%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO306+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:13:11 AM UTC 2026
% Result : Theorem 196.68s 72.86s
% Output : Refutation 198.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 140
% Syntax : Number of formulae : 819 ( 156 unt; 0 typ; 13 def)
% Number of atoms : 5036 (2158 equ; 0 cnn)
% Maximal formula atoms : 70 ( 6 avg)
% Number of connectives : 12161 (1628 ~;1338 |;2257 &;6669 @)
% ( 8 <=>; 261 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 48 usr; 18 con; 0-8 aty)
% Number of variables : 2426 ( 22 ^;1776 !; 615 ?;2426 :)
% ( 0 !>; 0 ?*; 0 @-; 13 @+)
% Comments :
%------------------------------------------------------------------------------
thf(vf_decl,type,
vf: $i > $i > $i ).
thf(vd1287_decl,type,
vd1287: $i ).
thf(vd1299_decl,type,
vd1299: $i ).
thf(rR_decl,type,
rR: $i > $i > $i > $o ).
thf(vd1302_decl,type,
vd1302: $i ).
thf(rpoint_decl,type,
rpoint: $i > $o ).
thf(vplus_decl,type,
vplus: $i > $i > $i ).
thf(rreal_decl,type,
rreal: $i > $o ).
thf(rless_decl,type,
rless: $i > $i > $o ).
thf(v0_decl,type,
v0: $i ).
thf(rcenter_decl,type,
rcenter: $i > $i > $o ).
thf(rcircle_decl,type,
rcircle: $i > $o ).
thf(ron_decl,type,
ron: $i > $i > $o ).
thf(vd1289_decl,type,
vd1289: $i ).
thf(vd1297_decl,type,
vd1297: $i ).
thf(rinside_decl,type,
rinside: $i > $i > $o ).
thf(rline_decl,type,
rline: $i > $o ).
thf(vd1288_decl,type,
vd1288: $i ).
thf(vd1295_decl,type,
vd1295: $i ).
thf(vd684_decl,type,
vd684: $i ).
thf(vtriangle_decl,type,
vtriangle: $i > $i > $i > $i ).
thf(rtriangle_decl,type,
rtriangle: $i > $o ).
thf(vg_decl,type,
vg: $i > $i > $i > $i ).
thf(vangle_decl,type,
vangle: $i > $i > $i > $i ).
thf(rS_decl,type,
rS: $i > $i > $i > $o ).
thf(vskolem1120_decl,type,
vskolem1120: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(rintersect_decl,type,
rintersect: $i > $i > $o ).
thf(vskolem1052_decl,type,
vskolem1052: $i > $i > $i > $i > $i ).
thf(vskolem1078_decl,type,
vskolem1078: $i > $i > $i > $i > $i ).
thf(rgeq_decl,type,
rgeq: $i > $i > $o ).
thf(vd14_decl,type,
vd14: $i ).
thf(vperp_decl,type,
vperp: $i ).
thf(vd1303_decl,type,
vd1303: $i ).
thf(vd1300_decl,type,
vd1300: $i ).
thf(rleq_decl,type,
rleq: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk37_decl,type,
sk37: $i > $i ).
thf(sk38_decl,type,
sk38: $i ).
thf(sk39_decl,type,
sk39: $i ).
thf(sk40_decl,type,
sk40: $i ).
thf(sk42_decl,type,
sk42: $i > $i ).
thf(sk45_decl,type,
sk45: $i > $i ).
thf(sk50_decl,type,
sk50: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ( D @ rreal )
& ( ( A @ ( C @ vplus ) )
= D ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i,C: $i,D: $i] :
@+[E: $i] :
( ( E @ rpoint )
& ( A @ ( B @ ( E @ rR ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ( D @ rpoint )
& ( A = D ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ( D @ rpoint )
& ( B = D ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ( D @ rpoint )
& ( C = D ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ rcircle )
& ( C @ ( B @ rcenter ) )
& ( C @ ( A @ ron ) ) ) ) ) ).
thf(sk37_def,definition,
( sk37
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ rpoint )
& ( A @ ( B @ ron ) ) ) ) ) ).
thf(sk38_def,definition,
( sk38
= ( @+[A: $i] :
( ( A @ rpoint )
& ( vd1289 = A ) ) ) ) ).
thf(sk39_def,definition,
( sk39
= ( @+[A: $i] :
( ( A @ rpoint )
& ( vd1288 = A ) ) ) ) ).
thf(sk40_def,definition,
( sk40
= ( @+[A: $i] :
( ( A @ rpoint )
& ( vd1287 = A ) ) ) ) ).
thf(sk42_def,definition,
( sk42
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ rpoint )
& ~ ( A @ ( B @ rinside ) )
& ~ ( A @ ( B @ ron ) ) ) ) ) ).
thf(sk45_def,definition,
( sk45
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ rpoint )
& ( A @ ( B @ ron ) ) ) ) ) ).
thf(sk50_def,definition,
( sk50
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ rpoint )
& ( B != A ) ) ) ) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ rpoint )
& ( A = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( B = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( E = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( F = G ) )
& ( ( B @ ( A @ vf ) )
= ( E @ ( D @ vf ) ) )
& ( ( C @ ( B @ vf ) )
= ( F @ ( E @ vf ) ) )
& ( ( A @ ( C @ vf ) )
= ( D @ ( F @ vf ) ) )
& ( ( C @ ( B @ ( A @ vangle ) ) )
= ( F @ ( E @ ( D @ vangle ) ) ) )
& ( ( A @ ( C @ ( B @ vangle ) ) )
= ( D @ ( F @ ( E @ vangle ) ) ) )
& ( ( B @ ( A @ ( C @ vangle ) ) )
= ( E @ ( D @ ( F @ vangle ) ) ) ) )
=> ( ( C @ ( B @ ( A @ vg ) ) )
= ( F @ ( E @ ( D @ vg ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(178), 0), imp(cond(axiom(178), 0)))') ).
thf(809,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ rpoint )
& ( A = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( B = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( E = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( F = G ) )
& ( ( B @ ( A @ vf ) )
= ( E @ ( D @ vf ) ) )
& ( ( C @ ( B @ vf ) )
= ( F @ ( E @ vf ) ) )
& ( ( A @ ( C @ vf ) )
= ( D @ ( F @ vf ) ) )
& ( ( C @ ( B @ ( A @ vangle ) ) )
= ( F @ ( E @ ( D @ vangle ) ) ) )
& ( ( A @ ( C @ ( B @ vangle ) ) )
= ( D @ ( F @ ( E @ vangle ) ) ) )
& ( ( B @ ( A @ ( C @ vangle ) ) )
= ( E @ ( D @ ( F @ vangle ) ) ) ) )
=> ( ( C @ ( B @ ( A @ vg ) ) )
= ( F @ ( E @ ( D @ vg ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(11,axiom,
vd1297 @ rline,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(347, 0)') ).
thf(164,plain,
vd1297 @ rline,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(97,axiom,
! [A: $i,B: $i] :
( ( ( B @ rline )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( A @ ( C @ ron ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(15), 0), imp(cond(axiom(15), 0)))') ).
thf(914,plain,
! [A: $i,B: $i] :
( ( ( B @ rline )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( A @ ( C @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(915,plain,
! [A: $i] :
( ? [B: $i] :
( ( B @ rline )
& ( A = B ) )
=> ? [B: $i] :
( ( B @ rpoint )
& ( A @ ( B @ ron ) ) ) ),
inference(miniscope,[status(thm)],[914]) ).
thf(916,plain,
! [B: $i,A: $i] :
( ( ( A @ sk45 @ rpoint )
| ~ ( B @ rline )
| ( A != B ) )
& ( ( A @ ( A @ sk45 @ ron ) )
| ~ ( B @ rline )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[915]) ).
thf(918,plain,
! [B: $i,A: $i] :
( ( A @ sk45 @ rpoint )
| ~ ( B @ rline )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[916]) ).
thf(921,plain,
! [B: $i,A: $i] :
( ( A @ sk45 @ rpoint )
| ~ ( B @ rline )
| ( A != B ) ),
inference(lifteq,[status(thm)],[918]) ).
thf(922,plain,
! [A: $i] :
( ( A @ sk45 @ rpoint )
| ~ ( A @ rline ) ),
inference(simp,[status(thm)],[921]) ).
thf(4978,plain,
! [A: $i] :
( ( ( vd1297 @ rline )
!= ( A @ rline ) )
| ( A @ sk45 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[164,922]) ).
thf(4979,plain,
! [A: $i] :
( ( ( vd1297 @ rline )
!= ( A @ rline ) )
| ( A @ sk45 @ rpoint ) ),
inference(simp,[status(thm)],[4978]) ).
thf(4980,plain,
vd1297 @ sk45 @ rpoint,
inference(pattern_uni,[status(thm)],[4979:[bind(A,$thf( vd1297 ))]]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) ) )
=> ( ( ( B @ ( A @ vf ) )
= v0 )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(162), 0), imp(cond(axiom(162), 0)))') ).
thf(194,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) ) )
=> ( ( ( A = B )
=> ( ( B @ ( A @ vf ) )
= v0 ) )
& ( ( ( B @ ( A @ vf ) )
= v0 )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( B @ ( A @ vf ) )
= v0 )
| ( A != B )
| ~ ( D @ rpoint )
| ( A != D )
| ~ ( C @ rpoint )
| ( B != C ) )
& ( ( A = B )
| ( ( B @ ( A @ vf ) )
!= v0 )
| ~ ( D @ rpoint )
| ( A != D )
| ~ ( C @ rpoint )
| ( B != C ) ) ),
inference(cnf,[status(esa)],[194]) ).
thf(197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ vf ) )
= v0 )
| ( A != B )
| ~ ( D @ rpoint )
| ( A != D )
| ~ ( C @ rpoint )
| ( B != C ) ),
inference(cnfConj,[status(thm)],[195]) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ rpoint )
| ~ ( C @ rpoint )
| ( ( B @ ( A @ vf ) )
= v0 )
| ( A != B )
| ( A != D )
| ( B != C ) ),
inference(lifteq,[status(thm)],[197]) ).
thf(201,plain,
! [A: $i] :
( ~ ( A @ rpoint )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[200]) ).
thf(5114,plain,
! [A: $i] :
( ( ( vd1297 @ sk45 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[4980,201]) ).
thf(5115,plain,
! [A: $i] :
( ( ( vd1297 @ sk45 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[5114]) ).
thf(5116,plain,
( ( vd1297 @ sk45 @ ( vd1297 @ sk45 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[5115:[bind(A,$thf( vd1297 @ sk45 ))]]) ).
thf(90,axiom,
( ? [A: $i] :
( ( A @ rpoint )
& ( vd1287 = A ) )
& ? [A: $i] :
( ( A @ rpoint )
& ( vd1288 = A ) )
& ? [A: $i] :
( ( A @ rpoint )
& ( vd1289 = A ) )
& ( vd1287 != vd1288 )
& ( vd1287 != vd1289 )
& ( vd1288 != vd1289 )
& ( ( vd1288 @ ( vd1287 @ vf ) )
= ( vd1289 @ ( vd1287 @ vf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))') ).
thf(835,plain,
( ? [A: $i] :
( ( A @ rpoint )
& ( vd1287 = A ) )
& ? [A: $i] :
( ( A @ rpoint )
& ( vd1288 = A ) )
& ? [A: $i] :
( ( A @ rpoint )
& ( vd1289 = A ) )
& ( vd1287 != vd1288 )
& ( vd1287 != vd1289 )
& ( vd1288 != vd1289 )
& ( ( vd1288 @ ( vd1287 @ vf ) )
= ( vd1289 @ ( vd1287 @ vf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(836,plain,
( ( sk40 @ rpoint )
& ( vd1287 = sk40 )
& ( sk39 @ rpoint )
& ( vd1288 = sk39 )
& ( sk38 @ rpoint )
& ( vd1289 = sk38 )
& ( vd1287 != vd1288 )
& ( vd1287 != vd1289 )
& ( vd1288 != vd1289 )
& ( ( vd1288 @ ( vd1287 @ vf ) )
= ( vd1289 @ ( vd1287 @ vf ) ) ) ),
inference(cnf,[status(esa)],[835]) ).
thf(846,plain,
sk38 @ rpoint,
inference(cnfConj,[status(thm)],[836]) ).
thf(839,plain,
vd1289 = sk38,
inference(cnfConj,[status(thm)],[836]) ).
thf(851,plain,
sk38 = vd1289,
inference(lifteq,[status(thm)],[839]) ).
thf(1203,plain,
vd1289 @ rpoint,
inference(rewrite,[status(thm)],[846,851]) ).
thf(111,axiom,
! [A: $i,B: $i] :
( ( ( B @ rpoint )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(7), 0), imp(cond(axiom(7), 0)))') ).
thf(1026,plain,
! [A: $i,B: $i] :
( ( ( B @ rpoint )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(1027,plain,
! [A: $i] :
( ? [B: $i] :
( ( B @ rpoint )
& ( A = B ) )
=> ? [B: $i] :
( ( B @ rpoint )
& ( B != A ) ) ),
inference(miniscope,[status(thm)],[1026]) ).
thf(1028,plain,
! [B: $i,A: $i] :
( ( ( A @ sk50 @ rpoint )
| ~ ( B @ rpoint )
| ( A != B ) )
& ( ( ( A @ sk50 )
!= A )
| ~ ( B @ rpoint )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[1027]) ).
thf(1030,plain,
! [B: $i,A: $i] :
( ( A @ sk50 @ rpoint )
| ~ ( B @ rpoint )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[1028]) ).
thf(1033,plain,
! [B: $i,A: $i] :
( ( A @ sk50 @ rpoint )
| ~ ( B @ rpoint )
| ( A != B ) ),
inference(lifteq,[status(thm)],[1030]) ).
thf(1034,plain,
! [A: $i] :
( ( A @ sk50 @ rpoint )
| ~ ( A @ rpoint ) ),
inference(simp,[status(thm)],[1033]) ).
thf(10289,plain,
! [A: $i] :
( ( ( vd1289 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1203,1034]) ).
thf(10290,plain,
! [A: $i] :
( ( ( vd1289 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[10289]) ).
thf(10291,plain,
vd1289 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[10290:[bind(A,$thf( vd1289 ))]]) ).
thf(10992,plain,
! [A: $i] :
( ( ( vd1289 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10291,1034]) ).
thf(10993,plain,
! [A: $i] :
( ( ( vd1289 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[10992]) ).
thf(10994,plain,
vd1289 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[10993:[bind(A,$thf( vd1289 @ sk50 ))]]) ).
thf(12079,plain,
! [A: $i] :
( ( ( vd1289 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10994,1034]) ).
thf(12080,plain,
! [A: $i] :
( ( ( vd1289 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[12079]) ).
thf(12081,plain,
vd1289 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[12080:[bind(A,$thf( vd1289 @ sk50 @ sk50 ))]]) ).
thf(13286,plain,
! [A: $i] :
( ( ( vd1289 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12081,1034]) ).
thf(13287,plain,
! [A: $i] :
( ( ( vd1289 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[13286]) ).
thf(13288,plain,
vd1289 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[13287:[bind(A,$thf( vd1289 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(18270,plain,
! [A: $i] :
( ( ( vd1289 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13288,1034]) ).
thf(18271,plain,
! [A: $i] :
( ( ( vd1289 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[18270]) ).
thf(18272,plain,
vd1289 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[18271:[bind(A,$thf( vd1289 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ rline )
& ( A = B )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( D = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( E = F ) )
& ( A @ ( C @ ron ) )
& ( A @ ( D @ ron ) )
& ( A @ ( E @ ron ) ) )
=> ? [F: $i] :
( ( F @ rpoint )
& ( A @ ( F @ ron ) )
& ( F != C )
& ( F != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(21), 0), imp(cond(axiom(21), 0)))') ).
thf(555,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ rline )
& ( A = B )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( D = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( E = F ) )
& ( A @ ( C @ ron ) )
& ( A @ ( D @ ron ) )
& ( A @ ( E @ ron ) ) )
=> ? [F: $i] :
( ( F @ rpoint )
& ( A @ ( F @ ron ) )
& ( F != C )
& ( F != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(840,plain,
sk39 @ rpoint,
inference(cnfConj,[status(thm)],[836]) ).
thf(838,plain,
vd1288 = sk39,
inference(cnfConj,[status(thm)],[836]) ).
thf(848,plain,
sk39 = vd1288,
inference(lifteq,[status(thm)],[838]) ).
thf(1202,plain,
vd1288 @ rpoint,
inference(rewrite,[status(thm)],[840,848]) ).
thf(10270,plain,
! [A: $i] :
( ( ( vd1288 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1202,1034]) ).
thf(10271,plain,
! [A: $i] :
( ( ( vd1288 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[10270]) ).
thf(10272,plain,
vd1288 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[10271:[bind(A,$thf( vd1288 ))]]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( D = E )
& ~ ( D @ ( A @ ron ) )
& ~ ( D @ ( B @ ron ) )
& ~ ( D @ ( C @ ron ) )
& ~ ( D @ ( B @ ( A @ rS ) ) ) )
=> ( ( D @ ( C @ ( B @ rS ) ) )
| ( D @ ( C @ ( A @ rS ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(103), 0), imp(cond(axiom(103), 0)))') ).
thf(909,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( D = E )
& ~ ( D @ ( A @ ron ) )
& ~ ( D @ ( B @ ron ) )
& ~ ( D @ ( C @ ron ) )
& ~ ( D @ ( B @ ( A @ rS ) ) ) )
=> ( ( D @ ( C @ ( B @ rS ) ) )
| ( D @ ( C @ ( A @ rS ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) ) )
=> ( ( B @ ( A @ ( A @ vg ) ) )
= v0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(172), 0), imp(cond(axiom(172), 0)))') ).
thf(249,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) ) )
=> ( ( B @ ( A @ ( A @ vg ) ) )
= v0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(58,axiom,
vd14 @ rpoint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(5), 0)') ).
thf(585,plain,
vd14 @ rpoint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(1,conjecture,
? [A: $i] :
( ( A @ rpoint )
& ( vd1302 @ ( vd1287 @ ( A @ rR ) ) )
& ( ( vd1299 @ ( vd1287 @ vf ) )
= ( A @ ( vd1287 @ vf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(352)') ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( A @ rpoint )
& ( vd1302 @ ( vd1287 @ ( A @ rR ) ) )
& ( ( vd1299 @ ( vd1287 @ vf ) )
= ( A @ ( vd1287 @ vf ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(129,plain,
~ ? [A: $i] :
( ( A @ rpoint )
& ( vd1302 @ ( vd1287 @ ( A @ rR ) ) )
& ( ( vd1299 @ ( vd1287 @ vf ) )
= ( A @ ( vd1287 @ vf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(130,plain,
! [A: $i] :
( ~ ( A @ rpoint )
| ~ ( vd1302 @ ( vd1287 @ ( A @ rR ) ) )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= ( A @ ( vd1287 @ vf ) ) ) ),
inference(cnf,[status(esa)],[129]) ).
thf(131,plain,
! [A: $i] :
( ~ ( A @ rpoint )
| ~ ( vd1302 @ ( vd1287 @ ( A @ rR ) ) )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= ( A @ ( vd1287 @ vf ) ) ) ),
inference(lifteq,[status(thm)],[130]) ).
thf(1156,plain,
! [A: $i] :
( ( ( vd14 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ~ ( vd1302 @ ( vd1287 @ ( A @ rR ) ) )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= ( A @ ( vd1287 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[585,131]) ).
thf(1157,plain,
! [A: $i] :
( ( ( vd14 @ rpoint )
!= ( A @ rpoint ) )
| ~ ( vd1302 @ ( vd1287 @ ( A @ rR ) ) )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= ( A @ ( vd1287 @ vf ) ) ) ),
inference(simp,[status(thm)],[1156]) ).
thf(1158,plain,
( ~ ( vd1302 @ ( vd1287 @ ( vd14 @ rR ) ) )
| ( ( vd14 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) ) ),
inference(pattern_uni,[status(thm)],[1157:[bind(A,$thf( vd14 ))]]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( D = E ) ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( E != A )
& ( E != B )
& ( E != C )
& ( E != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(13), 0), imp(cond(axiom(13), 0)))') ).
thf(683,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( D = E ) ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( E != A )
& ( E != B )
& ( E != C )
& ( E != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) )
& ( A != B ) )
=> ? [C: $i] :
( ( C @ rcircle )
& ( C @ ( A @ rcenter ) )
& ( C @ ( B @ ron ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(53), 0), imp(cond(axiom(53), 0)))') ).
thf(268,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) )
& ( A != B ) )
=> ? [C: $i] :
( ( C @ rcircle )
& ( C @ ( A @ rcenter ) )
& ( C @ ( B @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(269,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk6 ) @ rcircle )
| ~ ( D @ rpoint )
| ( A != D )
| ~ ( C @ rpoint )
| ( B != C )
| ( A = B ) )
& ( ( A @ ( B @ sk6 ) @ ( A @ rcenter ) )
| ~ ( D @ rpoint )
| ( A != D )
| ~ ( C @ rpoint )
| ( B != C )
| ( A = B ) )
& ( ( A @ ( B @ sk6 ) @ ( B @ ron ) )
| ~ ( D @ rpoint )
| ( A != D )
| ~ ( C @ rpoint )
| ( B != C )
| ( A = B ) ) ),
inference(cnf,[status(esa)],[268]) ).
thf(271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk6 ) @ ( A @ rcenter ) )
| ~ ( D @ rpoint )
| ( A != D )
| ~ ( C @ rpoint )
| ( B != C )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[269]) ).
thf(275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk6 ) @ ( A @ rcenter ) )
| ~ ( D @ rpoint )
| ~ ( C @ rpoint )
| ( A != D )
| ( B != C )
| ( A = B ) ),
inference(lifteq,[status(thm)],[271]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk6 ) @ ( B @ rcenter ) )
| ~ ( B @ rpoint )
| ~ ( A @ rpoint )
| ( B = A ) ),
inference(simp,[status(thm)],[275]) ).
thf(74,axiom,
( ( vd1299 @ ( vd1287 @ ( vd1288 @ rR ) ) )
& ( vd1303 @ rpoint )
& ( vd1302 @ ( vd1287 @ ( vd1289 @ rR ) ) )
& ( vd1302 = vd1303 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','and(pred(conjunct2(348), 4), and(holds(conjunct2(348), 1304, 0), and(pred(conjunct2(348), 1), holds(conjunct1(348), 1301, 0))))') ).
thf(737,plain,
( ( vd1299 @ ( vd1287 @ ( vd1288 @ rR ) ) )
& ( vd1303 @ rpoint )
& ( vd1302 @ ( vd1287 @ ( vd1289 @ rR ) ) )
& ( vd1302 = vd1303 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(738,plain,
( ( vd1299 @ ( vd1287 @ ( vd1288 @ rR ) ) )
& ( vd1303 @ rpoint )
& ( vd1302 @ ( vd1287 @ ( vd1289 @ rR ) ) )
& ( vd1302 = vd1303 ) ),
inference(cnf,[status(esa)],[737]) ).
thf(740,plain,
vd1302 @ ( vd1287 @ ( vd1289 @ rR ) ),
inference(cnfConj,[status(thm)],[738]) ).
thf(1762,plain,
( ( ( vd1302 @ ( vd1287 @ ( vd14 @ rR ) ) )
!= ( vd1302 @ ( vd1287 @ ( vd1289 @ rR ) ) ) )
| ~ $true
| ( ( vd14 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[740,1158]) ).
thf(1763,plain,
( ( ( vd1302 @ ( vd1287 @ ( vd14 @ rR ) ) )
!= ( vd1302 @ ( vd1287 @ ( vd1289 @ rR ) ) ) )
| ( ( vd14 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) ) ),
inference(simp,[status(thm)],[1762]) ).
thf(1788,plain,
( ( vd1302 != vd1302 )
| ( vd1287 != vd1287 )
| ( vd14 != vd1289 )
| ( vd14 != vd1299 )
| ( vd1287 != vd1287 ) ),
inference(simp,[status(thm)],[1763]) ).
thf(1808,plain,
( ( vd14 != vd1289 )
| ( vd14 != vd1299 ) ),
inference(simp,[status(thm)],[1788]) ).
thf(83,axiom,
vd1300 @ rpoint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(348, 1)') ).
thf(806,plain,
vd1300 @ rpoint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1155,plain,
( ~ ( vd1302 @ ( vd1287 @ ( vd1299 @ rR ) ) )
| ~ ( vd1299 @ rpoint ) ),
inference(pattern_uni,[status(thm)],[131:[bind(A,$thf( vd1299 ))]]) ).
thf(1172,plain,
( ( ( vd1300 @ rpoint )
!= ( vd1299 @ rpoint ) )
| ~ ( vd1302 @ ( vd1287 @ ( vd1299 @ rR ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[806,1155]) ).
thf(1173,plain,
( ( ( vd1300 @ rpoint )
!= ( vd1299 @ rpoint ) )
| ~ ( vd1302 @ ( vd1287 @ ( vd1299 @ rR ) ) ) ),
inference(simp,[status(thm)],[1172]) ).
thf(1177,plain,
( ( vd1300 != vd1299 )
| ~ ( vd1302 @ ( vd1287 @ ( vd1299 @ rR ) ) ) ),
inference(simp,[status(thm)],[1173]) ).
thf(84,axiom,
vd1299 = vd1300,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(348, 4)') ).
thf(807,plain,
vd1299 = vd1300,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(808,plain,
vd1300 = vd1299,
inference(lifteq,[status(thm)],[807]) ).
thf(1204,plain,
( ( vd1299 != vd1299 )
| ~ ( vd1302 @ ( vd1287 @ ( vd1299 @ rR ) ) ) ),
inference(rewrite,[status(thm)],[1177,808]) ).
thf(1205,plain,
~ ( vd1302 @ ( vd1287 @ ( vd1299 @ rR ) ) ),
inference(simp,[status(thm)],[1204]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( ( B @ rcircle )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ~ ( A @ ( C @ rinside ) )
& ~ ( A @ ( C @ ron ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(49), 0), imp(cond(axiom(49), 0)))') ).
thf(867,plain,
! [A: $i,B: $i] :
( ( ( B @ rcircle )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ~ ( A @ ( C @ rinside ) )
& ~ ( A @ ( C @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(868,plain,
! [A: $i] :
( ? [B: $i] :
( ( B @ rcircle )
& ( A = B ) )
=> ? [B: $i] :
( ( B @ rpoint )
& ~ ( A @ ( B @ rinside ) )
& ~ ( A @ ( B @ ron ) ) ) ),
inference(miniscope,[status(thm)],[867]) ).
thf(869,plain,
! [B: $i,A: $i] :
( ( ( A @ sk42 @ rpoint )
| ~ ( B @ rcircle )
| ( A != B ) )
& ( ~ ( A @ ( A @ sk42 @ rinside ) )
| ~ ( B @ rcircle )
| ( A != B ) )
& ( ~ ( A @ ( A @ sk42 @ ron ) )
| ~ ( B @ rcircle )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[868]) ).
thf(872,plain,
! [B: $i,A: $i] :
( ( A @ sk42 @ rpoint )
| ~ ( B @ rcircle )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[869]) ).
thf(877,plain,
! [B: $i,A: $i] :
( ( A @ sk42 @ rpoint )
| ~ ( B @ rcircle )
| ( A != B ) ),
inference(lifteq,[status(thm)],[872]) ).
thf(878,plain,
! [A: $i] :
( ( A @ sk42 @ rpoint )
| ~ ( A @ rcircle ) ),
inference(simp,[status(thm)],[877]) ).
thf(741,plain,
vd1303 @ rpoint,
inference(cnfConj,[status(thm)],[738]) ).
thf(1167,plain,
! [A: $i] :
( ( ( vd1303 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ~ ( vd1302 @ ( vd1287 @ ( A @ rR ) ) )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= ( A @ ( vd1287 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[741,131]) ).
thf(1168,plain,
! [A: $i] :
( ( ( vd1303 @ rpoint )
!= ( A @ rpoint ) )
| ~ ( vd1302 @ ( vd1287 @ ( A @ rR ) ) )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= ( A @ ( vd1287 @ vf ) ) ) ),
inference(simp,[status(thm)],[1167]) ).
thf(1169,plain,
( ~ ( vd1302 @ ( vd1287 @ ( vd1303 @ rR ) ) )
| ( ( vd1303 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) ) ),
inference(pattern_uni,[status(thm)],[1168:[bind(A,$thf( vd1303 ))]]) ).
thf(739,plain,
vd1302 = vd1303,
inference(cnfConj,[status(thm)],[738]) ).
thf(743,plain,
vd1303 = vd1302,
inference(lifteq,[status(thm)],[739]) ).
thf(1262,plain,
( ~ ( vd1302 @ ( vd1287 @ ( vd1302 @ rR ) ) )
| ( ( vd1302 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) ) ),
inference(rewrite,[status(thm)],[1169,743]) ).
thf(1768,plain,
( ( ( vd1302 @ ( vd1287 @ ( vd1289 @ rR ) ) )
!= ( vd1302 @ ( vd1287 @ ( vd1302 @ rR ) ) ) )
| ~ $true
| ( ( vd1302 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[740,1262]) ).
thf(1769,plain,
( ( ( vd1302 @ ( vd1287 @ ( vd1289 @ rR ) ) )
!= ( vd1302 @ ( vd1287 @ ( vd1302 @ rR ) ) ) )
| ( ( vd1302 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) ) ),
inference(simp,[status(thm)],[1768]) ).
thf(1792,plain,
( ( vd1302 != vd1302 )
| ( vd1287 != vd1287 )
| ( vd1289 != vd1302 )
| ( vd1302 != vd1299 )
| ( vd1287 != vd1287 ) ),
inference(simp,[status(thm)],[1769]) ).
thf(1793,plain,
( ( vd1289 != vd1302 )
| ( vd1302 != vd1299 ) ),
inference(simp,[status(thm)],[1792]) ).
thf(13,axiom,
vd1295 @ rline,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(346, 0)') ).
thf(166,plain,
vd1295 @ rline,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4971,plain,
! [A: $i] :
( ( ( vd1295 @ rline )
!= ( A @ rline ) )
| ( A @ sk45 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[166,922]) ).
thf(4972,plain,
! [A: $i] :
( ( ( vd1295 @ rline )
!= ( A @ rline ) )
| ( A @ sk45 @ rpoint ) ),
inference(simp,[status(thm)],[4971]) ).
thf(4973,plain,
vd1295 @ sk45 @ rpoint,
inference(pattern_uni,[status(thm)],[4972:[bind(A,$thf( vd1295 ))]]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rline )
& ( A = B )
& ? [E: $i] :
( ( E @ rpoint )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( D = E ) )
& ( A @ ( C @ ron ) )
& ( A @ ( D @ ron ) )
& ( C != D ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( D @ ( C @ ( E @ rR ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(23), 0), imp(cond(axiom(23), 0)))') ).
thf(202,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rline )
& ( A = B )
& ? [E: $i] :
( ( E @ rpoint )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( D = E ) )
& ( A @ ( C @ ron ) )
& ( A @ ( D @ ron ) )
& ( C != D ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( D @ ( C @ ( E @ rR ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(843,plain,
sk40 @ rpoint,
inference(cnfConj,[status(thm)],[836]) ).
thf(845,plain,
vd1287 = sk40,
inference(cnfConj,[status(thm)],[836]) ).
thf(852,plain,
sk40 = vd1287,
inference(lifteq,[status(thm)],[845]) ).
thf(1207,plain,
vd1287 @ rpoint,
inference(rewrite,[status(thm)],[843,852]) ).
thf(5125,plain,
! [A: $i] :
( ( ( vd1287 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[1207,201]) ).
thf(5126,plain,
! [A: $i] :
( ( ( vd1287 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[5125]) ).
thf(5127,plain,
( ( vd1287 @ ( vd1287 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[5126:[bind(A,$thf( vd1287 ))]]) ).
thf(32,axiom,
vd1302 @ ( vd1287 @ vf ) @ ( vd1299 @ ( vd1287 @ vf ) @ rless ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(351, 1305, 0)') ).
thf(344,plain,
vd1302 @ ( vd1287 @ vf ) @ ( vd1299 @ ( vd1287 @ vf ) @ rless ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(15,axiom,
vd684 @ rreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(137), 1)') ).
thf(172,plain,
vd684 @ rreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(19,axiom,
v0 = vd684,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(137), 2)') ).
thf(192,plain,
v0 = vd684,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(193,plain,
vd684 = v0,
inference(lifteq,[status(thm)],[192]) ).
thf(1153,plain,
v0 @ rreal,
inference(rewrite,[status(thm)],[172,193]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( B @ rreal )
& ( A = B ) )
=> ~ ( A @ ( A @ rless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(149), 0), imp(cond(axiom(149), 0)))') ).
thf(182,plain,
! [A: $i,B: $i] :
( ( ( B @ rreal )
& ( A = B ) )
=> ~ ( A @ ( A @ rless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(183,plain,
! [A: $i] :
( ? [B: $i] :
( ( B @ rreal )
& ( A = B ) )
=> ~ ( A @ ( A @ rless ) ) ),
inference(miniscope,[status(thm)],[182]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ rless ) )
| ~ ( B @ rreal )
| ( A != B ) ),
inference(cnf,[status(esa)],[183]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ rless ) )
| ~ ( B @ rreal )
| ( A != B ) ),
inference(lifteq,[status(thm)],[184]) ).
thf(186,plain,
! [A: $i] :
( ~ ( A @ ( A @ rless ) )
| ~ ( A @ rreal ) ),
inference(simp,[status(thm)],[185]) ).
thf(4531,plain,
! [A: $i] :
( ( ( v0 @ rreal )
!= ( A @ rreal ) )
| ~ ( A @ ( A @ rless ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1153,186]) ).
thf(4532,plain,
! [A: $i] :
( ( ( v0 @ rreal )
!= ( A @ rreal ) )
| ~ ( A @ ( A @ rless ) ) ),
inference(simp,[status(thm)],[4531]) ).
thf(4533,plain,
~ ( v0 @ ( v0 @ rless ) ),
inference(pattern_uni,[status(thm)],[4532:[bind(A,$thf( v0 ))]]) ).
thf(4582,plain,
( ( ( vd1302 @ ( vd1287 @ vf ) @ ( vd1299 @ ( vd1287 @ vf ) @ rless ) )
!= ( v0 @ ( v0 @ rless ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[344,4533]) ).
thf(4583,plain,
( ( vd1302 @ ( vd1287 @ vf ) @ ( vd1299 @ ( vd1287 @ vf ) @ rless ) )
!= ( v0 @ ( v0 @ rless ) ) ),
inference(simp,[status(thm)],[4582]) ).
thf(4631,plain,
( ( ( vd1302 @ ( vd1287 @ vf ) )
!= v0 )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[4583]) ).
thf(5388,plain,
( ( ( vd1302 @ ( vd1287 @ vf ) )
!= ( vd1287 @ ( vd1287 @ vf ) ) )
| ( v0 != v0 )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(paramod_ordered,[status(thm)],[5127,4631]) ).
thf(5389,plain,
( ( ( vd1302 @ ( vd1287 @ vf ) )
!= ( vd1287 @ ( vd1287 @ vf ) ) )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[5388]) ).
thf(5407,plain,
( ( vd1302 != vd1287 )
| ( vd1287 != vd1287 )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[5389]) ).
thf(5425,plain,
( ( vd1302 != vd1287 )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[5407]) ).
thf(10258,plain,
! [A: $i] :
( ( ( vd1297 @ sk45 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4980,1034]) ).
thf(10259,plain,
! [A: $i] :
( ( ( vd1297 @ sk45 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[10258]) ).
thf(10260,plain,
vd1297 @ sk45 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[10259:[bind(A,$thf( vd1297 @ sk45 ))]]) ).
thf(11466,plain,
! [A: $i] :
( ( ( vd1297 @ sk45 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10260,1034]) ).
thf(11467,plain,
! [A: $i] :
( ( ( vd1297 @ sk45 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[11466]) ).
thf(11468,plain,
vd1297 @ sk45 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[11467:[bind(A,$thf( vd1297 @ sk45 @ sk50 ))]]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ( D @ rline )
& ( C = D )
& ( C @ ( B @ ( A @ rS ) ) ) )
=> ( C @ ( A @ ( B @ rS ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(97), 0), imp(cond(axiom(97), 0)))') ).
thf(472,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ( D @ rline )
& ( C = D )
& ( C @ ( B @ ( A @ rS ) ) ) )
=> ( C @ ( A @ ( B @ rS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( B @ rreal )
& ( A = B ) )
=> ( ( v0 @ ( A @ vplus ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(141), 0), imp(cond(axiom(141), 0)))') ).
thf(142,plain,
! [A: $i,B: $i] :
( ( ( B @ rreal )
& ( A = B ) )
=> ( ( v0 @ ( A @ vplus ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(143,plain,
! [A: $i] :
( ? [B: $i] :
( ( B @ rreal )
& ( A = B ) )
=> ( ( v0 @ ( A @ vplus ) )
= A ) ),
inference(miniscope,[status(thm)],[142]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ( ( v0 @ ( A @ vplus ) )
= A )
| ~ ( B @ rreal )
| ( A != B ) ),
inference(cnf,[status(esa)],[143]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ~ ( B @ rreal )
| ( ( v0 @ ( A @ vplus ) )
= A )
| ( A != B ) ),
inference(lifteq,[status(thm)],[144]) ).
thf(146,plain,
! [A: $i] :
( ~ ( A @ rreal )
| ( ( v0 @ ( A @ vplus ) )
= A ) ),
inference(simp,[status(thm)],[145]) ).
thf(1231,plain,
! [A: $i] :
( ( ( v0 @ rreal )
!= ( A @ rreal ) )
| ~ $true
| ( ( v0 @ ( A @ vplus ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[1153,146]) ).
thf(1232,plain,
! [A: $i] :
( ( ( v0 @ rreal )
!= ( A @ rreal ) )
| ( ( v0 @ ( A @ vplus ) )
= A ) ),
inference(simp,[status(thm)],[1231]) ).
thf(1233,plain,
( ( v0 @ ( v0 @ vplus ) )
= v0 ),
inference(pattern_uni,[status(thm)],[1232:[bind(A,$thf( v0 ))]]) ).
thf(10311,plain,
! [A: $i] :
( ( ( vd14 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[585,1034]) ).
thf(10312,plain,
! [A: $i] :
( ( ( vd14 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[10311]) ).
thf(10313,plain,
vd14 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[10312:[bind(A,$thf( vd14 ))]]) ).
thf(11158,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[10313,201]) ).
thf(11159,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[11158]) ).
thf(11160,plain,
( ( vd14 @ sk50 @ ( vd14 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[11159:[bind(A,$thf( vd14 @ sk50 ))]]) ).
thf(1171,plain,
vd1302 @ rpoint,
inference(rewrite,[status(thm)],[741,743]) ).
thf(5137,plain,
! [A: $i] :
( ( ( vd1302 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[1171,201]) ).
thf(5138,plain,
! [A: $i] :
( ( ( vd1302 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[5137]) ).
thf(5139,plain,
( ( vd1302 @ ( vd1302 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[5138:[bind(A,$thf( vd1302 ))]]) ).
thf(1178,plain,
vd1299 @ rpoint,
inference(rewrite,[status(thm)],[806,808]) ).
thf(5122,plain,
! [A: $i] :
( ( ( vd1299 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[1178,201]) ).
thf(5123,plain,
! [A: $i] :
( ( ( vd1299 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[5122]) ).
thf(5124,plain,
( ( vd1299 @ ( vd1299 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[5123:[bind(A,$thf( vd1299 ))]]) ).
thf(5279,plain,
( ( ( vd1299 @ ( vd1299 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( ( vd1302 @ ( vd1287 @ vf ) )
!= v0 )
| ( v0 != v0 ) ),
inference(paramod_ordered,[status(thm)],[5124,4631]) ).
thf(5280,plain,
( ( ( vd1299 @ ( vd1299 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( ( vd1302 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[5279]) ).
thf(5300,plain,
( ( vd1299 != vd1299 )
| ( vd1299 != vd1287 )
| ( ( vd1302 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[5280]) ).
thf(5314,plain,
( ( vd1299 != vd1287 )
| ( ( vd1302 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[5300]) ).
thf(7501,plain,
( ( ( vd1302 @ ( vd1302 @ vf ) )
!= ( vd1302 @ ( vd1287 @ vf ) ) )
| ( vd1299 != vd1287 )
| ( v0 != v0 ) ),
inference(paramod_ordered,[status(thm)],[5139,5314]) ).
thf(7502,plain,
( ( ( vd1302 @ ( vd1302 @ vf ) )
!= ( vd1302 @ ( vd1287 @ vf ) ) )
| ( vd1299 != vd1287 ) ),
inference(simp,[status(thm)],[7501]) ).
thf(7552,plain,
( ( vd1302 != vd1302 )
| ( vd1302 != vd1287 )
| ( vd1299 != vd1287 ) ),
inference(simp,[status(thm)],[7502]) ).
thf(7556,plain,
( ( vd1302 != vd1287 )
| ( vd1299 != vd1287 ) ),
inference(simp,[status(thm)],[7552]) ).
thf(11169,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10313,1034]) ).
thf(11170,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[11169]) ).
thf(11171,plain,
vd14 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[11170:[bind(A,$thf( vd14 @ sk50 ))]]) ).
thf(5151,plain,
! [A: $i] :
( ( ( vd14 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[585,201]) ).
thf(5152,plain,
! [A: $i] :
( ( ( vd14 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[5151]) ).
thf(5153,plain,
( ( vd14 @ ( vd14 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[5152:[bind(A,$thf( vd14 ))]]) ).
thf(1192,plain,
! [A: $i] :
( ( ( sk40 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ~ ( vd1302 @ ( vd1287 @ ( A @ rR ) ) )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= ( A @ ( vd1287 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[843,131]) ).
thf(1193,plain,
! [A: $i] :
( ( ( sk40 @ rpoint )
!= ( A @ rpoint ) )
| ~ ( vd1302 @ ( vd1287 @ ( A @ rR ) ) )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= ( A @ ( vd1287 @ vf ) ) ) ),
inference(simp,[status(thm)],[1192]) ).
thf(1194,plain,
( ~ ( vd1302 @ ( vd1287 @ ( sk40 @ rR ) ) )
| ( ( sk40 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) ) ),
inference(pattern_uni,[status(thm)],[1193:[bind(A,$thf( sk40 ))]]) ).
thf(1658,plain,
( ~ ( vd1302 @ ( vd1287 @ ( vd1287 @ rR ) ) )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= ( vd1287 @ ( vd1287 @ vf ) ) ) ),
inference(rewrite,[status(thm)],[1194,852]) ).
thf(5319,plain,
( ~ ( vd1302 @ ( vd1287 @ ( vd1287 @ rR ) ) )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(rewrite,[status(thm)],[1658,5127]) ).
thf(9168,plain,
( ( ( vd14 @ ( vd14 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ~ ( vd1302 @ ( vd1287 @ ( vd1287 @ rR ) ) )
| ( v0 != v0 ) ),
inference(paramod_ordered,[status(thm)],[5153,5319]) ).
thf(9169,plain,
( ( ( vd14 @ ( vd14 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ~ ( vd1302 @ ( vd1287 @ ( vd1287 @ rR ) ) ) ),
inference(simp,[status(thm)],[9168]) ).
thf(9292,plain,
( ( vd14 != vd1299 )
| ( vd14 != vd1287 )
| ~ ( vd1302 @ ( vd1287 @ ( vd1287 @ rR ) ) ) ),
inference(simp,[status(thm)],[9169]) ).
thf(1787,plain,
( ( vd1302 != vd1302 )
| ( vd1287 != vd1287 )
| ( vd14 != vd1289 )
| ( ( vd14 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) ) ),
inference(simp,[status(thm)],[1763]) ).
thf(1807,plain,
( ( vd14 != vd1289 )
| ( ( vd14 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) ) ),
inference(simp,[status(thm)],[1787]) ).
thf(5368,plain,
( ( ( vd14 @ ( vd1287 @ vf ) )
!= ( vd1287 @ ( vd1287 @ vf ) ) )
| ( vd14 != vd1289 )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(paramod_ordered,[status(thm)],[5127,1807]) ).
thf(5408,plain,
( ( vd14 != vd1287 )
| ( vd1287 != vd1287 )
| ( vd14 != vd1289 )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[5368]) ).
thf(5426,plain,
( ( vd14 != vd1287 )
| ( vd14 != vd1289 )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[5408]) ).
thf(9884,plain,
( ( ( vd1299 @ ( vd1299 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( vd14 != vd1287 )
| ( vd14 != vd1289 )
| ( v0 != v0 ) ),
inference(paramod_ordered,[status(thm)],[5124,5426]) ).
thf(9885,plain,
( ( ( vd1299 @ ( vd1299 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( vd14 != vd1287 )
| ( vd14 != vd1289 ) ),
inference(simp,[status(thm)],[9884]) ).
thf(9935,plain,
( ( vd1299 != vd1299 )
| ( vd1299 != vd1287 )
| ( vd14 != vd1287 )
| ( vd14 != vd1289 ) ),
inference(simp,[status(thm)],[9885]) ).
thf(9971,plain,
( ( vd1299 != vd1287 )
| ( vd14 != vd1287 )
| ( vd14 != vd1289 ) ),
inference(simp,[status(thm)],[9935]) ).
thf(1263,plain,
( ~ ( vd1302 @ ( vd1287 @ ( vd1302 @ rR ) ) )
| ( vd1302 != vd1299 )
| ( vd1287 != vd1287 ) ),
inference(simp,[status(thm)],[1262]) ).
thf(1264,plain,
( ~ ( vd1302 @ ( vd1287 @ ( vd1302 @ rR ) ) )
| ( vd1302 != vd1299 ) ),
inference(simp,[status(thm)],[1263]) ).
thf(5128,plain,
! [A: $i] :
( ( ( vd1288 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[1202,201]) ).
thf(5129,plain,
! [A: $i] :
( ( ( vd1288 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[5128]) ).
thf(5130,plain,
( ( vd1288 @ ( vd1288 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[5129:[bind(A,$thf( vd1288 ))]]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rcenter ) )
=> ( B @ ( A @ rinside ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(77), 0), imp(cond(axiom(77), 0)))') ).
thf(157,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rcenter ) )
=> ( B @ ( A @ rinside ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(12188,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11171,1034]) ).
thf(12189,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[12188]) ).
thf(12190,plain,
vd14 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[12189:[bind(A,$thf( vd14 @ sk50 @ sk50 ))]]) ).
thf(14209,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12190,1034]) ).
thf(14210,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[14209]) ).
thf(14211,plain,
vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[14210:[bind(A,$thf( vd14 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(18470,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14211,1034]) ).
thf(18471,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[18470]) ).
thf(18472,plain,
vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[18471:[bind(A,$thf( vd14 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(28104,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18472,1034]) ).
thf(28105,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[28104]) ).
thf(28106,plain,
vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[28105:[bind(A,$thf( vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rline )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( A @ ( C @ ron ) )
& ( A @ ( E @ ron ) ) )
=> ? [G: $i] :
( ( G @ rpoint )
& ( A @ ( G @ ron ) )
& ( G != C )
& ( G != E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(19), 0), imp(cond(axiom(19), 0)))') ).
thf(570,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rline )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( A @ ( C @ ron ) )
& ( A @ ( E @ ron ) ) )
=> ? [G: $i] :
( ( G @ rpoint )
& ( A @ ( G @ ron ) )
& ( G != C )
& ( G != E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ rpoint )
& ( A = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( B = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( C = D ) )
& ( A != B )
& ( A != C ) )
=> ( ( C @ ( B @ ( A @ vangle ) ) )
= ( A @ ( B @ ( C @ vangle ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(168), 0), imp(cond(axiom(168), 0)))') ).
thf(802,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ rpoint )
& ( A = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( B = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( C = D ) )
& ( A != B )
& ( A != C ) )
=> ( ( C @ ( B @ ( A @ vangle ) ) )
= ( A @ ( B @ ( C @ vangle ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(11451,plain,
! [A: $i] :
( ( ( vd1297 @ sk45 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[10260,201]) ).
thf(11452,plain,
! [A: $i] :
( ( ( vd1297 @ sk45 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[11451]) ).
thf(11453,plain,
( ( vd1297 @ sk45 @ sk50 @ ( vd1297 @ sk45 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[11452:[bind(A,$thf( vd1297 @ sk45 @ sk50 ))]]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( D = E )
& ( A != B )
& ( D @ ( A @ ron ) )
& ( D @ ( B @ ron ) ) )
=> ( ( ( C @ ( B @ ( A @ vg ) ) )
= v0 )
<=> ( D @ ( C @ ron ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(200), 0), imp(cond(axiom(200), 0)))') ).
thf(817,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( D = E )
& ( A != B )
& ( D @ ( A @ ron ) )
& ( D @ ( B @ ron ) ) )
=> ( ( ( D @ ( C @ ron ) )
=> ( ( C @ ( B @ ( A @ vg ) ) )
= v0 ) )
& ( ( ( C @ ( B @ ( A @ vg ) ) )
= v0 )
=> ( D @ ( C @ ron ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(844,plain,
vd1287 != vd1289,
inference(cnfConj,[status(thm)],[836]) ).
thf(853,plain,
vd1289 != vd1287,
inference(lifteq,[status(thm)],[844]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( D = E )
& ( C @ ( A @ ( B @ rR ) ) )
& ( D @ ( C @ ( A @ rS ) ) ) )
=> ( D @ ( B @ ( A @ rS ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(105), 0), imp(cond(axiom(105), 0)))') ).
thf(770,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( D = E )
& ( C @ ( A @ ( B @ rR ) ) )
& ( D @ ( C @ ( A @ rS ) ) ) )
=> ( D @ ( B @ ( A @ rS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ rpoint )
& ( A = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( B = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ? [G: $i] :
( ( G @ rline )
& ( E = G ) )
& ? [G: $i] :
( ( G @ rline )
& ( F = G ) )
& ( E @ ( A @ ron ) )
& ( F @ ( A @ ron ) )
& ( E @ ( B @ ron ) )
& ( F @ ( C @ ron ) )
& ( A != B )
& ( A != C )
& ~ ( E @ ( D @ ron ) )
& ~ ( F @ ( D @ ron ) )
& ( E != F ) )
=> ( ( ( C @ ( A @ ( B @ vangle ) ) )
= ( C @ ( A @ ( D @ vangle ) ) @ ( D @ ( A @ ( B @ vangle ) ) @ vplus ) ) )
<=> ( ( F @ ( D @ ( B @ rS ) ) )
& ( E @ ( D @ ( C @ rS ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(190), 0), imp(cond(axiom(190), 0)))') ).
thf(253,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ rpoint )
& ( A = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( B = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ? [G: $i] :
( ( G @ rline )
& ( E = G ) )
& ? [G: $i] :
( ( G @ rline )
& ( F = G ) )
& ( E @ ( A @ ron ) )
& ( F @ ( A @ ron ) )
& ( E @ ( B @ ron ) )
& ( F @ ( C @ ron ) )
& ( A != B )
& ( A != C )
& ~ ( E @ ( D @ ron ) )
& ~ ( F @ ( D @ ron ) )
& ( E != F ) )
=> ( ( ( ( F @ ( D @ ( B @ rS ) ) )
& ( E @ ( D @ ( C @ rS ) ) ) )
=> ( ( C @ ( A @ ( B @ vangle ) ) )
= ( C @ ( A @ ( D @ vangle ) ) @ ( D @ ( A @ ( B @ vangle ) ) @ vplus ) ) ) )
& ( ( ( C @ ( A @ ( B @ vangle ) ) )
= ( C @ ( A @ ( D @ vangle ) ) @ ( D @ ( A @ ( B @ vangle ) ) @ vplus ) ) )
=> ( ( F @ ( D @ ( B @ rS ) ) )
& ( E @ ( D @ ( C @ rS ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(254,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ( C @ ( A @ ( B @ vangle ) ) )
= ( C @ ( A @ ( D @ vangle ) ) @ ( D @ ( A @ ( B @ vangle ) ) @ vplus ) ) )
| ~ ( F @ ( D @ ( B @ rS ) ) )
| ~ ( E @ ( D @ ( C @ rS ) ) )
| ~ ( L @ rpoint )
| ( A != L )
| ~ ( K @ rpoint )
| ( B != K )
| ~ ( J @ rpoint )
| ( C != J )
| ~ ( I @ rpoint )
| ( D != I )
| ~ ( H @ rline )
| ( E != H )
| ~ ( G @ rline )
| ( F != G )
| ~ ( E @ ( A @ ron ) )
| ~ ( F @ ( A @ ron ) )
| ~ ( E @ ( B @ ron ) )
| ~ ( F @ ( C @ ron ) )
| ( A = B )
| ( A = C )
| ( E @ ( D @ ron ) )
| ( F @ ( D @ ron ) )
| ( E = F ) )
& ( ( F @ ( D @ ( B @ rS ) ) )
| ( ( C @ ( A @ ( B @ vangle ) ) )
!= ( C @ ( A @ ( D @ vangle ) ) @ ( D @ ( A @ ( B @ vangle ) ) @ vplus ) ) )
| ~ ( L @ rpoint )
| ( A != L )
| ~ ( K @ rpoint )
| ( B != K )
| ~ ( J @ rpoint )
| ( C != J )
| ~ ( I @ rpoint )
| ( D != I )
| ~ ( H @ rline )
| ( E != H )
| ~ ( G @ rline )
| ( F != G )
| ~ ( E @ ( A @ ron ) )
| ~ ( F @ ( A @ ron ) )
| ~ ( E @ ( B @ ron ) )
| ~ ( F @ ( C @ ron ) )
| ( A = B )
| ( A = C )
| ( E @ ( D @ ron ) )
| ( F @ ( D @ ron ) )
| ( E = F ) )
& ( ( E @ ( D @ ( C @ rS ) ) )
| ( ( C @ ( A @ ( B @ vangle ) ) )
!= ( C @ ( A @ ( D @ vangle ) ) @ ( D @ ( A @ ( B @ vangle ) ) @ vplus ) ) )
| ~ ( L @ rpoint )
| ( A != L )
| ~ ( K @ rpoint )
| ( B != K )
| ~ ( J @ rpoint )
| ( C != J )
| ~ ( I @ rpoint )
| ( D != I )
| ~ ( H @ rline )
| ( E != H )
| ~ ( G @ rline )
| ( F != G )
| ~ ( E @ ( A @ ron ) )
| ~ ( F @ ( A @ ron ) )
| ~ ( E @ ( B @ ron ) )
| ~ ( F @ ( C @ ron ) )
| ( A = B )
| ( A = C )
| ( E @ ( D @ ron ) )
| ( F @ ( D @ ron ) )
| ( E = F ) ) ),
inference(cnf,[status(esa)],[253]) ).
thf(256,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( B @ rS ) ) )
| ( ( C @ ( A @ ( B @ vangle ) ) )
!= ( C @ ( A @ ( D @ vangle ) ) @ ( D @ ( A @ ( B @ vangle ) ) @ vplus ) ) )
| ~ ( L @ rpoint )
| ( A != L )
| ~ ( K @ rpoint )
| ( B != K )
| ~ ( J @ rpoint )
| ( C != J )
| ~ ( I @ rpoint )
| ( D != I )
| ~ ( H @ rline )
| ( E != H )
| ~ ( G @ rline )
| ( F != G )
| ~ ( E @ ( A @ ron ) )
| ~ ( F @ ( A @ ron ) )
| ~ ( E @ ( B @ ron ) )
| ~ ( F @ ( C @ ron ) )
| ( A = B )
| ( A = C )
| ( E @ ( D @ ron ) )
| ( F @ ( D @ ron ) )
| ( E = F ) ),
inference(cnfConj,[status(thm)],[254]) ).
thf(260,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( B @ rS ) ) )
| ~ ( L @ rpoint )
| ~ ( K @ rpoint )
| ~ ( J @ rpoint )
| ~ ( I @ rpoint )
| ~ ( H @ rline )
| ~ ( G @ rline )
| ~ ( E @ ( A @ ron ) )
| ~ ( F @ ( A @ ron ) )
| ~ ( E @ ( B @ ron ) )
| ~ ( F @ ( C @ ron ) )
| ( E @ ( D @ ron ) )
| ( F @ ( D @ ron ) )
| ( ( C @ ( A @ ( B @ vangle ) ) )
!= ( C @ ( A @ ( D @ vangle ) ) @ ( D @ ( A @ ( B @ vangle ) ) @ vplus ) ) )
| ( A != L )
| ( B != K )
| ( C != J )
| ( D != I )
| ( E != H )
| ( F != G )
| ( A = B )
| ( A = C )
| ( E = F ) ),
inference(lifteq,[status(thm)],[256]) ).
thf(261,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( E @ rS ) ) )
| ~ ( F @ rpoint )
| ~ ( E @ rpoint )
| ~ ( D @ rpoint )
| ~ ( C @ rpoint )
| ~ ( B @ rline )
| ~ ( A @ rline )
| ~ ( B @ ( F @ ron ) )
| ~ ( A @ ( F @ ron ) )
| ~ ( B @ ( E @ ron ) )
| ~ ( A @ ( D @ ron ) )
| ( B @ ( C @ ron ) )
| ( A @ ( C @ ron ) )
| ( ( D @ ( F @ ( E @ vangle ) ) )
!= ( D @ ( F @ ( C @ vangle ) ) @ ( C @ ( F @ ( E @ vangle ) ) @ vplus ) ) )
| ( F = E )
| ( F = D )
| ( B = A ) ),
inference(simp,[status(thm)],[260]) ).
thf(10277,plain,
! [A: $i] :
( ( ( vd1302 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1171,1034]) ).
thf(10278,plain,
! [A: $i] :
( ( ( vd1302 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[10277]) ).
thf(10279,plain,
vd1302 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[10278:[bind(A,$thf( vd1302 ))]]) ).
thf(10911,plain,
! [A: $i] :
( ( ( vd1302 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10279,1034]) ).
thf(10912,plain,
! [A: $i] :
( ( ( vd1302 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[10911]) ).
thf(10913,plain,
vd1302 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[10912:[bind(A,$thf( vd1302 @ sk50 ))]]) ).
thf(10255,plain,
! [A: $i] :
( ( ( vd1295 @ sk45 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4973,1034]) ).
thf(10256,plain,
! [A: $i] :
( ( ( vd1295 @ sk45 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[10255]) ).
thf(10257,plain,
vd1295 @ sk45 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[10256:[bind(A,$thf( vd1295 @ sk45 ))]]) ).
thf(11342,plain,
! [A: $i] :
( ( ( vd1295 @ sk45 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[10257,201]) ).
thf(11343,plain,
! [A: $i] :
( ( ( vd1295 @ sk45 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[11342]) ).
thf(11344,plain,
( ( vd1295 @ sk45 @ sk50 @ ( vd1295 @ sk45 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[11343:[bind(A,$thf( vd1295 @ sk45 @ sk50 ))]]) ).
thf(9006,plain,
( ( ( vd14 @ ( vd14 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( vd1302 != vd1287 )
| ( v0 != v0 ) ),
inference(paramod_ordered,[status(thm)],[5153,5425]) ).
thf(9007,plain,
( ( ( vd14 @ ( vd14 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( vd1302 != vd1287 ) ),
inference(simp,[status(thm)],[9006]) ).
thf(9088,plain,
( ( vd14 != vd1299 )
| ( vd14 != vd1287 )
| ( vd1302 != vd1287 ) ),
inference(simp,[status(thm)],[9007]) ).
thf(10829,plain,
! [A: $i] :
( ( ( vd1288 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10272,1034]) ).
thf(10830,plain,
! [A: $i] :
( ( ( vd1288 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[10829]) ).
thf(10831,plain,
vd1288 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[10830:[bind(A,$thf( vd1288 @ sk50 ))]]) ).
thf(11793,plain,
! [A: $i] :
( ( ( vd1288 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10831,1034]) ).
thf(11794,plain,
! [A: $i] :
( ( ( vd1288 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[11793]) ).
thf(11795,plain,
vd1288 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[11794:[bind(A,$thf( vd1288 @ sk50 @ sk50 ))]]) ).
thf(13011,plain,
! [A: $i] :
( ( ( vd1288 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11795,1034]) ).
thf(13012,plain,
! [A: $i] :
( ( ( vd1288 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[13011]) ).
thf(13013,plain,
vd1288 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[13012:[bind(A,$thf( vd1288 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(4729,plain,
( ( v0 != v0 )
| ( ( vd1302 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(eqfactor_ordered,[status(thm)],[4631]) ).
thf(4731,plain,
( ( vd1302 != vd1299 )
| ( vd1287 != vd1287 )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[4729]) ).
thf(4758,plain,
( ( vd1302 != vd1299 )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[4731]) ).
thf(5252,plain,
( ( ( vd1299 @ ( vd1299 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( vd1302 != vd1299 )
| ( v0 != v0 ) ),
inference(paramod_ordered,[status(thm)],[5124,4758]) ).
thf(5253,plain,
( ( ( vd1299 @ ( vd1299 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( vd1302 != vd1299 ) ),
inference(simp,[status(thm)],[5252]) ).
thf(5295,plain,
( ( vd1299 != vd1299 )
| ( vd1299 != vd1287 )
| ( vd1302 != vd1299 ) ),
inference(simp,[status(thm)],[5253]) ).
thf(5311,plain,
( ( vd1299 != vd1287 )
| ( vd1302 != vd1299 ) ),
inference(simp,[status(thm)],[5295]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( D = E ) )
& ( C @ ( A @ ( B @ rR ) ) )
& ( D @ ( A @ ( B @ rR ) ) ) )
=> ~ ( D @ ( C @ ( B @ rR ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(93), 0), imp(cond(axiom(93), 0)))') ).
thf(966,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( D = E ) )
& ( C @ ( A @ ( B @ rR ) ) )
& ( D @ ( A @ ( B @ rR ) ) ) )
=> ~ ( D @ ( C @ ( B @ rR ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(12536,plain,
! [A: $i] :
( ( ( vd1297 @ sk45 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11468,1034]) ).
thf(12537,plain,
! [A: $i] :
( ( ( vd1297 @ sk45 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[12536]) ).
thf(12538,plain,
vd1297 @ sk45 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[12537:[bind(A,$thf( vd1297 @ sk45 @ sk50 @ sk50 ))]]) ).
thf(16783,plain,
! [A: $i] :
( ( ( vd1297 @ sk45 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12538,1034]) ).
thf(16784,plain,
! [A: $i] :
( ( ( vd1297 @ sk45 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[16783]) ).
thf(16785,plain,
vd1297 @ sk45 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[16784:[bind(A,$thf( vd1297 @ sk45 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ rpoint )
& ( A = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( B = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ( A != B )
& ( A != C )
& ( B != C )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( E = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( F = G ) )
& ( ( B @ ( A @ vf ) )
= ( E @ ( D @ vf ) ) )
& ( ( C @ ( A @ vf ) )
= ( F @ ( D @ vf ) ) )
& ( ( C @ ( A @ ( B @ vangle ) ) )
= ( F @ ( D @ ( E @ vangle ) ) ) )
& ~ ? [G: $i] :
( ( G @ rline )
& ( G @ ( D @ ron ) )
& ( G @ ( E @ ron ) )
& ( G @ ( F @ ron ) ) ) )
=> ( ( C @ ( B @ vf ) )
= ( F @ ( E @ vf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(264), 0), 2)') ).
thf(492,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ rpoint )
& ( A = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( B = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ( A != B )
& ( A != C )
& ( B != C )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( E = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( F = G ) )
& ( ( B @ ( A @ vf ) )
= ( E @ ( D @ vf ) ) )
& ( ( C @ ( A @ vf ) )
= ( F @ ( D @ vf ) ) )
& ( ( C @ ( A @ ( B @ vangle ) ) )
= ( F @ ( D @ ( E @ vangle ) ) ) )
& ~ ? [G: $i] :
( ( G @ rline )
& ( G @ ( D @ ron ) )
& ( G @ ( E @ ron ) )
& ( G @ ( F @ ron ) ) ) )
=> ( ( C @ ( B @ vf ) )
= ( F @ ( E @ vf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(1791,plain,
( ( vd1302 != vd1302 )
| ( vd1287 != vd1287 )
| ( vd1289 != vd1302 )
| ( ( vd1302 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) ) ),
inference(simp,[status(thm)],[1769]) ).
thf(1811,plain,
( ( vd1289 != vd1302 )
| ( ( vd1302 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) ) ),
inference(simp,[status(thm)],[1791]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D ) )
=> ? [E: $i] :
( ( E @ rreal )
& ( ( C @ ( A @ vplus ) )
= E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(139), 0), imp(cond(axiom(139), 0)))') ).
thf(173,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D ) )
=> ? [E: $i] :
( ( E @ rreal )
& ( ( C @ ( A @ vplus ) )
= E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(174,plain,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] :
( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D ) )
=> ? [D: $i] :
( ( D @ rreal )
& ( ( C @ ( A @ vplus ) )
= D ) ) ),
inference(miniscope,[status(thm)],[173]) ).
thf(175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk1 ) ) @ rreal )
| ~ ( B @ rreal )
| ( A != B )
| ~ ( D @ rreal )
| ( C != D ) )
& ( ( ( C @ ( A @ vplus ) )
= ( A @ ( B @ ( C @ sk1 ) ) ) )
| ~ ( B @ rreal )
| ( A != B )
| ~ ( D @ rreal )
| ( C != D ) ) ),
inference(cnf,[status(esa)],[174]) ).
thf(176,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ vplus ) )
= ( A @ ( B @ ( C @ sk1 ) ) ) )
| ~ ( B @ rreal )
| ( A != B )
| ~ ( D @ rreal )
| ( C != D ) ),
inference(cnfConj,[status(thm)],[175]) ).
thf(178,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ rreal )
| ~ ( D @ rreal )
| ( ( A @ ( B @ ( C @ sk1 ) ) )
= ( C @ ( A @ vplus ) ) )
| ( A != B )
| ( C != D ) ),
inference(lifteq,[status(thm)],[176]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ~ ( A @ rreal )
| ~ ( B @ rreal )
| ( ( A @ ( A @ ( B @ sk1 ) ) )
= ( B @ ( A @ vplus ) ) ) ),
inference(simp,[status(thm)],[178]) ).
thf(10264,plain,
! [A: $i] :
( ( ( vd1299 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1178,1034]) ).
thf(10265,plain,
! [A: $i] :
( ( ( vd1299 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[10264]) ).
thf(10266,plain,
vd1299 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[10265:[bind(A,$thf( vd1299 ))]]) ).
thf(10471,plain,
! [A: $i] :
( ( ( vd1299 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10266,1034]) ).
thf(10472,plain,
! [A: $i] :
( ( ( vd1299 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[10471]) ).
thf(10473,plain,
vd1299 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[10472:[bind(A,$thf( vd1299 @ sk50 ))]]) ).
thf(11575,plain,
! [A: $i] :
( ( ( vd1299 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10473,1034]) ).
thf(11576,plain,
! [A: $i] :
( ( ( vd1299 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[11575]) ).
thf(11577,plain,
vd1299 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[11576:[bind(A,$thf( vd1299 @ sk50 @ sk50 ))]]) ).
thf(842,plain,
( ( vd1288 @ ( vd1287 @ vf ) )
= ( vd1289 @ ( vd1287 @ vf ) ) ),
inference(cnfConj,[status(thm)],[836]) ).
thf(849,plain,
( ( vd1288 @ ( vd1287 @ vf ) )
= ( vd1289 @ ( vd1287 @ vf ) ) ),
inference(lifteq,[status(thm)],[842]) ).
thf(7478,plain,
( ( ( vd1288 @ ( vd1287 @ vf ) )
!= ( vd1302 @ ( vd1287 @ vf ) ) )
| ( vd1299 != vd1287 )
| ( ( vd1289 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(paramod_ordered,[status(thm)],[849,5314]) ).
thf(7548,plain,
( ( vd1288 != vd1302 )
| ( vd1287 != vd1287 )
| ( vd1299 != vd1287 )
| ( ( vd1289 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[7478]) ).
thf(7581,plain,
( ( vd1288 != vd1302 )
| ( vd1299 != vd1287 )
| ( ( vd1289 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[7548]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rcircle )
& ( A = B )
& ( A @ ( C @ rcenter ) )
& ( A @ ( D @ rcenter ) ) )
=> ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(75), 0), imp(cond(axiom(75), 0)))') ).
thf(147,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rcircle )
& ( A = B )
& ( A @ ( C @ rcenter ) )
& ( A @ ( D @ rcenter ) ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( D = E )
& ( C @ ( A @ ( B @ rR ) ) )
& ( D @ ( B @ ron ) ) )
=> ~ ( D @ ( C @ ( A @ rS ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(109), 0), imp(cond(axiom(109), 0)))') ).
thf(397,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( D = E )
& ( C @ ( A @ ( B @ rR ) ) )
& ( D @ ( B @ ron ) ) )
=> ~ ( D @ ( C @ ( A @ rS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(10267,plain,
! [A: $i] :
( ( ( vd1287 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1207,1034]) ).
thf(10268,plain,
! [A: $i] :
( ( ( vd1287 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[10267]) ).
thf(10269,plain,
vd1287 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[10268:[bind(A,$thf( vd1287 ))]]) ).
thf(10748,plain,
! [A: $i] :
( ( ( vd1287 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10269,1034]) ).
thf(10749,plain,
! [A: $i] :
( ( ( vd1287 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[10748]) ).
thf(10750,plain,
vd1287 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[10749:[bind(A,$thf( vd1287 @ sk50 ))]]) ).
thf(11683,plain,
! [A: $i] :
( ( ( vd1287 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10750,1034]) ).
thf(11684,plain,
! [A: $i] :
( ( ( vd1287 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[11683]) ).
thf(11685,plain,
vd1287 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[11684:[bind(A,$thf( vd1287 @ sk50 @ sk50 ))]]) ).
thf(12876,plain,
! [A: $i] :
( ( ( vd1287 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11685,1034]) ).
thf(12877,plain,
! [A: $i] :
( ( ( vd1287 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[12876]) ).
thf(12878,plain,
vd1287 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[12877:[bind(A,$thf( vd1287 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(17672,plain,
! [A: $i] :
( ( ( vd1287 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12878,1034]) ).
thf(17673,plain,
! [A: $i] :
( ( ( vd1287 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[17672]) ).
thf(17674,plain,
vd1287 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[17673:[bind(A,$thf( vd1287 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( F @ rreal )
& ( E = F )
& ( ( E @ ( A @ vplus ) )
= ( E @ ( C @ vplus ) ) ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(156, 0), 0)') ).
thf(132,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( F @ rreal )
& ( E = F )
& ( ( E @ ( A @ vplus ) )
= ( E @ ( C @ vplus ) ) ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5584,plain,
( ( ( vd1302 @ ( vd1302 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( vd1302 != vd1299 )
| ( v0 != v0 ) ),
inference(paramod_ordered,[status(thm)],[5139,4758]) ).
thf(5585,plain,
( ( ( vd1302 @ ( vd1302 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( vd1302 != vd1299 ) ),
inference(simp,[status(thm)],[5584]) ).
thf(5625,plain,
( ( vd1302 != vd1299 )
| ( vd1302 != vd1287 )
| ( vd1302 != vd1299 ) ),
inference(simp,[status(thm)],[5585]) ).
thf(5648,plain,
( ( vd1302 != vd1287 )
| ( vd1302 != vd1299 ) ),
inference(simp,[status(thm)],[5625]) ).
thf(742,plain,
vd1299 @ ( vd1287 @ ( vd1288 @ rR ) ),
inference(cnfConj,[status(thm)],[738]) ).
thf(1830,plain,
( ( ( vd1299 @ ( vd1287 @ ( vd1288 @ rR ) ) )
!= ( vd1302 @ ( vd1287 @ ( vd1302 @ rR ) ) ) )
| ~ $true
| ( vd1302 != vd1299 ) ),
inference(paramod_ordered,[status(thm)],[742,1264]) ).
thf(1831,plain,
( ( ( vd1299 @ ( vd1287 @ ( vd1288 @ rR ) ) )
!= ( vd1302 @ ( vd1287 @ ( vd1302 @ rR ) ) ) )
| ( vd1302 != vd1299 ) ),
inference(simp,[status(thm)],[1830]) ).
thf(1867,plain,
( ( vd1302 != vd1299 )
| ( vd1287 != vd1287 )
| ( vd1288 != vd1302 )
| ( vd1302 != vd1299 ) ),
inference(simp,[status(thm)],[1831]) ).
thf(1886,plain,
( ( vd1288 != vd1302 )
| ( vd1302 != vd1299 ) ),
inference(simp,[status(thm)],[1867]) ).
thf(12741,plain,
! [A: $i] :
( ( ( vd1299 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11577,1034]) ).
thf(12742,plain,
! [A: $i] :
( ( ( vd1299 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[12741]) ).
thf(12743,plain,
vd1299 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[12742:[bind(A,$thf( vd1299 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(16976,plain,
! [A: $i] :
( ( ( vd1299 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12743,1034]) ).
thf(16977,plain,
! [A: $i] :
( ( ( vd1299 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[16976]) ).
thf(16978,plain,
vd1299 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[16977:[bind(A,$thf( vd1299 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ rtriangle )
& ( ( C @ ( B @ ( A @ vtriangle ) ) )
= D ) )
=> ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( C = E ) )
& ( A != B )
& ( A != C )
& ( B != C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(3), 0), imp(cond(axiom(3), 0)))') ).
thf(210,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ rtriangle )
& ( ( C @ ( B @ ( A @ vtriangle ) ) )
= D ) )
=> ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( C = E ) )
& ( A != B )
& ( A != C )
& ( B != C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(211,plain,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] :
( ( D @ rtriangle )
& ( ( C @ ( B @ ( A @ vtriangle ) ) )
= D ) )
=> ( ? [D: $i] :
( ( D @ rpoint )
& ( A = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( B = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( C = D ) )
& ( A != B )
& ( A != C )
& ( B != C ) ) ),
inference(miniscope,[status(thm)],[210]) ).
thf(212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk5 ) ) @ rpoint )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) )
& ( ( A
= ( A @ ( B @ ( C @ sk5 ) ) ) )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) )
& ( ( A @ ( B @ ( C @ sk4 ) ) @ rpoint )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) )
& ( ( B
= ( A @ ( B @ ( C @ sk4 ) ) ) )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) )
& ( ( A @ ( B @ ( C @ sk3 ) ) @ rpoint )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) )
& ( ( C
= ( A @ ( B @ ( C @ sk3 ) ) ) )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) )
& ( ( A != B )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) )
& ( ( A != C )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) )
& ( ( B != C )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ) ),
inference(cnf,[status(esa)],[211]) ).
thf(213,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ ( B @ ( C @ sk3 ) ) ) )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(cnfConj,[status(thm)],[212]) ).
thf(232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ rtriangle )
| ( ( A @ ( B @ ( C @ sk3 ) ) )
= C )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[213]) ).
thf(233,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ vtriangle ) ) @ rtriangle )
| ( ( A @ ( B @ ( C @ sk3 ) ) )
= C ) ),
inference(simp,[status(thm)],[232]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ rpoint )
& ( A = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( B = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ( A != B )
& ( A != C )
& ( A != D )
& ( B != C )
& ( B != D )
& ( C != D )
& ( F @ rline )
& ( E = F )
& ~ ( E @ ( D @ ron ) ) )
=> ( ( B @ ( A @ ( C @ rR ) ) )
<=> ( ( B @ ( C @ ( D @ vg ) ) @ ( D @ ( C @ ( A @ vg ) ) @ vplus ) )
= ( B @ ( D @ ( A @ vg ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(202), 0), imp(cond(axiom(202), 0)))') ).
thf(240,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ rpoint )
& ( A = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( B = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ( A != B )
& ( A != C )
& ( A != D )
& ( B != C )
& ( B != D )
& ( C != D )
& ( F @ rline )
& ( E = F )
& ~ ( E @ ( D @ ron ) ) )
=> ( ( ( ( B @ ( C @ ( D @ vg ) ) @ ( D @ ( C @ ( A @ vg ) ) @ vplus ) )
= ( B @ ( D @ ( A @ vg ) ) ) )
=> ( B @ ( A @ ( C @ rR ) ) ) )
& ( ( B @ ( A @ ( C @ rR ) ) )
=> ( ( B @ ( C @ ( D @ vg ) ) @ ( D @ ( C @ ( A @ vg ) ) @ vplus ) )
= ( B @ ( D @ ( A @ vg ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(241,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( G @ rpoint )
& ( A = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( B = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ( A != B )
& ( A != C )
& ( A != D )
& ( B != C )
& ( B != D )
& ( C != D )
& ( F @ rline )
& ( E = F ) )
& ~ ( E @ ( D @ ron ) ) )
=> ( ( ( ( B @ ( C @ ( D @ vg ) ) @ ( D @ ( C @ ( A @ vg ) ) @ vplus ) )
= ( B @ ( D @ ( A @ vg ) ) ) )
=> ( B @ ( A @ ( C @ rR ) ) ) )
& ( ( B @ ( A @ ( C @ rR ) ) )
=> ( ( B @ ( C @ ( D @ vg ) ) @ ( D @ ( C @ ( A @ vg ) ) @ vplus ) )
= ( B @ ( D @ ( A @ vg ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[240]) ).
thf(242,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ rR ) ) )
| ( ( B @ ( C @ ( D @ vg ) ) @ ( D @ ( C @ ( A @ vg ) ) @ vplus ) )
!= ( B @ ( D @ ( A @ vg ) ) ) )
| ~ ( J @ rpoint )
| ( A != J )
| ~ ( I @ rpoint )
| ( B != I )
| ~ ( H @ rpoint )
| ( C != H )
| ~ ( G @ rpoint )
| ( D != G )
| ( A = B )
| ( A = C )
| ( A = D )
| ( B = C )
| ( B = D )
| ( C = D )
| ~ ( F @ rline )
| ( E != F )
| ( E @ ( D @ ron ) ) )
& ( ( ( B @ ( C @ ( D @ vg ) ) @ ( D @ ( C @ ( A @ vg ) ) @ vplus ) )
= ( B @ ( D @ ( A @ vg ) ) ) )
| ~ ( B @ ( A @ ( C @ rR ) ) )
| ~ ( J @ rpoint )
| ( A != J )
| ~ ( I @ rpoint )
| ( B != I )
| ~ ( H @ rpoint )
| ( C != H )
| ~ ( G @ rpoint )
| ( D != G )
| ( A = B )
| ( A = C )
| ( A = D )
| ( B = C )
| ( B = D )
| ( C = D )
| ~ ( F @ rline )
| ( E != F )
| ( E @ ( D @ ron ) ) ) ),
inference(cnf,[status(esa)],[241]) ).
thf(244,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ rR ) ) )
| ( ( B @ ( C @ ( D @ vg ) ) @ ( D @ ( C @ ( A @ vg ) ) @ vplus ) )
!= ( B @ ( D @ ( A @ vg ) ) ) )
| ~ ( J @ rpoint )
| ( A != J )
| ~ ( I @ rpoint )
| ( B != I )
| ~ ( H @ rpoint )
| ( C != H )
| ~ ( G @ rpoint )
| ( D != G )
| ( A = B )
| ( A = C )
| ( A = D )
| ( B = C )
| ( B = D )
| ( C = D )
| ~ ( F @ rline )
| ( E != F )
| ( E @ ( D @ ron ) ) ),
inference(cnfConj,[status(thm)],[242]) ).
thf(247,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ rR ) ) )
| ~ ( J @ rpoint )
| ~ ( I @ rpoint )
| ~ ( H @ rpoint )
| ~ ( G @ rpoint )
| ~ ( F @ rline )
| ( E @ ( D @ ron ) )
| ( ( B @ ( C @ ( D @ vg ) ) @ ( D @ ( C @ ( A @ vg ) ) @ vplus ) )
!= ( B @ ( D @ ( A @ vg ) ) ) )
| ( A != J )
| ( B != I )
| ( C != H )
| ( D != G )
| ( A = B )
| ( A = C )
| ( A = D )
| ( B = C )
| ( B = D )
| ( C = D )
| ( E != F ) ),
inference(lifteq,[status(thm)],[244]) ).
thf(248,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( C @ rR ) ) )
| ~ ( E @ rpoint )
| ~ ( D @ rpoint )
| ~ ( C @ rpoint )
| ~ ( B @ rpoint )
| ~ ( A @ rline )
| ( A @ ( B @ ron ) )
| ( ( D @ ( C @ ( B @ vg ) ) @ ( B @ ( C @ ( E @ vg ) ) @ vplus ) )
!= ( D @ ( B @ ( E @ vg ) ) ) )
| ( E = D )
| ( E = C )
| ( E = B )
| ( D = C )
| ( D = B )
| ( C = B ) ),
inference(simp,[status(thm)],[247]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( ( B @ rcircle )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( A @ ( C @ ron ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(41), 0), imp(cond(axiom(41), 0)))') ).
thf(793,plain,
! [A: $i,B: $i] :
( ( ( B @ rcircle )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( A @ ( C @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(7483,plain,
( ( ( vd14 @ ( vd14 @ vf ) )
!= ( vd1302 @ ( vd1287 @ vf ) ) )
| ( vd1299 != vd1287 )
| ( v0 != v0 ) ),
inference(paramod_ordered,[status(thm)],[5153,5314]) ).
thf(7484,plain,
( ( ( vd14 @ ( vd14 @ vf ) )
!= ( vd1302 @ ( vd1287 @ vf ) ) )
| ( vd1299 != vd1287 ) ),
inference(simp,[status(thm)],[7483]) ).
thf(7550,plain,
( ( vd14 != vd1302 )
| ( vd14 != vd1287 )
| ( vd1299 != vd1287 ) ),
inference(simp,[status(thm)],[7484]) ).
thf(11357,plain,
! [A: $i] :
( ( ( vd1295 @ sk45 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10257,1034]) ).
thf(11358,plain,
! [A: $i] :
( ( ( vd1295 @ sk45 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[11357]) ).
thf(11359,plain,
vd1295 @ sk45 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[11358:[bind(A,$thf( vd1295 @ sk45 @ sk50 ))]]) ).
thf(12305,plain,
! [A: $i] :
( ( ( vd1295 @ sk45 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11359,1034]) ).
thf(12306,plain,
! [A: $i] :
( ( ( vd1295 @ sk45 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[12305]) ).
thf(12307,plain,
vd1295 @ sk45 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[12306:[bind(A,$thf( vd1295 @ sk45 @ sk50 @ sk50 ))]]) ).
thf(16590,plain,
! [A: $i] :
( ( ( vd1295 @ sk45 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12307,1034]) ).
thf(16591,plain,
! [A: $i] :
( ( ( vd1295 @ sk45 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[16590]) ).
thf(16592,plain,
vd1295 @ sk45 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[16591:[bind(A,$thf( vd1295 @ sk45 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(22202,plain,
! [A: $i] :
( ( ( vd1295 @ sk45 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16592,1034]) ).
thf(22203,plain,
! [A: $i] :
( ( ( vd1295 @ sk45 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[22202]) ).
thf(22204,plain,
vd1295 @ sk45 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[22203:[bind(A,$thf( vd1295 @ sk45 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ? [I: $i] :
( ( I @ rcircle )
& ( A = I ) )
& ? [I: $i] :
( ( I @ rcircle )
& ( B = I ) )
& ( A != B )
& ( B @ ( A @ rintersect ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( C = I ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( D = I ) )
& ( A @ ( C @ ron ) )
& ( B @ ( C @ ron ) )
& ( A @ ( D @ ron ) )
& ( B @ ( D @ ron ) )
& ( C != D )
& ( A @ ( E @ rcenter ) )
& ( B @ ( F @ rcenter ) )
& ( H @ rline )
& ( G = H )
& ( G @ ( E @ ron ) )
& ( G @ ( F @ ron ) ) )
=> ~ ( G @ ( D @ ( C @ rS ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(125), 0), imp(cond(axiom(125), 0)))') ).
thf(334,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ? [I: $i] :
( ( I @ rcircle )
& ( A = I ) )
& ? [I: $i] :
( ( I @ rcircle )
& ( B = I ) )
& ( A != B )
& ( B @ ( A @ rintersect ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( C = I ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( D = I ) )
& ( A @ ( C @ ron ) )
& ( B @ ( C @ ron ) )
& ( A @ ( D @ ron ) )
& ( B @ ( D @ ron ) )
& ( C != D )
& ( A @ ( E @ rcenter ) )
& ( B @ ( F @ rcenter ) )
& ( H @ rline )
& ( G = H )
& ( G @ ( E @ ron ) )
& ( G @ ( F @ ron ) ) )
=> ~ ( G @ ( D @ ( C @ rS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rcircle )
& ( A = B )
& ( D @ rline )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( A @ ( E @ rinside ) )
& ( C @ ( E @ ron ) )
& ( H @ rpoint )
& ( G = H )
& ( C @ ( G @ ron ) )
& ( G != E ) )
=> ? [I: $i] :
( ( I @ rpoint )
& ( A @ ( I @ ron ) )
& ( C @ ( I @ ron ) )
& ( G @ ( I @ ( E @ rR ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(63), 0), imp(cond(axiom(63), 0)))') ).
thf(894,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rcircle )
& ( A = B )
& ( D @ rline )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( A @ ( E @ rinside ) )
& ( C @ ( E @ ron ) )
& ( H @ rpoint )
& ( G = H )
& ( C @ ( G @ ron ) )
& ( G != E ) )
=> ? [I: $i] :
( ( I @ rpoint )
& ( A @ ( I @ ron ) )
& ( C @ ( I @ ron ) )
& ( G @ ( I @ ( E @ rR ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F ) )
=> ( v0 @ ( E @ ( C @ ( A @ vg ) ) @ rgeq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(174), 0), imp(cond(axiom(174), 0)))') ).
thf(392,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F ) )
=> ( v0 @ ( E @ ( C @ ( A @ vg ) ) @ rgeq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(12,axiom,
vd1295 @ ( vd1288 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(s2(plural(346)), 0)') ).
thf(165,plain,
vd1295 @ ( vd1288 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rline )
& ( C = D )
& ~ ( C @ ( A @ ron ) ) )
=> ( C @ ( A @ ( A @ rS ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(95), 0), imp(cond(axiom(95), 0)))') ).
thf(862,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rline )
& ( C = D )
& ~ ( C @ ( A @ ron ) ) )
=> ( C @ ( A @ ( A @ rS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ ( C @ rcenter ) )
& ( F @ rpoint )
& ( E = F )
& ( D @ ( E @ ron ) ) )
=> ( ( ( A @ ( C @ vf ) )
= ( E @ ( C @ vf ) ) )
<=> ( D @ ( A @ ron ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(184), 0), imp(cond(axiom(184), 0)))') ).
thf(349,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ ( C @ rcenter ) )
& ( F @ rpoint )
& ( E = F )
& ( D @ ( E @ ron ) ) )
=> ( ( ( D @ ( A @ ron ) )
=> ( ( A @ ( C @ vf ) )
= ( E @ ( C @ vf ) ) ) )
& ( ( ( A @ ( C @ vf ) )
= ( E @ ( C @ vf ) ) )
=> ( D @ ( A @ ron ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( H @ rpoint )
& ( A = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( B = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( C = H ) )
& ( E @ rline )
& ( D = E )
& ( G @ rcircle )
& ( F = G )
& ( D @ ( A @ ron ) )
& ( D @ ( B @ ron ) )
& ( D @ ( C @ ron ) )
& ( F @ ( A @ rinside ) )
& ( F @ ( B @ ron ) )
& ( F @ ( C @ ron ) )
& ( B != C ) )
=> ( C @ ( B @ ( A @ rR ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(119), 0), imp(cond(axiom(119), 0)))') ).
thf(788,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( H @ rpoint )
& ( A = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( B = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( C = H ) )
& ( E @ rline )
& ( D = E )
& ( G @ rcircle )
& ( F = G )
& ( D @ ( A @ ron ) )
& ( D @ ( B @ ron ) )
& ( D @ ( C @ ron ) )
& ( F @ ( A @ rinside ) )
& ( F @ ( B @ ron ) )
& ( F @ ( C @ ron ) )
& ( B != C ) )
=> ( C @ ( B @ ( A @ rR ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( F @ rreal )
& ( E = F )
& ( C @ ( A @ rless ) ) )
=> ( E @ ( C @ vplus ) @ ( E @ ( A @ vplus ) @ rless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(153), 0), imp(cond(axiom(153), 0)))') ).
thf(137,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( F @ rreal )
& ( E = F )
& ( C @ ( A @ rless ) ) )
=> ( E @ ( C @ vplus ) @ ( E @ ( A @ vplus ) @ rless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rcircle )
& ( C = D )
& ( C @ ( A @ rinside ) ) )
=> ~ ( C @ ( A @ ron ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(79), 0), imp(cond(axiom(79), 0)))') ).
thf(467,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rcircle )
& ( C = D )
& ( C @ ( A @ rinside ) ) )
=> ~ ( C @ ( A @ ron ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ vg ) ) )
= v0 )
| ~ ( D @ rpoint )
| ( A != D )
| ~ ( C @ rpoint )
| ( B != C ) ),
inference(cnf,[status(esa)],[249]) ).
thf(251,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ rpoint )
| ~ ( C @ rpoint )
| ( ( B @ ( A @ ( A @ vg ) ) )
= v0 )
| ( A != D )
| ( B != C ) ),
inference(lifteq,[status(thm)],[250]) ).
thf(252,plain,
! [B: $i,A: $i] :
( ~ ( B @ rpoint )
| ~ ( A @ rpoint )
| ( ( A @ ( B @ ( B @ vg ) ) )
= v0 ) ),
inference(simp,[status(thm)],[251]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( H @ rpoint )
& ( A = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( B = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( C = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( D = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( E = H ) )
& ? [H: $i] :
( ( H @ rline )
& ( F = H ) )
& ? [H: $i] :
( ( H @ rline )
& ( G = H ) )
& ( F @ ( A @ ron ) )
& ( F @ ( B @ ron ) )
& ( F @ ( D @ ron ) )
& ( G @ ( C @ ron ) )
& ( G @ ( E @ ron ) )
& ( B != A )
& ( C != A )
& ( D != A )
& ( E != A )
& ~ ( D @ ( B @ ( A @ rR ) ) )
& ~ ( E @ ( C @ ( A @ rR ) ) ) )
=> ( ( C @ ( A @ ( B @ vangle ) ) )
= ( E @ ( A @ ( D @ vangle ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(194), 0), imp(cond(axiom(194), 0)))') ).
thf(830,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( H @ rpoint )
& ( A = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( B = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( C = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( D = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( E = H ) )
& ? [H: $i] :
( ( H @ rline )
& ( F = H ) )
& ? [H: $i] :
( ( H @ rline )
& ( G = H ) )
& ( F @ ( A @ ron ) )
& ( F @ ( B @ ron ) )
& ( F @ ( D @ ron ) )
& ( G @ ( C @ ron ) )
& ( G @ ( E @ ron ) )
& ( B != A )
& ( C != A )
& ( D != A )
& ( E != A )
& ~ ( D @ ( B @ ( A @ rR ) ) )
& ~ ( E @ ( C @ ( A @ rR ) ) ) )
=> ( ( C @ ( A @ ( B @ vangle ) ) )
= ( E @ ( A @ ( D @ vangle ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(5111,plain,
! [A: $i] :
( ( ( vd1295 @ sk45 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[4973,201]) ).
thf(5112,plain,
! [A: $i] :
( ( ( vd1295 @ sk45 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[5111]) ).
thf(5113,plain,
( ( vd1295 @ sk45 @ ( vd1295 @ sk45 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[5112:[bind(A,$thf( vd1295 @ sk45 ))]]) ).
thf(11668,plain,
! [A: $i] :
( ( ( vd1287 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[10750,201]) ).
thf(11669,plain,
! [A: $i] :
( ( ( vd1287 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[11668]) ).
thf(11670,plain,
( ( vd1287 @ sk50 @ sk50 @ ( vd1287 @ sk50 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[11669:[bind(A,$thf( vd1287 @ sk50 @ sk50 ))]]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D ) )
=> ( ( A @ ( C @ rless ) )
| ( A = C )
| ( C @ ( A @ rless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(145), 0), imp(cond(axiom(145), 0)))') ).
thf(187,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D ) )
=> ( ( A @ ( C @ rless ) )
| ( A = C )
| ( C @ ( A @ rless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(188,plain,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] :
( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D ) )
=> ( ( A @ ( C @ rless ) )
| ( A = C )
| ( C @ ( A @ rless ) ) ) ),
inference(miniscope,[status(thm)],[187]) ).
thf(189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ rless ) )
| ( A = C )
| ( C @ ( A @ rless ) )
| ~ ( B @ rreal )
| ( A != B )
| ~ ( D @ rreal )
| ( C != D ) ),
inference(cnf,[status(esa)],[188]) ).
thf(190,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ rless ) )
| ( C @ ( A @ rless ) )
| ~ ( B @ rreal )
| ~ ( D @ rreal )
| ( A = C )
| ( A != B )
| ( C != D ) ),
inference(lifteq,[status(thm)],[189]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ rless ) )
| ( B @ ( A @ rless ) )
| ~ ( A @ rreal )
| ~ ( B @ rreal )
| ( A = B ) ),
inference(simp,[status(thm)],[190]) ).
thf(2079,plain,
! [B: $i,A: $i] :
( ( ( v0 @ rreal )
!= ( B @ rreal ) )
| ( A @ ( B @ rless ) )
| ( B @ ( A @ rless ) )
| ~ ( A @ rreal )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[1153,191]) ).
thf(2080,plain,
! [B: $i,A: $i] :
( ( ( v0 @ rreal )
!= ( B @ rreal ) )
| ( A @ ( B @ rless ) )
| ( B @ ( A @ rless ) )
| ~ ( A @ rreal )
| ( A = B ) ),
inference(simp,[status(thm)],[2079]) ).
thf(2081,plain,
! [A: $i] :
( ( A @ ( v0 @ rless ) )
| ( v0 @ ( A @ rless ) )
| ~ ( A @ rreal )
| ( A = v0 ) ),
inference(pattern_uni,[status(thm)],[2080:[bind(A,$thf( A )),bind(B,$thf( v0 ))]]) ).
thf(2768,plain,
! [A: $i] :
( ( A != vd1297 )
| ( v0 @ rline )
| ( A @ ( v0 @ rless ) )
| ( v0 @ ( A @ rless ) )
| ~ ( A @ rreal ) ),
inference(paramod_ordered,[status(thm)],[2081,164]) ).
thf(2769,plain,
( ( v0 @ rline )
| ( vd1297 @ ( v0 @ rless ) )
| ( v0 @ ( vd1297 @ rless ) )
| ~ ( vd1297 @ rreal ) ),
inference(pattern_uni,[status(thm)],[2768:[bind(A,$thf( vd1297 ))]]) ).
thf(220,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk4 ) ) @ rpoint )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(cnfConj,[status(thm)],[212]) ).
thf(228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk4 ) ) @ rpoint )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[220]) ).
thf(229,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk4 ) ) @ rpoint )
| ~ ( C @ ( B @ ( A @ vtriangle ) ) @ rtriangle ) ),
inference(simp,[status(thm)],[228]) ).
thf(841,plain,
vd1287 != vd1288,
inference(cnfConj,[status(thm)],[836]) ).
thf(847,plain,
vd1288 != vd1287,
inference(lifteq,[status(thm)],[841]) ).
thf(10460,plain,
! [A: $i] :
( ( ( vd1299 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[10266,201]) ).
thf(10461,plain,
! [A: $i] :
( ( ( vd1299 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[10460]) ).
thf(10462,plain,
( ( vd1299 @ sk50 @ ( vd1299 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[10461:[bind(A,$thf( vd1299 @ sk50 ))]]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rcircle )
& ( A = B )
& ( D @ rline )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( A @ ( E @ rinside ) )
& ( C @ ( E @ ron ) )
& ( H @ rpoint )
& ( G = H )
& ~ ( A @ ( G @ rinside ) )
& ~ ( A @ ( G @ ron ) )
& ( C @ ( G @ ron ) ) )
=> ? [I: $i] :
( ( I @ rpoint )
& ( C @ ( I @ ron ) )
& ( A @ ( I @ ron ) )
& ( G @ ( E @ ( I @ rR ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(61), 0), imp(cond(axiom(61), 0)))') ).
thf(879,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rcircle )
& ( A = B )
& ( D @ rline )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( A @ ( E @ rinside ) )
& ( C @ ( E @ ron ) )
& ( H @ rpoint )
& ( G = H )
& ~ ( A @ ( G @ rinside ) )
& ~ ( A @ ( G @ ron ) )
& ( C @ ( G @ ron ) ) )
=> ? [I: $i] :
( ( I @ rpoint )
& ( C @ ( I @ ron ) )
& ( A @ ( I @ ron ) )
& ( G @ ( E @ ( I @ rR ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( C != A )
& ( C != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(9), 0), imp(cond(axiom(9), 0)))') ).
thf(1111,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( C != A )
& ( C != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(72,axiom,
vd1295 @ ( vd1287 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(s1(plural(346)), 0)') ).
thf(725,plain,
vd1295 @ ( vd1287 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) ) )
=> ( B @ ( A @ vf ) @ ( v0 @ rleq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(164), 0), imp(cond(axiom(164), 0)))') ).
thf(1006,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) ) )
=> ( B @ ( A @ vf ) @ ( v0 @ rleq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(138,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( F @ rreal )
& ( E = F ) )
& ( C @ ( A @ rless ) ) )
=> ( E @ ( C @ vplus ) @ ( E @ ( A @ vplus ) @ rless ) ) ),
inference(miniscope,[status(thm)],[137]) ).
thf(139,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ vplus ) @ ( E @ ( A @ vplus ) @ rless ) )
| ~ ( B @ rreal )
| ( A != B )
| ~ ( D @ rreal )
| ( C != D )
| ~ ( F @ rreal )
| ( E != F )
| ~ ( C @ ( A @ rless ) ) ),
inference(cnf,[status(esa)],[138]) ).
thf(140,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ vplus ) @ ( E @ ( A @ vplus ) @ rless ) )
| ~ ( B @ rreal )
| ~ ( D @ rreal )
| ~ ( F @ rreal )
| ~ ( C @ ( A @ rless ) )
| ( A != B )
| ( C != D )
| ( E != F ) ),
inference(lifteq,[status(thm)],[139]) ).
thf(141,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ rless ) )
| ~ ( A @ rreal )
| ~ ( B @ rreal )
| ~ ( C @ rreal )
| ~ ( B @ ( A @ rless ) ) ),
inference(simp,[status(thm)],[140]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) )
& ( A != B ) )
=> ? [C: $i] :
( ( C @ rline )
& ( C @ ( A @ ron ) )
& ( C @ ( B @ ron ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(51), 0), imp(cond(axiom(51), 0)))') ).
thf(420,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) )
& ( A != B ) )
=> ? [C: $i] :
( ( C @ rline )
& ( C @ ( A @ ron ) )
& ( C @ ( B @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(8,axiom,
vd1297 @ ( vd1289 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(s2(plural(347)), 0)') ).
thf(156,plain,
vd1297 @ ( vd1289 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11971,plain,
! [A: $i] :
( ( ( vd1302 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10913,1034]) ).
thf(11972,plain,
! [A: $i] :
( ( ( vd1302 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[11971]) ).
thf(11973,plain,
vd1302 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[11972:[bind(A,$thf( vd1302 @ sk50 @ sk50 ))]]) ).
thf(13147,plain,
! [A: $i] :
( ( ( vd1302 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11973,1034]) ).
thf(13148,plain,
! [A: $i] :
( ( ( vd1302 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[13147]) ).
thf(13149,plain,
vd1302 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[13148:[bind(A,$thf( vd1302 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(18071,plain,
! [A: $i] :
( ( ( vd1302 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13149,1034]) ).
thf(18072,plain,
! [A: $i] :
( ( ( vd1302 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[18071]) ).
thf(18073,plain,
vd1302 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[18072:[bind(A,$thf( vd1302 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( A @ ( B @ ( C @ sk5 ) ) ) )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(cnfConj,[status(thm)],[212]) ).
thf(224,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ rtriangle )
| ( ( A @ ( B @ ( C @ sk5 ) ) )
= A )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[216]) ).
thf(225,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ vtriangle ) ) @ rtriangle )
| ( ( A @ ( B @ ( C @ sk5 ) ) )
= A ) ),
inference(simp,[status(thm)],[224]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( D = E )
& ( D @ ( B @ ( A @ rS ) ) )
& ( D @ ( C @ ( A @ rS ) ) ) )
=> ( D @ ( C @ ( B @ rS ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(101), 0), imp(cond(axiom(101), 0)))') ).
thf(339,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( D = E )
& ( D @ ( B @ ( A @ rS ) ) )
& ( D @ ( C @ ( A @ rS ) ) ) )
=> ( D @ ( C @ ( B @ rS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rcircle )
& ( D = E )
& ( ( D @ ( A @ rinside ) )
| ( D @ ( A @ ron ) ) )
& ~ ( D @ ( C @ rinside ) )
& ( B @ ( A @ ( C @ rR ) ) ) )
=> ( ~ ( D @ ( B @ ron ) )
& ~ ( D @ ( B @ ron ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(123), 0), imp(cond(axiom(123), 0)))') ).
thf(1075,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rcircle )
& ( D = E )
& ( ( D @ ( A @ rinside ) )
| ( D @ ( A @ ron ) ) )
& ~ ( D @ ( C @ rinside ) )
& ( B @ ( A @ ( C @ rR ) ) ) )
=> ~ ( D @ ( B @ ron ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ rpoint )
& ( A = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( B = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( C = D ) ) )
=> ? [D: $i] :
( ( D @ rpoint )
& ( D != A )
& ( D != B )
& ( D != C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(11), 0), imp(cond(axiom(11), 0)))') ).
thf(526,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ rpoint )
& ( A = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( B = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( C = D ) ) )
=> ? [D: $i] :
( ( D @ rpoint )
& ( D != A )
& ( D != B )
& ( D != C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ? [E: $i] :
( ( E @ rcircle )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rcircle )
& ( D = E ) )
& ( C @ ( A @ ron ) )
& ( ( C @ ( B @ rinside ) )
| ( C @ ( B @ ron ) ) )
& ( D @ ( A @ rinside ) )
& ~ ( D @ ( B @ ron ) )
& ~ ( D @ ( B @ rinside ) ) )
=> ( D @ ( C @ rintersect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(133), 0), imp(cond(axiom(133), 0)))') ).
thf(970,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ? [E: $i] :
( ( E @ rcircle )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rcircle )
& ( D = E ) )
& ( C @ ( A @ ron ) )
& ( ( C @ ( B @ rinside ) )
| ( C @ ( B @ ron ) ) )
& ( D @ ( A @ rinside ) )
& ~ ( D @ ( B @ ron ) )
& ~ ( D @ ( B @ rinside ) ) )
=> ( D @ ( C @ rintersect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ( D @ rline )
& ( C = D )
& ( C @ ( B @ ( A @ rS ) ) ) )
=> ~ ( C @ ( A @ ron ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(99), 0), imp(cond(axiom(99), 0)))') ).
thf(1060,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ( D @ rline )
& ( C = D )
& ( C @ ( B @ ( A @ rS ) ) ) )
=> ~ ( C @ ( A @ ron ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( A != C )
& ( C = D ) )
=> ( ( C @ ( A @ vf ) )
= ( D @ ( C @ ( B @ ( A @ vskolem1052 ) ) ) @ ( C @ vf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(206), 0), 1)') ).
thf(721,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( A != C )
& ( C = D ) )
=> ( ( C @ ( A @ vf ) )
= ( D @ ( C @ ( B @ ( A @ vskolem1052 ) ) ) @ ( C @ vf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1764,plain,
( ( ( vd1302 @ ( vd1287 @ ( vd1289 @ rR ) ) )
!= ( vd1302 @ ( vd1287 @ ( vd1299 @ rR ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[740,1205]) ).
thf(1765,plain,
( ( vd1302 @ ( vd1287 @ ( vd1289 @ rR ) ) )
!= ( vd1302 @ ( vd1287 @ ( vd1299 @ rR ) ) ) ),
inference(simp,[status(thm)],[1764]) ).
thf(1782,plain,
( ( vd1302 != vd1302 )
| ( vd1287 != vd1287 )
| ( vd1289 != vd1299 ) ),
inference(simp,[status(thm)],[1765]) ).
thf(1799,plain,
vd1289 != vd1299,
inference(simp,[status(thm)],[1782]) ).
thf(17871,plain,
! [A: $i] :
( ( ( vd1288 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13013,1034]) ).
thf(17872,plain,
! [A: $i] :
( ( ( vd1288 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[17871]) ).
thf(17873,plain,
vd1288 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[17872:[bind(A,$thf( vd1288 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( H @ rpoint )
& ( G = H )
& ( A != C )
& ( E != G )
& ( C @ ( A @ vf ) @ ( G @ ( E @ vf ) @ rless ) ) )
=> ( C @ ( A @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ vskolem1120 ) ) ) ) ) ) ) @ rR ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(238), 0), 1)') ).
thf(1131,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( H @ rpoint )
& ( G = H )
& ( A != C )
& ( E != G )
& ( C @ ( A @ vf ) @ ( G @ ( E @ vf ) @ rless ) ) )
=> ( C @ ( A @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ vskolem1120 ) ) ) ) ) ) ) @ rR ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != B )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(cnfConj,[status(thm)],[212]) ).
thf(236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ rtriangle )
| ( A != B )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[214]) ).
thf(237,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( A @ vtriangle ) ) @ rtriangle ),
inference(simp,[status(thm)],[236]) ).
thf(22480,plain,
! [A: $i] :
( ( ( vd1297 @ sk45 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16785,1034]) ).
thf(22481,plain,
! [A: $i] :
( ( ( vd1297 @ sk45 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[22480]) ).
thf(22482,plain,
vd1297 @ sk45 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[22481:[bind(A,$thf( vd1297 @ sk45 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(23035,plain,
! [A: $i] :
( ( ( vd1287 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17674,1034]) ).
thf(23036,plain,
! [A: $i] :
( ( ( vd1287 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[23035]) ).
thf(23037,plain,
vd1287 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[23036:[bind(A,$thf( vd1287 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( ( B @ rcircle )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( A @ ( C @ rinside ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(47), 0), imp(cond(axiom(47), 0)))') ).
thf(1035,plain,
! [A: $i,B: $i] :
( ( ( B @ rcircle )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( A @ ( C @ rinside ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ rpoint )
& ( A = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( B = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ( A != B )
& ( A != C )
& ( B != C )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( E = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( F = G ) )
& ( ( B @ ( A @ vf ) )
= ( E @ ( D @ vf ) ) )
& ( ( C @ ( A @ vf ) )
= ( F @ ( D @ vf ) ) )
& ( ( C @ ( A @ ( B @ vangle ) ) )
= ( F @ ( D @ ( E @ vangle ) ) ) )
& ~ ? [G: $i] :
( ( G @ rline )
& ( G @ ( D @ ron ) )
& ( G @ ( E @ ron ) )
& ( G @ ( F @ ron ) ) ) )
=> ( ( B @ ( C @ ( A @ vangle ) ) )
= ( E @ ( F @ ( D @ vangle ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(264), 0), 0)') ).
thf(586,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ rpoint )
& ( A = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( B = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ( A != B )
& ( A != C )
& ( B != C )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( E = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( F = G ) )
& ( ( B @ ( A @ vf ) )
= ( E @ ( D @ vf ) ) )
& ( ( C @ ( A @ vf ) )
= ( F @ ( D @ vf ) ) )
& ( ( C @ ( A @ ( B @ vangle ) ) )
= ( F @ ( D @ ( E @ vangle ) ) ) )
& ~ ? [G: $i] :
( ( G @ rline )
& ( G @ ( D @ ron ) )
& ( G @ ( E @ ron ) )
& ( G @ ( F @ ron ) ) ) )
=> ( ( B @ ( C @ ( A @ vangle ) ) )
= ( E @ ( F @ ( D @ vangle ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(10981,plain,
! [A: $i] :
( ( ( vd1289 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[10291,201]) ).
thf(10982,plain,
! [A: $i] :
( ( ( vd1289 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[10981]) ).
thf(10983,plain,
( ( vd1289 @ sk50 @ ( vd1289 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[10982:[bind(A,$thf( vd1289 @ sk50 ))]]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( C @ ( A @ ( B @ rR ) ) )
& ( D @ ( A @ ron ) )
& ( D @ ( B @ ron ) )
& ( D = E ) )
=> ( D @ ( C @ ron ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))') ).
thf(1135,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( C @ ( A @ ( B @ rR ) ) )
& ( D @ ( A @ ron ) )
& ( D @ ( B @ ron ) )
& ( D = E ) )
=> ( D @ ( C @ ron ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) ) )
=> ( ( B @ ( A @ vf ) )
= ( A @ ( B @ vf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(166), 0), imp(cond(axiom(166), 0)))') ).
thf(264,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) ) )
=> ( ( B @ ( A @ vf ) )
= ( A @ ( B @ vf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i] :
( ( ? [S: $i] :
( ( S @ rpoint )
& ( A = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( B = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( C = S ) )
& ( A != B )
& ( A != C )
& ( B != C )
& ? [S: $i] :
( ( S @ rpoint )
& ( D = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( E = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( F = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( G = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( H = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( I = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( J = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( K = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( L = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( M = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( N = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( O = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( P = S ) )
& ( R @ rline )
& ( Q @ ( D @ ron ) )
& ( Q @ ( E @ ron ) )
& ~ ( Q @ ( F @ ron ) )
& ! [S: $i,T: $i,U: $i] :
( ( ( S @ rpoint )
& ( T @ rpoint )
& ( U @ rpoint )
& ( S = D )
& ( ( S @ ( T @ ( U @ vangle ) ) )
= ( A @ ( B @ ( C @ vangle ) ) ) )
& ( ( U @ ( S @ ( T @ vangle ) ) )
= ( C @ ( A @ ( B @ vangle ) ) ) )
& ( ( T @ ( U @ ( S @ vangle ) ) )
= ( B @ ( C @ ( A @ vangle ) ) ) )
& ( ( B @ ( A @ vf ) )
= ( T @ ( S @ vf ) ) )
& ( ( C @ ( B @ vf ) )
= ( U @ ( T @ vf ) ) )
& ( ( C @ ( A @ vf ) )
= ( U @ ( S @ vf ) ) )
& ( Q @ ( T @ ron ) )
& ~ ( E @ ( T @ ( D @ rR ) ) )
& ( Q @ ( F @ ( U @ rS ) ) ) )
=> ( ( ( H @ ( G @ vf ) )
= ( J @ ( I @ vf ) ) )
& ( ( M @ ( L @ ( K @ vangle ) ) )
= ( P @ ( O @ ( N @ vangle ) ) ) ) ) )
& ( Q = R ) )
=> ( ( ( H @ ( G @ vf ) )
= ( J @ ( I @ vf ) ) )
& ( ( M @ ( L @ ( K @ vangle ) ) )
= ( P @ ( O @ ( N @ vangle ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(204), 0), imp(cond(axiom(204), 0)))') ).
thf(279,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i] :
( ( ? [S: $i] :
( ( S @ rpoint )
& ( A = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( B = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( C = S ) )
& ( A != B )
& ( A != C )
& ( B != C )
& ? [S: $i] :
( ( S @ rpoint )
& ( D = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( E = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( F = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( G = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( H = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( I = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( J = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( K = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( L = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( M = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( N = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( O = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( P = S ) )
& ( R @ rline )
& ( Q @ ( D @ ron ) )
& ( Q @ ( E @ ron ) )
& ~ ( Q @ ( F @ ron ) )
& ! [S: $i,T: $i,U: $i] :
( ( ( S @ rpoint )
& ( T @ rpoint )
& ( U @ rpoint )
& ( S = D )
& ( ( S @ ( T @ ( U @ vangle ) ) )
= ( A @ ( B @ ( C @ vangle ) ) ) )
& ( ( U @ ( S @ ( T @ vangle ) ) )
= ( C @ ( A @ ( B @ vangle ) ) ) )
& ( ( T @ ( U @ ( S @ vangle ) ) )
= ( B @ ( C @ ( A @ vangle ) ) ) )
& ( ( B @ ( A @ vf ) )
= ( T @ ( S @ vf ) ) )
& ( ( C @ ( B @ vf ) )
= ( U @ ( T @ vf ) ) )
& ( ( C @ ( A @ vf ) )
= ( U @ ( S @ vf ) ) )
& ( Q @ ( T @ ron ) )
& ~ ( E @ ( T @ ( D @ rR ) ) )
& ( Q @ ( F @ ( U @ rS ) ) ) )
=> ( ( ( H @ ( G @ vf ) )
= ( J @ ( I @ vf ) ) )
& ( ( M @ ( L @ ( K @ vangle ) ) )
= ( P @ ( O @ ( N @ vangle ) ) ) ) ) )
& ( Q = R ) )
=> ( ( ( H @ ( G @ vf ) )
= ( J @ ( I @ vf ) ) )
& ( ( M @ ( L @ ( K @ vangle ) ) )
= ( P @ ( O @ ( N @ vangle ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(7004,plain,
( ( ( vd14 @ ( vd14 @ vf ) )
!= ( vd1302 @ ( vd1287 @ vf ) ) )
| ( v0 != v0 )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(paramod_ordered,[status(thm)],[5153,4631]) ).
thf(7005,plain,
( ( ( vd14 @ ( vd14 @ vf ) )
!= ( vd1302 @ ( vd1287 @ vf ) ) )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[7004]) ).
thf(7010,plain,
( ( vd14 != vd1302 )
| ( vd14 != vd1287 )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[7005]) ).
thf(27775,plain,
! [A: $i] :
( ( ( vd1289 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18272,1034]) ).
thf(27776,plain,
! [A: $i] :
( ( ( vd1289 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[27775]) ).
thf(27777,plain,
vd1289 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[27776:[bind(A,$thf( vd1289 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(1846,plain,
( ( ( vd1302 @ ( vd1287 @ ( vd14 @ rR ) ) )
!= ( vd1299 @ ( vd1287 @ ( vd1288 @ rR ) ) ) )
| ~ $true
| ( ( vd14 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[742,1158]) ).
thf(1847,plain,
( ( ( vd1302 @ ( vd1287 @ ( vd14 @ rR ) ) )
!= ( vd1299 @ ( vd1287 @ ( vd1288 @ rR ) ) ) )
| ( ( vd14 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) ) ),
inference(simp,[status(thm)],[1846]) ).
thf(1865,plain,
( ( vd1302 != vd1299 )
| ( vd1287 != vd1287 )
| ( vd14 != vd1288 )
| ( vd14 != vd1299 )
| ( vd1287 != vd1287 ) ),
inference(simp,[status(thm)],[1847]) ).
thf(1884,plain,
( ( vd1302 != vd1299 )
| ( vd14 != vd1288 )
| ( vd14 != vd1299 ) ),
inference(simp,[status(thm)],[1865]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ rpoint )
& ( A = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( B = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( C = D ) )
& ( C @ ( A @ ( B @ rR ) ) ) )
=> ( ( C @ ( B @ vf ) @ ( B @ ( A @ vf ) @ vplus ) )
= ( C @ ( A @ vf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))') ).
thf(826,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ rpoint )
& ( A = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( B = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( C = D ) )
& ( C @ ( A @ ( B @ rR ) ) ) )
=> ( ( C @ ( B @ vf ) @ ( B @ ( A @ vf ) @ vplus ) )
= ( C @ ( A @ vf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(255,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ rS ) ) )
| ( ( C @ ( A @ ( B @ vangle ) ) )
!= ( C @ ( A @ ( D @ vangle ) ) @ ( D @ ( A @ ( B @ vangle ) ) @ vplus ) ) )
| ~ ( L @ rpoint )
| ( A != L )
| ~ ( K @ rpoint )
| ( B != K )
| ~ ( J @ rpoint )
| ( C != J )
| ~ ( I @ rpoint )
| ( D != I )
| ~ ( H @ rline )
| ( E != H )
| ~ ( G @ rline )
| ( F != G )
| ~ ( E @ ( A @ ron ) )
| ~ ( F @ ( A @ ron ) )
| ~ ( E @ ( B @ ron ) )
| ~ ( F @ ( C @ ron ) )
| ( A = B )
| ( A = C )
| ( E @ ( D @ ron ) )
| ( F @ ( D @ ron ) )
| ( E = F ) ),
inference(cnfConj,[status(thm)],[254]) ).
thf(258,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ rS ) ) )
| ~ ( L @ rpoint )
| ~ ( K @ rpoint )
| ~ ( J @ rpoint )
| ~ ( I @ rpoint )
| ~ ( H @ rline )
| ~ ( G @ rline )
| ~ ( E @ ( A @ ron ) )
| ~ ( F @ ( A @ ron ) )
| ~ ( E @ ( B @ ron ) )
| ~ ( F @ ( C @ ron ) )
| ( E @ ( D @ ron ) )
| ( F @ ( D @ ron ) )
| ( ( C @ ( A @ ( B @ vangle ) ) )
!= ( C @ ( A @ ( D @ vangle ) ) @ ( D @ ( A @ ( B @ vangle ) ) @ vplus ) ) )
| ( A != L )
| ( B != K )
| ( C != J )
| ( D != I )
| ( E != H )
| ( F != G )
| ( A = B )
| ( A = C )
| ( E = F ) ),
inference(lifteq,[status(thm)],[255]) ).
thf(259,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( D @ rS ) ) )
| ~ ( F @ rpoint )
| ~ ( E @ rpoint )
| ~ ( D @ rpoint )
| ~ ( C @ rpoint )
| ~ ( B @ rline )
| ~ ( A @ rline )
| ~ ( B @ ( F @ ron ) )
| ~ ( A @ ( F @ ron ) )
| ~ ( B @ ( E @ ron ) )
| ~ ( A @ ( D @ ron ) )
| ( B @ ( C @ ron ) )
| ( A @ ( C @ ron ) )
| ( ( D @ ( F @ ( E @ vangle ) ) )
!= ( D @ ( F @ ( C @ vangle ) ) @ ( C @ ( F @ ( E @ vangle ) ) @ vplus ) ) )
| ( F = E )
| ( F = D )
| ( B = A ) ),
inference(simp,[status(thm)],[258]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( D = E ) )
& ( C @ ( A @ ( B @ rR ) ) )
& ( B @ ( A @ ( D @ rR ) ) ) )
=> ( C @ ( A @ ( D @ rR ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(87), 0), imp(cond(axiom(87), 0)))') ).
thf(402,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( D = E ) )
& ( C @ ( A @ ( B @ rR ) ) )
& ( B @ ( A @ ( D @ rR ) ) ) )
=> ( C @ ( A @ ( D @ rR ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( A != C )
& ( C = D ) )
=> ( ( D @ ( C @ ( B @ ( A @ vskolem1052 ) ) ) @ ( C @ vf ) )
= ( A @ ( D @ ( C @ ( B @ ( A @ vskolem1052 ) ) ) @ vf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(206), 0), 0)') ).
thf(1107,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( A != C )
& ( C = D ) )
=> ( ( D @ ( C @ ( B @ ( A @ vskolem1052 ) ) ) @ ( C @ vf ) )
= ( A @ ( D @ ( C @ ( B @ ( A @ vskolem1052 ) ) ) @ vf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk1 ) ) @ rreal )
| ~ ( B @ rreal )
| ( A != B )
| ~ ( D @ rreal )
| ( C != D ) ),
inference(cnfConj,[status(thm)],[175]) ).
thf(180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk1 ) ) @ rreal )
| ~ ( B @ rreal )
| ~ ( D @ rreal )
| ( A != B )
| ( C != D ) ),
inference(lifteq,[status(thm)],[177]) ).
thf(181,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk1 ) ) @ rreal )
| ~ ( A @ rreal )
| ~ ( B @ rreal ) ),
inference(simp,[status(thm)],[180]) ).
thf(1257,plain,
( ~ ( vd1302 @ ( vd1287 @ ( vd14 @ rR ) ) )
| ( vd14 != vd1299 )
| ( vd1287 != vd1287 ) ),
inference(simp,[status(thm)],[1158]) ).
thf(1258,plain,
( ~ ( vd1302 @ ( vd1287 @ ( vd14 @ rR ) ) )
| ( vd14 != vd1299 ) ),
inference(simp,[status(thm)],[1257]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( H @ rpoint )
& ( A = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( B = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( C = H ) )
& ( E @ rline )
& ( D = E )
& ( G @ rcircle )
& ( F = G )
& ( ( F @ ( A @ rinside ) )
| ( F @ ( A @ ron ) ) )
& ( ( F @ ( B @ rinside ) )
| ( F @ ( B @ ron ) ) )
& ( B @ ( A @ ( C @ rR ) ) ) )
=> ( F @ ( C @ rinside ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(121), 0), imp(cond(axiom(121), 0)))') ).
thf(540,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( H @ rpoint )
& ( A = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( B = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( C = H ) )
& ( E @ rline )
& ( D = E )
& ( G @ rcircle )
& ( F = G )
& ( ( F @ ( A @ rinside ) )
| ( F @ ( A @ ron ) ) )
& ( ( F @ ( B @ rinside ) )
| ( F @ ( B @ ron ) ) )
& ( B @ ( A @ ( C @ rR ) ) ) )
=> ( F @ ( C @ rinside ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D ) )
=> ( ( C @ ( A @ vplus ) )
= ( A @ ( C @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(143), 0), imp(cond(axiom(143), 0)))') ).
thf(159,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D ) )
=> ( ( C @ ( A @ vplus ) )
= ( A @ ( C @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ( A != B )
& ? [E: $i] :
( ( E @ rline )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rline )
& ( D = E ) )
& ( C @ ( A @ ron ) )
& ( D @ ( A @ ron ) )
& ( C @ ( B @ ron ) )
& ( D @ ( B @ ron ) ) )
=> ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(73), 0), imp(cond(axiom(73), 0)))') ).
thf(979,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ( A != B )
& ? [E: $i] :
( ( E @ rline )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rline )
& ( D = E ) )
& ( C @ ( A @ ron ) )
& ( D @ ( A @ ron ) )
& ( C @ ( B @ ron ) )
& ( D @ ( B @ ron ) ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(23312,plain,
! [A: $i] :
( ( ( vd1288 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17873,1034]) ).
thf(23313,plain,
! [A: $i] :
( ( ( vd1288 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[23312]) ).
thf(23314,plain,
vd1288 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[23313:[bind(A,$thf( vd1288 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( H @ rcircle )
& ( A = H ) )
& ? [H: $i] :
( ( H @ rcircle )
& ( B = H ) )
& ( D @ rline )
& ( C = D )
& ( B @ ( A @ rintersect ) )
& ( A @ ( E @ rcenter ) )
& ( B @ ( F @ rcenter ) )
& ( C @ ( E @ ron ) )
& ( C @ ( F @ ron ) )
& ~ ( C @ ( G @ ron ) ) )
=> ? [H: $i] :
( ( H @ rpoint )
& ( A @ ( H @ ron ) )
& ( B @ ( H @ ron ) )
& ( C @ ( G @ ( H @ rS ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(69), 0), imp(cond(axiom(69), 0)))') ).
thf(406,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( H @ rcircle )
& ( A = H ) )
& ? [H: $i] :
( ( H @ rcircle )
& ( B = H ) )
& ( D @ rline )
& ( C = D )
& ( B @ ( A @ rintersect ) )
& ( A @ ( E @ rcenter ) )
& ( B @ ( F @ rcenter ) )
& ( C @ ( E @ ron ) )
& ( C @ ( F @ ron ) )
& ~ ( C @ ( G @ ron ) ) )
=> ? [H: $i] :
( ( H @ rpoint )
& ( A @ ( H @ ron ) )
& ( B @ ( H @ ron ) )
& ( C @ ( G @ ( H @ rS ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk6 ) @ ( B @ ron ) )
| ~ ( D @ rpoint )
| ( A != D )
| ~ ( C @ rpoint )
| ( B != C )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[269]) ).
thf(273,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk6 ) @ ( B @ ron ) )
| ~ ( D @ rpoint )
| ~ ( C @ rpoint )
| ( A != D )
| ( B != C )
| ( A = B ) ),
inference(lifteq,[status(thm)],[270]) ).
thf(274,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk6 ) @ ( A @ ron ) )
| ~ ( B @ rpoint )
| ~ ( A @ rpoint )
| ( B = A ) ),
inference(simp,[status(thm)],[273]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) ) )
=> ? [C: $i] :
( ( C @ rreal )
& ( ( B @ ( A @ vf ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(160), 0), imp(cond(axiom(160), 0)))') ).
thf(362,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) ) )
=> ? [C: $i] :
( ( C @ rreal )
& ( ( B @ ( A @ vf ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ rpoint )
& ( A = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( B = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( C = D ) )
& ( C @ ( A @ ( B @ rR ) ) ) )
=> ( ( A @ ( C @ ( B @ rR ) ) )
& ( A != B )
& ( A != C )
& ~ ( C @ ( B @ ( A @ rR ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(81), 0), imp(cond(axiom(81), 0)))') ).
thf(649,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ rpoint )
& ( A = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( B = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( C = D ) )
& ( C @ ( A @ ( B @ rR ) ) ) )
=> ( ( A @ ( C @ ( B @ rR ) ) )
& ( A != B )
& ( A != C )
& ~ ( C @ ( B @ ( A @ rR ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ? [I: $i] :
( ( I @ rpoint )
& ( A = I ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( B = I ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( C = I ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( D = I ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( E = I ) )
& ? [I: $i] :
( ( I @ rline )
& ( F = I ) )
& ? [I: $i] :
( ( I @ rline )
& ( G = I ) )
& ? [I: $i] :
( ( I @ rline )
& ( H = I ) )
& ( F @ ( A @ ron ) )
& ( F @ ( B @ ron ) )
& ( G @ ( B @ ron ) )
& ( G @ ( C @ ron ) )
& ( H @ ( C @ ron ) )
& ( H @ ( D @ ron ) )
& ( B != C )
& ( G @ ( D @ ( A @ rS ) ) )
& ( vperp @ ( vperp @ vplus ) @ ( D @ ( C @ ( B @ vangle ) ) @ ( C @ ( B @ ( A @ vangle ) ) @ vplus ) @ rless ) ) )
=> ( ( G @ ( F @ rintersect ) )
& ( ( ( F @ ( E @ ron ) )
& ( G @ ( E @ ron ) ) )
=> ( G @ ( A @ ( E @ rS ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(196), 0), imp(cond(axiom(196), 0)))') ).
thf(1122,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ? [I: $i] :
( ( I @ rpoint )
& ( A = I ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( B = I ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( C = I ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( D = I ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( E = I ) )
& ? [I: $i] :
( ( I @ rline )
& ( F = I ) )
& ? [I: $i] :
( ( I @ rline )
& ( G = I ) )
& ? [I: $i] :
( ( I @ rline )
& ( H = I ) )
& ( F @ ( A @ ron ) )
& ( F @ ( B @ ron ) )
& ( G @ ( B @ ron ) )
& ( G @ ( C @ ron ) )
& ( H @ ( C @ ron ) )
& ( H @ ( D @ ron ) )
& ( B != C )
& ( G @ ( D @ ( A @ rS ) ) )
& ( vperp @ ( vperp @ vplus ) @ ( D @ ( C @ ( B @ vangle ) ) @ ( C @ ( B @ ( A @ vangle ) ) @ vplus ) @ rless ) ) )
=> ( ( G @ ( F @ rintersect ) )
& ( ( ( F @ ( E @ ron ) )
& ( G @ ( E @ ron ) ) )
=> ( G @ ( A @ ( E @ rS ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(2852,plain,
! [A: $i] :
( ( A != sk40 )
| ( v0 = vd1287 )
| ( A @ ( v0 @ rless ) )
| ( v0 @ ( A @ rless ) )
| ~ ( A @ rreal ) ),
inference(paramod_ordered,[status(thm)],[2081,852]) ).
thf(2853,plain,
( ( v0 = vd1287 )
| ( sk40 @ ( v0 @ rless ) )
| ( v0 @ ( sk40 @ rless ) )
| ~ ( sk40 @ rreal ) ),
inference(pattern_uni,[status(thm)],[2852:[bind(A,$thf( sk40 ))]]) ).
thf(9623,plain,
( ( v0 = vd1287 )
| ( vd1287 @ ( v0 @ rless ) )
| ( v0 @ ( vd1287 @ rless ) )
| ~ ( vd1287 @ rreal ) ),
inference(rewrite,[status(thm)],[2853,852]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( A != B )
& ( A != C )
& ( B != C )
& ( E @ rline )
& ( D @ ( A @ ron ) )
& ( D @ ( B @ ron ) )
& ( D @ ( C @ ron ) )
& ( D = E ) )
=> ( ( B @ ( A @ ( C @ rR ) ) )
| ( C @ ( B @ ( A @ rR ) ) )
| ( C @ ( A @ ( B @ rR ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(91), 0), imp(cond(axiom(91), 0)))') ).
thf(477,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( A != B )
& ( A != C )
& ( B != C )
& ( E @ rline )
& ( D @ ( A @ ron ) )
& ( D @ ( B @ ron ) )
& ( D @ ( C @ ron ) )
& ( D = E ) )
=> ( ( B @ ( A @ ( C @ rR ) ) )
| ( C @ ( B @ ( A @ rR ) ) )
| ( C @ ( A @ ( B @ rR ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rcircle )
& ( A = B )
& ( D @ rline )
& ( C = D )
& ( A @ ( C @ rintersect ) ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( C @ ( E @ ron ) )
& ( A @ ( E @ ron ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(57), 0), imp(cond(axiom(57), 0)))') ).
thf(758,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rcircle )
& ( A = B )
& ( D @ rline )
& ( C = D )
& ( A @ ( C @ rintersect ) ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( C @ ( E @ ron ) )
& ( A @ ( E @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( A != C )
& ( C = D ) )
=> ( D @ ( C @ ( B @ ( A @ vskolem1052 ) ) ) @ rpoint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(206), 0), 2)') ).
thf(345,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( A != C )
& ( C = D ) )
=> ( D @ ( C @ ( B @ ( A @ vskolem1052 ) ) ) @ rpoint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ rline )
& ( A = B )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( D = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( E = F ) )
& ( A @ ( C @ ron ) )
& ( A @ ( D @ ron ) )
& ( D @ ( C @ ( E @ rR ) ) ) )
=> ? [F: $i] :
( ( F @ rpoint )
& ( D @ ( C @ ( F @ rR ) ) )
& ( F != E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(25), 0), imp(cond(axiom(25), 0)))') ).
thf(726,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ rline )
& ( A = B )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( D = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( E = F ) )
& ( A @ ( C @ ron ) )
& ( A @ ( D @ ron ) )
& ( D @ ( C @ ( E @ rR ) ) ) )
=> ? [F: $i] :
( ( F @ rpoint )
& ( D @ ( C @ ( F @ rR ) ) )
& ( F != E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rcircle )
& ( A = B )
& ? [E: $i] :
( ( E @ rpoint )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( D = E ) )
& ( A @ ( C @ ron ) )
& ( A @ ( D @ ron ) ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( A @ ( E @ ron ) )
& ( E != C )
& ( E != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(45), 0), imp(cond(axiom(45), 0)))') ).
thf(621,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rcircle )
& ( A = B )
& ? [E: $i] :
( ( E @ rpoint )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( D = E ) )
& ( A @ ( C @ ron ) )
& ( A @ ( D @ ron ) ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( A @ ( E @ ron ) )
& ( E != C )
& ( E != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(7481,plain,
( ( ( vd1295 @ sk45 @ ( vd1295 @ sk45 @ vf ) )
!= ( vd1302 @ ( vd1287 @ vf ) ) )
| ( vd1299 != vd1287 )
| ( v0 != v0 ) ),
inference(paramod_ordered,[status(thm)],[5113,5314]) ).
thf(7482,plain,
( ( ( vd1295 @ sk45 @ ( vd1295 @ sk45 @ vf ) )
!= ( vd1302 @ ( vd1287 @ vf ) ) )
| ( vd1299 != vd1287 ) ),
inference(simp,[status(thm)],[7481]) ).
thf(7551,plain,
( ( ( vd1295 @ sk45 )
!= vd1302 )
| ( ( vd1295 @ sk45 )
!= vd1287 )
| ( vd1299 != vd1287 ) ),
inference(simp,[status(thm)],[7482]) ).
thf(7104,plain,
( ( ( vd1295 @ sk45 @ ( vd1295 @ sk45 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( vd1302 != vd1299 )
| ( v0 != v0 ) ),
inference(paramod_ordered,[status(thm)],[5113,4758]) ).
thf(7105,plain,
( ( ( vd1295 @ sk45 @ ( vd1295 @ sk45 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( vd1302 != vd1299 ) ),
inference(simp,[status(thm)],[7104]) ).
thf(7186,plain,
( ( ( vd1295 @ sk45 )
!= vd1299 )
| ( ( vd1295 @ sk45 )
!= vd1287 )
| ( vd1302 != vd1299 ) ),
inference(simp,[status(thm)],[7105]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ( D @ ( C @ rcenter ) )
& ( E @ ( C @ rcenter ) )
& ( D @ ( A @ ron ) )
& ( E @ ( B @ ron ) )
& ( ( A @ ( C @ vf ) )
= ( B @ ( C @ vf ) ) ) )
=> ( D = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(182), 0), imp(cond(axiom(182), 0)))') ).
thf(1022,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ( D @ ( C @ rcenter ) )
& ( E @ ( C @ rcenter ) )
& ( D @ ( A @ ron ) )
& ( E @ ( B @ ron ) )
& ( ( A @ ( C @ vf ) )
= ( B @ ( C @ vf ) ) ) )
=> ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( F @ rreal )
& ( E = F )
& ( C @ ( A @ rless ) )
& ( E @ ( C @ rless ) ) )
=> ( E @ ( A @ rless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(151), 0), imp(cond(axiom(151), 0)))') ).
thf(151,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( F @ rreal )
& ( E = F )
& ( C @ ( A @ rless ) )
& ( E @ ( C @ rless ) ) )
=> ( E @ ( A @ rless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(152,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( F @ rreal )
& ( E = F ) )
& ( C @ ( A @ rless ) )
& ( E @ ( C @ rless ) ) )
=> ( E @ ( A @ rless ) ) ),
inference(miniscope,[status(thm)],[151]) ).
thf(153,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ rless ) )
| ~ ( B @ rreal )
| ( A != B )
| ~ ( D @ rreal )
| ( C != D )
| ~ ( F @ rreal )
| ( E != F )
| ~ ( C @ ( A @ rless ) )
| ~ ( E @ ( C @ rless ) ) ),
inference(cnf,[status(esa)],[152]) ).
thf(154,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ rless ) )
| ~ ( B @ rreal )
| ~ ( D @ rreal )
| ~ ( F @ rreal )
| ~ ( C @ ( A @ rless ) )
| ~ ( E @ ( C @ rless ) )
| ( A != B )
| ( C != D )
| ( E != F ) ),
inference(lifteq,[status(thm)],[153]) ).
thf(155,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ rless ) )
| ~ ( A @ rreal )
| ~ ( B @ rreal )
| ~ ( C @ rreal )
| ~ ( B @ ( A @ rless ) )
| ~ ( C @ ( B @ rless ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( H @ rpoint )
& ( G = H )
& ( A != C )
& ( E != G )
& ( C @ ( A @ vf ) @ ( G @ ( E @ vf ) @ rless ) ) )
=> ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ vskolem1120 ) ) ) ) ) ) ) @ rpoint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(238), 0), 2)') ).
thf(330,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( H @ rpoint )
& ( G = H )
& ( A != C )
& ( E != G )
& ( C @ ( A @ vf ) @ ( G @ ( E @ vf ) @ rless ) ) )
=> ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ vskolem1120 ) ) ) ) ) ) ) @ rpoint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rline )
& ( A = B )
& ( D @ rline )
& ( C = D )
& ( C @ ( A @ rintersect ) ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( A @ ( E @ ron ) )
& ( C @ ( E @ ron ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(55), 0), imp(cond(axiom(55), 0)))') ).
thf(700,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rline )
& ( A = B )
& ( D @ rline )
& ( C = D )
& ( C @ ( A @ rintersect ) ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( A @ ( E @ ron ) )
& ( C @ ( E @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rcircle )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rcircle )
& ( B = C ) )
& ( B @ ( A @ rintersect ) ) )
=> ? [C: $i,D: $i] :
( ( C @ rpoint )
& ( A @ ( C @ ron ) )
& ( B @ ( C @ ron ) )
& ( D @ rpoint )
& ( A @ ( D @ ron ) )
& ( B @ ( D @ ron ) )
& ( C != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(67), 0), imp(cond(axiom(67), 0)))') ).
thf(983,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rcircle )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rcircle )
& ( B = C ) )
& ( B @ ( A @ rintersect ) ) )
=> ? [C: $i,D: $i] :
( ( C @ rpoint )
& ( A @ ( C @ ron ) )
& ( B @ ( C @ ron ) )
& ( D @ rpoint )
& ( A @ ( D @ ron ) )
& ( B @ ( D @ ron ) )
& ( C != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ rpoint )
& ( A = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( B = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( C = D ) ) )
=> ( ( ( C @ ( B @ ( A @ vg ) ) )
= ( B @ ( A @ ( C @ vg ) ) ) )
& ( ( C @ ( B @ ( A @ vg ) ) )
= ( B @ ( C @ ( A @ vg ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(176), 0), imp(cond(axiom(176), 0)))') ).
thf(1044,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ rpoint )
& ( A = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( B = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( C = D ) ) )
=> ( ( ( C @ ( B @ ( A @ vg ) ) )
= ( B @ ( A @ ( C @ vg ) ) ) )
& ( ( C @ ( B @ ( A @ vg ) ) )
= ( B @ ( C @ ( A @ vg ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rline )
& ( A = B )
& ( D @ rpoint )
& ~ ( A @ ( C @ ron ) )
& ( C = D ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ~ ( A @ ( C @ ( E @ rS ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(39), 0), imp(cond(axiom(39), 0)))') ).
thf(1066,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rline )
& ( A = B )
& ( D @ rpoint )
& ~ ( A @ ( C @ ron ) )
& ( C = D ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ~ ( A @ ( C @ ( E @ rS ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rcenter ) )
=> ? [C: $i,D: $i] :
( ( C @ rpoint )
& ( A = C )
& ( D @ rcircle )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(1), 0), imp(cond(axiom(1), 0)))') ).
thf(780,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rcenter ) )
=> ? [C: $i,D: $i] :
( ( C @ rpoint )
& ( A = C )
& ( D @ rcircle )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rcircle )
& ( A = B )
& ( D @ rcircle )
& ( C = D )
& ( C @ ( A @ rintersect ) ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( A @ ( E @ ron ) )
& ( C @ ( E @ ron ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(65), 0), imp(cond(axiom(65), 0)))') ).
thf(455,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rcircle )
& ( A = B )
& ( D @ rcircle )
& ( C = D )
& ( C @ ( A @ rintersect ) ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( A @ ( E @ ron ) )
& ( C @ ( E @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk3 ) ) @ rpoint )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(cnfConj,[status(thm)],[212]) ).
thf(222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk3 ) ) @ rpoint )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[217]) ).
thf(223,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk3 ) ) @ rpoint )
| ~ ( C @ ( B @ ( A @ vtriangle ) ) @ rtriangle ) ),
inference(simp,[status(thm)],[222]) ).
thf(1978,plain,
( ( ( vd1288 @ ( vd1287 @ vf ) )
!= ( vd1302 @ ( vd1287 @ vf ) ) )
| ( vd1289 @ ( vd1287 @ vf ) @ ( vd1299 @ ( vd1287 @ vf ) @ rless ) ) ),
inference(paramod_ordered,[status(thm)],[849,344]) ).
thf(2013,plain,
( ( vd1288 != vd1302 )
| ( vd1287 != vd1287 )
| ( vd1289 @ ( vd1287 @ vf ) @ ( vd1299 @ ( vd1287 @ vf ) @ rless ) ) ),
inference(simp,[status(thm)],[1978]) ).
thf(2022,plain,
( ( vd1288 != vd1302 )
| ( vd1289 @ ( vd1287 @ vf ) @ ( vd1299 @ ( vd1287 @ vf ) @ rless ) ) ),
inference(simp,[status(thm)],[2013]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( A != B )
& ( A != C )
& ( B != C )
& ? [F: $i] :
( ( F @ rline )
& ( D = F ) )
& ? [F: $i] :
( ( F @ rline )
& ( E = F ) )
& ( D != E )
& ( E @ ( A @ ron ) )
& ( E @ ( C @ ron ) )
& ~ ( D @ ( C @ ( A @ rS ) ) )
& ( E @ ( B @ ron ) )
& ( D @ ( B @ ron ) ) )
=> ( C @ ( A @ ( B @ rR ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(111), 0), imp(cond(axiom(111), 0)))') ).
thf(521,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( A != B )
& ( A != C )
& ( B != C )
& ? [F: $i] :
( ( F @ rline )
& ( D = F ) )
& ? [F: $i] :
( ( F @ rline )
& ( E = F ) )
& ( D != E )
& ( E @ ( A @ ron ) )
& ( E @ ( C @ ron ) )
& ~ ( D @ ( C @ ( A @ rS ) ) )
& ( E @ ( B @ ron ) )
& ( D @ ( B @ ron ) ) )
=> ( C @ ( A @ ( B @ rR ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(265,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ vf ) )
= ( A @ ( B @ vf ) ) )
| ~ ( D @ rpoint )
| ( A != D )
| ~ ( C @ rpoint )
| ( B != C ) ),
inference(cnf,[status(esa)],[264]) ).
thf(266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ rpoint )
| ~ ( C @ rpoint )
| ( ( B @ ( A @ vf ) )
= ( A @ ( B @ vf ) ) )
| ( A != D )
| ( B != C ) ),
inference(lifteq,[status(thm)],[265]) ).
thf(267,plain,
! [B: $i,A: $i] :
( ~ ( B @ rpoint )
| ~ ( A @ rpoint )
| ( ( A @ ( B @ vf ) )
= ( B @ ( A @ vf ) ) ) ),
inference(simp,[status(thm)],[266]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( C @ ( A @ ( B @ rR ) ) )
& ( D @ ( A @ ron ) )
& ( D @ ( C @ ron ) )
& ( D = E ) )
=> ( D @ ( B @ ron ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(85), 0), imp(cond(axiom(85), 0)))') ).
thf(1102,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( C @ ( A @ ( B @ rR ) ) )
& ( D @ ( A @ ron ) )
& ( D @ ( C @ ron ) )
& ( D = E ) )
=> ( D @ ( B @ ron ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rcircle )
& ( A = B )
& ( D @ rline )
& ( C = D )
& ( A @ ( C @ rintersect ) ) )
=> ? [E: $i,F: $i] :
( ( E @ rpoint )
& ( C @ ( E @ ron ) )
& ( A @ ( E @ ron ) )
& ( F @ rpoint )
& ( C @ ( F @ ron ) )
& ( A @ ( F @ ron ) )
& ( E != F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(59), 0), imp(cond(axiom(59), 0)))') ).
thf(431,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rcircle )
& ( A = B )
& ( D @ rline )
& ( C = D )
& ( A @ ( C @ rintersect ) ) )
=> ? [E: $i,F: $i] :
( ( E @ rpoint )
& ( C @ ( E @ ron ) )
& ( A @ ( E @ ron ) )
& ( F @ rpoint )
& ( C @ ( F @ ron ) )
& ( A @ ( F @ ron ) )
& ( E != F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( C @ ( A @ rless ) ) )
=> ( ( A = C )
| ~ ( A @ ( C @ rless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(147), 0), imp(cond(axiom(147), 0)))') ).
thf(167,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( C @ ( A @ rless ) ) )
=> ( ( A = C )
| ~ ( A @ ( C @ rless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ rpoint )
& ( A = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( B = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( C = D ) ) )
=> ? [D: $i] :
( ( D @ rreal )
& ( ( C @ ( B @ ( A @ vg ) ) )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(198), 0), imp(cond(axiom(198), 0)))') ).
thf(675,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ rpoint )
& ( A = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( B = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( C = D ) ) )
=> ? [D: $i] :
( ( D @ rreal )
& ( ( C @ ( B @ ( A @ vg ) ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rline )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( A @ ( C @ ron ) ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( A @ ( E @ ron ) )
& ( E != C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(17), 0), imp(cond(axiom(17), 0)))') ).
thf(663,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rline )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( A @ ( C @ ron ) ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( A @ ( E @ ron ) )
& ( E != C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rline )
& ( A = B )
& ( D @ rpoint )
& ~ ( A @ ( C @ ron ) )
& ( F @ rpoint )
& ( A @ ( C @ ( E @ rS ) ) )
& ( H @ rpoint )
& ( A @ ( C @ ( G @ rS ) ) )
& ( G = H )
& ( E = F )
& ( C = D ) )
=> ? [I: $i] :
( ( I @ rpoint )
& ( A @ ( C @ ( I @ rS ) ) )
& ( I != C )
& ( I != E )
& ( I != G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(37), 0), imp(cond(axiom(37), 0)))') ).
thf(374,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rline )
& ( A = B )
& ( D @ rpoint )
& ~ ( A @ ( C @ ron ) )
& ( F @ rpoint )
& ( A @ ( C @ ( E @ rS ) ) )
& ( H @ rpoint )
& ( A @ ( C @ ( G @ rS ) ) )
& ( G = H )
& ( E = F )
& ( C = D ) )
=> ? [I: $i] :
( ( I @ rpoint )
& ( A @ ( C @ ( I @ rS ) ) )
& ( I != C )
& ( I != E )
& ( I != G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(28740,plain,
( ( ( vd14 @ ( vd14 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( vd14 != vd1302 )
| ( vd14 != vd1287 )
| ( v0 != v0 ) ),
inference(paramod_ordered,[status(thm)],[5153,7010]) ).
thf(28741,plain,
( ( ( vd14 @ ( vd14 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( vd14 != vd1302 )
| ( vd14 != vd1287 ) ),
inference(simp,[status(thm)],[28740]) ).
thf(28867,plain,
( ( vd14 != vd1299 )
| ( vd14 != vd1287 )
| ( vd14 != vd1302 )
| ( vd14 != vd1287 ) ),
inference(simp,[status(thm)],[28741]) ).
thf(28919,plain,
( ( vd14 != vd1299 )
| ( vd14 != vd1302 )
| ( vd14 != vd1287 ) ),
inference(simp,[status(thm)],[28867]) ).
thf(2783,plain,
! [A: $i] :
( ( A != vd1295 )
| ( v0 @ rline )
| ( A @ ( v0 @ rless ) )
| ( v0 @ ( A @ rless ) )
| ~ ( A @ rreal ) ),
inference(paramod_ordered,[status(thm)],[2081,166]) ).
thf(2784,plain,
( ( v0 @ rline )
| ( vd1295 @ ( v0 @ rless ) )
| ( v0 @ ( vd1295 @ rless ) )
| ~ ( vd1295 @ rreal ) ),
inference(pattern_uni,[status(thm)],[2783:[bind(A,$thf( vd1295 ))]]) ).
thf(203,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ sk2 ) ) ) @ rpoint )
| ~ ( B @ rline )
| ( A != B )
| ~ ( F @ rpoint )
| ( C != F )
| ~ ( E @ rpoint )
| ( D != E )
| ~ ( A @ ( C @ ron ) )
| ~ ( A @ ( D @ ron ) )
| ( C = D ) )
& ( ( D @ ( C @ ( A @ ( B @ ( C @ ( D @ sk2 ) ) ) @ rR ) ) )
| ~ ( B @ rline )
| ( A != B )
| ~ ( F @ rpoint )
| ( C != F )
| ~ ( E @ rpoint )
| ( D != E )
| ~ ( A @ ( C @ ron ) )
| ~ ( A @ ( D @ ron ) )
| ( C = D ) ) ),
inference(cnf,[status(esa)],[202]) ).
thf(205,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ sk2 ) ) ) @ rpoint )
| ~ ( B @ rline )
| ( A != B )
| ~ ( F @ rpoint )
| ( C != F )
| ~ ( E @ rpoint )
| ( D != E )
| ~ ( A @ ( C @ ron ) )
| ~ ( A @ ( D @ ron ) )
| ( C = D ) ),
inference(cnfConj,[status(thm)],[203]) ).
thf(208,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ sk2 ) ) ) @ rpoint )
| ~ ( B @ rline )
| ~ ( F @ rpoint )
| ~ ( E @ rpoint )
| ~ ( A @ ( C @ ron ) )
| ~ ( A @ ( D @ ron ) )
| ( A != B )
| ( C != F )
| ( D != E )
| ( C = D ) ),
inference(lifteq,[status(thm)],[205]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ sk2 ) ) ) @ rpoint )
| ~ ( A @ rline )
| ~ ( C @ rpoint )
| ~ ( B @ rpoint )
| ~ ( A @ ( C @ ron ) )
| ~ ( A @ ( B @ ron ) )
| ( C = B ) ),
inference(simp,[status(thm)],[208]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ rpoint )
& ( A = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( B = G ) )
& ( D @ rline )
& ~ ( C @ ( B @ ( A @ rS ) ) )
& ( F @ rline )
& ( E @ ( A @ ron ) )
& ( E @ ( B @ ron ) )
& ( E = F )
& ( C = D ) )
=> ( E @ ( C @ rintersect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(127), 0), imp(cond(axiom(127), 0)))') ).
thf(487,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ rpoint )
& ( A = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( B = G ) )
& ( D @ rline )
& ~ ( C @ ( B @ ( A @ rS ) ) )
& ( F @ rline )
& ( E @ ( A @ ron ) )
& ( E @ ( B @ ron ) )
& ( E = F )
& ( C = D ) )
=> ( E @ ( C @ rintersect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rcircle )
& ( C = D )
& ( F @ rline )
& ( E = F )
& ( C @ ( A @ rinside ) )
& ( E @ ( A @ ron ) ) )
=> ( C @ ( E @ rintersect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(131), 0), imp(cond(axiom(131), 0)))') ).
thf(712,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rcircle )
& ( C = D )
& ( F @ rline )
& ( E = F )
& ( C @ ( A @ rinside ) )
& ( E @ ( A @ ron ) ) )
=> ( C @ ( E @ rintersect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rcircle )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( A @ ( C @ ron ) ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( A @ ( E @ ron ) )
& ( E != C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(43), 0), imp(cond(axiom(43), 0)))') ).
thf(954,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rcircle )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( A @ ( C @ ron ) ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( A @ ( E @ ron ) )
& ( E != C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(7456,plain,
( ( ( vd1297 @ sk45 @ ( vd1297 @ sk45 @ vf ) )
!= ( vd1302 @ ( vd1287 @ vf ) ) )
| ( vd1299 != vd1287 )
| ( v0 != v0 ) ),
inference(paramod_ordered,[status(thm)],[5116,5314]) ).
thf(7457,plain,
( ( ( vd1297 @ sk45 @ ( vd1297 @ sk45 @ vf ) )
!= ( vd1302 @ ( vd1287 @ vf ) ) )
| ( vd1299 != vd1287 ) ),
inference(simp,[status(thm)],[7456]) ).
thf(7554,plain,
( ( ( vd1297 @ sk45 )
!= vd1302 )
| ( ( vd1297 @ sk45 )
!= vd1287 )
| ( vd1299 != vd1287 ) ),
inference(simp,[status(thm)],[7457]) ).
thf(148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ rcircle )
| ( A != B )
| ~ ( A @ ( C @ rcenter ) )
| ~ ( A @ ( D @ rcenter ) ) ),
inference(cnf,[status(esa)],[147]) ).
thf(149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ rcircle )
| ~ ( A @ ( C @ rcenter ) )
| ~ ( A @ ( D @ rcenter ) )
| ( C = D )
| ( A != B ) ),
inference(lifteq,[status(thm)],[148]) ).
thf(150,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ rcircle )
| ~ ( A @ ( B @ rcenter ) )
| ~ ( A @ ( C @ rcenter ) )
| ( B = C ) ),
inference(simp,[status(thm)],[149]) ).
thf(11560,plain,
! [A: $i] :
( ( ( vd1299 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[10473,201]) ).
thf(11561,plain,
! [A: $i] :
( ( ( vd1299 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[11560]) ).
thf(11562,plain,
( ( vd1299 @ sk50 @ sk50 @ ( vd1299 @ sk50 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[11561:[bind(A,$thf( vd1299 @ sk50 @ sk50 ))]]) ).
thf(257,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ vangle ) ) )
= ( C @ ( A @ ( D @ vangle ) ) @ ( D @ ( A @ ( B @ vangle ) ) @ vplus ) ) )
| ~ ( F @ ( D @ ( B @ rS ) ) )
| ~ ( E @ ( D @ ( C @ rS ) ) )
| ~ ( L @ rpoint )
| ( A != L )
| ~ ( K @ rpoint )
| ( B != K )
| ~ ( J @ rpoint )
| ( C != J )
| ~ ( I @ rpoint )
| ( D != I )
| ~ ( H @ rline )
| ( E != H )
| ~ ( G @ rline )
| ( F != G )
| ~ ( E @ ( A @ ron ) )
| ~ ( F @ ( A @ ron ) )
| ~ ( E @ ( B @ ron ) )
| ~ ( F @ ( C @ ron ) )
| ( A = B )
| ( A = C )
| ( E @ ( D @ ron ) )
| ( F @ ( D @ ron ) )
| ( E = F ) ),
inference(cnfConj,[status(thm)],[254]) ).
thf(262,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( B @ rS ) ) )
| ~ ( E @ ( D @ ( C @ rS ) ) )
| ~ ( L @ rpoint )
| ~ ( K @ rpoint )
| ~ ( J @ rpoint )
| ~ ( I @ rpoint )
| ~ ( H @ rline )
| ~ ( G @ rline )
| ~ ( E @ ( A @ ron ) )
| ~ ( F @ ( A @ ron ) )
| ~ ( E @ ( B @ ron ) )
| ~ ( F @ ( C @ ron ) )
| ( E @ ( D @ ron ) )
| ( F @ ( D @ ron ) )
| ( ( C @ ( A @ ( B @ vangle ) ) )
= ( C @ ( A @ ( D @ vangle ) ) @ ( D @ ( A @ ( B @ vangle ) ) @ vplus ) ) )
| ( A != L )
| ( B != K )
| ( C != J )
| ( D != I )
| ( E != H )
| ( F != G )
| ( A = B )
| ( A = C )
| ( E = F ) ),
inference(lifteq,[status(thm)],[257]) ).
thf(263,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( E @ rS ) ) )
| ~ ( B @ ( C @ ( D @ rS ) ) )
| ~ ( F @ rpoint )
| ~ ( E @ rpoint )
| ~ ( D @ rpoint )
| ~ ( C @ rpoint )
| ~ ( B @ rline )
| ~ ( A @ rline )
| ~ ( B @ ( F @ ron ) )
| ~ ( A @ ( F @ ron ) )
| ~ ( B @ ( E @ ron ) )
| ~ ( A @ ( D @ ron ) )
| ( B @ ( C @ ron ) )
| ( A @ ( C @ ron ) )
| ( ( D @ ( F @ ( E @ vangle ) ) )
= ( D @ ( F @ ( C @ vangle ) ) @ ( C @ ( F @ ( E @ vangle ) ) @ vplus ) ) )
| ( F = E )
| ( F = D )
| ( B = A ) ),
inference(simp,[status(thm)],[262]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ? [I: $i] :
( ( I @ rline )
& ( A = I ) )
& ? [I: $i] :
( ( I @ rline )
& ( B = I ) )
& ? [I: $i] :
( ( I @ rline )
& ( C = I ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( D = I ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( E = I ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( F = I ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( G = I ) )
& ( A @ ( D @ ron ) )
& ( B @ ( D @ ron ) )
& ( C @ ( D @ ron ) )
& ( A @ ( E @ ron ) )
& ( B @ ( F @ ron ) )
& ( C @ ( G @ ron ) )
& ( A @ ( G @ ( F @ rS ) ) )
& ( C @ ( F @ ( E @ rS ) ) )
& ( B @ ( H @ ( G @ rS ) ) )
& ( C @ ( H @ ( F @ rS ) ) ) )
=> ( A @ ( H @ ( F @ rS ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(117), 0), imp(cond(axiom(117), 0)))') ).
thf(1098,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ? [I: $i] :
( ( I @ rline )
& ( A = I ) )
& ? [I: $i] :
( ( I @ rline )
& ( B = I ) )
& ? [I: $i] :
( ( I @ rline )
& ( C = I ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( D = I ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( E = I ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( F = I ) )
& ? [I: $i] :
( ( I @ rpoint )
& ( G = I ) )
& ( A @ ( D @ ron ) )
& ( B @ ( D @ ron ) )
& ( C @ ( D @ ron ) )
& ( A @ ( E @ ron ) )
& ( B @ ( F @ ron ) )
& ( C @ ( G @ ron ) )
& ( A @ ( G @ ( F @ rS ) ) )
& ( C @ ( F @ ( E @ rS ) ) )
& ( B @ ( H @ ( G @ rS ) ) )
& ( C @ ( H @ ( F @ rS ) ) ) )
=> ( A @ ( H @ ( F @ rS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(10818,plain,
! [A: $i] :
( ( ( vd1288 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[10272,201]) ).
thf(10819,plain,
! [A: $i] :
( ( ( vd1288 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[10818]) ).
thf(10820,plain,
( ( vd1288 @ sk50 @ ( vd1288 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[10819:[bind(A,$thf( vd1288 @ sk50 ))]]) ).
thf(196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ vf ) )
!= v0 )
| ~ ( D @ rpoint )
| ( A != D )
| ~ ( C @ rpoint )
| ( B != C ) ),
inference(cnfConj,[status(thm)],[195]) ).
thf(198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ rpoint )
| ~ ( C @ rpoint )
| ( A = B )
| ( ( B @ ( A @ vf ) )
!= v0 )
| ( A != D )
| ( B != C ) ),
inference(lifteq,[status(thm)],[196]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ~ ( B @ rpoint )
| ~ ( A @ rpoint )
| ( B = A )
| ( ( A @ ( B @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[198]) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) )
& ( A != B ) )
=> ! [C: $i,D: $i] :
( ( ( D @ rpoint )
& ( C != A )
& ( C != B )
& ( C = D ) )
=> ( B @ ( A @ ( D @ ( C @ vskolem1078 ) ) ) @ rpoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(219), 0), 1)') ).
thf(717,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) )
& ( A != B ) )
=> ! [C: $i,D: $i] :
( ( ( D @ rpoint )
& ( C != A )
& ( C != B )
& ( C = D ) )
=> ( B @ ( A @ ( D @ ( C @ vskolem1078 ) ) ) @ rpoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(6950,plain,
( ( ( vd14 @ ( vd14 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( vd1302 != vd1299 )
| ( v0 != v0 ) ),
inference(paramod_ordered,[status(thm)],[5153,4758]) ).
thf(6951,plain,
( ( ( vd14 @ ( vd14 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( vd1302 != vd1299 ) ),
inference(simp,[status(thm)],[6950]) ).
thf(7009,plain,
( ( vd14 != vd1299 )
| ( vd14 != vd1287 )
| ( vd1302 != vd1299 ) ),
inference(simp,[status(thm)],[6951]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( H @ rline )
& ( A = H ) )
& ? [H: $i] :
( ( H @ rline )
& ( B = H ) )
& ? [H: $i] :
( ( H @ rline )
& ( C = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( D = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( E = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( F = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( G = H ) )
& ( A @ ( D @ ron ) )
& ( B @ ( D @ ron ) )
& ( C @ ( D @ ron ) )
& ( A @ ( E @ ron ) )
& ( C @ ( F @ ron ) )
& ( C @ ( G @ ron ) )
& ( A @ ( G @ ( F @ rS ) ) )
& ( C @ ( F @ ( E @ rS ) ) ) )
=> ~ ( B @ ( G @ ( E @ rS ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(113), 0), imp(cond(axiom(113), 0)))') ).
thf(370,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( H @ rline )
& ( A = H ) )
& ? [H: $i] :
( ( H @ rline )
& ( B = H ) )
& ? [H: $i] :
( ( H @ rline )
& ( C = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( D = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( E = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( F = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( G = H ) )
& ( A @ ( D @ ron ) )
& ( B @ ( D @ ron ) )
& ( C @ ( D @ ron ) )
& ( A @ ( E @ ron ) )
& ( C @ ( F @ ron ) )
& ( C @ ( G @ ron ) )
& ( A @ ( G @ ( F @ rS ) ) )
& ( C @ ( F @ ( E @ rS ) ) ) )
=> ~ ( B @ ( G @ ( E @ rS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(41139,plain,
! [B: $i,A: $i] :
( ( B != vd1289 )
| ( A != vd1299 )
| ( B @ ( A @ sk6 ) @ ( A @ ron ) )
| ~ ( B @ rpoint )
| ~ ( A @ rpoint ) ),
inference(paramod_ordered,[status(thm)],[274,1799]) ).
thf(41140,plain,
! [A: $i] :
( ( A != vd1299 )
| ( vd1289 @ ( A @ sk6 ) @ ( A @ ron ) )
| ~ ( vd1289 @ rpoint )
| ~ ( A @ rpoint ) ),
inference(pattern_uni,[status(thm)],[41139:[bind(A,$thf( A )),bind(B,$thf( vd1289 ))]]) ).
thf(42771,plain,
( ( vd1289 @ ( vd1299 @ sk6 ) @ ( vd1299 @ ron ) )
| ~ ( vd1289 @ rpoint )
| ~ ( vd1299 @ rpoint ) ),
inference(simp,[status(thm)],[41140]) ).
thf(46507,plain,
( ( vd1289 @ ( vd1299 @ sk6 ) @ ( vd1299 @ ron ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[42771,1203,1178]) ).
thf(46508,plain,
vd1289 @ ( vd1299 @ sk6 ) @ ( vd1299 @ ron ),
inference(simp,[status(thm)],[46507]) ).
thf(10737,plain,
! [A: $i] :
( ( ( vd1287 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[10269,201]) ).
thf(10738,plain,
! [A: $i] :
( ( ( vd1287 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[10737]) ).
thf(10739,plain,
( ( vd1287 @ sk50 @ ( vd1287 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[10738:[bind(A,$thf( vd1287 @ sk50 ))]]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rline )
& ( A = B )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( E = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( F = G ) )
& ( A @ ( C @ ron ) )
& ( A @ ( D @ ron ) )
& ( A @ ( E @ ron ) )
& ( D @ ( C @ ( E @ rR ) ) )
& ( D @ ( C @ ( F @ rR ) ) ) )
=> ? [G: $i] :
( ( G @ rpoint )
& ( D @ ( C @ ( G @ rR ) ) )
& ( G != E )
& ( G != F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(27), 0), imp(cond(axiom(27), 0)))') ).
thf(744,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rline )
& ( A = B )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( E = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( F = G ) )
& ( A @ ( C @ ron ) )
& ( A @ ( D @ ron ) )
& ( A @ ( E @ ron ) )
& ( D @ ( C @ ( E @ rR ) ) )
& ( D @ ( C @ ( F @ rR ) ) ) )
=> ? [G: $i] :
( ( G @ rpoint )
& ( D @ ( C @ ( G @ rR ) ) )
& ( G != E )
& ( G != F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(27447,plain,
! [A: $i] :
( ( ( vd1302 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18073,1034]) ).
thf(27448,plain,
! [A: $i] :
( ( ( vd1302 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[27447]) ).
thf(27449,plain,
vd1302 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[27448:[bind(A,$thf( vd1302 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ( D @ ( C @ rcenter ) )
& ( D @ ( B @ ron ) ) )
=> ( ( B @ ( C @ vf ) @ ( A @ ( C @ vf ) @ rless ) )
<=> ( D @ ( A @ rinside ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(186), 0), imp(cond(axiom(186), 0)))') ).
thf(1052,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ( D @ ( C @ rcenter ) )
& ( D @ ( B @ ron ) ) )
=> ( ( ( D @ ( A @ rinside ) )
=> ( B @ ( C @ vf ) @ ( A @ ( C @ vf ) @ rless ) ) )
& ( ( B @ ( C @ vf ) @ ( A @ ( C @ vf ) @ rless ) )
=> ( D @ ( A @ rinside ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ rpoint )
& ( A = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( B = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ( F @ rline )
& ( E = F )
& ( B @ ( A @ ( C @ rR ) ) )
& ~ ( E @ ( D @ ron ) ) )
=> ( ( ( D @ ( C @ ( A @ vangle ) ) )
= ( B @ ( C @ ( D @ vangle ) ) ) )
<=> ( ( D @ ( C @ ( A @ vangle ) ) )
= vperp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(192), 0), imp(cond(axiom(192), 0)))') ).
thf(612,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ rpoint )
& ( A = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( B = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ( F @ rline )
& ( E = F )
& ( B @ ( A @ ( C @ rR ) ) )
& ~ ( E @ ( D @ ron ) ) )
=> ( ( ( ( D @ ( C @ ( A @ vangle ) ) )
= vperp )
=> ( ( D @ ( C @ ( A @ vangle ) ) )
= ( B @ ( C @ ( D @ vangle ) ) ) ) )
& ( ( ( D @ ( C @ ( A @ vangle ) ) )
= ( B @ ( C @ ( D @ vangle ) ) ) )
=> ( ( D @ ( C @ ( A @ vangle ) ) )
= vperp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(5145,plain,
! [A: $i] :
( ( ( vd1289 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[1203,201]) ).
thf(5146,plain,
! [A: $i] :
( ( ( vd1289 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[5145]) ).
thf(5147,plain,
( ( vd1289 @ ( vd1289 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[5146:[bind(A,$thf( vd1289 ))]]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rline )
& ( A = B )
& ( D @ rpoint )
& ~ ( A @ ( C @ ron ) )
& ( C = D ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( A @ ( C @ ( E @ rS ) ) )
& ( E != C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(33), 0), imp(cond(axiom(33), 0)))') ).
thf(1141,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rline )
& ( A = B )
& ( D @ rpoint )
& ~ ( A @ ( C @ ron ) )
& ( C = D ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( A @ ( C @ ( E @ rS ) ) )
& ( E != C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(1948,plain,
! [A: $i] :
( ( ( vd1288 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ~ ( A @ rpoint )
| ~ ( vd1302 @ ( vd1287 @ ( A @ rR ) ) )
| ( ( vd1289 @ ( vd1287 @ vf ) )
!= ( A @ ( vd1287 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[849,131]) ).
thf(1956,plain,
! [A: $i] :
( ( vd1288 != vd1299 )
| ( vd1287 != vd1287 )
| ~ ( A @ rpoint )
| ~ ( vd1302 @ ( vd1287 @ ( A @ rR ) ) )
| ( vd1289 != A )
| ( vd1287 != vd1287 ) ),
inference(simp,[status(thm)],[1948]) ).
thf(1967,plain,
( ( vd1288 != vd1299 )
| ~ ( vd1289 @ rpoint )
| ~ ( vd1302 @ ( vd1287 @ ( vd1289 @ rR ) ) ) ),
inference(simp,[status(thm)],[1956]) ).
thf(4509,plain,
( ( vd1288 != vd1299 )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[1967,1203,740]) ).
thf(4510,plain,
vd1288 != vd1299,
inference(simp,[status(thm)],[4509]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rline )
& ( A = B )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ( A @ ( C @ ron ) )
& ( A @ ( D @ ron ) )
& ( F @ rpoint )
& ( E @ ( C @ ( D @ rR ) ) )
& ( E = F ) )
=> ? [G: $i] :
( ( G @ rpoint )
& ( G @ ( C @ ( D @ rR ) ) )
& ( G != E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(31), 0), imp(cond(axiom(31), 0)))') ).
thf(600,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rline )
& ( A = B )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ( A @ ( C @ ron ) )
& ( A @ ( D @ ron ) )
& ( F @ rpoint )
& ( E @ ( C @ ( D @ rR ) ) )
& ( E = F ) )
=> ? [G: $i] :
( ( G @ rpoint )
& ( G @ ( C @ ( D @ rR ) ) )
& ( G != E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(105,axiom,
vd1295 @ ( vd1299 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(conjunct1(349), 0)') ).
thf(978,plain,
vd1295 @ ( vd1299 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(127,axiom,
vd1297 @ ( vd1302 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(conjunct2(349), 0)') ).
thf(1140,plain,
vd1297 @ ( vd1302 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( B @ ( C @ sk4 ) ) ) )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(cnfConj,[status(thm)],[212]) ).
thf(230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ rtriangle )
| ( ( A @ ( B @ ( C @ sk4 ) ) )
= B )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[219]) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ vtriangle ) ) @ rtriangle )
| ( ( A @ ( B @ ( C @ sk4 ) ) )
= B ) ),
inference(simp,[status(thm)],[230]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( H @ rcircle )
& ( A = H ) )
& ? [H: $i] :
( ( H @ rcircle )
& ( B = H ) )
& ( D @ rline )
& ( C = D )
& ( B @ ( A @ rintersect ) )
& ( A @ ( E @ rcenter ) )
& ( B @ ( F @ rcenter ) )
& ( C @ ( E @ ron ) )
& ( C @ ( F @ ron ) )
& ~ ( C @ ( G @ ron ) ) )
=> ? [H: $i] :
( ( H @ rpoint )
& ( A @ ( H @ ron ) )
& ( B @ ( H @ ron ) )
& ~ ( C @ ( G @ ( H @ rS ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(71), 0), imp(cond(axiom(71), 0)))') ).
thf(1084,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( H @ rcircle )
& ( A = H ) )
& ? [H: $i] :
( ( H @ rcircle )
& ( B = H ) )
& ( D @ rline )
& ( C = D )
& ( B @ ( A @ rintersect ) )
& ( A @ ( E @ rcenter ) )
& ( B @ ( F @ rcenter ) )
& ( C @ ( E @ ron ) )
& ( C @ ( F @ ron ) )
& ~ ( C @ ( G @ ron ) ) )
=> ? [H: $i] :
( ( H @ rpoint )
& ( A @ ( H @ ron ) )
& ( B @ ( H @ ron ) )
& ~ ( C @ ( G @ ( H @ rS ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(7002,plain,
( ( ( vd14 @ ( vd14 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( ( vd1302 @ ( vd1287 @ vf ) )
!= v0 )
| ( v0 != v0 ) ),
inference(paramod_ordered,[status(thm)],[5153,4631]) ).
thf(7003,plain,
( ( ( vd14 @ ( vd14 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( ( vd1302 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[7002]) ).
thf(7024,plain,
( ( vd14 != vd1299 )
| ( vd14 != vd1287 )
| ( ( vd1302 @ ( vd1287 @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[7003]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( H @ rpoint )
& ( G = H )
& ( A != C )
& ( E != G )
& ( C @ ( A @ vf ) @ ( G @ ( E @ vf ) @ rless ) ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ vskolem1120 ) ) ) ) ) ) ) @ ( A @ vf ) )
= ( G @ ( E @ vf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(238), 0), 0)') ).
thf(931,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( H @ rpoint )
& ( G = H )
& ( A != C )
& ( E != G )
& ( C @ ( A @ vf ) @ ( G @ ( E @ vf ) @ rless ) ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ vskolem1120 ) ) ) ) ) ) ) @ ( A @ vf ) )
= ( G @ ( E @ vf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( D = E )
& ( C @ ( A @ ( B @ rR ) ) )
& ( D @ ( A @ ron ) )
& ~ ( D @ ( B @ ron ) ) )
=> ( D @ ( C @ ( B @ rS ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(107), 0), imp(cond(axiom(107), 0)))') ).
thf(482,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( D = E )
& ( C @ ( A @ ( B @ rR ) ) )
& ( D @ ( A @ ron ) )
& ~ ( D @ ( B @ ron ) ) )
=> ( D @ ( C @ ( B @ rS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(22758,plain,
! [A: $i] :
( ( ( vd1299 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16978,1034]) ).
thf(22759,plain,
! [A: $i] :
( ( ( vd1299 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[22758]) ).
thf(22760,plain,
vd1299 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[22759:[bind(A,$thf( vd1299 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( H @ rline )
& ( G = H )
& ( A != C )
& ( A != E )
& ( G @ ( A @ ron ) )
& ( G @ ( C @ ron ) ) )
=> ( ( ( G @ ( E @ ron ) )
& ~ ( E @ ( C @ ( A @ rR ) ) ) )
<=> ( ( E @ ( A @ ( C @ vangle ) ) )
= v0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(188), 0), imp(cond(axiom(188), 0)))') ).
thf(1010,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( H @ rline )
& ( G = H )
& ( A != C )
& ( A != E )
& ( G @ ( A @ ron ) )
& ( G @ ( C @ ron ) ) )
=> ( ( ( ( E @ ( A @ ( C @ vangle ) ) )
= v0 )
=> ( ( G @ ( E @ ron ) )
& ~ ( E @ ( C @ ( A @ rR ) ) ) ) )
& ( ( ( G @ ( E @ ron ) )
& ~ ( E @ ( C @ ( A @ rR ) ) ) )
=> ( ( E @ ( A @ ( C @ vangle ) ) )
= v0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(2791,plain,
! [A: $i] :
( ( A != vd1289 )
| ( v0 @ rpoint )
| ( A @ ( v0 @ rless ) )
| ( v0 @ ( A @ rless ) )
| ~ ( A @ rreal ) ),
inference(paramod_ordered,[status(thm)],[2081,1203]) ).
thf(2792,plain,
( ( v0 @ rpoint )
| ( vd1289 @ ( v0 @ rless ) )
| ( v0 @ ( vd1289 @ rless ) )
| ~ ( vd1289 @ rreal ) ),
inference(pattern_uni,[status(thm)],[2791:[bind(A,$thf( vd1289 ))]]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( D = E ) )
& ( C @ ( A @ ( B @ rR ) ) )
& ( D @ ( B @ ( C @ rR ) ) ) )
=> ( D @ ( A @ ( B @ rR ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(89), 0), imp(cond(axiom(89), 0)))') ).
thf(813,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( D = E ) )
& ( C @ ( A @ ( B @ rR ) ) )
& ( D @ ( B @ ( C @ rR ) ) ) )
=> ( D @ ( A @ ( B @ rR ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(12064,plain,
! [A: $i] :
( ( ( vd1289 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[10994,201]) ).
thf(12065,plain,
! [A: $i] :
( ( ( vd1289 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[12064]) ).
thf(12066,plain,
( ( vd1289 @ sk50 @ sk50 @ ( vd1289 @ sk50 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[12065:[bind(A,$thf( vd1289 @ sk50 @ sk50 ))]]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ rinside ) )
| ~ ( B @ ( A @ rcenter ) ) ),
inference(cnf,[status(esa)],[157]) ).
thf(168,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D ) )
& ( C @ ( A @ rless ) ) )
=> ( ( A = C )
| ~ ( A @ ( C @ rless ) ) ) ),
inference(miniscope,[status(thm)],[167]) ).
thf(169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( A @ ( C @ rless ) )
| ~ ( B @ rreal )
| ( A != B )
| ~ ( D @ rreal )
| ( C != D )
| ~ ( C @ ( A @ rless ) ) ),
inference(cnf,[status(esa)],[168]) ).
thf(170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ rless ) )
| ~ ( B @ rreal )
| ~ ( D @ rreal )
| ~ ( C @ ( A @ rless ) )
| ( A = C )
| ( A != B )
| ( C != D ) ),
inference(lifteq,[status(thm)],[169]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ rless ) )
| ~ ( A @ rreal )
| ~ ( B @ rreal )
| ~ ( B @ ( A @ rless ) )
| ( A = B ) ),
inference(simp,[status(thm)],[170]) ).
thf(11778,plain,
! [A: $i] :
( ( ( vd1288 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[10831,201]) ).
thf(11779,plain,
! [A: $i] :
( ( ( vd1288 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[11778]) ).
thf(11780,plain,
( ( vd1288 @ sk50 @ sk50 @ ( vd1288 @ sk50 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[11779:[bind(A,$thf( vd1288 @ sk50 @ sk50 ))]]) ).
thf(204,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ ( B @ ( C @ ( D @ sk2 ) ) ) @ rR ) ) )
| ~ ( B @ rline )
| ( A != B )
| ~ ( F @ rpoint )
| ( C != F )
| ~ ( E @ rpoint )
| ( D != E )
| ~ ( A @ ( C @ ron ) )
| ~ ( A @ ( D @ ron ) )
| ( C = D ) ),
inference(cnfConj,[status(thm)],[203]) ).
thf(206,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ ( B @ ( C @ ( D @ sk2 ) ) ) @ rR ) ) )
| ~ ( B @ rline )
| ~ ( F @ rpoint )
| ~ ( E @ rpoint )
| ~ ( A @ ( C @ ron ) )
| ~ ( A @ ( D @ ron ) )
| ( A != B )
| ( C != F )
| ( D != E )
| ( C = D ) ),
inference(lifteq,[status(thm)],[204]) ).
thf(207,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( A @ ( C @ ( B @ sk2 ) ) ) @ rR ) ) )
| ~ ( A @ rline )
| ~ ( C @ rpoint )
| ~ ( B @ rpoint )
| ~ ( A @ ( C @ ron ) )
| ~ ( A @ ( B @ ron ) )
| ( C = B ) ),
inference(simp,[status(thm)],[206]) ).
thf(1659,plain,
( ~ ( vd1302 @ ( vd1287 @ ( vd1287 @ rR ) ) )
| ( vd1299 != vd1287 )
| ( vd1287 != vd1287 ) ),
inference(simp,[status(thm)],[1658]) ).
thf(1689,plain,
( ~ ( vd1302 @ ( vd1287 @ ( vd1287 @ rR ) ) )
| ( vd1299 != vd1287 ) ),
inference(simp,[status(thm)],[1659]) ).
thf(218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != C )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(cnfConj,[status(thm)],[212]) ).
thf(234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ rtriangle )
| ( A != C )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[218]) ).
thf(235,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( B @ vtriangle ) ) @ rtriangle ),
inference(simp,[status(thm)],[234]) ).
thf(243,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( D @ vg ) ) @ ( D @ ( C @ ( A @ vg ) ) @ vplus ) )
= ( B @ ( D @ ( A @ vg ) ) ) )
| ~ ( B @ ( A @ ( C @ rR ) ) )
| ~ ( J @ rpoint )
| ( A != J )
| ~ ( I @ rpoint )
| ( B != I )
| ~ ( H @ rpoint )
| ( C != H )
| ~ ( G @ rpoint )
| ( D != G )
| ( A = B )
| ( A = C )
| ( A = D )
| ( B = C )
| ( B = D )
| ( C = D )
| ~ ( F @ rline )
| ( E != F )
| ( E @ ( D @ ron ) ) ),
inference(cnfConj,[status(thm)],[242]) ).
thf(245,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ rR ) ) )
| ~ ( J @ rpoint )
| ~ ( I @ rpoint )
| ~ ( H @ rpoint )
| ~ ( G @ rpoint )
| ~ ( F @ rline )
| ( E @ ( D @ ron ) )
| ( ( B @ ( C @ ( D @ vg ) ) @ ( D @ ( C @ ( A @ vg ) ) @ vplus ) )
= ( B @ ( D @ ( A @ vg ) ) ) )
| ( A != J )
| ( B != I )
| ( C != H )
| ( D != G )
| ( A = B )
| ( A = C )
| ( A = D )
| ( B = C )
| ( B = D )
| ( C = D )
| ( E != F ) ),
inference(lifteq,[status(thm)],[243]) ).
thf(246,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( C @ rR ) ) )
| ~ ( E @ rpoint )
| ~ ( D @ rpoint )
| ~ ( C @ rpoint )
| ~ ( B @ rpoint )
| ~ ( A @ rline )
| ( A @ ( B @ ron ) )
| ( ( D @ ( C @ ( B @ vg ) ) @ ( B @ ( C @ ( E @ vg ) ) @ vplus ) )
= ( D @ ( B @ ( E @ vg ) ) ) )
| ( E = D )
| ( E = C )
| ( E = B )
| ( D = C )
| ( D = B )
| ( C = B ) ),
inference(simp,[status(thm)],[245]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rline )
& ( A = B )
& ? [E: $i] :
( ( E @ rpoint )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( D = E ) )
& ( A @ ( C @ ron ) )
& ( A @ ( D @ ron ) )
& ( C != D ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( E @ ( C @ ( D @ rR ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(29), 0), imp(cond(axiom(29), 0)))') ).
thf(854,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rline )
& ( A = B )
& ? [E: $i] :
( ( E @ rpoint )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( D = E ) )
& ( A @ ( C @ ron ) )
& ( A @ ( D @ ron ) )
& ( C != D ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( E @ ( C @ ( D @ rR ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ( C @ ( A @ ron ) )
& ( C @ ( B @ rinside ) )
& ( D @ ( A @ rinside ) )
& ( D @ ( B @ ron ) ) )
=> ( D @ ( C @ rintersect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(135), 0), imp(cond(axiom(135), 0)))') ).
thf(950,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ( C @ ( A @ ron ) )
& ( C @ ( B @ rinside ) )
& ( D @ ( A @ rinside ) )
& ( D @ ( B @ ron ) ) )
=> ( D @ ( C @ rintersect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(215,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != C )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(cnfConj,[status(thm)],[212]) ).
thf(238,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ rtriangle )
| ( B != C )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[215]) ).
thf(239,plain,
! [B: $i,A: $i] :
~ ( B @ ( B @ ( A @ vtriangle ) ) @ rtriangle ),
inference(simp,[status(thm)],[238]) ).
thf(5333,plain,
( ( ( vd1302 @ ( vd1287 @ vf ) )
!= ( vd1287 @ ( vd1287 @ vf ) ) )
| ( v0 @ ( vd1299 @ ( vd1287 @ vf ) @ rless ) ) ),
inference(paramod_ordered,[status(thm)],[5127,344]) ).
thf(5395,plain,
( ( vd1302 != vd1287 )
| ( vd1287 != vd1287 )
| ( v0 @ ( vd1299 @ ( vd1287 @ vf ) @ rless ) ) ),
inference(simp,[status(thm)],[5333]) ).
thf(5413,plain,
( ( vd1302 != vd1287 )
| ( v0 @ ( vd1299 @ ( vd1287 @ vf ) @ rless ) ) ),
inference(simp,[status(thm)],[5395]) ).
thf(37914,plain,
! [A: $i] :
( ( ( vd1295 @ sk45 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22204,1034]) ).
thf(37915,plain,
! [A: $i] :
( ( ( vd1295 @ sk45 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[37914]) ).
thf(37916,plain,
vd1295 @ sk45 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[37915:[bind(A,$thf( vd1295 @ sk45 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ rpoint )
& ( A = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( B = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ( A != B )
& ( A != C )
& ( B != C )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( E = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( F = G ) )
& ( ( B @ ( A @ vf ) )
= ( E @ ( D @ vf ) ) )
& ( ( C @ ( A @ vf ) )
= ( F @ ( D @ vf ) ) )
& ( ( C @ ( A @ ( B @ vangle ) ) )
= ( F @ ( D @ ( E @ vangle ) ) ) )
& ~ ? [G: $i] :
( ( G @ rline )
& ( G @ ( D @ ron ) )
& ( G @ ( E @ ron ) )
& ( G @ ( F @ ron ) ) ) )
=> ( ( C @ ( B @ ( A @ vangle ) ) )
= ( F @ ( E @ ( D @ vangle ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(264), 0), 1)') ).
thf(635,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ rpoint )
& ( A = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( B = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ( A != B )
& ( A != C )
& ( B != C )
& ? [G: $i] :
( ( G @ rpoint )
& ( D = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( E = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( F = G ) )
& ( ( B @ ( A @ vf ) )
= ( E @ ( D @ vf ) ) )
& ( ( C @ ( A @ vf ) )
= ( F @ ( D @ vf ) ) )
& ( ( C @ ( A @ ( B @ vangle ) ) )
= ( F @ ( D @ ( E @ vangle ) ) ) )
& ~ ? [G: $i] :
( ( G @ rline )
& ( G @ ( D @ ron ) )
& ( G @ ( E @ ron ) )
& ( G @ ( F @ ron ) ) ) )
=> ( ( C @ ( B @ ( A @ vangle ) ) )
= ( F @ ( E @ ( D @ vangle ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(116,axiom,
vd1297 @ ( vd1287 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(s1(plural(347)), 0)') ).
thf(1065,plain,
vd1297 @ ( vd1287 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(12173,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[11171,201]) ).
thf(12174,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[12173]) ).
thf(12175,plain,
( ( vd14 @ sk50 @ sk50 @ ( vd14 @ sk50 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[12174:[bind(A,$thf( vd14 @ sk50 @ sk50 ))]]) ).
thf(794,plain,
! [A: $i] :
( ? [B: $i] :
( ( B @ rcircle )
& ( A = B ) )
=> ? [B: $i] :
( ( B @ rpoint )
& ( A @ ( B @ ron ) ) ) ),
inference(miniscope,[status(thm)],[793]) ).
thf(795,plain,
! [B: $i,A: $i] :
( ( ( A @ sk37 @ rpoint )
| ~ ( B @ rcircle )
| ( A != B ) )
& ( ( A @ ( A @ sk37 @ ron ) )
| ~ ( B @ rcircle )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[794]) ).
thf(797,plain,
! [B: $i,A: $i] :
( ( A @ sk37 @ rpoint )
| ~ ( B @ rcircle )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[795]) ).
thf(800,plain,
! [B: $i,A: $i] :
( ( A @ sk37 @ rpoint )
| ~ ( B @ rcircle )
| ( A != B ) ),
inference(lifteq,[status(thm)],[797]) ).
thf(801,plain,
! [A: $i] :
( ( A @ sk37 @ rpoint )
| ~ ( A @ rcircle ) ),
inference(simp,[status(thm)],[800]) ).
thf(133,plain,
! [A: $i,B: $i,C: $i] :
( ? [D: $i,E: $i] :
( ? [F: $i] :
( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( F @ rreal )
& ( E = F ) )
& ( ( E @ ( A @ vplus ) )
= ( E @ ( C @ vplus ) ) ) )
=> ( A = C ) ),
inference(miniscope,[status(thm)],[132]) ).
thf(134,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( B @ rreal )
| ( A != B )
| ~ ( D @ rreal )
| ( C != D )
| ~ ( F @ rreal )
| ( E != F )
| ( ( E @ ( A @ vplus ) )
!= ( E @ ( C @ vplus ) ) ) ),
inference(cnf,[status(esa)],[133]) ).
thf(135,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ rreal )
| ~ ( D @ rreal )
| ~ ( F @ rreal )
| ( A = C )
| ( A != B )
| ( C != D )
| ( E != F )
| ( ( E @ ( A @ vplus ) )
!= ( E @ ( C @ vplus ) ) ) ),
inference(lifteq,[status(thm)],[134]) ).
thf(136,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ rreal )
| ~ ( B @ rreal )
| ~ ( C @ rreal )
| ( A = B )
| ( ( C @ ( A @ vplus ) )
!= ( C @ ( B @ vplus ) ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ? [E: $i] :
( ( E @ rcircle )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rcircle )
& ( D = E ) )
& ( ( C @ ( A @ rinside ) )
| ( C @ ( A @ ron ) ) )
& ( ( C @ ( B @ rinside ) )
| ( C @ ( B @ ron ) ) )
& ~ ? [E: $i] : ( E @ ( B @ ( A @ rS ) ) ) )
=> ? [E: $i] : ( C @ ( E @ rintersect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(129), 0), imp(cond(axiom(129), 0)))') ).
thf(506,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( E @ rpoint )
& ( A = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( B = E ) )
& ? [E: $i] :
( ( E @ rcircle )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rcircle )
& ( D = E ) )
& ( ( C @ ( A @ rinside ) )
| ( C @ ( A @ ron ) ) )
& ( ( C @ ( B @ rinside ) )
| ( C @ ( B @ ron ) ) )
& ~ ? [E: $i] : ( E @ ( B @ ( A @ rS ) ) ) )
=> ? [E: $i] : ( C @ ( E @ rintersect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) )
& ( A != B ) )
=> ! [C: $i,D: $i] :
( ( ( D @ rpoint )
& ( C != A )
& ( C != B )
& ( C = D ) )
=> ( ( B @ ( A @ vf ) )
= ( B @ ( A @ ( D @ ( C @ vskolem1078 ) ) ) @ ( C @ vf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(219), 0), 0)') ).
thf(358,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) )
& ( A != B ) )
=> ! [C: $i,D: $i] :
( ( ( D @ rpoint )
& ( C != A )
& ( C != B )
& ( C = D ) )
=> ( ( B @ ( A @ vf ) )
= ( B @ ( A @ ( D @ ( C @ vskolem1078 ) ) ) @ ( C @ vf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(11956,plain,
! [A: $i] :
( ( ( vd1302 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[10913,201]) ).
thf(11957,plain,
! [A: $i] :
( ( ( vd1302 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[11956]) ).
thf(11958,plain,
( ( vd1302 @ sk50 @ sk50 @ ( vd1302 @ sk50 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[11957:[bind(A,$thf( vd1302 @ sk50 @ sk50 ))]]) ).
thf(160,plain,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] :
( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D ) )
=> ( ( C @ ( A @ vplus ) )
= ( A @ ( C @ vplus ) ) ) ),
inference(miniscope,[status(thm)],[159]) ).
thf(161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ vplus ) )
= ( A @ ( C @ vplus ) ) )
| ~ ( B @ rreal )
| ( A != B )
| ~ ( D @ rreal )
| ( C != D ) ),
inference(cnf,[status(esa)],[160]) ).
thf(162,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ rreal )
| ~ ( D @ rreal )
| ( ( C @ ( A @ vplus ) )
= ( A @ ( C @ vplus ) ) )
| ( A != B )
| ( C != D ) ),
inference(lifteq,[status(thm)],[161]) ).
thf(163,plain,
! [B: $i,A: $i] :
( ~ ( A @ rreal )
| ~ ( B @ rreal )
| ( ( B @ ( A @ vplus ) )
= ( A @ ( B @ vplus ) ) ) ),
inference(simp,[status(thm)],[162]) ).
thf(837,plain,
vd1288 != vd1289,
inference(cnfConj,[status(thm)],[836]) ).
thf(850,plain,
vd1288 != vd1289,
inference(lifteq,[status(thm)],[837]) ).
thf(221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk5 ) ) @ rpoint )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(cnfConj,[status(thm)],[212]) ).
thf(226,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk5 ) ) @ rpoint )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[221]) ).
thf(227,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk5 ) ) @ rpoint )
| ~ ( C @ ( B @ ( A @ vtriangle ) ) @ rtriangle ) ),
inference(simp,[status(thm)],[226]) ).
thf(7288,plain,
( ( ( vd1297 @ sk45 @ ( vd1297 @ sk45 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( vd1302 != vd1299 )
| ( v0 != v0 ) ),
inference(paramod_ordered,[status(thm)],[5116,4758]) ).
thf(7289,plain,
( ( ( vd1297 @ sk45 @ ( vd1297 @ sk45 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( vd1302 != vd1299 ) ),
inference(simp,[status(thm)],[7288]) ).
thf(7367,plain,
( ( ( vd1297 @ sk45 )
!= vd1299 )
| ( ( vd1297 @ sk45 )
!= vd1287 )
| ( vd1302 != vd1299 ) ),
inference(simp,[status(thm)],[7289]) ).
thf(5230,plain,
( ( ( vd1299 @ ( vd1299 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) )
| ( vd1302 @ ( vd1287 @ vf ) @ ( v0 @ rless ) ) ),
inference(paramod_ordered,[status(thm)],[5124,344]) ).
thf(5296,plain,
( ( vd1299 != vd1299 )
| ( vd1299 != vd1287 )
| ( vd1302 @ ( vd1287 @ vf ) @ ( v0 @ rless ) ) ),
inference(simp,[status(thm)],[5230]) ).
thf(5312,plain,
( ( vd1299 != vd1287 )
| ( vd1302 @ ( vd1287 @ vf ) @ ( v0 @ rless ) ) ),
inference(simp,[status(thm)],[5296]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rline )
& ( A = B )
& ( D @ rpoint )
& ~ ( A @ ( C @ ron ) )
& ( F @ rpoint )
& ( A @ ( C @ ( E @ rS ) ) )
& ( E = F )
& ( C = D ) )
=> ? [G: $i] :
( ( G @ rpoint )
& ( A @ ( C @ ( G @ rS ) ) )
& ( G != C )
& ( G != E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(35), 0), imp(cond(axiom(35), 0)))') ).
thf(935,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rline )
& ( A = B )
& ( D @ rpoint )
& ~ ( A @ ( C @ ron ) )
& ( F @ rpoint )
& ( A @ ( C @ ( E @ rS ) ) )
& ( E = F )
& ( C = D ) )
=> ? [G: $i] :
( ( G @ rpoint )
& ( A @ ( C @ ( G @ rS ) ) )
& ( G != C )
& ( G != E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ rpoint )
& ( A = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( B = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( C = D ) ) )
=> ( ( C @ ( B @ ( A @ vangle ) ) @ ( v0 @ rleq ) )
& ( vperp @ ( vperp @ vplus ) @ ( C @ ( B @ ( A @ vangle ) ) @ rleq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(170), 0), imp(cond(axiom(170), 0)))') ).
thf(923,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ rpoint )
& ( A = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( B = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( C = D ) ) )
=> ( ( C @ ( B @ ( A @ vangle ) ) @ ( v0 @ rleq ) )
& ( vperp @ ( vperp @ vplus ) @ ( C @ ( B @ ( A @ vangle ) ) @ rleq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(1774,plain,
! [A: $i] :
( ( ( vd1302 @ ( vd1287 @ ( vd1289 @ rR ) ) )
!= ( vd1302 @ ( vd1287 @ ( A @ rR ) ) ) )
| ~ ( A @ rpoint )
| ~ $true
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= ( A @ ( vd1287 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[740,131]) ).
thf(1775,plain,
! [A: $i] :
( ( ( vd1302 @ ( vd1287 @ ( vd1289 @ rR ) ) )
!= ( vd1302 @ ( vd1287 @ ( A @ rR ) ) ) )
| ~ ( A @ rpoint )
| ( ( vd1299 @ ( vd1287 @ vf ) )
!= ( A @ ( vd1287 @ vf ) ) ) ),
inference(simp,[status(thm)],[1774]) ).
thf(1776,plain,
( ~ ( vd1289 @ rpoint )
| ( ( vd1289 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) ) ),
inference(pattern_uni,[status(thm)],[1775:[bind(A,$thf( vd1289 ))]]) ).
thf(3932,plain,
( ~ $true
| ( ( vd1289 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) ) ),
inference(rewrite,[status(thm)],[1776,1203]) ).
thf(3933,plain,
( ( vd1289 @ ( vd1287 @ vf ) )
!= ( vd1299 @ ( vd1287 @ vf ) ) ),
inference(simp,[status(thm)],[3932]) ).
thf(41141,plain,
! [B: $i,A: $i] :
( ( A != vd1289 )
| ( B != vd1299 )
| ( B @ ( A @ sk6 ) @ ( A @ ron ) )
| ~ ( B @ rpoint )
| ~ ( A @ rpoint ) ),
inference(paramod_ordered,[status(thm)],[274,1799]) ).
thf(41142,plain,
! [A: $i] :
( ( A != vd1299 )
| ( A @ ( vd1289 @ sk6 ) @ ( vd1289 @ ron ) )
| ~ ( A @ rpoint )
| ~ ( vd1289 @ rpoint ) ),
inference(pattern_uni,[status(thm)],[41141:[bind(A,$thf( vd1289 ))]]) ).
thf(42772,plain,
( ( vd1299 @ ( vd1289 @ sk6 ) @ ( vd1289 @ ron ) )
| ~ ( vd1299 @ rpoint )
| ~ ( vd1289 @ rpoint ) ),
inference(simp,[status(thm)],[41142]) ).
thf(46771,plain,
( ( vd1299 @ ( vd1289 @ sk6 ) @ ( vd1289 @ ron ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[42772,1203,1178]) ).
thf(46772,plain,
vd1299 @ ( vd1289 @ sk6 ) @ ( vd1289 @ ron ),
inference(simp,[status(thm)],[46771]) ).
thf(10900,plain,
! [A: $i] :
( ( ( vd1302 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[10279,201]) ).
thf(10901,plain,
! [A: $i] :
( ( ( vd1302 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[10900]) ).
thf(10902,plain,
( ( vd1302 @ sk50 @ ( vd1302 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[10901:[bind(A,$thf( vd1302 @ sk50 ))]]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( H @ rline )
& ( A = H ) )
& ? [H: $i] :
( ( H @ rline )
& ( B = H ) )
& ? [H: $i] :
( ( H @ rline )
& ( C = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( D = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( E = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( F = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( G = H ) )
& ( A @ ( D @ ron ) )
& ( B @ ( D @ ron ) )
& ( C @ ( D @ ron ) )
& ( A @ ( E @ ron ) )
& ( B @ ( F @ ron ) )
& ( C @ ( G @ ron ) )
& ( A @ ( G @ ( F @ rS ) ) )
& ~ ( B @ ( G @ ( E @ rS ) ) )
& ~ ( B @ ( G @ ron ) )
& ( E != D ) )
=> ( C @ ( F @ ( E @ rS ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(115), 0), imp(cond(axiom(115), 0)))') ).
thf(775,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( H @ rline )
& ( A = H ) )
& ? [H: $i] :
( ( H @ rline )
& ( B = H ) )
& ? [H: $i] :
( ( H @ rline )
& ( C = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( D = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( E = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( F = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( G = H ) )
& ( A @ ( D @ ron ) )
& ( B @ ( D @ ron ) )
& ( C @ ( D @ ron ) )
& ( A @ ( E @ ron ) )
& ( B @ ( F @ ron ) )
& ( C @ ( G @ ron ) )
& ( A @ ( G @ ( F @ rS ) ) )
& ~ ( B @ ( G @ ( E @ rS ) ) )
& ~ ( B @ ( G @ ron ) )
& ( E != D ) )
=> ( C @ ( F @ ( E @ rS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(76008,plain,
$false,
inference(e,[status(thm)],[809,5116,18272,555,10272,909,249,1158,683,276,1808,1205,878,1793,4973,202,5425,11468,472,1233,11160,4980,7556,142,11171,9292,9971,1264,5130,157,28106,570,802,344,11453,817,853,5127,770,261,10913,11344,9088,13013,5311,966,16785,492,164,1811,179,11577,253,806,7581,147,397,17674,132,849,5648,1886,16978,233,248,10313,793,7550,201,10831,1153,22204,334,16592,894,12878,12190,392,192,165,862,349,788,137,467,252,852,1178,830,5113,11670,10473,2769,229,847,10462,879,742,12538,1111,725,10266,1006,141,420,156,18073,225,339,193,1075,526,1207,970,1060,173,721,1799,129,17873,1131,237,5153,1202,22482,23037,1035,1026,586,10983,18472,1135,264,279,7010,166,27777,1884,743,826,4758,259,191,402,10257,1107,5314,11973,181,1258,540,159,979,23314,406,172,274,10279,362,737,649,1122,187,9623,477,758,345,726,621,7551,240,7186,1022,155,330,848,700,983,1044,1066,780,455,223,2022,521,1171,267,851,1102,431,5139,922,167,11359,1034,675,1203,663,374,28919,11795,10269,2784,209,487,194,14211,712,954,7554,150,11562,263,1098,10820,10994,199,182,717,1262,13149,808,7009,585,370,46508,10739,744,27449,1052,612,5319,5147,1141,10260,4510,600,978,1140,231,1084,7024,931,482,22760,1010,5124,2792,1807,813,12066,12743,158,5426,186,171,11780,13288,914,207,11685,1689,2081,235,246,151,10291,146,12081,854,867,950,835,210,239,5413,37916,635,1065,12175,801,136,506,268,4631,358,807,12307,740,11958,131,163,850,4533,227,7367,5312,935,923,3933,10750,46772,10902,775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO306+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/10.41 % Computer : n013.cluster.edu
% 0.13/10.41 % Model : x86_64 x86_64
% 0.13/10.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.41 % Memory : 8046.5625MB
% 0.13/10.41 % OS : Linux 6.8.0-71-generic
% 0.13/10.41 % CPULimit : 300
% 0.13/10.41 % WCLimit : 300
% 0.13/10.41 % DateTime : Fri Sep 25 13:15:21 UTC 2026
% 0.13/10.42 % CPUTime :
% 0.13/10.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.17/11.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.85/11.34 % [INFO] Parsing done (342ms).
% 1.85/11.36 % [INFO] Running in sequential loop mode.
% 2.93/11.74 % [INFO] eprover registered as external prover.
% 2.93/11.75 % [INFO] Scanning for conjecture ...
% 3.12/11.89 % [INFO] Found a conjecture (or negated_conjecture) and 126 axioms. Running axiom selection ...
% 3.32/12.01 % [INFO] Axiom selection finished. Selected 126 axioms (removed 0 axioms).
% 4.48/12.32 % [INFO] Problem is first-order (TPTP FOF).
% 4.48/12.36 % [INFO] Type checking passed.
% 4.48/12.37 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 196.68/72.85 % External prover 'e' found a proof!
% 196.68/72.85 % [INFO] Killing All external provers ...
% 196.68/72.85 % Time passed: 62298ms (effective reasoning time: 61489ms)
% 196.68/72.85 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 196.68/72.86 % Axioms used in derivation (126): qu(cond(axiom(41), 0), imp(cond(axiom(41), 0))), qu(cond(axiom(71), 0), imp(cond(axiom(71), 0))), qu(cond(axiom(73), 0), imp(cond(axiom(73), 0))), qu(cond(axiom(119), 0), imp(cond(axiom(119), 0))), qu(cond(axiom(3), 0), imp(cond(axiom(3), 0))), qu(cond(axiom(164), 0), imp(cond(axiom(164), 0))), qu(cond(axiom(145), 0), imp(cond(axiom(145), 0))), ass(cond(goal(206), 0), 1), qu(cond(axiom(202), 0), imp(cond(axiom(202), 0))), holds(351, 1305, 0), qu(cond(axiom(19), 0), imp(cond(axiom(19), 0))), and(pred(conjunct2(348), 4), and(holds(conjunct2(348), 1304, 0), and(pred(conjunct2(348), 1), holds(conjunct1(348), 1301, 0)))), qu(cond(axiom(95), 0), imp(cond(axiom(95), 0))), qu(cond(axiom(43), 0), imp(cond(axiom(43), 0))), ass(cond(goal(264), 0), 2), qu(cond(axiom(133), 0), imp(cond(axiom(133), 0))), qu(cond(axiom(21), 0), imp(cond(axiom(21), 0))), qu(cond(axiom(151), 0), imp(cond(axiom(151), 0))), pred(axiom(5), 0), qu(cond(axiom(75), 0), imp(cond(axiom(75), 0))), qu(cond(axiom(194), 0), imp(cond(axiom(194), 0))), qu(cond(axiom(190), 0), imp(cond(axiom(190), 0))), qu(cond(axiom(53), 0), imp(cond(axiom(53), 0))), qu(cond(axiom(89), 0), imp(cond(axiom(89), 0))), ass(cond(goal(264), 0), 1), qu(cond(axiom(107), 0), imp(cond(axiom(107), 0))), pred(axiom(137), 2), qu(cond(axiom(31), 0), imp(cond(axiom(31), 0))), ass(cond(goal(206), 0), 0), qu(cond(axiom(103), 0), imp(cond(axiom(103), 0))), ass(cond(goal(238), 0), 0), and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345))))))))), qu(cond(axiom(77), 0), imp(cond(axiom(77), 0))), qu(cond(axiom(113), 0), imp(cond(axiom(113), 0))), pred(s2(plural(347)), 0), qu(cond(axiom(45), 0), imp(cond(axiom(45), 0))), qu(cond(axiom(11), 0), imp(cond(axiom(11), 0))), qu(cond(axiom(176), 0), imp(cond(axiom(176), 0))), qu(cond(axiom(33), 0), imp(cond(axiom(33), 0))), qu(cond(axiom(139), 0), imp(cond(axiom(139), 0))), qu(cond(axiom(59), 0), imp(cond(axiom(59), 0))), qu(cond(axiom(35), 0), imp(cond(axiom(35), 0))), qu(cond(axiom(23), 0), imp(cond(axiom(23), 0))), qu(cond(axiom(87), 0), imp(cond(axiom(87), 0))), qu(cond(axiom(1), 0), imp(cond(axiom(1), 0))), qu(cond(axiom(121), 0), imp(cond(axiom(121), 0))), qu(cond(axiom(83), 0), imp(cond(axiom(83), 0))), pred(348, 4), qu(cond(axiom(109), 0), imp(cond(axiom(109), 0))), qu(cond(axiom(79), 0), imp(cond(axiom(79), 0))), qu(cond(axiom(55), 0), imp(cond(axiom(55), 0))), qu(cond(axiom(81), 0), imp(cond(axiom(81), 0))), qu(cond(axiom(13), 0), imp(cond(axiom(13), 0))), qu(cond(axiom(143), 0), imp(cond(axiom(143), 0))), ass(cond(156, 0), 0), qu(cond(axiom(188), 0), imp(cond(axiom(188), 0))), qu(cond(axiom(99), 0), imp(cond(axiom(99), 0))), pred(conjunct1(349), 0), qu(cond(axiom(184), 0), imp(cond(axiom(184), 0))), ass(cond(goal(238), 0), 1), qu(cond(axiom(57), 0), imp(cond(axiom(57), 0))), qu(cond(axiom(65), 0), imp(cond(axiom(65), 0))), qu(cond(axiom(174), 0), imp(cond(axiom(174), 0))), qu(cond(axiom(61), 0), imp(cond(axiom(61), 0))), qu(cond(axiom(9), 0), imp(cond(axiom(9), 0))), qu(cond(axiom(182), 0), imp(cond(axiom(182), 0))), qu(cond(axiom(117), 0), imp(cond(axiom(117), 0))), pred(s1(plural(347)), 0), qu(cond(axiom(172), 0), imp(cond(axiom(172), 0))), qu(cond(axiom(115), 0), imp(cond(axiom(115), 0))), qu(cond(axiom(131), 0), imp(cond(axiom(131), 0))), qu(cond(axiom(196), 0), imp(cond(axiom(196), 0))), qu(cond(axiom(186), 0), imp(cond(axiom(186), 0))), qu(cond(axiom(127), 0), imp(cond(axiom(127), 0))), qu(cond(axiom(123), 0), imp(cond(axiom(123), 0))), qu(cond(axiom(25), 0), imp(cond(axiom(25), 0))), qu(cond(axiom(101), 0), imp(cond(axiom(101), 0))), qu(cond(axiom(125), 0), imp(cond(axiom(125), 0))), pred(346, 0), qu(cond(axiom(170), 0), imp(cond(axiom(170), 0))), qu(cond(axiom(111), 0), imp(cond(axiom(111), 0))), qu(cond(axiom(166), 0), imp(cond(axiom(166), 0))), ass(cond(goal(264), 0), 0), qu(cond(axiom(105), 0), imp(cond(axiom(105), 0))), qu(cond(axiom(37), 0), imp(cond(axiom(37), 0))), qu(cond(axiom(63), 0), imp(cond(axiom(63), 0))), qu(cond(axiom(192), 0), imp(cond(axiom(192), 0))), pred(conjunct2(349), 0), ass(cond(goal(219), 0), 0), pred(axiom(137), 1), ass(cond(goal(206), 0), 2), qu(cond(axiom(29), 0), imp(cond(axiom(29), 0))), pred(s1(plural(346)), 0), qu(cond(axiom(39), 0), imp(cond(axiom(39), 0))), qu(cond(axiom(129), 0), imp(cond(axiom(129), 0))), qu(cond(axiom(15), 0), imp(cond(axiom(15), 0))), pred(348, 1), qu(cond(axiom(85), 0), imp(cond(axiom(85), 0))), ass(cond(goal(238), 0), 2), qu(cond(axiom(200), 0), imp(cond(axiom(200), 0))), qu(cond(axiom(27), 0), imp(cond(axiom(27), 0))), qu(cond(axiom(91), 0), imp(cond(axiom(91), 0))), pred(s2(plural(346)), 0), ass(cond(goal(219), 0), 1), qu(cond(axiom(49), 0), imp(cond(axiom(49), 0))), qu(cond(axiom(149), 0), imp(cond(axiom(149), 0))), qu(cond(axiom(7), 0), imp(cond(axiom(7), 0))), qu(cond(axiom(17), 0), imp(cond(axiom(17), 0))), qu(cond(axiom(51), 0), imp(cond(axiom(51), 0))), qu(cond(axiom(141), 0), imp(cond(axiom(141), 0))), qu(cond(axiom(135), 0), imp(cond(axiom(135), 0))), qu(cond(axiom(47), 0), imp(cond(axiom(47), 0))), qu(cond(axiom(69), 0), imp(cond(axiom(69), 0))), qu(cond(axiom(147), 0), imp(cond(axiom(147), 0))), qu(cond(axiom(168), 0), imp(cond(axiom(168), 0))), qu(cond(axiom(204), 0), imp(cond(axiom(204), 0))), qu(cond(axiom(97), 0), imp(cond(axiom(97), 0))), qu(cond(axiom(162), 0), imp(cond(axiom(162), 0))), qu(cond(axiom(180), 0), imp(cond(axiom(180), 0))), qu(cond(axiom(153), 0), imp(cond(axiom(153), 0))), pred(347, 0), qu(cond(axiom(178), 0), imp(cond(axiom(178), 0))), qu(cond(axiom(160), 0), imp(cond(axiom(160), 0))), qu(cond(axiom(67), 0), imp(cond(axiom(67), 0))), qu(cond(axiom(93), 0), imp(cond(axiom(93), 0))), qu(cond(axiom(198), 0), imp(cond(axiom(198), 0)))
% 196.68/72.86 % No. of inferences in proof: 806
% 196.68/72.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 62298 ms resp. 61489 ms w/o parsing
% 198.70/73.20 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 198.70/73.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------