%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO043-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n016.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 07:12:09 AM UTC 2026
% Result : Unsatisfiable 5.56s 18.13s
% Output : Refutation 5.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 55
% Syntax : Number of formulae : 111 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 267 ( 62 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1200 ( 138 ~; 156 |; 0 &; 906 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 8 con; 0-6 aty)
% Number of variables : 360 ( 0 ^; 360 !; 0 ?; 360 :)
% Comments :
%------------------------------------------------------------------------------
thf(between_decl,type,
between: $i > $i > $i > $o ).
thf(v_decl,type,
v: $i ).
thf(w_decl,type,
w: $i ).
thf(x_decl,type,
x: $i ).
thf(equidistant_decl,type,
equidistant: $i > $i > $i > $i > $o ).
thf(reflection_decl,type,
reflection: $i > $i > $i ).
thf(extension_decl,type,
extension: $i > $i > $i > $i > $i ).
thf(continuous_decl,type,
continuous: $i > $i > $i > $i > $i > $i > $i ).
thf(u_decl,type,
u: $i ).
thf(euclid1_decl,type,
euclid1: $i > $i > $i > $i > $i > $i ).
thf(euclid2_decl,type,
euclid2: $i > $i > $i > $i > $i > $i ).
thf(inner_pasch_decl,type,
inner_pasch: $i > $i > $i > $i > $i > $i ).
thf(lower_dimension_point_2_decl,type,
lower_dimension_point_2: $i ).
thf(lower_dimension_point_3_decl,type,
lower_dimension_point_3: $i ).
thf(lower_dimension_point_1_decl,type,
lower_dimension_point_1: $i ).
thf(1,negated_conjecture,
~ ( x @ ( w @ ( v @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_w_between_v_and_x) ).
thf(56,plain,
~ ( x @ ( w @ ( v @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(55,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( C @ ( E @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( C @ between ) ) )
| ~ ( E @ ( B @ ( A @ between ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8) ).
thf(174,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( C @ ( E @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( C @ between ) ) )
| ~ ( E @ ( B @ ( A @ between ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(45,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( F @ ( G @ ( E @ equidistant ) ) ) )
| ( A = B )
| ~ ( F @ ( D @ ( C @ between ) ) )
| ~ ( E @ ( B @ ( A @ between ) ) )
| ~ ( H @ ( D @ ( G @ ( B @ equidistant ) ) ) )
| ~ ( H @ ( C @ ( G @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_five_segment) ).
thf(148,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( F @ ( G @ ( E @ equidistant ) ) ) )
| ( A = B )
| ~ ( F @ ( D @ ( C @ between ) ) )
| ~ ( E @ ( B @ ( A @ between ) ) )
| ~ ( H @ ( D @ ( G @ ( B @ equidistant ) ) ) )
| ~ ( H @ ( C @ ( G @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(32,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( D @ ( A @ ( E @ between ) ) )
| ( A @ ( E @ ( D @ between ) ) )
| ( E @ ( D @ ( A @ between ) ) )
| ~ ( C @ ( E @ ( B @ ( E @ equidistant ) ) ) )
| ~ ( C @ ( D @ ( B @ ( D @ equidistant ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upper_dimension) ).
thf(118,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( D @ ( A @ ( E @ between ) ) )
| ( A @ ( E @ ( D @ between ) ) )
| ( E @ ( D @ ( A @ between ) ) )
| ~ ( C @ ( E @ ( B @ ( E @ equidistant ) ) ) )
| ~ ( C @ ( D @ ( B @ ( D @ equidistant ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( A @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b2) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( A @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3) ).
thf(63,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A
!= ( A @ ( B @ reflection ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A
!= ( A @ ( B @ reflection ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).
thf(163,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( A = B )
| ~ ( D @ ( B @ ( C @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9) ).
thf(138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( A = B )
| ~ ( D @ ( B @ ( C @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( C @ ( C @ ( A @ ( B @ extension ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( C @ ( C @ ( A @ ( B @ extension ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( C @ ( B @ ( B @ ( A @ extension ) ) ) ) )
| ( A = B )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_1) ).
thf(164,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( C @ ( B @ ( B @ ( A @ extension ) ) ) ) )
| ( A = B )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(26,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ continuous ) ) ) ) ) @ ( A @ ( F @ ( A @ equidistant ) ) ) )
| ~ ( D @ ( F @ ( B @ between ) ) )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( E @ ( A @ ( D @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity2) ).
thf(106,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ continuous ) ) ) ) ) @ ( A @ ( F @ ( A @ equidistant ) ) ) )
| ~ ( D @ ( F @ ( B @ between ) ) )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( E @ ( A @ ( D @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ between ) ) )
| ~ ( D @ ( C @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b4) ).
thf(121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ between ) ) )
| ~ ( D @ ( C @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(15,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( B @ reflection ) @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_2) ).
thf(84,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( B @ reflection ) @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
thf(61,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(38,axiom,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(133,plain,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ reflection ) @ reflection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r6) ).
thf(74,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ reflection ) @ reflection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
thf(60,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_2) ).
thf(85,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_5) ).
thf(102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(8,axiom,
! [A: $i] :
( A
= ( A @ ( A @ reflection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_2) ).
thf(70,plain,
! [A: $i] :
( A
= ( A @ ( A @ reflection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(40,axiom,
x @ ( w @ ( u @ between ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_between_u_and_x) ).
thf(137,plain,
x @ ( w @ ( u @ between ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(6,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
thf(65,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = F )
| ( ( B @ ( A @ ( F @ ( E @ extension ) ) ) )
= ( D @ ( C @ ( F @ ( E @ extension ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_2) ).
thf(97,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = F )
| ( ( B @ ( A @ ( F @ ( E @ extension ) ) ) )
= ( D @ ( C @ ( F @ ( E @ extension ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(48,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( B @ ( D @ ( A @ euclid1 ) ) ) ) @ ( D @ ( A @ between ) ) )
| ( A = B )
| ~ ( E @ ( B @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid1) ).
thf(156,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( B @ ( D @ ( A @ euclid1 ) ) ) ) @ ( D @ ( A @ between ) ) )
| ( A = B )
| ~ ( E @ ( B @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(42,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( B @ ( D @ ( A @ euclid2 ) ) ) ) @ ( E @ ( A @ between ) ) )
| ( A = B )
| ~ ( E @ ( B @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid2) ).
thf(141,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( B @ ( D @ ( A @ euclid2 ) ) ) ) @ ( E @ ( A @ between ) ) )
| ( A = B )
| ~ ( E @ ( B @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(36,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ continuous ) ) ) ) ) @ ( C @ between ) ) )
| ~ ( D @ ( F @ ( B @ between ) ) )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( E @ ( A @ ( D @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity1) ).
thf(128,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ continuous ) ) ) ) ) @ ( C @ between ) ) )
| ~ ( D @ ( F @ ( B @ between ) ) )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( E @ ( A @ ( D @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(25,axiom,
! [B: $i,A: $i] : ( B @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
thf(105,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(43,axiom,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(144,plain,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( B @ ( C @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b3) ).
thf(159,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( B @ ( C @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(30,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
thf(113,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(13,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(81,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(39,axiom,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(135,plain,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(53,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ between ) ) )
| ( A
!= ( E @ ( D @ ( C @ ( B @ extension ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b0) ).
thf(167,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ between ) ) )
| ( A
!= ( E @ ( D @ ( C @ ( B @ extension ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(50,axiom,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
thf(162,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(29,axiom,
! [B: $i,A: $i] : ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_1) ).
thf(112,plain,
! [B: $i,A: $i] : ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(34,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( B @ ( D @ ( A @ euclid2 ) ) ) ) @ ( C @ ( C @ ( E @ ( B @ ( D @ ( A @ euclid1 ) ) ) ) @ between ) ) )
| ( A = B )
| ~ ( E @ ( B @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid3) ).
thf(123,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( B @ ( D @ ( A @ euclid2 ) ) ) ) @ ( C @ ( C @ ( E @ ( B @ ( D @ ( A @ euclid1 ) ) ) ) @ between ) ) )
| ( A = B )
| ~ ( E @ ( B @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
thf(154,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( D @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_4) ).
thf(72,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( D @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(17,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ reflection ) @ reflection ) @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5) ).
thf(87,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ reflection ) @ reflection ) @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ extension ) ) ) @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).
thf(104,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ extension ) ) ) @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(31,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ between ) ) )
| ( A != C )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).
thf(114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ between ) ) )
| ( A != C )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A = B )
| ~ ( C @ ( A @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_1) ).
thf(171,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A = B )
| ~ ( C @ ( A @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_1) ).
thf(58,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5) ).
thf(82,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A = B )
| ~ ( B @ ( C @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_2) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A = B )
| ~ ( B @ ( C @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(44,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( E @ ( C @ ( B @ ( A @ inner_pasch ) ) ) ) @ ( B @ between ) ) )
| ~ ( C @ ( E @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch1) ).
thf(146,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( E @ ( C @ ( B @ ( A @ inner_pasch ) ) ) ) @ ( B @ between ) ) )
| ~ ( C @ ( E @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(35,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( E @ ( C @ ( B @ ( A @ inner_pasch ) ) ) ) @ ( E @ between ) ) )
| ~ ( C @ ( E @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch2) ).
thf(126,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( E @ ( C @ ( B @ ( A @ inner_pasch ) ) ) ) @ ( E @ between ) ) )
| ~ ( C @ ( E @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ reflection ) )
= ( B @ ( A @ ( B @ ( A @ extension ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ reflection ) )
= ( B @ ( A @ ( B @ ( A @ extension ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ ( B @ ( A @ extension ) ) ) )
= ( A @ ( B @ ( B @ ( A @ extension ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_3) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ ( B @ ( A @ extension ) ) ) )
= ( A @ ( B @ ( B @ ( A @ extension ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_3) ).
thf(100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ reflection ) ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_1) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ reflection ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(28,axiom,
w @ ( v @ ( u @ between ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
thf(111,plain,
w @ ( v @ ( u @ between ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(179,plain,
$false,
inference(e,[status(thm)],[56,174,148,118,108,63,67,163,138,88,164,106,121,84,61,133,74,60,85,102,70,137,65,97,156,141,128,105,144,159,113,81,76,130,135,167,162,112,123,154,72,87,104,114,171,58,82,151,146,126,79,94,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO043-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.13/15.69 % CPULimit : 300
% 0.13/15.69 % WCLimit : 300
% 0.13/15.69 % DateTime : Fri Sep 25 12:34:53 UTC 2026
% 0.13/15.69 % CPUTime :
% 0.13/15.69 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.09/16.28 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.67/16.52 % [INFO] Parsing done (237ms).
% 1.67/16.54 % [INFO] Running in sequential loop mode.
% 2.38/16.95 % [INFO] eprover registered as external prover.
% 2.38/16.96 % [INFO] Scanning for conjecture ...
% 2.67/17.05 % [INFO] Found a conjecture (or negated_conjecture) and 54 axioms. Running axiom selection ...
% 2.67/17.13 % [INFO] Axiom selection finished. Selected 54 axioms (removed 0 axioms).
% 3.03/17.20 % [INFO] Problem is propositional (TPTP CNF).
% 3.03/17.21 % [INFO] Type checking passed.
% 3.03/17.22 % [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 ...
% 5.22/18.13 % External prover 'e' found a proof!
% 5.22/18.13 % [INFO] Killing All external provers ...
% 5.56/18.13 % Time passed: 2289ms (effective reasoning time: 1586ms)
% 5.56/18.13 % Axioms used in derivation (54): continuity1, w_between_u_and_x, d3, reflexivity_for_equidistance, r2_2, identity_for_betweeness, r5, outer_five_segment, t6_2, d8, euclid3, d5, lower_dimension1, d4_4, b2, continuity2, b3, r2_1, d4_5, transitivity_for_equidistance, e1, d9, r6, inner_pasch2, b4, lower_dimension2, t3, reflection, b1, r3_2, b0, upper_dimension, t2, euclid1, d7, d10_2, r4, segment_construction2, d2, d10_3, d4_2, d4_1, lower_dimension3, inner_pasch1, r3_1, segment_construction1, euclid2, d10_1, d1, t1, identity_for_equidistance, d4_3, v_between_u_and_w, t6_1
% 5.56/18.13 % No. of inferences in proof: 111
% 5.56/18.13 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2289 ms resp. 1586 ms w/o parsing
% 5.81/18.23 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.81/18.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------