( incident @ a1 @ a2b2 )
| ~ ( incident @ c1 @ a1c1 )
| ( line_equal @ a2b2 @ a1c1 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl327]) ).
thf(zip_derived_cl11_570,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl2183,plain,
( ( ( point_equal @ a1 @ c1 )
| ~ ( incident @ a1 @ a2b2 )
| ( line_equal @ a2b2 @ a1c1 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference(demod,[status(thm)],[zip_derived_cl2141,zip_derived_cl11]) ).
thf('125',plain,
( ~ ( incident @ a1 @ a2b2 )
| ~ ( incident @ c1 @ a2b2 )
| ( line_equal @ a2b2 @ a1c1 )
| ( point_equal @ a1 @ c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2183]) ).
thf(zip_derived_cl9_571,plain,
incident @ b2 @ a2b2,
inference(cnf,[status(esa)],[ib2a2]) ).
thf(zip_derived_cl314_572,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl49]) ).
thf(zip_derived_cl893,plain,
( ( point_equal @ b2 @ bc )
| ~ ( incident @ b2 @ b1c1 )
| ~ ( incident @ bc @ a2b2 )
| ( line_equal @ b1c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl9,zip_derived_cl314]) ).
thf(zip_derived_cl11128,plain,
( ~ ( incident @ b2 @ b1c1 )
<= ~ ( incident @ b2 @ b1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl893]) ).
thf(zip_derived_cl1619_573,plain,
( ( point_equal @ b2 @ bc )
<= ( point_equal @ b2 @ bc ) ),
inference(split,[status(esa)],[zip_derived_cl1424]) ).
thf(zip_derived_cl47_574,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl1623,plain,
( ! [X0: $i] :
( ~ ( incident @ bc @ X0 )
| ( incident @ b2 @ X0 ) )
<= ( point_equal @ b2 @ bc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1619,zip_derived_cl47]) ).
thf(zip_derived_cl34847,plain,
( ~ ( incident @ bc @ b1c1 )
<= ( ~ ( incident @ b2 @ b1c1 )
& ( point_equal @ b2 @ bc ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl11128,zip_derived_cl1623]) ).
thf(zip_derived_cl27_575,plain,
incident @ bc @ b1c1,
inference(cnf,[status(esa)],[ibc1]) ).
thf('126',plain,
( ~ ( point_equal @ b2 @ bc )
| ( incident @ b2 @ b1c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl34847,zip_derived_cl27]) ).
thf(zip_derived_cl1623_576,plain,
( ! [X0: $i] :
( ~ ( incident @ bc @ X0 )
| ( incident @ b2 @ X0 ) )
<= ( point_equal @ b2 @ bc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1619,zip_derived_cl47]) ).
thf(zip_derived_cl117_577,plain,
~ ( incident @ b2 @ a2c2 ),
inference(demod,[status(thm)],[zip_derived_cl116,zip_derived_cl12]) ).
thf(zip_derived_cl34814,plain,
( ~ ( incident @ bc @ a2c2 )
<= ( point_equal @ b2 @ bc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1623,zip_derived_cl117]) ).
thf(zip_derived_cl3760,plain,
( ( point_equal @ c2 @ bc )
<= ( point_equal @ c2 @ bc ) ),
inference(split,[status(esa)],[zip_derived_cl3357]) ).
thf(zip_derived_cl42_578,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl3971,plain,
( ( point_equal @ bc @ c2 )
<= ( point_equal @ c2 @ bc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl3760,zip_derived_cl42]) ).
thf(zip_derived_cl47_579,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl4171,plain,
( ! [X0: $i] :
( ~ ( incident @ c2 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( point_equal @ c2 @ bc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl3971,zip_derived_cl47]) ).
thf(zip_derived_cl13_580,plain,
incident @ c2 @ a2c2,
inference(cnf,[status(esa)],[ic2a2]) ).
thf(zip_derived_cl15200,plain,
( ( incident @ bc @ a2c2 )
<= ( point_equal @ c2 @ bc ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4171,zip_derived_cl13]) ).
thf('127',plain,
( ~ ( point_equal @ b2 @ bc )
| ~ ( point_equal @ c2 @ bc ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl34814,zip_derived_cl15200]) ).
thf(zip_derived_cl2317_581,plain,
( ( incident @ bc @ a1c1 )
<= ( ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1522,zip_derived_cl61]) ).
thf(zip_derived_cl327_582,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ a2b2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ a2b2 @ X1 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl49]) ).
thf(zip_derived_cl2338,plain,
( ( ( point_equal @ bc @ c1 )
| ~ ( incident @ bc @ a2b2 )
| ~ ( incident @ c1 @ a1c1 )
| ( line_equal @ a2b2 @ a1c1 ) )
<= ( ( incident @ c1 @ a2b2 )
& ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2317,zip_derived_cl327]) ).
thf(zip_derived_cl11_583,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl2356,plain,
( ( ( point_equal @ bc @ c1 )
| ~ ( incident @ bc @ a2b2 )
| ( line_equal @ a2b2 @ a1c1 ) )
<= ( ( incident @ c1 @ a2b2 )
& ( incident @ b2 @ a1c1 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2338,zip_derived_cl11]) ).
thf(zip_derived_cl2458,plain,
( ( line_equal @ a2b2 @ a1c1 )
<= ( line_equal @ a2b2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2356]) ).
thf(zip_derived_cl45_584,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl2462,plain,
( ( line_equal @ a1c1 @ a2b2 )
<= ( line_equal @ a2b2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2458,zip_derived_cl45]) ).
thf(zip_derived_cl48_585,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl2583,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ a1c1 )
| ( incident @ X0 @ a2b2 ) )
<= ( line_equal @ a2b2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2462,zip_derived_cl48]) ).
thf(zip_derived_cl29_586,plain,
incident @ ac @ a1c1,
inference(cnf,[status(esa)],[iac1]) ).
thf(zip_derived_cl9006,plain,
( ( incident @ ac @ a2b2 )
<= ( line_equal @ a2b2 @ a1c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2583,zip_derived_cl29]) ).
thf(zip_derived_cl183,plain,
( ~ ( incident @ ac @ a2b2 )
<= ~ ( incident @ ac @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl168]) ).
thf('128',plain,
( ~ ( line_equal @ a2b2 @ a1c1 )
| ( incident @ ac @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl9006,zip_derived_cl183]) ).
thf(zip_derived_cl444,plain,
( ( line_equal @ b2c2 @ a2b2 )
<= ( line_equal @ b2c2 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl366]) ).
thf(zip_derived_cl45_587,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl471,plain,
( ( line_equal @ a2b2 @ b2c2 )
<= ( line_equal @ b2c2 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl444,zip_derived_cl45]) ).
thf(zip_derived_cl48_588,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl484,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ a2b2 )
| ( incident @ X0 @ b2c2 ) )
<= ( line_equal @ b2c2 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl471,zip_derived_cl48]) ).
thf(zip_derived_cl8_589,plain,
incident @ a2 @ a2b2,
inference(cnf,[status(esa)],[ia2b2]) ).
thf(zip_derived_cl731,plain,
( ( incident @ a2 @ b2c2 )
<= ( line_equal @ b2c2 @ a2b2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl484,zip_derived_cl8]) ).
thf(zip_derived_cl173_590,plain,
~ ( incident @ a2 @ b2c2 ),
inference(demod,[status(thm)],[zip_derived_cl165,zip_derived_cl17]) ).
thf('129',plain,
~ ( line_equal @ b2c2 @ a2b2 ),
inference('s_sup-',[status(thm)],[zip_derived_cl731,zip_derived_cl173]) ).
thf(zip_derived_cl9_591,plain,
incident @ b2 @ a2b2,
inference(cnf,[status(esa)],[ib2a2]) ).
thf(zip_derived_cl313_592,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b2c2 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl28,zip_derived_cl49]) ).
thf(zip_derived_cl788,plain,
( ( point_equal @ b2 @ bc )
| ~ ( incident @ b2 @ b2c2 )
| ~ ( incident @ bc @ a2b2 )
| ( line_equal @ b2c2 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl9,zip_derived_cl313]) ).
thf(zip_derived_cl17_593,plain,
incident @ b2 @ b2c2,
inference(cnf,[status(esa)],[ib2c2]) ).
thf(zip_derived_cl822,plain,
( ( point_equal @ b2 @ bc )
| ~ ( incident @ bc @ a2b2 )
| ( line_equal @ b2c2 @ a2b2 ) ),
inference(demod,[status(thm)],[zip_derived_cl788,zip_derived_cl17]) ).
thf('130',plain,
( ( point_equal @ b2 @ bc )
| ( line_equal @ b2c2 @ a2b2 )
| ~ ( incident @ bc @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl822]) ).
thf(zip_derived_cl18_594,plain,
incident @ o @ oa,
inference(cnf,[status(esa)],[iooa]) ).
thf(zip_derived_cl327_595,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ a2b2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ a2b2 @ X1 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl49]) ).
thf(zip_derived_cl2168,plain,
( ( ( point_equal @ o @ c1 )
| ~ ( incident @ o @ a2b2 )
| ~ ( incident @ c1 @ oa )
| ( line_equal @ a2b2 @ oa ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl327]) ).
thf(zip_derived_cl51912,plain,
( ( point_equal @ o @ c1 )
<= ( point_equal @ o @ c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2168]) ).
thf(zip_derived_cl42_596,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl51918,plain,
( ( point_equal @ c1 @ o )
<= ( point_equal @ o @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl51912,zip_derived_cl42]) ).
thf(zip_derived_cl47_597,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl52171,plain,
( ! [X0: $i] :
( ~ ( incident @ o @ X0 )
| ( incident @ c1 @ X0 ) )
<= ( point_equal @ o @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl51918,zip_derived_cl47]) ).
thf(zip_derived_cl18_598,plain,
incident @ o @ oa,
inference(cnf,[status(esa)],[iooa]) ).
thf(zip_derived_cl54962,plain,
( ( incident @ c1 @ oa )
<= ( point_equal @ o @ c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl52171,zip_derived_cl18]) ).
thf(zip_derived_cl31485_599,plain,
( ~ ( incident @ c1 @ oa )
<= ~ ( incident @ c1 @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl1553]) ).
thf('131',plain,
( ~ ( point_equal @ o @ c1 )
| ( incident @ c1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl54962,zip_derived_cl31485]) ).
thf(zip_derived_cl32_600,plain,
incident @ ab @ a2b2,
inference(cnf,[status(esa)],[iab2]) ).
thf(zip_derived_cl322_601,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ oa )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ oa @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl49]) ).
thf(zip_derived_cl1533,plain,
( ( point_equal @ ab @ a1 )
| ~ ( incident @ ab @ oa )
| ~ ( incident @ a1 @ a2b2 )
| ( line_equal @ oa @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl32,zip_derived_cl322]) ).
thf(zip_derived_cl31279,plain,
( ( line_equal @ oa @ a2b2 )
<= ( line_equal @ oa @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl1533]) ).
thf(zip_derived_cl48_602,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl31285,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ oa )
| ( incident @ X0 @ a2b2 ) )
<= ( line_equal @ oa @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl31279,zip_derived_cl48]) ).
thf(zip_derived_cl18_603,plain,
incident @ o @ oa,
inference(cnf,[status(esa)],[iooa]) ).
thf(zip_derived_cl41749,plain,
( ( incident @ o @ a2b2 )
<= ( line_equal @ oa @ a2b2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl31285,zip_derived_cl18]) ).
thf(zip_derived_cl18_604,plain,
incident @ o @ oa,
inference(cnf,[status(esa)],[iooa]) ).
thf(zip_derived_cl317_605,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ab )
| ~ ( incident @ X0 @ a2b2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ab @ X1 )
| ( line_equal @ a2b2 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl32,zip_derived_cl49]) ).
thf(zip_derived_cl1151,plain,
( ( point_equal @ o @ ab )
| ~ ( incident @ o @ a2b2 )
| ~ ( incident @ ab @ oa )
| ( line_equal @ a2b2 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl317]) ).
thf(zip_derived_cl19341,plain,
( ~ ( incident @ o @ a2b2 )
<= ~ ( incident @ o @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl1151]) ).
thf('132',plain,
( ~ ( line_equal @ oa @ a2b2 )
| ( incident @ o @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl41749,zip_derived_cl19341]) ).
thf(zip_derived_cl25_606,plain,
incident @ c1 @ oc,
inference(cnf,[status(esa)],[ic1oc]) ).
thf(zip_derived_cl317_607,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ab )
| ~ ( incident @ X0 @ a2b2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ab @ X1 )
| ( line_equal @ a2b2 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl32,zip_derived_cl49]) ).
thf(zip_derived_cl1138,plain,
( ( point_equal @ c1 @ ab )
| ~ ( incident @ c1 @ a2b2 )
| ~ ( incident @ ab @ oc )
| ( line_equal @ a2b2 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl25,zip_derived_cl317]) ).
thf(zip_derived_cl18919,plain,
( ( line_equal @ a2b2 @ oc )
<= ( line_equal @ a2b2 @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl1138]) ).
thf(zip_derived_cl45_608,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl18923,plain,
( ( line_equal @ oc @ a2b2 )
<= ( line_equal @ a2b2 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl18919,zip_derived_cl45]) ).
thf(zip_derived_cl48_609,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl18927,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ oc )
| ( incident @ X0 @ a2b2 ) )
<= ( line_equal @ a2b2 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl18923,zip_derived_cl48]) ).
thf(zip_derived_cl26_610,plain,
incident @ c2 @ oc,
inference(cnf,[status(esa)],[ic2oc]) ).
thf(zip_derived_cl35626,plain,
( ( incident @ c2 @ a2b2 )
<= ( line_equal @ a2b2 @ oc ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl18927,zip_derived_cl26]) ).
thf(zip_derived_cl107_611,plain,
! [X0: $i] :
( ~ ( incident @ a2 @ X0 )
| ~ ( incident @ b2 @ X0 )
| ~ ( incident @ c2 @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl69,'9']) ).
thf(zip_derived_cl35824,plain,
( ( ~ ( incident @ a2 @ a2b2 )
| ~ ( incident @ b2 @ a2b2 ) )
<= ( line_equal @ a2b2 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl35626,zip_derived_cl107]) ).
thf(zip_derived_cl8_612,plain,
incident @ a2 @ a2b2,
inference(cnf,[status(esa)],[ia2b2]) ).
thf(zip_derived_cl9_613,plain,
incident @ b2 @ a2b2,
inference(cnf,[status(esa)],[ib2a2]) ).
thf('133',plain,
~ ( line_equal @ a2b2 @ oc ),
inference(demod,[status(thm)],[zip_derived_cl35824,zip_derived_cl8,zip_derived_cl9]) ).
thf(zip_derived_cl20_614,plain,
incident @ o @ oc,
inference(cnf,[status(esa)],[iooc]) ).
thf(zip_derived_cl327_615,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ a2b2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ a2b2 @ X1 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl49]) ).
thf(zip_derived_cl2170,plain,
( ( ( point_equal @ o @ c1 )
| ~ ( incident @ o @ a2b2 )
| ~ ( incident @ c1 @ oc )
| ( line_equal @ a2b2 @ oc ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl327]) ).
thf(zip_derived_cl25_616,plain,
incident @ c1 @ oc,
inference(cnf,[status(esa)],[ic1oc]) ).
thf(zip_derived_cl2201,plain,
( ( ( point_equal @ o @ c1 )
| ~ ( incident @ o @ a2b2 )
| ( line_equal @ a2b2 @ oc ) )
<= ( incident @ c1 @ a2b2 ) ),
inference(demod,[status(thm)],[zip_derived_cl2170,zip_derived_cl25]) ).
thf('134',plain,
( ( point_equal @ o @ c1 )
| ( line_equal @ a2b2 @ oc )
| ~ ( incident @ c1 @ a2b2 )
| ~ ( incident @ o @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl2201]) ).
thf(zip_derived_cl21_617,plain,
incident @ a1 @ oa,
inference(cnf,[status(esa)],[ia1oa]) ).
thf(zip_derived_cl327_618,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ a2b2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ a2b2 @ X1 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl49]) ).
thf(zip_derived_cl2143,plain,
( ( ( point_equal @ a1 @ c1 )
| ~ ( incident @ a1 @ a2b2 )
| ~ ( incident @ c1 @ oa )
| ( line_equal @ a2b2 @ oa ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl327]) ).
thf('135',plain,
( ~ ( incident @ a1 @ a2b2 )
| ~ ( incident @ c1 @ oa )
| ( line_equal @ a2b2 @ oa )
| ~ ( incident @ c1 @ a2b2 )
| ( point_equal @ a1 @ c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2143]) ).
thf(zip_derived_cl62_619,plain,
( ( incident @ a1 @ b2c2 )
<= ( incident @ a1 @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl3]) ).
thf(zip_derived_cl327_620,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ a2b2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ a2b2 @ X1 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl49]) ).
thf(zip_derived_cl2134,plain,
( ( ( point_equal @ a1 @ c1 )
| ~ ( incident @ a1 @ a2b2 )
| ~ ( incident @ c1 @ b2c2 )
| ( line_equal @ a2b2 @ b2c2 ) )
<= ( ( incident @ a1 @ b2c2 )
& ( incident @ c1 @ a2b2 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl327]) ).
thf(zip_derived_cl50405,plain,
( ( point_equal @ a1 @ c1 )
<= ( point_equal @ a1 @ c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2134]) ).
thf(zip_derived_cl47_621,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl50409,plain,
( ! [X0: $i] :
( ~ ( incident @ c1 @ X0 )
| ( incident @ a1 @ X0 ) )
<= ( point_equal @ a1 @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl50405,zip_derived_cl47]) ).
thf(zip_derived_cl14_622,plain,
incident @ c1 @ b1c1,
inference(cnf,[status(esa)],[ic1b1]) ).
thf(zip_derived_cl54465,plain,
( ( incident @ a1 @ b1c1 )
<= ( point_equal @ a1 @ c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl50409,zip_derived_cl14]) ).
thf(zip_derived_cl137_623,plain,
~ ( incident @ a1 @ b1c1 ),
inference(demod,[status(thm)],[zip_derived_cl134,zip_derived_cl15]) ).
thf('136',plain,
~ ( point_equal @ a1 @ c1 ),
inference('s_sup-',[status(thm)],[zip_derived_cl54465,zip_derived_cl137]) ).
thf(zip_derived_cl52171_624,plain,
( ! [X0: $i] :
( ~ ( incident @ o @ X0 )
| ( incident @ c1 @ X0 ) )
<= ( point_equal @ o @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl51918,zip_derived_cl47]) ).
thf(zip_derived_cl19_625,plain,
incident @ o @ ob,
inference(cnf,[status(esa)],[ioob]) ).
thf(zip_derived_cl54963,plain,
( ( incident @ c1 @ ob )
<= ( point_equal @ o @ c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl52171,zip_derived_cl19]) ).
thf(zip_derived_cl2318_626,plain,
( ( incident @ bc @ ob )
<= ( ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1522,zip_derived_cl24]) ).
thf(zip_derived_cl327_627,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ a2b2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ a2b2 @ X1 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl49]) ).
thf(zip_derived_cl2696,plain,
( ( ( point_equal @ bc @ c1 )
| ~ ( incident @ bc @ a2b2 )
| ~ ( incident @ c1 @ ob )
| ( line_equal @ a2b2 @ ob ) )
<= ( ( incident @ c1 @ a2b2 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2318,zip_derived_cl327]) ).
thf(zip_derived_cl2316_628,plain,
( ( incident @ bc @ a2b2 )
<= ( ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1522,zip_derived_cl9]) ).
thf(zip_derived_cl2715,plain,
( ( ( point_equal @ bc @ c1 )
| ~ ( incident @ c1 @ ob )
| ( line_equal @ a2b2 @ ob ) )
<= ( ( incident @ c1 @ a2b2 )
& ( point_equal @ b2 @ a1 )
& ( point_equal @ bc @ a1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2696,zip_derived_cl2316]) ).
thf(zip_derived_cl2845,plain,
( ~ ( incident @ c1 @ ob )
<= ~ ( incident @ c1 @ ob ) ),
inference(split,[status(esa)],[zip_derived_cl2715]) ).
thf('137',plain,
( ~ ( point_equal @ o @ c1 )
| ( incident @ c1 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl54963,zip_derived_cl2845]) ).
thf(zip_derived_cl2583_629,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ a1c1 )
| ( incident @ X0 @ a2b2 ) )
<= ( line_equal @ a2b2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2462,zip_derived_cl48]) ).
thf(zip_derived_cl10_630,plain,
incident @ a1 @ a1c1,
inference(cnf,[status(esa)],[ia1c1]) ).
thf(zip_derived_cl9007,plain,
( ( incident @ a1 @ a2b2 )
<= ( line_equal @ a2b2 @ a1c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2583,zip_derived_cl10]) ).
thf(zip_derived_cl100_631,plain,
( ~ ( incident @ a1 @ a2b2 )
<= ~ ( incident @ a1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl97]) ).
thf('138',plain,
( ~ ( line_equal @ a2b2 @ a1c1 )
| ( incident @ a1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl9007,zip_derived_cl100]) ).
thf(zip_derived_cl4518,plain,
( ( line_equal @ a1c1 @ ob )
<= ( line_equal @ a1c1 @ ob ) ),
inference(split,[status(esa)],[zip_derived_cl3409]) ).
thf(zip_derived_cl45_632,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl4790,plain,
( ( line_equal @ ob @ a1c1 )
<= ( line_equal @ a1c1 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4518,zip_derived_cl45]) ).
thf(zip_derived_cl48_633,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl4893,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ ob )
| ( incident @ X0 @ a1c1 ) )
<= ( line_equal @ a1c1 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4790,zip_derived_cl48]) ).
thf(zip_derived_cl23_634,plain,
incident @ b1 @ ob,
inference(cnf,[status(esa)],[ib1ob]) ).
thf(zip_derived_cl19746,plain,
( ( incident @ b1 @ a1c1 )
<= ( line_equal @ a1c1 @ ob ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4893,zip_derived_cl23]) ).
thf(zip_derived_cl96_635,plain,
! [X0: $i] :
( ~ ( incident @ a1 @ X0 )
| ~ ( incident @ b1 @ X0 )
| ~ ( incident @ c1 @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl67,'19']) ).
thf(zip_derived_cl11_636,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl102,plain,
( ~ ( incident @ b1 @ a1c1 )
| ~ ( incident @ a1 @ a1c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl96,zip_derived_cl11]) ).
thf(zip_derived_cl10_637,plain,
incident @ a1 @ a1c1,
inference(cnf,[status(esa)],[ia1c1]) ).
thf(zip_derived_cl103,plain,
~ ( incident @ b1 @ a1c1 ),
inference(demod,[status(thm)],[zip_derived_cl102,zip_derived_cl10]) ).
thf('139',plain,
~ ( line_equal @ a1c1 @ ob ),
inference('s_sup-',[status(thm)],[zip_derived_cl19746,zip_derived_cl103]) ).
thf(zip_derived_cl24_638,plain,
incident @ b2 @ ob,
inference(cnf,[status(esa)],[ib2ob]) ).
thf(zip_derived_cl329_639,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ a1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ a1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl49]) ).
thf(zip_derived_cl2402,plain,
( ( point_equal @ b2 @ c1 )
| ~ ( incident @ b2 @ a1c1 )
| ~ ( incident @ c1 @ ob )
| ( line_equal @ a1c1 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl329]) ).
thf('140',plain,
( ( point_equal @ b2 @ c1 )
| ( line_equal @ a1c1 @ ob )
| ~ ( incident @ b2 @ a1c1 )
| ~ ( incident @ c1 @ ob ) ),
inference(split,[status(esa)],[zip_derived_cl2402]) ).
thf(zip_derived_cl61_640,plain,
( ( incident @ b2 @ a1c1 )
<= ( incident @ b2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl3]) ).
thf(zip_derived_cl327_641,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ c1 )
| ~ ( incident @ X0 @ a2b2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ c1 @ X1 )
| ( line_equal @ a2b2 @ X1 ) )
<= ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl49]) ).
thf(zip_derived_cl2162,plain,
( ( ( point_equal @ b2 @ c1 )
| ~ ( incident @ b2 @ a2b2 )
| ~ ( incident @ c1 @ a1c1 )
| ( line_equal @ a2b2 @ a1c1 ) )
<= ( ( incident @ c1 @ a2b2 )
& ( incident @ b2 @ a1c1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl327]) ).
thf(zip_derived_cl9_642,plain,
incident @ b2 @ a2b2,
inference(cnf,[status(esa)],[ib2a2]) ).
thf(zip_derived_cl11_643,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl2198,plain,
( ( ( point_equal @ b2 @ c1 )
| ( line_equal @ a2b2 @ a1c1 ) )
<= ( ( incident @ c1 @ a2b2 )
& ( incident @ b2 @ a1c1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2162,zip_derived_cl9,zip_derived_cl11]) ).
thf('141',plain,
( ~ ( incident @ b2 @ a1c1 )
| ~ ( incident @ c1 @ a2b2 )
| ( line_equal @ a2b2 @ a1c1 )
| ( point_equal @ b2 @ c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2198]) ).
thf(zip_derived_cl53765_644,plain,
( ! [X0: $i] :
( ~ ( incident @ b2 @ X0 )
| ( incident @ c1 @ X0 ) )
<= ( point_equal @ b2 @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl53756,zip_derived_cl47]) ).
thf(zip_derived_cl17_645,plain,
incident @ b2 @ b2c2,
inference(cnf,[status(esa)],[ib2c2]) ).
thf(zip_derived_cl55814,plain,
( ( incident @ c1 @ b2c2 )
<= ( point_equal @ b2 @ c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl53765,zip_derived_cl17]) ).
thf(zip_derived_cl314_646,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl49]) ).
thf(zip_derived_cl55847,plain,
( ( ( point_equal @ c1 @ bc )
| ~ ( incident @ c1 @ b1c1 )
| ~ ( incident @ bc @ b2c2 )
| ( line_equal @ b1c1 @ b2c2 ) )
<= ( point_equal @ b2 @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl55814,zip_derived_cl314]) ).
thf(zip_derived_cl14_647,plain,
incident @ c1 @ b1c1,
inference(cnf,[status(esa)],[ic1b1]) ).
thf(zip_derived_cl28_648,plain,
incident @ bc @ b2c2,
inference(cnf,[status(esa)],[ibc2]) ).
thf(zip_derived_cl87_649,plain,
~ ( line_equal @ b1c1 @ b2c2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl77,'3']) ).
thf(zip_derived_cl55915,plain,
( ( point_equal @ c1 @ bc )
<= ( point_equal @ b2 @ c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl55847,zip_derived_cl14,zip_derived_cl28,zip_derived_cl87]) ).
thf(zip_derived_cl42_650,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl56213,plain,
( ( point_equal @ bc @ c1 )
<= ( point_equal @ b2 @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl55915,zip_derived_cl42]) ).
thf(zip_derived_cl47_651,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl56233,plain,
( ! [X0: $i] :
( ~ ( incident @ c1 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( point_equal @ b2 @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl56213,zip_derived_cl47]) ).
thf(zip_derived_cl55815_652,plain,
( ( incident @ c1 @ a2b2 )
<= ( point_equal @ b2 @ c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl53765,zip_derived_cl9]) ).
thf(zip_derived_cl56917,plain,
( ( incident @ bc @ a2b2 )
<= ( point_equal @ b2 @ c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl56233,zip_derived_cl55815]) ).
thf(zip_derived_cl184_653,plain,
( ~ ( incident @ bc @ a2b2 )
<= ~ ( incident @ bc @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl168]) ).
thf('142',plain,
( ~ ( point_equal @ b2 @ c1 )
| ( incident @ bc @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl56917,zip_derived_cl184]) ).
thf(zip_derived_cl8_654,plain,
incident @ a2 @ a2b2,
inference(cnf,[status(esa)],[ia2b2]) ).
thf(zip_derived_cl44_655,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X0 )
| ~ ( incident @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[reflexivity_of_line_equal]) ).
thf(zip_derived_cl156,plain,
line_equal @ a2b2 @ a2b2,
inference('s_sup-',[status(thm)],[zip_derived_cl8,zip_derived_cl44]) ).
thf(zip_derived_cl114_656,plain,
! [X0: $i] :
( ~ ( line_equal @ X0 @ X0 )
| ~ ( incident @ bc @ X0 )
| ~ ( incident @ ac @ X0 )
| ~ ( incident @ ab @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl51,'6']) ).
thf(zip_derived_cl455,plain,
( ~ ( incident @ bc @ a2b2 )
| ~ ( incident @ ac @ a2b2 )
| ~ ( incident @ ab @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl156,zip_derived_cl114]) ).
thf(zip_derived_cl32_657,plain,
incident @ ab @ a2b2,
inference(cnf,[status(esa)],[iab2]) ).
thf(zip_derived_cl459,plain,
( ~ ( incident @ bc @ a2b2 )
| ~ ( incident @ ac @ a2b2 ) ),
inference(demod,[status(thm)],[zip_derived_cl455,zip_derived_cl32]) ).
thf('143',plain,
( ~ ( incident @ bc @ a2b2 )
| ~ ( incident @ ac @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl459]) ).
thf(zip_derived_cl55764_658,plain,
( ! [X0: $i] :
( ~ ( incident @ c1 @ X0 )
| ( incident @ ac @ X0 ) )
<= ( point_equal @ a2 @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl55747,zip_derived_cl47]) ).
thf(zip_derived_cl53659_659,plain,
( ! [X0: $i] :
( ~ ( incident @ a2 @ X0 )
| ( incident @ c1 @ X0 ) )
<= ( point_equal @ a2 @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl53643,zip_derived_cl47]) ).
thf(zip_derived_cl8_660,plain,
incident @ a2 @ a2b2,
inference(cnf,[status(esa)],[ia2b2]) ).
thf(zip_derived_cl55361,plain,
( ( incident @ c1 @ a2b2 )
<= ( point_equal @ a2 @ c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl53659,zip_derived_cl8]) ).
thf(zip_derived_cl56346,plain,
( ( incident @ ac @ a2b2 )
<= ( point_equal @ a2 @ c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl55764,zip_derived_cl55361]) ).
thf(zip_derived_cl183_661,plain,
( ~ ( incident @ ac @ a2b2 )
<= ~ ( incident @ ac @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl168]) ).
thf('144',plain,
( ~ ( point_equal @ a2 @ c1 )
| ( incident @ ac @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl56346,zip_derived_cl183]) ).
thf(zip_derived_cl53659_662,plain,
( ! [X0: $i] :
( ~ ( incident @ a2 @ X0 )
| ( incident @ c1 @ X0 ) )
<= ( point_equal @ a2 @ c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl53643,zip_derived_cl47]) ).
thf(zip_derived_cl22_663,plain,
incident @ a2 @ oa,
inference(cnf,[status(esa)],[ia2oa]) ).
thf(zip_derived_cl55367,plain,
( ( incident @ c1 @ oa )
<= ( point_equal @ a2 @ c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl53659,zip_derived_cl22]) ).
thf(zip_derived_cl31485_664,plain,
( ~ ( incident @ c1 @ oa )
<= ~ ( incident @ c1 @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl1553]) ).
thf('145',plain,
( ~ ( point_equal @ a2 @ c1 )
| ( incident @ c1 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl55367,zip_derived_cl31485]) ).
thf(zip_derived_cl55361_665,plain,
( ( incident @ c1 @ a2b2 )
<= ( point_equal @ a2 @ c1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl53659,zip_derived_cl8]) ).
thf(zip_derived_cl55_666,plain,
( ~ ( incident @ c1 @ a2b2 )
<= ~ ( incident @ c1 @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl1]) ).
thf('146',plain,
( ~ ( point_equal @ a2 @ c1 )
| ( incident @ c1 @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl55361,zip_derived_cl55]) ).
thf(zip_derived_cl18337_667,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ oa )
| ( incident @ X0 @ a2b2 ) )
<= ( line_equal @ a2b2 @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl18333,zip_derived_cl48]) ).
thf(zip_derived_cl18_668,plain,
incident @ o @ oa,
inference(cnf,[status(esa)],[iooa]) ).
thf(zip_derived_cl33850,plain,
( ( incident @ o @ a2b2 )
<= ( line_equal @ a2b2 @ oa ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl18337,zip_derived_cl18]) ).
thf(zip_derived_cl19341_669,plain,
( ~ ( incident @ o @ a2b2 )
<= ~ ( incident @ o @ a2b2 ) ),
inference(split,[status(esa)],[zip_derived_cl1151]) ).
thf('147',plain,
( ~ ( line_equal @ a2b2 @ oa )
| ( incident @ o @ a2b2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl33850,zip_derived_cl19341]) ).
thf('148',plain,
( ( incident @ a1 @ b2c2 )
| ( incident @ b2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl3]) ).
thf(zip_derived_cl23_670,plain,
incident @ b1 @ ob,
inference(cnf,[status(esa)],[ib1ob]) ).
thf(zip_derived_cl319_671,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ b2c2 @ X1 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl49]) ).
thf(zip_derived_cl365,plain,
( ( ( point_equal @ b1 @ a1 )
| ~ ( incident @ b1 @ b2c2 )
| ~ ( incident @ a1 @ ob )
| ( line_equal @ b2c2 @ ob ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl319]) ).
thf(zip_derived_cl4777,plain,
( ( line_equal @ b2c2 @ ob )
<= ( line_equal @ b2c2 @ ob ) ),
inference(split,[status(esa)],[zip_derived_cl365]) ).
thf(zip_derived_cl45_672,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl4782,plain,
( ( line_equal @ ob @ b2c2 )
<= ( line_equal @ b2c2 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4777,zip_derived_cl45]) ).
thf(zip_derived_cl48_673,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( incident @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[lcon]) ).
thf(zip_derived_cl4890,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ ob )
| ( incident @ X0 @ b2c2 ) )
<= ( line_equal @ b2c2 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4782,zip_derived_cl48]) ).
thf(zip_derived_cl23_674,plain,
incident @ b1 @ ob,
inference(cnf,[status(esa)],[ib1ob]) ).
thf(zip_derived_cl19408,plain,
( ( incident @ b1 @ b2c2 )
<= ( line_equal @ b2c2 @ ob ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4890,zip_derived_cl23]) ).
thf(zip_derived_cl314_675,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b1c1 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b1c1 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl49]) ).
thf(zip_derived_cl19437,plain,
( ( ( point_equal @ b1 @ bc )
| ~ ( incident @ b1 @ b1c1 )
| ~ ( incident @ bc @ b2c2 )
| ( line_equal @ b1c1 @ b2c2 ) )
<= ( line_equal @ b2c2 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl19408,zip_derived_cl314]) ).
thf(zip_derived_cl15_676,plain,
incident @ b1 @ b1c1,
inference(cnf,[status(esa)],[ib1c1]) ).
thf(zip_derived_cl28_677,plain,
incident @ bc @ b2c2,
inference(cnf,[status(esa)],[ibc2]) ).
thf(zip_derived_cl87_678,plain,
~ ( line_equal @ b1c1 @ b2c2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl77,'3']) ).
thf(zip_derived_cl19492,plain,
( ( point_equal @ b1 @ bc )
<= ( line_equal @ b2c2 @ ob ) ),
inference(demod,[status(thm)],[zip_derived_cl19437,zip_derived_cl15,zip_derived_cl28,zip_derived_cl87]) ).
thf(zip_derived_cl42_679,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl19698,plain,
( ( point_equal @ bc @ b1 )
<= ( line_equal @ b2c2 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl19492,zip_derived_cl42]) ).
thf(zip_derived_cl47_680,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl19707,plain,
( ! [X0: $i] :
( ~ ( incident @ b1 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( line_equal @ b2c2 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl19698,zip_derived_cl47]) ).
thf(zip_derived_cl7_681,plain,
incident @ b1 @ a1b1,
inference(cnf,[status(esa)],[ib1a1]) ).
thf(zip_derived_cl37221,plain,
( ( incident @ bc @ a1b1 )
<= ( line_equal @ b2c2 @ ob ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl19707,zip_derived_cl7]) ).
thf(zip_derived_cl63_682,plain,
( ( incident @ c2 @ a1b1 )
<= ( incident @ c2 @ a1b1 ) ),
inference(split,[status(esa)],[zip_derived_cl4]) ).
thf(zip_derived_cl44_683,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X0 )
| ~ ( incident @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[reflexivity_of_line_equal]) ).
thf(zip_derived_cl161,plain,
( ( line_equal @ a1b1 @ a1b1 )
<= ( incident @ c2 @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl63,zip_derived_cl44]) ).
thf(zip_derived_cl114_684,plain,
! [X0: $i] :
( ~ ( line_equal @ X0 @ X0 )
| ~ ( incident @ bc @ X0 )
| ~ ( incident @ ac @ X0 )
| ~ ( incident @ ab @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl51,'6']) ).
thf(zip_derived_cl174,plain,
( ( ~ ( incident @ bc @ a1b1 )
| ~ ( incident @ ac @ a1b1 )
| ~ ( incident @ ab @ a1b1 ) )
<= ( incident @ c2 @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl161,zip_derived_cl114]) ).
thf(zip_derived_cl197,plain,
( ~ ( incident @ bc @ a1b1 )
<= ~ ( incident @ bc @ a1b1 ) ),
inference(split,[status(esa)],[zip_derived_cl174]) ).
thf('149',plain,
( ~ ( line_equal @ b2c2 @ ob )
| ( incident @ bc @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl37221,zip_derived_cl197]) ).
thf(zip_derived_cl20_685,plain,
incident @ o @ oc,
inference(cnf,[status(esa)],[iooc]) ).
thf(zip_derived_cl319_686,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ b2c2 @ X1 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl49]) ).
thf(zip_derived_cl384,plain,
( ( ( point_equal @ o @ a1 )
| ~ ( incident @ o @ b2c2 )
| ~ ( incident @ a1 @ oc )
| ( line_equal @ b2c2 @ oc ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl319]) ).
thf(zip_derived_cl4855,plain,
( ( point_equal @ o @ a1 )
<= ( point_equal @ o @ a1 ) ),
inference(split,[status(esa)],[zip_derived_cl384]) ).
thf(zip_derived_cl42_687,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl4860,plain,
( ( point_equal @ a1 @ o )
<= ( point_equal @ o @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4855,zip_derived_cl42]) ).
thf(zip_derived_cl47_688,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl4909,plain,
( ! [X0: $i] :
( ~ ( incident @ o @ X0 )
| ( incident @ a1 @ X0 ) )
<= ( point_equal @ o @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4860,zip_derived_cl47]) ).
thf(zip_derived_cl19_689,plain,
incident @ o @ ob,
inference(cnf,[status(esa)],[ioob]) ).
thf(zip_derived_cl20182,plain,
( ( incident @ a1 @ ob )
<= ( point_equal @ o @ a1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4909,zip_derived_cl19]) ).
thf(zip_derived_cl4778,plain,
( ~ ( incident @ a1 @ ob )
<= ~ ( incident @ a1 @ ob ) ),
inference(split,[status(esa)],[zip_derived_cl365]) ).
thf('150',plain,
( ~ ( point_equal @ o @ a1 )
| ( incident @ a1 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl20182,zip_derived_cl4778]) ).
thf(zip_derived_cl6_690,plain,
incident @ a1 @ a1b1,
inference(cnf,[status(esa)],[ia1b1]) ).
thf(zip_derived_cl44_691,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X0 )
| ~ ( incident @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[reflexivity_of_line_equal]) ).
thf(zip_derived_cl148,plain,
line_equal @ a1b1 @ a1b1,
inference('s_sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl44]) ).
thf(zip_derived_cl114_692,plain,
! [X0: $i] :
( ~ ( line_equal @ X0 @ X0 )
| ~ ( incident @ bc @ X0 )
| ~ ( incident @ ac @ X0 )
| ~ ( incident @ ab @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl51,'6']) ).
thf(zip_derived_cl293,plain,
( ~ ( incident @ bc @ a1b1 )
| ~ ( incident @ ac @ a1b1 )
| ~ ( incident @ ab @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl148,zip_derived_cl114]) ).
thf(zip_derived_cl31_693,plain,
incident @ ab @ a1b1,
inference(cnf,[status(esa)],[iab1]) ).
thf(zip_derived_cl296,plain,
( ~ ( incident @ bc @ a1b1 )
| ~ ( incident @ ac @ a1b1 ) ),
inference(demod,[status(thm)],[zip_derived_cl293,zip_derived_cl31]) ).
thf('151',plain,
( ~ ( incident @ ac @ a1b1 )
| ~ ( incident @ bc @ a1b1 ) ),
inference(split,[status(esa)],[zip_derived_cl296]) ).
thf(zip_derived_cl20_694,plain,
incident @ o @ oc,
inference(cnf,[status(esa)],[iooc]) ).
thf(zip_derived_cl322_695,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ oa )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ oa @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl49]) ).
thf(zip_derived_cl1572,plain,
( ( point_equal @ o @ a1 )
| ~ ( incident @ o @ oa )
| ~ ( incident @ a1 @ oc )
| ( line_equal @ oa @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl322]) ).
thf(zip_derived_cl18_696,plain,
incident @ o @ oa,
inference(cnf,[status(esa)],[iooa]) ).
thf(zip_derived_cl1606,plain,
( ( point_equal @ o @ a1 )
| ~ ( incident @ a1 @ oc )
| ( line_equal @ oa @ oc ) ),
inference(demod,[status(thm)],[zip_derived_cl1572,zip_derived_cl18]) ).
thf('152',plain,
( ~ ( incident @ a1 @ oc )
| ( point_equal @ o @ a1 )
| ( line_equal @ oa @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl1606]) ).
thf(zip_derived_cl1075_697,plain,
( ( point_equal @ a1 @ ac )
<= ( point_equal @ c2 @ a1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1035,zip_derived_cl10,zip_derived_cl30,zip_derived_cl88]) ).
thf(zip_derived_cl42_698,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ X1 )
| ~ ( point_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_point_equal]) ).
thf(zip_derived_cl1097,plain,
( ( point_equal @ ac @ a1 )
<= ( point_equal @ c2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1075,zip_derived_cl42]) ).
thf(zip_derived_cl47_699,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( point_equal @ X0 @ X1 )
| ~ ( incident @ X1 @ X2 )
| ( incident @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[pcon]) ).
thf(zip_derived_cl1100,plain,
( ! [X0: $i] :
( ~ ( incident @ a1 @ X0 )
| ( incident @ ac @ X0 ) )
<= ( point_equal @ c2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1097,zip_derived_cl47]) ).
thf(zip_derived_cl6_700,plain,
incident @ a1 @ a1b1,
inference(cnf,[status(esa)],[ia1b1]) ).
thf(zip_derived_cl4430,plain,
( ( incident @ ac @ a1b1 )
<= ( point_equal @ c2 @ a1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1100,zip_derived_cl6]) ).
thf(zip_derived_cl196,plain,
( ~ ( incident @ ac @ a1b1 )
<= ~ ( incident @ ac @ a1b1 ) ),
inference(split,[status(esa)],[zip_derived_cl174]) ).
thf('153',plain,
( ~ ( point_equal @ c2 @ a1 )
| ( incident @ ac @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4430,zip_derived_cl196]) ).
thf(zip_derived_cl435_701,plain,
( ! [X0: $i] :
( ~ ( incident @ c2 @ X0 )
| ( incident @ a1 @ X0 ) )
<= ( point_equal @ c2 @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl420,zip_derived_cl47]) ).
thf(zip_derived_cl26_702,plain,
incident @ c2 @ oc,
inference(cnf,[status(esa)],[ic2oc]) ).
thf(zip_derived_cl560,plain,
( ( incident @ a1 @ oc )
<= ( point_equal @ c2 @ a1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl435,zip_derived_cl26]) ).
thf(zip_derived_cl25_703,plain,
incident @ c1 @ oc,
inference(cnf,[status(esa)],[ic1oc]) ).
thf(zip_derived_cl96_704,plain,
! [X0: $i] :
( ~ ( incident @ a1 @ X0 )
| ~ ( incident @ b1 @ X0 )
| ~ ( incident @ c1 @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl67,'19']) ).
thf(zip_derived_cl217,plain,
( ~ ( incident @ a1 @ oc )
| ~ ( incident @ b1 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl25,zip_derived_cl96]) ).
thf(zip_derived_cl232,plain,
( ~ ( incident @ a1 @ oc )
<= ~ ( incident @ a1 @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl217]) ).
thf('154',plain,
( ~ ( point_equal @ c2 @ a1 )
| ( incident @ a1 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl560,zip_derived_cl232]) ).
thf(zip_derived_cl24_705,plain,
incident @ b2 @ ob,
inference(cnf,[status(esa)],[ib2ob]) ).
thf(zip_derived_cl319_706,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ b2c2 @ X1 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl49]) ).
thf(zip_derived_cl377,plain,
( ( ( point_equal @ b2 @ a1 )
| ~ ( incident @ b2 @ b2c2 )
| ~ ( incident @ a1 @ ob )
| ( line_equal @ b2c2 @ ob ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl319]) ).
thf(zip_derived_cl17_707,plain,
incident @ b2 @ b2c2,
inference(cnf,[status(esa)],[ib2c2]) ).
thf(zip_derived_cl405,plain,
( ( ( point_equal @ b2 @ a1 )
| ~ ( incident @ a1 @ ob )
| ( line_equal @ b2c2 @ ob ) )
<= ( incident @ a1 @ b2c2 ) ),
inference(demod,[status(thm)],[zip_derived_cl377,zip_derived_cl17]) ).
thf('155',plain,
( ~ ( incident @ a1 @ ob )
| ( line_equal @ b2c2 @ ob )
| ( point_equal @ b2 @ a1 )
| ~ ( incident @ a1 @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl405]) ).
thf(zip_derived_cl26_708,plain,
incident @ c2 @ oc,
inference(cnf,[status(esa)],[ic2oc]) ).
thf(zip_derived_cl319_709,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ a1 )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ a1 @ X1 )
| ( line_equal @ b2c2 @ X1 ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl49]) ).
thf(zip_derived_cl381,plain,
( ( ( point_equal @ c2 @ a1 )
| ~ ( incident @ c2 @ b2c2 )
| ~ ( incident @ a1 @ oc )
| ( line_equal @ b2c2 @ oc ) )
<= ( incident @ a1 @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl319]) ).
thf(zip_derived_cl16_710,plain,
incident @ c2 @ b2c2,
inference(cnf,[status(esa)],[ic2b2]) ).
thf(zip_derived_cl409,plain,
( ( ( point_equal @ c2 @ a1 )
| ~ ( incident @ a1 @ oc )
| ( line_equal @ b2c2 @ oc ) )
<= ( incident @ a1 @ b2c2 ) ),
inference(demod,[status(thm)],[zip_derived_cl381,zip_derived_cl16]) ).
thf('156',plain,
( ~ ( incident @ a1 @ oc )
| ( point_equal @ c2 @ a1 )
| ~ ( incident @ a1 @ b2c2 )
| ( line_equal @ b2c2 @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl409]) ).
thf(zip_derived_cl4909_711,plain,
( ! [X0: $i] :
( ~ ( incident @ o @ X0 )
| ( incident @ a1 @ X0 ) )
<= ( point_equal @ o @ a1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4860,zip_derived_cl47]) ).
thf(zip_derived_cl20_712,plain,
incident @ o @ oc,
inference(cnf,[status(esa)],[iooc]) ).
thf(zip_derived_cl20183,plain,
( ( incident @ a1 @ oc )
<= ( point_equal @ o @ a1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4909,zip_derived_cl20]) ).
thf(zip_derived_cl232_713,plain,
( ~ ( incident @ a1 @ oc )
<= ~ ( incident @ a1 @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl217]) ).
thf('157',plain,
( ~ ( point_equal @ o @ a1 )
| ( incident @ a1 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl20183,zip_derived_cl232]) ).
thf('158',plain,
( ~ ( incident @ o @ b2c2 )
| ( point_equal @ o @ a1 )
| ( line_equal @ b2c2 @ oa )
| ~ ( incident @ a1 @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl410]) ).
thf(zip_derived_cl4890_714,plain,
( ! [X0: $i] :
( ~ ( incident @ X0 @ ob )
| ( incident @ X0 @ b2c2 ) )
<= ( line_equal @ b2c2 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4782,zip_derived_cl48]) ).
thf(zip_derived_cl19_715,plain,
incident @ o @ ob,
inference(cnf,[status(esa)],[ioob]) ).
thf(zip_derived_cl19413,plain,
( ( incident @ o @ b2c2 )
<= ( line_equal @ b2c2 @ ob ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4890,zip_derived_cl19]) ).
thf(zip_derived_cl4826_716,plain,
( ~ ( incident @ o @ b2c2 )
<= ~ ( incident @ o @ b2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl383]) ).
thf('159',plain,
( ~ ( line_equal @ b2c2 @ ob )
| ( incident @ o @ b2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl19413,zip_derived_cl4826]) ).
thf(zip_derived_cl24_717,plain,
incident @ b2 @ ob,
inference(cnf,[status(esa)],[ib2ob]) ).
thf(zip_derived_cl313_718,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ bc )
| ~ ( incident @ X0 @ b2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ bc @ X1 )
| ( line_equal @ b2c2 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl28,zip_derived_cl49]) ).
thf(zip_derived_cl790,plain,
( ( point_equal @ b2 @ bc )
| ~ ( incident @ b2 @ b2c2 )
| ~ ( incident @ bc @ ob )
| ( line_equal @ b2c2 @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl313]) ).
thf(zip_derived_cl17_719,plain,
incident @ b2 @ b2c2,
inference(cnf,[status(esa)],[ib2c2]) ).
thf(zip_derived_cl824,plain,
( ( point_equal @ b2 @ bc )
| ~ ( incident @ bc @ ob )
| ( line_equal @ b2c2 @ ob ) ),
inference(demod,[status(thm)],[zip_derived_cl790,zip_derived_cl17]) ).
thf('160',plain,
( ~ ( incident @ bc @ ob )
| ( line_equal @ b2c2 @ ob )
| ( point_equal @ b2 @ bc ) ),
inference(split,[status(esa)],[zip_derived_cl824]) ).
thf(zip_derived_cl939_720,plain,
( ! [X0: $i] :
( ~ ( incident @ b1 @ X0 )
| ( incident @ bc @ X0 ) )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl934,zip_derived_cl47]) ).
thf(zip_derived_cl23_721,plain,
incident @ b1 @ ob,
inference(cnf,[status(esa)],[ib1ob]) ).
thf(zip_derived_cl1178,plain,
( ( incident @ bc @ ob )
<= ( line_equal @ b2c2 @ a1b1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl939,zip_derived_cl23]) ).
thf(zip_derived_cl542_722,plain,
( ~ ( incident @ bc @ ob )
<= ~ ( incident @ bc @ ob ) ),
inference(split,[status(esa)],[zip_derived_cl536]) ).
thf('161',plain,
( ~ ( line_equal @ b2c2 @ a1b1 )
| ( incident @ bc @ ob ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1178,zip_derived_cl542]) ).
thf('162',plain,
( ~ ( incident @ c2 @ a1b1 )
| ( line_equal @ b2c2 @ a1b1 )
| ~ ( incident @ a1 @ b2c2 )
| ( point_equal @ c2 @ a1 ) ),
inference(split,[status(esa)],[zip_derived_cl408]) ).
thf('163',plain,
( ( incident @ b1 @ a2c2 )
| ( incident @ c2 @ a1b1 ) ),
inference(split,[status(esa)],[zip_derived_cl4]) ).
thf(zip_derived_cl13795_723,plain,
( ! [X0: $i] :
( ~ ( incident @ c1 @ X0 )
| ( incident @ ac @ X0 ) )
<= ( point_equal @ c1 @ ac ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl13780,zip_derived_cl47]) ).
thf(zip_derived_cl14_724,plain,
incident @ c1 @ b1c1,
inference(cnf,[status(esa)],[ic1b1]) ).
thf(zip_derived_cl29520,plain,
( ( incident @ ac @ b1c1 )
<= ( point_equal @ c1 @ ac ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl13795,zip_derived_cl14]) ).
thf(zip_derived_cl189_725,plain,
( ~ ( incident @ ac @ b1c1 )
<= ~ ( incident @ ac @ b1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl169]) ).
thf('164',plain,
( ~ ( point_equal @ c1 @ ac )
| ( incident @ ac @ b1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl29520,zip_derived_cl189]) ).
thf(zip_derived_cl11134_726,plain,
( ( incident @ bc @ a2c2 )
<= ( line_equal @ b1c1 @ a2c2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2973,zip_derived_cl27]) ).
thf(zip_derived_cl181_727,plain,
( ~ ( incident @ bc @ a2c2 )
<= ~ ( incident @ bc @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl167]) ).
thf('165',plain,
( ~ ( line_equal @ b1c1 @ a2c2 )
| ( incident @ bc @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11134,zip_derived_cl181]) ).
thf(zip_derived_cl2723,plain,
( ( line_equal @ a2c2 @ a1c1 )
<= ( line_equal @ a2c2 @ a1c1 ) ),
inference(split,[status(esa)],[zip_derived_cl2346]) ).
thf(zip_derived_cl45_728,plain,
! [X0: $i,X1: $i] :
( ( line_equal @ X0 @ X1 )
| ~ ( line_equal @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_of_line_equal]) ).
thf(zip_derived_cl2727,plain,
( ( line_equal @ a1c1 @ a2c2 )
<= ( line_equal @ a2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2723,zip_derived_cl45]) ).
thf(zip_derived_cl88_729,plain,
~ ( line_equal @ a1c1 @ a2c2 ),
inference(simpl_trail,[status(thm)],[zip_derived_cl79,'15']) ).
thf('166',plain,
~ ( line_equal @ a2c2 @ a1c1 ),
inference('s_sup-',[status(thm)],[zip_derived_cl2727,zip_derived_cl88]) ).
thf(zip_derived_cl11_730,plain,
incident @ c1 @ a1c1,
inference(cnf,[status(esa)],[ic1a1]) ).
thf(zip_derived_cl315_731,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ ac )
| ~ ( incident @ X0 @ a2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ ac @ X1 )
| ( line_equal @ a2c2 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl49]) ).
thf(zip_derived_cl975,plain,
( ( point_equal @ c1 @ ac )
| ~ ( incident @ c1 @ a2c2 )
| ~ ( incident @ ac @ a1c1 )
| ( line_equal @ a2c2 @ a1c1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl315]) ).
thf(zip_derived_cl29_732,plain,
incident @ ac @ a1c1,
inference(cnf,[status(esa)],[iac1]) ).
thf(zip_derived_cl1002,plain,
( ( point_equal @ c1 @ ac )
| ~ ( incident @ c1 @ a2c2 )
| ( line_equal @ a2c2 @ a1c1 ) ),
inference(demod,[status(thm)],[zip_derived_cl975,zip_derived_cl29]) ).
thf('167',plain,
( ( point_equal @ c1 @ ac )
| ( line_equal @ a2c2 @ a1c1 )
| ~ ( incident @ c1 @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl1002]) ).
thf(zip_derived_cl25675_733,plain,
( ( incident @ c1 @ a2c2 )
<= ( line_equal @ a2c2 @ oc ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl12459,zip_derived_cl25]) ).
thf(zip_derived_cl2213_734,plain,
( ~ ( incident @ c1 @ a2c2 )
<= ~ ( incident @ c1 @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl2121]) ).
thf('168',plain,
( ~ ( line_equal @ a2c2 @ oc )
| ( incident @ c1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl25675,zip_derived_cl2213]) ).
thf(zip_derived_cl26_735,plain,
incident @ c2 @ oc,
inference(cnf,[status(esa)],[ic2oc]) ).
thf(zip_derived_cl323_736,plain,
( ! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ b1 )
| ~ ( incident @ X0 @ a2c2 )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ b1 @ X1 )
| ( line_equal @ a2c2 @ X1 ) )
<= ( incident @ b1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl49]) ).
thf(zip_derived_cl1675,plain,
( ( ( point_equal @ c2 @ b1 )
| ~ ( incident @ c2 @ a2c2 )
| ~ ( incident @ b1 @ oc )
| ( line_equal @ a2c2 @ oc ) )
<= ( incident @ b1 @ a2c2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl323]) ).
thf(zip_derived_cl13_737,plain,
incident @ c2 @ a2c2,
inference(cnf,[status(esa)],[ic2a2]) ).
thf(zip_derived_cl1717,plain,
( ( ( point_equal @ c2 @ b1 )
| ~ ( incident @ b1 @ oc )
| ( line_equal @ a2c2 @ oc ) )
<= ( incident @ b1 @ a2c2 ) ),
inference(demod,[status(thm)],[zip_derived_cl1675,zip_derived_cl13]) ).
thf('169',plain,
( ~ ( incident @ b1 @ oc )
| ( line_equal @ a2c2 @ oc )
| ( point_equal @ c2 @ b1 )
| ~ ( incident @ b1 @ a2c2 ) ),
inference(split,[status(esa)],[zip_derived_cl1717]) ).
thf(zip_derived_cl36150_738,plain,
( ! [X0: $i] :
( ~ ( incident @ o @ X0 )
| ( incident @ b1 @ X0 ) )
<= ( point_equal @ o @ b1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl35943,zip_derived_cl47]) ).
thf(zip_derived_cl20_739,plain,
incident @ o @ oc,
inference(cnf,[status(esa)],[iooc]) ).
thf(zip_derived_cl44890,plain,
( ( incident @ b1 @ oc )
<= ( point_equal @ o @ b1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl36150,zip_derived_cl20]) ).
thf(zip_derived_cl231,plain,
( ~ ( incident @ b1 @ oc )
<= ~ ( incident @ b1 @ oc ) ),
inference(split,[status(esa)],[zip_derived_cl217]) ).
thf('170',plain,
( ~ ( point_equal @ o @ b1 )
| ( incident @ b1 @ oc ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl44890,zip_derived_cl231]) ).
thf(zip_derived_cl18_740,plain,
incident @ o @ oa,
inference(cnf,[status(esa)],[iooa]) ).
thf(zip_derived_cl326_741,plain,
! [X0: $i,X1: $i] :
( ( point_equal @ X0 @ b1 )
| ~ ( incident @ X0 @ ob )
| ~ ( incident @ X0 @ X1 )
| ~ ( incident @ b1 @ X1 )
| ( line_equal @ ob @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl49]) ).
thf(zip_derived_cl2029,plain,
( ( point_equal @ o @ b1 )
| ~ ( incident @ o @ ob )
| ~ ( incident @ b1 @ oa )
| ( line_equal @ ob @ oa ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl326]) ).
thf(zip_derived_cl19_742,plain,
incident @ o @ ob,
inference(cnf,[status(esa)],[ioob]) ).
thf(zip_derived_cl2062,plain,
( ( point_equal @ o @ b1 )
| ~ ( incident @ b1 @ oa )
| ( line_equal @ ob @ oa ) ),
inference(demod,[status(thm)],[zip_derived_cl2029,zip_derived_cl19]) ).
thf('171',plain,
( ( point_equal @ o @ b1 )
| ~ ( incident @ b1 @ oa )
| ( line_equal @ ob @ oa ) ),
inference(split,[status(esa)],[zip_derived_cl2062]) ).
thf(zip_derived_cl59682,plain,
$false,
inference('sat_resolution*',[status(thm)],['0','4','7','10','11','12','13','16','17','20','21','22','23','24','25','26','29','30','31','32','33','34','35','36','39','40','41','42','45','46','47','48','49','50','51','52','53','54','55','56','57','58','59','60','61','62','63','64','65','66','67','68','69','70','71','72','73','74','75','76','77','78','79','80','81','82','83','84','85','86','87','90','91','92','93','94','95','96','97','98','99','100','101','102','103','104','105','106','107','108','109','110','111','112','113','1','114','115','116','117','118','119','120','121','122','123','124','125','126','127','128','129','130','131','132','133','134','135','136','137','138','139','140','141','142','143','144','145','146','147','148','149','150','151','152','153','154','155','156','157','158','159','160','161','162','163','164','165','166','167','168','169','170','171']) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GEO169+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.j1xAtovNfz true
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 23:50:21 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.37 % Running in FO mode
% 0.22/0.67 % Total configuration time : 435
% 0.22/0.67 % Estimated wc time : 1092
% 0.22/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.79 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.80 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.80 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.81 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.82 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.16/0.87 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 59.45/9.16 % Solved by fo/fo1_av.sh.
% 59.45/9.16 % done 7987 iterations in 8.231s
% 59.45/9.16 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 59.45/9.16 % SZS output start Refutation
% See solution above
% 59.80/9.18
% 59.80/9.18
% 59.80/9.18 % Terminating...
% 60.87/9.46 % Runner terminated.
% 60.87/9.49 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------