TSTP Solution File: GEO526+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO526+1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 11:11:08 EDT 2023
% Result : Theorem 14.13s 4.08s
% Output : Refutation 14.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 262
% Syntax : Number of formulae : 474 ( 41 unt; 52 typ; 0 def)
% Number of atoms : 1952 ( 420 equ; 0 cnn)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 9081 (1079 ~;1348 |; 182 &;6472 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 181 ( 181 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 52 usr; 10 con; 0-8 aty)
% Number of variables : 1775 ( 0 ^;1775 !; 0 ?;1775 :)
% Comments :
%------------------------------------------------------------------------------
thf(s_r_type,type,
s_r: $i > $i > $i > $o ).
thf(s_e_type,type,
s_e: $i > $i > $i > $i > $o ).
thf(midpoint_type,type,
midpoint: $i > $i > $i ).
thf(alpha_type,type,
alpha: $i ).
thf(beta_type,type,
beta: $i ).
thf(gamma_type,type,
gamma: $i ).
thf(opposite_type,type,
opposite: $i > $i > $i > $i > $o ).
thf(samesideline_type,type,
samesideline: $i > $i > $i > $i > $o ).
thf(sameside_type,type,
sameside: $i > $i > $i > $o ).
thf(s_col_type,type,
s_col: $i > $i > $i > $o ).
thf(foot_type,type,
foot: $i > $i > $i > $i ).
thf(s_t_type,type,
s_t: $i > $i > $i > $o ).
thf(il_type,type,
il: $i > $i > $i > $i > $i ).
thf(ext_type,type,
ext: $i > $i > $i > $i > $i ).
thf(perp_type,type,
perp: $i > $i > $i > $i > $o ).
thf(s_type,type,
s: $i > $i > $i ).
thf(ip_type,type,
ip: $i > $i > $i > $i > $i > $i ).
thf(s_m_type,type,
s_m: $i > $i > $i > $o ).
thf(perpAt_type,type,
perpAt: $i > $i > $i > $i > $i > $o ).
thf(reflect_type,type,
reflect: $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(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(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(f813_type,type,
f813: $i > $i > $i > $i > $i > $i ).
thf(g813_type,type,
g813: $i > $i > $i > $i > $i > $i ).
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(f811_type,type,
f811: $i > $i > $i > $i > $i > $i ).
thf(g811_type,type,
g811: $i > $i > $i > $i > $i > $i ).
thf(ins_type,type,
ins: $i > $i > $i > $i > $i ).
thf(isomidpoint_type,type,
isomidpoint: $i > $i > $i > $i ).
thf(120,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/sandbox/benchmark/theBenchmark.p',d_Defn9_7) ).
thf(645,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)],[120]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ( sameside @ A @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_5) ).
thf(629,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( sameside @ A @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( ( reflect @ A @ B @ C )
!= D )
| ( ( reflect @ A @ B @ D )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz10_4) ).
thf(479,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)],[75]) ).
thf(175,axiom,
! [A: $i,B: $i] :
( ~ ( s_r @ A @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_8) ).
thf(962,plain,
! [A: $i,B: $i] :
( ~ ( s_r @ A @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(7,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/sandbox/benchmark/theBenchmark.p',aLemma9_13e) ).
thf(234,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)],[7]) ).
thf(169,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/sandbox/benchmark/theBenchmark.p',aSatz5_6) ).
thf(941,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)],[169]) ).
thf(93,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/sandbox/benchmark/theBenchmark.p',aSatz9_6) ).
thf(555,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)],[93]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ B @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_14) ).
thf(909,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)],[164]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( sameside @ A @ B @ C )
| ~ ( s_col @ A @ B @ C )
| ( s_t @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_4b) ).
thf(333,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)],[32]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( s_m @ A @ B @ A )
| ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_3b) ).
thf(408,plain,
! [A: $i,B: $i] :
( ( s_m @ A @ B @ A )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(201,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/sandbox/benchmark/theBenchmark.p',aSatz5_5b) ).
thf(1068,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)],[201]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( s @ A @ ( s @ B @ C ) )
!= ( s @ B @ ( s @ A @ C ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_19) ).
thf(308,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)],[26]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ( ( reflect @ A @ B @ C )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz10_8b) ).
thf(614,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)],[111]) ).
thf(195,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/sandbox/benchmark/theBenchmark.p',d_Defn7_1) ).
thf(1041,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)],[195]) ).
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/sandbox/benchmark/theBenchmark.p',aSatz10_6) ).
thf(384,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(132,axiom,
! [A: $i,B: $i,C: $i] : ( le @ A @ A @ B @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_11) ).
thf(715,plain,
! [A: $i,B: $i,C: $i] : ( le @ A @ A @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',aSatz3_7a) ).
thf(472,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)],[73]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_m @ A @ B @ C )
| ~ ( s_m @ A @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_4b) ).
thf(698,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)],[127]) ).
thf(146,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/sandbox/benchmark/theBenchmark.p',aSatz10_2a) ).
thf(782,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)],[146]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_m @ A @ B @ C )
| ~ ( s_m @ A @ D @ C )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_17) ).
thf(709,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)],[130]) ).
thf(160,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/sandbox/benchmark/theBenchmark.p',aSatz2_15) ).
thf(885,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)],[160]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',aSatz8_18a) ).
thf(301,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)],[24]) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',aLemma9_13f_case1) ).
thf(257,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)],[11]) ).
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/sandbox/benchmark/theBenchmark.p',aSatz6_16a) ).
thf(389,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(198,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/sandbox/benchmark/theBenchmark.p',aSatz2_3) ).
thf(1055,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)],[198]) ).
thf(97,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/sandbox/benchmark/theBenchmark.p',aSatz6_15c) ).
thf(570,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)],[97]) ).
thf(134,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/sandbox/benchmark/theBenchmark.p',aSatz8_21) ).
thf(719,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)],[134]) ).
thf(81,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/sandbox/benchmark/theBenchmark.p',aSatz9_4a) ).
thf(504,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)],[81]) ).
thf(128,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/sandbox/benchmark/theBenchmark.p',aSatz7_22b) ).
thf(702,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)],[128]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',aSatz6_4a) ).
thf(357,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)],[38]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',aSatz8_21a) ).
thf(460,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)],[71]) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',aSatz5_12a2) ).
thf(421,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)],[57]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ~ ( s_t @ A @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA6) ).
thf(325,plain,
! [A: $i,B: $i] :
( ~ ( s_t @ A @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(67,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/sandbox/benchmark/theBenchmark.p',aSatz9_4c) ).
thf(448,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)],[67]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ A @ C )
| ( s_m @ B @ ( isomidpoint @ B @ C @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_25) ).
thf(1100,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)],[210]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ~ ( samesideline @ A @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz9_9) ).
thf(261,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)],[12]) ).
thf(139,axiom,
! [A: $i,B: $i] : ( s_m @ A @ B @ ( s @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_4a) ).
thf(756,plain,
! [A: $i,B: $i] : ( s_m @ A @ B @ ( s @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',d_Defn4_1) ).
thf(789,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)],[147]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( s @ A @ B )
!= ( s @ A @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_9) ).
thf(321,plain,
! [A: $i,B: $i,C: $i] :
( ( ( s @ A @ B )
!= ( s @ A @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',aSatz8_22b) ).
thf(574,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)],[98]) ).
thf(149,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/sandbox/benchmark/theBenchmark.p',aSatz8_13a) ).
thf(806,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)],[149]) ).
thf(197,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/sandbox/benchmark/theBenchmark.p',aSatz8_13b) ).
thf(1051,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)],[197]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_r @ A @ B @ C )
| ( s_r @ A @ B @ ( s @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_4) ).
thf(766,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)],[142]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ( ( reflect @ A @ B @ ( reflect @ A @ B @ C ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz10_5) ).
thf(687,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)],[124]) ).
thf(18,axiom,
alpha != gamma,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_13c) ).
thf(280,plain,
alpha != gamma,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(155,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/sandbox/benchmark/theBenchmark.p',aA4) ).
thf(866,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)],[155]) ).
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/sandbox/benchmark/theBenchmark.p',aSatz3_7b) ).
thf(396,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(60,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( sameside @ A @ B @ C )
| ~ ( le @ B @ A @ B @ C )
| ( s_t @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_13a) ).
thf(428,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)],[60]) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',aSatz8_18) ).
thf(312,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)],[27]) ).
thf(68,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/sandbox/benchmark/theBenchmark.p',aSatz5_12b) ).
thf(452,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)],[68]) ).
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/sandbox/benchmark/theBenchmark.p',aSatz6_15a) ).
thf(380,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(83,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/sandbox/benchmark/theBenchmark.p',aSatz9_5) ).
thf(512,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)],[83]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( samesideline @ C @ D @ A @ B )
| ( samesideline @ C @ D @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aExtSameSide2) ).
thf(270,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)],[15]) ).
thf(40,axiom,
! [A: $i,B: $i] : ( s_t @ A @ B @ ( ext @ A @ B @ alpha @ gamma ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_14a) ).
thf(366,plain,
! [A: $i,B: $i] : ( s_t @ A @ B @ ( ext @ A @ B @ alpha @ gamma ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ C @ A @ B )
| ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aNarbouxLemma1) ).
thf(952,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)],[172]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( s @ A @ B )
!= C )
| ( ( s @ A @ D )
!= C )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_8) ).
thf(729,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)],[135]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',aA2) ).
thf(916,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)],[167]) ).
thf(191,axiom,
! [A: $i,B: $i] : ( s_e @ A @ A @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_8) ).
thf(1032,plain,
! [A: $i,B: $i] : ( s_e @ A @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11a) ).
thf(435,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)],[63]) ).
thf(188,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/sandbox/benchmark/theBenchmark.p',aSatz6_11a) ).
thf(1012,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)],[188]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( opposite @ A @ B @ C @ D )
| ( opposite @ D @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz9_2) ).
thf(229,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)],[5]) ).
thf(96,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/sandbox/benchmark/theBenchmark.p',aSatz5_2) ).
thf(566,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)],[96]) ).
thf(76,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/sandbox/benchmark/theBenchmark.p',aSatz6_2a) ).
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)],[76]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11b) ).
thf(583,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)],[101]) ).
thf(150,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/sandbox/benchmark/theBenchmark.p',aSatz4_3) ).
thf(830,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)],[150]) ).
thf(28,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/sandbox/benchmark/theBenchmark.p',aSatz6_18) ).
thf(317,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)],[28]) ).
thf(209,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/sandbox/benchmark/theBenchmark.p',aSatz8_16b) ).
thf(1096,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)],[209]) ).
thf(80,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/sandbox/benchmark/theBenchmark.p',aSatz3_17) ).
thf(499,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)],[80]) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',aA7) ).
thf(328,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)],[31]) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',d_insert) ).
thf(488,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)],[77]) ).
thf(103,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/sandbox/benchmark/theBenchmark.p',aSatz7_22a) ).
thf(590,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)],[103]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_5) ).
thf(1039,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)],[194]) ).
thf(1,conjecture,
! [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/sandbox/benchmark/theBenchmark.p',aSatz10_12c) ).
thf(2,negated_conjecture,
~ ! [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(neg_conjecture,[status(cth)],[1]) ).
thf(212,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)],[2]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_4) ).
thf(1075,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)],[203]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ ( pointOffLine @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_25) ).
thf(476,plain,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ ( pointOffLine @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ~ ( s_m @ A @ B @ A )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_3a) ).
thf(393,plain,
! [A: $i,B: $i] :
( ~ ( s_m @ A @ B @ A )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(185,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/sandbox/benchmark/theBenchmark.p',aSatz10_12b) ).
thf(997,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)],[185]) ).
thf(84,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/sandbox/benchmark/theBenchmark.p',aSatz6_3a) ).
thf(515,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)],[84]) ).
thf(137,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/sandbox/benchmark/theBenchmark.p',d_Defn6_1) ).
thf(738,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)],[137]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( s @ A @ B )
!= ( s @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_18) ).
thf(371,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(108,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/sandbox/benchmark/theBenchmark.p',aExtCol2) ).
thf(605,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)],[108]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( sameside @ A @ B @ C )
| ( sameside @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_6) ).
thf(622,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( sameside @ A @ B @ C )
| ( sameside @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',d_Defn4_15) ).
thf(837,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)],[152]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_2) ).
thf(984,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)],[181]) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',aSatz7_22) ).
thf(911,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)],[165]) ).
thf(8,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/sandbox/benchmark/theBenchmark.p',aLemma9_13f_case2) ).
thf(237,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)],[8]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] : ( s_e @ A @ B @ ( s @ C @ A ) @ ( s @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_13) ).
thf(1086,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)],[206]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( samesideline @ C @ D @ A @ B )
| ( samesideline @ D @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aLemma9_13d) ).
thf(266,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)],[14]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',aSatz6_15b) ).
thf(508,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)],[82]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( sameside @ A @ B @ C )
| ~ ( sameside @ C @ B @ D )
| ( sameside @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_7) ).
thf(541,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)],[89]) ).
thf(202,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/sandbox/benchmark/theBenchmark.p',aSatz10_10a) ).
thf(1071,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)],[202]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11d) ).
thf(530,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)],[85]) ).
thf(161,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/sandbox/benchmark/theBenchmark.p',aSatz4_16) ).
thf(888,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)],[161]) ).
thf(163,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/sandbox/benchmark/theBenchmark.p',aSatz8_10) ).
thf(906,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)],[163]) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',aExtPerp6) ).
thf(412,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)],[54]) ).
thf(176,axiom,
! [A: $i,B: $i] : ( s_r @ A @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_5) ).
thf(965,plain,
! [A: $i,B: $i] : ( s_r @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( ( s @ A @ B )
= B )
| ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_10b) ).
thf(618,plain,
! [A: $i,B: $i] :
( ( ( s @ A @ B )
= B )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( le @ A @ B @ C @ D )
| ( le @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_10) ).
thf(430,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)],[61]) ).
thf(66,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/sandbox/benchmark/theBenchmark.p',aLemma9_13b) ).
thf(444,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)],[66]) ).
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/sandbox/benchmark/theBenchmark.p',aSatz3_6a) ).
thf(375,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(58,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/sandbox/benchmark/theBenchmark.p',aSatz9_3a) ).
thf(423,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)],[58]) ).
thf(126,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/sandbox/benchmark/theBenchmark.p',aSatz5_1) ).
thf(694,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)],[126]) ).
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/sandbox/benchmark/theBenchmark.p',aSatz3_6b) ).
thf(402,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(99,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/sandbox/benchmark/theBenchmark.p',aSatz8_14c) ).
thf(577,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)],[99]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',aExtSameSide1) ).
thf(291,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)],[21]) ).
thf(174,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/sandbox/benchmark/theBenchmark.p',aA5) ).
thf(958,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)],[174]) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',aSatz6_3b) ).
thf(562,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)],[95]) ).
thf(179,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/sandbox/benchmark/theBenchmark.p',aSatz10_2b) ).
thf(975,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)],[179]) ).
thf(118,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/sandbox/benchmark/theBenchmark.p',aSatz8_14a) ).
thf(641,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)],[118]) ).
thf(110,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/sandbox/benchmark/theBenchmark.p',aSatz5_8) ).
thf(611,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)],[110]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_m @ A @ B @ C )
| ( s_m @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_2) ).
thf(713,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)],[131]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_col @ A @ B @ C )
| ( A = B )
| ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_9) ).
thf(1058,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)],[199]) ).
thf(208,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/sandbox/benchmark/theBenchmark.p',aSatz2_12) ).
thf(1092,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)],[208]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_m @ A @ B @ C )
| ( C
= ( s @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_6) ).
thf(335,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_m @ A @ B @ C )
| ( C
= ( s @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(171,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/sandbox/benchmark/theBenchmark.p',aSatz8_24b) ).
thf(947,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)],[171]) ).
thf(168,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/sandbox/benchmark/theBenchmark.p',d_Defn8_11a) ).
thf(919,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)],[168]) ).
thf(148,axiom,
! [A: $i,B: $i] : ( s_e @ A @ B @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA1) ).
thf(804,plain,
! [A: $i,B: $i] : ( s_e @ A @ B @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',aLemma9_13c) ).
thf(274,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)],[16]) ).
thf(196,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/sandbox/benchmark/theBenchmark.p',aSatz8_20a) ).
thf(1048,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)],[196]) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',aLemma9_13g) ).
thf(362,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)],[39]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',d_Defn9_1) ).
thf(245,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)],[10]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',aSatz6_28) ).
thf(880,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)],[158]) ).
thf(106,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/sandbox/benchmark/theBenchmark.p',aSatz9_19b) ).
thf(599,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)],[106]) ).
thf(154,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/sandbox/benchmark/theBenchmark.p',aSatz7_16b) ).
thf(863,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)],[154]) ).
thf(140,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/sandbox/benchmark/theBenchmark.p',d_Defn8_1) ).
thf(758,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)],[140]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',aSatz8_14b) ).
thf(552,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)],[92]) ).
thf(87,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/sandbox/benchmark/theBenchmark.p',aext1) ).
thf(535,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)],[87]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( perp @ A @ B @ C @ D )
| ( perp @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_12b) ).
thf(609,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)],[109]) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',d_Defn2_10) ).
thf(848,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)],[153]) ).
thf(200,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/sandbox/benchmark/theBenchmark.p',aSatz8_16a) ).
thf(1061,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)],[200]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_r @ A @ C @ B )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_7) ).
thf(768,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)],[143]) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',d_Defn8_11b) ).
thf(636,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)],[117]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( samesideline @ A @ B @ C @ D )
| ( samesideline @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aLemma9_13a) ).
thf(278,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)],[17]) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',aSatz5_9) ).
thf(883,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)],[159]) ).
thf(3,axiom,
alpha != beta,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_13a) ).
thf(223,plain,
alpha != beta,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(182,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/sandbox/benchmark/theBenchmark.p',aSatz4_5) ).
thf(986,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)],[182]) ).
thf(186,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/sandbox/benchmark/theBenchmark.p',aSatz10_10) ).
thf(1000,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)],[186]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( perp @ A @ B @ C @ D )
| ( perp @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aperp1) ).
thf(299,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)],[23]) ).
thf(4,axiom,
beta != gamma,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_13b) ).
thf(226,plain,
beta != gamma,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(211,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/sandbox/benchmark/theBenchmark.p',aSatz2_11) ).
thf(1102,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)],[211]) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',aLemma9_13f) ).
thf(241,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)],[9]) ).
thf(192,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/sandbox/benchmark/theBenchmark.p',aSatz7_20) ).
thf(1034,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)],[192]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_t @ A @ B @ C )
| ( s_t @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_2) ).
thf(426,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)],[59]) ).
thf(170,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/sandbox/benchmark/theBenchmark.p',aSatz7_16a) ).
thf(944,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)],[170]) ).
thf(122,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/sandbox/benchmark/theBenchmark.p',aSatz9_4) ).
thf(680,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)],[122]) ).
thf(91,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/sandbox/benchmark/theBenchmark.p',aSatz6_16b) ).
thf(548,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)],[91]) ).
thf(205,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/sandbox/benchmark/theBenchmark.p',aSatz8_20b) ).
thf(1081,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)],[205]) ).
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/sandbox/benchmark/theBenchmark.p',aExtPerp2) ).
thf(342,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(37,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11e) ).
thf(355,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)],[37]) ).
thf(138,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/sandbox/benchmark/theBenchmark.p',aSatz5_12a1) ).
thf(754,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)],[138]) ).
thf(70,axiom,
! [A: $i,B: $i] : ( s_t @ A @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_1) ).
thf(458,plain,
! [A: $i,B: $i] : ( s_t @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(100,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/sandbox/benchmark/theBenchmark.p',aSatz4_6) ).
thf(580,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)],[100]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( A
!= ( ext @ B @ A @ alpha @ gamma ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_14b) ).
thf(295,plain,
! [A: $i,B: $i] :
( A
!= ( ext @ B @ A @ alpha @ gamma ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(129,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/sandbox/benchmark/theBenchmark.p',aExtPerp3) ).
thf(705,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)],[129]) ).
thf(178,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/sandbox/benchmark/theBenchmark.p',aSatz8_3) ).
thf(971,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)],[178]) ).
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/sandbox/benchmark/theBenchmark.p',aSatz9_8) ).
thf(263,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(65,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/sandbox/benchmark/theBenchmark.p',aSatz7_15a) ).
thf(441,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)],[65]) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',aSatz9_4b) ).
thf(585,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)],[102]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( sameside @ A @ B @ C )
| ( le @ B @ A @ B @ C )
| ~ ( s_t @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_13b) ).
thf(717,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)],[133]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',aSatz6_21) ).
thf(338,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)],[34]) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',aSatz8_12a) ).
thf(470,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)],[72]) ).
thf(119,axiom,
! [A: $i,B: $i] : ( s_col @ A @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_12b) ).
thf(643,plain,
! [A: $i,B: $i] : ( s_col @ A @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ( s_col @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_17b) ).
thf(544,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)],[90]) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',d_Defn4_4) ).
thf(1023,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)],[190]) ).
thf(157,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/sandbox/benchmark/theBenchmark.p',aSatz8_6) ).
thf(876,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)],[157]) ).
thf(183,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/sandbox/benchmark/theBenchmark.p',aSatz4_18) ).
thf(991,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)],[183]) ).
thf(6,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/sandbox/benchmark/theBenchmark.p',aSatz9_16) ).
thf(231,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)],[6]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11c) ).
thf(539,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)],[88]) ).
thf(79,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/sandbox/benchmark/theBenchmark.p',aExtPerp) ).
thf(495,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)],[79]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',d_Defn7_23) ).
thf(891,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)],[162]) ).
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/sandbox/benchmark/theBenchmark.p',aSatz7_15b) ).
thf(368,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(144,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/sandbox/benchmark/theBenchmark.p',aSatz4_19) ).
thf(771,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)],[144]) ).
thf(116,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/sandbox/benchmark/theBenchmark.p',aSatz9_4a2) ).
thf(632,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)],[116]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( s @ A @ ( s @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_7) ).
thf(418,plain,
! [A: $i,B: $i] :
( ( s @ A @ ( s @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(184,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/sandbox/benchmark/theBenchmark.p',aSatz4_2) ).
thf(995,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)],[184]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ C @ C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA3) ).
thf(1077,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ C @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(141,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/sandbox/benchmark/theBenchmark.p',aSatz4_14) ).
thf(763,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)],[141]) ).
thf(123,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/sandbox/benchmark/theBenchmark.p',aSatz5_3) ).
thf(684,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)],[123]) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',d_Defn4_10) ).
thf(346,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)],[36]) ).
thf(20,axiom,
( ~ ( s_t @ alpha @ beta @ gamma )
& ~ ( s_t @ beta @ gamma @ alpha )
& ~ ( s_t @ gamma @ alpha @ beta ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA8) ).
thf(287,plain,
( ~ ( s_t @ alpha @ beta @ gamma )
& ~ ( s_t @ beta @ gamma @ alpha )
& ~ ( s_t @ gamma @ alpha @ beta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(166,axiom,
! [A: $i,B: $i] : ( s_m @ A @ ( midpoint @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_22) ).
thf(914,plain,
! [A: $i,B: $i] : ( s_m @ A @ ( midpoint @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(44,axiom,
! [A: $i,B: $i] : ( s_t @ A @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_3) ).
thf(378,plain,
! [A: $i,B: $i] : ( s_t @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ( s_col @ A @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_17a) ).
thf(432,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( s_col @ A @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
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/sandbox/benchmark/theBenchmark.p',aSatz4_13) ).
thf(405,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(107,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( perp @ A @ B @ C @ D )
| ( perp @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aExtPerp4) ).
thf(603,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)],[107]) ).
thf(136,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/sandbox/benchmark/theBenchmark.p',aSatz3_5a) ).
thf(735,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)],[136]) ).
thf(151,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/sandbox/benchmark/theBenchmark.p',aSatz4_17) ).
thf(833,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)],[151]) ).
thf(177,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/sandbox/benchmark/theBenchmark.p',aSatz6_11b) ).
thf(967,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)],[177]) ).
thf(25,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/sandbox/benchmark/theBenchmark.p',aSatz3_5b) ).
thf(305,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)],[25]) ).
thf(64,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/sandbox/benchmark/theBenchmark.p',aSatz6_2b) ).
thf(437,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)],[64]) ).
thf(50,axiom,
! [A: $i,B: $i] : ( s_col @ A @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_12) ).
thf(400,plain,
! [A: $i,B: $i] : ( s_col @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',aSideReflect) ).
thf(532,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)],[86]) ).
thf(173,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/sandbox/benchmark/theBenchmark.p',aSatz8_24) ).
thf(955,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)],[173]) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',aSatz9_13) ).
thf(283,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)],[19]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( s @ A @ B )
!= B )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_10a) ).
thf(415,plain,
! [A: $i,B: $i] :
( ( ( s @ A @ B )
!= B )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',aSatz6_15d) ).
thf(624,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)],[114]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ A @ C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_4) ).
thf(596,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)],[105]) ).
thf(189,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/sandbox/benchmark/theBenchmark.p',aSatz7_21) ).
thf(1019,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)],[189]) ).
thf(125,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/sandbox/benchmark/theBenchmark.p',aSatz9_3) ).
thf(691,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)],[125]) ).
thf(156,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/sandbox/benchmark/theBenchmark.p',aSatz8_24a) ).
thf(871,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)],[156]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_r @ A @ B @ C )
| ( s_r @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_2) ).
thf(982,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)],[180]) ).
thf(187,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/sandbox/benchmark/theBenchmark.p',aSatz5_5a) ).
thf(1004,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)],[187]) ).
thf(121,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/sandbox/benchmark/theBenchmark.p',aSatz8_15) ).
thf(676,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)],[121]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ( ( reflect @ A @ B @ C )
!= C )
| ( s_col @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz10_8a) ).
thf(592,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)],[104]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( ( reflect @ A @ B @ C )
!= ( reflect @ A @ B @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz10_7) ).
thf(454,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)],[69]) ).
thf(193,axiom,
! [A: $i,B: $i] : ( s_e @ A @ B @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_1) ).
thf(1037,plain,
! [A: $i,B: $i] : ( s_e @ A @ B @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(145,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/sandbox/benchmark/theBenchmark.p',d_Defn5_4) ).
thf(775,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)],[145]) ).
thf(94,axiom,
! [A: $i,B: $i] : ( le @ A @ B @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_7) ).
thf(560,plain,
! [A: $i,B: $i] : ( le @ A @ B @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',aExtPerp5) ).
thf(491,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)],[78]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ C @ C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_13) ).
thf(1088,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ C @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(1164,plain,
$false,
inference(e,[status(thm)],[645,629,479,962,234,941,555,909,333,408,1068,308,614,1041,384,715,472,698,782,709,885,301,257,389,1055,570,719,504,702,357,460,421,325,448,1100,261,756,789,321,574,806,1051,766,687,280,866,396,428,312,452,380,512,270,366,952,729,916,1032,435,1012,229,566,484,583,830,317,1096,499,328,488,590,1039,212,1075,476,393,997,515,738,371,605,622,837,984,911,237,1086,266,508,541,1071,530,888,906,412,965,618,430,444,375,423,694,402,577,291,958,562,975,641,611,713,1058,1092,335,947,919,804,274,1048,362,245,880,599,863,758,552,535,609,848,1061,768,636,278,883,223,986,1000,299,226,1102,241,1034,426,944,680,548,1081,342,355,754,458,580,295,705,971,263,441,585,717,338,470,643,544,1023,876,991,231,539,495,891,368,771,632,418,995,1077,763,684,346,287,914,378,432,405,603,735,833,967,305,437,400,532,955,283,415,624,596,1019,691,871,982,1004,676,592,454,1037,775,560,491,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GEO526+1 : TPTP v8.1.2. Released v7.0.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 19 03:53:01 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.94/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.60/1.07 % [INFO] Parsing done (223ms).
% 1.77/1.08 % [INFO] Running in sequential loop mode.
% 2.37/1.32 % [INFO] eprover registered as external prover.
% 2.37/1.33 % [INFO] cvc4 registered as external prover.
% 2.37/1.33 % [INFO] Scanning for conjecture ...
% 2.49/1.42 % [INFO] Found a conjecture and 209 axioms. Running axiom selection ...
% 2.87/1.51 % [INFO] Axiom selection finished. Selected 209 axioms (removed 0 axioms).
% 3.57/1.71 % [INFO] Problem is first-order (TPTP FOF).
% 3.57/1.73 % [INFO] Type checking passed.
% 3.57/1.73 % [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 ...
% 14.13/4.07 % External prover 'e' found a proof!
% 14.13/4.07 % [INFO] Killing All external provers ...
% 14.13/4.07 % Time passed: 3564ms (effective reasoning time: 2986ms)
% 14.13/4.07 % 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)>
% 14.13/4.07 % Axioms used in derivation (209): 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, 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, aSatz8_24b, aA5, aSatz7_10a, aExtPerp2, aSatz5_12a1, aSatz7_15b, d_Defn6_1, aExtPerp, aSatz6_6, aSatz8_7, d_Defn4_15, aSatz2_12, aSatz3_3, aperp1, aSatz3_13a, aSatz6_18, aSatz7_3b, d_Defn9_1, aSatz6_2b, aSatz10_8a, aSatz8_16b, aSatz3_5b, aSatz9_4b, aSatz8_14a, aSatz3_17, aSatz7_7, aSatz4_11c, d_Defn4_10, aSatz5_1, aSatz5_12b, aSatz9_4a, aLemma9_13f_case2, 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, aSatz2_5, aSatz3_6b, aExtPerp3, aA3, aSatz3_2, aLemma9_13g, aSatz9_2, aA6, aSatz3_6a, aSatz7_15a, aSatz5_12a2, aNarbouxLemma1, aSatz8_22, aSatz6_17a, aSatz8_13a, aSatz7_22b, d_Defn8_11b, aSatz8_14b, aSatz4_3, aSatz7_6, aExtSameSide2, d_Defn7_1, aSatz9_4c, aSatz4_18, aSatz2_2, aSatz7_20, aSatz5_5a, aSatz5_11, aExtPerp5, aSatz6_28, aSatz7_22, aSatz7_21, aSatz4_12b, aSatz2_15, aSatz8_22b, aLemma9_13f, aSatz4_11a, aSatz6_11a, aA7, aSatz6_15b, aSatz10_12b, aSatz8_6, aSatz10_6, aSatz9_13, aSatz2_4, aSatz7_16a, aSatz3_14a, d_Defn8_1, aLemma9_13c, aSatz7_9, d_Defn8_11a, aSatz9_16, aA4, aSatz9_3, aSatz5_8, aSatz6_16a, aSatz3_7a, aSatz8_2, aSatz7_17, aSatz8_18, aSatz6_21, aSatz8_13b, aSatz10_10, aSatz8_14c, aSatz8_12a, aSatz4_6, aSatz7_4b, aSatz6_17b, aLemma9_13f_case1, aSatz5_7, aSatz4_13, aSatz2_11, aSatz7_13, d_Defn9_7, aSatz8_9, aSatz2_14, aSatz4_11e, aSatz5_10, d_Defn2_10, aSatz7_22a, aSatz5_5b, aSatz4_12, aSatz8_24, aExtPerp4, aSatz8_16a, aSatz4_17, aSatz9_4a2, aSatz5_3, aSatz6_13b, aSatz7_8, aSatz7_16b, aSatz8_5, aSatz2_8, aSatz4_2, aSatz6_4a, aA8, aSatz3_7b, aSatz7_3a, aSatz6_7, aSatz9_6, aSatz9_19b
% 14.13/4.07 % No. of inferences in proof: 422
% 14.13/4.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3564 ms resp. 2986 ms w/o parsing
% 14.30/4.20 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.30/4.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------