%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO271+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 : n018.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 07:13:06 AM UTC 2026
% Result : Theorem 31.81s 10.27s
% Output : Refutation 32.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 105
% Syntax : Number of formulae : 212 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 2354 ( 924 equ; 0 cnn)
% Maximal formula atoms : 57 ( 11 avg)
% Number of connectives : 5154 ( 244 ~; 24 |;1889 &;2768 @)
% ( 8 <=>; 221 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 10 con; 0-3 aty)
% Number of variables : 1455 ( 0 ^; 929 !; 526 ?;1455 :)
% Comments :
%------------------------------------------------------------------------------
thf(ron_decl,type,
ron: $i > $i > $o ).
thf(vd1057_decl,type,
vd1057: $i ).
thf(rcenter_decl,type,
rcenter: $i > $i > $o ).
thf(vd1055_decl,type,
vd1055: $i ).
thf(rcircle_decl,type,
rcircle: $i > $o ).
thf(vd1061_decl,type,
vd1061: $i ).
thf(rreal_decl,type,
rreal: $i > $o ).
thf(vd684_decl,type,
vd684: $i ).
thf(vplus_decl,type,
vplus: $i > $i > $i ).
thf(rless_decl,type,
rless: $i > $i > $o ).
thf(vtriangle_decl,type,
vtriangle: $i > $i > $i > $i ).
thf(rtriangle_decl,type,
rtriangle: $i > $o ).
thf(rpoint_decl,type,
rpoint: $i > $o ).
thf(vg_decl,type,
vg: $i > $i > $i > $i ).
thf(v0_decl,type,
v0: $i ).
thf(vf_decl,type,
vf: $i > $i > $i ).
thf(vangle_decl,type,
vangle: $i > $i > $i > $i ).
thf(rS_decl,type,
rS: $i > $i > $i > $o ).
thf(rR_decl,type,
rR: $i > $i > $i > $o ).
thf(rline_decl,type,
rline: $i > $o ).
thf(rleq_decl,type,
rleq: $i > $i > $o ).
thf(rgeq_decl,type,
rgeq: $i > $i > $o ).
thf(vd14_decl,type,
vd14: $i ).
thf(vperp_decl,type,
vperp: $i ).
thf(vd1058_decl,type,
vd1058: $i ).
thf(vd1056_decl,type,
vd1056: $i ).
thf(rintersect_decl,type,
rintersect: $i > $i > $o ).
thf(rinside_decl,type,
rinside: $i > $i > $o ).
thf(92,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(902,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)],[92]) ).
thf(85,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(843,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)],[85]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( D = E )
& ( C @ ( A @ ( B @ rR ) ) )
& ( D @ ( B @ ron ) ) )
=> ~ ( D @ ( C @ ( A @ rS ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(109), 0), imp(cond(axiom(109), 0)))') ).
thf(490,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)],[49]) ).
thf(31,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(300,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)],[31]) ).
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 )
& ( 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(760,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)],[76]) ).
thf(63,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(628,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)],[63]) ).
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 )
& ( ( E @ ( A @ vplus ) )
= ( E @ ( C @ vplus ) ) ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(156, 0), 0)') ).
thf(115,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)],[4]) ).
thf(73,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(741,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)],[73]) ).
thf(5,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(120,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)],[5]) ).
thf(65,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(655,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)],[65]) ).
thf(52,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(511,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)],[52]) ).
thf(48,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(472,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)],[48]) ).
thf(82,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(814,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)],[82]) ).
thf(36,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(340,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)],[36]) ).
thf(83,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(829,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)],[83]) ).
thf(91,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(898,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)],[91]) ).
thf(103,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(1001,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)],[103]) ).
thf(79,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(782,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)],[79]) ).
thf(6,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(125,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)],[6]) ).
thf(94,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(934,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)],[94]) ).
thf(23,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(253,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)],[23]) ).
thf(84,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(834,plain,
! [A: $i,B: $i] :
( ( ( B @ rline )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( A @ ( C @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(28,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(280,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)],[28]) ).
thf(97,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(956,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)],[97]) ).
thf(78,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(774,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)],[78]) ).
thf(101,axiom,
( ( vd1061 @ rcircle )
& ( vd1061 @ ( vd1055 @ rcenter ) )
& ( vd1061 @ ( vd1057 @ ron ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','and(pred(comma_conjunct2(the(211)), 0), and(pred(comma_conjunct1(the(211)), 0), pred(the(211), 0)))') ).
thf(988,plain,
( ( vd1061 @ rcircle )
& ( vd1061 @ ( vd1055 @ rcenter ) )
& ( vd1061 @ ( vd1057 @ ron ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(21,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(243,plain,
! [A: $i,B: $i] :
( ( ( B @ rreal )
& ( A = B ) )
=> ( ( v0 @ ( A @ vplus ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(22,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(248,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)],[22]) ).
thf(95,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(942,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)],[95]) ).
thf(67,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(678,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)],[67]) ).
thf(54,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(546,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)],[54]) ).
thf(93,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(925,plain,
! [A: $i,B: $i] :
( ( ( B @ rcircle )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( A @ ( C @ rinside ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(14,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(201,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)],[14]) ).
thf(74,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(746,plain,
! [A: $i,B: $i] :
( ( ( B @ rcircle )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( A @ ( C @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(87,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(862,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)],[87]) ).
thf(61,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(598,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)],[61]) ).
thf(12,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(192,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)],[12]) ).
thf(27,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(275,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)],[27]) ).
thf(13,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(197,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)],[13]) ).
thf(53,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(522,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)],[53]) ).
thf(29,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(285,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)],[29]) ).
thf(59,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(578,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)],[59]) ).
thf(88,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(874,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)],[88]) ).
thf(11,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(188,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)],[11]) ).
thf(38,axiom,
v0 = vd684,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(137), 2)') ).
thf(356,plain,
v0 = vd684,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(60,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(593,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)],[60]) ).
thf(43,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(393,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)],[43]) ).
thf(71,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(721,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)],[71]) ).
thf(25,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(266,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)],[25]) ).
thf(15,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(205,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)],[15]) ).
thf(55,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(558,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)],[55]) ).
thf(106,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(1026,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)],[106]) ).
thf(98,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(965,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)],[98]) ).
thf(58,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(573,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)],[58]) ).
thf(10,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(180,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)],[10]) ).
thf(44,axiom,
( ( vd1056 @ rpoint )
& ( vd1055 = vd1056 )
& ( vd1058 @ rpoint )
& ( vd1055 != vd1057 )
& ( vd1057 = vd1058 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','and(pred(conjunct2(210), 4), and(holds(conjunct2(210), 1059, 0), and(pred(conjunct2(210), 1), and(pred(conjunct1(210), 2), pred(conjunct1(210), 1)))))') ).
thf(444,plain,
( ( vd1056 @ rpoint )
& ( vd1055 = vd1056 )
& ( vd1058 @ rpoint )
& ( vd1055 != vd1057 )
& ( vd1057 = vd1058 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(72,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(733,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)],[72]) ).
thf(42,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(382,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)],[42]) ).
thf(80,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(787,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)],[80]) ).
thf(35,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(335,plain,
! [A: $i,B: $i] :
( ( ( B @ rreal )
& ( A = B ) )
=> ~ ( A @ ( A @ rless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(96,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(947,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)],[96]) ).
thf(8,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(159,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)],[8]) ).
thf(99,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(979,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)],[99]) ).
thf(26,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(271,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)],[26]) ).
thf(33,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(323,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)],[33]) ).
thf(81,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(799,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)],[81]) ).
thf(77,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(769,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)],[77]) ).
thf(7,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(155,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)],[7]) ).
thf(37,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(345,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)],[37]) ).
thf(86,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(858,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)],[86]) ).
thf(40,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(367,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)],[40]) ).
thf(100,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(983,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)],[100]) ).
thf(69,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(695,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)],[69]) ).
thf(105,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(1015,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)],[105]) ).
thf(56,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(563,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)],[56]) ).
thf(30,axiom,
vd14 @ rpoint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(5), 0)') ).
thf(299,plain,
vd14 @ rpoint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(68,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(690,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)],[68]) ).
thf(70,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(707,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)],[70]) ).
thf(102,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(993,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)],[102]) ).
thf(34,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(331,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)],[34]) ).
thf(47,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(463,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)],[47]) ).
thf(64,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(643,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)],[64]) ).
thf(62,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(613,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)],[62]) ).
thf(32,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(314,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)],[32]) ).
thf(51,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(497,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)],[51]) ).
thf(50,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(495,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rcenter ) )
=> ( B @ ( A @ rinside ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(18,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(218,plain,
! [A: $i,B: $i] :
( ( ( B @ rpoint )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(104,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(1010,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)],[104]) ).
thf(24,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(258,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)],[24]) ).
thf(3,axiom,
vd684 @ rreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(137), 1)') ).
thf(114,plain,
vd684 @ rreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(57,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(568,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)],[57]) ).
thf(41,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(378,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)],[41]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) ) )
=> ( ( ( B @ ( A @ vf ) )
= v0 )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(162), 0), imp(cond(axiom(162), 0)))') ).
thf(235,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) ) )
=> ( ( ( A = B )
=> ( ( B @ ( A @ vf ) )
= v0 ) )
& ( ( ( B @ ( A @ vf ) )
= v0 )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(17,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(214,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)],[17]) ).
thf(16,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(210,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)],[16]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ rcircle )
& ( A @ ( vd1055 @ rcenter ) )
& ( A @ ( vd1057 @ ron ) ) )
=> ( A = vd1061 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(theu(the(211), 1), imp(the(211)))') ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ rcircle )
& ( A @ ( vd1055 @ rcenter ) )
& ( A @ ( vd1057 @ ron ) ) )
=> ( A = vd1061 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(107,plain,
~ ! [A: $i] :
( ( ( A @ rcircle )
& ( A @ ( vd1055 @ rcenter ) )
& ( A @ ( vd1057 @ ron ) ) )
=> ( A = vd1061 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(39,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(358,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)],[39]) ).
thf(66,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(664,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)],[66]) ).
thf(90,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(886,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)],[90]) ).
thf(46,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(459,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)],[46]) ).
thf(9,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(163,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)],[9]) ).
thf(19,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(227,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)],[19]) ).
thf(75,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(755,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)],[75]) ).
thf(45,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(454,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)],[45]) ).
thf(89,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(882,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)],[89]) ).
thf(1324,plain,
$false,
inference(e,[status(thm)],[902,843,490,300,760,628,115,741,120,655,511,472,814,340,829,898,1001,782,125,934,253,834,280,956,774,988,243,248,942,678,546,925,201,746,862,598,192,275,197,522,285,578,874,188,356,593,393,721,266,205,558,1026,965,573,180,444,733,382,787,335,947,159,979,271,323,799,769,155,345,858,367,983,695,1015,563,299,690,707,993,331,463,643,613,314,497,495,218,1010,258,114,568,378,235,214,210,107,358,664,886,459,163,227,755,454,882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO271+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.12 % 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
% 0.23/0.47 % Computer : n018.cluster.edu
% 0.23/0.47 % Model : x86_64 x86_64
% 0.23/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.47 % Memory : 8046.5625MB
% 0.23/0.47 % OS : Linux 6.8.0-71-generic
% 0.23/0.47 % CPULimit : 300
% 0.23/0.47 % WCLimit : 300
% 0.23/0.47 % DateTime : Fri Sep 25 13:13:50 UTC 2026
% 0.23/0.47 % CPUTime :
% 0.23/0.47 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
% 1.43/1.33 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.94/1.82 % [INFO] Parsing done (493ms).
% 2.94/1.84 % [INFO] Running in sequential loop mode.
% 4.25/2.42 % [INFO] eprover registered as external prover.
% 4.25/2.43 % [INFO] Scanning for conjecture ...
% 4.60/2.63 % [INFO] Found a conjecture (or negated_conjecture) and 104 axioms. Running axiom selection ...
% 5.12/2.81 % [INFO] Axiom selection finished. Selected 104 axioms (removed 0 axioms).
% 6.43/3.31 % [INFO] Problem is first-order (TPTP FOF).
% 6.43/3.37 % [INFO] Type checking passed.
% 6.43/3.38 % [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 ...
% 31.81/10.26 % External prover 'e' found a proof!
% 31.81/10.27 % [INFO] Killing All external provers ...
% 31.81/10.27 % Time passed: 9579ms (effective reasoning time: 8414ms)
% 31.81/10.27 % 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)>
% 31.81/10.27 % Axioms used in derivation (104): qu(cond(axiom(103), 0), imp(cond(axiom(103), 0))), qu(cond(axiom(71), 0), imp(cond(axiom(71), 0))), qu(cond(axiom(73), 0), imp(cond(axiom(73), 0))), and(pred(conjunct2(210), 4), and(holds(conjunct2(210), 1059, 0), and(pred(conjunct2(210), 1), and(pred(conjunct1(210), 2), pred(conjunct1(210), 1))))), qu(cond(axiom(41), 0), imp(cond(axiom(41), 0))), qu(cond(axiom(145), 0), imp(cond(axiom(145), 0))), qu(cond(axiom(119), 0), imp(cond(axiom(119), 0))), qu(cond(axiom(3), 0), imp(cond(axiom(3), 0))), qu(cond(axiom(164), 0), imp(cond(axiom(164), 0))), qu(cond(axiom(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))), qu(cond(axiom(133), 0), imp(cond(axiom(133), 0))), qu(cond(axiom(21), 0), imp(cond(axiom(21), 0))), qu(cond(axiom(151), 0), imp(cond(axiom(151), 0))), pred(axiom(5), 0), qu(cond(axiom(75), 0), imp(cond(axiom(75), 0))), qu(cond(axiom(194), 0), imp(cond(axiom(194), 0))), qu(cond(axiom(190), 0), imp(cond(axiom(190), 0))), qu(cond(axiom(53), 0), imp(cond(axiom(53), 0))), qu(cond(axiom(89), 0), imp(cond(axiom(89), 0))), qu(cond(axiom(107), 0), imp(cond(axiom(107), 0))), pred(axiom(137), 2), qu(cond(axiom(31), 0), imp(cond(axiom(31), 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))), 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))), 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))), and(pred(comma_conjunct2(the(211)), 0), and(pred(comma_conjunct1(the(211)), 0), pred(the(211), 0))), qu(cond(axiom(57), 0), imp(cond(axiom(57), 0))), qu(cond(axiom(65), 0), imp(cond(axiom(65), 0))), qu(cond(axiom(174), 0), imp(cond(axiom(174), 0))), qu(cond(axiom(61), 0), imp(cond(axiom(61), 0))), qu(cond(axiom(9), 0), imp(cond(axiom(9), 0))), qu(cond(axiom(182), 0), imp(cond(axiom(182), 0))), qu(cond(axiom(117), 0), imp(cond(axiom(117), 0))), 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))), qu(cond(axiom(166), 0), imp(cond(axiom(166), 0))), qu(cond(axiom(105), 0), imp(cond(axiom(105), 0))), qu(cond(axiom(37), 0), imp(cond(axiom(37), 0))), qu(cond(axiom(63), 0), imp(cond(axiom(63), 0))), qu(cond(axiom(192), 0), imp(cond(axiom(192), 0))), pred(axiom(137), 1), 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))), qu(cond(axiom(15), 0), imp(cond(axiom(15), 0))), qu(cond(axiom(85), 0), imp(cond(axiom(85), 0))), 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))), 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)))
% 31.81/10.27 % No. of inferences in proof: 212
% 31.81/10.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9579 ms resp. 8414 ms w/o parsing
% 32.09/10.48 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 32.09/10.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------