TSTP Solution File: GEO523+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO523+1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 11:11:07 EDT 2023
% Result : Theorem 7.42s 2.82s
% Output : Refutation 7.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 114
% Syntax : Number of formulae : 209 ( 19 unt; 21 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 : 47 ( 47 >; 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_type,type,
reflect: $i > $i > $i > $i ).
thf(s_t_type,type,
s_t: $i > $i > $i > $o ).
thf(s_e_type,type,
s_e: $i > $i > $i > $i > $o ).
thf(s_col_type,type,
s_col: $i > $i > $i > $o ).
thf(s_m_type,type,
s_m: $i > $i > $i > $o ).
thf(s_r_type,type,
s_r: $i > $i > $i > $o ).
thf(perpAt_type,type,
perpAt: $i > $i > $i > $i > $i > $o ).
thf(perp_type,type,
perp: $i > $i > $i > $i > $o ).
thf(midpoint_type,type,
midpoint: $i > $i > $i ).
thf(foot_type,type,
foot: $i > $i > $i > $i ).
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(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(erect_type,type,
erect: $i > $i > $i > $i ).
thf(erectAux_type,type,
erectAux: $i > $i > $i > $i ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
| ( perp @ A @ B @ ( erect21a @ A @ B @ C ) @ A )
| ( s_col @ A @ B @ C ) )
& ( ( A = B )
| ( s_col @ A @ B @ ( erectAux21a @ A @ B @ C ) )
| ( s_col @ A @ B @ C ) )
& ( ( A = B )
| ( s_t @ C @ ( erectAux21a @ A @ B @ C ) @ ( erect21a @ A @ B @ C ) )
| ( s_col @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_21a) ).
thf(379,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)],[87]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ B @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_14) ).
thf(153,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)],[19]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_5) ).
thf(129,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)],[12]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_r @ A @ B @ C )
| ( A = B )
| ~ ( s_col @ B @ A @ D )
| ( s_r @ D @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_3) ).
thf(218,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)],[40]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( s_m @ A @ B @ C )
| ( s_t @ A @ B @ C ) )
& ( ~ ( s_m @ A @ B @ C )
| ( s_e @ B @ A @ B @ C ) )
& ( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ B @ A @ B @ C )
| ( s_m @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn7_1) ).
thf(131,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)],[13]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_4) ).
thf(138,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)],[14]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( perp @ A @ B @ C @ D )
| ~ ( s_col @ A @ B @ E )
| ~ ( s_col @ C @ D @ E )
| ( perpAt @ A @ B @ E @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_14b) ).
thf(347,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)],[77]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ( C = D )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ~ ( s_col @ C @ D @ E )
| ( s_col @ A @ B @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtCol2) ).
thf(352,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)],[79]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( A = B )
| ( s_col @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aext1) ).
thf(333,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)],[73]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( s_col @ A @ B @ C )
| ( s_t @ A @ B @ C )
| ( s_t @ B @ C @ A )
| ( s_t @ C @ A @ B ) )
& ( ( s_col @ A @ B @ C )
| ~ ( s_t @ A @ B @ C ) )
& ( ( s_col @ A @ B @ C )
| ~ ( s_t @ B @ C @ A ) )
& ( ( s_col @ A @ B @ C )
| ~ ( s_t @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn4_10) ).
thf(249,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)],[49]) ).
thf(29,axiom,
! [A: $i,B: $i] : ( s_t @ A @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_3) ).
thf(185,plain,
! [A: $i,B: $i] : ( s_t @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ~ ( s_t @ B @ A @ C )
| ( D != A )
| ( s_col @ D @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_15d) ).
thf(288,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)],[59]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ ( pointOffLine @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_25) ).
thf(389,plain,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ ( pointOffLine @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ B @ E )
| ~ ( s_e @ B @ A @ B @ D )
| ~ ( s_e @ B @ C @ B @ E )
| ~ ( s_m @ A @ F @ D )
| ~ ( s_m @ C @ G @ E )
| ( s_t @ F @ B @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_22) ).
thf(110,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)],[5]) ).
thf(39,axiom,
! [A: $i,B: $i] : ( s_r @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_5) ).
thf(216,plain,
! [A: $i,B: $i] : ( s_r @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ D @ C )
| ( s_t @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_5b) ).
thf(179,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)],[27]) ).
thf(68,axiom,
( ~ ( s_col @ xa @ xb @ xp )
| ~ ( s_col @ xa @ xb @ xq )
| ( xp = xq )
| ( xa = xb )
| ( perp @ xc @ xd @ xp @ xq )
| ~ ( perp @ xc @ xd @ xa @ xb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp6) ).
thf(321,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)],[68]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_e @ A @ D @ A @ E )
| ~ ( s_e @ B @ D @ B @ E )
| ( s_e @ C @ D @ C @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_17) ).
thf(106,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)],[4]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ D @ C )
| ( s_t @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_5a) ).
thf(293,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)],[60]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( D = C )
| ( perp @ A @ B @ E @ C )
| ( s_col @ A @ B @ E )
| ~ ( s_r @ E @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_16b) ).
thf(396,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)],[90]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ( s_e @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_2) ).
thf(116,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)],[7]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_col @ A @ B @ C )
| ( A = B )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_9) ).
thf(243,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)],[47]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ( C = D )
| ~ ( s_col @ C @ D @ A )
| ~ ( s_col @ C @ D @ B )
| ~ ( s_col @ C @ D @ E )
| ( s_col @ A @ B @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_18) ).
thf(307,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)],[64]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A = B )
| ( C = D )
| ~ ( s_col @ C @ D @ E )
| ~ ( s_col @ A @ B @ E )
| ~ ( s_col @ A @ B @ F )
| ~ ( s_col @ C @ D @ G )
| ( E = F )
| ( E = G )
| ~ ( s_r @ F @ E @ G )
| ( perpAt @ A @ B @ E @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_13b) ).
thf(233,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)],[44]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( s_m @ A @ B @ A )
| ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_3b) ).
thf(201,plain,
! [A: $i,B: $i] :
( ( s_m @ A @ B @ A )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( A = C )
| ( B = C )
| ( D = C )
| ( A = D )
| ~ ( perp @ B @ A @ A @ C )
| ~ ( s_col @ A @ C @ D )
| ( perp @ B @ A @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp3) ).
thf(366,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)],[84]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( s_col @ A @ B @ C )
| ( s_col @ A @ B @ ( foot @ A @ B @ C ) ) )
& ( ( s_col @ A @ B @ C )
| ( perp @ A @ B @ C @ ( foot @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_18) ).
thf(302,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)],[63]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( C = D )
| ( A = B )
| ( perp @ C @ D @ E @ F )
| ~ ( perp @ A @ B @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp5) ).
thf(392,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)],[89]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( C = D )
| ( A = B )
| ~ ( perpAt @ C @ D @ E @ F @ G )
| ( perpAt @ A @ B @ E @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp) ).
thf(275,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)],[55]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11a) ).
thf(329,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)],[71]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ( s_col @ A @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_17a) ).
thf(324,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( s_col @ A @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ A @ C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_4) ).
thf(285,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)],[58]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( perp @ A @ B @ C @ D )
| ( perp @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_12b) ).
thf(356,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)],[80]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ C @ D @ E @ F )
| ( s_e @ A @ B @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_3) ).
thf(169,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)],[24]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_e @ B @ A @ B @ C )
| ( A = C )
| ( s_m @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_20) ).
thf(124,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)],[10]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ( s_col @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_17b) ).
thf(339,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)],[75]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_t @ A @ B @ C )
| ( s_t @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_2) ).
thf(266,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)],[52]) ).
thf(82,axiom,
! [A: $i,B: $i] : ( s_col @ A @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_12b) ).
thf(360,plain,
! [A: $i,B: $i] : ( s_col @ A @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(35,axiom,
! [A: $i,B: $i] : ( s_t @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_1) ).
thf(205,plain,
! [A: $i,B: $i] : ( s_t @ A @ B @ B ),
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] :
( ( A = B )
| ( C = D )
| ~ ( s_col @ A @ B @ E )
| ~ ( s_col @ C @ D @ E )
| ~ ( s_col @ A @ B @ F )
| ~ ( s_col @ C @ D @ F )
| ( E = F )
| ~ ( s_col @ A @ B @ G )
| ( s_col @ C @ D @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_21) ).
thf(311,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)],[65]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( C = A )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( s_col @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_16b) ).
thf(343,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)],[76]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_m @ A @ B @ C )
| ~ ( s_m @ A @ D @ C )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_17) ).
thf(237,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)],[45]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ~ ( s_col @ A @ B @ E )
| ~ ( perp @ A @ B @ C @ D )
| ~ ( perp @ A @ B @ C @ E )
| ( D = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_18a) ).
thf(298,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)],[62]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
| ( s_col @ A @ B @ ( midpoint @ C @ ( reflect @ A @ B @ C ) ) ) )
& ( ( A = B )
| ( C
= ( reflect @ A @ B @ C ) )
| ( perp @ A @ B @ C @ ( reflect @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_2a) ).
thf(412,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)],[93]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ F )
| ~ ( s_e @ A @ B @ D @ E )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_11) ).
thf(166,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)],[23]) ).
thf(17,axiom,
! [A: $i,B: $i] : ( s_e @ A @ B @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA1) ).
thf(148,plain,
! [A: $i,B: $i] : ( s_e @ A @ B @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_r @ A @ B @ C )
| ( s_r @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_2) ).
thf(279,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)],[56]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( perp @ A @ B @ C @ D )
| ( perp @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aperp1) ).
thf(296,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)],[61]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_r @ A @ C @ B )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_7) ).
thf(176,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)],[26]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_e @ A @ C @ A @ D )
| ~ ( s_e @ B @ C @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_18) ).
thf(118,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)],[8]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ B @ D )
| ( s_t @ B @ C @ D )
| ( s_t @ B @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_2) ).
thf(281,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)],[57]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ~ ( s_m @ A @ B @ A )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_3a) ).
thf(191,plain,
! [A: $i,B: $i] :
( ~ ( s_m @ A @ B @ A )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
| ( perp @ A @ B @ ( erect @ A @ B @ C ) @ A ) )
& ( ( A = B )
| ( s_col @ A @ B @ ( erectAux @ A @ B @ C ) ) )
& ( ( A = B )
| ( s_t @ C @ ( erectAux @ A @ B @ C ) @ ( erect @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_21) ).
thf(402,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)],[92]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ B @ A @ D )
| ~ ( s_e @ C @ B @ C @ D )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_19) ).
thf(144,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)],[16]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( perp @ A @ B @ C @ D )
| ( perp @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp4) ).
thf(350,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)],[78]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_t @ C @ A @ B )
| ~ ( s_t @ D @ A @ B )
| ( s_t @ D @ C @ B )
| ( s_t @ C @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_16a) ).
thf(187,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)],[30]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ C @ C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_13) ).
thf(172,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ C @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ A @ B @ E @ F )
| ( s_e @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA2) ).
thf(113,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)],[6]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A = B )
| ~ ( s_col @ A @ B @ ( midpoint @ C @ D ) )
| ~ ( perp @ A @ B @ C @ D )
| ( D
= ( reflect @ A @ B @ C ) ) )
& ( ( A = B )
| ~ ( s_col @ A @ B @ ( midpoint @ C @ D ) )
| ( C != D )
| ( D
= ( reflect @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_2b) ).
thf(419,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)],[94]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ A @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11e) ).
thf(377,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)],[86]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ D @ C )
| ( s_t @ A @ B @ D )
| ( s_t @ A @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_3) ).
thf(230,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)],[43]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( perp @ A @ B @ D @ C )
| ( perpAt @ A @ B @ C @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_15) ).
thf(362,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)],[83]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ F )
| ~ ( s_e @ A @ C @ D @ F )
| ~ ( s_e @ B @ C @ E @ F )
| ( s_e @ A @ B @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_3) ).
thf(103,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)],[3]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ C @ C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA3) ).
thf(140,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( s_e @ A @ B @ C @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( perp @ A @ B @ B @ C )
| ~ ( perp @ D @ C @ B @ C )
| ~ ( s_col @ B @ C @ E )
| ~ ( s_t @ A @ E @ D )
| ~ ( s_t @ C @ F @ D )
| ~ ( s_e @ B @ A @ C @ F )
| ( s_m @ A @ ( midpoint @ B @ C ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_24) ).
thf(213,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)],[38]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_e @ A @ C @ A @ B )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aNarbouxLemma1) ).
thf(155,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)],[20]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ C @ D )
| ( s_t @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_6b) ).
thf(198,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)],[33]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_m @ A @ B @ C )
| ~ ( s_m @ A @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_4b) ).
thf(226,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)],[42]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_m @ A @ B @ C )
| ( s_m @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_2) ).
thf(241,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)],[46]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( s_col @ A @ B @ C )
| ( B = D )
| ~ ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ B @ C @ D @ A )
| ~ ( s_col @ A @ E @ C )
| ~ ( s_col @ B @ E @ D )
| ( s_m @ A @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_21) ).
thf(162,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)],[22]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ C @ D )
| ( B = C )
| ( s_t @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_7a) ).
thf(209,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)],[37]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ B @ C @ D )
| ( B = C )
| ( s_t @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_7b) ).
thf(194,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)],[32]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ D @ E @ F )
| ~ ( s_e @ A @ B @ E @ F )
| ~ ( s_e @ B @ C @ D @ E )
| ( s_e @ A @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_15) ).
thf(150,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)],[18]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( ( reflect @ A @ B @ C )
!= D )
| ( ( reflect @ A @ B @ D )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_4) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ( ( reflect @ A @ B @ C )
!= D )
| ( ( reflect @ A @ B @ D )
= C ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(95,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)],[2]) ).
thf(70,axiom,
! [A: $i,B: $i] : ( s_m @ A @ ( midpoint @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_22) ).
thf(327,plain,
! [A: $i,B: $i] : ( s_m @ A @ ( midpoint @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ C @ D )
| ( s_t @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_6a) ).
thf(182,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)],[28]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11d) ).
thf(331,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)],[72]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( D = C )
| ~ ( s_col @ A @ B @ E )
| ~ ( perp @ A @ B @ E @ C ) )
& ( ( A = B )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( D = C )
| ( s_r @ E @ C @ D )
| ~ ( perp @ A @ B @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_16a) ).
thf(370,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)],[85]) ).
thf(11,axiom,
! [A: $i,B: $i] : ( s_e @ A @ B @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_1) ).
thf(127,plain,
! [A: $i,B: $i] : ( s_e @ A @ B @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(67,axiom,
! [A: $i,B: $i] : ( s_col @ A @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_12) ).
thf(319,plain,
! [A: $i,B: $i] : ( s_col @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( perpAt @ A @ B @ C @ D @ C )
| ~ ( perpAt @ A @ B @ C @ E @ C )
| ( D = C )
| ( s_col @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13g) ).
thf(258,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)],[50]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( s_e @ A @ B @ C @ D )
| ~ ( s_e @ B @ E @ D @ F )
| ~ ( s_e @ A @ G @ C @ H )
| ~ ( s_e @ B @ G @ D @ H )
| ~ ( s_t @ A @ B @ E )
| ~ ( s_t @ C @ D @ F )
| ( A = B )
| ( s_e @ E @ G @ F @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA5) ).
thf(158,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)],[21]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ~ ( s_t @ A @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aA6) ).
thf(246,plain,
! [A: $i,B: $i] :
( ~ ( s_t @ A @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( perpAt @ A @ B @ C @ D @ E )
| ( perpAt @ D @ E @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_12a) ).
thf(207,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)],[36]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ~ ( s_r @ A @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_8) ).
thf(272,plain,
! [A: $i,B: $i] :
( ~ ( s_r @ A @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D )
| ( C = D )
| ( A = B )
| ~ ( perp @ C @ D @ E @ F )
| ( perp @ A @ B @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp2) ).
thf(315,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)],[66]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( s_r @ A @ B @ C )
| ~ ( s_r @ D @ B @ C )
| ~ ( s_t @ A @ C @ D )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_6) ).
thf(262,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)],[51]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A = B )
| ~ ( s_m @ C @ D @ E )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ E )
| ( s_col @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13b) ).
thf(268,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)],[53]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( perp @ A @ B @ C @ D )
| ~ ( s_col @ A @ B @ C )
| ~ ( s_col @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_14a) ).
thf(358,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)],[81]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11b) ).
thf(400,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)],[91]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A = B )
| ~ ( s_t @ A @ B @ C )
| ~ ( s_t @ A @ B @ D )
| ( s_t @ A @ C @ D )
| ( s_t @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_1) ).
thf(222,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)],[41]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( s_col @ A @ B @ C )
| ( s_col @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11c) ).
thf(337,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)],[74]) ).
thf(9,axiom,
! [A: $i,B: $i] : ( s_e @ A @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_8) ).
thf(122,plain,
! [A: $i,B: $i] : ( s_e @ A @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(456,plain,
$false,
inference(e,[status(thm)],[379,153,129,218,131,138,347,352,333,249,185,288,389,110,216,179,321,106,293,396,116,243,307,233,201,366,302,392,275,329,324,285,356,169,124,339,266,360,205,311,343,237,298,412,166,148,279,296,176,118,281,191,402,144,350,187,172,113,419,377,230,362,103,140,213,155,198,226,241,162,209,194,150,95,327,182,331,370,127,319,258,158,246,207,272,315,262,268,358,400,222,337,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO523+1 : TPTP v8.1.2. Released v7.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n023.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 04:19:14 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.94/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.68/1.10 % [INFO] Parsing done (234ms).
% 1.68/1.12 % [INFO] Running in sequential loop mode.
% 2.39/1.39 % [INFO] eprover registered as external prover.
% 2.39/1.40 % [INFO] cvc4 registered as external prover.
% 2.39/1.40 % [INFO] Scanning for conjecture ...
% 2.65/1.50 % [INFO] Found a conjecture and 200 axioms. Running axiom selection ...
% 2.83/1.58 % [INFO] Axiom selection finished. Selected 92 axioms (removed 108 axioms).
% 3.37/1.69 % [INFO] Problem is first-order (TPTP FOF).
% 3.37/1.71 % [INFO] Type checking passed.
% 3.37/1.71 % [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 ...
% 7.42/2.82 % External prover 'e' found a proof!
% 7.42/2.82 % [INFO] Killing All external provers ...
% 7.42/2.82 % Time passed: 2289ms (effective reasoning time: 1692ms)
% 7.42/2.82 % 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)>
% 7.42/2.82 % 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
% 7.42/2.82 % No. of inferences in proof: 188
% 7.42/2.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2289 ms resp. 1692 ms w/o parsing
% 7.45/2.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.45/2.88 % [INFO] Killing All external provers ...
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