%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO336+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 : n017.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 07:13:13 AM UTC 2026
% Result : Theorem 141.90s 38.03s
% Output : Refutation 144.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 138
% Syntax : Number of formulae : 565 ( 103 unt; 0 typ; 12 def)
% Number of atoms : 3923 (1580 equ; 0 cnn)
% Maximal formula atoms : 57 ( 6 avg)
% Number of connectives : 9282 ( 954 ~; 582 |;2262 &;5210 @)
% ( 8 <=>; 266 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 12 con; 0-8 aty)
% Number of variables : 2119 ( 20 ^;1466 !; 621 ?;2119 :)
% ( 0 !>; 0 ?*; 0 @-; 12 @+)
% Comments :
%------------------------------------------------------------------------------
thf(vf_decl,type,
vf: $i > $i > $i ).
thf(vd1363_decl,type,
vd1363: $i ).
thf(vd1361_decl,type,
vd1361: $i ).
thf(vd1362_decl,type,
vd1362: $i ).
thf(rR_decl,type,
rR: $i > $i > $i > $o ).
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(rinside_decl,type,
rinside: $i > $i > $o ).
thf(vd684_decl,type,
vd684: $i ).
thf(ron_decl,type,
ron: $i > $i > $o ).
thf(rline_decl,type,
rline: $i > $o ).
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(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(sk32_decl,type,
sk32: $i ).
thf(sk33_decl,type,
sk33: $i ).
thf(sk39_decl,type,
sk39: $i > $i ).
thf(sk41_decl,type,
sk41: $i > $i ).
thf(sk44_decl,type,
sk44: $i > $i ).
thf(sk47_decl,type,
sk47: $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(sk32_def,definition,
( sk32
= ( @+[A: $i] :
( ( A @ rpoint )
& ( vd1361 = A ) ) ) ) ).
thf(sk33_def,definition,
( sk33
= ( @+[A: $i] :
( ( A @ rpoint )
& ( vd1362 = A ) ) ) ) ).
thf(sk39_def,definition,
( sk39
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ rpoint )
& ( A @ ( B @ ron ) ) ) ) ) ).
thf(sk41_def,definition,
( sk41
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ rpoint )
& ~ ( A @ ( B @ rinside ) )
& ~ ( A @ ( B @ ron ) ) ) ) ) ).
thf(sk44_def,definition,
( sk44
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ rpoint )
& ( A @ ( B @ ron ) ) ) ) ) ).
thf(sk47_def,definition,
( sk47
= ( @+[A: $i] :
( ( A @ rpoint )
& ( vd1363 = A ) ) ) ) ).
thf(sk50_def,definition,
( sk50
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ rpoint )
& ( B != A ) ) ) ) ).
thf(68,axiom,
? [A: $i] :
( ( A @ rpoint )
& ( vd1361 = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(s1(plural(386)))') ).
thf(721,plain,
? [A: $i] :
( ( A @ rpoint )
& ( vd1361 = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(722,plain,
( ( sk32 @ rpoint )
& ( vd1361 = sk32 ) ),
inference(cnf,[status(esa)],[721]) ).
thf(724,plain,
sk32 @ rpoint,
inference(cnfConj,[status(thm)],[722]) ).
thf(723,plain,
vd1361 = sk32,
inference(cnfConj,[status(thm)],[722]) ).
thf(725,plain,
sk32 = vd1361,
inference(lifteq,[status(thm)],[723]) ).
thf(1169,plain,
vd1361 @ rpoint,
inference(rewrite,[status(thm)],[724,725]) ).
thf(109,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(1023,plain,
! [A: $i,B: $i] :
( ( ( B @ rpoint )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(1024,plain,
! [A: $i] :
( ? [B: $i] :
( ( B @ rpoint )
& ( A = B ) )
=> ? [B: $i] :
( ( B @ rpoint )
& ( B != A ) ) ),
inference(miniscope,[status(thm)],[1023]) ).
thf(1025,plain,
! [B: $i,A: $i] :
( ( ( A @ sk50 @ rpoint )
| ~ ( B @ rpoint )
| ( A != B ) )
& ( ( ( A @ sk50 )
!= A )
| ~ ( B @ rpoint )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[1024]) ).
thf(1027,plain,
! [B: $i,A: $i] :
( ( A @ sk50 @ rpoint )
| ~ ( B @ rpoint )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[1025]) ).
thf(1030,plain,
! [B: $i,A: $i] :
( ( A @ sk50 @ rpoint )
| ~ ( B @ rpoint )
| ( A != B ) ),
inference(lifteq,[status(thm)],[1027]) ).
thf(1031,plain,
! [A: $i] :
( ( A @ sk50 @ rpoint )
| ~ ( A @ rpoint ) ),
inference(simp,[status(thm)],[1030]) ).
thf(2785,plain,
! [A: $i] :
( ( ( vd1361 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1169,1031]) ).
thf(2786,plain,
! [A: $i] :
( ( ( vd1361 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[2785]) ).
thf(2787,plain,
vd1361 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[2786:[bind(A,$thf( vd1361 ))]]) ).
thf(2829,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2787,1031]) ).
thf(2830,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[2829]) ).
thf(2831,plain,
vd1361 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[2830:[bind(A,$thf( vd1361 @ sk50 ))]]) ).
thf(3028,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2831,1031]) ).
thf(3029,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[3028]) ).
thf(3030,plain,
vd1361 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[3029:[bind(A,$thf( vd1361 @ sk50 @ sk50 ))]]) ).
thf(3442,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3030,1031]) ).
thf(3443,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[3442]) ).
thf(3444,plain,
vd1361 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[3443:[bind(A,$thf( vd1361 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(4824,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3444,1031]) ).
thf(4825,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[4824]) ).
thf(4826,plain,
vd1361 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[4825:[bind(A,$thf( vd1361 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(5536,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4826,1031]) ).
thf(5537,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[5536]) ).
thf(5538,plain,
vd1361 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[5537:[bind(A,$thf( vd1361 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(6165,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5538,1031]) ).
thf(6166,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[6165]) ).
thf(6167,plain,
vd1361 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[6166:[bind(A,$thf( vd1361 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
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(1105,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(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(1110,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(46,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(481,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)],[46]) ).
thf(117,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(1083,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)],[117]) ).
thf(101,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(962,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)],[101]) ).
thf(69,axiom,
? [A: $i] :
( ( A @ rpoint )
& ( vd1362 = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(s2(plural(386)))') ).
thf(726,plain,
? [A: $i] :
( ( A @ rpoint )
& ( vd1362 = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(727,plain,
( ( sk33 @ rpoint )
& ( vd1362 = sk33 ) ),
inference(cnf,[status(esa)],[726]) ).
thf(728,plain,
vd1362 = sk33,
inference(cnfConj,[status(thm)],[727]) ).
thf(730,plain,
sk33 = vd1362,
inference(lifteq,[status(thm)],[728]) ).
thf(104,axiom,
? [A: $i] :
( ( A @ rpoint )
& ( vd1363 = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(s3(plural(386)))') ).
thf(975,plain,
? [A: $i] :
( ( A @ rpoint )
& ( vd1363 = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(976,plain,
( ( sk47 @ rpoint )
& ( vd1363 = sk47 ) ),
inference(cnf,[status(esa)],[975]) ).
thf(978,plain,
sk47 @ rpoint,
inference(cnfConj,[status(thm)],[976]) ).
thf(977,plain,
vd1363 = sk47,
inference(cnfConj,[status(thm)],[976]) ).
thf(979,plain,
sk47 = vd1363,
inference(lifteq,[status(thm)],[977]) ).
thf(1187,plain,
vd1363 @ rpoint,
inference(rewrite,[status(thm)],[978,979]) ).
thf(2797,plain,
! [A: $i] :
( ( ( vd1363 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1187,1031]) ).
thf(2798,plain,
! [A: $i] :
( ( ( vd1363 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[2797]) ).
thf(2799,plain,
vd1363 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[2798:[bind(A,$thf( vd1363 ))]]) ).
thf(17,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(192,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)],[17]) ).
thf(193,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)],[192]) ).
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 ) ),
inference(cnfConj,[status(thm)],[193]) ).
thf(198,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)],[195]) ).
thf(199,plain,
! [A: $i] :
( ~ ( A @ rpoint )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[198]) ).
thf(8795,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[2799,199]) ).
thf(8796,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[8795]) ).
thf(8797,plain,
( ( vd1363 @ sk50 @ ( vd1363 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[8796:[bind(A,$thf( vd1363 @ sk50 ))]]) ).
thf(56,axiom,
vd14 @ rpoint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(5), 0)') ).
thf(589,plain,
vd14 @ rpoint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(2807,plain,
! [A: $i] :
( ( ( vd14 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[589,1031]) ).
thf(2808,plain,
! [A: $i] :
( ( ( vd14 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[2807]) ).
thf(2809,plain,
vd14 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[2808:[bind(A,$thf( vd14 ))]]) ).
thf(2998,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2809,1031]) ).
thf(2999,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[2998]) ).
thf(3000,plain,
vd14 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[2999:[bind(A,$thf( vd14 @ sk50 ))]]) ).
thf(1,conjecture,
? [A: $i] :
( ( A @ rpoint )
& ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
& ( ( A @ ( vd1363 @ vf ) )
= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(396)') ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( A @ rpoint )
& ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
& ( ( A @ ( vd1363 @ vf ) )
= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(128,plain,
~ ? [A: $i] :
( ( A @ rpoint )
& ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
& ( ( A @ ( vd1363 @ vf ) )
= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(129,plain,
! [A: $i] :
( ~ ( A @ rpoint )
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(cnf,[status(esa)],[128]) ).
thf(130,plain,
! [A: $i] :
( ~ ( A @ rpoint )
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(lifteq,[status(thm)],[129]) ).
thf(3415,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[3000,130]) ).
thf(3416,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(simp,[status(thm)],[3415]) ).
thf(3417,plain,
( ~ ( vd1363 @ ( vd1361 @ ( vd14 @ sk50 @ sk50 @ rR ) ) )
| ( ( vd1362 @ ( vd1361 @ vf ) )
!= ( vd14 @ sk50 @ sk50 @ ( vd1363 @ vf ) ) ) ),
inference(pattern_uni,[status(thm)],[3416:[bind(A,$thf( vd14 @ sk50 @ sk50 ))]]) ).
thf(729,plain,
sk33 @ rpoint,
inference(cnfConj,[status(thm)],[727]) ).
thf(1173,plain,
vd1362 @ rpoint,
inference(rewrite,[status(thm)],[729,730]) ).
thf(2794,plain,
! [A: $i] :
( ( ( vd1362 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1173,1031]) ).
thf(2795,plain,
! [A: $i] :
( ( ( vd1362 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[2794]) ).
thf(2796,plain,
vd1362 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[2795:[bind(A,$thf( vd1362 ))]]) ).
thf(2940,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2796,1031]) ).
thf(2941,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[2940]) ).
thf(2942,plain,
vd1362 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[2941:[bind(A,$thf( vd1362 @ sk50 ))]]) ).
thf(3151,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2942,1031]) ).
thf(3152,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[3151]) ).
thf(3153,plain,
vd1362 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[3152:[bind(A,$thf( vd1362 @ sk50 @ sk50 ))]]) ).
thf(2951,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[2796,130]) ).
thf(2952,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(simp,[status(thm)],[2951]) ).
thf(2953,plain,
( ~ ( vd1363 @ ( vd1361 @ ( vd1362 @ sk50 @ rR ) ) )
| ( ( vd1362 @ ( vd1361 @ vf ) )
!= ( vd1362 @ sk50 @ ( vd1363 @ vf ) ) ) ),
inference(pattern_uni,[status(thm)],[2952:[bind(A,$thf( vd1362 @ sk50 ))]]) ).
thf(3400,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3000,1031]) ).
thf(3401,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[3400]) ).
thf(3402,plain,
vd14 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[3401:[bind(A,$thf( vd14 @ sk50 @ sk50 ))]]) ).
thf(25,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(269,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)],[25]) ).
thf(111,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(1041,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)],[111]) ).
thf(10,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(162,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)],[10]) ).
thf(163,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)],[162]) ).
thf(164,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)],[163]) ).
thf(165,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)],[164]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ rless ) )
| ~ ( A @ rreal )
| ~ ( B @ rreal )
| ~ ( B @ ( A @ rless ) )
| ( A = B ) ),
inference(simp,[status(thm)],[165]) ).
thf(16,axiom,
vd1361 != vd1362,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(386, 7)') ).
thf(189,plain,
vd1361 != vd1362,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(190,plain,
vd1361 != vd1362,
inference(polarity_switch,[status(thm)],[189]) ).
thf(191,plain,
vd1362 != vd1361,
inference(lifteq,[status(thm)],[190]) ).
thf(4222,plain,
! [B: $i,A: $i] :
( ( A != vd1362 )
| ( B != vd1361 )
| ~ ( A @ ( B @ rless ) )
| ~ ( A @ rreal )
| ~ ( B @ rreal )
| ~ ( B @ ( A @ rless ) ) ),
inference(paramod_ordered,[status(thm)],[166,191]) ).
thf(4223,plain,
! [A: $i] :
( ( A != vd1361 )
| ~ ( vd1362 @ ( A @ rless ) )
| ~ ( vd1362 @ rreal )
| ~ ( A @ rreal )
| ~ ( A @ ( vd1362 @ rless ) ) ),
inference(pattern_uni,[status(thm)],[4222:[bind(A,$thf( vd1362 ))]]) ).
thf(4564,plain,
( ~ ( vd1362 @ ( vd1361 @ rless ) )
| ~ ( vd1362 @ rreal )
| ~ ( vd1361 @ rreal )
| ~ ( vd1361 @ ( vd1362 @ rless ) ) ),
inference(simp,[status(thm)],[4223]) ).
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 ) ) )
=> ( 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(340,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)],[29]) ).
thf(12,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(168,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)],[12]) ).
thf(169,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)],[168]) ).
thf(170,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)],[169]) ).
thf(171,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)],[170]) ).
thf(173,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)],[171]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ~ ( A @ rreal )
| ~ ( B @ rreal )
| ( ( A @ ( A @ ( B @ sk1 ) ) )
= ( B @ ( A @ vplus ) ) ) ),
inference(simp,[status(thm)],[173]) ).
thf(92,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(898,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)],[92]) ).
thf(3495,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3153,1031]) ).
thf(3496,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[3495]) ).
thf(3497,plain,
vd1362 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[3496:[bind(A,$thf( vd1362 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(4914,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3497,1031]) ).
thf(4915,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[4914]) ).
thf(4916,plain,
vd1362 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[4915:[bind(A,$thf( vd1362 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(4750,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3402,1031]) ).
thf(4751,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[4750]) ).
thf(4752,plain,
vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[4751:[bind(A,$thf( vd14 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(5282,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4752,1031]) ).
thf(5283,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[5282]) ).
thf(5284,plain,
vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[5283:[bind(A,$thf( vd14 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(86,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(838,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)],[86]) ).
thf(30,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 )
& ( B != C )
& ( ( B @ ( A @ vf ) )
= ( C @ ( A @ vf ) ) ) )
=> ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( E @ rpoint )
& ( D @ ( A @ ( B @ rR ) ) )
& ( G @ rpoint )
& ( F @ ( A @ ( C @ rR ) ) )
& ( F = G )
& ( D = E ) )
=> ( ( C @ ( B @ ( A @ vangle ) ) )
= ( B @ ( C @ ( A @ vangle ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(340), 0), 1)') ).
thf(344,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 )
& ( B != C )
& ( ( B @ ( A @ vf ) )
= ( C @ ( A @ vf ) ) ) )
=> ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( E @ rpoint )
& ( D @ ( A @ ( B @ rR ) ) )
& ( G @ rpoint )
& ( F @ ( A @ ( C @ rR ) ) )
& ( F = G )
& ( D = E ) )
=> ( ( C @ ( B @ ( A @ vangle ) ) )
= ( B @ ( C @ ( A @ vangle ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(9,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(157,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)],[9]) ).
thf(82,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(817,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)],[82]) ).
thf(54,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(559,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)],[54]) ).
thf(3461,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[3030,130]) ).
thf(3462,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(simp,[status(thm)],[3461]) ).
thf(3463,plain,
( ~ ( vd1363 @ ( vd1361 @ ( vd1361 @ sk50 @ sk50 @ sk50 @ rR ) ) )
| ( ( vd1362 @ ( vd1361 @ vf ) )
!= ( vd1361 @ sk50 @ sk50 @ sk50 @ ( vd1363 @ vf ) ) ) ),
inference(pattern_uni,[status(thm)],[3462:[bind(A,$thf( vd1361 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(119,axiom,
~ ( vd1362 @ ( vd1361 @ vf ) @ ( vd1363 @ ( vd1361 @ vf ) @ rless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','neg(389)') ).
thf(1099,plain,
~ ( vd1362 @ ( vd1361 @ vf ) @ ( vd1363 @ ( vd1361 @ vf ) @ rless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(1100,plain,
~ ( vd1362 @ ( vd1361 @ vf ) @ ( vd1363 @ ( vd1361 @ vf ) @ rless ) ),
inference(polarity_switch,[status(thm)],[1099]) ).
thf(8900,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[2796,199]) ).
thf(8901,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[8900]) ).
thf(8902,plain,
( ( vd1362 @ sk50 @ ( vd1362 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[8901:[bind(A,$thf( vd1362 @ sk50 ))]]) ).
thf(96,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(924,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)],[96]) ).
thf(85,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(834,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)],[85]) ).
thf(20,axiom,
vd1362 != vd1363,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(386, 9)') ).
thf(238,plain,
vd1362 != vd1363,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(11,axiom,
vd684 @ rreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(137), 1)') ).
thf(167,plain,
vd684 @ rreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
v0 = vd684,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(137), 2)') ).
thf(187,plain,
v0 = vd684,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(188,plain,
vd684 = v0,
inference(lifteq,[status(thm)],[187]) ).
thf(1156,plain,
v0 @ rreal,
inference(rewrite,[status(thm)],[167,188]) ).
thf(13,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(177,plain,
! [A: $i,B: $i] :
( ( ( B @ rreal )
& ( A = B ) )
=> ~ ( A @ ( A @ rless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(178,plain,
! [A: $i] :
( ? [B: $i] :
( ( B @ rreal )
& ( A = B ) )
=> ~ ( A @ ( A @ rless ) ) ),
inference(miniscope,[status(thm)],[177]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ rless ) )
| ~ ( B @ rreal )
| ( A != B ) ),
inference(cnf,[status(esa)],[178]) ).
thf(180,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ rless ) )
| ~ ( B @ rreal )
| ( A != B ) ),
inference(lifteq,[status(thm)],[179]) ).
thf(181,plain,
! [A: $i] :
( ~ ( A @ ( A @ rless ) )
| ~ ( A @ rreal ) ),
inference(simp,[status(thm)],[180]) ).
thf(2289,plain,
! [A: $i] :
( ( ( v0 @ rreal )
!= ( A @ rreal ) )
| ~ ( A @ ( A @ rless ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1156,181]) ).
thf(2290,plain,
! [A: $i] :
( ( ( v0 @ rreal )
!= ( A @ rreal ) )
| ~ ( A @ ( A @ rless ) ) ),
inference(simp,[status(thm)],[2289]) ).
thf(2291,plain,
~ ( v0 @ ( v0 @ rless ) ),
inference(pattern_uni,[status(thm)],[2290:[bind(A,$thf( v0 ))]]) ).
thf(55,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(574,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)],[55]) ).
thf(32,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(353,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)],[32]) ).
thf(102,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(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 @ 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)],[102]) ).
thf(112,axiom,
( ( vd1362 @ ( vd1361 @ vf ) )
!= ( vd1363 @ ( vd1361 @ vf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(387, 1369, 0)') ).
thf(1049,plain,
( ( vd1362 @ ( vd1361 @ vf ) )
!= ( vd1363 @ ( vd1361 @ vf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(1050,plain,
( ( vd1362 @ ( vd1361 @ vf ) )
!= ( vd1363 @ ( vd1361 @ vf ) ) ),
inference(polarity_switch,[status(thm)],[1049]) ).
thf(1051,plain,
( ( vd1362 @ ( vd1361 @ vf ) )
!= ( vd1363 @ ( vd1361 @ vf ) ) ),
inference(lifteq,[status(thm)],[1050]) ).
thf(83,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(821,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)],[83]) ).
thf(26,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(280,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)],[26]) ).
thf(37,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(396,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)],[37]) ).
thf(24,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(265,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)],[24]) ).
thf(2980,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[2799,130]) ).
thf(2981,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(simp,[status(thm)],[2980]) ).
thf(2982,plain,
( ~ ( vd1363 @ ( vd1361 @ ( vd1363 @ sk50 @ rR ) ) )
| ( ( vd1362 @ ( vd1361 @ vf ) )
!= ( vd1363 @ sk50 @ ( vd1363 @ vf ) ) ) ),
inference(pattern_uni,[status(thm)],[2981:[bind(A,$thf( vd1363 @ sk50 ))]]) ).
thf(65,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(687,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)],[65]) ).
thf(2969,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2799,1031]) ).
thf(2970,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[2969]) ).
thf(2971,plain,
vd1363 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[2970:[bind(A,$thf( vd1363 @ sk50 ))]]) ).
thf(3359,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2971,1031]) ).
thf(3360,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[3359]) ).
thf(3361,plain,
vd1363 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[3360:[bind(A,$thf( vd1363 @ sk50 @ sk50 ))]]) ).
thf(116,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(1074,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)],[116]) ).
thf(3009,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[2809,130]) ).
thf(3010,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(simp,[status(thm)],[3009]) ).
thf(3011,plain,
( ~ ( vd1363 @ ( vd1361 @ ( vd14 @ sk50 @ rR ) ) )
| ( ( vd1362 @ ( vd1361 @ vf ) )
!= ( vd14 @ sk50 @ ( vd1363 @ vf ) ) ) ),
inference(pattern_uni,[status(thm)],[3010:[bind(A,$thf( vd14 @ sk50 ))]]) ).
thf(95,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(920,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)],[95]) ).
thf(34,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(366,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)],[34]) ).
thf(5643,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4916,1031]) ).
thf(5644,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[5643]) ).
thf(5645,plain,
vd1362 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[5644:[bind(A,$thf( vd1362 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(6562,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5645,1031]) ).
thf(6563,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[6562]) ).
thf(6564,plain,
vd1362 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[6563:[bind(A,$thf( vd1362 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(7076,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6564,1031]) ).
thf(7077,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[7076]) ).
thf(7078,plain,
vd1362 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[7077:[bind(A,$thf( vd1362 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(8781,plain,
! [A: $i] :
( ( ( vd1362 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[1173,199]) ).
thf(8782,plain,
! [A: $i] :
( ( ( vd1362 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[8781]) ).
thf(8783,plain,
( ( vd1362 @ ( vd1362 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[8782:[bind(A,$thf( vd1362 ))]]) ).
thf(84,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(825,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)],[84]) ).
thf(31,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(349,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)],[31]) ).
thf(41,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(424,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)],[41]) ).
thf(19,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(208,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)],[19]) ).
thf(209,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)],[208]) ).
thf(210,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)],[209]) ).
thf(218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != B )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(cnfConj,[status(thm)],[210]) ).
thf(228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ rtriangle )
| ( A != B )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[218]) ).
thf(229,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( A @ vtriangle ) ) @ rtriangle ),
inference(simp,[status(thm)],[228]) ).
thf(110,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(1032,plain,
! [A: $i,B: $i] :
( ( ( B @ rcircle )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( A @ ( C @ rinside ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(194,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)],[193]) ).
thf(196,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)],[194]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ~ ( B @ rpoint )
| ~ ( A @ rpoint )
| ( B = A )
| ( ( A @ ( B @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[196]) ).
thf(60,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(625,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)],[60]) ).
thf(42,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(435,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)],[42]) ).
thf(1166,plain,
! [A: $i] :
( ( ( sk32 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[724,130]) ).
thf(1167,plain,
! [A: $i] :
( ( ( sk32 @ rpoint )
!= ( A @ rpoint ) )
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(simp,[status(thm)],[1166]) ).
thf(1168,plain,
( ~ ( vd1363 @ ( vd1361 @ ( sk32 @ rR ) ) )
| ( ( vd1362 @ ( vd1361 @ vf ) )
!= ( sk32 @ ( vd1363 @ vf ) ) ) ),
inference(pattern_uni,[status(thm)],[1167:[bind(A,$thf( sk32 ))]]) ).
thf(1178,plain,
( ~ ( vd1363 @ ( vd1361 @ ( vd1361 @ rR ) ) )
| ( ( vd1362 @ ( vd1361 @ vf ) )
!= ( vd1361 @ ( vd1363 @ vf ) ) ) ),
inference(rewrite,[status(thm)],[1168,725]) ).
thf(103,axiom,
vd1363 @ ( vd1361 @ vf ) @ ( vd1362 @ ( vd1361 @ vf ) @ rless ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(395, 1377, 0)') ).
thf(974,plain,
vd1363 @ ( vd1361 @ vf ) @ ( vd1362 @ ( vd1361 @ vf ) @ rless ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(3631,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3361,1031]) ).
thf(3632,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[3631]) ).
thf(3633,plain,
vd1363 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[3632:[bind(A,$thf( vd1363 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(5004,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3633,1031]) ).
thf(5005,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[5004]) ).
thf(5006,plain,
vd1363 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[5005:[bind(A,$thf( vd1363 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(8,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(155,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rcenter ) )
=> ( B @ ( A @ rinside ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ rinside ) )
| ~ ( B @ ( A @ rcenter ) ) ),
inference(cnf,[status(esa)],[155]) ).
thf(105,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(980,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)],[105]) ).
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(141,plain,
! [A: $i,B: $i] :
( ( ( B @ rreal )
& ( A = B ) )
=> ( ( v0 @ ( A @ vplus ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(44,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(471,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)],[44]) ).
thf(219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != C )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(cnfConj,[status(thm)],[210]) ).
thf(224,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ rtriangle )
| ( B != C )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[219]) ).
thf(225,plain,
! [B: $i,A: $i] :
~ ( B @ ( B @ ( A @ vtriangle ) ) @ rtriangle ),
inference(simp,[status(thm)],[224]) ).
thf(45,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(476,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)],[45]) ).
thf(57,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(590,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)],[57]) ).
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 ) ) )
=> ? [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(679,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)],[64]) ).
thf(8818,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[3000,199]) ).
thf(8819,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[8818]) ).
thf(8820,plain,
( ( vd14 @ sk50 @ sk50 @ ( vd14 @ sk50 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[8819:[bind(A,$thf( vd14 @ sk50 @ sk50 ))]]) ).
thf(239,plain,
vd1362 != vd1363,
inference(polarity_switch,[status(thm)],[238]) ).
thf(240,plain,
vd1362 != vd1363,
inference(lifteq,[status(thm)],[239]) ).
thf(4276,plain,
! [B: $i,A: $i] :
( ( A != vd1362 )
| ( B != vd1363 )
| ~ ( A @ ( B @ rless ) )
| ~ ( A @ rreal )
| ~ ( B @ rreal )
| ~ ( B @ ( A @ rless ) ) ),
inference(paramod_ordered,[status(thm)],[166,240]) ).
thf(4277,plain,
! [A: $i] :
( ( A != vd1363 )
| ~ ( vd1362 @ ( A @ rless ) )
| ~ ( vd1362 @ rreal )
| ~ ( A @ rreal )
| ~ ( A @ ( vd1362 @ rless ) ) ),
inference(pattern_uni,[status(thm)],[4276:[bind(A,$thf( vd1362 ))]]) ).
thf(4582,plain,
( ~ ( vd1362 @ ( vd1363 @ rless ) )
| ~ ( vd1362 @ rreal )
| ~ ( vd1363 @ rreal )
| ~ ( vd1363 @ ( vd1362 @ rless ) ) ),
inference(simp,[status(thm)],[4277]) ).
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(1114,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(114,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)],[114]) ).
thf(93,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(903,plain,
! [A: $i,B: $i] :
( ( ( B @ rline )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( A @ ( C @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(904,plain,
! [A: $i] :
( ? [B: $i] :
( ( B @ rline )
& ( A = B ) )
=> ? [B: $i] :
( ( B @ rpoint )
& ( A @ ( B @ ron ) ) ) ),
inference(miniscope,[status(thm)],[903]) ).
thf(905,plain,
! [B: $i,A: $i] :
( ( ( A @ sk44 @ rpoint )
| ~ ( B @ rline )
| ( A != B ) )
& ( ( A @ ( A @ sk44 @ ron ) )
| ~ ( B @ rline )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[904]) ).
thf(907,plain,
! [B: $i,A: $i] :
( ( A @ sk44 @ rpoint )
| ~ ( B @ rline )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[905]) ).
thf(910,plain,
! [B: $i,A: $i] :
( ( A @ sk44 @ rpoint )
| ~ ( B @ rline )
| ( A != B ) ),
inference(lifteq,[status(thm)],[907]) ).
thf(911,plain,
! [A: $i] :
( ( A @ sk44 @ rpoint )
| ~ ( A @ rline ) ),
inference(simp,[status(thm)],[910]) ).
thf(5750,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5006,1031]) ).
thf(5751,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[5750]) ).
thf(5752,plain,
vd1363 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[5751:[bind(A,$thf( vd1363 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(6686,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5752,1031]) ).
thf(6687,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[6686]) ).
thf(6688,plain,
vd1363 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[6687:[bind(A,$thf( vd1363 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(7617,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6688,1031]) ).
thf(7618,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[7617]) ).
thf(7619,plain,
vd1363 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[7618:[bind(A,$thf( vd1363 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(18,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(200,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)],[18]) ).
thf(201,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)],[200]) ).
thf(202,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)],[201]) ).
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 )
| ~ ( F @ rpoint )
| ~ ( E @ rpoint )
| ~ ( A @ ( C @ ron ) )
| ~ ( A @ ( D @ ron ) )
| ( A != B )
| ( C != F )
| ( D != E )
| ( C = D ) ),
inference(lifteq,[status(thm)],[202]) ).
thf(205,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)],[204]) ).
thf(5857,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5284,1031]) ).
thf(5858,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[5857]) ).
thf(5859,plain,
vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[5858:[bind(A,$thf( vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(6810,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5859,1031]) ).
thf(6811,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[6810]) ).
thf(6812,plain,
vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[6811:[bind(A,$thf( vd14 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(52,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(530,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)],[52]) ).
thf(2301,plain,
( ( ( vd1363 @ ( vd1361 @ vf ) @ ( vd1362 @ ( vd1361 @ vf ) @ rless ) )
!= ( v0 @ ( v0 @ rless ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[974,2291]) ).
thf(2302,plain,
( ( vd1363 @ ( vd1361 @ vf ) @ ( vd1362 @ ( vd1361 @ vf ) @ rless ) )
!= ( v0 @ ( v0 @ rless ) ) ),
inference(simp,[status(thm)],[2301]) ).
thf(2338,plain,
( ( ( vd1363 @ ( vd1361 @ vf ) )
!= v0 )
| ( ( vd1362 @ ( vd1361 @ vf ) )
!= v0 ) ),
inference(simp,[status(thm)],[2302]) ).
thf(73,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(750,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)],[73]) ).
thf(89,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(856,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)],[89]) ).
thf(158,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)],[157]) ).
thf(159,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)],[158]) ).
thf(160,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)],[159]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ~ ( A @ rreal )
| ~ ( B @ rreal )
| ( ( B @ ( A @ vplus ) )
= ( A @ ( B @ vplus ) ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(8872,plain,
! [A: $i] :
( ( ( vd14 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[589,199]) ).
thf(8873,plain,
! [A: $i] :
( ( ( vd14 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[8872]) ).
thf(8874,plain,
( ( vd14 @ ( vd14 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[8873:[bind(A,$thf( vd14 ))]]) ).
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(146,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(147,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)],[146]) ).
thf(148,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)],[147]) ).
thf(149,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ rcircle )
| ~ ( A @ ( B @ rcenter ) )
| ~ ( A @ ( C @ rcenter ) )
| ( B = C ) ),
inference(simp,[status(thm)],[148]) ).
thf(172,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)],[170]) ).
thf(175,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)],[172]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk1 ) ) @ rreal )
| ~ ( A @ rreal )
| ~ ( B @ rreal ) ),
inference(simp,[status(thm)],[175]) ).
thf(107,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(1007,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)],[107]) ).
thf(142,plain,
! [A: $i] :
( ? [B: $i] :
( ( B @ rreal )
& ( A = B ) )
=> ( ( v0 @ ( A @ vplus ) )
= A ) ),
inference(miniscope,[status(thm)],[141]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( ( v0 @ ( A @ vplus ) )
= A )
| ~ ( B @ rreal )
| ( A != B ) ),
inference(cnf,[status(esa)],[142]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ~ ( B @ rreal )
| ( ( v0 @ ( A @ vplus ) )
= A )
| ( A != B ) ),
inference(lifteq,[status(thm)],[143]) ).
thf(145,plain,
! [A: $i] :
( ~ ( A @ rreal )
| ( ( v0 @ ( A @ vplus ) )
= A ) ),
inference(simp,[status(thm)],[144]) ).
thf(1224,plain,
! [A: $i] :
( ( ( v0 @ rreal )
!= ( A @ rreal ) )
| ~ $true
| ( ( v0 @ ( A @ vplus ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[1156,145]) ).
thf(1225,plain,
! [A: $i] :
( ( ( v0 @ rreal )
!= ( A @ rreal ) )
| ( ( v0 @ ( A @ vplus ) )
= A ) ),
inference(simp,[status(thm)],[1224]) ).
thf(1226,plain,
( ( v0 @ ( v0 @ vplus ) )
= v0 ),
inference(pattern_uni,[status(thm)],[1225:[bind(A,$thf( v0 ))]]) ).
thf(87,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(843,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)],[87]) ).
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(1125,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(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(1139,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(6935,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6167,1031]) ).
thf(6936,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( A @ sk50 @ rpoint ) ),
inference(simp,[status(thm)],[6935]) ).
thf(6937,plain,
vd1361 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ rpoint,
inference(pattern_uni,[status(thm)],[6936:[bind(A,$thf( vd1361 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 @ sk50 ))]]) ).
thf(28,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(335,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)],[28]) ).
thf(80,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(804,plain,
! [A: $i,B: $i] :
( ( ( B @ rcircle )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( A @ ( C @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(66,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(704,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)],[66]) ).
thf(39,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(406,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)],[39]) ).
thf(33,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(362,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)],[33]) ).
thf(127,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(1144,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)],[127]) ).
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 ) )
& ? [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(616,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)],[59]) ).
thf(8792,plain,
! [A: $i] :
( ( ( vd1361 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[1169,199]) ).
thf(8793,plain,
! [A: $i] :
( ( ( vd1361 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[8792]) ).
thf(8794,plain,
( ( vd1361 @ ( vd1361 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[8793:[bind(A,$thf( vd1361 ))]]) ).
thf(74,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(764,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)],[74]) ).
thf(58,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(604,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)],[58]) ).
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(136,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(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(miniscope,[status(thm)],[136]) ).
thf(138,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)],[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 )
| ~ ( D @ rreal )
| ~ ( F @ rreal )
| ~ ( C @ ( A @ rless ) )
| ( A != B )
| ( C != D )
| ( E != F ) ),
inference(lifteq,[status(thm)],[138]) ).
thf(140,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)],[139]) ).
thf(98,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(943,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)],[98]) ).
thf(79,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(799,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)],[79]) ).
thf(1160,plain,
! [A: $i] :
( ( ( vd14 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[589,130]) ).
thf(1161,plain,
! [A: $i] :
( ( ( vd14 @ rpoint )
!= ( A @ rpoint ) )
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(simp,[status(thm)],[1160]) ).
thf(1162,plain,
( ~ ( vd1363 @ ( vd1361 @ ( vd14 @ rR ) ) )
| ( ( vd1362 @ ( vd1361 @ vf ) )
!= ( vd14 @ ( vd1363 @ vf ) ) ) ),
inference(pattern_uni,[status(thm)],[1161:[bind(A,$thf( vd14 ))]]) ).
thf(100,axiom,
vd1361 != vd1363,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(386, 8)') ).
thf(959,plain,
vd1361 != vd1363,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(960,plain,
vd1361 != vd1363,
inference(polarity_switch,[status(thm)],[959]) ).
thf(961,plain,
vd1361 != vd1363,
inference(lifteq,[status(thm)],[960]) ).
thf(4444,plain,
! [B: $i,A: $i] :
( ( A != vd1361 )
| ( B != vd1363 )
| ~ ( A @ ( B @ rless ) )
| ~ ( A @ rreal )
| ~ ( B @ rreal )
| ~ ( B @ ( A @ rless ) ) ),
inference(paramod_ordered,[status(thm)],[166,961]) ).
thf(4445,plain,
! [A: $i] :
( ( A != vd1363 )
| ~ ( vd1361 @ ( A @ rless ) )
| ~ ( vd1361 @ rreal )
| ~ ( A @ rreal )
| ~ ( A @ ( vd1361 @ rless ) ) ),
inference(pattern_uni,[status(thm)],[4444:[bind(A,$thf( vd1361 ))]]) ).
thf(4684,plain,
( ~ ( vd1361 @ ( vd1363 @ rless ) )
| ~ ( vd1361 @ rreal )
| ~ ( vd1363 @ rreal )
| ~ ( vd1363 @ ( vd1361 @ rless ) ) ),
inference(simp,[status(thm)],[4445]) ).
thf(2840,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[2787,130]) ).
thf(2841,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(simp,[status(thm)],[2840]) ).
thf(2842,plain,
( ~ ( vd1363 @ ( vd1361 @ ( vd1361 @ sk50 @ rR ) ) )
| ( ( vd1362 @ ( vd1361 @ vf ) )
!= ( vd1361 @ sk50 @ ( vd1363 @ vf ) ) ) ),
inference(pattern_uni,[status(thm)],[2841:[bind(A,$thf( vd1361 @ sk50 ))]]) ).
thf(94,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(912,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)],[94]) ).
thf(90,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(868,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)],[90]) ).
thf(91,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(883,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)],[91]) ).
thf(212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != C )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(cnfConj,[status(thm)],[210]) ).
thf(222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ rtriangle )
| ( A != C )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[212]) ).
thf(223,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( B @ vtriangle ) ) @ rtriangle ),
inference(simp,[status(thm)],[222]) ).
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(131,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(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(miniscope,[status(thm)],[131]) ).
thf(133,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)],[132]) ).
thf(134,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)],[133]) ).
thf(135,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)],[134]) ).
thf(88,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(851,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)],[88]) ).
thf(21,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(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(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(62,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(653,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)],[62]) ).
thf(8802,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[2809,199]) ).
thf(8803,plain,
! [A: $i] :
( ( ( vd14 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[8802]) ).
thf(8804,plain,
( ( vd14 @ sk50 @ ( vd14 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[8803:[bind(A,$thf( vd14 @ sk50 ))]]) ).
thf(35,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(374,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)],[35]) ).
thf(125,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(1134,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)],[125]) ).
thf(805,plain,
! [A: $i] :
( ? [B: $i] :
( ( B @ rcircle )
& ( A = B ) )
=> ? [B: $i] :
( ( B @ rpoint )
& ( A @ ( B @ ron ) ) ) ),
inference(miniscope,[status(thm)],[804]) ).
thf(806,plain,
! [B: $i,A: $i] :
( ( ( A @ sk39 @ rpoint )
| ~ ( B @ rcircle )
| ( A != B ) )
& ( ( A @ ( A @ sk39 @ ron ) )
| ~ ( B @ rcircle )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[805]) ).
thf(808,plain,
! [B: $i,A: $i] :
( ( A @ sk39 @ rpoint )
| ~ ( B @ rcircle )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[806]) ).
thf(811,plain,
! [B: $i,A: $i] :
( ( A @ sk39 @ rpoint )
| ~ ( B @ rcircle )
| ( A != B ) ),
inference(lifteq,[status(thm)],[808]) ).
thf(812,plain,
! [A: $i] :
( ( A @ sk39 @ rpoint )
| ~ ( A @ rcircle ) ),
inference(simp,[status(thm)],[811]) ).
thf(8834,plain,
! [A: $i] :
( ( ( vd1363 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[1187,199]) ).
thf(8835,plain,
! [A: $i] :
( ( ( vd1363 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[8834]) ).
thf(8836,plain,
( ( vd1363 @ ( vd1363 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[8835:[bind(A,$thf( vd1363 ))]]) ).
thf(97,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(939,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)],[97]) ).
thf(75,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 )
& ( B != C )
& ( ( B @ ( A @ vf ) )
= ( C @ ( A @ vf ) ) ) )
=> ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( E @ rpoint )
& ( D @ ( A @ ( B @ rR ) ) )
& ( G @ rpoint )
& ( F @ ( A @ ( C @ rR ) ) )
& ( F = G )
& ( D = E ) )
=> ( ( D @ ( B @ ( C @ vangle ) ) )
= ( F @ ( C @ ( B @ vangle ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(340), 0), 0)') ).
thf(776,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 )
& ( B != C )
& ( ( B @ ( A @ vf ) )
= ( C @ ( A @ vf ) ) ) )
=> ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( E @ rpoint )
& ( D @ ( A @ ( B @ rR ) ) )
& ( G @ rpoint )
& ( F @ ( A @ ( C @ rR ) ) )
& ( F = G )
& ( D = E ) )
=> ( ( D @ ( B @ ( C @ vangle ) ) )
= ( F @ ( C @ ( B @ vangle ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(51,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(525,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)],[51]) ).
thf(8770,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(paramod_ordered,[status(thm)],[2787,199]) ).
thf(8771,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ ( A @ vf ) )
= v0 ) ),
inference(simp,[status(thm)],[8770]) ).
thf(8772,plain,
( ( vd1361 @ sk50 @ ( vd1361 @ sk50 @ vf ) )
= v0 ),
inference(pattern_uni,[status(thm)],[8771:[bind(A,$thf( vd1361 @ sk50 ))]]) ).
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(150,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(72,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(739,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)],[72]) ).
thf(118,axiom,
( ( vd1363 @ ( vd1362 @ ( vd1361 @ vangle ) ) )
= ( vd1362 @ ( vd1363 @ ( vd1361 @ vangle ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(386, 1365, 0)') ).
thf(1097,plain,
( ( vd1363 @ ( vd1362 @ ( vd1361 @ vangle ) ) )
= ( vd1362 @ ( vd1363 @ ( vd1361 @ vangle ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1098,plain,
( ( vd1363 @ ( vd1362 @ ( vd1361 @ vangle ) ) )
= ( vd1362 @ ( vd1363 @ ( vd1361 @ vangle ) ) ) ),
inference(lifteq,[status(thm)],[1097]) ).
thf(106,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(1003,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)],[106]) ).
thf(3374,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[2971,130]) ).
thf(3375,plain,
! [A: $i] :
( ( ( vd1363 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(simp,[status(thm)],[3374]) ).
thf(3376,plain,
( ~ ( vd1363 @ ( vd1361 @ ( vd1363 @ sk50 @ sk50 @ rR ) ) )
| ( ( vd1362 @ ( vd1361 @ vf ) )
!= ( vd1363 @ sk50 @ sk50 @ ( vd1363 @ vf ) ) ) ),
inference(pattern_uni,[status(thm)],[3375:[bind(A,$thf( vd1363 @ sk50 @ sk50 ))]]) ).
thf(27,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(331,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)],[27]) ).
thf(53,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(544,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)],[53]) ).
thf(78,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(791,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)],[78]) ).
thf(14,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(182,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)],[14]) ).
thf(183,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)],[182]) ).
thf(184,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)],[183]) ).
thf(185,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)],[184]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ rless ) )
| ( B @ ( A @ rless ) )
| ~ ( A @ rreal )
| ~ ( B @ rreal )
| ( A = B ) ),
inference(simp,[status(thm)],[185]) ).
thf(1541,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)],[1156,186]) ).
thf(1542,plain,
! [B: $i,A: $i] :
( ( ( v0 @ rreal )
!= ( B @ rreal ) )
| ( A @ ( B @ rless ) )
| ( B @ ( A @ rless ) )
| ~ ( A @ rreal )
| ( A = B ) ),
inference(simp,[status(thm)],[1541]) ).
thf(1543,plain,
! [A: $i] :
( ( A @ ( v0 @ rless ) )
| ( v0 @ ( A @ rless ) )
| ~ ( A @ rreal )
| ( A = v0 ) ),
inference(pattern_uni,[status(thm)],[1542:[bind(A,$thf( A )),bind(B,$thf( v0 ))]]) ).
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(miniscope,[status(thm)],[150]) ).
thf(152,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)],[151]) ).
thf(153,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)],[152]) ).
thf(154,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)],[153]) ).
thf(113,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)],[113]) ).
thf(3166,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[2942,130]) ).
thf(3167,plain,
! [A: $i] :
( ( ( vd1362 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(simp,[status(thm)],[3166]) ).
thf(3168,plain,
( ~ ( vd1363 @ ( vd1361 @ ( vd1362 @ sk50 @ sk50 @ rR ) ) )
| ( ( vd1362 @ ( vd1361 @ vf ) )
!= ( vd1362 @ sk50 @ sk50 @ ( vd1363 @ vf ) ) ) ),
inference(pattern_uni,[status(thm)],[3167:[bind(A,$thf( vd1362 @ sk50 @ sk50 ))]]) ).
thf(22,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(250,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)],[22]) ).
thf(1170,plain,
! [A: $i] :
( ( ( sk33 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[729,130]) ).
thf(1171,plain,
! [A: $i] :
( ( ( sk33 @ rpoint )
!= ( A @ rpoint ) )
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(simp,[status(thm)],[1170]) ).
thf(1172,plain,
( ~ ( vd1363 @ ( vd1361 @ ( sk33 @ rR ) ) )
| ( ( vd1362 @ ( vd1361 @ vf ) )
!= ( sk33 @ ( vd1363 @ vf ) ) ) ),
inference(pattern_uni,[status(thm)],[1171:[bind(A,$thf( sk33 ))]]) ).
thf(1216,plain,
( ~ ( vd1363 @ ( vd1361 @ ( vd1362 @ rR ) ) )
| ( ( vd1362 @ ( vd1361 @ vf ) )
!= ( vd1362 @ ( vd1363 @ vf ) ) ) ),
inference(rewrite,[status(thm)],[1172,730]) ).
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(1101,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(38,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(401,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)],[38]) ).
thf(76,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(781,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)],[76]) ).
thf(81,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(813,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)],[81]) ).
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(731,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(77,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(786,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)],[77]) ).
thf(63,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(667,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)],[63]) ).
thf(67,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(716,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)],[67]) ).
thf(36,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(378,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)],[36]) ).
thf(50,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(510,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)],[50]) ).
thf(1175,plain,
! [A: $i] :
( ( ( sk47 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[978,130]) ).
thf(1176,plain,
! [A: $i] :
( ( ( sk47 @ rpoint )
!= ( A @ rpoint ) )
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(simp,[status(thm)],[1175]) ).
thf(1177,plain,
( ~ ( vd1363 @ ( vd1361 @ ( sk47 @ rR ) ) )
| ( ( vd1362 @ ( vd1361 @ vf ) )
!= ( sk47 @ ( vd1363 @ vf ) ) ) ),
inference(pattern_uni,[status(thm)],[1176:[bind(A,$thf( sk47 ))]]) ).
thf(1222,plain,
( ~ ( vd1363 @ ( vd1361 @ ( vd1363 @ rR ) ) )
| ( ( vd1362 @ ( vd1361 @ vf ) )
!= ( vd1363 @ ( vd1363 @ vf ) ) ) ),
inference(rewrite,[status(thm)],[1177,979]) ).
thf(9239,plain,
( ~ ( vd1363 @ ( vd1361 @ ( vd1363 @ rR ) ) )
| ( ( vd1362 @ ( vd1361 @ vf ) )
!= v0 ) ),
inference(rewrite,[status(thm)],[1222,8836]) ).
thf(40,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(410,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)],[40]) ).
thf(857,plain,
! [A: $i] :
( ? [B: $i] :
( ( B @ rcircle )
& ( A = B ) )
=> ? [B: $i] :
( ( B @ rpoint )
& ~ ( A @ ( B @ rinside ) )
& ~ ( A @ ( B @ ron ) ) ) ),
inference(miniscope,[status(thm)],[856]) ).
thf(858,plain,
! [B: $i,A: $i] :
( ( ( A @ sk41 @ rpoint )
| ~ ( B @ rcircle )
| ( A != B ) )
& ( ~ ( A @ ( A @ sk41 @ rinside ) )
| ~ ( B @ rcircle )
| ( A != B ) )
& ( ~ ( A @ ( A @ sk41 @ ron ) )
| ~ ( B @ rcircle )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[857]) ).
thf(861,plain,
! [B: $i,A: $i] :
( ( A @ sk41 @ rpoint )
| ~ ( B @ rcircle )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[858]) ).
thf(866,plain,
! [B: $i,A: $i] :
( ( A @ sk41 @ rpoint )
| ~ ( B @ rcircle )
| ( A != B ) ),
inference(lifteq,[status(thm)],[861]) ).
thf(867,plain,
! [A: $i] :
( ( A @ sk41 @ rpoint )
| ~ ( A @ rcircle ) ),
inference(simp,[status(thm)],[866]) ).
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(735,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(115,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(1065,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)],[115]) ).
thf(3043,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(paramod_ordered,[status(thm)],[2831,130]) ).
thf(3044,plain,
! [A: $i] :
( ( ( vd1361 @ sk50 @ sk50 @ rpoint )
!= ( A @ rpoint ) )
| ~ ( vd1363 @ ( vd1361 @ ( A @ rR ) ) )
| ( ( A @ ( vd1363 @ vf ) )
!= ( vd1362 @ ( vd1361 @ vf ) ) ) ),
inference(simp,[status(thm)],[3043]) ).
thf(3045,plain,
( ~ ( vd1363 @ ( vd1361 @ ( vd1361 @ sk50 @ sk50 @ rR ) ) )
| ( ( vd1362 @ ( vd1361 @ vf ) )
!= ( vd1361 @ sk50 @ sk50 @ ( vd1363 @ vf ) ) ) ),
inference(pattern_uni,[status(thm)],[3044:[bind(A,$thf( vd1361 @ sk50 @ sk50 ))]]) ).
thf(99,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(955,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)],[99]) ).
thf(108,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(1019,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)],[108]) ).
thf(43,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(459,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)],[43]) ).
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 ) )
& ? [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(254,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)],[23]) ).
thf(47,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(486,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)],[47]) ).
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 ) )
& ( 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(639,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)],[61]) ).
thf(48,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(491,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)],[48]) ).
thf(49,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(496,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)],[49]) ).
thf(26128,plain,
$false,
inference(e,[status(thm)],[6167,1105,1031,2787,1110,481,1083,962,730,8797,3417,3153,2953,3402,269,1041,1173,4564,340,174,898,4916,5284,838,344,157,817,559,3463,1100,8902,189,924,834,238,2291,574,353,966,1051,821,280,396,2799,265,2982,1169,687,3361,2809,1074,3011,920,366,7078,8783,825,349,424,192,229,1032,197,625,435,1178,974,5006,156,725,980,188,141,471,225,476,590,679,8820,3000,4582,1114,1099,1060,911,721,7619,128,205,6812,530,2338,1187,6688,750,166,856,161,8874,149,975,176,1007,191,5752,1226,843,1125,1139,6937,5859,335,804,181,704,187,406,362,1144,616,208,8794,764,979,604,140,240,943,155,799,1162,726,4684,2842,912,130,959,868,883,223,135,851,167,241,653,3444,5538,589,162,8804,374,1134,812,8836,939,6564,145,1049,2942,776,525,8772,1156,150,739,1098,2831,1003,3376,199,331,544,177,791,182,1543,1023,154,1052,3168,250,903,1216,1101,186,2971,401,781,961,813,731,786,667,716,2796,378,3497,510,9239,410,146,867,735,1097,168,136,3030,3633,1065,3045,955,1019,459,131,200,5645,254,4826,486,4752,639,491,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO336+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
% 0.13/0.40 % Computer : n017.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Fri Sep 25 13:15:32 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 1.23/1.19 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.95/1.72 % [INFO] Parsing done (522ms).
% 2.95/1.74 % [INFO] Running in sequential loop mode.
% 4.02/2.37 % [INFO] eprover registered as external prover.
% 4.02/2.38 % [INFO] Scanning for conjecture ...
% 4.58/2.60 % [INFO] Found a conjecture (or negated_conjecture) and 125 axioms. Running axiom selection ...
% 4.80/2.78 % [INFO] Axiom selection finished. Selected 125 axioms (removed 0 axioms).
% 6.49/3.36 % [INFO] Problem is first-order (TPTP FOF).
% 6.74/3.43 % [INFO] Type checking passed.
% 6.74/3.44 % [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 ...
% 141.90/38.02 % External prover 'e' found a proof!
% 141.90/38.02 % [INFO] Killing All external provers ...
% 141.90/38.03 % Time passed: 37420ms (effective reasoning time: 36275ms)
% 141.90/38.03 % 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)>
% 141.90/38.03 % Axioms used in derivation (125): qu(cond(axiom(71), 0), imp(cond(axiom(71), 0))), qu(cond(axiom(41), 0), imp(cond(axiom(41), 0))), pred(386, 7), 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), qe(s3(plural(386))), qu(cond(axiom(202), 0), imp(cond(axiom(202), 0))), qu(cond(axiom(19), 0), imp(cond(axiom(19), 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(386, 8), 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), ass(cond(goal(340), 0), 0), 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))), neg(389), ass(cond(goal(238), 0), 0), qu(cond(axiom(77), 0), imp(cond(axiom(77), 0))), qu(cond(axiom(113), 0), imp(cond(axiom(113), 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))), ass(cond(goal(340), 0), 1), 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))), 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))), holds(395, 1377, 0), ass(cond(156, 0), 0), qu(cond(axiom(184), 0), imp(cond(axiom(184), 0))), qu(cond(axiom(188), 0), imp(cond(axiom(188), 0))), qu(cond(axiom(99), 0), imp(cond(axiom(99), 0))), ass(cond(goal(238), 0), 1), pred(386, 9), 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))), qe(s2(plural(386))), 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))), 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))), qu(cond(axiom(170), 0), imp(cond(axiom(170), 0))), qu(cond(axiom(111), 0), imp(cond(axiom(111), 0))), holds(386, 1365, 0), holds(387, 1369, 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))), 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))), qu(cond(axiom(39), 0), imp(cond(axiom(39), 0))), qu(cond(axiom(129), 0), imp(cond(axiom(129), 0))), qe(s1(plural(386))), qu(cond(axiom(73), 0), imp(cond(axiom(73), 0))), qu(cond(axiom(15), 0), imp(cond(axiom(15), 0))), 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))), 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))), 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)))
% 141.90/38.03 % No. of inferences in proof: 553
% 141.90/38.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 37420 ms resp. 36275 ms w/o parsing
% 144.31/38.48 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 144.31/38.49 % [INFO] Killing All external provers ...
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