%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO528+1 : TPTP v9.3.1. Released v7.0.0.
% 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 : n012.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 07:13:27 AM UTC 2026
% Result : Theorem 19.40s 4.64s
% Output : Refutation 18.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 206
% Syntax : Number of formulae : 414 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 1959 ( 414 equ; 0 cnn)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 9114 (1079 ~;1367 |; 178 &;6490 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 49 usr; 7 con; 0-8 aty)
% Number of variables : 1788 ( 0 ^;1788 !; 0 ?;1788 :)
% Comments :
%------------------------------------------------------------------------------
thf(reflect_decl,type,
reflect: $i > $i > $i > $i ).
thf(s_col_decl,type,
s_col: $i > $i > $i > $o ).
thf(opposite_decl,type,
opposite: $i > $i > $i > $i > $o ).
thf(le_decl,type,
le: $i > $i > $i > $i > $o ).
thf(s_t_decl,type,
s_t: $i > $i > $i > $o ).
thf(insert_decl,type,
insert: $i > $i > $i > $i > $i ).
thf(s_e_decl,type,
s_e: $i > $i > $i > $i > $o ).
thf(s_decl,type,
s: $i > $i > $i ).
thf(s_r_decl,type,
s_r: $i > $i > $i > $o ).
thf(perp_decl,type,
perp: $i > $i > $i > $i > $o ).
thf(samesideline_decl,type,
samesideline: $i > $i > $i > $i > $o ).
thf(sameside_decl,type,
sameside: $i > $i > $i > $o ).
thf(ip_decl,type,
ip: $i > $i > $i > $i > $i > $i ).
thf(s_m_decl,type,
s_m: $i > $i > $i > $o ).
thf(midpoint_decl,type,
midpoint: $i > $i > $i ).
thf(s_ifs_decl,type,
s_ifs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(s_afs_decl,type,
s_afs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(ext_decl,type,
ext: $i > $i > $i > $i > $i ).
thf(s_fs_decl,type,
s_fs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(s_kf_decl,type,
s_kf: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(s_e3_decl,type,
s_e3: $i > $i > $i > $i > $i > $i > $o ).
thf(perpAt_decl,type,
perpAt: $i > $i > $i > $i > $i > $o ).
thf(crossbar_decl,type,
crossbar: $i > $i > $i > $i > $i > $i > $i ).
thf(op_decl,type,
op: $i > $i > $i > $i > $i > $i ).
thf(isomidpoint_decl,type,
isomidpoint: $i > $i > $i > $i ).
thf(il_decl,type,
il: $i > $i > $i > $i > $i ).
thf(ins_decl,type,
ins: $i > $i > $i > $i > $i ).
thf(xb_decl,type,
xb: $i ).
thf(c63_decl,type,
c63: $i > $i > $i > $i ).
thf(foot_decl,type,
foot: $i > $i > $i > $i ).
thf(insert5_decl,type,
insert5: $i > $i > $i > $i > $i > $i ).
thf(f813_decl,type,
f813: $i > $i > $i > $i > $i > $i ).
thf(g813_decl,type,
g813: $i > $i > $i > $i > $i > $i ).
thf(xa_decl,type,
xa: $i ).
thf(xp_decl,type,
xp: $i ).
thf(xq_decl,type,
xq: $i ).
thf(xc_decl,type,
xc: $i ).
thf(xd_decl,type,
xd: $i ).
thf(f811_decl,type,
f811: $i > $i > $i > $i > $i > $i ).
thf(g811_decl,type,
g811: $i > $i > $i > $i > $i > $i ).
thf(erect21a_decl,type,
erect21a: $i > $i > $i > $i ).
thf(erectAux21a_decl,type,
erectAux21a: $i > $i > $i > $i ).
thf(pointOffLine_decl,type,
pointOffLine: $i > $i > $i ).
thf(midpointAux_decl,type,
midpointAux: $i > $i > $i > $i > $i > $i ).
thf(ss1_decl,type,
ss1: $i > $i > $i > $i > $i ).
thf(ss2_decl,type,
ss2: $i > $i > $i > $i > $i ).
thf(ss3_decl,type,
ss3: $i > $i > $i > $i > $i ).
thf(erect_decl,type,
erect: $i > $i > $i > $i ).
thf(erectAux_decl,type,
erectAux: $i > $i > $i > $i ).
thf(177,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_18) ).
thf(969,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ sameside ) ) )
| ( C = B )
| ( A = B )
| ~ ( A @ ( C @ ( B @ s_t ) ) ) )
& ( ( C @ ( B @ ( A @ sameside ) ) )
| ( xb = B )
| ( A = B )
| ~ ( C @ ( A @ ( B @ s_t ) ) ) )
& ( ( A @ ( C @ ( B @ s_t ) ) )
| ( C @ ( A @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( C != B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( A != B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn6_1) ).
thf(645,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ sameside ) ) )
| ( C = B )
| ( A = B )
| ~ ( A @ ( C @ ( B @ s_t ) ) ) )
& ( ( C @ ( B @ ( A @ sameside ) ) )
| ( xb = B )
| ( A = B )
| ~ ( C @ ( A @ ( B @ s_t ) ) ) )
& ( ( A @ ( C @ ( B @ s_t ) ) )
| ( C @ ( A @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( C != B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( A != B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_4) ).
thf(629,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( E @ ( D @ ( B @ ( A @ insert ) ) ) @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( E @ ( E @ ( D @ ( B @ ( A @ insert ) ) ) @ ( D @ s_t ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_5) ).
thf(479,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( E @ ( D @ ( B @ ( A @ insert ) ) ) @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( E @ ( E @ ( D @ ( B @ ( A @ insert ) ) ) @ ( D @ s_t ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ perpAt ) ) ) ) )
| ( A = B )
| ( C = D )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp) ).
thf(909,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ perpAt ) ) ) ) )
| ( A = B )
| ( C = D )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( G @ ( D @ ( A @ ( D @ le ) ) ) )
| ( F @ ( D @ ( B @ s_t ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_22a) ).
thf(518,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( G @ ( D @ ( A @ ( D @ le ) ) ) )
| ( F @ ( D @ ( B @ s_t ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ sameside ) ) )
| ~ ( D @ ( B @ ( C @ sameside ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_7) ).
thf(468,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ sameside ) ) )
| ~ ( D @ ( B @ ( C @ sameside ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11d) ).
thf(941,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ erect ) ) @ ( C @ ( B @ ( A @ erectAux ) ) @ ( C @ s_t ) ) )
| ( A = B ) )
& ( ( C @ ( B @ ( A @ erectAux ) ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) )
& ( ( A @ ( C @ ( B @ ( A @ erect ) ) @ ( B @ ( A @ perp ) ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_21) ).
thf(1110,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ erect ) ) @ ( C @ ( B @ ( A @ erectAux ) ) @ ( C @ s_t ) ) )
| ( A = B ) )
& ( ( C @ ( B @ ( A @ erectAux ) ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) )
& ( ( A @ ( C @ ( B @ ( A @ erect ) ) @ ( B @ ( A @ perp ) ) ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ s_col ) ) )
| ( D = C )
| ~ ( C @ ( E @ ( C @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( C @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13g) ).
thf(777,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ s_col ) ) )
| ( D = C )
| ~ ( C @ ( E @ ( C @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( C @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ ( C @ perp ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_12b) ).
thf(555,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ ( C @ perp ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ ( A @ s_m ) ) )
| ~ ( D @ ( E @ ( B @ s_col ) ) )
| ~ ( C @ ( E @ ( A @ s_col ) ) )
| ~ ( A @ ( D @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) )
| ( B = D )
| ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_21) ).
thf(994,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ ( A @ s_m ) ) )
| ~ ( D @ ( E @ ( B @ s_col ) ) )
| ~ ( C @ ( E @ ( A @ s_col ) ) )
| ~ ( A @ ( D @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) )
| ( B = D )
| ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( C @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( E @ s_t ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn2_10) ).
thf(308,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( C @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( E @ s_t ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_afs ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( A @ ( E @ ( D @ samesideline ) ) ) )
| ~ ( B @ ( A @ ( E @ ( D @ samesideline ) ) ) )
| ( A = C )
| ( A = B )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtSameSide1) ).
thf(1073,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( A @ ( E @ ( D @ samesideline ) ) ) )
| ~ ( B @ ( A @ ( E @ ( D @ samesideline ) ) ) )
| ( A = C )
| ( A = B )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ crossbar ) ) ) ) ) @ ( B @ s_t ) ) )
| ~ ( D @ ( F @ ( A @ s_t ) ) )
| ~ ( C @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ crossbar ) ) ) ) ) @ ( F @ s_t ) ) )
| ~ ( D @ ( F @ ( A @ s_t ) ) )
| ~ ( C @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_17) ).
thf(449,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ crossbar ) ) ) ) ) @ ( B @ s_t ) ) )
| ~ ( D @ ( F @ ( A @ s_t ) ) )
| ~ ( C @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ crossbar ) ) ) ) ) @ ( F @ s_t ) ) )
| ~ ( D @ ( F @ ( A @ s_t ) ) )
| ~ ( C @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ erect21a ) ) @ ( C @ ( B @ ( A @ erectAux21a ) ) @ ( C @ s_t ) ) )
| ( A = B ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ erectAux21a ) ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ( A @ ( C @ ( B @ ( A @ erect21a ) ) @ ( B @ ( A @ perp ) ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_21a) ).
thf(878,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ erect21a ) ) @ ( C @ ( B @ ( A @ erectAux21a ) ) @ ( C @ s_t ) ) )
| ( A = B ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ erectAux21a ) ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ( A @ ( C @ ( B @ ( A @ erect21a ) ) @ ( B @ ( A @ perp ) ) ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C = E )
| ( B
!= ( E @ ( C @ midpoint ) ) )
| ( E @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( E @ ( B @ ( C @ ( B @ s_e ) ) ) )
| ~ ( B @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( E @ ( B @ ( D @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_12c) ).
thf(269,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C = E )
| ( B
!= ( E @ ( C @ midpoint ) ) )
| ( E @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( E @ ( B @ ( C @ ( B @ s_e ) ) ) )
| ~ ( B @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( E @ ( B @ ( D @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_4b) ).
thf(597,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ perp ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ perp ) ) ) )
| ( A = B )
| ( C = D )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp2) ).
thf(730,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ perp ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ perp ) ) ) )
| ( A = B )
| ( C = D )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ ( B @ ( A @ le ) ) ) )
| ~ ( E @ ( C @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( E @ ( C @ s_t ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ insert ) ) ) @ ( C @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) )
& ( ( D @ ( D @ ( C @ ( B @ ( A @ insert ) ) ) @ ( C @ s_t ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn5_4) ).
thf(217,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ ( B @ ( A @ le ) ) ) )
| ~ ( E @ ( C @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( E @ ( C @ s_t ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ insert ) ) ) @ ( C @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) )
& ( ( D @ ( D @ ( C @ ( B @ ( A @ insert ) ) ) @ ( C @ s_t ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ sameside ) ) )
| ( B @ ( A @ ( D @ sameside ) ) )
| ( D = A )
| ~ ( B @ ( A @ ( D @ s_col ) ) )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ( A = C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_15a) ).
thf(797,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ sameside ) ) )
| ( B @ ( A @ ( D @ sameside ) ) )
| ( D = A )
| ~ ( B @ ( A @ ( D @ s_col ) ) )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ( A = C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ ( C @ opposite ) ) ) )
| ( B @ ( A @ ( D @ ( C @ samesideline ) ) ) )
| ( D @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13f) ).
thf(913,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ ( C @ opposite ) ) ) )
| ( B @ ( A @ ( D @ ( C @ samesideline ) ) ) )
| ( D @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( H @ ( G @ s ) @ sameside ) ) )
| ( F = E )
| ~ ( A @ ( F @ ( D @ ( E @ le ) ) ) )
| ~ ( A @ ( F @ ( H @ sameside ) ) )
| ~ ( E @ ( G @ ( F @ s_m ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( A @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( C @ ( B @ s_col ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_4a) ).
thf(930,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( H @ ( G @ s ) @ sameside ) ) )
| ( F = E )
| ~ ( A @ ( F @ ( D @ ( E @ le ) ) ) )
| ~ ( A @ ( F @ ( H @ sameside ) ) )
| ~ ( E @ ( G @ ( F @ s_m ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( A @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( C @ ( B @ s_col ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( E @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_14b) ).
thf(973,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( E @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA6) ).
thf(257,plain,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_m ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13b) ).
thf(841,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_m ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( G @ ( F @ ( E @ le ) ) ) )
| ~ ( H @ ( G @ ( D @ ( C @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_6) ).
thf(417,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( G @ ( F @ ( E @ le ) ) ) )
| ~ ( H @ ( G @ ( D @ ( C @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) )
& ( ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn4_15) ).
thf(785,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) )
& ( ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( G @ ( D @ ( C @ s_e ) ) ) )
| ( A = B )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_16) ).
thf(372,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( G @ ( D @ ( C @ s_e ) ) ) )
| ( A = B )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_fs ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( D @ ( C @ il ) ) ) @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ ( C @ opposite ) ) ) ) )
& ( ( D @ ( B @ ( A @ ( D @ ( C @ il ) ) ) @ ( C @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ ( C @ opposite ) ) ) ) )
& ( ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ ( C @ opposite ) ) ) ) )
& ( ~ ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ ( C @ opposite ) ) ) ) )
& ( ( D @ ( B @ ( A @ ( C @ opposite ) ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( E @ ( C @ s_t ) ) )
| ( D @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn9_1) ).
thf(917,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( D @ ( C @ il ) ) ) @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ ( C @ opposite ) ) ) ) )
& ( ( D @ ( B @ ( A @ ( D @ ( C @ il ) ) ) @ ( C @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ ( C @ opposite ) ) ) ) )
& ( ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ ( C @ opposite ) ) ) ) )
& ( ~ ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ ( C @ opposite ) ) ) ) )
& ( ( D @ ( B @ ( A @ ( C @ opposite ) ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( E @ ( C @ s_t ) ) )
| ( D @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B != A )
| ( A @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_3b) ).
thf(344,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( A @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ s_col ) ) )
| ~ ( B @ ( A @ ( D @ sameside ) ) )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ( A = C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_15b) ).
thf(934,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ s_col ) ) )
| ~ ( B @ ( A @ ( D @ sameside ) ) )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ( A = C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ op ) ) ) ) @ ( E @ ( C @ s_t ) ) )
| ~ ( B @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( D @ ( A @ ( B @ ( C @ ( D @ ( E @ op ) ) ) ) @ ( A @ s_t ) ) )
| ~ ( B @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_6) ).
thf(485,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ op ) ) ) ) @ ( E @ ( C @ s_t ) ) )
| ~ ( B @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( D @ ( A @ ( B @ ( C @ ( D @ ( E @ op ) ) ) ) @ ( A @ s_t ) ) )
| ~ ( B @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ perp ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aperp1) ).
thf(238,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ perp ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ ext ) ) ) @ ( B @ s_e ) ) ) )
& ( D @ ( C @ ( B @ ( A @ ext ) ) ) @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA4) ).
thf(348,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ ext ) ) ) @ ( B @ s_e ) ) ) )
& ( D @ ( C @ ( B @ ( A @ ext ) ) ) @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ samesideline ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_9) ).
thf(806,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ samesideline ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( F @ ( E @ ( B @ ( A @ perp ) ) ) )
| ( F @ ( E @ ( D @ ( C @ perp ) ) ) )
| ( A = B )
| ( C = D )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp5) ).
thf(905,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( F @ ( E @ ( B @ ( A @ perp ) ) ) )
| ( F @ ( E @ ( D @ ( C @ perp ) ) ) )
| ( A = B )
| ( C = D )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( E @ ( D @ ( B @ ( A @ g813 ) ) ) ) @ ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ f813 ) ) ) ) @ s_r ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C
!= ( C @ ( E @ ( D @ ( B @ ( A @ g813 ) ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C
!= ( C @ ( E @ ( D @ ( B @ ( A @ f813 ) ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( E @ ( D @ ( B @ ( A @ g813 ) ) ) ) @ ( E @ ( D @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( E @ ( D @ ( B @ ( A @ f813 ) ) ) ) @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( D != E )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( A != B )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_13a) ).
thf(734,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( E @ ( D @ ( B @ ( A @ g813 ) ) ) ) @ ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ f813 ) ) ) ) @ s_r ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C
!= ( C @ ( E @ ( D @ ( B @ ( A @ g813 ) ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C
!= ( C @ ( E @ ( D @ ( B @ ( A @ f813 ) ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( E @ ( D @ ( B @ ( A @ g813 ) ) ) ) @ ( E @ ( D @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( E @ ( D @ ( B @ ( A @ f813 ) ) ) ) @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( D != E )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( A != B )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_2) ).
thf(396,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtCol2) ).
thf(998,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( A @ ( C @ ( B @ le ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ le ) ) ) )
| ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_12b) ).
thf(849,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( A @ ( C @ ( B @ le ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ le ) ) ) )
| ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C
= ( E @ ( D @ ( B @ ( A @ il ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_14c) ).
thf(507,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C
= ( E @ ( D @ ( B @ ( A @ il ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_3) ).
thf(292,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ s ) @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ( C @ ( B @ ( A @ s_r ) ) ) )
& ( ( C @ ( B @ s ) @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn8_1) ).
thf(248,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ s ) @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ( C @ ( B @ ( A @ s_r ) ) ) )
& ( ( C @ ( B @ s ) @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ ( A @ ( B @ ( D @ ( C @ insert ) ) ) @ ( B @ s_e ) ) ) )
| ( C = D )
| ( A = B ) )
& ( ( A @ ( B @ ( A @ ( B @ ( D @ ( C @ insert ) ) ) @ sameside ) ) )
| ( C = D )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_11a) ).
thf(529,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ ( A @ ( B @ ( D @ ( C @ insert ) ) ) @ ( B @ s_e ) ) ) )
| ( C = D )
| ( A = B ) )
& ( ( A @ ( B @ ( A @ ( B @ ( D @ ( C @ insert ) ) ) @ sameside ) ) )
| ( C = D )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( B = A )
| ( ( B @ ( A @ s ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_10a) ).
thf(366,plain,
! [A: $i,B: $i] :
( ( B = A )
| ( ( B @ ( A @ s ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( B @ ( D @ opposite ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_2) ).
thf(714,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( B @ ( D @ opposite ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ s_t ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_7b) ).
thf(334,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ s_t ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( C @ ( B @ midpoint ) @ ( A @ s_m ) ) )
| ~ ( F @ ( C @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( F @ ( C @ s_t ) ) )
| ~ ( D @ ( E @ ( A @ s_t ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( C @ ( D @ perp ) ) ) )
| ~ ( C @ ( B @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_24) ).
thf(894,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( C @ ( B @ midpoint ) @ ( A @ s_m ) ) )
| ~ ( F @ ( C @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( F @ ( C @ s_t ) ) )
| ~ ( D @ ( E @ ( A @ s_t ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( C @ ( D @ perp ) ) ) )
| ~ ( C @ ( B @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ ip ) ) ) ) @ ( E @ s_t ) ) )
| ~ ( C @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ ip ) ) ) ) @ ( B @ s_t ) ) )
| ~ ( C @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA7) ).
thf(260,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ ip ) ) ) ) @ ( E @ s_t ) ) )
| ~ ( C @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ ip ) ) ) ) @ ( B @ s_t ) ) )
| ~ ( C @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(146,axiom,
( ~ ( xb @ ( xa @ ( xd @ ( xc @ perp ) ) ) )
| ( xq @ ( xp @ ( xd @ ( xc @ perp ) ) ) )
| ( xa = xb )
| ( xp = xq )
| ~ ( xq @ ( xb @ ( xa @ s_col ) ) )
| ~ ( xp @ ( xb @ ( xa @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp6) ).
thf(820,plain,
( ~ ( xb @ ( xa @ ( xd @ ( xc @ perp ) ) ) )
| ( xq @ ( xp @ ( xd @ ( xc @ perp ) ) ) )
| ( xa = xb )
| ( xp = xq )
| ~ ( xq @ ( xb @ ( xa @ s_col ) ) )
| ~ ( xp @ ( xb @ ( xa @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA2) ).
thf(407,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A
!= ( C @ ( B @ ( A @ foot ) ) ) )
| ( D @ ( B @ ( A @ ( C @ opposite ) ) ) )
| ( B @ ( A @ ( D @ ( C @ samesideline ) ) ) )
| ( D @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13f_case1) ).
thf(693,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A
!= ( C @ ( B @ ( A @ foot ) ) ) )
| ( D @ ( B @ ( A @ ( C @ opposite ) ) ) )
| ( B @ ( A @ ( D @ ( C @ samesideline ) ) ) )
| ( D @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ sameside ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_5) ).
thf(566,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ sameside ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ s_e ) ) ) )
| ~ ( B @ ( A @ ( D @ ( C @ le ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_9) ).
thf(361,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ s_e ) ) ) )
| ~ ( B @ ( A @ ( D @ ( C @ le ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ ( A @ le ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_11) ).
thf(625,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ ( A @ le ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( F @ ( G @ ( A @ s_m ) ) )
| ( G
!= ( F @ ( C @ ( D @ ( E @ ( A @ ip ) ) ) ) ) )
| ~ ( F @ ( C @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( F @ ( C @ s_t ) ) )
| ~ ( D @ ( E @ ( A @ s_t ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( C @ ( D @ perp ) ) ) )
| ~ ( C @ ( B @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_24b) ).
thf(889,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( F @ ( G @ ( A @ s_m ) ) )
| ( G
!= ( F @ ( C @ ( D @ ( E @ ( A @ ip ) ) ) ) ) )
| ~ ( F @ ( C @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( F @ ( C @ s_t ) ) )
| ~ ( D @ ( E @ ( A @ s_t ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( C @ ( D @ perp ) ) ) )
| ~ ( C @ ( B @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ s ) @ ( B @ ( D @ s ) @ ( A @ ( D @ s ) @ sameside ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSideReflect) ).
thf(461,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ s ) @ ( B @ ( D @ s ) @ ( A @ ( D @ s ) @ sameside ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ ( B @ ( C @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ( D = B )
| ( C = B )
| ( A = B )
| ( C @ ( B @ ( A @ sameside ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_3b) ).
thf(493,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ ( B @ ( C @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ( D = B )
| ( C = B )
| ( A = B )
| ( C @ ( B @ ( A @ sameside ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( B @ ( D @ ( C @ s_col ) ) )
| ~ ( A @ ( D @ ( C @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_18) ).
thf(710,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( B @ ( D @ ( C @ s_col ) ) )
| ~ ( A @ ( D @ ( C @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ ( C @ s_t ) ) )
| ( B @ ( C @ ( D @ s_t ) ) )
| ~ ( B @ ( A @ ( D @ s_t ) ) )
| ~ ( B @ ( A @ ( C @ s_t ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_16a) ).
thf(324,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ ( C @ s_t ) ) )
| ( B @ ( C @ ( D @ s_t ) ) )
| ~ ( B @ ( A @ ( D @ s_t ) ) )
| ~ ( B @ ( A @ ( C @ s_t ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ reflect ) ) @ ( C @ ( B @ ( A @ reflect ) ) @ ( D @ ( C @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_10a) ).
thf(1106,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ reflect ) ) @ ( C @ ( B @ ( A @ reflect ) ) @ ( D @ ( C @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_5) ).
thf(583,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( A @ ( G @ ( F @ s_t ) ) )
| ( D @ ( C @ ( B @ ( G @ opposite ) ) ) )
| ~ ( G @ ( F @ ( A @ sameside ) ) )
| ~ ( F @ ( C @ ( B @ s_col ) ) )
| ~ ( D @ ( E @ ( A @ s_m ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_3a) ).
thf(830,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( A @ ( G @ ( F @ s_t ) ) )
| ( D @ ( C @ ( B @ ( G @ opposite ) ) ) )
| ~ ( G @ ( F @ ( A @ sameside ) ) )
| ~ ( F @ ( C @ ( B @ s_col ) ) )
| ~ ( D @ ( E @ ( A @ s_m ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D = E )
| ~ ( E @ ( C @ ( B @ ( A @ perp ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_18a) ).
thf(697,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D = E )
| ~ ( E @ ( C @ ( B @ ( A @ perp ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ ( D @ ( B @ ( C @ ( A @ midpointAux ) ) ) ) @ ( A @ s_m ) ) )
| ~ ( E @ ( C @ ( A @ s_col ) ) )
| ~ ( D @ ( E @ ( B @ s_t ) ) )
| ~ ( D @ ( C @ ( C @ ( A @ perp ) ) ) )
| ~ ( B @ ( A @ ( C @ ( A @ perp ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_22b) ).
thf(980,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ ( D @ ( B @ ( C @ ( A @ midpointAux ) ) ) ) @ ( A @ s_m ) ) )
| ~ ( E @ ( C @ ( A @ s_col ) ) )
| ~ ( D @ ( E @ ( B @ s_t ) ) )
| ~ ( D @ ( C @ ( C @ ( A @ perp ) ) ) )
| ~ ( B @ ( A @ ( C @ ( A @ perp ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ s_t ) ) )
| ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_1) ).
thf(593,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ s_t ) ) )
| ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( A @ ( B @ s_r ) ) )
| ~ ( C @ ( B @ s ) @ ( D @ ( C @ ( A @ s ) @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_20a) ).
thf(610,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( A @ ( B @ s_r ) ) )
| ~ ( C @ ( B @ s ) @ ( D @ ( C @ ( A @ s ) @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(52,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ s_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_1) ).
thf(420,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ s_t ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
| ( ( B @ ( A @ s ) )
!= ( C @ ( A @ s ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_9) ).
thf(225,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
| ( ( B @ ( A @ s ) )
!= ( C @ ( A @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_4) ).
thf(537,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_13) ).
thf(669,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( D @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_5a) ).
thf(642,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( D @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(190,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ s_col ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_12b) ).
thf(1016,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ s_col ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( E @ s ) @ ( C @ ( E @ s ) @ ( B @ ( E @ s ) @ ( A @ ( E @ s ) @ s_e ) ) ) )
| ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_16b) ).
thf(328,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( E @ s ) @ ( C @ ( E @ s ) @ ( B @ ( E @ s ) @ ( A @ ( E @ s ) @ s_e ) ) ) )
| ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_2) ).
thf(471,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ s_e ) ) ) )
| ~ ( E @ ( B @ ( A @ s_t ) ) )
| ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_5b) ).
thf(622,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ s_e ) ) ) )
| ~ ( E @ ( B @ ( A @ s_t ) ) )
| ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( H @ ( G @ s ) @ sameside ) ) )
| ( F != E )
| ~ ( A @ ( F @ ( H @ sameside ) ) )
| ~ ( E @ ( G @ ( F @ s_m ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( A @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( C @ ( B @ s_col ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_4b) ).
thf(985,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( H @ ( G @ s ) @ sameside ) ) )
| ( F != E )
| ~ ( A @ ( F @ ( H @ sameside ) ) )
| ~ ( E @ ( G @ ( F @ s_m ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( A @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( C @ ( B @ s_col ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ insert5 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_14) ).
thf(701,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ insert5 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( B @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( D @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_12b) ).
thf(515,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( B @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( D @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( C @ ( D @ ( B @ ( A @ perp ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_15) ).
thf(1050,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( C @ ( D @ ( B @ ( A @ perp ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ s_col ) ) )
| ( D != A )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ( A = C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_15d) ).
thf(1002,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ s_col ) ) )
| ( D != A )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ( A = C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ sameside ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_6) ).
thf(569,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ sameside ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ s_t ) ) )
| ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_2) ).
thf(503,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ s_t ) ) )
| ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ~ ( D @ ( C @ ( B @ ( C @ s_e ) ) ) )
| ~ ( D @ ( A @ ( B @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_19) ).
thf(244,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ~ ( D @ ( C @ ( B @ ( C @ s_e ) ) ) )
| ~ ( D @ ( A @ ( B @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( F @ opposite ) ) ) )
| ~ ( F @ ( E @ ( A @ sameside ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_5) ).
thf(938,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( F @ opposite ) ) ) )
| ~ ( F @ ( E @ ( A @ sameside ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( A @ ( B @ s ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_6) ).
thf(266,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( A @ ( B @ s ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( H @ ( G @ s ) @ sameside ) ) )
| ~ ( A @ ( F @ ( H @ sameside ) ) )
| ~ ( E @ ( G @ ( F @ s_m ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( A @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( C @ ( B @ s_col ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_4) ).
thf(1054,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( H @ ( G @ s ) @ sameside ) ) )
| ~ ( A @ ( F @ ( H @ sameside ) ) )
| ~ ( E @ ( G @ ( F @ s_m ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( A @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( C @ ( B @ s_col ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ ( B @ le ) ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_13a) ).
thf(398,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ ( B @ le ) ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( C @ ( B @ ( A @ reflect ) ) ) )
| ( C != D )
| ~ ( D @ ( C @ midpoint ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) )
& ( ( D
= ( C @ ( B @ ( A @ reflect ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) )
| ~ ( D @ ( C @ midpoint ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_2b) ).
thf(953,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( C @ ( B @ ( A @ reflect ) ) ) )
| ( C != D )
| ~ ( D @ ( C @ midpoint ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) )
& ( ( D
= ( C @ ( B @ ( A @ reflect ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) )
| ~ ( D @ ( C @ midpoint ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != D )
| ( B = C )
| ~ ( C @ ( B @ s ) @ ( D @ ( C @ ( A @ s ) @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_20b) ).
thf(662,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != D )
| ( B = C )
| ~ ( C @ ( B @ s ) @ ( D @ ( C @ ( A @ s ) @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( D @ ( C @ s_col ) ) )
| ~ ( G @ ( B @ ( A @ s_col ) ) )
| ( E = F )
| ~ ( F @ ( D @ ( C @ s_col ) ) )
| ~ ( F @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_21) ).
thf(718,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( D @ ( C @ s_col ) ) )
| ~ ( G @ ( B @ ( A @ s_col ) ) )
| ( E = F )
| ~ ( F @ ( D @ ( C @ s_col ) ) )
| ~ ( F @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = C )
| ( ( B @ ( A @ s ) )
!= ( B @ ( C @ s ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_18) ).
thf(298,plain,
! [A: $i,B: $i,C: $i] :
( ( A = C )
| ( ( B @ ( A @ s ) )
!= ( B @ ( C @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( C = A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_16b) ).
thf(965,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( C = A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ ( C @ ( E @ ( D @ perpAt ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_12a) ).
thf(425,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ ( C @ ( E @ ( D @ perpAt ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_2) ).
thf(513,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( F @ ( D @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( D @ ( C @ ( E @ ( B @ ( A @ perpAt ) ) ) ) )
| ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) )
& ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ il ) ) ) @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn8_11b) ).
thf(573,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( D @ ( C @ ( E @ ( B @ ( A @ perpAt ) ) ) ) )
| ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) )
& ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ il ) ) ) @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ ( E @ ( C @ samesideline ) ) ) )
| ~ ( B @ ( A @ ( E @ ( D @ samesideline ) ) ) )
| ~ ( B @ ( A @ ( D @ ( C @ samesideline ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_13) ).
thf(689,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ ( E @ ( C @ samesideline ) ) ) )
| ~ ( B @ ( A @ ( E @ ( D @ samesideline ) ) ) )
| ~ ( B @ ( A @ ( D @ ( C @ samesideline ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) )
| ~ ( E @ ( F @ ( G @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) )
| ~ ( E @ ( D @ ( G @ ( D @ s_e ) ) ) )
| ~ ( C @ ( D @ ( A @ ( D @ s_e ) ) ) )
| ~ ( E @ ( D @ ( C @ s_t ) ) )
| ~ ( G @ ( D @ ( A @ s_t ) ) ) )
& ( ( E @ ( F @ ( G @ s_m ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_m ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( E @ ( D @ ( G @ ( D @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( C @ ( D @ ( A @ ( D @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ s_t ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( G @ ( D @ ( A @ s_t ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn7_23) ).
thf(375,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) )
| ~ ( E @ ( F @ ( G @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) )
| ~ ( E @ ( D @ ( G @ ( D @ s_e ) ) ) )
| ~ ( C @ ( D @ ( A @ ( D @ s_e ) ) ) )
| ~ ( E @ ( D @ ( C @ s_t ) ) )
| ~ ( G @ ( D @ ( A @ s_t ) ) ) )
& ( ( E @ ( F @ ( G @ s_m ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_m ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( E @ ( D @ ( G @ ( D @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( C @ ( D @ ( A @ ( D @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ s_t ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) )
& ( ( G @ ( D @ ( A @ s_t ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_11) ).
thf(601,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( B != A )
| ( ( B @ ( A @ s ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_10b) ).
thf(562,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( ( B @ ( A @ s ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( D @ ( E @ ( H @ ( G @ s ) @ sameside ) ) )
| ( F = E )
| ~ ( A @ ( F @ ( D @ ( E @ le ) ) ) )
| ( A @ ( F @ ( H @ sameside ) ) )
| ~ ( E @ ( G @ ( F @ s_m ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( A @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( C @ ( B @ s_col ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_4a2) ).
thf(1007,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( D @ ( E @ ( H @ ( G @ s ) @ sameside ) ) )
| ( F = E )
| ~ ( A @ ( F @ ( D @ ( E @ le ) ) ) )
| ( A @ ( F @ ( H @ sameside ) ) )
| ~ ( E @ ( G @ ( F @ s_m ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( A @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( C @ ( B @ s_col ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( B @ ( F @ s_t ) ) )
| ~ ( E @ ( G @ ( C @ s_m ) ) )
| ~ ( D @ ( F @ ( A @ s_m ) ) )
| ~ ( E @ ( B @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( E @ ( B @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_22) ).
thf(402,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( B @ ( F @ s_t ) ) )
| ~ ( E @ ( G @ ( C @ s_m ) ) )
| ~ ( D @ ( F @ ( A @ s_m ) ) )
| ~ ( E @ ( B @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( E @ ( B @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(96,axiom,
! [A: $i,B: $i] : ( A @ ( B @ s ) @ ( B @ ( A @ s_m ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_4a) ).
thf(579,plain,
! [A: $i,B: $i] : ( A @ ( B @ s ) @ ( B @ ( A @ s_m ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ s_r ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_10) ).
thf(391,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ s_r ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( C @ ( B @ ( G @ opposite ) ) ) )
| ~ ( G @ ( F @ ( A @ sameside ) ) )
| ~ ( F @ ( C @ ( B @ s_col ) ) )
| ~ ( D @ ( E @ ( A @ s_m ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_3) ).
thf(1058,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( C @ ( B @ ( G @ opposite ) ) ) )
| ~ ( G @ ( F @ ( A @ sameside ) ) )
| ~ ( F @ ( C @ ( B @ s_col ) ) )
| ~ ( D @ ( E @ ( A @ s_m ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( C @ ( E @ s_r ) ) )
| ( E @ ( B @ ( A @ s_col ) ) )
| ( C @ ( E @ ( B @ ( A @ perp ) ) ) )
| ( D = C )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_16b) ).
thf(1090,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( C @ ( E @ s_r ) ) )
| ( E @ ( B @ ( A @ s_col ) ) )
| ( C @ ( E @ ( B @ ( A @ perp ) ) ) )
| ( D = C )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ foot ) ) @ ( C @ ( B @ ( A @ perp ) ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ( C @ ( B @ ( A @ foot ) ) @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_18) ).
thf(704,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ foot ) ) @ ( C @ ( B @ ( A @ perp ) ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ( C @ ( B @ ( A @ foot ) ) @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ s_r ) ) )
| ~ ( D @ ( A @ ( B @ s_col ) ) )
| ( A = B )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_3) ).
thf(947,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ s_r ) ) )
| ~ ( D @ ( A @ ( B @ s_col ) ) )
| ( A = B )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_12) ).
thf(540,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( F @ ( D @ ( B @ s_t ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_22b) ).
thf(604,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( F @ ( D @ ( B @ s_t ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_kf ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ reflect ) ) )
= C )
| ( ( C @ ( B @ ( A @ reflect ) ) )
!= D )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_4) ).
thf(900,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ reflect ) ) )
= C )
| ( ( C @ ( B @ ( A @ reflect ) ) )
!= D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) )
| ~ ( H @ ( G @ ( D @ ( C @ s_e ) ) ) )
| ~ ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( C @ ( B @ s_e ) ) ) )
| ~ ( G @ ( E @ ( C @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( H @ ( G @ ( D @ ( C @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( C @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( G @ ( E @ ( C @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( E @ s_t ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn4_1) ).
thf(274,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) )
| ~ ( H @ ( G @ ( D @ ( C @ s_e ) ) ) )
| ~ ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( C @ ( B @ s_e ) ) ) )
| ~ ( G @ ( E @ ( C @ ( A @ s_e ) ) ) )
| ~ ( G @ ( F @ ( E @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( H @ ( G @ ( D @ ( C @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( H @ ( E @ ( D @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( C @ ( B @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( G @ ( E @ ( C @ ( A @ s_e ) ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( E @ s_t ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_ifs ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ s_m ) ) )
| ( A = C )
| ~ ( C @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_20) ).
thf(1011,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ s_m ) ) )
| ( A = C )
| ~ ( C @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ ( E @ ( D @ samesideline ) ) ) )
| ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( C @ ( D @ sameside ) ) )
| ~ ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_19b) ).
thf(990,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ ( E @ ( D @ samesideline ) ) ) )
| ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( C @ ( D @ sameside ) ) )
| ~ ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ s ) @ ( B @ ( A @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_4) ).
thf(230,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ s ) @ ( B @ ( A @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( F @ ( G @ ( E @ s_e ) ) ) )
| ( A = B )
| ~ ( F @ ( D @ ( C @ s_t ) ) )
| ~ ( E @ ( B @ ( A @ s_t ) ) )
| ~ ( H @ ( D @ ( G @ ( B @ s_e ) ) ) )
| ~ ( H @ ( C @ ( G @ ( A @ s_e ) ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA5) ).
thf(434,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( F @ ( G @ ( E @ s_e ) ) ) )
| ( A = B )
| ~ ( F @ ( D @ ( C @ s_t ) ) )
| ~ ( E @ ( B @ ( A @ s_t ) ) )
| ~ ( H @ ( D @ ( G @ ( B @ s_e ) ) ) )
| ~ ( H @ ( C @ ( G @ ( A @ s_e ) ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ ( C @ opposite ) ) ) )
| ( C @ ( B @ ( A @ s_col ) ) )
| ( ( C @ ( B @ ( A @ reflect ) ) )
!= D )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_14) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ ( C @ opposite ) ) ) )
| ( C @ ( B @ ( A @ s_col ) ) )
| ( ( C @ ( B @ ( A @ reflect ) ) )
!= D )
| ( A = B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(208,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ ( C @ opposite ) ) ) )
| ( C @ ( B @ ( A @ s_col ) ) )
| ( ( C @ ( B @ ( A @ reflect ) ) )
!= D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ~ ( C @ ( D @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_17) ).
thf(616,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ~ ( C @ ( D @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_6a) ).
thf(303,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ ( C @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_2) ).
thf(477,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ ( C @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(143,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( A @ s_col ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_12) ).
thf(811,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( A @ s_col ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( C @ ( E @ ( B @ ( A @ perp ) ) ) )
| ( D @ ( C @ ( E @ s_r ) ) )
| ( D = C )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) )
& ( ~ ( C @ ( E @ ( B @ ( A @ perp ) ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ( D = C )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_16a) ).
thf(1080,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( C @ ( E @ ( B @ ( A @ perp ) ) ) )
| ( D @ ( C @ ( E @ s_r ) ) )
| ( D = C )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) )
& ( ~ ( C @ ( E @ ( B @ ( A @ perp ) ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ( D = C )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA3) ).
thf(631,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A
= ( C @ ( B @ ( A @ foot ) ) ) )
| ( D @ ( B @ ( A @ ( C @ opposite ) ) ) )
| ( B @ ( A @ ( D @ ( C @ samesideline ) ) ) )
| ( D @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13f_case2) ).
thf(816,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A
= ( C @ ( B @ ( A @ foot ) ) ) )
| ( D @ ( B @ ( A @ ( C @ opposite ) ) ) )
| ( B @ ( A @ ( D @ ( C @ samesideline ) ) ) )
| ( D @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B @ ( A @ ( D @ ( C @ ins ) ) ) )
= ( D @ ( D @ ( C @ ( B @ ( A @ insert ) ) ) @ ( B @ ( A @ ext ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ ( D @ ( C @ ins ) ) ) @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) )
& ( ( B @ ( A @ ( D @ ( C @ ins ) ) ) @ ( B @ ( A @ s_t ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_5a) ).
thf(520,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B @ ( A @ ( D @ ( C @ ins ) ) ) )
= ( D @ ( D @ ( C @ ( B @ ( A @ insert ) ) ) @ ( B @ ( A @ ext ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ ( D @ ( C @ ins ) ) ) @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) )
& ( ( B @ ( A @ ( D @ ( C @ ins ) ) ) @ ( B @ ( A @ s_t ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ( ( C @ ( B @ s ) @ ( A @ s ) )
!= ( C @ ( A @ s ) @ ( B @ s ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_19) ).
thf(240,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ( ( C @ ( B @ s ) @ ( A @ s ) )
!= ( C @ ( A @ s ) @ ( B @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11e) ).
thf(769,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ s_col ) ) )
| ( A = B )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aext1) ).
thf(943,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ s_col ) ) )
| ( A = B )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ reflect ) ) @ ( B @ ( A @ reflect ) ) )
= C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_5) ).
thf(1061,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ reflect ) ) @ ( B @ ( A @ reflect ) ) )
= C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11b) ).
thf(983,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C
= ( E @ ( D @ ( B @ ( A @ ext ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_12) ).
thf(455,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C
= ( E @ ( D @ ( B @ ( A @ ext ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ ( D @ samesideline ) ) ) )
| ~ ( B @ ( A @ ( D @ ( C @ samesideline ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13d) ).
thf(438,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ ( D @ samesideline ) ) ) )
| ~ ( B @ ( A @ ( D @ ( C @ samesideline ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
| ~ ( B @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aNarbouxLemma1) ).
thf(431,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
| ~ ( B @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_14) ).
thf(394,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(23,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( A @ s_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_3) ).
thf(306,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( A @ s_t ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ reflect ) ) )
!= ( D @ ( B @ ( A @ reflect ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_7) ).
thf(851,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ reflect ) ) )
!= ( D @ ( B @ ( A @ reflect ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ reflect ) ) )
= C )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_8b) ).
thf(1102,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ reflect ) ) )
= C )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ samesideline ) ) ) )
| ~ ( B @ ( A @ ( D @ ( C @ samesideline ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtSameSide2) ).
thf(473,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ samesideline ) ) ) )
| ~ ( B @ ( A @ ( D @ ( C @ samesideline ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ reflect ) ) @ ( C @ ( B @ ( A @ perp ) ) ) )
| ( C
= ( C @ ( B @ ( A @ reflect ) ) ) )
| ( A = B ) )
& ( ( C @ ( B @ ( A @ reflect ) ) @ ( C @ midpoint ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_2a) ).
thf(722,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ reflect ) ) @ ( C @ ( B @ ( A @ perp ) ) ) )
| ( C
= ( C @ ( B @ ( A @ reflect ) ) ) )
| ( A = B ) )
& ( ( C @ ( B @ ( A @ reflect ) ) @ ( C @ midpoint ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) )
| ( B @ ( D @ ( C @ s_col ) ) )
| ( A @ ( D @ ( C @ s_col ) ) )
| ( B = G )
| ( A = E )
| ( F = G )
| ( F = E )
| ( C = D )
| ~ ( G @ ( D @ ( C @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( F @ ( G @ ( B @ s_t ) ) )
| ~ ( F @ ( E @ ( A @ s_t ) ) ) )
& ( ~ ( B @ ( D @ ( C @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ~ ( A @ ( D @ ( C @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ( C != D )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ( ( D @ ( C @ ( B @ ( A @ ss3 ) ) ) )
!= ( D @ ( C @ ( B @ ( A @ ss2 ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ( ( D @ ( C @ ( B @ ( A @ ss3 ) ) ) )
!= ( D @ ( C @ ( B @ ( A @ ss1 ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ( B
!= ( D @ ( C @ ( B @ ( A @ ss2 ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ( A
!= ( D @ ( C @ ( B @ ( A @ ss1 ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ ss3 ) ) ) @ ( D @ ( C @ ( B @ ( A @ ss2 ) ) ) @ ( B @ s_t ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ ss3 ) ) ) @ ( D @ ( C @ ( B @ ( A @ ss1 ) ) ) @ ( A @ s_t ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ ss2 ) ) ) @ ( D @ ( C @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ ss1 ) ) ) @ ( D @ ( C @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn9_7) ).
thf(1018,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) )
| ( B @ ( D @ ( C @ s_col ) ) )
| ( A @ ( D @ ( C @ s_col ) ) )
| ( B = G )
| ( A = E )
| ( F = G )
| ( F = E )
| ( C = D )
| ~ ( G @ ( D @ ( C @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( F @ ( G @ ( B @ s_t ) ) )
| ~ ( F @ ( E @ ( A @ s_t ) ) ) )
& ( ~ ( B @ ( D @ ( C @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ~ ( A @ ( D @ ( C @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ( C != D )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ( ( D @ ( C @ ( B @ ( A @ ss3 ) ) ) )
!= ( D @ ( C @ ( B @ ( A @ ss2 ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ( ( D @ ( C @ ( B @ ( A @ ss3 ) ) ) )
!= ( D @ ( C @ ( B @ ( A @ ss1 ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ( B
!= ( D @ ( C @ ( B @ ( A @ ss2 ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ( A
!= ( D @ ( C @ ( B @ ( A @ ss1 ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ ss3 ) ) ) @ ( D @ ( C @ ( B @ ( A @ ss2 ) ) ) @ ( B @ s_t ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ ss3 ) ) ) @ ( D @ ( C @ ( B @ ( A @ ss1 ) ) ) @ ( A @ s_t ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ ss2 ) ) ) @ ( D @ ( C @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ ss1 ) ) ) @ ( D @ ( C @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ ( A @ perp ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp4) ).
thf(553,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ ( A @ perp ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( G @ ( B @ s_m ) ) )
| ( G
!= ( F @ ( C @ ( D @ ( E @ ( A @ ip ) ) ) ) ) )
| ~ ( F @ ( C @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( F @ ( C @ s_t ) ) )
| ~ ( D @ ( E @ ( A @ s_t ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( C @ ( D @ perp ) ) ) )
| ~ ( C @ ( B @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_24a) ).
thf(823,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( G @ ( B @ s_m ) ) )
| ( G
!= ( F @ ( C @ ( D @ ( E @ ( A @ ip ) ) ) ) ) )
| ~ ( F @ ( C @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( F @ ( C @ s_t ) ) )
| ~ ( D @ ( E @ ( A @ s_t ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( C @ ( D @ perp ) ) ) )
| ~ ( C @ ( B @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_17a) ).
thf(836,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ le ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ le ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_8) ).
thf(557,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ le ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ le ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( C @ ( E @ ( D @ ( B @ ( A @ g811 ) ) ) ) @ ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ f811 ) ) ) ) @ s_r ) ) )
| ~ ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( D = E )
| ( A = B )
| ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( E @ ( D @ ( B @ ( A @ g811 ) ) ) ) @ ( E @ ( D @ s_col ) ) )
| ~ ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( D = E )
| ( A = B )
| ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( E @ ( D @ ( B @ ( A @ f811 ) ) ) ) @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( D = E )
| ( A = B )
| ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( G @ ( C @ ( F @ s_r ) ) )
| ~ ( G @ ( E @ ( D @ s_col ) ) )
| ~ ( F @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( D != E )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( A != B )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn8_11a) ).
thf(855,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( C @ ( E @ ( D @ ( B @ ( A @ g811 ) ) ) ) @ ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ f811 ) ) ) ) @ s_r ) ) )
| ~ ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( D = E )
| ( A = B )
| ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( E @ ( D @ ( B @ ( A @ g811 ) ) ) ) @ ( E @ ( D @ s_col ) ) )
| ~ ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( D = E )
| ( A = B )
| ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( E @ ( D @ ( B @ ( A @ f811 ) ) ) ) @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( D = E )
| ( A = B )
| ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( G @ ( C @ ( F @ s_r ) ) )
| ~ ( G @ ( E @ ( D @ s_col ) ) )
| ~ ( F @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( D != E )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( A != B )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( E @ ( D @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( D @ s ) @ ( B @ ( D @ s ) @ ( A @ ( D @ s ) @ s_t ) ) )
| ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_15b) ).
thf(295,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( D @ s ) @ ( B @ ( D @ s ) @ ( A @ ( D @ s ) @ s_t ) ) )
| ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ s ) @ ( B @ ( D @ s ) @ ( A @ ( D @ s ) @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_15a) ).
thf(414,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ s ) @ ( B @ ( D @ s ) @ ( A @ ( D @ s ) @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ s_col ) ) )
| ( ( C @ ( B @ ( A @ reflect ) ) )
!= C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_8a) ).
thf(1098,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ s_col ) ) )
| ( ( C @ ( B @ ( A @ reflect ) ) )
!= C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ c63 ) ) @ ( B @ ( C @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( C @ ( B @ ( A @ c63 ) ) @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( ( C @ ( B @ ( A @ c63 ) ) )
!= B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( C != B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( A != B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_3a) ).
thf(673,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ c63 ) ) @ ( B @ ( C @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( C @ ( B @ ( A @ c63 ) ) @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( ( C @ ( B @ ( A @ c63 ) ) )
!= B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( C != B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( A != B )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_3a) ).
thf(331,plain,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( C @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) )
& ( ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn7_1) ).
thf(585,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( C @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) )
& ( ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_6b) ).
thf(338,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11c) ).
thf(951,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( C @ ( B @ ( A @ opposite ) ) ) )
| ~ ( C @ ( B @ ( E @ ( D @ samesideline ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13e) ).
thf(808,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( C @ ( B @ ( A @ opposite ) ) ) )
| ~ ( C @ ( B @ ( E @ ( D @ samesideline ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_3) ).
thf(613,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ reflect ) ) @ ( C @ ( B @ ( A @ reflect ) ) @ ( D @ ( C @ s_e ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_10) ).
thf(1094,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ reflect ) ) @ ( C @ ( B @ ( A @ reflect ) ) @ ( D @ ( C @ s_e ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ ( E @ ( D @ samesideline ) ) ) )
| ~ ( B @ ( C @ ( E @ ( D @ samesideline ) ) ) )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13c) ).
thf(497,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ ( E @ ( D @ samesideline ) ) ) )
| ~ ( B @ ( C @ ( E @ ( D @ samesideline ) ) ) )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_8) ).
thf(446,plain,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(94,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ ( A @ s_e ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_8) ).
thf(571,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ ( A @ s_e ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( I @ ( C @ ( B @ ( H @ opposite ) ) ) )
| ~ ( D @ ( E @ ( I @ sameside ) ) )
| ~ ( A @ ( F @ ( H @ sameside ) ) )
| ~ ( E @ ( G @ ( F @ s_m ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( A @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( C @ ( B @ s_col ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_4c) ).
thf(845,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( I @ ( C @ ( B @ ( H @ opposite ) ) ) )
| ~ ( D @ ( E @ ( I @ sameside ) ) )
| ~ ( A @ ( F @ ( H @ sameside ) ) )
| ~ ( E @ ( G @ ( F @ s_m ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( A @ ( C @ ( B @ perp ) ) ) )
| ~ ( F @ ( C @ ( B @ s_col ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( A @ ( B @ s_t ) ) )
| ( C @ ( B @ ( A @ ( B @ le ) ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_13b) ).
thf(627,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( A @ ( B @ s_t ) ) )
| ( C @ ( B @ ( A @ ( B @ le ) ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_15) ).
thf(363,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ s_col ) ) )
| ~ ( C @ ( A @ ( D @ sameside ) ) )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ( A = C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_15c) ).
thf(976,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ s_col ) ) )
| ~ ( C @ ( A @ ( D @ sameside ) ) )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ( A = C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(97,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( A @ s_e ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_1) ).
thf(581,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( A @ s_e ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( A @ ( C @ s_t ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ~ ( A @ ( C @ ( B @ s_t ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ( B @ ( A @ ( C @ s_t ) ) )
| ( A @ ( C @ ( B @ s_t ) ) )
| ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn4_10) ).
thf(759,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( A @ ( C @ s_t ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ~ ( A @ ( C @ ( B @ s_t ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ( B @ ( A @ ( C @ s_t ) ) )
| ( A @ ( C @ ( B @ s_t ) ) )
| ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_4a) ).
thf(771,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( C @ ( D @ ( C @ s_e ) ) ) )
| ~ ( E @ ( B @ ( D @ ( B @ s_e ) ) ) )
| ~ ( E @ ( A @ ( D @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_17) ).
thf(781,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( C @ ( D @ ( C @ s_e ) ) ) )
| ~ ( E @ ( B @ ( D @ ( B @ s_e ) ) ) )
| ~ ( E @ ( A @ ( D @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_17b) ).
thf(961,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ s_col ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_13) ).
thf(813,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ s_col ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(18,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( B @ ( A @ s_e ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA1) ).
thf(290,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( B @ ( A @ s_e ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ s_t ) ) )
| ~ ( C @ ( D @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_5b) ).
thf(235,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ s_t ) ) )
| ~ ( C @ ( D @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_6) ).
thf(510,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i] : ( B @ ( C @ s ) @ ( A @ ( C @ s ) @ ( B @ ( A @ s_e ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_13) ).
thf(667,plain,
! [A: $i,B: $i,C: $i] : ( B @ ( C @ s ) @ ( A @ ( C @ s ) @ ( B @ ( A @ s_e ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
| ( A = B )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_9) ).
thf(1077,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
| ( A = B )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ sameside ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_4b) ).
thf(716,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ sameside ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_2) ).
thf(620,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(47,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ midpoint ) @ ( A @ s_m ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_22) ).
thf(405,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ midpoint ) @ ( A @ s_m ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ s ) @ ( C @ ( E @ s ) @ ( B @ ( E @ s ) @ ( A @ ( E @ s ) @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_16a) ).
thf(422,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ s ) @ ( C @ ( E @ s ) @ ( B @ ( E @ s ) @ ( A @ ( E @ s ) @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( C @ ( B @ ( E @ ( A @ samesideline ) ) ) )
| ( D @ ( C @ ( B @ ( E @ opposite ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_8) ).
thf(833,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( C @ ( B @ ( E @ ( A @ samesideline ) ) ) )
| ( D @ ( C @ ( B @ ( E @ opposite ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ opposite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( B @ ( A @ sameside ) ) )
| ( D @ ( B @ ( C @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ( D = B )
| ( C = B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_2b) ).
thf(410,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( B @ ( A @ sameside ) ) )
| ( D @ ( B @ ( C @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ( D = B )
| ( C = B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C
= ( D @ ( B @ ( A @ reflect ) ) ) )
| ( ( C @ ( B @ ( A @ reflect ) ) )
!= D )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_6) ).
thf(801,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C
= ( D @ ( B @ ( A @ reflect ) ) ) )
| ( ( C @ ( B @ ( A @ reflect ) ) )
!= D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( E @ ( B @ ( C @ ( B @ s_e ) ) ) )
| ~ ( B @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( E @ ( B @ ( D @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_12a) ).
thf(341,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( E @ ( B @ ( C @ ( B @ s_e ) ) ) )
| ~ ( B @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( E @ ( B @ ( D @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( E @ ( A @ ( B @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ sameside ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_28) ).
thf(358,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( E @ ( A @ ( B @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ sameside ) ) )
| ~ ( C @ ( B @ ( A @ sameside ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ pointOffLine ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_25) ).
thf(897,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ pointOffLine ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ ( C @ le ) ) ) )
| ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_10) ).
thf(400,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ ( C @ le ) ) ) )
| ( D @ ( C @ ( B @ ( A @ le ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ ( A @ le ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_12a1) ).
thf(828,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ ( A @ le ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ( ( D @ ( A @ s ) )
!= C )
| ( ( B @ ( A @ s ) )
!= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_8) ).
thf(635,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ( ( D @ ( A @ s ) )
!= C )
| ( ( B @ ( A @ s ) )
!= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( C @ ( E @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( G @ ( E @ ( F @ s_r ) ) )
| ( E = G )
| ( E = F )
| ~ ( G @ ( D @ ( C @ s_col ) ) )
| ~ ( F @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_13b) ).
thf(1065,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( C @ ( E @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( G @ ( E @ ( F @ s_r ) ) )
| ( E = G )
| ( E = F )
| ~ ( G @ ( D @ ( C @ s_col ) ) )
| ~ ( F @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11a) ).
thf(839,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E = F )
| ~ ( D @ ( C @ ( F @ ( B @ s_e ) ) ) )
| ~ ( A @ ( B @ ( F @ sameside ) ) )
| ~ ( D @ ( C @ ( E @ ( B @ s_e ) ) ) )
| ~ ( A @ ( B @ ( E @ sameside ) ) )
| ( C = D )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_11b) ).
thf(464,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E = F )
| ~ ( D @ ( C @ ( F @ ( B @ s_e ) ) ) )
| ~ ( A @ ( B @ ( F @ sameside ) ) )
| ~ ( D @ ( C @ ( E @ ( B @ s_e ) ) ) )
| ~ ( A @ ( B @ ( E @ sameside ) ) )
| ( C = D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ s_t ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_7a) ).
thf(427,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ s_t ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(63,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ s_r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_5) ).
thf(459,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ s_r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ sameside ) ) )
| ~ ( D @ ( B @ ( C @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ( D = B )
| ( C = B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_2a) ).
thf(442,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ sameside ) ) )
| ~ ( D @ ( B @ ( C @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ( D = B )
| ( C = B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( C @ ( B @ isomidpoint ) ) @ ( B @ s_m ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_25) ).
thf(501,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( C @ ( B @ isomidpoint ) ) @ ( B @ s_m ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ s ) @ ( A @ s ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_7) ).
thf(369,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ s ) @ ( A @ s ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ ( A @ s_t ) ) )
| ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( D @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_3) ).
thf(607,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ ( A @ s_t ) ) )
| ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( D @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( E @ samesideline ) ) ) )
| ~ ( E @ ( D @ ( A @ sameside ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_16) ).
thf(254,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( E @ samesideline ) ) ) )
| ~ ( E @ ( D @ ( A @ sameside ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = C )
| ~ ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( D @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_6) ).
thf(354,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = C )
| ~ ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( D @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ s_e ) ) ) ) )
& ( ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) ) )
& ( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) ) )
& ( ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn4_4) ).
thf(543,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ s_e ) ) ) ) )
& ( ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) ) )
& ( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) ) )
& ( ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ s_e3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ ( A @ samesideline ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13a) ).
thf(560,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ ( A @ samesideline ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ samesideline ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( A @ ( A @ ( B @ perp ) ) ) )
| ~ ( D @ ( C @ ( A @ s_col ) ) )
| ~ ( C @ ( A @ ( A @ ( B @ perp ) ) ) )
| ( A = D )
| ( D = C )
| ( B = C )
| ( A = C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp3) ).
thf(1069,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( A @ ( A @ ( B @ perp ) ) ) )
| ~ ( D @ ( C @ ( A @ s_col ) ) )
| ~ ( C @ ( A @ ( A @ ( B @ perp ) ) ) )
| ( A = D )
| ( D = C )
| ( B = C )
| ( A = C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
| ~ ( B @ ( C @ ( A @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_7) ).
thf(232,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
| ~ ( B @ ( C @ ( A @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_14a) ).
thf(1014,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(72,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( A @ le ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_7) ).
thf(491,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( A @ le ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( C @ ( B @ le ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_12a2) ).
thf(1088,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( C @ ( B @ le ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(5405,plain,
$false,
inference(e,[status(thm)],[969,645,629,479,909,518,468,941,1110,777,555,994,308,1073,449,878,269,597,730,217,797,913,930,973,257,841,417,785,372,917,344,934,485,238,348,806,905,734,396,998,849,507,292,248,529,366,714,334,894,260,820,407,693,566,361,625,889,461,493,710,324,1106,583,830,697,980,593,610,420,225,537,669,642,1016,328,471,622,985,701,515,1050,1002,569,503,244,938,266,1054,398,953,662,718,298,965,425,513,573,689,375,601,562,1007,402,579,391,1058,1090,704,947,540,604,900,274,1011,990,230,434,208,616,303,477,811,1080,631,816,520,240,769,943,1061,983,455,438,431,394,306,851,1102,473,722,1018,553,823,836,557,855,295,414,1098,673,331,585,338,951,808,613,1094,497,446,571,845,627,363,976,581,759,771,781,961,813,290,235,510,667,1077,716,620,405,422,833,410,801,341,358,897,400,828,635,1065,839,464,427,459,442,501,369,607,254,354,543,560,1069,232,1014,491,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO528+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % 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
% 0.06/0.32 % Computer : n012.cluster.edu
% 0.06/0.32 % Model : x86_64 x86_64
% 0.06/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.32 % Memory : 8046.5625MB
% 0.06/0.32 % OS : Linux 6.8.0-71-generic
% 0.06/0.32 % CPULimit : 300
% 0.06/0.32 % WCLimit : 300
% 0.06/0.32 % DateTime : Fri Sep 25 13:38:50 UTC 2026
% 0.06/0.33 % CPUTime :
% 0.06/0.33 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.49/0.64 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.99/0.83 % [INFO] Parsing done (189ms).
% 0.99/0.84 % [INFO] Running in sequential loop mode.
% 1.74/1.06 % [INFO] eprover registered as external prover.
% 1.74/1.06 % [INFO] Scanning for conjecture ...
% 2.03/1.15 % [INFO] Found a conjecture (or negated_conjecture) and 212 axioms. Running axiom selection ...
% 2.19/1.22 % [INFO] Axiom selection finished. Selected 205 axioms (removed 7 axioms).
% 2.59/1.39 % [INFO] Problem is first-order (TPTP FOF).
% 2.95/1.41 % [INFO] Type checking passed.
% 2.95/1.41 % [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 ...
% 19.40/4.63 % External prover 'e' found a proof!
% 19.40/4.63 % [INFO] Killing All external provers ...
% 19.40/4.63 % Time passed: 4228ms (effective reasoning time: 3786ms)
% 19.40/4.63 % 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)>
% 19.40/4.64 % Axioms used in derivation (205): aSatz5_9, aSatz8_8, aSatz3_4, aSatz7_19, aSatz6_5, aSatz2_13, aSatz7_10b, aSatz7_2, aSatz10_7, aSatz2_3, aSatz6_16b, aSatz9_5, aSatz8_24a, aSatz4_5, d_Defn5_4, aSatz4_11d, aSatz5_6, aSatz6_2a, aSatz8_20b, d_Defn4_4, aSatz3_1, aSatz10_8b, aSatz9_9, aSatz10_2a, aSatz6_3a, aSatz10_4, aSatz5_2, d_Defn7_23, aExtCol2, aSatz6_15d, aSatz6_4b, aA1, aext1, aLemma9_13a, aSatz8_3, aSatz4_16, aSatz8_12b, aLemma9_13d, aSatz6_13a, aSatz6_3b, aSatz8_24b, aA5, aSatz7_10a, aExtPerp2, aSatz5_12a1, aSatz7_15b, d_Defn6_1, aExtPerp, aSatz6_6, aSatz8_7, d_Defn4_15, aSatz2_12, aSatz3_3, aperp1, aSatz6_18, aSatz7_3b, d_Defn9_1, aSatz6_2b, aSatz10_12c, aSatz10_12, aSatz10_8a, aSatz8_16b, aSatz3_5b, aSatz9_4b, aSatz8_14a, aSatz3_17, aSatz7_7, aSatz4_11c, d_Defn4_10, aSatz5_1, aSatz5_12b, aSatz9_4a, aLemma9_13f_case2, aSatz9_4, aSatz4_19, aSatz10_5, aExtPerp6, aLemma9_13b, aSatz9_3a, aSatz3_5a, aExtSameSide1, aLemma9_13e, aSatz8_21, aSatz8_18a, aSatz6_15a, aSatz4_14, aSatz6_15c, aSatz2_1, aSideReflect, aSatz8_20a, aSatz6_11b, aSatz8_4, aSatz9_8, aSatz7_18, aSatz8_10, aSatz6_25, aSatz10_10a, aSatz8_15, aSatz7_25, d_Defn4_1, aA2, aSatz7_4a, aSatz4_11b, aSatz10_2b, aSatz8_21a, aSatz2_5, aSatz3_6b, aExtPerp3, aA3, aSatz3_2, aLemma9_13g, aSatz9_2, aA6, aSatz3_6a, aSatz7_15a, aSatz5_12a2, aNarbouxLemma1, aSatz8_22, aSatz6_17a, aSatz8_13a, aSatz7_22b, d_Defn8_11b, aSatz8_14b, aSatz4_3, aSatz7_6, aExtSameSide2, d_Defn7_1, aSatz9_4c, aSatz4_18, aSatz2_2, aSatz7_20, aSatz5_5a, aSatz5_11, aExtPerp5, aSatz6_28, aSatz7_22, aSatz7_21, aSatz4_12b, aSatz2_15, aSatz8_22b, aLemma9_13f, aSatz4_11a, aSatz6_11a, aA7, aSatz6_15b, aSatz10_12b, aSatz8_6, aSatz10_6, aSatz9_13, aSatz2_4, aSatz7_16a, d_Defn8_1, aLemma9_13c, aSatz7_9, d_Defn8_11a, aSatz9_16, aA4, aSatz9_3, aSatz5_8, aSatz6_16a, aSatz3_7a, aSatz8_2, aSatz7_17, aSatz8_18, aSatz6_21, aSatz8_13b, aSatz10_10, aSatz8_14c, aSatz8_12a, aSatz4_6, aSatz7_4b, aSatz6_17b, aLemma9_13f_case1, aSatz5_7, aSatz4_13, aSatz2_11, aSatz7_13, d_Defn9_7, aSatz8_9, aSatz2_14, aSatz4_11e, aSatz5_10, d_Defn2_10, aSatz7_22a, aSatz5_5b, aSatz10_12a, aSatz4_12, aSatz8_24, aExtPerp4, aSatz8_16a, aSatz4_17, aSatz9_4a2, aSatz5_3, aSatz6_13b, aSatz7_8, aSatz7_16b, aSatz8_5, aSatz2_8, aSatz4_2, aSatz6_4a, aSatz3_7b, aSatz7_3a, aSatz6_7, aSatz9_6, aSatz9_19b
% 19.40/4.64 % No. of inferences in proof: 414
% 19.40/4.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4228 ms resp. 3786 ms w/o parsing
% 18.91/4.82 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.91/4.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------