%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO298+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 : n004.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 07:13:09 AM UTC 2026
% Result : Theorem 113.02s 34.13s
% Output : Refutation 105.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 171
% Syntax : Number of formulae : 469 ( 154 unt; 0 typ; 13 def)
% Number of atoms : 3510 (1315 equ; 0 cnn)
% Maximal formula atoms : 57 ( 7 avg)
% Number of connectives : 8770 ( 928 ~; 601 |;2125 &;4850 @)
% ( 8 <=>; 258 =>; 0 <=; 0 <~>)
% Maximal formula depth : 48 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 51 usr; 27 con; 0-8 aty)
% Number of variables : 1903 ( 10 ^;1307 !; 573 ?;1903 :)
% ( 0 !>; 0 ?*; 0 @-; 13 @+)
% Comments :
%------------------------------------------------------------------------------
thf(rR_decl,type,
rR: $i > $i > $i > $o ).
thf(vd1201_decl,type,
vd1201: $i ).
thf(vd1185_decl,type,
vd1185: $i ).
thf(vd1187_decl,type,
vd1187: $i ).
thf(rreal_decl,type,
rreal: $i > $o ).
thf(vd684_decl,type,
vd684: $i ).
thf(rless_decl,type,
rless: $i > $i > $o ).
thf(vplus_decl,type,
vplus: $i > $i > $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(ron_decl,type,
ron: $i > $i > $o ).
thf(rline_decl,type,
rline: $i > $o ).
thf(rpoint_decl,type,
rpoint: $i > $o ).
thf(rintersect_decl,type,
rintersect: $i > $i > $o ).
thf(vtriangle_decl,type,
vtriangle: $i > $i > $i > $i ).
thf(rtriangle_decl,type,
rtriangle: $i > $o ).
thf(vg_decl,type,
vg: $i > $i > $i > $i ).
thf(v0_decl,type,
v0: $i ).
thf(vf_decl,type,
vf: $i > $i > $i ).
thf(rcenter_decl,type,
rcenter: $i > $i > $o ).
thf(rcircle_decl,type,
rcircle: $i > $o ).
thf(vd1199_decl,type,
vd1199: $i ).
thf(vd1197_decl,type,
vd1197: $i ).
thf(vskolem1120_decl,type,
vskolem1120: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(vskolem1052_decl,type,
vskolem1052: $i > $i > $i > $i > $i ).
thf(vskolem1078_decl,type,
vskolem1078: $i > $i > $i > $i > $i ).
thf(vd1200_decl,type,
vd1200: $i ).
thf(vd1186_decl,type,
vd1186: $i ).
thf(vd1234_decl,type,
vd1234: $i ).
thf(rgeq_decl,type,
rgeq: $i > $i > $o ).
thf(rinside_decl,type,
rinside: $i > $i > $o ).
thf(vd14_decl,type,
vd14: $i ).
thf(rleq_decl,type,
rleq: $i > $i > $o ).
thf(vd1232_decl,type,
vd1232: $i ).
thf(vd1178_decl,type,
vd1178: $i ).
thf(vd1179_decl,type,
vd1179: $i ).
thf(vd1180_decl,type,
vd1180: $i ).
thf(sk1_decl,type,
sk1: $i > $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i > $i ).
thf(sk25_decl,type,
sk25: $i ).
thf(sk33_decl,type,
sk33: $i > $i ).
thf(sk38_decl,type,
sk38: $i ).
thf(sk41_decl,type,
sk41: $i ).
thf(sk42_decl,type,
sk42: $i ).
thf(sk43_decl,type,
sk43: $i ).
thf(sk44_decl,type,
sk44: $i ).
thf(sk45_decl,type,
sk45: $i ).
thf(sk46_decl,type,
sk46: $i ).
thf(sk57_decl,type,
sk57: $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ( D @ rpoint )
& ( A = D ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ( D @ rpoint )
& ( B = D ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ( D @ rpoint )
& ( C = D ) ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( @+[A: $i] :
( ( A @ rpoint )
& ( vd1199 = A ) ) ) ) ).
thf(sk33_def,definition,
( sk33
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ rpoint )
& ( B != A ) ) ) ) ).
thf(sk38_def,definition,
( sk38
= ( @+[A: $i] :
( ( A @ rpoint )
& ( vd1200 = A ) ) ) ) ).
thf(sk41_def,definition,
( sk41
= ( @+[A: $i] :
( ( A @ rpoint )
& ( vd1187 = A ) ) ) ) ).
thf(sk42_def,definition,
( sk42
= ( @+[A: $i] :
( ( A @ rpoint )
& ( vd1186 = A ) ) ) ) ).
thf(sk43_def,definition,
( sk43
= ( @+[A: $i] :
( ( A @ rpoint )
& ( vd1185 = A ) ) ) ) ).
thf(sk44_def,definition,
( sk44
= ( @+[A: $i] :
( ( A @ rpoint )
& ( vd1180 = A ) ) ) ) ).
thf(sk45_def,definition,
( sk45
= ( @+[A: $i] :
( ( A @ rpoint )
& ( vd1179 = A ) ) ) ) ).
thf(sk46_def,definition,
( sk46
= ( @+[A: $i] :
( ( A @ rpoint )
& ( vd1178 = A ) ) ) ) ).
thf(sk57_def,definition,
( sk57
= ( @+[A: $i] :
( ( A @ rpoint )
& ( vd1201 = A ) ) ) ) ).
thf(97,axiom,
( ? [A: $i] :
( ( A @ rpoint )
& ( vd1178 = A ) )
& ? [A: $i] :
( ( A @ rpoint )
& ( vd1179 = A ) )
& ? [A: $i] :
( ( A @ rpoint )
& ( vd1180 = A ) )
& ( vd1178 != vd1179 )
& ( vd1178 != vd1180 )
& ( vd1179 != vd1180 )
& ? [A: $i] :
( ( A @ rpoint )
& ( vd1185 = A ) )
& ? [A: $i] :
( ( A @ rpoint )
& ( vd1186 = A ) )
& ? [A: $i] :
( ( A @ rpoint )
& ( vd1187 = A ) )
& ( ( vd1179 @ ( vd1178 @ vf ) )
= ( vd1186 @ ( vd1185 @ vf ) ) )
& ( ( vd1180 @ ( vd1178 @ vf ) )
= ( vd1187 @ ( vd1185 @ vf ) ) )
& ( ( vd1180 @ ( vd1178 @ ( vd1179 @ vangle ) ) )
= ( vd1187 @ ( vd1185 @ ( vd1186 @ vangle ) ) ) )
& ~ ? [A: $i] :
( ( A @ rline )
& ( A @ ( vd1185 @ ron ) )
& ( A @ ( vd1186 @ ron ) )
& ( A @ ( vd1187 @ ron ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(268))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(268))))), 1194, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(268)))), 1193, 0), and(holds(conjunct1(plural(comma_conjunct2(268))), 1192, 0), and(qe(s3(plural(comma_conjunct2(268)))), and(qe(s2(plural(comma_conjunct2(268)))), and(qe(s1(plural(comma_conjunct2(268)))), and(pred(comma_conjunct1(268), 9), and(pred(comma_conjunct1(268), 8), and(pred(comma_conjunct1(268), 7), and(qe(s3(plural(268))), and(qe(s2(plural(268))), qe(s1(plural(268)))))))))))))))') ).
thf(860,plain,
( ? [A: $i] :
( ( A @ rpoint )
& ( vd1178 = A ) )
& ? [A: $i] :
( ( A @ rpoint )
& ( vd1179 = A ) )
& ? [A: $i] :
( ( A @ rpoint )
& ( vd1180 = A ) )
& ( vd1178 != vd1179 )
& ( vd1178 != vd1180 )
& ( vd1179 != vd1180 )
& ? [A: $i] :
( ( A @ rpoint )
& ( vd1185 = A ) )
& ? [A: $i] :
( ( A @ rpoint )
& ( vd1186 = A ) )
& ? [A: $i] :
( ( A @ rpoint )
& ( vd1187 = A ) )
& ( ( vd1179 @ ( vd1178 @ vf ) )
= ( vd1186 @ ( vd1185 @ vf ) ) )
& ( ( vd1180 @ ( vd1178 @ vf ) )
= ( vd1187 @ ( vd1185 @ vf ) ) )
& ( ( vd1180 @ ( vd1178 @ ( vd1179 @ vangle ) ) )
= ( vd1187 @ ( vd1185 @ ( vd1186 @ vangle ) ) ) )
& ~ ? [A: $i] :
( ( A @ rline )
& ( A @ ( vd1185 @ ron ) )
& ( A @ ( vd1186 @ ron ) )
& ( A @ ( vd1187 @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(861,plain,
! [A: $i] :
( ( sk46 @ rpoint )
& ( vd1178 = sk46 )
& ( sk45 @ rpoint )
& ( vd1179 = sk45 )
& ( sk44 @ rpoint )
& ( vd1180 = sk44 )
& ( vd1178 != vd1179 )
& ( vd1178 != vd1180 )
& ( vd1179 != vd1180 )
& ( sk43 @ rpoint )
& ( vd1185 = sk43 )
& ( sk42 @ rpoint )
& ( vd1186 = sk42 )
& ( sk41 @ rpoint )
& ( vd1187 = sk41 )
& ( ( vd1179 @ ( vd1178 @ vf ) )
= ( vd1186 @ ( vd1185 @ vf ) ) )
& ( ( vd1180 @ ( vd1178 @ vf ) )
= ( vd1187 @ ( vd1185 @ vf ) ) )
& ( ( vd1180 @ ( vd1178 @ ( vd1179 @ vangle ) ) )
= ( vd1187 @ ( vd1185 @ ( vd1186 @ vangle ) ) ) )
& ( ~ ( A @ rline )
| ~ ( A @ ( vd1185 @ ron ) )
| ~ ( A @ ( vd1186 @ ron ) )
| ~ ( A @ ( vd1187 @ ron ) ) ) ),
inference(cnf,[status(esa)],[860]) ).
thf(865,plain,
vd1178 != vd1180,
inference(cnfConj,[status(thm)],[861]) ).
thf(892,plain,
vd1180 != vd1178,
inference(lifteq,[status(thm)],[865]) ).
thf(121,axiom,
( ( vd1200 @ ( vd1199 @ vf ) )
= ( vd1186 @ ( vd1185 @ vf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(273, 1215, 0)') ).
thf(1036,plain,
( ( vd1200 @ ( vd1199 @ vf ) )
= ( vd1186 @ ( vd1185 @ vf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(89,axiom,
v0 = vd684,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(137), 2)') ).
thf(809,plain,
v0 = vd684,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ rpoint )
& ( A = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( B = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( C = D ) ) )
=> ( ( C @ ( 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(629,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)],[64]) ).
thf(150,axiom,
( ( vd1201 @ ( vd1199 @ ( vd1200 @ vangle ) ) )
= ( vd1187 @ ( vd1185 @ ( vd1186 @ vangle ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(292, 1231, 0)') ).
thf(1190,plain,
( ( vd1201 @ ( vd1199 @ ( vd1200 @ vangle ) ) )
= ( vd1187 @ ( vd1185 @ ( vd1186 @ vangle ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(98,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(893,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)],[98]) ).
thf(14,axiom,
vd1197 @ ( vd1199 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(s1(plural(274)), 0)') ).
thf(253,plain,
vd1197 @ ( vd1199 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(108,axiom,
vd1199 = vd1185,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(291, 1230, 0)') ).
thf(976,plain,
vd1199 = vd1185,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(977,plain,
vd1199 = vd1185,
inference(lifteq,[status(thm)],[976]) ).
thf(6905,plain,
vd1197 @ ( vd1185 @ ron ),
inference(rewrite,[status(thm)],[253,977]) ).
thf(111,axiom,
~ ( vd1197 @ ( vd1187 @ ron ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','neg(neg(270))') ).
thf(984,plain,
~ ( vd1197 @ ( vd1187 @ ron ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(985,plain,
~ ( vd1197 @ ( vd1187 @ ron ) ),
inference(polarity_switch,[status(thm)],[984]) ).
thf(6938,plain,
( ( ( vd1197 @ ( vd1187 @ ron ) )
!= ( vd1197 @ ( vd1185 @ ron ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6905,985]) ).
thf(6939,plain,
( ( vd1197 @ ( vd1187 @ ron ) )
!= ( vd1197 @ ( vd1185 @ ron ) ) ),
inference(simp,[status(thm)],[6938]) ).
thf(6979,plain,
( ( vd1197 != vd1197 )
| ( vd1187 != vd1185 ) ),
inference(simp,[status(thm)],[6939]) ).
thf(6986,plain,
vd1187 != vd1185,
inference(simp,[status(thm)],[6979]) ).
thf(32,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(352,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)],[32]) ).
thf(155,axiom,
( ( vd1200 @ ( vd1201 @ ( vd1199 @ vangle ) ) )
= ( vd1179 @ ( vd1180 @ ( vd1178 @ vangle ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(conjunct2(plural(271))), 1207, 0)') ).
thf(1200,plain,
( ( vd1200 @ ( vd1201 @ ( vd1199 @ vangle ) ) )
= ( vd1179 @ ( vd1180 @ ( vd1178 @ vangle ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(83,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(762,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)],[83]) ).
thf(128,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(1068,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)],[128]) ).
thf(871,plain,
sk44 @ rpoint,
inference(cnfConj,[status(thm)],[861]) ).
thf(880,plain,
vd1180 = sk44,
inference(cnfConj,[status(thm)],[861]) ).
thf(889,plain,
sk44 = vd1180,
inference(lifteq,[status(thm)],[880]) ).
thf(3529,plain,
vd1180 @ rpoint,
inference(rewrite,[status(thm)],[871,889]) ).
thf(76,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(717,plain,
! [A: $i,B: $i] :
( ( ( B @ rpoint )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(718,plain,
! [A: $i] :
( ? [B: $i] :
( ( B @ rpoint )
& ( A = B ) )
=> ? [B: $i] :
( ( B @ rpoint )
& ( B != A ) ) ),
inference(miniscope,[status(thm)],[717]) ).
thf(719,plain,
! [B: $i,A: $i] :
( ( ( A @ sk33 @ rpoint )
| ~ ( B @ rpoint )
| ( A != B ) )
& ( ( ( A @ sk33 )
!= A )
| ~ ( B @ rpoint )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[718]) ).
thf(720,plain,
! [B: $i,A: $i] :
( ( ( A @ sk33 )
!= A )
| ~ ( B @ rpoint )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[719]) ).
thf(722,plain,
! [B: $i,A: $i] :
( ~ ( B @ rpoint )
| ( ( A @ sk33 )
!= A )
| ( A != B ) ),
inference(lifteq,[status(thm)],[720]) ).
thf(723,plain,
! [A: $i] :
( ~ ( A @ rpoint )
| ( ( A @ sk33 )
!= A ) ),
inference(simp,[status(thm)],[722]) ).
thf(5876,plain,
! [A: $i] :
( ( ( vd1180 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ sk33 )
!= A ) ),
inference(paramod_ordered,[status(thm)],[3529,723]) ).
thf(5877,plain,
! [A: $i] :
( ( ( vd1180 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ sk33 )
!= A ) ),
inference(simp,[status(thm)],[5876]) ).
thf(5878,plain,
( ( vd1180 @ sk33 )
!= vd1180 ),
inference(pattern_uni,[status(thm)],[5877:[bind(A,$thf( vd1180 ))]]) ).
thf(145,axiom,
? [A: $i] :
( ( A @ rpoint )
& ( vd1201 = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(s3(plural(271)))') ).
thf(1169,plain,
? [A: $i] :
( ( A @ rpoint )
& ( vd1201 = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(1170,plain,
( ( sk57 @ rpoint )
& ( vd1201 = sk57 ) ),
inference(cnf,[status(esa)],[1169]) ).
thf(1171,plain,
vd1201 = sk57,
inference(cnfConj,[status(thm)],[1170]) ).
thf(1173,plain,
sk57 = vd1201,
inference(lifteq,[status(thm)],[1171]) ).
thf(41,axiom,
vd14 @ rpoint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(5), 0)') ).
thf(462,plain,
vd14 @ rpoint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(24,axiom,
vd1234 @ rline,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(294, 0)') ).
thf(299,plain,
vd1234 @ rline,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(4,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(165,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)],[4]) ).
thf(166,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(miniscope,[status(thm)],[165]) ).
thf(167,plain,
! [P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( F @ rintersect ) )
| ~ ( P @ rpoint )
| ( A != P )
| ~ ( O @ rpoint )
| ( B != O )
| ~ ( N @ rpoint )
| ( C != N )
| ~ ( M @ rpoint )
| ( D != M )
| ~ ( L @ rpoint )
| ( E != L )
| ~ ( K @ rline )
| ( F != K )
| ~ ( J @ rline )
| ( G != J )
| ~ ( 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 @ ( A @ ( E @ rS ) ) )
| ~ ( F @ ( E @ ron ) )
| ~ ( G @ ( E @ ron ) )
| ~ ( P @ rpoint )
| ( A != P )
| ~ ( O @ rpoint )
| ( B != O )
| ~ ( N @ rpoint )
| ( C != N )
| ~ ( M @ rpoint )
| ( D != M )
| ~ ( L @ rpoint )
| ( E != L )
| ~ ( K @ rline )
| ( F != K )
| ~ ( J @ rline )
| ( G != J )
| ~ ( 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 ) ) ) ),
inference(cnf,[status(esa)],[166]) ).
thf(168,plain,
! [P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( A @ ( E @ rS ) ) )
| ~ ( F @ ( E @ ron ) )
| ~ ( G @ ( E @ ron ) )
| ~ ( P @ rpoint )
| ( A != P )
| ~ ( O @ rpoint )
| ( B != O )
| ~ ( N @ rpoint )
| ( C != N )
| ~ ( M @ rpoint )
| ( D != M )
| ~ ( L @ rpoint )
| ( E != L )
| ~ ( K @ rline )
| ( F != K )
| ~ ( J @ rline )
| ( G != J )
| ~ ( 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 ) ) ),
inference(cnfConj,[status(thm)],[167]) ).
thf(170,plain,
! [P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( A @ ( E @ rS ) ) )
| ~ ( F @ ( E @ ron ) )
| ~ ( G @ ( E @ ron ) )
| ~ ( P @ rpoint )
| ~ ( O @ rpoint )
| ~ ( N @ rpoint )
| ~ ( M @ rpoint )
| ~ ( L @ rpoint )
| ~ ( K @ rline )
| ~ ( J @ rline )
| ~ ( I @ rline )
| ~ ( F @ ( A @ ron ) )
| ~ ( F @ ( B @ ron ) )
| ~ ( G @ ( B @ ron ) )
| ~ ( G @ ( C @ ron ) )
| ~ ( H @ ( C @ ron ) )
| ~ ( H @ ( D @ ron ) )
| ~ ( G @ ( D @ ( A @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( D @ ( C @ ( B @ vangle ) ) @ ( C @ ( B @ ( A @ vangle ) ) @ vplus ) @ rless ) )
| ( A != P )
| ( B != O )
| ( C != N )
| ( D != M )
| ( E != L )
| ( F != K )
| ( G != J )
| ( H != I )
| ( B = C ) ),
inference(lifteq,[status(thm)],[168]) ).
thf(171,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( H @ ( D @ rS ) ) )
| ~ ( C @ ( D @ ron ) )
| ~ ( B @ ( D @ ron ) )
| ~ ( H @ rpoint )
| ~ ( G @ rpoint )
| ~ ( F @ rpoint )
| ~ ( E @ rpoint )
| ~ ( D @ rpoint )
| ~ ( C @ rline )
| ~ ( B @ rline )
| ~ ( A @ rline )
| ~ ( C @ ( H @ ron ) )
| ~ ( C @ ( G @ ron ) )
| ~ ( B @ ( G @ ron ) )
| ~ ( B @ ( F @ ron ) )
| ~ ( A @ ( F @ ron ) )
| ~ ( A @ ( E @ ron ) )
| ~ ( B @ ( E @ ( H @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( E @ ( F @ ( G @ vangle ) ) @ ( F @ ( G @ ( H @ vangle ) ) @ vplus ) @ rless ) )
| ( G = F ) ),
inference(simp,[status(thm)],[170]) ).
thf(1,conjecture,
( ( vd1201 @ ( vd1185 @ ( vd1187 @ rR ) ) )
| ( vd1187 @ ( vd1185 @ ( vd1201 @ rR ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dis(321)') ).
thf(2,negated_conjecture,
~ ( ( vd1201 @ ( vd1185 @ ( vd1187 @ rR ) ) )
| ( vd1187 @ ( vd1185 @ ( vd1201 @ rR ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(160,plain,
~ ( ( vd1201 @ ( vd1185 @ ( vd1187 @ rR ) ) )
| ( vd1187 @ ( vd1185 @ ( vd1201 @ rR ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(161,plain,
( ~ ( vd1201 @ ( vd1185 @ ( vd1187 @ rR ) ) )
& ~ ( vd1187 @ ( vd1185 @ ( vd1201 @ rR ) ) ) ),
inference(cnf,[status(esa)],[160]) ).
thf(162,plain,
~ ( vd1187 @ ( vd1185 @ ( vd1201 @ rR ) ) ),
inference(cnfConj,[status(thm)],[161]) ).
thf(1283,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G != vd1201 )
| ~ ( vd1187 @ ( vd1185 @ ( F @ rR ) ) )
| ( B @ ( H @ ( D @ rS ) ) )
| ~ ( C @ ( D @ ron ) )
| ~ ( B @ ( D @ ron ) )
| ~ ( H @ rpoint )
| ~ ( G @ rpoint )
| ~ ( F @ rpoint )
| ~ ( E @ rpoint )
| ~ ( D @ rpoint )
| ~ ( C @ rline )
| ~ ( B @ rline )
| ~ ( A @ rline )
| ~ ( C @ ( H @ ron ) )
| ~ ( C @ ( G @ ron ) )
| ~ ( B @ ( G @ ron ) )
| ~ ( B @ ( F @ ron ) )
| ~ ( A @ ( F @ ron ) )
| ~ ( A @ ( E @ ron ) )
| ~ ( B @ ( E @ ( H @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( E @ ( F @ ( G @ vangle ) ) @ ( F @ ( G @ ( H @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(paramod_ordered,[status(thm)],[171,162]) ).
thf(1284,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( vd1187 @ ( vd1185 @ ( F @ rR ) ) )
| ( B @ ( G @ ( D @ rS ) ) )
| ~ ( C @ ( D @ ron ) )
| ~ ( B @ ( D @ ron ) )
| ~ ( G @ rpoint )
| ~ ( vd1201 @ rpoint )
| ~ ( F @ rpoint )
| ~ ( E @ rpoint )
| ~ ( D @ rpoint )
| ~ ( C @ rline )
| ~ ( B @ rline )
| ~ ( A @ rline )
| ~ ( C @ ( G @ ron ) )
| ~ ( C @ ( vd1201 @ ron ) )
| ~ ( B @ ( vd1201 @ ron ) )
| ~ ( B @ ( F @ ron ) )
| ~ ( A @ ( F @ ron ) )
| ~ ( A @ ( E @ ron ) )
| ~ ( B @ ( E @ ( G @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( E @ ( F @ ( vd1201 @ vangle ) ) @ ( F @ ( vd1201 @ ( G @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(pattern_uni,[status(thm)],[1283:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( vd1201 ))]]) ).
thf(1399,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( vd1187 @ ( vd1185 @ ( F @ rR ) ) )
| ( B @ ( G @ ( D @ rS ) ) )
| ~ ( C @ ( D @ ron ) )
| ~ ( B @ ( D @ ron ) )
| ~ ( G @ rpoint )
| ~ ( vd1201 @ rpoint )
| ~ ( F @ rpoint )
| ~ ( E @ rpoint )
| ~ ( D @ rpoint )
| ~ ( C @ rline )
| ~ ( B @ rline )
| ~ ( A @ rline )
| ~ ( C @ ( G @ ron ) )
| ~ ( C @ ( vd1201 @ ron ) )
| ~ ( B @ ( vd1201 @ ron ) )
| ~ ( B @ ( F @ ron ) )
| ~ ( A @ ( F @ ron ) )
| ~ ( A @ ( E @ ron ) )
| ~ ( B @ ( E @ ( G @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( E @ ( F @ ( vd1201 @ vangle ) ) @ ( F @ ( vd1201 @ ( G @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(simp,[status(thm)],[1284]) ).
thf(1691,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( G @ ron ) )
!= ( B @ ( vd1201 @ ron ) ) )
| ~ ( vd1187 @ ( vd1185 @ ( F @ rR ) ) )
| ( B @ ( G @ ( D @ rS ) ) )
| ~ ( C @ ( D @ ron ) )
| ~ ( B @ ( D @ ron ) )
| ~ ( G @ rpoint )
| ~ ( vd1201 @ rpoint )
| ~ ( F @ rpoint )
| ~ ( E @ rpoint )
| ~ ( D @ rpoint )
| ~ ( C @ rline )
| ~ ( B @ rline )
| ~ ( A @ rline )
| ~ ( C @ ( vd1201 @ ron ) )
| ~ ( B @ ( vd1201 @ ron ) )
| ~ ( B @ ( F @ ron ) )
| ~ ( A @ ( F @ ron ) )
| ~ ( A @ ( E @ ron ) )
| ~ ( B @ ( E @ ( G @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( E @ ( F @ ( vd1201 @ vangle ) ) @ ( F @ ( vd1201 @ ( G @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(eqfactor_ordered,[status(thm)],[1399]) ).
thf(1710,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( vd1187 @ ( vd1185 @ ( E @ rR ) ) )
| ( B @ ( vd1201 @ ( C @ rS ) ) )
| ~ ( B @ ( C @ ron ) )
| ~ ( B @ ( C @ ron ) )
| ~ ( vd1201 @ rpoint )
| ~ ( vd1201 @ rpoint )
| ~ ( E @ rpoint )
| ~ ( D @ rpoint )
| ~ ( C @ rpoint )
| ~ ( B @ rline )
| ~ ( B @ rline )
| ~ ( A @ rline )
| ~ ( B @ ( vd1201 @ ron ) )
| ~ ( B @ ( vd1201 @ ron ) )
| ~ ( B @ ( E @ ron ) )
| ~ ( A @ ( E @ ron ) )
| ~ ( A @ ( D @ ron ) )
| ~ ( B @ ( D @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( D @ ( E @ ( vd1201 @ vangle ) ) @ ( E @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(pattern_uni,[status(thm)],[1691:[bind(A,$thf( A )),bind(B,$thf( C )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( vd1201 ))]]) ).
thf(1750,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( vd1187 @ ( vd1185 @ ( E @ rR ) ) )
| ( B @ ( vd1201 @ ( C @ rS ) ) )
| ~ ( B @ ( C @ ron ) )
| ~ ( vd1201 @ rpoint )
| ~ ( E @ rpoint )
| ~ ( D @ rpoint )
| ~ ( C @ rpoint )
| ~ ( B @ rline )
| ~ ( A @ rline )
| ~ ( B @ ( vd1201 @ ron ) )
| ~ ( B @ ( E @ ron ) )
| ~ ( A @ ( E @ ron ) )
| ~ ( A @ ( D @ ron ) )
| ~ ( B @ ( D @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( D @ ( E @ ( vd1201 @ vangle ) ) @ ( E @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(simp,[status(thm)],[1710]) ).
thf(2782,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( A @ ( D @ ron ) )
!= ( B @ ( vd1201 @ ron ) ) )
| ~ ( vd1187 @ ( vd1185 @ ( E @ rR ) ) )
| ( B @ ( vd1201 @ ( C @ rS ) ) )
| ~ ( B @ ( C @ ron ) )
| ~ ( vd1201 @ rpoint )
| ~ ( E @ rpoint )
| ~ ( D @ rpoint )
| ~ ( C @ rpoint )
| ~ ( B @ rline )
| ~ ( A @ rline )
| ~ ( B @ ( vd1201 @ ron ) )
| ~ ( B @ ( E @ ron ) )
| ~ ( A @ ( E @ ron ) )
| ~ ( B @ ( D @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( D @ ( E @ ( vd1201 @ vangle ) ) @ ( E @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(eqfactor_ordered,[status(thm)],[1750]) ).
thf(2793,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( vd1187 @ ( vd1185 @ ( C @ rR ) ) )
| ( A @ ( vd1201 @ ( B @ rS ) ) )
| ~ ( A @ ( B @ ron ) )
| ~ ( vd1201 @ rpoint )
| ~ ( C @ rpoint )
| ~ ( vd1201 @ rpoint )
| ~ ( B @ rpoint )
| ~ ( A @ rline )
| ~ ( A @ rline )
| ~ ( A @ ( vd1201 @ ron ) )
| ~ ( A @ ( C @ ron ) )
| ~ ( A @ ( C @ ron ) )
| ~ ( A @ ( vd1201 @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( vd1201 @ ( C @ ( vd1201 @ vangle ) ) @ ( C @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(pattern_uni,[status(thm)],[2782:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( vd1201 ))]]) ).
thf(2888,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( vd1187 @ ( vd1185 @ ( C @ rR ) ) )
| ( A @ ( vd1201 @ ( B @ rS ) ) )
| ~ ( A @ ( B @ ron ) )
| ~ ( C @ rpoint )
| ~ ( vd1201 @ rpoint )
| ~ ( B @ rpoint )
| ~ ( A @ rline )
| ~ ( A @ ( vd1201 @ ron ) )
| ~ ( A @ ( C @ ron ) )
| ~ ( A @ ( vd1201 @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( vd1201 @ ( C @ ( vd1201 @ vangle ) ) @ ( C @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(simp,[status(thm)],[2793]) ).
thf(3340,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vd1234 @ rline )
!= ( A @ rline ) )
| ~ ( vd1187 @ ( vd1185 @ ( C @ rR ) ) )
| ( A @ ( vd1201 @ ( B @ rS ) ) )
| ~ ( A @ ( B @ ron ) )
| ~ ( C @ rpoint )
| ~ ( vd1201 @ rpoint )
| ~ ( B @ rpoint )
| ~ $true
| ~ ( A @ ( vd1201 @ ron ) )
| ~ ( A @ ( C @ ron ) )
| ~ ( A @ ( vd1201 @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( vd1201 @ ( C @ ( vd1201 @ vangle ) ) @ ( C @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(paramod_ordered,[status(thm)],[299,2888]) ).
thf(3341,plain,
! [C: $i,B: $i,A: $i] :
( ( ( vd1234 @ rline )
!= ( A @ rline ) )
| ~ ( vd1187 @ ( vd1185 @ ( C @ rR ) ) )
| ( A @ ( vd1201 @ ( B @ rS ) ) )
| ~ ( A @ ( B @ ron ) )
| ~ ( C @ rpoint )
| ~ ( vd1201 @ rpoint )
| ~ ( B @ rpoint )
| ~ ( A @ ( vd1201 @ ron ) )
| ~ ( A @ ( C @ ron ) )
| ~ ( A @ ( vd1201 @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( vd1201 @ ( C @ ( vd1201 @ vangle ) ) @ ( C @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(simp,[status(thm)],[3340]) ).
thf(3342,plain,
! [B: $i,A: $i] :
( ~ ( vd1187 @ ( vd1185 @ ( B @ rR ) ) )
| ( vd1234 @ ( vd1201 @ ( A @ rS ) ) )
| ~ ( vd1234 @ ( A @ ron ) )
| ~ ( B @ rpoint )
| ~ ( vd1201 @ rpoint )
| ~ ( A @ rpoint )
| ~ ( vd1234 @ ( vd1201 @ ron ) )
| ~ ( vd1234 @ ( B @ ron ) )
| ~ ( vd1234 @ ( vd1201 @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( vd1201 @ ( B @ ( vd1201 @ vangle ) ) @ ( B @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(pattern_uni,[status(thm)],[3341:[bind(A,$thf( vd1234 ))]]) ).
thf(3391,plain,
! [B: $i,A: $i] :
( ~ ( vd1187 @ ( vd1185 @ ( B @ rR ) ) )
| ( vd1234 @ ( vd1201 @ ( A @ rS ) ) )
| ~ ( vd1234 @ ( A @ ron ) )
| ~ ( B @ rpoint )
| ~ ( vd1201 @ rpoint )
| ~ ( A @ rpoint )
| ~ ( vd1234 @ ( vd1201 @ ron ) )
| ~ ( vd1234 @ ( B @ ron ) )
| ~ ( vd1234 @ ( vd1201 @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( vd1201 @ ( B @ ( vd1201 @ vangle ) ) @ ( B @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(simp,[status(thm)],[3342]) ).
thf(3711,plain,
! [B: $i,A: $i] :
( ( ( vd14 @ rpoint )
!= ( B @ rpoint ) )
| ~ ( vd1187 @ ( vd1185 @ ( B @ rR ) ) )
| ( vd1234 @ ( vd1201 @ ( A @ rS ) ) )
| ~ ( vd1234 @ ( A @ ron ) )
| ~ $true
| ~ ( vd1201 @ rpoint )
| ~ ( A @ rpoint )
| ~ ( vd1234 @ ( vd1201 @ ron ) )
| ~ ( vd1234 @ ( B @ ron ) )
| ~ ( vd1234 @ ( vd1201 @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( vd1201 @ ( B @ ( vd1201 @ vangle ) ) @ ( B @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(paramod_ordered,[status(thm)],[462,3391]) ).
thf(3712,plain,
! [B: $i,A: $i] :
( ( ( vd14 @ rpoint )
!= ( B @ rpoint ) )
| ~ ( vd1187 @ ( vd1185 @ ( B @ rR ) ) )
| ( vd1234 @ ( vd1201 @ ( A @ rS ) ) )
| ~ ( vd1234 @ ( A @ ron ) )
| ~ ( vd1201 @ rpoint )
| ~ ( A @ rpoint )
| ~ ( vd1234 @ ( vd1201 @ ron ) )
| ~ ( vd1234 @ ( B @ ron ) )
| ~ ( vd1234 @ ( vd1201 @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( vd1201 @ ( B @ ( vd1201 @ vangle ) ) @ ( B @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(simp,[status(thm)],[3711]) ).
thf(3713,plain,
! [A: $i] :
( ~ ( vd1187 @ ( vd1185 @ ( vd14 @ rR ) ) )
| ( vd1234 @ ( vd1201 @ ( A @ rS ) ) )
| ~ ( vd1234 @ ( A @ ron ) )
| ~ ( vd1201 @ rpoint )
| ~ ( A @ rpoint )
| ~ ( vd1234 @ ( vd1201 @ ron ) )
| ~ ( vd1234 @ ( vd14 @ ron ) )
| ~ ( vd1234 @ ( vd1201 @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( vd1201 @ ( vd14 @ ( vd1201 @ vangle ) ) @ ( vd14 @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(pattern_uni,[status(thm)],[3712:[bind(A,$thf( A )),bind(B,$thf( vd14 ))]]) ).
thf(4029,plain,
! [A: $i] :
( ( ( vd14 @ rpoint )
!= ( A @ rpoint ) )
| ~ ( vd1187 @ ( vd1185 @ ( vd14 @ rR ) ) )
| ( vd1234 @ ( vd1201 @ ( A @ rS ) ) )
| ~ ( vd1234 @ ( A @ ron ) )
| ~ ( vd1201 @ rpoint )
| ~ $true
| ~ ( vd1234 @ ( vd1201 @ ron ) )
| ~ ( vd1234 @ ( vd14 @ ron ) )
| ~ ( vd1234 @ ( vd1201 @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( vd1201 @ ( vd14 @ ( vd1201 @ vangle ) ) @ ( vd14 @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(paramod_ordered,[status(thm)],[462,3713]) ).
thf(4030,plain,
! [A: $i] :
( ( ( vd14 @ rpoint )
!= ( A @ rpoint ) )
| ~ ( vd1187 @ ( vd1185 @ ( vd14 @ rR ) ) )
| ( vd1234 @ ( vd1201 @ ( A @ rS ) ) )
| ~ ( vd1234 @ ( A @ ron ) )
| ~ ( vd1201 @ rpoint )
| ~ ( vd1234 @ ( vd1201 @ ron ) )
| ~ ( vd1234 @ ( vd14 @ ron ) )
| ~ ( vd1234 @ ( vd1201 @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( vd1201 @ ( vd14 @ ( vd1201 @ vangle ) ) @ ( vd14 @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(simp,[status(thm)],[4029]) ).
thf(4031,plain,
( ~ ( vd1187 @ ( vd1185 @ ( vd14 @ rR ) ) )
| ( vd1234 @ ( vd1201 @ ( vd14 @ rS ) ) )
| ~ ( vd1234 @ ( vd14 @ ron ) )
| ~ ( vd1201 @ rpoint )
| ~ ( vd1234 @ ( vd1201 @ ron ) )
| ~ ( vd1234 @ ( vd14 @ ron ) )
| ~ ( vd1234 @ ( vd1201 @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( vd1201 @ ( vd14 @ ( vd1201 @ vangle ) ) @ ( vd14 @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(pattern_uni,[status(thm)],[4030:[bind(A,$thf( vd14 ))]]) ).
thf(4366,plain,
( ~ ( vd1187 @ ( vd1185 @ ( vd14 @ rR ) ) )
| ( vd1234 @ ( vd1201 @ ( vd14 @ rS ) ) )
| ~ ( vd1201 @ rpoint )
| ~ ( vd1234 @ ( vd1201 @ ron ) )
| ~ ( vd1234 @ ( vd14 @ ron ) )
| ~ ( vd1234 @ ( vd1201 @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( vd1201 @ ( vd14 @ ( vd1201 @ vangle ) ) @ ( vd14 @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(simp,[status(thm)],[4031]) ).
thf(1172,plain,
sk57 @ rpoint,
inference(cnfConj,[status(thm)],[1170]) ).
thf(4421,plain,
vd1201 @ rpoint,
inference(rewrite,[status(thm)],[1172,1173]) ).
thf(6850,plain,
( ~ ( vd1187 @ ( vd1185 @ ( vd14 @ rR ) ) )
| ( vd1234 @ ( vd1201 @ ( vd14 @ rS ) ) )
| ~ $true
| ~ ( vd1234 @ ( vd1201 @ ron ) )
| ~ ( vd1234 @ ( vd14 @ ron ) )
| ~ ( vd1234 @ ( vd1201 @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( vd1201 @ ( vd14 @ ( vd1201 @ vangle ) ) @ ( vd14 @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(rewrite,[status(thm)],[4366,4421]) ).
thf(6851,plain,
( ~ ( vd1187 @ ( vd1185 @ ( vd14 @ rR ) ) )
| ( vd1234 @ ( vd1201 @ ( vd14 @ rS ) ) )
| ~ ( vd1234 @ ( vd1201 @ ron ) )
| ~ ( vd1234 @ ( vd14 @ ron ) )
| ~ ( vd1234 @ ( vd1201 @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( vd1201 @ ( vd14 @ ( vd1201 @ vangle ) ) @ ( vd14 @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(simp,[status(thm)],[6850]) ).
thf(102,axiom,
( ( vd1199 != vd1185 )
=> ~ ( vd1186 @ ( vd1185 @ ( vd1199 @ rR ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(271), 3), 2)') ).
thf(913,plain,
( ( vd1199 != vd1185 )
=> ~ ( vd1186 @ ( vd1185 @ ( vd1199 @ rR ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(875,plain,
sk41 @ rpoint,
inference(cnfConj,[status(thm)],[861]) ).
thf(868,plain,
vd1187 = sk41,
inference(cnfConj,[status(thm)],[861]) ).
thf(883,plain,
sk41 = vd1187,
inference(lifteq,[status(thm)],[868]) ).
thf(3103,plain,
vd1187 @ rpoint,
inference(rewrite,[status(thm)],[875,883]) ).
thf(74,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(709,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)],[74]) ).
thf(94,axiom,
( ( vd1179 @ ( vd1178 @ vf ) )
= ( vd1200 @ ( vd1199 @ vf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(conjunct2(conjunct2(conjunct2(plural(271))))), 1209, 0)') ).
thf(841,plain,
( ( vd1179 @ ( vd1178 @ vf ) )
= ( vd1200 @ ( vd1199 @ vf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(878,plain,
vd1179 = sk45,
inference(cnfConj,[status(thm)],[861]) ).
thf(885,plain,
sk45 = vd1179,
inference(lifteq,[status(thm)],[878]) ).
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 ) )
& ? [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(565,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)],[54]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( F @ rreal )
& ( E = F )
& ( ( E @ ( A @ vplus ) )
= ( E @ ( C @ vplus ) ) ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(156, 0), 0)') ).
thf(174,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)],[5]) ).
thf(133,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(1095,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)],[133]) ).
thf(7,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(184,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)],[7]) ).
thf(80,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(751,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)],[80]) ).
thf(876,plain,
vd1186 = sk42,
inference(cnfConj,[status(thm)],[861]) ).
thf(891,plain,
sk42 = vd1186,
inference(lifteq,[status(thm)],[876]) ).
thf(23,axiom,
vd1200 = vd1186,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(comma_conjunct2(plural(271))), 1212, 0)') ).
thf(297,plain,
vd1200 = vd1186,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(298,plain,
vd1186 = vd1200,
inference(lifteq,[status(thm)],[297]) ).
thf(3542,plain,
sk42 = vd1200,
inference(rewrite,[status(thm)],[891,298]) ).
thf(862,plain,
vd1178 = sk46,
inference(cnfConj,[status(thm)],[861]) ).
thf(881,plain,
sk46 = vd1178,
inference(lifteq,[status(thm)],[862]) ).
thf(29,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(325,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rcenter ) )
=> ( B @ ( A @ rinside ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(57,axiom,
? [A: $i] :
( ( A @ rpoint )
& ( vd1199 = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(s1(plural(271)))') ).
thf(583,plain,
? [A: $i] :
( ( A @ rpoint )
& ( vd1199 = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(584,plain,
( ( sk25 @ rpoint )
& ( vd1199 = sk25 ) ),
inference(cnf,[status(esa)],[583]) ).
thf(585,plain,
vd1199 = sk25,
inference(cnfConj,[status(thm)],[584]) ).
thf(587,plain,
sk25 = vd1199,
inference(lifteq,[status(thm)],[585]) ).
thf(3557,plain,
sk25 = vd1185,
inference(rewrite,[status(thm)],[587,977]) ).
thf(105,axiom,
( ~ ( vd1232 @ ( vd1201 @ ron ) )
=> ~ ( vd1232 @ ( vd1201 @ ( vd1186 @ rS ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(271), 9), 2)') ).
thf(969,plain,
( ~ ( vd1232 @ ( vd1201 @ ron ) )
=> ~ ( vd1232 @ ( vd1201 @ ( vd1186 @ rS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(61,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(606,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)],[61]) ).
thf(3,axiom,
vd684 @ rreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(137), 1)') ).
thf(164,plain,
vd684 @ rreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(81,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(756,plain,
! [A: $i,B: $i] :
( ( ( B @ rreal )
& ( A = B ) )
=> ~ ( A @ ( A @ rless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(6,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(179,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)],[6]) ).
thf(123,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(1040,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)],[123]) ).
thf(33,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(376,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)],[33]) ).
thf(140,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(1136,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)],[140]) ).
thf(12,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(238,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)],[12]) ).
thf(46,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(514,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)],[46]) ).
thf(141,axiom,
( ( vd1199 != vd1185 )
=> ( ( vd1186 @ ( vd1199 @ ( vd1185 @ rR ) ) )
| ( vd1186 @ ( vd1185 @ ( vd1199 @ rR ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(271), 3), 3)') ).
thf(1151,plain,
( ( vd1199 != vd1185 )
=> ( ( vd1186 @ ( vd1199 @ ( vd1185 @ rR ) ) )
| ( vd1186 @ ( vd1185 @ ( vd1199 @ rR ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(125,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(1051,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)],[125]) ).
thf(22,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(293,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)],[22]) ).
thf(138,axiom,
( ( vd1199 @ ( vd1200 @ ( vd1201 @ vangle ) ) )
= ( vd1178 @ ( vd1179 @ ( vd1180 @ vangle ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(conjunct2(conjunct2(plural(271)))), 1208, 0)') ).
thf(1119,plain,
( ( vd1199 @ ( vd1200 @ ( vd1201 @ vangle ) ) )
= ( vd1178 @ ( vd1179 @ ( vd1180 @ vangle ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(68,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(660,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)],[68]) ).
thf(11,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(233,plain,
! [A: $i,B: $i] :
( ( ( B @ rreal )
& ( A = B ) )
=> ( ( v0 @ ( A @ vplus ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(185,plain,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] :
( ( D @ rtriangle )
& ( ( C @ ( B @ ( A @ vtriangle ) ) )
= D ) )
=> ( ? [D: $i] :
( ( D @ rpoint )
& ( A = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( B = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( C = D ) )
& ( A != B )
& ( A != C )
& ( B != C ) ) ),
inference(miniscope,[status(thm)],[184]) ).
thf(186,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk3 ) ) @ rpoint )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) )
& ( ( A
= ( A @ ( B @ ( C @ sk3 ) ) ) )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) )
& ( ( A @ ( B @ ( C @ sk2 ) ) @ rpoint )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) )
& ( ( B
= ( A @ ( B @ ( C @ sk2 ) ) ) )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) )
& ( ( A @ ( B @ ( C @ sk1 ) ) @ rpoint )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) )
& ( ( C
= ( A @ ( B @ ( C @ sk1 ) ) ) )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) )
& ( ( A != B )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) )
& ( ( A != C )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) )
& ( ( B != C )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ) ),
inference(cnf,[status(esa)],[185]) ).
thf(188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ ( B @ ( C @ sk1 ) ) ) )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(cnfConj,[status(thm)],[186]) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ rtriangle )
| ( ( A @ ( B @ ( C @ sk1 ) ) )
= C )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[188]) ).
thf(201,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ vtriangle ) ) @ rtriangle )
| ( ( A @ ( B @ ( C @ sk1 ) ) )
= C ) ),
inference(simp,[status(thm)],[200]) ).
thf(82,axiom,
vd1197 @ ( vd1186 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(s2(plural(269)), 0)') ).
thf(761,plain,
vd1197 @ ( vd1186 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(810,plain,
v0 = vd684,
inference(lifteq,[status(thm)],[809]) ).
thf(127,axiom,
vd1232 @ ( vd1185 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(s1(plural(315)), 0)') ).
thf(1067,plain,
vd1232 @ ( vd1185 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(88,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(798,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)],[88]) ).
thf(586,plain,
sk25 @ rpoint,
inference(cnfConj,[status(thm)],[584]) ).
thf(1472,plain,
vd1199 @ rpoint,
inference(rewrite,[status(thm)],[586,587]) ).
thf(4434,plain,
vd1185 @ rpoint,
inference(rewrite,[status(thm)],[1472,977]) ).
thf(146,axiom,
vd1201 != vd1187,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(320, 1251, 0)') ).
thf(1174,plain,
vd1201 != vd1187,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(872,plain,
sk45 @ rpoint,
inference(cnfConj,[status(thm)],[861]) ).
thf(3154,plain,
vd1179 @ rpoint,
inference(rewrite,[status(thm)],[872,885]) ).
thf(158,axiom,
~ ( vd1185 @ ( vd1199 @ ( vd1186 @ rR ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','neg(neg(conjunct2(conjunct2(comma_conjunct2(plural(271))))))') ).
thf(1217,plain,
~ ( vd1185 @ ( vd1199 @ ( vd1186 @ rR ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(90,axiom,
? [A: $i] :
( ( A @ rpoint )
& ( vd1200 = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(s2(plural(271)))') ).
thf(811,plain,
? [A: $i] :
( ( A @ rpoint )
& ( vd1200 = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(812,plain,
( ( sk38 @ rpoint )
& ( vd1200 = sk38 ) ),
inference(cnf,[status(esa)],[811]) ).
thf(813,plain,
vd1200 = sk38,
inference(cnfConj,[status(thm)],[812]) ).
thf(815,plain,
sk38 = vd1200,
inference(lifteq,[status(thm)],[813]) ).
thf(103,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(916,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)],[103]) ).
thf(10,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(229,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)],[10]) ).
thf(189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( B @ ( C @ sk2 ) ) ) )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(cnfConj,[status(thm)],[186]) ).
thf(196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ rtriangle )
| ( ( A @ ( B @ ( C @ sk2 ) ) )
= B )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[189]) ).
thf(197,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ vtriangle ) ) @ rtriangle )
| ( ( A @ ( B @ ( C @ sk2 ) ) )
= B ) ),
inference(simp,[status(thm)],[196]) ).
thf(867,plain,
sk46 @ rpoint,
inference(cnfConj,[status(thm)],[861]) ).
thf(3090,plain,
vd1178 @ rpoint,
inference(rewrite,[status(thm)],[867,881]) ).
thf(1218,plain,
~ ( vd1185 @ ( vd1199 @ ( vd1186 @ rR ) ) ),
inference(polarity_switch,[status(thm)],[1217]) ).
thf(3117,plain,
~ ( vd1185 @ ( vd1199 @ ( vd1200 @ rR ) ) ),
inference(rewrite,[status(thm)],[1218,298]) ).
thf(3556,plain,
~ ( vd1185 @ ( vd1185 @ ( vd1200 @ rR ) ) ),
inference(rewrite,[status(thm)],[3117,977]) ).
thf(28,axiom,
vd1197 @ ( vd1199 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(272, 0)') ).
thf(324,plain,
vd1197 @ ( vd1199 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(21,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(285,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)],[21]) ).
thf(72,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(682,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)],[72]) ).
thf(154,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(1195,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)],[154]) ).
thf(56,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(578,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)],[56]) ).
thf(131,axiom,
vd1197 @ ( vd1201 @ ( vd1187 @ rS ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(295, 1236, 0)') ).
thf(1089,plain,
vd1197 @ ( vd1201 @ ( vd1187 @ rS ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(62,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(615,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)],[62]) ).
thf(139,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(1121,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)],[139]) ).
thf(37,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(403,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)],[37]) ).
thf(34,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(388,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)],[34]) ).
thf(59,axiom,
vd1197 @ rline,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(269, 0)') ).
thf(593,plain,
vd1197 @ rline,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(129,axiom,
( ( vd1180 @ ( vd1179 @ vf ) )
= ( vd1201 @ ( vd1200 @ vf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(plural(271)))))), 1210, 0)') ).
thf(1082,plain,
( ( vd1180 @ ( vd1179 @ vf ) )
= ( vd1201 @ ( vd1200 @ vf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(47,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(526,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)],[47]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( H @ rpoint )
& ( G = H )
& ( A != C )
& ( E != G )
& ( C @ ( A @ vf ) @ ( G @ ( E @ vf ) @ rless ) ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ vskolem1120 ) ) ) ) ) ) ) @ ( A @ vf ) )
= ( G @ ( E @ vf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(238), 0), 0)') ).
thf(637,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( H @ rpoint )
& ( G = H )
& ( A != C )
& ( E != G )
& ( C @ ( A @ vf ) @ ( G @ ( E @ vf ) @ rless ) ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ vskolem1120 ) ) ) ) ) ) ) @ ( A @ vf ) )
= ( G @ ( E @ vf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(44,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(489,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)],[44]) ).
thf(51,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(547,plain,
! [A: $i,B: $i] :
( ( ( B @ rcircle )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( A @ ( C @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(99,axiom,
( ( vd1180 @ ( vd1178 @ vf ) )
= ( vd1201 @ ( vd1199 @ vf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(plural(271)))))), 1211, 0)') ).
thf(901,plain,
( ( vd1180 @ ( vd1178 @ vf ) )
= ( vd1201 @ ( vd1199 @ vf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(73,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(686,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)],[73]) ).
thf(35,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(393,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)],[35]) ).
thf(115,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(997,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)],[115]) ).
thf(151,axiom,
vd1232 @ ( vd1187 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(s2(plural(293)), 0)') ).
thf(1192,plain,
vd1232 @ ( vd1187 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( C = F ) )
& ( 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(1002,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)],[116]) ).
thf(55,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(569,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)],[55]) ).
thf(134,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(1099,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)],[134]) ).
thf(169,plain,
! [P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ rintersect ) )
| ~ ( P @ rpoint )
| ( A != P )
| ~ ( O @ rpoint )
| ( B != O )
| ~ ( N @ rpoint )
| ( C != N )
| ~ ( M @ rpoint )
| ( D != M )
| ~ ( L @ rpoint )
| ( E != L )
| ~ ( K @ rline )
| ( F != K )
| ~ ( J @ rline )
| ( G != J )
| ~ ( 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 ) ) ),
inference(cnfConj,[status(thm)],[167]) ).
thf(172,plain,
! [P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ rintersect ) )
| ~ ( P @ rpoint )
| ~ ( O @ rpoint )
| ~ ( N @ rpoint )
| ~ ( M @ rpoint )
| ~ ( L @ rpoint )
| ~ ( K @ rline )
| ~ ( J @ rline )
| ~ ( I @ rline )
| ~ ( F @ ( A @ ron ) )
| ~ ( F @ ( B @ ron ) )
| ~ ( G @ ( B @ ron ) )
| ~ ( G @ ( C @ ron ) )
| ~ ( H @ ( C @ ron ) )
| ~ ( H @ ( D @ ron ) )
| ~ ( G @ ( D @ ( A @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( D @ ( C @ ( B @ vangle ) ) @ ( C @ ( B @ ( A @ vangle ) ) @ vplus ) @ rless ) )
| ( A != P )
| ( B != O )
| ( C != N )
| ( D != M )
| ( E != L )
| ( F != K )
| ( G != J )
| ( H != I )
| ( B = C ) ),
inference(lifteq,[status(thm)],[169]) ).
thf(173,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ rintersect ) )
| ~ ( H @ rpoint )
| ~ ( G @ rpoint )
| ~ ( F @ rpoint )
| ~ ( E @ rpoint )
| ~ ( D @ rpoint )
| ~ ( C @ rline )
| ~ ( B @ rline )
| ~ ( A @ rline )
| ~ ( C @ ( H @ ron ) )
| ~ ( C @ ( G @ ron ) )
| ~ ( B @ ( G @ ron ) )
| ~ ( B @ ( F @ ron ) )
| ~ ( A @ ( F @ ron ) )
| ~ ( A @ ( E @ ron ) )
| ~ ( B @ ( E @ ( H @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( E @ ( F @ ( G @ vangle ) ) @ ( F @ ( G @ ( H @ vangle ) ) @ vplus ) @ rless ) )
| ( G = F ) ),
inference(simp,[status(thm)],[172]) ).
thf(156,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(1202,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)],[156]) ).
thf(191,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk1 ) ) @ rpoint )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(cnfConj,[status(thm)],[186]) ).
thf(204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk1 ) ) @ rpoint )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[191]) ).
thf(205,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk1 ) ) @ rpoint )
| ~ ( C @ ( B @ ( A @ vtriangle ) ) @ rtriangle ) ),
inference(simp,[status(thm)],[204]) ).
thf(87,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(794,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)],[87]) ).
thf(874,plain,
vd1185 = sk43,
inference(cnfConj,[status(thm)],[861]) ).
thf(888,plain,
sk43 = vd1185,
inference(lifteq,[status(thm)],[874]) ).
thf(36,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(398,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)],[36]) ).
thf(120,axiom,
vd1232 @ ( vd1187 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(s3(plural(315)), 0)') ).
thf(1035,plain,
vd1232 @ ( vd1187 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(135,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(1103,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)],[135]) ).
thf(159,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(1219,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)],[159]) ).
thf(142,axiom,
~ ( vd1187 @ ( vd1201 @ ( vd1185 @ rR ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','neg(316)') ).
thf(1154,plain,
~ ( vd1187 @ ( vd1201 @ ( vd1185 @ rR ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(7178,plain,
( ( ( vd1234 @ ( vd14 @ ron ) )
!= ( vd1197 @ ( vd1185 @ ron ) ) )
| ~ ( vd1187 @ ( vd1185 @ ( vd14 @ rR ) ) )
| ( vd1234 @ ( vd1201 @ ( vd14 @ rS ) ) )
| ~ ( vd1234 @ ( vd1201 @ ron ) )
| ~ $true
| ~ ( vd1234 @ ( vd1201 @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( vd1201 @ ( vd14 @ ( vd1201 @ vangle ) ) @ ( vd14 @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(paramod_ordered,[status(thm)],[6905,6851]) ).
thf(7179,plain,
( ( ( vd1234 @ ( vd14 @ ron ) )
!= ( vd1197 @ ( vd1185 @ ron ) ) )
| ~ ( vd1187 @ ( vd1185 @ ( vd14 @ rR ) ) )
| ( vd1234 @ ( vd1201 @ ( vd14 @ rS ) ) )
| ~ ( vd1234 @ ( vd1201 @ ron ) )
| ~ ( vd1234 @ ( vd1201 @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( vd1201 @ ( vd14 @ ( vd1201 @ vangle ) ) @ ( vd14 @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) ) ),
inference(simp,[status(thm)],[7178]) ).
thf(7287,plain,
( ( vd1234 != vd1197 )
| ( vd14 != vd1185 )
| ~ ( vd1187 @ ( vd1185 @ ( vd14 @ rR ) ) )
| ~ ( vd1234 @ ( vd1201 @ ron ) )
| ~ ( vd1234 @ ( vd1201 @ ( vd1201 @ rS ) ) )
| ~ ( vperp @ ( vperp @ vplus ) @ ( vd1201 @ ( vd14 @ ( vd1201 @ vangle ) ) @ ( vd14 @ ( vd1201 @ ( vd1201 @ vangle ) ) @ vplus ) @ rless ) )
| ( vd1234 @ ( vd1201 @ ( vd14 @ rS ) ) ) ),
inference(simp,[status(thm)],[7179]) ).
thf(117,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(1007,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)],[117]) ).
thf(95,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(843,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)],[95]) ).
thf(79,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(743,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)],[79]) ).
thf(20,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(281,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)],[20]) ).
thf(101,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(904,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)],[101]) ).
thf(107,axiom,
vd1197 @ ( vd1185 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(s3(plural(274)), 0)') ).
thf(975,plain,
vd1197 @ ( vd1185 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(66,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(641,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)],[66]) ).
thf(75,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(713,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)],[75]) ).
thf(132,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(1090,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)],[132]) ).
thf(69,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(672,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)],[69]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ rpoint )
& ( A = F ) )
& ? [F: $i] :
( ( F @ rpoint )
& ( B = F ) )
& ? [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(979,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)],[110]) ).
thf(153,axiom,
vd1234 @ ( vd1201 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(s2(plural(294)), 0)') ).
thf(1194,plain,
vd1234 @ ( vd1201 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(71,axiom,
vd1197 @ ( vd1200 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(s2(plural(274)), 0)') ).
thf(681,plain,
vd1197 @ ( vd1200 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(113,axiom,
( ( vd1201 @ ( vd1199 @ vf ) )
= ( vd1187 @ ( vd1185 @ vf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(314, 1247, 0)') ).
thf(990,plain,
( ( vd1201 @ ( vd1199 @ vf ) )
= ( vd1187 @ ( vd1185 @ vf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(26,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(318,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)],[26]) ).
thf(43,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(477,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)],[43]) ).
thf(49,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(535,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)],[49]) ).
thf(91,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(816,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)],[91]) ).
thf(27,axiom,
vd1197 @ ( vd1199 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(conjunct1(conjunct2(comma_conjunct2(plural(271)))), 0)') ).
thf(323,plain,
vd1197 @ ( vd1199 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(60,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(594,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)],[60]) ).
thf(96,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(848,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)],[96]) ).
thf(118,axiom,
vd1232 @ ( vd1185 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(s1(plural(293)), 0)') ).
thf(1022,plain,
vd1232 @ ( vd1185 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(147,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(1177,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)],[147]) ).
thf(195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != C )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(cnfConj,[status(thm)],[186]) ).
thf(212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ rtriangle )
| ( B != C )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[195]) ).
thf(213,plain,
! [B: $i,A: $i] :
~ ( B @ ( B @ ( A @ vtriangle ) ) @ rtriangle ),
inference(simp,[status(thm)],[212]) ).
thf(77,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(726,plain,
! [A: $i,B: $i] :
( ( ( B @ rcircle )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( A @ ( C @ rinside ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(157,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(1213,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)],[157]) ).
thf(1175,plain,
vd1201 != vd1187,
inference(polarity_switch,[status(thm)],[1174]) ).
thf(1176,plain,
vd1187 != vd1201,
inference(lifteq,[status(thm)],[1175]) ).
thf(112,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(986,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)],[112]) ).
thf(70,axiom,
vd1232 @ rline,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(293, 0)') ).
thf(680,plain,
vd1232 @ rline,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(104,axiom,
~ ( vd1187 @ ( vd1201 @ ( vd1185 @ rR ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','neg(neg(319))') ).
thf(967,plain,
~ ( vd1187 @ ( vd1201 @ ( vd1185 @ rR ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(968,plain,
~ ( vd1187 @ ( vd1201 @ ( vd1185 @ rR ) ) ),
inference(polarity_switch,[status(thm)],[967]) ).
thf(93,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(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 )
& ( D @ ( B @ ( A @ rS ) ) )
& ( D @ ( C @ ( A @ rS ) ) ) )
=> ( D @ ( C @ ( B @ rS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(124,axiom,
( ( vd1201 @ ( vd1199 @ ( vd1200 @ vangle ) ) )
= ( vd1180 @ ( vd1178 @ ( vd1179 @ vangle ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(plural(271)), 1206, 0)') ).
thf(1049,plain,
( ( vd1201 @ ( vd1199 @ ( vd1200 @ vangle ) ) )
= ( vd1180 @ ( vd1178 @ ( vd1179 @ vangle ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(814,plain,
sk38 @ rpoint,
inference(cnfConj,[status(thm)],[812]) ).
thf(2238,plain,
vd1200 @ rpoint,
inference(rewrite,[status(thm)],[814,815]) ).
thf(5879,plain,
! [A: $i] :
( ( ( vd1200 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ sk33 )
!= A ) ),
inference(paramod_ordered,[status(thm)],[2238,723]) ).
thf(5880,plain,
! [A: $i] :
( ( ( vd1200 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ sk33 )
!= A ) ),
inference(simp,[status(thm)],[5879]) ).
thf(5881,plain,
( ( vd1200 @ sk33 )
!= vd1200 ),
inference(pattern_uni,[status(thm)],[5880:[bind(A,$thf( vd1200 ))]]) ).
thf(48,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(531,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)],[48]) ).
thf(85,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(776,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)],[85]) ).
thf(143,axiom,
vd1232 @ ( vd1201 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(s2(plural(315)), 0)') ).
thf(1156,plain,
vd1232 @ ( vd1201 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(866,plain,
vd1178 != vd1179,
inference(cnfConj,[status(thm)],[861]) ).
thf(887,plain,
vd1179 != vd1178,
inference(lifteq,[status(thm)],[866]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( H @ rpoint )
& ( G = H )
& ( A != C )
& ( E != G )
& ( C @ ( A @ vf ) @ ( G @ ( E @ vf ) @ rless ) ) )
=> ( C @ ( A @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ vskolem1120 ) ) ) ) ) ) ) @ rR ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(238), 0), 1)') ).
thf(971,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( H @ rpoint )
& ( G = H )
& ( A != C )
& ( E != G )
& ( C @ ( A @ vf ) @ ( G @ ( E @ vf ) @ rless ) ) )
=> ( C @ ( A @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ vskolem1120 ) ) ) ) ) ) ) @ rR ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(30,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(327,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)],[30]) ).
thf(17,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(263,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)],[17]) ).
thf(192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != C )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(cnfConj,[status(thm)],[186]) ).
thf(198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ rtriangle )
| ( A != C )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[192]) ).
thf(199,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( B @ vtriangle ) ) @ rtriangle ),
inference(simp,[status(thm)],[198]) ).
thf(148,axiom,
( ( vd1199 != vd1185 )
=> ( ( vd1186 @ ( vd1185 @ ( vd1199 @ rR ) ) )
| ( vd1186 @ ( vd1199 @ ( vd1185 @ rR ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(271), 3), 0)') ).
thf(1186,plain,
( ( vd1199 != vd1185 )
=> ( ( vd1186 @ ( vd1185 @ ( vd1199 @ rR ) ) )
| ( vd1186 @ ( vd1199 @ ( vd1185 @ rR ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(122,axiom,
( ~ ( vd1232 @ ( vd1201 @ ron ) )
=> ~ ( vd1234 @ ( vd1187 @ ( vd1200 @ rS ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(271), 9), 1)') ).
thf(1038,plain,
( ~ ( vd1232 @ ( vd1201 @ ron ) )
=> ~ ( vd1234 @ ( vd1187 @ ( vd1200 @ rS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(42,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(463,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)],[42]) ).
thf(109,axiom,
vd1197 @ ( vd1185 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(s1(plural(269)), 0)') ).
thf(978,plain,
vd1197 @ ( vd1185 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(45,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(497,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)],[45]) ).
thf(67,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(656,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)],[67]) ).
thf(119,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(1023,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)],[119]) ).
thf(130,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(1084,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)],[130]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ rpoint )
& ( A = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( B = D ) )
& ? [D: $i] :
( ( D @ rpoint )
& ( C = D ) )
& ( 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(556,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)],[52]) ).
thf(50,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(539,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)],[50]) ).
thf(193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != B )
| ~ ( D @ rtriangle )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(cnfConj,[status(thm)],[186]) ).
thf(202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ rtriangle )
| ( A != B )
| ( ( C @ ( B @ ( A @ vtriangle ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[193]) ).
thf(203,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( A @ vtriangle ) ) @ rtriangle ),
inference(simp,[status(thm)],[202]) ).
thf(144,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(1157,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)],[144]) ).
thf(9,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(218,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)],[9]) ).
thf(149,axiom,
vd1232 @ ( vd1201 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(313, 0)') ).
thf(1189,plain,
vd1232 @ ( vd1201 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(136,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(1108,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)],[136]) ).
thf(100,axiom,
vd1234 @ ( vd1185 @ ron ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(s1(plural(294)), 0)') ).
thf(903,plain,
vd1234 @ ( vd1185 @ ron ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(58,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(588,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)],[58]) ).
thf(16,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(258,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)],[16]) ).
thf(38,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(418,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)],[38]) ).
thf(19,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(272,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)],[19]) ).
thf(8,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(214,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)],[8]) ).
thf(152,axiom,
vd1197 @ ( vd1187 @ ( vd1201 @ rS ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(comma_conjunct2(comma_conjunct2(plural(271))), 1214, 0)') ).
thf(1193,plain,
vd1197 @ ( vd1187 @ ( vd1201 @ rS ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(137,axiom,
( ( vd1199 != vd1185 )
=> ~ ( vd1186 @ ( vd1199 @ ( vd1185 @ rR ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(271), 3), 1)') ).
thf(1116,plain,
( ( vd1199 != vd1185 )
=> ~ ( vd1186 @ ( vd1199 @ ( vd1185 @ rR ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(25,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(300,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)],[25]) ).
thf(63,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(620,plain,
! [A: $i,B: $i] :
( ( ( B @ rline )
& ( A = B ) )
=> ? [C: $i] :
( ( C @ rpoint )
& ( A @ ( C @ ron ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(40,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(447,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)],[40]) ).
thf(39,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(432,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)],[39]) ).
thf(86,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(790,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)],[86]) ).
thf(78,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(735,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)],[78]) ).
thf(180,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( F @ rreal )
& ( E = F ) )
& ( C @ ( A @ rless ) ) )
=> ( E @ ( C @ vplus ) @ ( E @ ( A @ vplus ) @ rless ) ) ),
inference(miniscope,[status(thm)],[179]) ).
thf(181,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ vplus ) @ ( E @ ( A @ vplus ) @ rless ) )
| ~ ( B @ rreal )
| ( A != B )
| ~ ( D @ rreal )
| ( C != D )
| ~ ( F @ rreal )
| ( E != F )
| ~ ( C @ ( A @ rless ) ) ),
inference(cnf,[status(esa)],[180]) ).
thf(182,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ vplus ) @ ( E @ ( A @ vplus ) @ rless ) )
| ~ ( B @ rreal )
| ~ ( D @ rreal )
| ~ ( F @ rreal )
| ~ ( C @ ( A @ rless ) )
| ( A != B )
| ( C != D )
| ( E != F ) ),
inference(lifteq,[status(thm)],[181]) ).
thf(183,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ rless ) )
| ~ ( A @ rreal )
| ~ ( B @ rreal )
| ~ ( C @ rreal )
| ~ ( B @ ( A @ rless ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(5882,plain,
! [A: $i] :
( ( ( vd1187 @ rpoint )
!= ( A @ rpoint ) )
| ~ $true
| ( ( A @ sk33 )
!= A ) ),
inference(paramod_ordered,[status(thm)],[3103,723]) ).
thf(5883,plain,
! [A: $i] :
( ( ( vd1187 @ rpoint )
!= ( A @ rpoint ) )
| ( ( A @ sk33 )
!= A ) ),
inference(simp,[status(thm)],[5882]) ).
thf(5884,plain,
( ( vd1187 @ sk33 )
!= vd1187 ),
inference(pattern_uni,[status(thm)],[5883:[bind(A,$thf( vd1187 ))]]) ).
thf(13,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(242,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)],[13]) ).
thf(31,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(341,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)],[31]) ).
thf(18,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(268,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)],[18]) ).
thf(84,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(767,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)],[84]) ).
thf(92,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(828,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)],[92]) ).
thf(126,axiom,
( ~ ( vd1232 @ ( vd1201 @ ron ) )
=> ( ( vd1232 @ ( vd1201 @ ( vd1186 @ rS ) ) )
| ( vd1234 @ ( vd1187 @ ( vd1200 @ rS ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(271), 9), 0)') ).
thf(1065,plain,
( ~ ( vd1232 @ ( vd1201 @ ron ) )
=> ( ( vd1232 @ ( vd1201 @ ( vd1186 @ rS ) ) )
| ( vd1234 @ ( vd1187 @ ( vd1200 @ rS ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(877,plain,
vd1179 != vd1180,
inference(cnfConj,[status(thm)],[861]) ).
thf(886,plain,
vd1180 != vd1179,
inference(lifteq,[status(thm)],[877]) ).
thf(114,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(992,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)],[114]) ).
thf(163,plain,
~ ( vd1201 @ ( vd1185 @ ( vd1187 @ rR ) ) ),
inference(cnfConj,[status(thm)],[161]) ).
thf(175,plain,
! [A: $i,B: $i,C: $i] :
( ? [D: $i,E: $i] :
( ? [F: $i] :
( ( B @ rreal )
& ( A = B )
& ( D @ rreal )
& ( C = D )
& ( F @ rreal )
& ( E = F ) )
& ( ( E @ ( A @ vplus ) )
= ( E @ ( C @ vplus ) ) ) )
=> ( A = C ) ),
inference(miniscope,[status(thm)],[174]) ).
thf(176,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( B @ rreal )
| ( A != B )
| ~ ( D @ rreal )
| ( C != D )
| ~ ( F @ rreal )
| ( E != F )
| ( ( E @ ( A @ vplus ) )
!= ( E @ ( C @ vplus ) ) ) ),
inference(cnf,[status(esa)],[175]) ).
thf(177,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ rreal )
| ~ ( D @ rreal )
| ~ ( F @ rreal )
| ( A = C )
| ( A != B )
| ( C != D )
| ( E != F )
| ( ( E @ ( A @ vplus ) )
!= ( E @ ( C @ vplus ) ) ) ),
inference(lifteq,[status(thm)],[176]) ).
thf(178,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ rreal )
| ~ ( B @ rreal )
| ~ ( C @ rreal )
| ( A = B )
| ( ( C @ ( A @ vplus ) )
!= ( C @ ( B @ vplus ) ) ) ),
inference(simp,[status(thm)],[177]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( H @ rpoint )
& ( G = H )
& ( A != C )
& ( E != G )
& ( C @ ( A @ vf ) @ ( G @ ( E @ vf ) @ rless ) ) )
=> ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ vskolem1120 ) ) ) ) ) ) ) @ rpoint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(238), 0), 2)') ).
thf(254,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( B @ rpoint )
& ( A = B )
& ( D @ rpoint )
& ( C = D )
& ( F @ rpoint )
& ( E = F )
& ( H @ rpoint )
& ( G = H )
& ( A != C )
& ( E != G )
& ( C @ ( A @ vf ) @ ( G @ ( E @ vf ) @ rless ) ) )
=> ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ vskolem1120 ) ) ) ) ) ) ) @ rpoint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(53,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(560,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)],[53]) ).
thf(9298,plain,
$false,
inference(e,[status(thm)],[892,1036,809,629,1190,893,6986,352,1200,977,762,1068,5878,1173,6851,913,3103,709,841,885,565,174,1095,184,751,3542,6905,881,325,3557,969,606,164,756,179,1040,376,253,1136,238,514,1151,1051,1169,293,1119,660,233,201,761,810,1067,798,4434,1174,297,3154,1217,160,165,815,916,229,197,3090,3556,583,889,324,285,682,1195,578,1089,615,1121,403,388,593,1082,4421,526,637,489,547,901,686,393,997,1192,1002,569,1099,985,984,173,1202,205,794,888,398,1035,298,1103,1219,1154,7287,1007,843,743,281,904,975,641,713,1090,672,979,1194,681,990,318,477,811,535,816,323,594,848,1022,1177,462,213,726,1213,883,1176,986,299,680,968,836,1049,162,5881,531,776,1156,887,971,327,263,199,1186,1038,717,463,978,497,656,1023,1084,556,539,203,1157,218,1189,1108,976,903,588,258,171,418,272,214,3529,1193,1116,300,620,447,432,967,790,735,183,5884,242,341,268,767,828,1065,886,860,992,723,163,178,254,2238,560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO298+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.11 % 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
% 0.19/0.46 % Computer : n004.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Fri Sep 25 13:14:37 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.47 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.22/1.28 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.46/1.72 % [INFO] Parsing done (438ms).
% 2.46/1.74 % [INFO] Running in sequential loop mode.
% 3.64/2.29 % [INFO] eprover registered as external prover.
% 3.85/2.30 % [INFO] Scanning for conjecture ...
% 4.01/2.50 % [INFO] Found a conjecture (or negated_conjecture) and 157 axioms. Running axiom selection ...
% 4.44/2.68 % [INFO] Axiom selection finished. Selected 157 axioms (removed 0 axioms).
% 5.84/3.19 % [INFO] Problem is first-order (TPTP FOF).
% 5.95/3.25 % [INFO] Type checking passed.
% 5.95/3.26 % [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 ...
% 113.02/34.12 % External prover 'e' found a proof!
% 113.02/34.12 % [INFO] Killing All external provers ...
% 113.02/34.12 % Time passed: 33456ms (effective reasoning time: 32377ms)
% 113.02/34.12 % 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)>
% 113.02/34.13 % Axioms used in derivation (157): holds(292, 1231, 0), qu(cond(axiom(41), 0), imp(cond(axiom(41), 0))), qe(s2(plural(271))), pred(s1(plural(315)), 0), qu(cond(axiom(119), 0), imp(cond(axiom(119), 0))), qu(cond(axiom(3), 0), imp(cond(axiom(3), 0))), pred(294, 0), qu(cond(axiom(164), 0), imp(cond(axiom(164), 0))), qu(cond(axiom(145), 0), imp(cond(axiom(145), 0))), ass(cond(goal(206), 0), 1), qu(cond(axiom(202), 0), imp(cond(axiom(202), 0))), holds(320, 1251, 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))), pred(s1(plural(293)), 0), pred(s3(plural(274)), 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))), ass(cond(conseq(271), 9), 0), pred(313, 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))), qe(s1(plural(271))), qu(cond(axiom(190), 0), imp(cond(axiom(190), 0))), qu(cond(axiom(53), 0), imp(cond(axiom(53), 0))), pred(s1(plural(274)), 0), qu(cond(axiom(89), 0), imp(cond(axiom(89), 0))), holds(273, 1215, 0), pred(272, 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), ass(cond(goal(238), 0), 0), qu(cond(axiom(103), 0), imp(cond(axiom(103), 0))), holds(comma_conjunct2(comma_conjunct2(plural(271))), 1214, 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))), pred(conjunct1(conjunct2(comma_conjunct2(plural(271)))), 0), qu(cond(axiom(59), 0), imp(cond(axiom(59), 0))), pred(s2(plural(269)), 0), holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(plural(271)))))), 1210, 0), holds(295, 1236, 0), qu(cond(axiom(35), 0), imp(cond(axiom(35), 0))), qu(cond(axiom(23), 0), imp(cond(axiom(23), 0))), qu(cond(axiom(87), 0), imp(cond(axiom(87), 0))), qu(cond(axiom(1), 0), imp(cond(axiom(1), 0))), qu(cond(axiom(121), 0), imp(cond(axiom(121), 0))), qu(cond(axiom(83), 0), imp(cond(axiom(83), 0))), pred(s2(plural(294)), 0), qu(cond(axiom(109), 0), imp(cond(axiom(109), 0))), pred(293, 0), qu(cond(axiom(79), 0), imp(cond(axiom(79), 0))), qu(cond(axiom(55), 0), imp(cond(axiom(55), 0))), qu(cond(axiom(81), 0), imp(cond(axiom(81), 0))), qu(cond(axiom(13), 0), imp(cond(axiom(13), 0))), qu(cond(axiom(143), 0), imp(cond(axiom(143), 0))), ass(cond(156, 0), 0), qu(cond(axiom(184), 0), imp(cond(axiom(184), 0))), holds(291, 1230, 0), qu(cond(axiom(188), 0), imp(cond(axiom(188), 0))), qu(cond(axiom(99), 0), imp(cond(axiom(99), 0))), qu(cond(axiom(71), 0), imp(cond(axiom(71), 0))), pred(s2(plural(293)), 0), ass(cond(conseq(271), 3), 2), pred(s2(plural(274)), 0), ass(cond(goal(238), 0), 1), qu(cond(axiom(57), 0), imp(cond(axiom(57), 0))), qu(cond(axiom(65), 0), imp(cond(axiom(65), 0))), pred(s1(plural(294)), 0), qu(cond(axiom(174), 0), imp(cond(axiom(174), 0))), ass(cond(conseq(271), 3), 1), neg(316), qu(cond(axiom(61), 0), imp(cond(axiom(61), 0))), pred(s2(plural(315)), 0), neg(neg(conjunct2(conjunct2(comma_conjunct2(plural(271)))))), qu(cond(axiom(9), 0), imp(cond(axiom(9), 0))), neg(neg(270)), holds(conjunct1(conjunct2(conjunct2(conjunct2(plural(271))))), 1209, 0), pred(269, 0), qu(cond(axiom(182), 0), imp(cond(axiom(182), 0))), qu(cond(axiom(117), 0), imp(cond(axiom(117), 0))), qu(cond(axiom(172), 0), imp(cond(axiom(172), 0))), qu(cond(axiom(115), 0), imp(cond(axiom(115), 0))), qu(cond(axiom(131), 0), imp(cond(axiom(131), 0))), qu(cond(axiom(196), 0), imp(cond(axiom(196), 0))), qu(cond(axiom(186), 0), imp(cond(axiom(186), 0))), qu(cond(axiom(127), 0), imp(cond(axiom(127), 0))), ass(cond(conseq(271), 9), 1), qu(cond(axiom(123), 0), imp(cond(axiom(123), 0))), qu(cond(axiom(25), 0), imp(cond(axiom(25), 0))), qu(cond(axiom(101), 0), imp(cond(axiom(101), 0))), qu(cond(axiom(125), 0), imp(cond(axiom(125), 0))), qu(cond(axiom(170), 0), imp(cond(axiom(170), 0))), qu(cond(axiom(111), 0), imp(cond(axiom(111), 0))), qu(cond(axiom(166), 0), imp(cond(axiom(166), 0))), qu(cond(axiom(105), 0), imp(cond(axiom(105), 0))), qu(cond(axiom(37), 0), imp(cond(axiom(37), 0))), qu(cond(axiom(63), 0), imp(cond(axiom(63), 0))), holds(conjunct1(comma_conjunct2(plural(271))), 1212, 0), qu(cond(axiom(192), 0), imp(cond(axiom(192), 0))), ass(cond(conseq(271), 9), 2), holds(conjunct1(plural(271)), 1206, 0), ass(cond(goal(219), 0), 0), pred(axiom(137), 1), ass(cond(goal(206), 0), 2), qu(cond(axiom(29), 0), imp(cond(axiom(29), 0))), qu(cond(axiom(39), 0), imp(cond(axiom(39), 0))), qu(cond(axiom(129), 0), imp(cond(axiom(129), 0))), qe(s3(plural(271))), pred(s1(plural(269)), 0), qu(cond(axiom(73), 0), imp(cond(axiom(73), 0))), qu(cond(axiom(15), 0), imp(cond(axiom(15), 0))), holds(conjunct1(conjunct2(conjunct2(plural(271)))), 1208, 0), ass(cond(goal(238), 0), 2), qu(cond(axiom(200), 0), imp(cond(axiom(200), 0))), qu(cond(axiom(27), 0), imp(cond(axiom(27), 0))), qu(cond(axiom(85), 0), imp(cond(axiom(85), 0))), ass(cond(conseq(271), 3), 3), qu(cond(axiom(91), 0), imp(cond(axiom(91), 0))), ass(cond(goal(219), 0), 1), qu(cond(axiom(49), 0), imp(cond(axiom(49), 0))), qu(cond(axiom(7), 0), imp(cond(axiom(7), 0))), pred(s3(plural(315)), 0), qu(cond(axiom(149), 0), imp(cond(axiom(149), 0))), qu(cond(axiom(17), 0), imp(cond(axiom(17), 0))), qu(cond(axiom(51), 0), imp(cond(axiom(51), 0))), neg(neg(319)), holds(conjunct1(conjunct2(plural(271))), 1207, 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))), holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(plural(271)))))), 1211, 0), qu(cond(axiom(69), 0), imp(cond(axiom(69), 0))), qu(cond(axiom(147), 0), imp(cond(axiom(147), 0))), qu(cond(axiom(168), 0), imp(cond(axiom(168), 0))), qu(cond(axiom(204), 0), imp(cond(axiom(204), 0))), qu(cond(axiom(97), 0), imp(cond(axiom(97), 0))), holds(314, 1247, 0), qu(cond(axiom(162), 0), imp(cond(axiom(162), 0))), qu(cond(axiom(180), 0), imp(cond(axiom(180), 0))), qu(cond(axiom(153), 0), imp(cond(axiom(153), 0))), qu(cond(axiom(178), 0), imp(cond(axiom(178), 0))), qu(cond(axiom(160), 0), imp(cond(axiom(160), 0))), qu(cond(axiom(67), 0), imp(cond(axiom(67), 0))), qu(cond(axiom(93), 0), imp(cond(axiom(93), 0))), and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(268))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(268))))), 1194, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(268)))), 1193, 0), and(holds(conjunct1(plural(comma_conjunct2(268))), 1192, 0), and(qe(s3(plural(comma_conjunct2(268)))), and(qe(s2(plural(comma_conjunct2(268)))), and(qe(s1(plural(comma_conjunct2(268)))), and(pred(comma_conjunct1(268), 9), and(pred(comma_conjunct1(268), 8), and(pred(comma_conjunct1(268), 7), and(qe(s3(plural(268))), and(qe(s2(plural(268))), qe(s1(plural(268))))))))))))))), qu(cond(axiom(198), 0), imp(cond(axiom(198), 0))), ass(cond(conseq(271), 3), 0)
% 113.02/34.13 % No. of inferences in proof: 456
% 113.02/34.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 33456 ms resp. 32377 ms w/o parsing
% 105.25/34.46 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 105.25/34.46 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------