TSTP Solution File: GEO535+1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO535+1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:11:09 EDT 2023
% Result : Theorem 14.66s 4.30s
% Output : Refutation 14.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 288
% Syntax : Number of formulae : 518 ( 41 unt; 60 typ; 0 def)
% Number of atoms : 2251 ( 506 equ; 0 cnn)
% Maximal formula atoms : 42 ( 4 avg)
% Number of connectives : 10620 (1191 ~;1585 |; 208 &;7636 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 227 ( 227 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 60 usr; 10 con; 0-8 aty)
% Number of variables : 2016 ( 0 ^;2016 !; 0 ?;2016 :)
% Comments :
%------------------------------------------------------------------------------
thf(congruent_type,type,
congruent: $i > $i > $i > $i > $i > $i > $o ).
thf(s_e_type,type,
s_e: $i > $i > $i > $i > $o ).
thf(alpha_type,type,
alpha: $i ).
thf(beta_type,type,
beta: $i ).
thf(perpAt_type,type,
perpAt: $i > $i > $i > $i > $i > $o ).
thf(il_type,type,
il: $i > $i > $i > $i > $i ).
thf(gamma_type,type,
gamma: $i ).
thf(perp_type,type,
perp: $i > $i > $i > $i > $o ).
thf(s_col_type,type,
s_col: $i > $i > $i > $o ).
thf(s_t_type,type,
s_t: $i > $i > $i > $o ).
thf(opposite_type,type,
opposite: $i > $i > $i > $i > $o ).
thf(samesideline_type,type,
samesideline: $i > $i > $i > $i > $o ).
thf(ext_type,type,
ext: $i > $i > $i > $i > $i ).
thf(foot_type,type,
foot: $i > $i > $i > $i ).
thf(s_r_type,type,
s_r: $i > $i > $i > $o ).
thf(s_type,type,
s: $i > $i > $i ).
thf(sameside_type,type,
sameside: $i > $i > $i > $o ).
thf(ip_type,type,
ip: $i > $i > $i > $i > $i > $i ).
thf(s_m_type,type,
s_m: $i > $i > $i > $o ).
thf(midpoint_type,type,
midpoint: $i > $i > $i ).
thf(reflect_type,type,
reflect: $i > $i > $i > $i ).
thf(f813_type,type,
f813: $i > $i > $i > $i > $i > $i ).
thf(g813_type,type,
g813: $i > $i > $i > $i > $i > $i ).
thf(s_e3_type,type,
s_e3: $i > $i > $i > $i > $i > $i > $o ).
thf(xa_type,type,
xa: $i ).
thf(xb_type,type,
xb: $i ).
thf(xp_type,type,
xp: $i ).
thf(xq_type,type,
xq: $i ).
thf(xc_type,type,
xc: $i ).
thf(xd_type,type,
xd: $i ).
thf(le_type,type,
le: $i > $i > $i > $i > $o ).
thf(f811_type,type,
f811: $i > $i > $i > $i > $i > $i ).
thf(g811_type,type,
g811: $i > $i > $i > $i > $i > $i ).
thf(erect21a_type,type,
erect21a: $i > $i > $i > $i ).
thf(erectAux21a_type,type,
erectAux21a: $i > $i > $i > $i ).
thf(pointOffLine_type,type,
pointOffLine: $i > $i > $i ).
thf(insert_type,type,
insert: $i > $i > $i > $i > $i ).
thf(crossbar_type,type,
crossbar: $i > $i > $i > $i > $i > $i > $i ).
thf(c63_type,type,
c63: $i > $i > $i > $i ).
thf(op_type,type,
op: $i > $i > $i > $i > $i > $i ).
thf(midpointAux_type,type,
midpointAux: $i > $i > $i > $i > $i > $i ).
thf(s_kf_type,type,
s_kf: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(ss1_type,type,
ss1: $i > $i > $i > $i > $i ).
thf(ss2_type,type,
ss2: $i > $i > $i > $i > $i ).
thf(ss3_type,type,
ss3: $i > $i > $i > $i > $i ).
thf(erectsameside_type,type,
erectsameside: $i > $i > $i > $i > $i ).
thf(erect_type,type,
erect: $i > $i > $i > $i ).
thf(erectAux_type,type,
erectAux: $i > $i > $i > $i ).
thf(insert5_type,type,
insert5: $i > $i > $i > $i > $i > $i ).
thf(s_ifs_type,type,
s_ifs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(s_fs_type,type,
s_fs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(s_afs_type,type,
s_afs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(f113a_type,type,
f113a: $i > $i > $i > $i > $i > $i > $i ).
thf(f113c_type,type,
f113c: $i > $i > $i > $i > $i > $i > $i ).
thf(f113d_type,type,
f113d: $i > $i > $i > $i > $i > $i > $i ).
thf(f113f_type,type,
f113f: $i > $i > $i > $i > $i > $i > $i ).
thf(constructAngle_type,type,
constructAngle: $i > $i > $i > $i > $i > $i > $i ).
thf(isomidpoint_type,type,
isomidpoint: $i > $i > $i > $i ).
thf(ins_type,type,
ins: $i > $i > $i > $i > $i ).
thf(triangle_type,type,
triangle: $i > $i > $i > $i > $i > $i > $i ).
thf(104,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( perp @ A @ B @ C @ D )
| ~ ( s_col @ A @ B @ E )
| ~ ( s_col @ C @ D @ E )
| ( perpAt @ A @ B @ E @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_14b) ).
thf(645,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( perp @ A @ B @ C @ D )
| ~ ( s_col @ A @ B @ E )
| ~ ( s_col @ C @ D @ E )
| ( perpAt @ A @ B @ E @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ B @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_14) ).
thf(1036,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ B @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_m @ ( s @ A @ C ) @ D @ ( s @ B @ C ) )
| ( s_r @ B @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_20a) ).
thf(809,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_m @ ( s @ A @ C ) @ D @ ( s @ B @ C ) )
| ( s_r @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ B @ C @ D @ E )
| ( C
= ( ext @ A @ B @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_12) ).
thf(1190,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ B @ C @ D @ E )
| ( C
= ( ext @ A @ B @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
| ( s_col @ A @ B @ ( midpoint @ C @ ( reflect @ A @ B @ C ) ) ) )
& ( ( A = B )
| ( C
= ( reflect @ A @ B @ C ) )
| ( perp @ A @ B @ C @ ( reflect @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_2a) ).
thf(347,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
| ( s_col @ A @ B @ ( midpoint @ C @ ( reflect @ A @ B @ C ) ) ) )
& ( ( A = B )
| ( C
= ( reflect @ A @ B @ C ) )
| ( perp @ A @ B @ C @ ( reflect @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( s_r @ A @ B @ C )
| ( s_e @ A @ C @ A @ ( s @ B @ C ) ) )
& ( ( s_r @ A @ B @ C )
| ~ ( s_e @ A @ C @ A @ ( s @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn8_1) ).
thf(893,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( s_r @ A @ B @ C )
| ( s_e @ A @ C @ A @ ( s @ B @ C ) ) )
& ( ( s_r @ A @ B @ C )
| ~ ( s_e @ A @ C @ A @ ( s @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_m @ A @ E @ D )
| ~ ( s_col @ B @ C @ F )
| ~ ( sameside @ A @ F @ G )
| ( opposite @ G @ B @ C @ D )
| ~ ( s_t @ F @ G @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_3a) ).
thf(468,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_m @ A @ E @ D )
| ~ ( s_col @ B @ C @ F )
| ~ ( sameside @ A @ F @ G )
| ( opposite @ G @ B @ C @ D )
| ~ ( s_t @ F @ G @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_col @ A @ B @ C ) )
& ( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e3 @ A @ B @ C @ E @ F @ G ) )
& ( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ D @ E @ H ) )
& ( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ D @ F @ H ) )
& ( ~ ( s_col @ A @ B @ C )
| ~ ( s_e3 @ A @ B @ C @ E @ F @ G )
| ~ ( s_e @ A @ D @ E @ H )
| ~ ( s_e @ B @ D @ F @ H )
| ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn4_15) ).
thf(941,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_col @ A @ B @ C ) )
& ( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e3 @ A @ B @ C @ E @ F @ G ) )
& ( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ D @ E @ H ) )
& ( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ D @ F @ H ) )
& ( ~ ( s_col @ A @ B @ C )
| ~ ( s_e3 @ A @ B @ C @ E @ F @ G )
| ~ ( s_e @ A @ D @ E @ H )
| ~ ( s_e @ B @ D @ F @ H )
| ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( C = B )
| ( D = B )
| ~ ( s_t @ A @ B @ D )
| ~ ( s_t @ C @ B @ D )
| ( sameside @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_2a) ).
thf(555,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( C = B )
| ( D = B )
| ~ ( s_t @ A @ B @ D )
| ~ ( s_t @ C @ B @ D )
| ( sameside @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ C )
| ( s_t @ B @ ( ip @ A @ B @ C @ D @ E ) @ D ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ C )
| ( s_t @ E @ ( ip @ A @ B @ C @ D @ E ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA7) ).
thf(333,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ C )
| ( s_t @ B @ ( ip @ A @ B @ C @ D @ E ) @ D ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ C )
| ( s_t @ E @ ( ip @ A @ B @ C @ D @ E ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( C = D )
| ( A = B )
| ~ ( perpAt @ C @ D @ E @ F @ G )
| ( perpAt @ A @ B @ E @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp) ).
thf(249,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( C = D )
| ( A = B )
| ~ ( perpAt @ C @ D @ E @ F @ G )
| ( perpAt @ A @ B @ E @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ~ ( s_t @ B @ A @ C )
| ~ ( sameside @ D @ A @ B )
| ( s_col @ D @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_15b) ).
thf(582,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ~ ( s_t @ B @ A @ C )
| ~ ( sameside @ D @ A @ B )
| ( s_col @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( perp @ A @ B @ B @ C )
| ~ ( perp @ D @ C @ B @ C )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_t @ A @ E @ D )
| ~ ( s_t @ C @ F @ D )
| ~ ( s_e @ B @ A @ C @ F )
| ( G
!= ( ip @ A @ E @ D @ C @ F ) )
| ( s_m @ B @ G @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_24a) ).
thf(1005,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( perp @ A @ B @ B @ C )
| ~ ( perp @ D @ C @ B @ C )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_t @ A @ E @ D )
| ~ ( s_t @ C @ F @ D )
| ~ ( s_e @ B @ A @ C @ F )
| ( G
!= ( ip @ A @ E @ D @ C @ F ) )
| ( s_m @ B @ G @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ( B = C )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_col @ B @ C @ F )
| ~ ( perp @ B @ C @ A @ F )
| ~ ( perp @ B @ C @ D @ E )
| ~ ( s_m @ F @ G @ E )
| ~ ( sameside @ H @ F @ A )
| ( F != E )
| ( sameside @ ( s @ G @ H ) @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_4b) ).
thf(683,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ( B = C )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_col @ B @ C @ F )
| ~ ( perp @ B @ C @ A @ F )
| ~ ( perp @ B @ C @ D @ E )
| ~ ( s_m @ F @ G @ E )
| ~ ( sameside @ H @ F @ A )
| ( F != E )
| ( sameside @ ( s @ G @ H ) @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ( opposite @ E @ B @ C @ D )
| ~ ( samesideline @ A @ E @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_8) ).
thf(276,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ( opposite @ E @ B @ C @ D )
| ~ ( samesideline @ A @ E @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( samesideline @ C @ D @ A @ B )
| ~ ( samesideline @ D @ E @ A @ B )
| ( samesideline @ C @ E @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_13) ).
thf(741,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( samesideline @ C @ D @ A @ B )
| ~ ( samesideline @ D @ E @ A @ B )
| ( samesideline @ C @ E @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( s_col @ A @ B @ C )
| ( s_col @ D @ E @ F )
| ~ ( congruent @ A @ B @ C @ D @ E @ G )
| ~ ( samesideline @ G @ F @ E @ D )
| ~ ( congruent @ A @ B @ C @ D @ E @ H )
| ~ ( samesideline @ H @ F @ E @ D )
| ( sameside @ G @ E @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz11_15b) ).
thf(1142,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( s_col @ A @ B @ C )
| ( s_col @ D @ E @ F )
| ~ ( congruent @ A @ B @ C @ D @ E @ G )
| ~ ( samesideline @ G @ F @ E @ D )
| ~ ( congruent @ A @ B @ C @ D @ E @ H )
| ~ ( samesideline @ H @ F @ E @ D )
| ( sameside @ G @ E @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( s @ A @ B )
!= C )
| ( ( s @ A @ D )
!= C )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_8) ).
thf(861,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( s @ A @ B )
!= C )
| ( ( s @ A @ D )
!= C )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( s_col @ A @ B @ C )
| ( s_col @ A @ B @ D )
| ( samesideline @ C @ D @ A @ B )
| ( opposite @ C @ A @ B @ D )
| ( A
= ( foot @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13f_case2) ).
thf(440,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( s_col @ A @ B @ C )
| ( s_col @ A @ B @ D )
| ( samesideline @ C @ D @ A @ B )
| ( opposite @ C @ A @ B @ D )
| ( A
= ( foot @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( sameside @ A @ B @ C )
| ( A = B )
| ( C = B )
| ( D = B )
| ~ ( s_t @ A @ B @ D )
| ~ ( s_t @ C @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_3b) ).
thf(655,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( sameside @ A @ B @ C )
| ( A = B )
| ( C = B )
| ( D = B )
| ~ ( s_t @ A @ B @ D )
| ~ ( s_t @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( ( reflect @ A @ B @ C )
!= D )
| ( ( reflect @ A @ B @ D )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_4) ).
thf(550,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( ( reflect @ A @ B @ C )
!= D )
| ( ( reflect @ A @ B @ D )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_m @ A @ B @ C )
| ( C
= ( s @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_6) ).
thf(340,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_m @ A @ B @ C )
| ( C
= ( s @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_e @ A @ B @ D @ E )
| ( s_e3 @ A @ B @ C @ D @ E @ ( insert5 @ A @ B @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_14) ).
thf(898,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_e @ A @ B @ D @ E )
| ( s_e3 @ A @ B @ C @ D @ E @ ( insert5 @ A @ B @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( A
!= ( ext @ B @ A @ alpha @ gamma ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_14b) ).
thf(288,plain,
! [A: $i,B: $i] :
( A
!= ( ext @ B @ A @ alpha @ gamma ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ C )
| ~ ( s_t @ A @ F @ D )
| ( s_t @ F @ ( crossbar @ A @ B @ C @ D @ E @ F ) @ C ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ C )
| ~ ( s_t @ A @ F @ D )
| ( s_t @ B @ ( crossbar @ A @ B @ C @ D @ E @ F ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_17) ).
thf(565,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ C )
| ~ ( s_t @ A @ F @ D )
| ( s_t @ F @ ( crossbar @ A @ B @ C @ D @ E @ F ) @ C ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ C )
| ~ ( s_t @ A @ F @ D )
| ( s_t @ B @ ( crossbar @ A @ B @ C @ D @ E @ F ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( s_col @ A @ B @ C )
| ( s_col @ A @ B @ D )
| ( samesideline @ C @ D @ A @ B )
| ( opposite @ C @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13f) ).
thf(570,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( s_col @ A @ B @ C )
| ( s_col @ A @ B @ D )
| ( samesideline @ C @ D @ A @ B )
| ( opposite @ C @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11c) ).
thf(619,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_m @ A @ B @ C )
| ~ ( s_m @ A @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_4b) ).
thf(802,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_m @ A @ B @ C )
| ~ ( s_m @ A @ B @ D )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ F )
| ~ ( s_e @ A @ C @ D @ F )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ B @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_3) ).
thf(934,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ F )
| ~ ( s_e @ A @ C @ D @ F )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ B @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ( congruent @ D @ E @ F @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz11_7) ).
thf(1132,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ( congruent @ D @ E @ F @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( s @ A @ ( s @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_7) ).
thf(460,plain,
! [A: $i,B: $i] :
( ( s @ A @ ( s @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_t @ A @ B @ C ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_t @ E @ F @ G ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ C @ E @ G ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ C @ F @ G ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ D @ E @ H ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ C @ D @ G @ H ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ E @ F @ G )
| ~ ( s_e @ A @ C @ E @ G )
| ~ ( s_e @ B @ C @ F @ G )
| ~ ( s_e @ A @ D @ E @ H )
| ~ ( s_e @ C @ D @ G @ H )
| ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn4_1) ).
thf(917,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_t @ A @ B @ C ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_t @ E @ F @ G ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ C @ E @ G ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ C @ F @ G ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ D @ E @ H ) )
& ( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ C @ D @ G @ H ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ E @ F @ G )
| ~ ( s_e @ A @ C @ E @ G )
| ~ ( s_e @ B @ C @ F @ G )
| ~ ( s_e @ A @ D @ E @ H )
| ~ ( s_e @ C @ D @ G @ H )
| ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ D @ E @ C )
| ~ ( sameside @ D @ C @ E )
| ( s_col @ A @ B @ D )
| ( samesideline @ D @ E @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_19b) ).
thf(702,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ D @ E @ C )
| ~ ( sameside @ D @ C @ E )
| ( s_col @ A @ B @ D )
| ( samesideline @ D @ E @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(135,axiom,
! [A: $i,B: $i] : ( s_col @ A @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_12b) ).
thf(751,plain,
! [A: $i,B: $i] : ( s_col @ A @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( insert @ A @ B @ C @ D )
= ( ext @ ( ext @ D @ C @ alpha @ gamma ) @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_insert) ).
thf(559,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( insert @ A @ B @ C @ D )
= ( ext @ ( ext @ D @ C @ alpha @ gamma ) @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ~ ( congruent @ D @ E @ F @ G @ H @ I )
| ( congruent @ A @ B @ C @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz11_8) ).
thf(1087,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ~ ( congruent @ D @ E @ F @ G @ H @ I )
| ( congruent @ A @ B @ C @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_5) ).
thf(1147,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ A @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11d) ).
thf(606,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( ( reflect @ A @ B @ C )
!= D )
| ( C
= ( reflect @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_6) ).
thf(416,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( ( reflect @ A @ B @ C )
!= D )
| ( C
= ( reflect @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(55,axiom,
( ~ ( s_col @ xa @ xb @ xp )
| ~ ( s_col @ xa @ xb @ xq )
| ( xp = xq )
| ( xa = xb )
| ( perp @ xc @ xd @ xp @ xq )
| ~ ( perp @ xc @ xd @ xa @ xb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp6) ).
thf(448,plain,
( ~ ( s_col @ xa @ xb @ xp )
| ~ ( s_col @ xa @ xb @ xq )
| ( xp = xq )
| ( xa = xb )
| ( perp @ xc @ xd @ xp @ xq )
| ~ ( perp @ xc @ xd @ xa @ xb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_t @ C @ A @ B )
| ~ ( s_t @ D @ A @ B )
| ( s_t @ D @ C @ B )
| ( s_t @ C @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_16a) ).
thf(421,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_t @ C @ A @ B )
| ~ ( s_t @ D @ A @ B )
| ( s_t @ D @ C @ B )
| ( s_t @ C @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( sameside @ A @ B @ C )
| ( A != B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( C != B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( s_t @ B @ A @ C )
| ( s_t @ B @ C @ A ) )
& ( ~ ( s_t @ B @ A @ C )
| ( A = B )
| ( xb = B )
| ( sameside @ A @ B @ C ) )
& ( ~ ( s_t @ B @ C @ A )
| ( A = B )
| ( C = B )
| ( sameside @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn6_1) ).
thf(870,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( sameside @ A @ B @ C )
| ( A != B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( C != B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( s_t @ B @ A @ C )
| ( s_t @ B @ C @ A ) )
& ( ~ ( s_t @ B @ A @ C )
| ( A = B )
| ( xb = B )
| ( sameside @ A @ B @ C ) )
& ( ~ ( s_t @ B @ C @ A )
| ( A = B )
| ( C = B )
| ( sameside @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( le @ A @ B @ C @ D )
| ~ ( le @ C @ D @ A @ B )
| ( s_e @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_9) ).
thf(1013,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( le @ A @ B @ C @ D )
| ~ ( le @ C @ D @ A @ B )
| ( s_e @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(16,axiom,
( ~ ( s_t @ alpha @ beta @ gamma )
& ~ ( s_t @ beta @ gamma @ alpha )
& ~ ( s_t @ gamma @ alpha @ beta ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA8) ).
thf(284,plain,
( ~ ( s_t @ alpha @ beta @ gamma )
& ~ ( s_t @ beta @ gamma @ alpha )
& ~ ( s_t @ gamma @ alpha @ beta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( le @ A @ B @ C @ D )
| ( le @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_10) ).
thf(475,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( le @ A @ B @ C @ D )
| ( le @ C @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A = B )
| ( C = D )
| ( sameside @ ( insert @ C @ D @ B @ A ) @ B @ A ) )
& ( ( A = B )
| ( C = D )
| ( s_e @ B @ ( insert @ C @ D @ B @ A ) @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_11a) ).
thf(1109,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A = B )
| ( C = D )
| ( sameside @ ( insert @ C @ D @ B @ A ) @ B @ A ) )
& ( ( A = B )
| ( C = D )
| ( s_e @ B @ ( insert @ C @ D @ B @ A ) @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A = B )
| ( s_col @ A @ B @ C )
| ( s_col @ A @ B @ D )
| ~ ( s_t @ C @ E @ D )
| ~ ( s_col @ A @ B @ E )
| ( opposite @ C @ A @ B @ D ) )
& ( ~ ( opposite @ C @ A @ B @ D )
| ~ ( s_col @ A @ B @ C ) )
& ( ~ ( opposite @ C @ A @ B @ D )
| ~ ( s_col @ A @ B @ D ) )
& ( ~ ( opposite @ C @ A @ B @ D )
| ( s_t @ C @ ( il @ C @ D @ A @ B ) @ D ) )
& ( ~ ( opposite @ C @ A @ B @ D )
| ( s_col @ A @ B @ ( il @ C @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn9_1) ).
thf(253,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A = B )
| ( s_col @ A @ B @ C )
| ( s_col @ A @ B @ D )
| ~ ( s_t @ C @ E @ D )
| ~ ( s_col @ A @ B @ E )
| ( opposite @ C @ A @ B @ D ) )
& ( ~ ( opposite @ C @ A @ B @ D )
| ~ ( s_col @ A @ B @ C ) )
& ( ~ ( opposite @ C @ A @ B @ D )
| ~ ( s_col @ A @ B @ D ) )
& ( ~ ( opposite @ C @ A @ B @ D )
| ( s_t @ C @ ( il @ C @ D @ A @ B ) @ D ) )
& ( ~ ( opposite @ C @ A @ B @ D )
| ( s_col @ A @ B @ ( il @ C @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_e @ B @ A @ B @ C )
| ( A = C )
| ( s_m @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_20) ).
thf(1136,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_e @ B @ A @ B @ C )
| ( A = C )
| ( s_m @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( C
= ( il @ A @ B @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_14c) ).
thf(238,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( C
= ( il @ A @ B @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_e @ A @ D @ A @ E )
| ~ ( s_e @ B @ D @ B @ E )
| ( s_e @ C @ D @ C @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_17) ).
thf(937,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_e @ A @ D @ A @ E )
| ~ ( s_e @ B @ D @ B @ E )
| ( s_e @ C @ D @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( C = D )
| ( A = B )
| ( perp @ C @ D @ E @ F )
| ~ ( perp @ A @ B @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp5) ).
thf(574,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( C = D )
| ( A = B )
| ( perp @ C @ D @ E @ F )
| ~ ( perp @ A @ B @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_t @ B @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_22b) ).
thf(806,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_t @ B @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( le @ A @ B @ C @ D )
| ~ ( s_e @ A @ B @ E @ F )
| ~ ( s_e @ C @ D @ G @ H )
| ( le @ E @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_6) ).
thf(1051,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( le @ A @ B @ C @ D )
| ~ ( s_e @ A @ B @ E @ F )
| ~ ( s_e @ C @ D @ G @ H )
| ( le @ E @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( le @ A @ B @ C @ D )
| ( s_t @ C @ ( insert @ A @ B @ C @ D ) @ D ) )
& ( ~ ( le @ A @ B @ C @ D )
| ( s_e @ A @ B @ C @ ( insert @ A @ B @ C @ D ) ) )
& ( ~ ( s_t @ C @ E @ D )
| ~ ( s_e @ A @ B @ C @ E )
| ( le @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn5_4) ).
thf(905,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( le @ A @ B @ C @ D )
| ( s_t @ C @ ( insert @ A @ B @ C @ D ) @ D ) )
& ( ~ ( le @ A @ B @ C @ D )
| ( s_e @ A @ B @ C @ ( insert @ A @ B @ C @ D ) ) )
& ( ~ ( s_t @ C @ E @ D )
| ~ ( s_e @ A @ B @ C @ E )
| ( le @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(67,axiom,
! [A: $i,B: $i] : ( s_m @ A @ ( midpoint @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_22) ).
thf(480,plain,
! [A: $i,B: $i] : ( s_m @ A @ ( midpoint @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i] : ( s_e @ A @ B @ ( s @ C @ A ) @ ( s @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_13) ).
thf(1169,plain,
! [A: $i,B: $i,C: $i] : ( s_e @ A @ B @ ( s @ C @ A ) @ ( s @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ( sameside @ A @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_5) ).
thf(734,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( sameside @ A @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i] :
( ~ ( sameside @ A @ B @ C )
| ~ ( sameside @ D @ B @ E )
| ~ ( sameside @ F @ G @ H )
| ~ ( sameside @ I @ G @ J )
| ~ ( s_e3 @ A @ B @ D @ F @ G @ I )
| ( K = B )
| ( L = B )
| ( M = G )
| ( N = G )
| ~ ( sameside @ C @ B @ K )
| ~ ( sameside @ E @ B @ L )
| ~ ( sameside @ H @ G @ M )
| ~ ( sameside @ J @ G @ N )
| ~ ( s_e @ B @ C @ G @ H )
| ~ ( s_e @ B @ E @ G @ J )
| ( s_e @ C @ E @ H @ J ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz11_4d) ).
thf(1072,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i] :
( ~ ( sameside @ A @ B @ C )
| ~ ( sameside @ D @ B @ E )
| ~ ( sameside @ F @ G @ H )
| ~ ( sameside @ I @ G @ J )
| ~ ( s_e3 @ A @ B @ D @ F @ G @ I )
| ( K = B )
| ( L = B )
| ( M = G )
| ( N = G )
| ~ ( sameside @ C @ B @ K )
| ~ ( sameside @ E @ B @ L )
| ~ ( sameside @ H @ G @ M )
| ~ ( sameside @ J @ G @ N )
| ~ ( s_e @ B @ C @ G @ H )
| ~ ( s_e @ B @ E @ G @ J )
| ( s_e @ C @ E @ H @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( s_col @ A @ B @ C )
| ( B = D )
| ~ ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ B @ C @ D @ A )
| ~ ( s_col @ A @ E @ C )
| ~ ( s_col @ B @ E @ D )
| ( s_m @ A @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_21) ).
thf(1119,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( s_col @ A @ B @ C )
| ( B = D )
| ~ ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ B @ C @ D @ A )
| ~ ( s_col @ A @ E @ C )
| ~ ( s_col @ B @ E @ D )
| ( s_m @ A @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ C @ D )
| ( B = C )
| ( s_t @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_7b) ).
thf(428,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ C @ D )
| ( B = C )
| ( s_t @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(76,axiom,
! [A: $i,B: $i] : ( s_t @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_1) ).
thf(527,plain,
! [A: $i,B: $i] : ( s_t @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ( opposite @ D @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_2) ).
thf(265,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ( opposite @ D @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( sameside @ A @ B @ C )
| ( le @ B @ A @ B @ C )
| ~ ( s_t @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_13b) ).
thf(849,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( sameside @ A @ B @ C )
| ( le @ B @ A @ B @ C )
| ~ ( s_t @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ D @ C )
| ( s_t @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_5b) ).
thf(307,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ D @ C )
| ( s_t @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( perp @ A @ B @ C @ D )
| ( perp @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aperp1) ).
thf(292,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( perp @ A @ B @ C @ D )
| ( perp @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_t @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_6) ).
thf(678,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_t @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
| ( perp @ A @ B @ ( erect21a @ A @ B @ C ) @ A )
| ( s_col @ A @ B @ C ) )
& ( ( A = B )
| ( s_col @ A @ B @ ( erectAux21a @ A @ B @ C ) )
| ( s_col @ A @ B @ C ) )
& ( ( A = B )
| ( s_t @ C @ ( erectAux21a @ A @ B @ C ) @ ( erect21a @ A @ B @ C ) )
| ( s_col @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_21a) ).
thf(529,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
| ( perp @ A @ B @ ( erect21a @ A @ B @ C ) @ A )
| ( s_col @ A @ B @ C ) )
& ( ( A = B )
| ( s_col @ A @ B @ ( erectAux21a @ A @ B @ C ) )
| ( s_col @ A @ B @ C ) )
& ( ( A = B )
| ( s_t @ C @ ( erectAux21a @ A @ B @ C ) @ ( erect21a @ A @ B @ C ) )
| ( s_col @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( samesideline @ C @ D @ A @ B )
| ( samesideline @ D @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13d) ).
thf(546,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( samesideline @ C @ D @ A @ B )
| ( samesideline @ D @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( le @ A @ B @ C @ D )
| ~ ( le @ C @ D @ E @ F )
| ( le @ A @ B @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_8) ).
thf(714,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( le @ A @ B @ C @ D )
| ~ ( le @ C @ D @ E @ F )
| ( le @ A @ B @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ B @ D )
| ( s_t @ A @ C @ D )
| ( s_t @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_1) ).
thf(798,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ B @ D )
| ( s_t @ A @ C @ D )
| ( s_t @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_4) ).
thf(1163,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_t @ A @ D @ G ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_t @ C @ D @ E ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_e @ D @ A @ D @ C ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_e @ D @ G @ D @ E ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_m @ A @ B @ C ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_m @ G @ F @ E ) )
& ( ~ ( s_t @ A @ D @ G )
| ~ ( s_t @ C @ D @ E )
| ~ ( s_e @ D @ A @ D @ C )
| ~ ( s_e @ D @ G @ D @ E )
| ~ ( s_m @ A @ B @ C )
| ~ ( s_m @ G @ F @ E )
| ( s_kf @ A @ B @ C @ D @ E @ F @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn7_23) ).
thf(1021,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_t @ A @ D @ G ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_t @ C @ D @ E ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_e @ D @ A @ D @ C ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_e @ D @ G @ D @ E ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_m @ A @ B @ C ) )
& ( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_m @ G @ F @ E ) )
& ( ~ ( s_t @ A @ D @ G )
| ~ ( s_t @ C @ D @ E )
| ~ ( s_e @ D @ A @ D @ C )
| ~ ( s_e @ D @ G @ D @ E )
| ~ ( s_m @ A @ B @ C )
| ~ ( s_m @ G @ F @ E )
| ( s_kf @ A @ B @ C @ D @ E @ F @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_r @ A @ B @ C )
| ( s_r @ A @ B @ ( s @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_4) ).
thf(302,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_r @ A @ B @ C )
| ( s_r @ A @ B @ ( s @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_e @ A @ B @ D @ E ) )
& ( ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_e @ A @ C @ D @ F ) )
& ( ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_e @ B @ C @ E @ F ) )
& ( ~ ( s_e @ A @ B @ D @ E )
| ~ ( s_e @ A @ C @ D @ F )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e3 @ A @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn4_4) ).
thf(1123,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_e @ A @ B @ D @ E ) )
& ( ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_e @ A @ C @ D @ F ) )
& ( ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_e @ B @ C @ E @ F ) )
& ( ~ ( s_e @ A @ B @ D @ E )
| ~ ( s_e @ A @ C @ D @ F )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e3 @ A @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_m @ A @ B @ C )
| ~ ( s_m @ A @ D @ C )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_17) ).
thf(820,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_m @ A @ B @ C )
| ~ ( s_m @ A @ D @ C )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ C @ D )
| ( s_t @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_6a) ).
thf(407,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ C @ D )
| ( s_t @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ D @ C )
| ( s_t @ A @ B @ D )
| ( s_t @ A @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_3) ).
thf(788,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ D @ C )
| ( s_t @ A @ B @ D )
| ( s_t @ A @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ~ ( s_t @ B @ A @ C )
| ( D != A )
| ( s_col @ D @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_15d) ).
thf(729,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ~ ( s_t @ B @ A @ C )
| ( D != A )
| ( s_col @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ B @ E )
| ~ ( s_e @ B @ A @ B @ D )
| ~ ( s_e @ B @ C @ B @ E )
| ~ ( s_m @ A @ F @ D )
| ~ ( s_m @ C @ G @ E )
| ( s_t @ F @ B @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_22) ).
thf(1042,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ B @ E )
| ~ ( s_e @ B @ A @ B @ D )
| ~ ( s_e @ B @ C @ B @ E )
| ~ ( s_m @ A @ F @ D )
| ~ ( s_m @ C @ G @ E )
| ( s_t @ F @ B @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_t @ A @ B @ C ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_t @ E @ F @ G ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ B @ E @ F ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ C @ F @ G ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ D @ E @ H ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ D @ F @ H ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ E @ F @ G )
| ~ ( s_e @ A @ B @ E @ F )
| ~ ( s_e @ B @ C @ F @ G )
| ~ ( s_e @ A @ D @ E @ H )
| ~ ( s_e @ B @ D @ F @ H )
| ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn2_10) ).
thf(952,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_t @ A @ B @ C ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_t @ E @ F @ G ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ B @ E @ F ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ C @ F @ G ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ A @ D @ E @ H ) )
& ( ~ ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ D @ F @ H ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ E @ F @ G )
| ~ ( s_e @ A @ B @ E @ F )
| ~ ( s_e @ B @ C @ F @ G )
| ~ ( s_e @ A @ D @ E @ H )
| ~ ( s_e @ B @ D @ F @ H )
| ( s_afs @ A @ B @ C @ D @ E @ F @ G @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( C = B )
| ( D = B )
| ~ ( s_t @ A @ B @ D )
| ( s_t @ C @ B @ D )
| ~ ( sameside @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_2b) ).
thf(484,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( C = B )
| ( D = B )
| ~ ( s_t @ A @ B @ D )
| ( s_t @ C @ B @ D )
| ~ ( sameside @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_col @ A @ B @ C )
| ( A = B )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_9) ).
thf(830,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_col @ A @ B @ C )
| ( A = B )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ( s_e @ C @ D @ ( reflect @ A @ B @ C ) @ ( reflect @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_10a) ).
thf(1159,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ( s_e @ C @ D @ ( reflect @ A @ B @ C ) @ ( reflect @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ( s_col @ A @ B @ D )
| ( perp @ A @ B @ ( erectsameside @ A @ B @ C @ D ) @ C ) )
& ( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ( s_col @ A @ B @ D )
| ( samesideline @ ( erectsameside @ A @ B @ C @ D ) @ D @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_15) ).
thf(842,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ( s_col @ A @ B @ D )
| ( perp @ A @ B @ ( erectsameside @ A @ B @ C @ D ) @ C ) )
& ( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ( s_col @ A @ B @ D )
| ( samesideline @ ( erectsameside @ A @ B @ C @ D ) @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ( B = C )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_col @ B @ C @ F )
| ~ ( perp @ B @ C @ A @ F )
| ~ ( perp @ B @ C @ D @ E )
| ~ ( s_m @ F @ G @ E )
| ~ ( sameside @ H @ F @ A )
| ~ ( le @ E @ D @ F @ A )
| ( F = E )
| ( sameside @ ( s @ G @ H ) @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_4a) ).
thf(578,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ( B = C )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_col @ B @ C @ F )
| ~ ( perp @ B @ C @ A @ F )
| ~ ( perp @ B @ C @ D @ E )
| ~ ( s_m @ F @ G @ E )
| ~ ( sameside @ H @ F @ A )
| ~ ( le @ E @ D @ F @ A )
| ( F = E )
| ( sameside @ ( s @ G @ H ) @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_r @ A @ B @ C )
| ( A = B )
| ~ ( s_col @ B @ A @ D )
| ( s_r @ D @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_3) ).
thf(615,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_r @ A @ B @ C )
| ( A = B )
| ~ ( s_col @ B @ A @ D )
| ( s_r @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( s @ A @ B )
!= ( s @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_18) ).
thf(403,plain,
! [A: $i,B: $i,C: $i] :
( ( ( s @ A @ B )
!= ( s @ C @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_t @ A @ B @ C )
| ~ ( le @ A @ B @ A @ C )
| ~ ( le @ B @ C @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_12b) ).
thf(499,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_t @ A @ B @ C )
| ~ ( le @ A @ B @ A @ C )
| ~ ( le @ B @ C @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_t @ A @ B @ C )
| ( s_t @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_2) ).
thf(471,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_t @ A @ B @ C )
| ( s_t @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ C @ D @ E )
| ( s_t @ D @ ( insert @ A @ B @ D @ E ) @ E ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ C @ D @ E )
| ( s_e3 @ A @ B @ C @ D @ ( insert @ A @ B @ D @ E ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_5) ).
thf(1082,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ C @ D @ E )
| ( s_t @ D @ ( insert @ A @ B @ D @ E ) @ E ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ C @ D @ E )
| ( s_e3 @ A @ B @ C @ D @ ( insert @ A @ B @ D @ E ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ( s_t @ ( s @ D @ A ) @ ( s @ D @ B ) @ ( s @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_15a) ).
thf(488,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ( s_t @ ( s @ D @ A ) @ ( s @ D @ B ) @ ( s @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( samesideline @ A @ B @ C @ D )
| ( s_col @ C @ D @ ( ss1 @ A @ B @ C @ D ) ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ( s_col @ C @ D @ ( ss2 @ A @ B @ C @ D ) ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ( s_t @ A @ ( ss1 @ A @ B @ C @ D ) @ ( ss3 @ A @ B @ C @ D ) ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ( s_t @ B @ ( ss2 @ A @ B @ C @ D ) @ ( ss3 @ A @ B @ C @ D ) ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ( A
!= ( ss1 @ A @ B @ C @ D ) ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ( B
!= ( ss2 @ A @ B @ C @ D ) ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ( ( ss3 @ A @ B @ C @ D )
!= ( ss1 @ A @ B @ C @ D ) ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ( ( ss3 @ A @ B @ C @ D )
!= ( ss2 @ A @ B @ C @ D ) ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ( C != D ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ~ ( s_col @ C @ D @ A ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ~ ( s_col @ C @ D @ B ) )
& ( ~ ( s_t @ A @ E @ F )
| ~ ( s_t @ B @ G @ F )
| ~ ( s_col @ C @ D @ E )
| ~ ( s_col @ C @ D @ G )
| ( C = D )
| ( F = E )
| ( F = G )
| ( A = E )
| ( B = G )
| ( s_col @ C @ D @ A )
| ( s_col @ C @ D @ B )
| ( samesideline @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn9_7) ).
thf(753,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( samesideline @ A @ B @ C @ D )
| ( s_col @ C @ D @ ( ss1 @ A @ B @ C @ D ) ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ( s_col @ C @ D @ ( ss2 @ A @ B @ C @ D ) ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ( s_t @ A @ ( ss1 @ A @ B @ C @ D ) @ ( ss3 @ A @ B @ C @ D ) ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ( s_t @ B @ ( ss2 @ A @ B @ C @ D ) @ ( ss3 @ A @ B @ C @ D ) ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ( A
!= ( ss1 @ A @ B @ C @ D ) ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ( B
!= ( ss2 @ A @ B @ C @ D ) ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ( ( ss3 @ A @ B @ C @ D )
!= ( ss1 @ A @ B @ C @ D ) ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ( ( ss3 @ A @ B @ C @ D )
!= ( ss2 @ A @ B @ C @ D ) ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ( C != D ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ~ ( s_col @ C @ D @ A ) )
& ( ~ ( samesideline @ A @ B @ C @ D )
| ~ ( s_col @ C @ D @ B ) )
& ( ~ ( s_t @ A @ E @ F )
| ~ ( s_t @ B @ G @ F )
| ~ ( s_col @ C @ D @ E )
| ~ ( s_col @ C @ D @ G )
| ( C = D )
| ( F = E )
| ( F = G )
| ( A = E )
| ( B = G )
| ( s_col @ C @ D @ A )
| ( s_col @ C @ D @ B )
| ( samesideline @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ B @ A @ D )
| ~ ( s_e @ C @ B @ C @ D )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_19) ).
thf(901,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ B @ A @ D )
| ~ ( s_e @ C @ B @ C @ D )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ( s_col @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_17b) ).
thf(637,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ( s_col @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A = B )
| ( C = B )
| ( D = E )
| ( F = E )
| ( sameside @ ( f113a @ A @ B @ C @ D @ E @ F ) @ B @ A )
| ( congruent @ A @ B @ C @ D @ E @ F ) )
& ( ( A = B )
| ( C = B )
| ( D = E )
| ( F = E )
| ( sameside @ ( f113c @ A @ B @ C @ D @ E @ F ) @ B @ C )
| ( congruent @ A @ B @ C @ D @ E @ F ) )
& ( ( A = B )
| ( C = B )
| ( D = E )
| ( F = E )
| ( sameside @ ( f113d @ A @ B @ C @ D @ E @ F ) @ E @ D )
| ( congruent @ A @ B @ C @ D @ E @ F ) )
& ( ( A = B )
| ( C = B )
| ( D = E )
| ( F = E )
| ( sameside @ ( f113f @ A @ B @ C @ D @ E @ F ) @ E @ F )
| ( congruent @ A @ B @ C @ D @ E @ F ) )
& ( ( A = B )
| ( C = B )
| ( D = E )
| ( F = E )
| ( s_e @ B @ ( f113a @ A @ B @ C @ D @ E @ F ) @ E @ ( f113d @ A @ B @ C @ D @ E @ F ) )
| ( congruent @ A @ B @ C @ D @ E @ F ) )
& ( ( A = B )
| ( C = B )
| ( D = E )
| ( F = E )
| ( s_e @ B @ ( f113c @ A @ B @ C @ D @ E @ F ) @ E @ ( f113f @ A @ B @ C @ D @ E @ F ) )
| ( congruent @ A @ B @ C @ D @ E @ F ) )
& ( ( A = B )
| ( C = B )
| ( D = E )
| ( F = E )
| ~ ( s_e @ ( f113a @ A @ B @ C @ D @ E @ F ) @ ( f113c @ A @ B @ C @ D @ E @ F ) @ ( f113d @ A @ B @ C @ D @ E @ F ) @ ( f113f @ A @ B @ C @ D @ E @ F ) )
| ( congruent @ A @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz11_4b) ).
thf(970,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A = B )
| ( C = B )
| ( D = E )
| ( F = E )
| ( sameside @ ( f113a @ A @ B @ C @ D @ E @ F ) @ B @ A )
| ( congruent @ A @ B @ C @ D @ E @ F ) )
& ( ( A = B )
| ( C = B )
| ( D = E )
| ( F = E )
| ( sameside @ ( f113c @ A @ B @ C @ D @ E @ F ) @ B @ C )
| ( congruent @ A @ B @ C @ D @ E @ F ) )
& ( ( A = B )
| ( C = B )
| ( D = E )
| ( F = E )
| ( sameside @ ( f113d @ A @ B @ C @ D @ E @ F ) @ E @ D )
| ( congruent @ A @ B @ C @ D @ E @ F ) )
& ( ( A = B )
| ( C = B )
| ( D = E )
| ( F = E )
| ( sameside @ ( f113f @ A @ B @ C @ D @ E @ F ) @ E @ F )
| ( congruent @ A @ B @ C @ D @ E @ F ) )
& ( ( A = B )
| ( C = B )
| ( D = E )
| ( F = E )
| ( s_e @ B @ ( f113a @ A @ B @ C @ D @ E @ F ) @ E @ ( f113d @ A @ B @ C @ D @ E @ F ) )
| ( congruent @ A @ B @ C @ D @ E @ F ) )
& ( ( A = B )
| ( C = B )
| ( D = E )
| ( F = E )
| ( s_e @ B @ ( f113c @ A @ B @ C @ D @ E @ F ) @ E @ ( f113f @ A @ B @ C @ D @ E @ F ) )
| ( congruent @ A @ B @ C @ D @ E @ F ) )
& ( ( A = B )
| ( C = B )
| ( D = E )
| ( F = E )
| ~ ( s_e @ ( f113a @ A @ B @ C @ D @ E @ F ) @ ( f113c @ A @ B @ C @ D @ E @ F ) @ ( f113d @ A @ B @ C @ D @ E @ F ) @ ( f113f @ A @ B @ C @ D @ E @ F ) )
| ( congruent @ A @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( perp @ A @ B @ C @ D )
| ( perp @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp4) ).
thf(706,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( perp @ A @ B @ C @ D )
| ( perp @ A @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( sameside @ A @ B @ C )
| ( s_col @ A @ B @ C ) )
& ( ~ ( sameside @ A @ B @ C )
| ~ ( s_t @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_4a) ).
thf(393,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( sameside @ A @ B @ C )
| ( s_col @ A @ B @ C ) )
& ( ~ ( sameside @ A @ B @ C )
| ~ ( s_t @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_r @ D @ B @ E )
| ~ ( s_e @ A @ B @ D @ B )
| ~ ( s_e @ B @ C @ B @ E )
| ( s_e @ A @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_12a) ).
thf(997,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_r @ D @ B @ E )
| ~ ( s_e @ A @ B @ D @ B )
| ~ ( s_e @ B @ C @ B @ E )
| ( s_e @ A @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( ( s @ A @ B )
!= B )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_10a) ).
thf(457,plain,
! [A: $i,B: $i] :
( ( ( s @ A @ B )
!= B )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( samesideline @ A @ B @ C @ D )
| ( samesideline @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13a) ).
thf(721,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( samesideline @ A @ B @ C @ D )
| ( samesideline @ A @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A = B )
| ( C = D )
| ~ ( s_col @ A @ B @ E )
| ~ ( s_col @ C @ D @ E )
| ~ ( s_col @ A @ B @ F )
| ~ ( s_col @ C @ D @ F )
| ( E = F )
| ~ ( s_col @ A @ B @ G )
| ( s_col @ C @ D @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_21) ).
thf(343,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A = B )
| ( C = D )
| ~ ( s_col @ A @ B @ E )
| ~ ( s_col @ C @ D @ E )
| ~ ( s_col @ A @ B @ F )
| ~ ( s_col @ C @ D @ F )
| ( E = F )
| ~ ( s_col @ A @ B @ G )
| ( s_col @ C @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( perp @ A @ B @ C @ D )
| ( perpAt @ A @ B @ ( il @ A @ B @ C @ D ) @ C @ D ) )
& ( ( perp @ A @ B @ C @ D )
| ~ ( perpAt @ A @ B @ E @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn8_11b) ).
thf(244,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( perp @ A @ B @ C @ D )
| ( perpAt @ A @ B @ ( il @ A @ B @ C @ D ) @ C @ D ) )
& ( ( perp @ A @ B @ C @ D )
| ~ ( perpAt @ A @ B @ E @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A = B )
| ( s_col @ A @ B @ C )
| ( s_col @ D @ E @ F )
| ~ ( s_e @ A @ B @ D @ E )
| ( s_e3 @ A @ B @ C @ D @ E @ ( triangle @ A @ B @ C @ D @ E @ F ) ) )
& ( ( A = B )
| ( s_col @ A @ B @ C )
| ( s_col @ D @ E @ F )
| ~ ( s_e @ A @ B @ D @ E )
| ( samesideline @ ( triangle @ A @ B @ C @ D @ E @ F ) @ F @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_16a) ).
thf(1202,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A = B )
| ( s_col @ A @ B @ C )
| ( s_col @ D @ E @ F )
| ~ ( s_e @ A @ B @ D @ E )
| ( s_e3 @ A @ B @ C @ D @ E @ ( triangle @ A @ B @ C @ D @ E @ F ) ) )
& ( ( A = B )
| ( s_col @ A @ B @ C )
| ( s_col @ D @ E @ F )
| ~ ( s_e @ A @ B @ D @ E )
| ( samesideline @ ( triangle @ A @ B @ C @ D @ E @ F ) @ F @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( samesideline @ C @ D @ A @ B )
| ( samesideline @ C @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtSameSide2) ).
thf(633,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( samesideline @ C @ D @ A @ B )
| ( samesideline @ C @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A = B )
| ( s_col @ A @ B @ C )
| ( s_col @ D @ E @ F )
| ~ ( s_e @ A @ B @ D @ E )
| ~ ( s_e3 @ A @ B @ C @ D @ E @ G )
| ~ ( samesideline @ G @ F @ D @ E )
| ~ ( s_e3 @ A @ B @ C @ D @ E @ H )
| ~ ( samesideline @ H @ F @ D @ E )
| ( G = H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_16b) ).
thf(1054,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A = B )
| ( s_col @ A @ B @ C )
| ( s_col @ D @ E @ F )
| ~ ( s_e @ A @ B @ D @ E )
| ~ ( s_e3 @ A @ B @ C @ D @ E @ G )
| ~ ( samesideline @ G @ F @ D @ E )
| ~ ( s_e3 @ A @ B @ C @ D @ E @ H )
| ~ ( samesideline @ H @ F @ D @ E )
| ( G = H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(40,axiom,
! [A: $i,B: $i] : ( s_t @ A @ B @ ( ext @ A @ B @ alpha @ gamma ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_14a) ).
thf(398,plain,
! [A: $i,B: $i] : ( s_t @ A @ B @ ( ext @ A @ B @ alpha @ gamma ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ~ ( s_col @ B @ C @ E )
| ~ ( sameside @ A @ E @ F )
| ( opposite @ F @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_5) ).
thf(586,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ~ ( s_col @ B @ C @ E )
| ~ ( sameside @ A @ E @ F )
| ( opposite @ F @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( s_col @ A @ B @ C )
| ( s_col @ A @ B @ D )
| ( samesideline @ C @ D @ A @ B )
| ( opposite @ C @ A @ B @ D )
| ( A
!= ( foot @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13f_case1) ).
thf(298,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( s_col @ A @ B @ C )
| ( s_col @ A @ B @ D )
| ( samesideline @ C @ D @ A @ B )
| ( opposite @ C @ A @ B @ D )
| ( A
!= ( foot @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ~ ( s_t @ B @ A @ C )
| ~ ( s_col @ D @ A @ B )
| ( D = A )
| ( sameside @ D @ A @ B )
| ( sameside @ D @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_15a) ).
thf(412,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ~ ( s_t @ B @ A @ C )
| ~ ( s_col @ D @ A @ B )
| ( D = A )
| ( sameside @ D @ A @ B )
| ( sameside @ D @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ~ ( s_m @ A @ B @ A )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_3a) ).
thf(425,plain,
! [A: $i,B: $i] :
( ~ ( s_m @ A @ B @ A )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_m @ A @ B @ C )
| ( s_m @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_2) ).
thf(824,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_m @ A @ B @ C )
| ( s_m @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( perp @ A @ B @ D @ C )
| ( perpAt @ A @ B @ C @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_15) ).
thf(745,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( perp @ A @ B @ D @ C )
| ( perpAt @ A @ B @ C @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( perpAt @ D @ E @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_12a) ).
thf(279,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( perpAt @ D @ E @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( s_m @ A @ B @ A )
| ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_3b) ).
thf(444,plain,
! [A: $i,B: $i] :
( ( s_m @ A @ B @ A )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ~ ( s_r @ A @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_8) ).
thf(562,plain,
! [A: $i,B: $i] :
( ~ ( s_r @ A @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( ( reflect @ A @ B @ C )
!= D )
| ( s_col @ A @ B @ C )
| ( opposite @ C @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_14) ).
thf(694,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( ( reflect @ A @ B @ C )
!= D )
| ( s_col @ A @ B @ C )
| ( opposite @ C @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( s_col @ A @ B @ C )
| ( A = B )
| ( A = C )
| ~ ( samesideline @ D @ E @ A @ B )
| ( samesideline @ D @ E @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtSameSide1) ).
thf(826,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( s_col @ A @ B @ C )
| ( A = B )
| ( A = C )
| ~ ( samesideline @ D @ E @ A @ B )
| ( samesideline @ D @ E @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(15,axiom,
alpha != gamma,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_13c) ).
thf(281,plain,
alpha != gamma,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( C = A )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( s_col @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_16b) ).
thf(641,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( C = A )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( s_col @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( s_col @ A @ B @ C )
| ( s_t @ A @ B @ C )
| ( s_t @ B @ C @ A )
| ( s_t @ C @ A @ B ) )
& ( ( s_col @ A @ B @ C )
| ~ ( s_t @ A @ B @ C ) )
& ( ( s_col @ A @ B @ C )
| ~ ( s_t @ B @ C @ A ) )
& ( ( s_col @ A @ B @ C )
| ~ ( s_t @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn4_10) ).
thf(382,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( s_col @ A @ B @ C )
| ( s_t @ A @ B @ C )
| ( s_t @ B @ C @ A )
| ( s_t @ C @ A @ B ) )
& ( ( s_col @ A @ B @ C )
| ~ ( s_t @ A @ B @ C ) )
& ( ( s_col @ A @ B @ C )
| ~ ( s_t @ B @ C @ A ) )
& ( ( s_col @ A @ B @ C )
| ~ ( s_t @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( A = B )
| ( s_col @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aext1) ).
thf(611,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( A = B )
| ( s_col @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ ( s @ E @ A ) @ ( s @ E @ B ) @ ( s @ E @ C ) @ ( s @ E @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_16a) ).
thf(1058,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ ( s @ E @ A ) @ ( s @ E @ B ) @ ( s @ E @ C ) @ ( s @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ D @ F @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_2) ).
thf(1092,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( s_ifs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( s_e @ B @ D @ F @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ A @ C )
| ( s_m @ B @ ( isomidpoint @ B @ C @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_25) ).
thf(1090,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ A @ C )
| ( s_m @ B @ ( isomidpoint @ B @ C @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ A @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11e) ).
thf(391,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ~ ( sameside @ A @ B @ C )
| ~ ( sameside @ D @ B @ E )
| ~ ( sameside @ F @ G @ H )
| ~ ( sameside @ I @ G @ J )
| ~ ( s_e3 @ A @ B @ D @ F @ G @ I )
| ( congruent @ C @ B @ E @ H @ G @ J ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz11_3d) ).
thf(1139,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ~ ( sameside @ A @ B @ C )
| ~ ( sameside @ D @ B @ E )
| ~ ( sameside @ F @ G @ H )
| ~ ( sameside @ I @ G @ J )
| ~ ( s_e3 @ A @ B @ D @ F @ G @ I )
| ( congruent @ C @ B @ E @ H @ G @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(92,axiom,
! [A: $i,B: $i] : ( s_r @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_5) ).
thf(604,plain,
! [A: $i,B: $i] : ( s_r @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A = B )
| ( C = D )
| ~ ( sameside @ E @ B @ A )
| ~ ( s_e @ B @ E @ C @ D )
| ~ ( sameside @ F @ B @ A )
| ~ ( s_e @ B @ F @ C @ D )
| ( E = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_11b) ).
thf(1194,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A = B )
| ( C = D )
| ~ ( sameside @ E @ B @ A )
| ~ ( s_e @ B @ E @ C @ D )
| ~ ( sameside @ F @ B @ A )
| ~ ( s_e @ B @ F @ C @ D )
| ( E = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ F )
| ~ ( s_e @ A @ B @ D @ E )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_11) ).
thf(1209,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ F )
| ~ ( s_e @ A @ B @ D @ E )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11b) ).
thf(681,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ( B = C )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_col @ B @ C @ F )
| ~ ( perp @ B @ C @ A @ F )
| ~ ( perp @ B @ C @ D @ E )
| ~ ( s_m @ F @ G @ E )
| ~ ( sameside @ H @ F @ A )
| ( sameside @ ( s @ G @ H ) @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_4) ).
thf(784,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ( B = C )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_col @ B @ C @ F )
| ~ ( perp @ B @ C @ A @ F )
| ~ ( perp @ B @ C @ D @ E )
| ~ ( s_m @ F @ G @ E )
| ~ ( sameside @ H @ F @ A )
| ( sameside @ ( s @ G @ H ) @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ~ ( sameside @ G @ B @ A )
| ~ ( sameside @ H @ B @ C )
| ~ ( sameside @ I @ E @ D )
| ~ ( sameside @ J @ E @ F )
| ~ ( s_e @ B @ G @ E @ I )
| ~ ( s_e @ B @ H @ E @ J )
| ( s_e @ G @ H @ I @ J ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz11_4) ).
thf(1048,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ~ ( sameside @ G @ B @ A )
| ~ ( sameside @ H @ B @ C )
| ~ ( sameside @ I @ E @ D )
| ~ ( sameside @ J @ E @ F )
| ~ ( s_e @ B @ G @ E @ I )
| ~ ( s_e @ B @ H @ E @ J )
| ( s_e @ G @ H @ I @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ~ ( s_e @ B @ A @ E @ D )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz11_49a) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ~ ( s_e @ B @ A @ E @ D )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ C @ D @ F ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(230,plain,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ~ ( s_e @ B @ A @ E @ D )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_r @ D @ B @ C )
| ~ ( s_t @ A @ C @ D )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_6) ).
thf(451,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_r @ D @ B @ C )
| ~ ( s_t @ A @ C @ D )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ( B = C )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_col @ B @ C @ F )
| ~ ( perp @ B @ C @ A @ F )
| ~ ( perp @ B @ C @ D @ E )
| ~ ( s_m @ F @ G @ E )
| ( sameside @ H @ F @ A )
| ~ ( le @ E @ D @ F @ A )
| ( F = E )
| ~ ( sameside @ ( s @ G @ H ) @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_4a2) ).
thf(737,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ( B = C )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_col @ B @ C @ F )
| ~ ( perp @ B @ C @ A @ F )
| ~ ( perp @ B @ C @ D @ E )
| ~ ( s_m @ F @ G @ E )
| ( sameside @ H @ F @ A )
| ~ ( le @ E @ D @ F @ A )
| ( F = E )
| ~ ( sameside @ ( s @ G @ H ) @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ C @ D )
| ( s_t @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_6b) ).
thf(434,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ C @ D )
| ( s_t @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ~ ( samesideline @ A @ D @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_9) ).
thf(271,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ~ ( samesideline @ A @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ( sameside @ ( ext @ B @ A @ E @ D ) @ B @ A ) )
& ( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ( sameside @ ( ext @ B @ C @ E @ F ) @ B @ C ) )
& ( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ( sameside @ ( ext @ E @ D @ B @ A ) @ E @ D ) )
& ( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ( sameside @ ( ext @ E @ F @ B @ C ) @ E @ F ) )
& ( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ( s_e3 @ ( ext @ B @ A @ E @ D ) @ B @ ( ext @ B @ C @ E @ F ) @ ( ext @ E @ D @ B @ A ) @ E @ ( ext @ E @ F @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz11_3a) ).
thf(1175,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ( sameside @ ( ext @ B @ A @ E @ D ) @ B @ A ) )
& ( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ( sameside @ ( ext @ B @ C @ E @ F ) @ B @ C ) )
& ( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ( sameside @ ( ext @ E @ D @ B @ A ) @ E @ D ) )
& ( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ( sameside @ ( ext @ E @ F @ B @ C ) @ E @ F ) )
& ( ~ ( congruent @ A @ B @ C @ D @ E @ F )
| ( s_e3 @ ( ext @ B @ A @ E @ D ) @ B @ ( ext @ B @ C @ E @ F ) @ ( ext @ E @ D @ B @ A ) @ E @ ( ext @ E @ F @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ( s_col @ A @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_17a) ).
thf(477,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( s_col @ A @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_2) ).
thf(1080,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ C @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_r @ A @ B @ C )
| ( s_r @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_2) ).
thf(631,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_r @ A @ B @ C )
| ( s_r @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ( B = C )
| ( D = C )
| ( A = D )
| ~ ( perp @ B @ A @ A @ C )
| ~ ( s_col @ A @ C @ D )
| ( perp @ B @ A @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp3) ).
thf(816,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ( B = C )
| ( D = C )
| ( A = D )
| ~ ( perp @ B @ A @ A @ C )
| ~ ( s_col @ A @ C @ D )
| ( perp @ B @ A @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( s @ A @ B )
!= ( s @ A @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_9) ).
thf(323,plain,
! [A: $i,B: $i,C: $i] :
( ( ( s @ A @ B )
!= ( s @ A @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( sameside @ A @ B @ C )
| ~ ( sameside @ C @ B @ D )
| ( sameside @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_7) ).
thf(621,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( sameside @ A @ B @ C )
| ~ ( sameside @ C @ B @ D )
| ( sameside @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( s_m @ A @ B @ C )
| ( s_t @ A @ B @ C ) )
& ( ~ ( s_m @ A @ B @ C )
| ( s_e @ B @ A @ B @ C ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ B @ A @ B @ C )
| ( s_m @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn7_1) ).
thf(1149,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( s_m @ A @ B @ C )
| ( s_t @ A @ B @ C ) )
& ( ~ ( s_m @ A @ B @ C )
| ( s_e @ B @ A @ B @ C ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ B @ A @ B @ C )
| ( s_m @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ~ ( s_t @ A @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA6) ).
thf(330,plain,
! [A: $i,B: $i] :
( ~ ( s_t @ A @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(167,axiom,
! [A: $i,B: $i] : ( s_e @ A @ B @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA1) ).
thf(932,plain,
! [A: $i,B: $i] : ( s_e @ A @ B @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( perp @ A @ B @ B @ C )
| ~ ( perp @ D @ C @ B @ C )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_t @ A @ E @ D )
| ~ ( s_t @ C @ F @ D )
| ~ ( s_e @ B @ A @ C @ F )
| ( G
!= ( ip @ A @ E @ D @ C @ F ) )
| ( s_m @ A @ G @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_24b) ).
thf(1061,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( perp @ A @ B @ B @ C )
| ~ ( perp @ D @ C @ B @ C )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_t @ A @ E @ D )
| ~ ( s_t @ C @ F @ D )
| ~ ( s_e @ B @ A @ C @ F )
| ( G
!= ( ip @ A @ E @ D @ C @ F ) )
| ( s_m @ A @ G @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ( C = B )
| ( congruent @ A @ B @ C @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz11_6) ).
thf(1198,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ( C = B )
| ( congruent @ A @ B @ C @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ C @ A @ B )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aNarbouxLemma1) ).
thf(1066,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ C @ A @ B )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_t @ A @ B @ C )
| ( le @ A @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_12a1) ).
thf(455,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_t @ A @ B @ C )
| ( le @ A @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ F )
| ~ ( s_e @ A @ B @ E @ F )
| ~ ( s_e @ B @ C @ D @ E )
| ( s_e @ A @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_15) ).
thf(1015,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ F )
| ~ ( s_e @ A @ B @ E @ F )
| ~ ( s_e @ B @ C @ D @ E )
| ( s_e @ A @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( sameside @ A @ B @ C )
| ( sameside @ ( s @ D @ A ) @ ( s @ D @ B ) @ ( s @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSideReflect) ).
thf(608,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( sameside @ A @ B @ C )
| ( sameside @ ( s @ D @ A ) @ ( s @ D @ B ) @ ( s @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s_t @ A @ B @ ( ext @ A @ B @ C @ D ) )
& ( s_e @ B @ ( ext @ A @ B @ C @ D ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA4) ).
thf(1000,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s_t @ A @ B @ ( ext @ A @ B @ C @ D ) )
& ( s_e @ B @ ( ext @ A @ B @ C @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( s_col @ A @ B @ C ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( s_col @ D @ E @ C ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( A != B ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( D != E ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ~ ( s_col @ A @ B @ F )
| ~ ( s_col @ D @ E @ G )
| ( s_r @ F @ C @ G ) )
& ( ( perpAt @ A @ B @ C @ D @ E )
| ( A = B )
| ( D = E )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ D @ E @ C )
| ( s_col @ A @ B @ ( f811 @ A @ B @ D @ E @ C ) ) )
& ( ( perpAt @ A @ B @ C @ D @ E )
| ( A = B )
| ( D = E )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ D @ E @ C )
| ( s_col @ D @ E @ ( g811 @ A @ B @ D @ E @ C ) ) )
& ( ( perpAt @ A @ B @ C @ D @ E )
| ( A = B )
| ( D = E )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ D @ E @ C )
| ~ ( s_r @ ( f811 @ A @ B @ D @ E @ C ) @ C @ ( g811 @ A @ B @ D @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn8_11a) ).
thf(505,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( s_col @ A @ B @ C ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( s_col @ D @ E @ C ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( A != B ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( D != E ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ~ ( s_col @ A @ B @ F )
| ~ ( s_col @ D @ E @ G )
| ( s_r @ F @ C @ G ) )
& ( ( perpAt @ A @ B @ C @ D @ E )
| ( A = B )
| ( D = E )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ D @ E @ C )
| ( s_col @ A @ B @ ( f811 @ A @ B @ D @ E @ C ) ) )
& ( ( perpAt @ A @ B @ C @ D @ E )
| ( A = B )
| ( D = E )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ D @ E @ C )
| ( s_col @ D @ E @ ( g811 @ A @ B @ D @ E @ C ) ) )
& ( ( perpAt @ A @ B @ C @ D @ E )
| ( A = B )
| ( D = E )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ D @ E @ C )
| ~ ( s_r @ ( f811 @ A @ B @ D @ E @ C ) @ C @ ( g811 @ A @ B @ D @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_r @ D @ B @ E )
| ~ ( s_e @ A @ B @ D @ B )
| ~ ( s_e @ B @ C @ B @ E )
| ( s_e @ A @ C @ D @ E )
| ( B
!= ( midpoint @ C @ E ) )
| ( C = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_12c) ).
thf(912,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_r @ D @ B @ E )
| ~ ( s_e @ A @ B @ D @ B )
| ~ ( s_e @ B @ C @ B @ E )
| ( s_e @ A @ C @ D @ E )
| ( B
!= ( midpoint @ C @ E ) )
| ( C = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ C @ C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_13) ).
thf(1171,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ C @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( perpAt @ A @ B @ C @ D @ C )
| ~ ( perpAt @ A @ B @ C @ E @ C )
| ( D = C )
| ( s_col @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13g) ).
thf(267,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( perpAt @ A @ B @ C @ D @ C )
| ~ ( perpAt @ A @ B @ C @ E @ C )
| ( D = C )
| ( s_col @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
| ( perp @ A @ B @ ( erect @ A @ B @ C ) @ A ) )
& ( ( A = B )
| ( s_col @ A @ B @ ( erectAux @ A @ B @ C ) ) )
& ( ( A = B )
| ( s_t @ C @ ( erectAux @ A @ B @ C ) @ ( erect @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_21) ).
thf(851,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
| ( perp @ A @ B @ ( erect @ A @ B @ C ) @ A ) )
& ( ( A = B )
| ( s_col @ A @ B @ ( erectAux @ A @ B @ C ) ) )
& ( ( A = B )
| ( s_t @ C @ ( erectAux @ A @ B @ C ) @ ( erect @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(5,axiom,
beta != gamma,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_13b) ).
thf(241,plain,
beta != gamma,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(106,axiom,
! [A: $i,B: $i] : ( le @ A @ B @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_7) ).
thf(653,plain,
! [A: $i,B: $i] : ( le @ A @ B @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( le @ A @ B @ C @ D )
| ~ ( perp @ A @ C @ A @ B )
| ~ ( perp @ A @ C @ C @ D )
| ~ ( s_t @ B @ E @ D )
| ~ ( s_col @ A @ C @ E )
| ( s_m @ A @ ( midpointAux @ A @ C @ B @ D @ E ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_22b) ).
thf(675,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( le @ A @ B @ C @ D )
| ~ ( perp @ A @ C @ A @ B )
| ~ ( perp @ A @ C @ C @ D )
| ~ ( s_t @ B @ E @ D )
| ~ ( s_col @ A @ C @ E )
| ( s_m @ A @ ( midpointAux @ A @ C @ B @ D @ E ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( sameside @ A @ B @ C )
| ( A != B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( C != B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( ( c63 @ A @ B @ C )
!= B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( s_t @ A @ B @ ( c63 @ A @ B @ C ) ) )
& ( ~ ( sameside @ A @ B @ C )
| ( s_t @ C @ B @ ( c63 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_3a) ).
thf(589,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( sameside @ A @ B @ C )
| ( A != B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( C != B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( ( c63 @ A @ B @ C )
!= B ) )
& ( ~ ( sameside @ A @ B @ C )
| ( s_t @ A @ B @ ( c63 @ A @ B @ C ) ) )
& ( ~ ( sameside @ A @ B @ C )
| ( s_t @ C @ B @ ( c63 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_m @ A @ E @ D )
| ~ ( s_col @ B @ C @ F )
| ~ ( sameside @ A @ F @ G )
| ( opposite @ G @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_3) ).
thf(795,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_m @ A @ E @ D )
| ~ ( s_col @ B @ C @ F )
| ~ ( sameside @ A @ F @ G )
| ( opposite @ G @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_t @ B @ A @ C )
| ~ ( samesideline @ D @ E @ C @ B )
| ( samesideline @ D @ E @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13c) ).
thf(663,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_t @ B @ A @ C )
| ~ ( samesideline @ D @ E @ C @ B )
| ( samesideline @ D @ E @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A = B )
| ( C = D )
| ~ ( s_col @ C @ D @ E )
| ~ ( s_col @ A @ B @ E )
| ~ ( s_col @ A @ B @ F )
| ~ ( s_col @ C @ D @ G )
| ( E = F )
| ( E = G )
| ~ ( s_r @ F @ E @ G )
| ( perpAt @ A @ B @ E @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_13b) ).
thf(812,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A = B )
| ( C = D )
| ~ ( s_col @ C @ D @ E )
| ~ ( s_col @ A @ B @ E )
| ~ ( s_col @ A @ B @ F )
| ~ ( s_col @ C @ D @ G )
| ( E = F )
| ( E = G )
| ~ ( s_r @ F @ E @ G )
| ( perpAt @ A @ B @ E @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( perp @ A @ B @ C @ D )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_14a) ).
thf(749,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( perp @ A @ B @ C @ D )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( sameside @ A @ B @ C )
| ~ ( le @ B @ A @ B @ C )
| ( s_t @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_13a) ).
thf(473,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( sameside @ A @ B @ C )
| ~ ( le @ B @ A @ B @ C )
| ( s_t @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_e @ A @ C @ A @ D )
| ~ ( s_e @ B @ C @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_18) ).
thf(1076,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_e @ A @ C @ A @ D )
| ~ ( s_e @ B @ C @ B @ D )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(209,axiom,
! [A: $i,B: $i] : ( s_e @ A @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_8) ).
thf(1134,plain,
! [A: $i,B: $i] : ( s_e @ A @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ B )
| ( s_t @ A @ ( op @ E @ D @ C @ B @ A ) @ D ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ B )
| ( s_t @ C @ E @ ( op @ E @ D @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_6) ).
thf(648,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ B )
| ( s_t @ A @ ( op @ E @ D @ C @ B @ A ) @ D ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ B )
| ( s_t @ C @ E @ ( op @ E @ D @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(213,axiom,
! [A: $i,B: $i] : ( s_e @ A @ B @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_1) ).
thf(1145,plain,
! [A: $i,B: $i] : ( s_e @ A @ B @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( A = B )
| ( s_e @ C @ D @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_16) ).
thf(1018,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( s_fs @ A @ B @ C @ D @ E @ F @ G @ H )
| ( A = B )
| ( s_e @ C @ D @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( perp @ A @ B @ C @ D )
| ( perp @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_12b) ).
thf(712,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( perp @ A @ B @ C @ D )
| ( perp @ C @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ( ( reflect @ A @ B @ C )
!= C )
| ( s_col @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_8a) ).
thf(690,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ( ( reflect @ A @ B @ C )
!= C )
| ( s_col @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( le @ A @ B @ C @ D )
| ~ ( s_t @ A @ B @ E )
| ~ ( s_e @ A @ E @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_5b) ).
thf(1156,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( le @ A @ B @ C @ D )
| ~ ( s_t @ A @ B @ E )
| ~ ( s_e @ A @ E @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( samesideline @ A @ B @ C @ D )
| ~ ( sameside @ A @ D @ E )
| ( samesideline @ E @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_16) ).
thf(327,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( samesideline @ A @ B @ C @ D )
| ~ ( sameside @ A @ D @ E )
| ( samesideline @ E @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( s @ A @ ( s @ B @ C ) )
!= ( s @ B @ ( s @ A @ C ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_19) ).
thf(310,plain,
! [A: $i,B: $i,C: $i] :
( ( ( s @ A @ ( s @ B @ C ) )
!= ( s @ B @ ( s @ A @ C ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ( ( reflect @ A @ B @ ( reflect @ A @ B @ C ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_5) ).
thf(791,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ( ( reflect @ A @ B @ ( reflect @ A @ B @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ B @ E @ D @ F )
| ~ ( s_e @ A @ G @ C @ H )
| ~ ( s_e @ B @ G @ D @ H )
| ~ ( s_t @ A @ B @ E )
| ~ ( s_t @ C @ D @ F )
| ( A = B )
| ( s_e @ E @ G @ F @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA5) ).
thf(1186,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ B @ E @ D @ F )
| ~ ( s_e @ A @ G @ C @ H )
| ~ ( s_e @ B @ G @ D @ H )
| ~ ( s_t @ A @ B @ E )
| ~ ( s_t @ C @ D @ F )
| ( A = B )
| ( s_e @ E @ G @ F @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ( C = B )
| ( congruent @ A @ B @ C @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz11_9) ).
thf(1038,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ( C = B )
| ( congruent @ A @ B @ C @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ( ( reflect @ A @ B @ C )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_8b) ).
thf(717,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ( ( reflect @ A @ B @ C )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] : ( le @ A @ A @ B @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_11) ).
thf(840,plain,
! [A: $i,B: $i,C: $i] : ( le @ A @ A @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_t @ A @ B @ C )
| ( le @ B @ C @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_12a2) ).
thf(463,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_t @ A @ B @ C )
| ( le @ B @ C @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( sameside @ A @ B @ C )
| ~ ( s_col @ A @ B @ C )
| ( s_t @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_4b) ).
thf(338,plain,
! [A: $i,B: $i,C: $i] :
( ( sameside @ A @ B @ C )
| ~ ( s_col @ A @ B @ C )
| ( s_t @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( sameside @ A @ B @ C )
| ( sameside @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_6) ).
thf(727,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( sameside @ A @ B @ C )
| ( sameside @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_r @ D @ B @ C )
| ~ ( s_e @ A @ B @ D @ B )
| ( s_e @ A @ C @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_12b) ).
thf(1094,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_r @ D @ B @ C )
| ~ ( s_e @ A @ B @ D @ B )
| ( s_e @ A @ C @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( s_col @ A @ B @ C )
| ( s_col @ A @ B @ ( foot @ A @ B @ C ) ) )
& ( ( s_col @ A @ B @ C )
| ( perp @ A @ B @ C @ ( foot @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_18) ).
thf(314,plain,
! [A: $i,B: $i,C: $i] :
( ( ( s_col @ A @ B @ C )
| ( s_col @ A @ B @ ( foot @ A @ B @ C ) ) )
& ( ( s_col @ A @ B @ C )
| ( perp @ A @ B @ C @ ( foot @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_r @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_10) ).
thf(465,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_r @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ C @ D )
| ( B = C )
| ( s_t @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_7a) ).
thf(539,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ C @ D )
| ( B = C )
| ( s_t @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11a) ).
thf(482,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ~ ( s_t @ B @ A @ C )
| ~ ( sameside @ D @ A @ C )
| ( s_col @ D @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_15c) ).
thf(671,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ~ ( s_t @ B @ A @ C )
| ~ ( sameside @ D @ A @ C )
| ( s_col @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_t @ B @ D @ F )
| ~ ( le @ D @ A @ D @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_22a) ).
thf(688,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( s_kf @ A @ B @ C @ D @ E @ F @ G )
| ( s_t @ B @ D @ F )
| ~ ( le @ D @ A @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ( B = C )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_col @ B @ C @ F )
| ~ ( perp @ B @ C @ A @ F )
| ~ ( perp @ B @ C @ D @ E )
| ~ ( s_m @ F @ G @ E )
| ~ ( sameside @ H @ F @ A )
| ~ ( sameside @ I @ E @ D )
| ( opposite @ H @ B @ C @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_4c) ).
thf(495,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ( B = C )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_col @ B @ C @ F )
| ~ ( perp @ B @ C @ A @ F )
| ~ ( perp @ B @ C @ D @ E )
| ~ ( s_m @ F @ G @ E )
| ~ ( sameside @ H @ F @ A )
| ~ ( sameside @ I @ E @ D )
| ( opposite @ H @ B @ C @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(160,axiom,
! [A: $i,B: $i] : ( s_m @ A @ B @ ( s @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_4a) ).
thf(891,plain,
! [A: $i,B: $i] : ( s_m @ A @ B @ ( s @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( sameside @ A @ B @ C )
| ~ ( sameside @ D @ E @ F )
| ~ ( s_e @ B @ A @ E @ D )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_28) ).
thf(1010,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( sameside @ A @ B @ C )
| ~ ( sameside @ D @ E @ F )
| ~ ( s_e @ B @ A @ E @ D )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ A @ C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_4) ).
thf(699,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ A @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ( C = D )
| ~ ( s_col @ C @ D @ A )
| ~ ( s_col @ C @ D @ B )
| ~ ( s_col @ C @ D @ E )
| ( s_col @ A @ B @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_18) ).
thf(319,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ( C = D )
| ~ ( s_col @ C @ D @ A )
| ~ ( s_col @ C @ D @ B )
| ~ ( s_col @ C @ D @ E )
| ( s_col @ A @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_r @ A @ C @ B )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_7) ).
thf(304,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_r @ A @ C @ B )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( le @ A @ B @ C @ D )
| ( s_t @ A @ B @ ( ins @ C @ D @ A @ B ) ) )
& ( ~ ( le @ A @ B @ C @ D )
| ( s_e @ A @ ( ins @ C @ D @ A @ B ) @ C @ D ) )
& ( ~ ( le @ A @ B @ C @ D )
| ( ( ins @ C @ D @ A @ B )
= ( ext @ A @ B @ ( insert @ A @ B @ C @ D ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_5a) ).
thf(1101,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( le @ A @ B @ C @ D )
| ( s_t @ A @ B @ ( ins @ C @ D @ A @ B ) ) )
& ( ~ ( le @ A @ B @ C @ D )
| ( s_e @ A @ ( ins @ C @ D @ A @ B ) @ C @ D ) )
& ( ~ ( le @ A @ B @ C @ D )
| ( ( ins @ C @ D @ A @ B )
= ( ext @ A @ B @ ( insert @ A @ B @ C @ D ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(3,axiom,
alpha != beta,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_13a) ).
thf(235,plain,
alpha != beta,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ B @ D )
| ( s_t @ B @ C @ D )
| ( s_t @ B @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_2) ).
thf(667,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ B @ D )
| ( s_t @ B @ C @ D )
| ( s_t @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ C @ D @ E @ F )
| ( s_e @ A @ B @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_3) ).
thf(1212,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ C @ D @ E @ F )
| ( s_e @ A @ B @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ A @ B @ E @ F )
| ( s_e @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA2) ).
thf(1045,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ A @ B @ E @ F )
| ( s_e @ C @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_r @ D @ E @ F )
| ~ ( s_e @ A @ B @ D @ E )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_12) ).
thf(1116,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_r @ D @ E @ F )
| ~ ( s_e @ A @ B @ D @ E )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(50,axiom,
! [A: $i,B: $i] : ( s_col @ A @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_12) ).
thf(432,plain,
! [A: $i,B: $i] : ( s_col @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( s_e @ C @ D @ ( reflect @ A @ B @ C ) @ ( reflect @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_10) ).
thf(1097,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( s_e @ C @ D @ ( reflect @ A @ B @ C ) @ ( reflect @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( D = C )
| ~ ( s_col @ A @ B @ E )
| ~ ( perp @ A @ B @ E @ C ) )
& ( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( D = C )
| ( s_r @ E @ C @ D )
| ~ ( perp @ A @ B @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_16a) ).
thf(833,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( D = C )
| ~ ( s_col @ A @ B @ E )
| ~ ( perp @ A @ B @ E @ C ) )
& ( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( D = C )
| ( s_r @ E @ C @ D )
| ~ ( perp @ A @ B @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(44,axiom,
! [A: $i,B: $i] : ( s_t @ A @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_3) ).
thf(410,plain,
! [A: $i,B: $i] : ( s_t @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ ( s @ E @ A ) @ ( s @ E @ B ) @ ( s @ E @ C ) @ ( s @ E @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_16b) ).
thf(967,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ ( s @ E @ A ) @ ( s @ E @ B ) @ ( s @ E @ C ) @ ( s @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ D @ C )
| ( s_t @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_5a) ).
thf(867,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ D @ C )
| ( s_t @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ~ ( samesideline @ D @ E @ B @ C )
| ( opposite @ A @ B @ C @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13e) ).
thf(273,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ~ ( samesideline @ D @ E @ B @ C )
| ( opposite @ A @ B @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ~ ( s_col @ A @ B @ E )
| ~ ( perp @ A @ B @ C @ D )
| ~ ( perp @ A @ B @ C @ E )
| ( D = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_18a) ).
thf(294,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ~ ( s_col @ A @ B @ E )
| ~ ( perp @ A @ B @ C @ D )
| ~ ( perp @ A @ B @ C @ E )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( A != B ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( D != E ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( s_col @ D @ E @ C ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( s_col @ A @ B @ C ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( s_col @ A @ B @ ( f813 @ A @ B @ D @ E @ C ) ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( s_col @ D @ E @ ( g813 @ A @ B @ D @ E @ C ) ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( C
!= ( f813 @ A @ B @ D @ E @ C ) ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( C
!= ( g813 @ A @ B @ D @ E @ C ) ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( s_r @ ( f813 @ A @ B @ D @ E @ C ) @ C @ ( g813 @ A @ B @ D @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_13a) ).
thf(358,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( A != B ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( D != E ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( s_col @ D @ E @ C ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( s_col @ A @ B @ C ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( s_col @ A @ B @ ( f813 @ A @ B @ D @ E @ C ) ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( s_col @ D @ E @ ( g813 @ A @ B @ D @ E @ C ) ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( C
!= ( f813 @ A @ B @ D @ E @ C ) ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( C
!= ( g813 @ A @ B @ D @ E @ C ) ) )
& ( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( s_r @ ( f813 @ A @ B @ D @ E @ C ) @ C @ ( g813 @ A @ B @ D @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_col @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_13) ).
thf(437,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_e3 @ A @ B @ C @ D @ E @ F )
| ( s_col @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s_t @ A @ B @ C )
| ~ ( s_t @ ( s @ D @ A ) @ ( s @ D @ B ) @ ( s @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_15b) ).
thf(400,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s_t @ A @ B @ C )
| ~ ( s_t @ ( s @ D @ A ) @ ( s @ D @ B ) @ ( s @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ C @ C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA3) ).
thf(1165,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ C @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_m @ ( s @ A @ C ) @ D @ ( s @ B @ C ) )
| ( B = C )
| ( A != D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_20b) ).
thf(886,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_m @ ( s @ A @ C ) @ D @ ( s @ B @ C ) )
| ( B = C )
| ( A != D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A = B )
| ~ ( s_col @ A @ B @ ( midpoint @ C @ D ) )
| ~ ( perp @ A @ B @ C @ D )
| ( D
= ( reflect @ A @ B @ C ) ) )
& ( ( A = B )
| ~ ( s_col @ A @ B @ ( midpoint @ C @ D ) )
| ( C != D )
| ( D
= ( reflect @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_2b) ).
thf(624,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A = B )
| ~ ( s_col @ A @ B @ ( midpoint @ C @ D ) )
| ~ ( perp @ A @ B @ C @ D )
| ( D
= ( reflect @ A @ B @ C ) ) )
& ( ( A = B )
| ~ ( s_col @ A @ B @ ( midpoint @ C @ D ) )
| ( C != D )
| ( D
= ( reflect @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( s_col @ A @ B @ C )
| ( s_col @ D @ E @ F )
| ( congruent @ A @ B @ C @ D @ E @ ( constructAngle @ A @ B @ C @ D @ E @ F ) ) )
& ( ( s_col @ A @ B @ C )
| ( s_col @ D @ E @ F )
| ( samesideline @ ( constructAngle @ A @ B @ C @ D @ E @ F ) @ F @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz11_15a) ).
thf(992,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( s_col @ A @ B @ C )
| ( s_col @ D @ E @ F )
| ( congruent @ A @ B @ C @ D @ E @ ( constructAngle @ A @ B @ C @ D @ E @ F ) ) )
& ( ( s_col @ A @ B @ C )
| ( s_col @ D @ E @ F )
| ( samesideline @ ( constructAngle @ A @ B @ C @ D @ E @ F ) @ F @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(127,axiom,
! [A: $i,B: $i] :
( ( ( s @ A @ B )
= B )
| ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_10b) ).
thf(723,plain,
! [A: $i,B: $i] :
( ( ( s @ A @ B )
= B )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( ( reflect @ A @ B @ C )
!= ( reflect @ A @ B @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_7) ).
thf(501,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( ( reflect @ A @ B @ C )
!= ( reflect @ A @ B @ D ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( C = D )
| ( A = B )
| ~ ( perp @ C @ D @ E @ F )
| ( perp @ A @ B @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp2) ).
thf(354,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( C = D )
| ( A = B )
| ~ ( perp @ C @ D @ E @ F )
| ( perp @ A @ B @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( D = C )
| ( perp @ A @ B @ E @ C )
| ( s_col @ A @ B @ E )
| ~ ( s_r @ E @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_16b) ).
thf(659,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( D = C )
| ( perp @ A @ B @ E @ C )
| ( s_col @ A @ B @ E )
| ~ ( s_r @ E @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ ( pointOffLine @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_25) ).
thf(543,plain,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ ( pointOffLine @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_m @ C @ D @ E )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ E )
| ( s_col @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13b) ).
thf(491,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_m @ C @ D @ E )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ E )
| ( s_col @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( perp @ A @ B @ B @ C )
| ~ ( perp @ D @ C @ B @ C )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_t @ A @ E @ D )
| ~ ( s_t @ C @ F @ D )
| ~ ( s_e @ B @ A @ C @ F )
| ( s_m @ A @ ( midpoint @ B @ C ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_24) ).
thf(1069,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( perp @ A @ B @ B @ C )
| ~ ( perp @ D @ C @ B @ C )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_t @ A @ E @ D )
| ~ ( s_t @ C @ F @ D )
| ~ ( s_e @ B @ A @ C @ F )
| ( s_m @ A @ ( midpoint @ B @ C ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ( C = D )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ~ ( s_col @ C @ D @ E )
| ( s_col @ A @ B @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtCol2) ).
thf(708,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ( C = D )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ~ ( s_col @ C @ D @ E )
| ( s_col @ A @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(1334,plain,
$false,
inference(cvc4,[status(thm)],[645,1036,809,1190,347,893,468,941,555,333,249,582,1005,683,276,741,1142,861,440,655,550,340,898,288,565,570,619,802,934,1132,460,917,702,751,559,1087,1147,606,416,448,421,870,1013,284,475,1109,253,1136,238,937,574,806,1051,905,480,1169,734,1072,1119,428,527,265,849,307,292,678,529,546,714,798,1163,1021,302,1123,820,407,788,729,1042,952,484,830,1159,842,578,615,403,499,471,1082,488,753,901,637,970,706,393,997,457,721,343,244,1202,633,1054,398,586,298,412,425,824,745,279,444,562,694,826,281,641,382,611,1058,1092,1090,391,1139,604,1194,1209,681,784,1048,230,451,737,434,271,1175,477,1080,631,816,323,621,1149,330,932,1061,1198,1066,455,1015,608,1000,505,912,1171,267,851,241,653,675,589,795,663,812,749,473,1076,1134,648,1145,1018,712,690,1156,327,310,791,1186,1038,717,840,463,338,727,1094,314,465,539,482,671,688,495,891,1010,699,319,304,1101,235,667,1212,1045,1116,432,1097,833,410,967,867,273,294,358,437,400,1165,886,624,992,723,501,354,659,543,491,1069,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO535+1 : TPTP v8.1.2. Released v7.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n029.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri May 19 04:52:44 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.93/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.70/1.14 % [INFO] Parsing done (226ms).
% 1.84/1.15 % [INFO] Running in sequential loop mode.
% 2.33/1.36 % [INFO] eprover registered as external prover.
% 2.33/1.36 % [INFO] cvc4 registered as external prover.
% 2.33/1.36 % [INFO] Scanning for conjecture ...
% 2.59/1.46 % [INFO] Found a conjecture and 227 axioms. Running axiom selection ...
% 2.88/1.54 % [INFO] Axiom selection finished. Selected 227 axioms (removed 0 axioms).
% 3.58/1.77 % [INFO] Problem is first-order (TPTP FOF).
% 3.58/1.80 % [INFO] Type checking passed.
% 3.58/1.80 % [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 ...
% 14.66/4.30 % External prover 'cvc4' found a proof!
% 14.66/4.30 % [INFO] Killing All external provers ...
% 14.66/4.30 % Time passed: 3759ms (effective reasoning time: 3144ms)
% 14.66/4.30 % 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)>
% 14.66/4.30 % Axioms used in derivation (227): aSatz5_9, aSatz8_8, aSatz3_4, aSatz7_19, aSatz6_5, aSatz2_13, aSatz7_10b, aSatz3_14b, aSatz7_2, aSatz10_7, aSatz2_3, aSatz6_16b, aSatz9_5, aSatz8_24a, aSatz4_5, d_Defn5_4, aSatz4_11d, aSatz5_6, aSatz10_16a, aSatz6_2a, aSatz8_20b, d_Defn4_4, aSatz3_1, aSatz9_9, aSatz10_2a, aSatz6_3a, aSatz3_13c, aSatz10_8b, aSatz10_4, aSatz5_2, d_Defn7_23, aExtCol2, aSatz6_15d, aSatz6_4b, aA1, aext1, aLemma9_13a, aSatz8_3, aSatz4_16, aSatz8_12b, d_insert, aLemma9_13d, aSatz6_13a, aSatz6_3b, aSatz10_16b, aSatz8_24b, aA5, aSatz7_10a, aExtPerp2, aSatz5_12a1, aSatz7_15b, d_Defn6_1, aExtPerp, aSatz6_6, aSatz8_7, d_Defn4_15, aSatz2_12, aSatz11_6, aSatz3_3, aperp1, aSatz3_13a, aSatz6_18, aSatz7_3b, d_Defn9_1, aSatz6_2b, aSatz10_15, aSatz10_12c, aSatz10_12, aSatz10_8a, aSatz8_16b, aSatz3_5b, aSatz9_4b, aSatz8_14a, aSatz11_9, aSatz3_17, aSatz7_7, aSatz4_11c, d_Defn4_10, aSatz5_1, aSatz5_12b, aSatz9_4a, aLemma9_13f_case2, aSatz4_19, aSatz10_5, aExtPerp6, aSatz9_4, aSatz3_13b, 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, aSatz11_4, aSatz2_5, aSatz3_6b, aExtPerp3, aA3, aSatz3_2, aLemma9_13g, aSatz11_15a, 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, aSatz11_3d, aLemma9_13f, aSatz4_11a, aSatz6_11a, aA7, aSatz6_15b, aSatz10_12b, aSatz8_6, aSatz9_13, aSatz11_7, aSatz2_4, aSatz11_4b, aSatz7_16a, aSatz3_14a, d_Defn8_1, aLemma9_13c, aSatz10_6, aSatz11_3a, 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, aSatz6_17b, aLemma9_13f_case1, aSatz7_4b, aSatz11_15b, aSatz5_7, aSatz4_13, aSatz2_11, aSatz7_13, d_Defn9_7, aSatz8_9, aSatz2_14, aSatz4_11e, aSatz5_10, d_Defn2_10, aSatz7_22a, aSatz11_4d, aSatz5_5b, aSatz10_12a, aSatz4_12, aSatz8_24, aSatz8_16a, aSatz4_17, aSatz9_4a2, aSatz5_3, aExtPerp4, aSatz10_14, aSatz6_13b, aSatz7_8, aSatz7_16b, aSatz8_5, aSatz2_8, aSatz4_2, aSatz11_8, aSatz6_4a, aA8, aSatz3_7b, aSatz7_3a, aSatz6_7, aSatz9_6, aSatz9_19b
% 14.66/4.30 % No. of inferences in proof: 458
% 14.66/4.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3759 ms resp. 3144 ms w/o parsing
% 14.66/4.43 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.66/4.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------