%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO286+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 : n014.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 07:13:08 AM UTC 2026
% Result : Theorem 56.54s 15.16s
% Output : Refutation 57.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 135
% Syntax : Number of formulae : 272 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 2578 (1051 equ; 0 cnn)
% Maximal formula atoms : 57 ( 9 avg)
% Number of connectives : 5663 ( 324 ~; 24 |;2000 &;3033 @)
% ( 8 <=>; 274 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 42 usr; 22 con; 0-4 aty)
% Number of variables : 1503 ( 0 ^; 966 !; 537 ?;1503 :)
% Comments :
%------------------------------------------------------------------------------
thf(rR_decl,type,
rR: $i > $i > $i > $o ).
thf(vd1123_decl,type,
vd1123: $i ).
thf(vd1125_decl,type,
vd1125: $i ).
thf(ron_decl,type,
ron: $i > $i > $o ).
thf(vd1152_decl,type,
vd1152: $i ).
thf(vd1151_decl,type,
vd1151: $i ).
thf(rpoint_decl,type,
rpoint: $i > $o ).
thf(vplus_decl,type,
vplus: $i > $i > $i ).
thf(rreal_decl,type,
rreal: $i > $o ).
thf(rless_decl,type,
rless: $i > $i > $o ).
thf(v0_decl,type,
v0: $i ).
thf(rcenter_decl,type,
rcenter: $i > $i > $o ).
thf(rcircle_decl,type,
rcircle: $i > $o ).
thf(rinside_decl,type,
rinside: $i > $i > $o ).
thf(vd684_decl,type,
vd684: $i ).
thf(vf_decl,type,
vf: $i > $i > $i ).
thf(rline_decl,type,
rline: $i > $o ).
thf(vd1127_decl,type,
vd1127: $i ).
thf(vskolem1147_decl,type,
vskolem1147: $i ).
thf(vskolem1145_decl,type,
vskolem1145: $i ).
thf(vangle_decl,type,
vangle: $i > $i > $i > $i ).
thf(vperp_decl,type,
vperp: $i ).
thf(rS_decl,type,
rS: $i > $i > $i > $o ).
thf(rintersect_decl,type,
rintersect: $i > $i > $o ).
thf(vd1129_decl,type,
vd1129: $i ).
thf(vskolem1140_decl,type,
vskolem1140: $i ).
thf(vtriangle_decl,type,
vtriangle: $i > $i > $i > $i ).
thf(rtriangle_decl,type,
rtriangle: $i > $o ).
thf(vg_decl,type,
vg: $i > $i > $i > $i ).
thf(vskolem1136_decl,type,
vskolem1136: $i ).
thf(vskolem1139_decl,type,
vskolem1139: $i ).
thf(vskolem1138_decl,type,
vskolem1138: $i ).
thf(vskolem1052_decl,type,
vskolem1052: $i > $i > $i > $i > $i ).
thf(vskolem1078_decl,type,
vskolem1078: $i > $i > $i > $i > $i ).
thf(vskolem1146_decl,type,
vskolem1146: $i ).
thf(rgeq_decl,type,
rgeq: $i > $i > $o ).
thf(vd14_decl,type,
vd14: $i ).
thf(rleq_decl,type,
rleq: $i > $i > $o ).
thf(vd1130_decl,type,
vd1130: $i ).
thf(vd1128_decl,type,
vd1128: $i ).
thf(vd1126_decl,type,
vd1126: $i ).
thf(vd1124_decl,type,
vd1124: $i ).
thf(30,axiom,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( ( vd1129 @ ( vd1127 @ vf ) )
= ( vskolem1136 @ ( vd1123 @ vf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 10)') ).
thf(365,plain,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( ( vd1129 @ ( vd1127 @ vf ) )
= ( vskolem1136 @ ( vd1123 @ vf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(115,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(1031,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)],[115]) ).
thf(136,axiom,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( vskolem1139 @ ( vskolem1140 @ ron ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 3)') ).
thf(1179,plain,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( vskolem1139 @ ( vskolem1140 @ ron ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(41,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(440,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)],[41]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( H @ rline )
& ( A = H ) )
& ? [H: $i] :
( ( H @ rline )
& ( B = H ) )
& ? [H: $i] :
( ( H @ rline )
& ( C = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( D = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( E = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( F = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( G = H ) )
& ( A @ ( D @ ron ) )
& ( B @ ( D @ ron ) )
& ( C @ ( D @ ron ) )
& ( A @ ( E @ ron ) )
& ( C @ ( F @ ron ) )
& ( C @ ( G @ ron ) )
& ( A @ ( G @ ( F @ rS ) ) )
& ( C @ ( F @ ( E @ rS ) ) ) )
=> ~ ( B @ ( G @ ( E @ rS ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(113), 0), imp(cond(axiom(113), 0)))') ).
thf(408,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( H @ rline )
& ( A = H ) )
& ? [H: $i] :
( ( H @ rline )
& ( B = H ) )
& ? [H: $i] :
( ( H @ rline )
& ( C = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( D = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( E = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( F = H ) )
& ? [H: $i] :
( ( H @ rpoint )
& ( G = H ) )
& ( A @ ( D @ ron ) )
& ( B @ ( D @ ron ) )
& ( C @ ( D @ ron ) )
& ( A @ ( E @ ron ) )
& ( C @ ( F @ ron ) )
& ( C @ ( G @ ron ) )
& ( A @ ( G @ ( F @ rS ) ) )
& ( C @ ( F @ ( E @ rS ) ) ) )
=> ~ ( B @ ( G @ ( E @ rS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(111,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(977,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)],[111]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( C @ ( A @ rless ) ) )
=> ( ( A = C )
| ~ ( A @ ( C @ rless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(147), 0), imp(cond(axiom(147), 0)))') ).
thf(170,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( C @ ( A @ rless ) ) )
=> ( ( A = C )
| ~ ( A @ ( C @ rless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) )
& ( A != B ) )
=> ! [C: $i,D: $i] :
( ( ( D @ rpoint )
& ( C != A )
& ( C != B )
& ( C = D ) )
=> ( ( B @ ( A @ vf ) )
= ( B @ ( A @ ( D @ ( C @ vskolem1078 ) ) ) @ ( C @ vf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(219), 0), 0)') ).
thf(384,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) )
& ( A != B ) )
=> ! [C: $i,D: $i] :
( ( ( D @ rpoint )
& ( C != A )
& ( C != B )
& ( C = D ) )
=> ( ( B @ ( A @ vf ) )
= ( B @ ( A @ ( D @ ( C @ vskolem1078 ) ) ) @ ( C @ vf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(85,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(797,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)],[85]) ).
thf(78,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(747,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)],[78]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( B @ rreal )
& ( A = B ) )
=> ~ ( A @ ( A @ rless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(149), 0), imp(cond(axiom(149), 0)))') ).
thf(185,plain,
! [A: $i,B: $i] :
( ( ( B @ rreal )
& ( A = B ) )
=> ~ ( A @ ( A @ rless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(110,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(973,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)],[110]) ).
thf(103,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(917,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)],[103]) ).
thf(86,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(802,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)],[86]) ).
thf(102,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(902,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)],[102]) ).
thf(57,axiom,
( ( vd1123 = vd1127 )
=> ( vskolem1145 @ rline ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 1), 8)') ).
thf(559,plain,
( ( vd1123 = vd1127 )
=> ( vskolem1145 @ rline ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(21,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(228,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)],[21]) ).
thf(43,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(448,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)],[43]) ).
thf(19,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(216,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)],[19]) ).
thf(49,axiom,
~ ( vd1152 @ ( vd1125 @ rinside ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','neg(neg(260))') ).
thf(514,plain,
~ ( vd1152 @ ( vd1125 @ rinside ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(118,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(1051,plain,
! [A: $i,B: $i] :
( ( ( B @ rpoint )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(36,axiom,
( ( vd1123 = vd1127 )
=> ( ( vskolem1145 @ ( vd1123 @ ron ) )
& ( vskolem1145 @ ( vd1125 @ ron ) )
& ( vskolem1146 @ rcircle )
& ( vskolem1146 @ ( vd1123 @ rcenter ) )
& ( vskolem1146 @ ( vd1129 @ ron ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 1), 7)') ).
thf(396,plain,
( ( vd1123 = vd1127 )
=> ( ( vskolem1145 @ ( vd1123 @ ron ) )
& ( vskolem1145 @ ( vd1125 @ ron ) )
& ( vskolem1146 @ rcircle )
& ( vskolem1146 @ ( vd1123 @ rcenter ) )
& ( vskolem1146 @ ( vd1129 @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(94,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(849,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)],[94]) ).
thf(44,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(452,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)],[44]) ).
thf(87,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(810,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)],[87]) ).
thf(117,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(1047,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)],[117]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rline )
& ( C = D )
& ~ ( C @ ( A @ ron ) ) )
=> ( C @ ( A @ ( A @ rS ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(95), 0), imp(cond(axiom(95), 0)))') ).
thf(862,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rline )
& ( C = D )
& ~ ( C @ ( A @ ron ) ) )
=> ( C @ ( A @ ( A @ rS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(135,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(1174,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)],[135]) ).
thf(1,conjecture,
? [A: $i] :
( ( A @ rpoint )
& ( vd1151 @ ( A @ ron ) )
& ( vd1152 @ ( A @ ron ) )
& ( vd1125 @ ( vd1123 @ ( A @ rR ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(261)') ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( A @ rpoint )
& ( vd1151 @ ( A @ ron ) )
& ( vd1152 @ ( A @ ron ) )
& ( vd1125 @ ( vd1123 @ ( A @ rR ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(137,plain,
~ ? [A: $i] :
( ( A @ rpoint )
& ( vd1151 @ ( A @ ron ) )
& ( vd1152 @ ( A @ ron ) )
& ( vd1125 @ ( vd1123 @ ( A @ rR ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D ) )
=> ( ( C @ ( A @ vplus ) )
= ( A @ ( C @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(143), 0), imp(cond(axiom(143), 0)))') ).
thf(165,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D ) )
=> ( ( C @ ( A @ vplus ) )
= ( A @ ( C @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(88,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(815,plain,
! [A: $i,B: $i] :
( ( ( B @ rcircle )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( A @ ( C @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(16,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(197,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)],[16]) ).
thf(98,axiom,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( vskolem1140 @ rpoint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 5)') ).
thf(879,plain,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( vskolem1140 @ rpoint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( D = E )
& ( C @ ( A @ ( B @ rR ) ) )
& ( D @ ( B @ ron ) ) )
=> ~ ( D @ ( C @ ( A @ rS ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(109), 0), imp(cond(axiom(109), 0)))') ).
thf(435,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( D = E )
& ( C @ ( A @ ( B @ rR ) ) )
& ( D @ ( B @ ron ) ) )
=> ~ ( D @ ( C @ ( A @ rS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(68,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(665,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)],[68]) ).
thf(133,axiom,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( ( vskolem1140 @ ( vd1123 @ vf ) )
= ( vskolem1136 @ ( vd1123 @ vf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 1)') ).
thf(1159,plain,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( ( vskolem1140 @ ( vd1123 @ vf ) )
= ( vskolem1136 @ ( vd1123 @ vf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(126,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(1111,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)],[126]) ).
thf(35,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(388,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)],[35]) ).
thf(130,axiom,
( ( vd1151 @ ( vd1123 @ ron ) )
& ( vd1151 @ ( vd1125 @ ron ) )
& ( vd1152 @ rcircle )
& ( vd1152 @ ( vd1123 @ rcenter ) )
& ( vd1152 @ ( vd1127 @ ron ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','and(and(pred(comma_conjunct2(comma_conjunct2(comma_conjunct2(259))), 0), and(pred(comma_conjunct1(comma_conjunct2(comma_conjunct2(259))), 0), and(pred(comma_conjunct2(comma_conjunct2(259)), 0), pred(comma_conjunct1(comma_conjunct2(259)), 0)))), pred(comma_conjunct1(259), 0))') ).
thf(1138,plain,
( ( vd1151 @ ( vd1123 @ ron ) )
& ( vd1151 @ ( vd1125 @ ron ) )
& ( vd1152 @ rcircle )
& ( vd1152 @ ( vd1123 @ rcenter ) )
& ( vd1152 @ ( vd1127 @ ron ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(113,axiom,
( ( vd1124 @ rpoint )
& ( vd1123 = vd1124 )
& ( vd1126 @ rpoint )
& ( vd1125 = vd1126 )
& ( vd1128 @ rpoint )
& ( vd1127 = vd1128 )
& ( vd1130 @ rpoint )
& ( vd1129 = vd1130 )
& ( vd1123 != vd1125 )
& ( vd1127 != vd1129 )
& ( vd1125 @ ( vd1123 @ vf ) @ ( vd1129 @ ( vd1127 @ vf ) @ rless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','and(and(and(and(holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1133, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1132, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(242))))), 1131, 0), and(pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 2), pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 1))))), and(pred(conjunct1(conjunct2(conjunct2(242))), 2), pred(conjunct1(conjunct2(conjunct2(242))), 1))), and(pred(conjunct1(conjunct2(242)), 2), pred(conjunct1(conjunct2(242)), 1))), and(pred(conjunct1(242), 2), pred(conjunct1(242), 1)))') ).
thf(989,plain,
( ( vd1124 @ rpoint )
& ( vd1123 = vd1124 )
& ( vd1126 @ rpoint )
& ( vd1125 = vd1126 )
& ( vd1128 @ rpoint )
& ( vd1127 = vd1128 )
& ( vd1130 @ rpoint )
& ( vd1129 = vd1130 )
& ( vd1123 != vd1125 )
& ( vd1127 != vd1129 )
& ( vd1125 @ ( vd1123 @ vf ) @ ( vd1129 @ ( vd1127 @ vf ) @ rless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(100,axiom,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( vskolem1138 @ ( vskolem1140 @ ron ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 4)') ).
thf(884,plain,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( vskolem1138 @ ( vskolem1140 @ ron ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(20,axiom,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( ( vskolem1140 @ ( vd1123 @ vf ) )
= ( vd1129 @ ( vd1127 @ vf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 0)') ).
thf(225,plain,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( ( vskolem1140 @ ( vd1123 @ vf ) )
= ( vd1129 @ ( vd1127 @ vf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(52,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(526,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)],[52]) ).
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(679,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(112,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(985,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)],[112]) ).
thf(119,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(1060,plain,
! [A: $i,B: $i] :
( ( ( B @ rcircle )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( A @ ( C @ rinside ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( A != C )
& ( C = D ) )
=> ( D @ ( C @ ( B @ ( A @ vskolem1052 ) ) ) @ rpoint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(206), 0), 2)') ).
thf(371,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( A != C )
& ( C = D ) )
=> ( D @ ( C @ ( B @ ( A @ vskolem1052 ) ) ) @ rpoint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( D = E )
& ( 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(792,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)],[84]) ).
thf(29,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(360,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)],[29]) ).
thf(17,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(205,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)],[17]) ).
thf(55,axiom,
( ( vd1123 = vd1127 )
=> ~ ( vskolem1146 @ ( vd1125 @ ron ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 1), 5)') ).
thf(541,plain,
( ( vd1123 = vd1127 )
=> ~ ( vskolem1146 @ ( vd1125 @ ron ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(116,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(1035,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)],[116]) ).
thf(67,axiom,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ~ ( vskolem1139 @ ( vd1125 @ rinside ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 7)') ).
thf(662,plain,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ~ ( vskolem1139 @ ( vd1125 @ rinside ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) )
& ( A != B ) )
=> ? [C: $i] :
( ( C @ rcircle )
& ( C @ ( A @ rcenter ) )
& ( C @ ( B @ ron ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(53), 0), imp(cond(axiom(53), 0)))') ).
thf(298,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) )
& ( A != B ) )
=> ? [C: $i] :
( ( C @ rcircle )
& ( C @ ( A @ rcenter ) )
& ( C @ ( B @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rline )
& ( A = B )
& ( D @ rpoint )
& ~ ( A @ ( C @ ron ) )
& ( F @ rpoint )
& ( A @ ( C @ ( E @ rS ) ) )
& ( H @ rpoint )
& ( A @ ( C @ ( G @ rS ) ) )
& ( G = H )
& ( E = F )
& ( C = D ) )
=> ? [I: $i] :
( ( I @ rpoint )
& ( A @ ( C @ ( I @ rS ) ) )
& ( I != C )
& ( I != E )
& ( I != G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(37), 0), imp(cond(axiom(37), 0)))') ).
thf(412,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rline )
& ( A = B )
& ( D @ rpoint )
& ~ ( A @ ( C @ ron ) )
& ( F @ rpoint )
& ( A @ ( C @ ( E @ rS ) ) )
& ( H @ rpoint )
& ( A @ ( C @ ( G @ rS ) ) )
& ( G = H )
& ( E = F )
& ( C = D ) )
=> ? [I: $i] :
( ( I @ rpoint )
& ( A @ ( C @ ( I @ rS ) ) )
& ( I != C )
& ( I != E )
& ( I != G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(89,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(824,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)],[89]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( B @ rreal )
& ( A = B ) )
=> ( ( v0 @ ( A @ vplus ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(141), 0), imp(cond(axiom(141), 0)))') ).
thf(149,plain,
! [A: $i,B: $i] :
( ( ( B @ rreal )
& ( A = B ) )
=> ( ( v0 @ ( A @ vplus ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(48,axiom,
vd1151 @ rline,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(259, 0)') ).
thf(513,plain,
vd1151 @ rline,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F ) )
=> ( v0 @ ( E @ ( C @ ( A @ vg ) ) @ rgeq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(174), 0), imp(cond(axiom(174), 0)))') ).
thf(430,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F ) )
=> ( v0 @ ( E @ ( C @ ( A @ vg ) ) @ rgeq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(33,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(375,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)],[33]) ).
thf(74,axiom,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( vskolem1138 @ rline ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 9)') ).
thf(733,plain,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( vskolem1138 @ rline ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(58,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(562,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)],[58]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D ) )
=> ? [E: $i] :
( ( E @ rreal )
& ( ( C @ ( A @ vplus ) )
= E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(139), 0), imp(cond(axiom(139), 0)))') ).
thf(176,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D ) )
=> ? [E: $i] :
( ( E @ rreal )
& ( ( C @ ( A @ vplus ) )
= E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(127,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(1125,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)],[127]) ).
thf(80,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(772,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)],[80]) ).
thf(26,axiom,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( ( vskolem1138 @ ( vd1123 @ ron ) )
& ( vskolem1138 @ ( vd1125 @ ron ) )
& ( vskolem1139 @ rcircle )
& ( vskolem1139 @ ( vd1123 @ rcenter ) )
& ( vskolem1139 @ ( vskolem1136 @ ron ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 8)') ).
thf(286,plain,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( ( vskolem1138 @ ( vd1123 @ ron ) )
& ( vskolem1138 @ ( vd1125 @ ron ) )
& ( vskolem1139 @ rcircle )
& ( vskolem1139 @ ( vd1123 @ rcenter ) )
& ( vskolem1139 @ ( vskolem1136 @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( A != C )
& ( C = D ) )
=> ( ( C @ ( A @ vf ) )
= ( D @ ( C @ ( B @ ( A @ vskolem1052 ) ) ) @ ( C @ vf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(206), 0), 1)') ).
thf(743,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( A != C )
& ( C = D ) )
=> ( ( C @ ( A @ vf ) )
= ( D @ ( C @ ( B @ ( A @ vskolem1052 ) ) ) @ ( C @ vf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(108,axiom,
( ( vd1123 = vd1127 )
=> ( vskolem1147 @ rpoint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 1), 4)') ).
thf(958,plain,
( ( vd1123 = vd1127 )
=> ( vskolem1147 @ rpoint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(42,axiom,
( ( vd1123 = vd1127 )
=> ( vd1125 @ ( vd1123 @ ( vskolem1147 @ rR ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 1), 1)') ).
thf(445,plain,
( ( vd1123 = vd1127 )
=> ( vd1125 @ ( vd1123 @ ( vskolem1147 @ rR ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( F @ rreal )
& ( E = F )
& ( C @ ( A @ rless ) ) )
=> ( E @ ( C @ vplus ) @ ( E @ ( A @ vplus ) @ rless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(153), 0), imp(cond(axiom(153), 0)))') ).
thf(144,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( F @ rreal )
& ( E = F )
& ( C @ ( A @ rless ) ) )
=> ( E @ ( C @ vplus ) @ ( E @ ( A @ vplus ) @ rless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(45,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(466,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)],[45]) ).
thf(123,axiom,
( ( vd1123 = vd1127 )
=> ( vskolem1146 @ ( vskolem1147 @ ron ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 1), 2)') ).
thf(1090,plain,
( ( vd1123 = vd1127 )
=> ( vskolem1146 @ ( vskolem1147 @ ron ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(62,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(611,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)],[62]) ).
thf(82,axiom,
( ( vd1123 = vd1127 )
=> ~ ( vskolem1146 @ ( vd1125 @ rinside ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 1), 6)') ).
thf(787,plain,
( ( vd1123 = vd1127 )
=> ~ ( vskolem1146 @ ( vd1125 @ rinside ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(81,axiom,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( vskolem1136 @ rpoint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 11)') ).
thf(784,plain,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( vskolem1136 @ rpoint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(75,axiom,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( vd1125 @ ( vd1123 @ ( vskolem1140 @ rR ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 2)') ).
thf(736,plain,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ( vd1125 @ ( vd1123 @ ( vskolem1140 @ rR ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(59,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(567,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)],[59]) ).
thf(24,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(271,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)],[24]) ).
thf(46,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(477,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)],[46]) ).
thf(79,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(758,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)],[79]) ).
thf(63,axiom,
vd14 @ rpoint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(5), 0)') ).
thf(626,plain,
vd14 @ rpoint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(18,axiom,
( ( vd1123 = vd1127 )
=> ( vskolem1145 @ ( vskolem1147 @ ron ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 1), 3)') ).
thf(213,plain,
( ( vd1123 = vd1127 )
=> ( vskolem1145 @ ( vskolem1147 @ ron ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(134,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(1162,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)],[134]) ).
thf(51,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(521,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)],[51]) ).
thf(104,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(922,plain,
! [A: $i,B: $i] :
( ( ( B @ rline )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( A @ ( C @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(23,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(267,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)],[23]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ 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(1102,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ 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)],[125]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( 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(531,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)],[53]) ).
thf(50,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(516,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)],[50]) ).
thf(106,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(939,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)],[106]) ).
thf(131,axiom,
( ( vd1123 = vd1127 )
=> ( ( vskolem1147 @ ( vd1123 @ vf ) )
= ( vd1129 @ ( vd1127 @ vf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 1), 0)') ).
thf(1145,plain,
( ( vd1123 = vd1127 )
=> ( ( vskolem1147 @ ( vd1123 @ vf ) )
= ( vd1129 @ ( vd1127 @ vf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( E @ rline )
& ( D = E )
& ( 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(836,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)],[92]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( A != C )
& ( C = D ) )
=> ( ( D @ ( C @ ( B @ ( A @ vskolem1052 ) ) ) @ ( C @ vf ) )
= ( A @ ( D @ ( C @ ( B @ ( A @ vskolem1052 ) ) ) @ vf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(206), 0), 0)') ).
thf(1134,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( A != C )
& ( C = D ) )
=> ( ( D @ ( C @ ( B @ ( A @ vskolem1052 ) ) ) @ ( C @ vf ) )
= ( A @ ( D @ ( C @ ( B @ ( A @ vskolem1052 ) ) ) @ vf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
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(648,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(25,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(282,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)],[25]) ).
thf(101,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(887,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)],[101]) ).
thf(107,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(954,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)],[107]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) )
& ( A != B ) )
=> ! [C: $i,D: $i] :
( ( ( D @ rpoint )
& ( C != A )
& ( C != B )
& ( C = D ) )
=> ( B @ ( A @ ( D @ ( C @ vskolem1078 ) ) ) @ rpoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(219), 0), 1)') ).
thf(739,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ rpoint )
& ( A = C ) )
& ? [C: $i] :
( ( C @ rpoint )
& ( B = C ) )
& ( A != B ) )
=> ! [C: $i,D: $i] :
( ( ( D @ rpoint )
& ( C != A )
& ( C != B )
& ( C = D ) )
=> ( B @ ( A @ ( D @ ( C @ vskolem1078 ) ) ) @ rpoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(122,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(1085,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)],[122]) ).
thf(56,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(544,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)],[56]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rcircle )
& ( A = B )
& ( A @ ( C @ rcenter ) )
& ( A @ ( D @ rcenter ) ) )
=> ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(75), 0), imp(cond(axiom(75), 0)))') ).
thf(154,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rcircle )
& ( A = B )
& ( A @ ( C @ rcenter ) )
& ( A @ ( D @ rcenter ) ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
vd684 @ rreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(137), 1)') ).
thf(175,plain,
vd684 @ rreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(114,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(1008,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)],[114]) ).
thf(93,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(845,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)],[93]) ).
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(627,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(105,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(931,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)],[105]) ).
thf(60,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(581,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)],[60]) ).
thf(31,axiom,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ~ ( vskolem1139 @ ( vd1125 @ ron ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(242), 0), 6)') ).
thf(368,plain,
( ( ( vd1123 != vd1127 )
& ( vd1123 != vd1129 ) )
=> ~ ( vskolem1139 @ ( vd1125 @ ron ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(71,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(699,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)],[71]) ).
thf(109,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(961,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)],[109]) ).
thf(22,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(258,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)],[22]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( F @ rreal )
& ( E = F )
& ( C @ ( A @ rless ) )
& ( E @ ( C @ rless ) ) )
=> ( E @ ( A @ rless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(151), 0), imp(cond(axiom(151), 0)))') ).
thf(158,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( F @ rreal )
& ( E = F )
& ( C @ ( A @ rless ) )
& ( E @ ( C @ rless ) ) )
=> ( E @ ( A @ rless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( F @ rreal )
& ( E = F )
& ( ( E @ ( A @ vplus ) )
= ( E @ ( C @ vplus ) ) ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(156, 0), 0)') ).
thf(139,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( F @ rreal )
& ( E = F )
& ( ( E @ ( A @ vplus ) )
= ( E @ ( C @ vplus ) ) ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(121,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(1077,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)],[121]) ).
thf(91,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(832,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)],[91]) ).
thf(54,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(536,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)],[54]) ).
thf(72,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(716,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)],[72]) ).
thf(132,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(1148,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)],[132]) ).
thf(83,axiom,
~ ( vd1152 @ ( vd1125 @ ron ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','neg(neg(comma_conjunct2(260)))') ).
thf(790,plain,
~ ( vd1152 @ ( vd1125 @ ron ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(97,axiom,
! [A: $i,B: $i] :
( ( ( B @ rcircle )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ~ ( A @ ( C @ rinside ) )
& ~ ( A @ ( C @ ron ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(49), 0), imp(cond(axiom(49), 0)))') ).
thf(867,plain,
! [A: $i,B: $i] :
( ( ( B @ rcircle )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ~ ( A @ ( C @ rinside ) )
& ~ ( A @ ( C @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rline )
& ( A = B )
& ? [E: $i] :
( ( E @ rpoint )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( D = E ) )
& ( A @ ( C @ ron ) )
& ( A @ ( D @ ron ) )
& ( C != D ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( E @ ( C @ ( D @ rR ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(29), 0), imp(cond(axiom(29), 0)))') ).
thf(854,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rline )
& ( A = B )
& ? [E: $i] :
( ( E @ rpoint )
& ( C = E ) )
& ? [E: $i] :
( ( E @ rpoint )
& ( D = E ) )
& ( A @ ( C @ ron ) )
& ( A @ ( D @ ron ) )
& ( C != D ) )
=> ? [E: $i] :
( ( E @ rpoint )
& ( E @ ( C @ ( D @ rR ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D ) )
=> ( ( A @ ( C @ rless ) )
| ( A = C )
| ( C @ ( A @ rless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(145), 0), imp(cond(axiom(145), 0)))') ).
thf(190,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D ) )
=> ( ( A @ ( C @ rless ) )
| ( A = C )
| ( C @ ( A @ rless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(15,axiom,
v0 = vd684,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(137), 2)') ).
thf(195,plain,
v0 = vd684,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(90,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(828,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)],[90]) ).
thf(124,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(1093,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)],[124]) ).
thf(73,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(728,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)],[73]) ).
thf(128,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(1129,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)],[128]) ).
thf(61,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(596,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)],[61]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rcenter ) )
=> ( B @ ( A @ rinside ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(77), 0), imp(cond(axiom(77), 0)))') ).
thf(163,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rcenter ) )
=> ( B @ ( A @ rinside ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(70,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(691,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)],[70]) ).
thf(47,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(501,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)],[47]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i] :
( ( ? [S: $i] :
( ( S @ rpoint )
& ( A = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( B = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( C = S ) )
& ( A != B )
& ( A != C )
& ( B != C )
& ? [S: $i] :
( ( S @ rpoint )
& ( D = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( E = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( F = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( G = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( H = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( I = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( J = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( K = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( L = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( M = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( N = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( O = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( P = S ) )
& ( R @ rline )
& ( Q @ ( D @ ron ) )
& ( Q @ ( E @ ron ) )
& ~ ( Q @ ( F @ ron ) )
& ! [S: $i,T: $i,U: $i] :
( ( ( S @ rpoint )
& ( T @ rpoint )
& ( U @ rpoint )
& ( S = D )
& ( ( S @ ( T @ ( U @ vangle ) ) )
= ( A @ ( B @ ( C @ vangle ) ) ) )
& ( ( U @ ( S @ ( T @ vangle ) ) )
= ( C @ ( A @ ( B @ vangle ) ) ) )
& ( ( T @ ( U @ ( S @ vangle ) ) )
= ( B @ ( C @ ( A @ vangle ) ) ) )
& ( ( B @ ( A @ vf ) )
= ( T @ ( S @ vf ) ) )
& ( ( C @ ( B @ vf ) )
= ( U @ ( T @ vf ) ) )
& ( ( C @ ( A @ vf ) )
= ( U @ ( S @ vf ) ) )
& ( Q @ ( T @ ron ) )
& ~ ( E @ ( T @ ( D @ rR ) ) )
& ( Q @ ( F @ ( U @ rS ) ) ) )
=> ( ( ( H @ ( G @ vf ) )
= ( J @ ( I @ vf ) ) )
& ( ( M @ ( L @ ( K @ vangle ) ) )
= ( P @ ( O @ ( N @ vangle ) ) ) ) ) )
& ( Q = R ) )
=> ( ( ( H @ ( G @ vf ) )
= ( J @ ( I @ vf ) ) )
& ( ( M @ ( L @ ( K @ vangle ) ) )
= ( P @ ( O @ ( N @ vangle ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(204), 0), imp(cond(axiom(204), 0)))') ).
thf(309,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i] :
( ( ? [S: $i] :
( ( S @ rpoint )
& ( A = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( B = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( C = S ) )
& ( A != B )
& ( A != C )
& ( B != C )
& ? [S: $i] :
( ( S @ rpoint )
& ( D = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( E = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( F = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( G = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( H = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( I = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( J = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( K = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( L = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( M = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( N = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( O = S ) )
& ? [S: $i] :
( ( S @ rpoint )
& ( P = S ) )
& ( R @ rline )
& ( Q @ ( D @ ron ) )
& ( Q @ ( E @ ron ) )
& ~ ( Q @ ( F @ ron ) )
& ! [S: $i,T: $i,U: $i] :
( ( ( S @ rpoint )
& ( T @ rpoint )
& ( U @ rpoint )
& ( S = D )
& ( ( S @ ( T @ ( U @ vangle ) ) )
= ( A @ ( B @ ( C @ vangle ) ) ) )
& ( ( U @ ( S @ ( T @ vangle ) ) )
= ( C @ ( A @ ( B @ vangle ) ) ) )
& ( ( T @ ( U @ ( S @ vangle ) ) )
= ( B @ ( C @ ( A @ vangle ) ) ) )
& ( ( B @ ( A @ vf ) )
= ( T @ ( S @ vf ) ) )
& ( ( C @ ( B @ vf ) )
= ( U @ ( T @ vf ) ) )
& ( ( C @ ( A @ vf ) )
= ( U @ ( S @ vf ) ) )
& ( Q @ ( T @ ron ) )
& ~ ( E @ ( T @ ( D @ rR ) ) )
& ( Q @ ( F @ ( U @ rS ) ) ) )
=> ( ( ( H @ ( G @ vf ) )
= ( J @ ( I @ vf ) ) )
& ( ( M @ ( L @ ( K @ vangle ) ) )
= ( P @ ( O @ ( N @ vangle ) ) ) ) ) )
& ( Q = R ) )
=> ( ( ( H @ ( G @ vf ) )
= ( J @ ( I @ vf ) ) )
& ( ( M @ ( L @ ( K @ vangle ) ) )
= ( P @ ( O @ ( N @ vangle ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(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(639,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ rpoint )
& ( A = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( B = G ) )
& ? [G: $i] :
( ( G @ rpoint )
& ( C = G ) )
& ? [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(120,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(1069,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)],[120]) ).
thf(99,axiom,
vd1123 = vd1129,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(258, 1150, 0)') ).
thf(882,plain,
vd1123 = vd1129,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(12213,plain,
$false,
inference(e,[status(thm)],[365,1031,1179,440,408,977,170,384,797,747,185,973,917,802,902,559,228,448,216,514,1051,396,849,452,810,1047,862,1174,137,165,815,197,879,435,665,1159,1111,388,1138,989,884,225,526,679,985,1060,371,792,360,205,541,1035,662,298,412,824,149,513,430,375,733,562,176,1125,772,286,743,958,445,144,466,1090,611,787,784,736,567,271,477,758,626,213,1162,521,922,267,1102,531,516,939,1145,836,1134,648,282,887,954,739,1085,544,154,175,1008,845,627,931,581,368,699,961,258,158,139,1077,832,536,716,1148,790,867,854,190,195,828,1093,728,1129,596,163,691,501,309,639,1069,882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO286+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.42 % Computer : n014.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Fri Sep 25 13:13:32 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.92/1.33 % [INFO] Parsing done (325ms).
% 1.92/1.34 % [INFO] Running in sequential loop mode.
% 2.67/1.73 % [INFO] eprover registered as external prover.
% 2.67/1.74 % [INFO] Scanning for conjecture ...
% 2.89/1.89 % [INFO] Found a conjecture (or negated_conjecture) and 134 axioms. Running axiom selection ...
% 3.10/2.02 % [INFO] Axiom selection finished. Selected 134 axioms (removed 0 axioms).
% 4.34/2.34 % [INFO] Problem is first-order (TPTP FOF).
% 4.34/2.38 % [INFO] Type checking passed.
% 4.34/2.39 % [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 ...
% 56.54/15.15 % External prover 'e' found a proof!
% 56.54/15.15 % [INFO] Killing All external provers ...
% 56.54/15.16 % Time passed: 14593ms (effective reasoning time: 13810ms)
% 56.54/15.16 % 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)>
% 56.54/15.16 % Axioms used in derivation (134): qu(cond(axiom(41), 0), imp(cond(axiom(41), 0))), qu(cond(axiom(103), 0), imp(cond(axiom(103), 0))), qu(cond(axiom(73), 0), imp(cond(axiom(73), 0))), qu(cond(axiom(119), 0), imp(cond(axiom(119), 0))), qu(cond(axiom(3), 0), imp(cond(axiom(3), 0))), ass(cond(conseq(242), 0), 8), ass(cond(conseq(242), 0), 4), qu(cond(axiom(164), 0), imp(cond(axiom(164), 0))), ass(cond(conseq(242), 0), 0), qu(cond(axiom(145), 0), imp(cond(axiom(145), 0))), ass(cond(goal(206), 0), 1), holds(258, 1150, 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))), ass(cond(conseq(242), 1), 3), qu(cond(axiom(190), 0), imp(cond(axiom(190), 0))), ass(cond(conseq(242), 0), 1), ass(cond(conseq(242), 0), 9), qu(cond(axiom(53), 0), imp(cond(axiom(53), 0))), ass(cond(conseq(242), 0), 5), 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))), ass(cond(goal(206), 0), 0), qu(cond(axiom(77), 0), imp(cond(axiom(77), 0))), qu(cond(axiom(113), 0), imp(cond(axiom(113), 0))), qu(cond(axiom(45), 0), imp(cond(axiom(45), 0))), qu(cond(axiom(11), 0), imp(cond(axiom(11), 0))), qu(cond(axiom(176), 0), imp(cond(axiom(176), 0))), qu(cond(axiom(33), 0), imp(cond(axiom(33), 0))), qu(cond(axiom(139), 0), imp(cond(axiom(139), 0))), qu(cond(axiom(59), 0), imp(cond(axiom(59), 0))), neg(neg(260)), 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))), ass(cond(conseq(242), 1), 0), ass(cond(conseq(242), 1), 4), qu(cond(axiom(109), 0), imp(cond(axiom(109), 0))), qu(cond(axiom(79), 0), imp(cond(axiom(79), 0))), qu(cond(axiom(55), 0), imp(cond(axiom(55), 0))), qu(cond(axiom(81), 0), imp(cond(axiom(81), 0))), ass(cond(conseq(242), 1), 6), 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(and(and(and(holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1133, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1132, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(242))))), 1131, 0), and(pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 2), pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 1))))), and(pred(conjunct1(conjunct2(conjunct2(242))), 2), pred(conjunct1(conjunct2(conjunct2(242))), 1))), and(pred(conjunct1(conjunct2(242)), 2), pred(conjunct1(conjunct2(242)), 1))), and(pred(conjunct1(242), 2), pred(conjunct1(242), 1))), qu(cond(axiom(71), 0), imp(cond(axiom(71), 0))), ass(cond(conseq(242), 0), 6), ass(cond(conseq(242), 0), 2), 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))), ass(cond(conseq(242), 1), 1), ass(cond(conseq(242), 1), 5), 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))), ass(cond(conseq(242), 1), 7), qu(cond(axiom(123), 0), imp(cond(axiom(123), 0))), qu(cond(axiom(25), 0), imp(cond(axiom(25), 0))), qu(cond(axiom(125), 0), imp(cond(axiom(125), 0))), qu(cond(axiom(170), 0), imp(cond(axiom(170), 0))), neg(neg(comma_conjunct2(260))), qu(cond(axiom(111), 0), imp(cond(axiom(111), 0))), pred(259, 0), qu(cond(axiom(101), 0), imp(cond(axiom(101), 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))), ass(cond(goal(219), 0), 0), pred(axiom(137), 1), ass(cond(conseq(242), 0), 7), ass(cond(goal(206), 0), 2), qu(cond(axiom(29), 0), imp(cond(axiom(29), 0))), qu(cond(axiom(39), 0), imp(cond(axiom(39), 0))), qu(cond(axiom(129), 0), imp(cond(axiom(129), 0))), qu(cond(axiom(15), 0), imp(cond(axiom(15), 0))), qu(cond(axiom(85), 0), imp(cond(axiom(85), 0))), ass(cond(conseq(242), 0), 10), qu(cond(axiom(200), 0), imp(cond(axiom(200), 0))), qu(cond(axiom(27), 0), imp(cond(axiom(27), 0))), qu(cond(axiom(91), 0), imp(cond(axiom(91), 0))), ass(cond(conseq(242), 1), 8), ass(cond(goal(219), 0), 1), qu(cond(axiom(49), 0), imp(cond(axiom(49), 0))), qu(cond(axiom(149), 0), imp(cond(axiom(149), 0))), qu(cond(axiom(7), 0), imp(cond(axiom(7), 0))), qu(cond(axiom(17), 0), imp(cond(axiom(17), 0))), qu(cond(axiom(51), 0), imp(cond(axiom(51), 0))), qu(cond(axiom(141), 0), imp(cond(axiom(141), 0))), qu(cond(axiom(135), 0), imp(cond(axiom(135), 0))), qu(cond(axiom(47), 0), imp(cond(axiom(47), 0))), qu(cond(axiom(69), 0), imp(cond(axiom(69), 0))), ass(cond(conseq(242), 1), 2), 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))), and(and(pred(comma_conjunct2(comma_conjunct2(comma_conjunct2(259))), 0), and(pred(comma_conjunct1(comma_conjunct2(comma_conjunct2(259))), 0), and(pred(comma_conjunct2(comma_conjunct2(259)), 0), pred(comma_conjunct1(comma_conjunct2(259)), 0)))), pred(comma_conjunct1(259), 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))), ass(cond(conseq(242), 0), 11), 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))), ass(cond(conseq(242), 0), 3)
% 56.54/15.16 % No. of inferences in proof: 272
% 56.54/15.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 14593 ms resp. 13810 ms w/o parsing
% 57.27/15.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 57.27/15.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------