%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO026-2 : 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 : n002.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 07:12:05 AM UTC 2026
% Result : Unsatisfiable 41.17s 29.18s
% Output : Refutation 34.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 23
% Syntax : Number of formulae : 126 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 332 ( 110 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1274 ( 213 ~; 162 |; 0 &; 899 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 9 con; 0-6 aty)
% Number of variables : 264 ( 0 ^; 264 !; 0 ?; 264 :)
% Comments :
%------------------------------------------------------------------------------
thf(w_decl,type,
w: $i ).
thf(x_decl,type,
x: $i ).
thf(equidistant_decl,type,
equidistant: $i > $i > $i > $i > $o ).
thf(between_decl,type,
between: $i > $i > $i > $o ).
thf(euclid1_decl,type,
euclid1: $i > $i > $i > $i > $i > $i ).
thf(u_decl,type,
u: $i ).
thf(v_decl,type,
v: $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(continuous_decl,type,
continuous: $i > $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(extension_decl,type,
extension: $i > $i > $i > $i > $i ).
thf(20,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(69,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)],[20]) ).
thf(18,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(67,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)],[18]) ).
thf(10,axiom,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(47,plain,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(48,plain,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
inference(polarity_switch,[status(thm)],[47]) ).
thf(194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) )
!= ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[67,48]) ).
thf(195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) )
!= ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ) ),
inference(simp,[status(thm)],[194]) ).
thf(198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ extension ) ) ) )
!= lower_dimension_point_3 )
| ( B != lower_dimension_point_2 )
| ( A != lower_dimension_point_1 ) ),
inference(simp,[status(thm)],[195]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ extension ) ) ) )
!= lower_dimension_point_3 ),
inference(simp,[status(thm)],[198]) ).
thf(13,axiom,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(55,plain,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(56,plain,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
inference(polarity_switch,[status(thm)],[55]) ).
thf(12,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(52,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)],[12]) ).
thf(9,axiom,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(45,plain,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(46,plain,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
inference(polarity_switch,[status(thm)],[45]) ).
thf(186,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) )
!= ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[67,46]) ).
thf(187,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) )
!= ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ) ),
inference(simp,[status(thm)],[186]) ).
thf(197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ extension ) ) ) )
!= lower_dimension_point_1 )
| ( B != lower_dimension_point_3 )
| ( A != lower_dimension_point_2 ) ),
inference(simp,[status(thm)],[187]) ).
thf(201,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ extension ) ) ) )
!= lower_dimension_point_1 ),
inference(simp,[status(thm)],[197]) ).
thf(21,axiom,
x @ ( v @ ( u @ between ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_x) ).
thf(70,plain,
x @ ( v @ ( u @ between ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(22,axiom,
w @ ( v @ ( u @ between ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
thf(71,plain,
w @ ( v @ ( u @ between ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,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(29,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)],[3]) ).
thf(30,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(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( B @ ( D @ ( A @ euclid1 ) ) ) ) @ ( D @ ( A @ between ) ) )
| ~ ( E @ ( B @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(308,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( w @ ( v @ ( u @ between ) ) )
!= ( C @ ( B @ ( A @ between ) ) ) )
| ( C @ ( E @ ( B @ ( D @ ( A @ euclid1 ) ) ) ) @ ( D @ ( A @ between ) ) )
| ~ ( E @ ( B @ ( D @ between ) ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[71,31]) ).
thf(309,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( w @ ( v @ ( u @ between ) ) )
!= ( C @ ( B @ ( A @ between ) ) ) )
| ( C @ ( E @ ( B @ ( D @ ( A @ euclid1 ) ) ) ) @ ( D @ ( A @ between ) ) )
| ~ ( E @ ( B @ ( D @ between ) ) )
| ( A = B ) ),
inference(simp,[status(thm)],[308]) ).
thf(310,plain,
! [B: $i,A: $i] :
( ( w @ ( B @ ( v @ ( A @ ( u @ euclid1 ) ) ) ) @ ( A @ ( u @ between ) ) )
| ~ ( B @ ( v @ ( A @ between ) ) )
| ( v = u ) ),
inference(pattern_uni,[status(thm)],[309:[bind(A,$thf( u )),bind(B,$thf( v )),bind(C,$thf( w ))]]) ).
thf(463,plain,
! [B: $i,A: $i] :
( ( w @ ( B @ ( v @ ( A @ ( u @ euclid1 ) ) ) ) @ ( A @ ( u @ between ) ) )
| ~ ( B @ ( v @ ( A @ between ) ) )
| ( v = u ) ),
inference(simp,[status(thm)],[310]) ).
thf(4,axiom,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_not_v) ).
thf(32,plain,
u != v,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(33,plain,
u != v,
inference(polarity_switch,[status(thm)],[32]) ).
thf(34,plain,
v != u,
inference(lifteq,[status(thm)],[33]) ).
thf(966,plain,
! [B: $i,A: $i] :
( ( w @ ( B @ ( v @ ( A @ ( u @ euclid1 ) ) ) ) @ ( A @ ( u @ between ) ) )
| ~ ( B @ ( v @ ( A @ between ) ) ) ),
inference(simplifyReflect,[status(thm)],[463,34]) ).
thf(1010,plain,
! [B: $i,A: $i] :
( ( ( x @ ( v @ ( u @ between ) ) )
!= ( B @ ( v @ ( A @ between ) ) ) )
| ( w @ ( B @ ( v @ ( A @ ( u @ euclid1 ) ) ) ) @ ( A @ ( u @ between ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,966]) ).
thf(1011,plain,
! [B: $i,A: $i] :
( ( ( x @ ( v @ ( u @ between ) ) )
!= ( B @ ( v @ ( A @ between ) ) ) )
| ( w @ ( B @ ( v @ ( A @ ( u @ euclid1 ) ) ) ) @ ( A @ ( u @ between ) ) ) ),
inference(simp,[status(thm)],[1010]) ).
thf(1012,plain,
w @ ( x @ ( v @ ( u @ ( u @ euclid1 ) ) ) ) @ ( u @ ( u @ between ) ),
inference(pattern_uni,[status(thm)],[1011:[bind(A,$thf( u )),bind(B,$thf( x ))]]) ).
thf(7,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(40,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)],[7]) ).
thf(41,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(cnf,[status(esa)],[40]) ).
thf(99,plain,
( ( ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) )
!= ( x @ ( v @ ( u @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,56]) ).
thf(100,plain,
( ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) )
!= ( x @ ( v @ ( u @ between ) ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(113,plain,
( ( lower_dimension_point_2 != x )
| ( lower_dimension_point_1 != v )
| ( lower_dimension_point_3 != u ) ),
inference(simp,[status(thm)],[100]) ).
thf(5,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(35,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)],[5]) ).
thf(23,axiom,
x @ ( v @ ( w @ ( v @ equidistant ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_to_w_equals_v_to_x) ).
thf(72,plain,
x @ ( v @ ( w @ ( v @ equidistant ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(cnf,[status(esa)],[42]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ between ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(632,plain,
! [B: $i,A: $i] :
( ( B != v )
| ( A != u )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,34]) ).
thf(633,plain,
! [A: $i] :
( ( A != u )
| ~ ( A @ ( v @ ( A @ between ) ) ) ),
inference(pattern_uni,[status(thm)],[632:[bind(A,$thf( A )),bind(B,$thf( v ))]]) ).
thf(788,plain,
~ ( u @ ( v @ ( u @ between ) ) ),
inference(simp,[status(thm)],[633]) ).
thf(905,plain,
( ( ( u @ ( v @ ( u @ between ) ) )
!= ( w @ ( v @ ( u @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[71,788]) ).
thf(906,plain,
( ( u @ ( v @ ( u @ between ) ) )
!= ( w @ ( v @ ( u @ between ) ) ) ),
inference(simp,[status(thm)],[905]) ).
thf(923,plain,
( ( u != w )
| ( v != v )
| ( u != u ) ),
inference(simp,[status(thm)],[906]) ).
thf(935,plain,
u != w,
inference(simp,[status(thm)],[923]) ).
thf(944,plain,
! [B: $i,A: $i] :
( ( B != u )
| ( A != w )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,935]) ).
thf(945,plain,
! [A: $i] :
( ( A != w )
| ~ ( A @ ( u @ ( A @ between ) ) ) ),
inference(pattern_uni,[status(thm)],[944:[bind(A,$thf( A )),bind(B,$thf( u ))]]) ).
thf(950,plain,
~ ( w @ ( u @ ( w @ between ) ) ),
inference(simp,[status(thm)],[945]) ).
thf(1,negated_conjecture,
w != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_w_is_x) ).
thf(24,plain,
w != x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(36,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(cnf,[status(esa)],[35]) ).
thf(37,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 ) ) )
| ~ ( E @ ( B @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(14,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(57,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)],[14]) ).
thf(903,plain,
( ( ( u @ ( v @ ( u @ between ) ) )
!= ( x @ ( v @ ( u @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,788]) ).
thf(904,plain,
( ( u @ ( v @ ( u @ between ) ) )
!= ( x @ ( v @ ( u @ between ) ) ) ),
inference(simp,[status(thm)],[903]) ).
thf(924,plain,
( ( u != x )
| ( v != v )
| ( u != u ) ),
inference(simp,[status(thm)],[904]) ).
thf(937,plain,
u != x,
inference(simp,[status(thm)],[924]) ).
thf(2,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(27,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)],[2]) ).
thf(28,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(cnf,[status(esa)],[27]) ).
thf(6,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(38,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)],[6]) ).
thf(116,plain,
( ( ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) )
!= ( w @ ( v @ ( u @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[71,56]) ).
thf(117,plain,
( ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) )
!= ( w @ ( v @ ( u @ between ) ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(128,plain,
( ( lower_dimension_point_2 != w )
| ( lower_dimension_point_1 != v )
| ( lower_dimension_point_3 != u ) ),
inference(simp,[status(thm)],[117]) ).
thf(942,plain,
! [B: $i,A: $i] :
( ( A != u )
| ( B != w )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,935]) ).
thf(943,plain,
! [A: $i] :
( ( A != w )
| ~ ( u @ ( A @ ( u @ between ) ) ) ),
inference(pattern_uni,[status(thm)],[942:[bind(A,$thf( u ))]]) ).
thf(953,plain,
~ ( u @ ( w @ ( u @ between ) ) ),
inference(simp,[status(thm)],[943]) ).
thf(17,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(64,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)],[17]) ).
thf(15,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(59,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)],[15]) ).
thf(630,plain,
! [B: $i,A: $i] :
( ( A != v )
| ( B != u )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,34]) ).
thf(631,plain,
! [A: $i] :
( ( A != u )
| ~ ( v @ ( A @ ( v @ between ) ) ) ),
inference(pattern_uni,[status(thm)],[630:[bind(A,$thf( v ))]]) ).
thf(787,plain,
~ ( v @ ( u @ ( v @ between ) ) ),
inference(simp,[status(thm)],[631]) ).
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(49,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(25,plain,
w != x,
inference(polarity_switch,[status(thm)],[24]) ).
thf(26,plain,
x != w,
inference(lifteq,[status(thm)],[25]) ).
thf(700,plain,
! [B: $i,A: $i] :
( ( A != x )
| ( B != w )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,26]) ).
thf(701,plain,
! [A: $i] :
( ( A != w )
| ~ ( x @ ( A @ ( x @ between ) ) ) ),
inference(pattern_uni,[status(thm)],[700:[bind(A,$thf( x ))]]) ).
thf(811,plain,
~ ( x @ ( w @ ( x @ between ) ) ),
inference(simp,[status(thm)],[701]) ).
thf(956,plain,
! [B: $i,A: $i] :
( ( B != u )
| ( A != x )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,937]) ).
thf(957,plain,
! [A: $i] :
( ( A != x )
| ~ ( A @ ( u @ ( A @ between ) ) ) ),
inference(pattern_uni,[status(thm)],[956:[bind(A,$thf( A )),bind(B,$thf( u ))]]) ).
thf(964,plain,
~ ( x @ ( u @ ( x @ between ) ) ),
inference(simp,[status(thm)],[957]) ).
thf(101,plain,
( ( ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) )
!= ( x @ ( v @ ( u @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,46]) ).
thf(102,plain,
( ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) )
!= ( x @ ( v @ ( u @ between ) ) ) ),
inference(simp,[status(thm)],[101]) ).
thf(112,plain,
( ( lower_dimension_point_1 != x )
| ( lower_dimension_point_3 != v )
| ( lower_dimension_point_2 != u ) ),
inference(simp,[status(thm)],[102]) ).
thf(702,plain,
! [B: $i,A: $i] :
( ( B != x )
| ( A != w )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,26]) ).
thf(703,plain,
! [A: $i] :
( ( A != w )
| ~ ( A @ ( x @ ( A @ between ) ) ) ),
inference(pattern_uni,[status(thm)],[702:[bind(A,$thf( A )),bind(B,$thf( x ))]]) ).
thf(812,plain,
~ ( w @ ( x @ ( w @ between ) ) ),
inference(simp,[status(thm)],[703]) ).
thf(954,plain,
! [B: $i,A: $i] :
( ( A != u )
| ( B != x )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,937]) ).
thf(955,plain,
! [A: $i] :
( ( A != x )
| ~ ( u @ ( A @ ( u @ between ) ) ) ),
inference(pattern_uni,[status(thm)],[954:[bind(A,$thf( u ))]]) ).
thf(963,plain,
~ ( u @ ( x @ ( u @ between ) ) ),
inference(simp,[status(thm)],[955]) ).
thf(184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) )
!= ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[67,56]) ).
thf(185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) )
!= ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ extension ) ) ) )
!= lower_dimension_point_2 )
| ( B != lower_dimension_point_1 )
| ( A != lower_dimension_point_3 ) ),
inference(simp,[status(thm)],[185]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ extension ) ) ) )
!= lower_dimension_point_2 ),
inference(simp,[status(thm)],[196]) ).
thf(19,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(68,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,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(62,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)],[16]) ).
thf(109,plain,
( ( ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) )
!= ( x @ ( v @ ( u @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,48]) ).
thf(110,plain,
( ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) )
!= ( x @ ( v @ ( u @ between ) ) ) ),
inference(simp,[status(thm)],[109]) ).
thf(111,plain,
( ( lower_dimension_point_3 != x )
| ( lower_dimension_point_2 != v )
| ( lower_dimension_point_1 != u ) ),
inference(simp,[status(thm)],[110]) ).
thf(12321,plain,
$false,
inference(e,[status(thm)],[69,202,56,52,201,1012,41,113,35,48,72,950,42,24,37,46,57,29,937,966,70,788,28,38,128,953,45,64,32,34,44,59,27,71,787,49,811,964,112,812,67,31,963,40,26,55,47,200,68,62,111,935]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO026-2 : 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
% 0.15/20.43 % Computer : n002.cluster.edu
% 0.15/20.43 % Model : x86_64 x86_64
% 0.15/20.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/20.43 % Memory : 8046.5625MB
% 0.15/20.43 % OS : Linux 6.8.0-71-generic
% 0.15/20.43 % CPULimit : 300
% 0.15/20.43 % WCLimit : 300
% 0.15/20.43 % DateTime : Fri Sep 25 12:36:26 UTC 2026
% 0.15/20.43 % CPUTime :
% 0.15/20.43 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
% 0.19/21.03 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.36/21.23 % [INFO] Parsing done (202ms).
% 1.36/21.25 % [INFO] Running in sequential loop mode.
% 2.09/21.66 % [INFO] eprover registered as external prover.
% 2.09/21.66 % [INFO] Scanning for conjecture ...
% 2.32/21.76 % [INFO] Found a conjecture (or negated_conjecture) and 22 axioms. Running axiom selection ...
% 2.51/21.82 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 2.51/21.87 % [INFO] Problem is propositional (TPTP CNF).
% 2.51/21.88 % [INFO] Type checking passed.
% 2.51/21.88 % [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 ...
% 41.17/29.17 % External prover 'e' found a proof!
% 41.17/29.17 % [INFO] Killing All external provers ...
% 41.17/29.18 % Time passed: 8596ms (effective reasoning time: 7924ms)
% 41.17/29.18 % Axioms used in derivation (22): euclid3, continuity1, continuity2, transitivity_for_equidistance, inner_pasch2, reflexivity_for_equidistance, lower_dimension2, identity_for_betweeness, outer_five_segment, upper_dimension, euclid1, segment_construction2, lower_dimension3, v_to_w_equals_v_to_x, inner_pasch1, v_between_u_and_x, identity_for_equidistance, v_between_u_and_w, lower_dimension1, u_not_v, segment_construction1, euclid2
% 41.17/29.18 % No. of inferences in proof: 126
% 41.17/29.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8596 ms resp. 7924 ms w/o parsing
% 34.88/29.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 34.88/29.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------