%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO523+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:13:27 AM UTC 2026
% Result : Theorem 10.45s 5.56s
% Output : Refutation 11.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 93
% Syntax : Number of formulae : 188 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 742 ( 179 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 2939 ( 375 ~; 528 |; 26 &;2010 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 7 con; 0-5 aty)
% Number of variables : 722 ( 0 ^; 722 !; 0 ?; 722 :)
% Comments :
%------------------------------------------------------------------------------
thf(reflect_decl,type,
reflect: $i > $i > $i > $i ).
thf(s_t_decl,type,
s_t: $i > $i > $i > $o ).
thf(s_e_decl,type,
s_e: $i > $i > $i > $i > $o ).
thf(s_col_decl,type,
s_col: $i > $i > $i > $o ).
thf(s_m_decl,type,
s_m: $i > $i > $i > $o ).
thf(s_r_decl,type,
s_r: $i > $i > $i > $o ).
thf(perpAt_decl,type,
perpAt: $i > $i > $i > $i > $i > $o ).
thf(perp_decl,type,
perp: $i > $i > $i > $i > $o ).
thf(midpoint_decl,type,
midpoint: $i > $i > $i ).
thf(foot_decl,type,
foot: $i > $i > $i > $i ).
thf(xa_decl,type,
xa: $i ).
thf(xb_decl,type,
xb: $i ).
thf(xp_decl,type,
xp: $i ).
thf(xq_decl,type,
xq: $i ).
thf(xc_decl,type,
xc: $i ).
thf(xd_decl,type,
xd: $i ).
thf(erect21a_decl,type,
erect21a: $i > $i > $i > $i ).
thf(erectAux21a_decl,type,
erectAux21a: $i > $i > $i > $i ).
thf(pointOffLine_decl,type,
pointOffLine: $i > $i > $i ).
thf(erect_decl,type,
erect: $i > $i > $i > $i ).
thf(erectAux_decl,type,
erectAux: $i > $i > $i > $i ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ s_t ) ) )
| ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_1) ).
thf(224,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ s_t ) ) )
| ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aExtCol2) ).
thf(356,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( D @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_5a) ).
thf(296,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( D @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( C = A )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_16b) ).
thf(347,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( C = A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11a) ).
thf(333,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ erect ) ) @ ( C @ ( B @ ( A @ erectAux ) ) @ ( C @ s_t ) ) )
| ( A = B ) )
& ( ( C @ ( B @ ( A @ erectAux ) ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) )
& ( ( A @ ( C @ ( B @ ( A @ erect ) ) @ ( B @ ( A @ perp ) ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_21) ).
thf(408,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ erect ) ) @ ( C @ ( B @ ( A @ erectAux ) ) @ ( C @ s_t ) ) )
| ( A = B ) )
& ( ( C @ ( B @ ( A @ erectAux ) ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) )
& ( ( A @ ( C @ ( B @ ( A @ erect ) ) @ ( B @ ( A @ perp ) ) ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_2) ).
thf(269,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ erect21a ) ) @ ( C @ ( B @ ( A @ erectAux21a ) ) @ ( C @ s_t ) ) )
| ( A = B ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ erectAux21a ) ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ( A @ ( C @ ( B @ ( A @ erect21a ) ) @ ( B @ ( A @ perp ) ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_21a) ).
thf(384,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ erect21a ) ) @ ( C @ ( B @ ( A @ erectAux21a ) ) @ ( C @ s_t ) ) )
| ( A = B ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ erectAux21a ) ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) )
& ( ( C @ ( B @ ( A @ s_col ) ) )
| ( A @ ( C @ ( B @ ( A @ erect21a ) ) @ ( B @ ( A @ perp ) ) ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA3) ).
thf(142,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_13) ).
thf(174,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_4) ).
thf(288,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D = E )
| ~ ( E @ ( C @ ( B @ ( A @ perp ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_18a) ).
thf(301,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D = E )
| ~ ( E @ ( C @ ( B @ ( A @ perp ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_6a) ).
thf(184,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ s_m ) ) )
| ( A = C )
| ~ ( C @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_20) ).
thf(125,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ s_m ) ) )
| ( A = C )
| ~ ( C @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ s_t ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_7b) ).
thf(196,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ s_t ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
| ~ ( B @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aNarbouxLemma1) ).
thf(157,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
| ~ ( B @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ ( C @ s_t ) ) )
| ( B @ ( C @ ( D @ s_t ) ) )
| ~ ( B @ ( A @ ( D @ s_t ) ) )
| ~ ( B @ ( A @ ( C @ s_t ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_16a) ).
thf(189,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ ( C @ s_t ) ) )
| ( B @ ( C @ ( D @ s_t ) ) )
| ~ ( B @ ( A @ ( D @ s_t ) ) )
| ~ ( B @ ( A @ ( C @ s_t ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ s_t ) ) )
| ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_2) ).
thf(284,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ s_t ) ) )
| ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(68,axiom,
( ~ ( xb @ ( xa @ ( xd @ ( xc @ perp ) ) ) )
| ( xq @ ( xp @ ( xd @ ( xc @ perp ) ) ) )
| ( xa = xb )
| ( xp = xq )
| ~ ( xq @ ( xb @ ( xa @ s_col ) ) )
| ~ ( xp @ ( xb @ ( xa @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aExtPerp6) ).
thf(325,plain,
( ~ ( xb @ ( xa @ ( xd @ ( xc @ perp ) ) ) )
| ( xq @ ( xp @ ( xd @ ( xc @ perp ) ) ) )
| ( xa = xb )
| ( xp = xq )
| ~ ( xq @ ( xb @ ( xa @ s_col ) ) )
| ~ ( xp @ ( xb @ ( xa @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_15) ).
thf(152,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_4b) ).
thf(228,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ s_col ) ) )
| ( D = C )
| ~ ( C @ ( E @ ( C @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( C @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aLemma9_13g) ).
thf(261,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ s_col ) ) )
| ( D = C )
| ~ ( C @ ( E @ ( C @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( C @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ ( A @ s_m ) ) )
| ~ ( D @ ( E @ ( B @ s_col ) ) )
| ~ ( C @ ( E @ ( A @ s_col ) ) )
| ~ ( A @ ( D @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) )
| ( B = D )
| ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_21) ).
thf(164,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ ( A @ s_m ) ) )
| ~ ( D @ ( E @ ( B @ s_col ) ) )
| ~ ( C @ ( E @ ( A @ s_col ) ) )
| ~ ( A @ ( D @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) )
| ( B = D )
| ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ s_t ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_7a) ).
thf(211,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ s_t ) ) )
| ( B = C )
| ~ ( D @ ( C @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( C @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) )
& ( ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn7_1) ).
thf(132,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) )
& ( ( C @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) )
& ( ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_2) ).
thf(243,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = C )
| ~ ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( D @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_6) ).
thf(265,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = C )
| ~ ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( D @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA6) ).
thf(248,plain,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ ( C @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_2) ).
thf(117,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ ( C @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ s_r ) ) )
| ~ ( D @ ( A @ ( B @ s_col ) ) )
| ( A = B )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_3) ).
thf(220,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ s_r ) ) )
| ~ ( D @ ( A @ ( B @ s_col ) ) )
| ( A = B )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( C @ ( D @ ( B @ ( A @ perp ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_15) ).
thf(366,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( C @ ( D @ ( B @ ( A @ perp ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( F @ ( G @ ( E @ s_e ) ) ) )
| ( A = B )
| ~ ( F @ ( D @ ( C @ s_t ) ) )
| ~ ( E @ ( B @ ( A @ s_t ) ) )
| ~ ( H @ ( D @ ( G @ ( B @ s_e ) ) ) )
| ~ ( H @ ( C @ ( G @ ( A @ s_e ) ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA5) ).
thf(160,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( F @ ( G @ ( E @ s_e ) ) ) )
| ( A = B )
| ~ ( F @ ( D @ ( C @ s_t ) ) )
| ~ ( E @ ( B @ ( A @ s_t ) ) )
| ~ ( H @ ( D @ ( G @ ( B @ s_e ) ) ) )
| ~ ( H @ ( C @ ( G @ ( A @ s_e ) ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_8) ).
thf(275,plain,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_17a) ).
thf(328,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_3a) ).
thf(193,plain,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ ( C @ perp ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_12b) ).
thf(360,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ ( C @ perp ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( B @ ( D @ ( C @ s_col ) ) )
| ~ ( A @ ( D @ ( C @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_18) ).
thf(311,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( B @ ( D @ ( C @ s_col ) ) )
| ~ ( A @ ( D @ ( C @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( F @ ( E @ ( B @ ( A @ perp ) ) ) )
| ( F @ ( E @ ( D @ ( C @ perp ) ) ) )
| ( A = B )
| ( C = D )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aExtPerp5) ).
thf(398,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( F @ ( E @ ( B @ ( A @ perp ) ) ) )
| ( F @ ( E @ ( D @ ( C @ perp ) ) ) )
| ( A = B )
| ( C = D )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(11,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( A @ s_e ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_1) ).
thf(128,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( A @ s_e ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_17b) ).
thf(343,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( C @ ( E @ s_r ) ) )
| ( E @ ( B @ ( A @ s_col ) ) )
| ( C @ ( E @ ( B @ ( A @ perp ) ) ) )
| ( D = C )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_16b) ).
thf(402,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( C @ ( E @ s_r ) ) )
| ( E @ ( B @ ( A @ s_col ) ) )
| ( C @ ( E @ ( B @ ( A @ perp ) ) ) )
| ( D = C )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ s_col ) ) )
| ( D != A )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ( A = C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_15d) ).
thf(291,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ s_col ) ) )
| ( D != A )
| ~ ( C @ ( A @ ( B @ s_t ) ) )
| ( A = C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11e) ).
thf(382,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11d) ).
thf(335,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ s_t ) ) )
| ~ ( C @ ( D @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_5b) ).
thf(181,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ s_t ) ) )
| ~ ( C @ ( D @ ( B @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(29,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( A @ s_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_3) ).
thf(187,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( A @ s_t ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11b) ).
thf(406,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ reflect ) ) @ ( C @ ( B @ ( A @ perp ) ) ) )
| ( C
= ( C @ ( B @ ( A @ reflect ) ) ) )
| ( A = B ) )
& ( ( C @ ( B @ ( A @ reflect ) ) @ ( C @ midpoint ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz10_2a) ).
thf(419,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ reflect ) ) @ ( C @ ( B @ ( A @ perp ) ) ) )
| ( C
= ( C @ ( B @ ( A @ reflect ) ) ) )
| ( A = B ) )
& ( ( C @ ( B @ ( A @ reflect ) ) @ ( C @ midpoint ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_14a) ).
thf(362,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
| ( A = B )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_9) ).
thf(245,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
| ( A = B )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_m ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aLemma9_13b) ).
thf(271,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_m ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(67,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( A @ s_col ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_12) ).
thf(323,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( A @ s_col ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_4) ).
thf(140,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( A @ ( C @ s_t ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ~ ( A @ ( C @ ( B @ s_t ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ( B @ ( A @ ( C @ s_t ) ) )
| ( A @ ( C @ ( B @ s_t ) ) )
| ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn4_10) ).
thf(251,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( A @ ( C @ s_t ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ~ ( A @ ( C @ ( B @ s_t ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ~ ( C @ ( B @ ( A @ s_t ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ( B @ ( A @ ( C @ s_t ) ) )
| ( A @ ( C @ ( B @ s_t ) ) )
| ( C @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_14) ).
thf(155,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_5) ).
thf(130,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ perpAt ) ) ) ) )
| ( A = B )
| ( C = D )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aExtPerp) ).
thf(278,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ perpAt ) ) ) ) )
| ( A = B )
| ( C = D )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ perp ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aperp1) ).
thf(299,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ perp ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( C @ ( E @ ( B @ ( A @ perp ) ) ) )
| ( D @ ( C @ ( E @ s_r ) ) )
| ( D = C )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) )
& ( ~ ( C @ ( E @ ( B @ ( A @ perp ) ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ( D = C )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_16a) ).
thf(374,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( C @ ( E @ ( B @ ( A @ perp ) ) ) )
| ( D @ ( C @ ( E @ s_r ) ) )
| ( D = C )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) )
& ( ~ ( C @ ( E @ ( B @ ( A @ perp ) ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ( D = C )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ ( C @ ( E @ ( D @ perpAt ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_12a) ).
thf(209,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ ( C @ ( E @ ( D @ perpAt ) ) ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ perpAt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(9,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ ( A @ s_e ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_8) ).
thf(123,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ ( A @ s_e ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_2) ).
thf(282,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(17,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( B @ ( A @ s_e ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA1) ).
thf(150,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( B @ ( A @ s_e ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ reflect ) ) )
= C )
| ( ( C @ ( B @ ( A @ reflect ) ) )
!= D )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz10_4) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ reflect ) ) )
= C )
| ( ( C @ ( B @ ( A @ reflect ) ) )
!= D )
| ( A = B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(95,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ reflect ) ) )
= C )
| ( ( C @ ( B @ ( A @ reflect ) ) )
!= D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(70,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ midpoint ) @ ( A @ s_m ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_22) ).
thf(331,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ midpoint ) @ ( A @ s_m ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( A @ ( A @ ( B @ perp ) ) ) )
| ~ ( D @ ( C @ ( A @ s_col ) ) )
| ~ ( C @ ( A @ ( A @ ( B @ perp ) ) ) )
| ( A = D )
| ( D = C )
| ( B = C )
| ( A = C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aExtPerp3) ).
thf(370,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( A @ ( A @ ( B @ perp ) ) ) )
| ~ ( D @ ( C @ ( A @ s_col ) ) )
| ~ ( C @ ( A @ ( A @ ( B @ perp ) ) ) )
| ( A = D )
| ( D = C )
| ( B = C )
| ( A = C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B != A )
| ( A @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_3b) ).
thf(203,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( A @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(39,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ s_r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_5) ).
thf(218,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ s_r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_3) ).
thf(104,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ perp ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ perp ) ) ) )
| ( A = B )
| ( C = D )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aExtPerp2) ).
thf(319,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ perp ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ perp ) ) ) )
| ( A = B )
| ( C = D )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( E @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_14b) ).
thf(351,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( E @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA2) ).
thf(114,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ s_e ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_3) ).
thf(171,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ s_e ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ s_e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_18) ).
thf(119,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( A @ ( C @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( C @ ( E @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( G @ ( E @ ( F @ s_r ) ) )
| ( E = G )
| ( E = F )
| ~ ( G @ ( D @ ( C @ s_col ) ) )
| ~ ( F @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_13b) ).
thf(235,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( C @ ( E @ ( B @ ( A @ perpAt ) ) ) ) )
| ~ ( G @ ( E @ ( F @ s_r ) ) )
| ( E = G )
| ( E = F )
| ~ ( G @ ( D @ ( C @ s_col ) ) )
| ~ ( F @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(35,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ s_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_1) ).
thf(207,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ s_t ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( D @ ( C @ s_col ) ) )
| ~ ( G @ ( B @ ( A @ s_col ) ) )
| ( E = F )
| ~ ( F @ ( D @ ( C @ s_col ) ) )
| ~ ( F @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_21) ).
thf(315,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( D @ ( C @ s_col ) ) )
| ~ ( G @ ( B @ ( A @ s_col ) ) )
| ( E = F )
| ~ ( F @ ( D @ ( C @ s_col ) ) )
| ~ ( F @ ( B @ ( A @ s_col ) ) )
| ~ ( E @ ( D @ ( C @ s_col ) ) )
| ~ ( E @ ( B @ ( A @ s_col ) ) )
| ( C = D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_11) ).
thf(168,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( C @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ s_e ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ s_e ) ) ) )
| ~ ( F @ ( E @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ~ ( D @ ( C @ ( B @ ( C @ s_e ) ) ) )
| ~ ( D @ ( A @ ( B @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_19) ).
thf(146,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ~ ( D @ ( C @ ( B @ ( C @ s_e ) ) ) )
| ~ ( D @ ( A @ ( B @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ foot ) ) @ ( C @ ( B @ ( A @ perp ) ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ( C @ ( B @ ( A @ foot ) ) @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_18) ).
thf(305,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ foot ) ) @ ( C @ ( B @ ( A @ perp ) ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) )
& ( ( C @ ( B @ ( A @ foot ) ) @ ( B @ ( A @ s_col ) ) )
| ( C @ ( B @ ( A @ s_col ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( C @ ( D @ ( C @ s_e ) ) ) )
| ~ ( E @ ( B @ ( D @ ( B @ s_e ) ) ) )
| ~ ( E @ ( A @ ( D @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_17) ).
thf(107,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( C @ ( D @ ( C @ s_e ) ) ) )
| ~ ( E @ ( B @ ( D @ ( B @ s_e ) ) ) )
| ~ ( E @ ( A @ ( D @ ( A @ s_e ) ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ~ ( C @ ( D @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_17) ).
thf(239,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ~ ( C @ ( D @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11c) ).
thf(341,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ pointOffLine ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_25) ).
thf(395,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ pointOffLine ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( C @ ( B @ ( A @ reflect ) ) ) )
| ( C != D )
| ~ ( D @ ( C @ midpoint ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) )
& ( ( D
= ( C @ ( B @ ( A @ reflect ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) )
| ~ ( D @ ( C @ midpoint ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz10_2b) ).
thf(427,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( C @ ( B @ ( A @ reflect ) ) ) )
| ( C != D )
| ~ ( D @ ( C @ midpoint ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) )
& ( ( D
= ( C @ ( B @ ( A @ reflect ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) )
| ~ ( D @ ( C @ midpoint ) @ ( B @ ( A @ s_col ) ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_6b) ).
thf(200,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( D @ ( C @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
| ~ ( B @ ( C @ ( A @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_7) ).
thf(178,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
| ~ ( B @ ( C @ ( A @ s_r ) ) )
| ~ ( C @ ( B @ ( A @ s_r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( B @ ( F @ s_t ) ) )
| ~ ( E @ ( G @ ( C @ s_m ) ) )
| ~ ( D @ ( F @ ( A @ s_m ) ) )
| ~ ( E @ ( B @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( E @ ( B @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_22) ).
thf(111,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( B @ ( F @ s_t ) ) )
| ~ ( E @ ( G @ ( C @ s_m ) ) )
| ~ ( D @ ( F @ ( A @ s_m ) ) )
| ~ ( E @ ( B @ ( C @ ( B @ s_e ) ) ) )
| ~ ( D @ ( B @ ( A @ ( B @ s_e ) ) ) )
| ~ ( E @ ( B @ ( D @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ s_col ) ) )
| ( A = B )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aext1) ).
thf(337,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ s_col ) ) )
| ( A = B )
| ~ ( D @ ( B @ ( A @ s_col ) ) )
| ~ ( C @ ( B @ ( A @ s_col ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ ( A @ perp ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aExtPerp4) ).
thf(354,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( B @ ( A @ perp ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( C @ ( B @ midpoint ) @ ( A @ s_m ) ) )
| ~ ( F @ ( C @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( F @ ( C @ s_t ) ) )
| ~ ( D @ ( E @ ( A @ s_t ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( C @ ( D @ perp ) ) ) )
| ~ ( C @ ( B @ ( B @ ( A @ perp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_24) ).
thf(215,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( C @ ( B @ midpoint ) @ ( A @ s_m ) ) )
| ~ ( F @ ( C @ ( A @ ( B @ s_e ) ) ) )
| ~ ( D @ ( F @ ( C @ s_t ) ) )
| ~ ( D @ ( E @ ( A @ s_t ) ) )
| ~ ( E @ ( C @ ( B @ s_col ) ) )
| ~ ( C @ ( B @ ( C @ ( D @ perp ) ) ) )
| ~ ( C @ ( B @ ( B @ ( A @ perp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(82,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ s_col ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_12b) ).
thf(364,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ s_col ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ ( A @ s_t ) ) )
| ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( D @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz5_3) ).
thf(232,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ ( A @ s_t ) ) )
| ( D @ ( B @ ( A @ s_t ) ) )
| ~ ( C @ ( D @ ( A @ s_t ) ) )
| ~ ( C @ ( B @ ( A @ s_t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(593,plain,
$false,
inference(e,[status(thm)],[224,356,296,347,333,408,269,384,142,174,288,301,184,125,196,157,189,284,325,152,228,261,164,211,132,243,265,248,117,220,366,160,275,328,193,360,311,398,128,343,402,291,382,335,181,187,406,419,362,245,271,323,140,251,155,130,278,299,374,209,123,282,150,95,331,370,203,218,104,319,351,114,171,119,235,207,315,168,146,305,107,239,341,395,427,200,178,111,337,354,215,364,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO523+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.47 % Computer : n009.cluster.edu
% 0.13/0.47 % Model : x86_64 x86_64
% 0.13/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.47 % Memory : 8046.5625MB
% 0.13/0.47 % OS : Linux 6.8.0-71-generic
% 0.13/0.47 % CPULimit : 300
% 0.13/0.47 % WCLimit : 300
% 0.13/0.47 % DateTime : Fri Sep 25 13:38:59 UTC 2026
% 0.13/0.47 % CPUTime :
% 0.13/0.47 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.80/1.29 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.76/1.70 % [INFO] Parsing done (405ms).
% 1.76/1.71 % [INFO] Running in sequential loop mode.
% 2.90/2.33 % [INFO] eprover registered as external prover.
% 2.90/2.34 % [INFO] Scanning for conjecture ...
% 3.19/2.57 % [INFO] Found a conjecture (or negated_conjecture) and 200 axioms. Running axiom selection ...
% 3.47/2.76 % [INFO] Axiom selection finished. Selected 92 axioms (removed 108 axioms).
% 3.90/2.97 % [INFO] Problem is first-order (TPTP FOF).
% 3.90/3.01 % [INFO] Type checking passed.
% 3.90/3.01 % [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 ...
% 10.45/5.55 % External prover 'e' found a proof!
% 10.45/5.55 % [INFO] Killing All external provers ...
% 10.45/5.55 % Time passed: 4866ms (effective reasoning time: 3828ms)
% 10.45/5.55 % 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)>
% 10.45/5.56 % Axioms used in derivation (92): aSatz6_16b, aSatz4_11d, aSatz8_16b, aSatz2_1, aSatz8_6, aSatz2_4, aSatz8_8, aSatz3_4, aSatz2_13, aSatz7_2, aSatz2_3, aSatz3_1, aSatz10_2a, aSatz5_2, aExtCol2, aSatz6_15d, aA1, aext1, aSatz8_3, aSatz8_12b, aA5, aExtPerp2, aExtPerp, aSatz8_7, aSatz7_3b, aSatz3_3, aperp1, aSatz6_18, aSatz3_5b, aSatz8_14a, aSatz4_11c, d_Defn4_10, aSatz5_1, aExtPerp6, aSatz4_19, aLemma9_13b, aSatz3_5a, aSatz8_21, aSatz8_18a, aSatz6_25, aSatz8_15, aA2, aSatz4_11b, aSatz10_2b, aSatz8_21a, aSatz2_5, aSatz3_6b, aExtPerp3, aA3, aSatz3_2, aLemma9_13g, aA6, aSatz3_6a, aNarbouxLemma1, aSatz8_22, aSatz6_17a, aSatz8_14b, aSatz4_3, d_Defn7_1, aExtPerp5, aSatz4_18, aSatz2_2, aSatz7_20, aSatz7_22, aSatz7_21, aSatz4_12b, aSatz2_15, aSatz4_11a, aSatz6_16a, aSatz3_7a, aSatz8_2, aSatz7_17, aSatz8_18, aSatz6_21, aSatz8_13b, aSatz8_12a, aSatz6_17b, aSatz7_4b, aSatz2_11, aSatz8_9, aSatz2_14, aSatz4_11e, aSatz4_12, aSatz8_24, aExtPerp4, aSatz8_16a, aSatz4_17, aSatz5_3, aSatz8_5, aSatz2_8, aSatz3_7b, aSatz7_3a
% 10.45/5.56 % No. of inferences in proof: 188
% 10.45/5.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4866 ms resp. 3828 ms w/o parsing
% 11.04/5.77 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.04/5.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------