%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO053-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n010.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 07:12:11 AM UTC 2026
% Result : Unsatisfiable 17.97s 5.42s
% Output : Refutation 17.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 21
% Syntax : Number of formulae : 128 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 379 ( 133 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1484 ( 251 ~; 195 |; 0 &;1038 @)
% ( 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 : 16 ( 13 usr; 8 con; 0-6 aty)
% Number of variables : 333 ( 0 ^; 333 !; 0 ?; 333 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_decl,type,
v: $i ).
thf(w_decl,type,
w: $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(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(euclid2_decl,type,
euclid2: $i > $i > $i > $i > $i > $i ).
thf(extension_decl,type,
extension: $i > $i > $i > $i > $i ).
thf(u_decl,type,
u: $i ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
thf(62,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)],[17]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ between ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(1,negated_conjecture,
v != w,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v_equals_w) ).
thf(22,plain,
v != w,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(23,plain,
v != w,
inference(polarity_switch,[status(thm)],[22]) ).
thf(24,plain,
w != v,
inference(lifteq,[status(thm)],[23]) ).
thf(266,plain,
! [B: $i,A: $i] :
( ( B != w )
| ( A != v )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,24]) ).
thf(267,plain,
! [A: $i] :
( ( A != v )
| ~ ( A @ ( w @ ( A @ between ) ) ) ),
inference(pattern_uni,[status(thm)],[266:[bind(A,$thf( A )),bind(B,$thf( w ))]]) ).
thf(440,plain,
~ ( v @ ( w @ ( v @ between ) ) ),
inference(simp,[status(thm)],[267]) ).
thf(916,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) )
!= ( v @ ( w @ ( v @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,440]) ).
thf(917,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) )
!= ( v @ ( w @ ( v @ between ) ) ) ),
inference(simp,[status(thm)],[916]) ).
thf(936,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ extension ) ) ) )
!= v )
| ( B != w )
| ( A != v ) ),
inference(simp,[status(thm)],[917]) ).
thf(941,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( w @ ( v @ extension ) ) ) )
!= v ),
inference(simp,[status(thm)],[936]) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',upper_dimension) ).
thf(56,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)],[15]) ).
thf(20,axiom,
w @ ( v @ ( u @ between ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
thf(65,plain,
w @ ( v @ ( u @ between ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(11,axiom,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).
thf(47,plain,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(48,plain,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
inference(polarity_switch,[status(thm)],[47]) ).
thf(107,plain,
( ( ( w @ ( v @ ( u @ between ) ) )
!= ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,48]) ).
thf(108,plain,
( ( w @ ( v @ ( u @ between ) ) )
!= ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ) ),
inference(simp,[status(thm)],[107]) ).
thf(121,plain,
( ( lower_dimension_point_2 != w )
| ( lower_dimension_point_1 != v )
| ( u != lower_dimension_point_3 ) ),
inference(simp,[status(thm)],[108]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( A != w )
| ( B != v )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,24]) ).
thf(265,plain,
! [A: $i] :
( ( A != v )
| ~ ( w @ ( A @ ( w @ between ) ) ) ),
inference(pattern_uni,[status(thm)],[264:[bind(A,$thf( w ))]]) ).
thf(439,plain,
~ ( w @ ( v @ ( w @ between ) ) ),
inference(simp,[status(thm)],[265]) ).
thf(214,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)],[62,48]) ).
thf(215,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)],[214]) ).
thf(219,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)],[215]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ extension ) ) ) )
!= lower_dimension_point_2 ),
inference(simp,[status(thm)],[219]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(21,axiom,
w @ ( u @ ( v @ ( u @ equidistant ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_u_to_w) ).
thf(66,plain,
w @ ( u @ ( v @ ( u @ equidistant ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(8,axiom,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).
thf(39,plain,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(40,plain,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
inference(polarity_switch,[status(thm)],[39]) ).
thf(216,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)],[62,40]) ).
thf(217,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)],[216]) ).
thf(220,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)],[217]) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ extension ) ) ) )
!= lower_dimension_point_3 ),
inference(simp,[status(thm)],[220]) ).
thf(4,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/sandbox/benchmark/theBenchmark.p',inner_pasch2) ).
thf(30,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)],[4]) ).
thf(31,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(cnf,[status(esa)],[30]) ).
thf(873,plain,
( ( ( w @ ( v @ ( u @ between ) ) )
!= ( w @ ( v @ ( w @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,439]) ).
thf(874,plain,
( ( w @ ( v @ ( u @ between ) ) )
!= ( w @ ( v @ ( w @ between ) ) ) ),
inference(simp,[status(thm)],[873]) ).
thf(876,plain,
( ( w != w )
| ( v != v )
| ( u != w ) ),
inference(simp,[status(thm)],[874]) ).
thf(881,plain,
u != w,
inference(simp,[status(thm)],[876]) ).
thf(894,plain,
! [B: $i,A: $i] :
( ( B != u )
| ( A != w )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,881]) ).
thf(895,plain,
! [A: $i] :
( ( A != w )
| ~ ( A @ ( u @ ( A @ between ) ) ) ),
inference(pattern_uni,[status(thm)],[894:[bind(A,$thf( A )),bind(B,$thf( u ))]]) ).
thf(903,plain,
~ ( w @ ( u @ ( w @ between ) ) ),
inference(simp,[status(thm)],[895]) ).
thf(109,plain,
( ( ( w @ ( v @ ( u @ between ) ) )
!= ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,40]) ).
thf(110,plain,
( ( w @ ( v @ ( u @ between ) ) )
!= ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ) ),
inference(simp,[status(thm)],[109]) ).
thf(119,plain,
( ( lower_dimension_point_3 != w )
| ( lower_dimension_point_2 != v )
| ( u != lower_dimension_point_1 ) ),
inference(simp,[status(thm)],[110]) ).
thf(7,axiom,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).
thf(37,plain,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(38,plain,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
inference(polarity_switch,[status(thm)],[37]) ).
thf(111,plain,
( ( ( w @ ( v @ ( u @ between ) ) )
!= ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,38]) ).
thf(112,plain,
( ( w @ ( v @ ( u @ between ) ) )
!= ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(120,plain,
( ( lower_dimension_point_1 != w )
| ( lower_dimension_point_3 != v )
| ( u != lower_dimension_point_2 ) ),
inference(simp,[status(thm)],[112]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ( B != u )
| ( lower_dimension_point_1 != w )
| ( lower_dimension_point_3 != v )
| ( A != lower_dimension_point_2 )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,120]) ).
thf(259,plain,
! [A: $i] :
( ( lower_dimension_point_1 != w )
| ( lower_dimension_point_3 != v )
| ( A != lower_dimension_point_2 )
| ~ ( A @ ( u @ ( A @ between ) ) ) ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( A )),bind(B,$thf( u ))]]) ).
thf(436,plain,
( ( lower_dimension_point_1 != w )
| ( lower_dimension_point_3 != v )
| ~ ( lower_dimension_point_2 @ ( u @ ( lower_dimension_point_2 @ between ) ) ) ),
inference(simp,[status(thm)],[259]) ).
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/sandbox/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
thf(25,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(892,plain,
! [B: $i,A: $i] :
( ( A != u )
| ( B != w )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,881]) ).
thf(893,plain,
! [A: $i] :
( ( A != w )
| ~ ( u @ ( A @ ( u @ between ) ) ) ),
inference(pattern_uni,[status(thm)],[892:[bind(A,$thf( u ))]]) ).
thf(902,plain,
~ ( u @ ( w @ ( u @ between ) ) ),
inference(simp,[status(thm)],[893]) ).
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/sandbox/benchmark/theBenchmark.p',euclid1) ).
thf(27,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(28,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)],[27]) ).
thf(29,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)],[28]) ).
thf(684,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)],[65,29]) ).
thf(685,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)],[684]) ).
thf(686,plain,
! [B: $i,A: $i] :
( ( w @ ( B @ ( v @ ( A @ ( u @ euclid1 ) ) ) ) @ ( A @ ( u @ between ) ) )
| ~ ( B @ ( v @ ( A @ between ) ) )
| ( u = v ) ),
inference(pattern_uni,[status(thm)],[685:[bind(A,$thf( u )),bind(B,$thf( v )),bind(C,$thf( w ))]]) ).
thf(815,plain,
! [B: $i,A: $i] :
( ( w @ ( B @ ( v @ ( A @ ( u @ euclid1 ) ) ) ) @ ( A @ ( u @ between ) ) )
| ~ ( B @ ( v @ ( A @ between ) ) )
| ( u = v ) ),
inference(simp,[status(thm)],[686]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',continuity1) ).
thf(32,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)],[5]) ).
thf(33,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)],[32]) ).
thf(1172,plain,
! [B: $i,A: $i] :
( ( ( w @ ( v @ ( u @ between ) ) )
!= ( B @ ( v @ ( A @ between ) ) ) )
| ( w @ ( B @ ( v @ ( A @ ( u @ euclid1 ) ) ) ) @ ( A @ ( u @ between ) ) )
| ~ $true
| ( u = v ) ),
inference(paramod_ordered,[status(thm)],[65,815]) ).
thf(1173,plain,
! [B: $i,A: $i] :
( ( ( w @ ( v @ ( u @ between ) ) )
!= ( B @ ( v @ ( A @ between ) ) ) )
| ( w @ ( B @ ( v @ ( A @ ( u @ euclid1 ) ) ) ) @ ( A @ ( u @ between ) ) )
| ( u = v ) ),
inference(simp,[status(thm)],[1172]) ).
thf(1174,plain,
( ( w @ ( w @ ( v @ ( u @ ( u @ euclid1 ) ) ) ) @ ( u @ ( u @ between ) ) )
| ( u = v ) ),
inference(pattern_uni,[status(thm)],[1173:[bind(A,$thf( u )),bind(B,$thf( w ))]]) ).
thf(869,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) )
!= ( w @ ( v @ ( w @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,439]) ).
thf(870,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) )
!= ( w @ ( v @ ( w @ between ) ) ) ),
inference(simp,[status(thm)],[869]) ).
thf(875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ extension ) ) ) )
!= w )
| ( B != v )
| ( A != w ) ),
inference(simp,[status(thm)],[870]) ).
thf(879,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( v @ ( w @ extension ) ) ) )
!= w ),
inference(simp,[status(thm)],[875]) ).
thf(857,plain,
! [B: $i,A: $i] :
( ( A != w )
| ~ ( w @ ( v @ ( B @ between ) ) )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,439]) ).
thf(858,plain,
! [A: $i] :
( ~ ( w @ ( v @ ( A @ between ) ) )
| ~ ( w @ ( A @ ( w @ between ) ) ) ),
inference(pattern_uni,[status(thm)],[857:[bind(A,$thf( w ))]]) ).
thf(889,plain,
! [A: $i] :
( ~ ( w @ ( v @ ( A @ between ) ) )
| ~ ( w @ ( A @ ( w @ between ) ) ) ),
inference(simp,[status(thm)],[858]) ).
thf(206,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)],[62,38]) ).
thf(207,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)],[206]) ).
thf(218,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)],[207]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ extension ) ) ) )
!= lower_dimension_point_1 ),
inference(simp,[status(thm)],[218]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ extension ) ) ) @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
thf(64,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)],[19]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',euclid2) ).
thf(44,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)],[10]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',euclid3) ).
thf(59,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)],[16]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',continuity2) ).
thf(54,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)],[14]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',inner_pasch1) ).
thf(49,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)],[12]) ).
thf(69,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ continuous ) ) ) ) ) @ ( C @ between ) ) )
!= ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ) )
| ~ $true
| ~ ( D @ ( F @ ( B @ between ) ) )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( E @ ( A @ ( D @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,40]) ).
thf(70,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ continuous ) ) ) ) ) @ ( C @ between ) ) )
!= ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ) )
| ~ ( D @ ( F @ ( B @ between ) ) )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( E @ ( A @ ( D @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(81,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E != lower_dimension_point_3 )
| ( ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ continuous ) ) ) ) ) )
!= lower_dimension_point_2 )
| ( C != lower_dimension_point_1 )
| ~ ( D @ ( F @ ( B @ between ) ) )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( E @ ( A @ ( D @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(simp,[status(thm)],[70]) ).
thf(86,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( lower_dimension_point_3 @ ( C @ ( D @ ( lower_dimension_point_1 @ ( B @ ( A @ continuous ) ) ) ) ) )
!= lower_dimension_point_2 )
| ~ ( C @ ( D @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) )
| ~ ( lower_dimension_point_3 @ ( A @ ( C @ ( A @ equidistant ) ) ) )
| ~ ( lower_dimension_point_1 @ ( A @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(simp,[status(thm)],[81]) ).
thf(1014,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) )
!= ( w @ ( u @ ( w @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,903]) ).
thf(1015,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) )
!= ( w @ ( u @ ( w @ between ) ) ) ),
inference(simp,[status(thm)],[1014]) ).
thf(1036,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ extension ) ) ) )
!= w )
| ( B != u )
| ( A != w ) ),
inference(simp,[status(thm)],[1015]) ).
thf(1043,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( u @ ( w @ extension ) ) ) )
!= w ),
inference(simp,[status(thm)],[1036]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( A != lower_dimension_point_1 )
| ( B != w )
| ( lower_dimension_point_3 != v )
| ( u != lower_dimension_point_2 )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,120]) ).
thf(257,plain,
! [A: $i] :
( ( A != w )
| ( lower_dimension_point_3 != v )
| ( u != lower_dimension_point_2 )
| ~ ( lower_dimension_point_1 @ ( A @ ( lower_dimension_point_1 @ between ) ) ) ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( lower_dimension_point_1 ))]]) ).
thf(434,plain,
( ( lower_dimension_point_3 != v )
| ( u != lower_dimension_point_2 )
| ~ ( lower_dimension_point_1 @ ( w @ ( lower_dimension_point_1 @ between ) ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(18,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(63,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(26,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)],[25]) ).
thf(965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) )
!= ( u @ ( w @ ( u @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[62,902]) ).
thf(966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) )
!= ( u @ ( w @ ( u @ between ) ) ) ),
inference(simp,[status(thm)],[965]) ).
thf(985,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ extension ) ) ) )
!= u )
| ( B != w )
| ( A != u ) ),
inference(simp,[status(thm)],[966]) ).
thf(995,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( w @ ( u @ extension ) ) ) )
!= u ),
inference(simp,[status(thm)],[985]) ).
thf(13,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/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).
thf(51,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)],[13]) ).
thf(3934,plain,
$false,
inference(e,[status(thm)],[941,56,121,439,225,41,66,226,31,903,119,120,440,24,436,37,25,902,881,29,815,33,1174,38,65,879,889,224,64,32,34,22,44,59,27,54,49,86,39,1043,434,48,63,40,26,995,36,30,51,47,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO053-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n010.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 12:37:14 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.81/0.93 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/1.18 % [INFO] Parsing done (241ms).
% 1.32/1.21 % [INFO] Running in sequential loop mode.
% 1.96/1.71 % [INFO] eprover registered as external prover.
% 1.96/1.72 % [INFO] Scanning for conjecture ...
% 2.11/1.81 % [INFO] Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ...
% 2.24/1.90 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 2.24/1.97 % [INFO] Problem is propositional (TPTP CNF).
% 2.24/1.98 % [INFO] Type checking passed.
% 2.24/1.98 % [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 ...
% 17.97/5.41 % External prover 'e' found a proof!
% 17.97/5.41 % [INFO] Killing All external provers ...
% 17.97/5.41 % Time passed: 4875ms (effective reasoning time: 4199ms)
% 17.97/5.41 % Axioms used in derivation (20): euclid3, continuity1, lower_dimension1, transitivity_for_equidistance, inner_pasch2, reflexivity_for_equidistance, lower_dimension2, identity_for_betweeness, outer_five_segment, upper_dimension, euclid1, segment_construction2, lower_dimension3, inner_pasch1, identity_for_equidistance, v_between_u_and_w, continuity2, u_to_v_equals_u_to_w, segment_construction1, euclid2
% 17.97/5.41 % No. of inferences in proof: 128
% 17.97/5.42 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4875 ms resp. 4199 ms w/o parsing
% 17.97/5.48 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.97/5.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------