%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO032-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 : n012.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 07:12:06 AM UTC 2026
% Result : Unsatisfiable 31.74s 6.96s
% Output : Refutation 31.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 71
% Syntax : Number of formulae : 213 ( 92 unt; 0 typ; 0 def)
% Number of atoms : 536 ( 156 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 2110 ( 294 ~; 263 |; 0 &;1553 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 11 con; 0-6 aty)
% Number of variables : 555 ( 0 ^; 555 !; 0 ?; 555 :)
% Comments :
%------------------------------------------------------------------------------
thf(equidistant_decl,type,
equidistant: $i > $i > $i > $i > $o ).
thf(v_decl,type,
v: $i ).
thf(w_decl,type,
w: $i ).
thf(v1_decl,type,
v1: $i ).
thf(w1_decl,type,
w1: $i ).
thf(between_decl,type,
between: $i > $i > $i > $o ).
thf(reflection_decl,type,
reflection: $i > $i > $i ).
thf(extension_decl,type,
extension: $i > $i > $i > $i > $i ).
thf(euclid1_decl,type,
euclid1: $i > $i > $i > $i > $i > $i ).
thf(lower_dimension_point_1_decl,type,
lower_dimension_point_1: $i ).
thf(lower_dimension_point_2_decl,type,
lower_dimension_point_2: $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_3_decl,type,
lower_dimension_point_3: $i ).
thf(continuous_decl,type,
continuous: $i > $i > $i > $i > $i > $i > $i ).
thf(u_decl,type,
u: $i ).
thf(u1_decl,type,
u1: $i ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( C @ ( C @ ( A @ ( B @ extension ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e1) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( C @ ( C @ ( A @ ( B @ extension ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,axiom,
! [B: $i,A: $i] : ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_1) ).
thf(74,plain,
! [B: $i,A: $i] : ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,axiom,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).
thf(131,plain,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(132,plain,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
inference(polarity_switch,[status(thm)],[131]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) )
!= ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[74,132]) ).
thf(248,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) )
!= ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ) ),
inference(simp,[status(thm)],[247]) ).
thf(252,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ reflection ) )
!= lower_dimension_point_2 )
| ( B != lower_dimension_point_1 )
| ( A != lower_dimension_point_3 ) ),
inference(simp,[status(thm)],[248]) ).
thf(255,plain,
( ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ reflection ) )
!= lower_dimension_point_2 ),
inference(simp,[status(thm)],[252]) ).
thf(57,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( B @ reflection ) @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_2) ).
thf(203,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( B @ reflection ) @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(29,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_2) ).
thf(138,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(13,axiom,
! [A: $i] :
( A
= ( A @ ( A @ reflection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3_2) ).
thf(100,plain,
! [A: $i] :
( A
= ( A @ ( A @ reflection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(101,plain,
! [A: $i] :
( ( A @ ( A @ reflection ) )
= A ),
inference(lifteq,[status(thm)],[100]) ).
thf(49,axiom,
w @ ( v @ ( u @ between ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
thf(187,plain,
w @ ( v @ ( u @ between ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(229,plain,
( ( ( w @ ( v @ ( u @ between ) ) )
!= ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[187,132]) ).
thf(230,plain,
( ( w @ ( v @ ( u @ between ) ) )
!= ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ) ),
inference(simp,[status(thm)],[229]) ).
thf(234,plain,
( ( lower_dimension_point_2 != w )
| ( lower_dimension_point_1 != v )
| ( u != lower_dimension_point_3 ) ),
inference(simp,[status(thm)],[230]) ).
thf(19,axiom,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).
thf(115,plain,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(65,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_3) ).
thf(217,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)],[65]) ).
thf(21,axiom,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).
thf(120,plain,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(48,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( A = B )
| ~ ( D @ ( B @ ( C @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( A @ ( C @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11) ).
thf(184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( A = B )
| ~ ( D @ ( B @ ( C @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( A @ ( C @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ ( B @ ( A @ extension ) ) ) )
= ( A @ ( B @ ( B @ ( A @ extension ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_3) ).
thf(110,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)],[17]) ).
thf(39,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ between ) ) )
| ( A
!= ( E @ ( D @ ( C @ ( B @ extension ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b0) ).
thf(164,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)],[39]) ).
thf(121,plain,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
inference(polarity_switch,[status(thm)],[120]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ between ) ) )
| ~ ( C @ ( D @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b8) ).
thf(147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ between ) ) )
| ~ ( C @ ( D @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(279,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ reflection ) )
!= ( C @ ( B @ reflection ) ) )
| ( A @ ( C @ ( B @ between ) ) ) ),
inference(paramod_ordered,[status(thm)],[101,74]) ).
thf(280,plain,
! [A: $i] : ( A @ ( A @ ( A @ between ) ) ),
inference(pattern_uni,[status(thm)],[279:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( C @ ( D @ extension ) ) ) @ ( C @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( A @ ( B @ extension ) ) ) @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_2) ).
thf(221,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( C @ ( D @ extension ) ) ) @ ( C @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( A @ ( B @ extension ) ) ) @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(27,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(133,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)],[27]) ).
thf(116,plain,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
inference(polarity_switch,[status(thm)],[115]) ).
thf(59,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ reflection ) @ reflection ) @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r5) ).
thf(206,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ reflection ) @ reflection ) @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(cnf,[status(esa)],[76]) ).
thf(310,plain,
! [C: $i,B: $i,A: $i] :
( ( ( w @ ( v @ ( u @ between ) ) )
!= ( C @ ( B @ ( A @ between ) ) ) )
| ( A @ ( B @ ( C @ between ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[187,77]) ).
thf(311,plain,
! [C: $i,B: $i,A: $i] :
( ( ( w @ ( v @ ( u @ between ) ) )
!= ( C @ ( B @ ( A @ between ) ) ) )
| ( A @ ( B @ ( C @ between ) ) ) ),
inference(simp,[status(thm)],[310]) ).
thf(312,plain,
u @ ( v @ ( w @ between ) ),
inference(pattern_uni,[status(thm)],[311:[bind(A,$thf( u )),bind(B,$thf( v )),bind(C,$thf( w ))]]) ).
thf(227,plain,
( ( ( w @ ( v @ ( u @ between ) ) )
!= ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[187,121]) ).
thf(228,plain,
( ( w @ ( v @ ( u @ between ) ) )
!= ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ) ),
inference(simp,[status(thm)],[227]) ).
thf(233,plain,
( ( lower_dimension_point_3 != w )
| ( lower_dimension_point_2 != v )
| ( u != lower_dimension_point_1 ) ),
inference(simp,[status(thm)],[228]) ).
thf(20,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_3) ).
thf(117,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',d5) ).
thf(201,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)],[56]) ).
thf(14,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(102,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)],[14]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( A
!= ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( A @ ( B @ extension ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_1) ).
thf(158,plain,
! [B: $i,A: $i] :
( A
!= ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( A @ ( B @ extension ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(159,plain,
! [B: $i,A: $i] :
( A
!= ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( A @ ( B @ extension ) ) ) ) ),
inference(polarity_switch,[status(thm)],[158]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( A @ ( B @ extension ) ) ) )
!= A ),
inference(lifteq,[status(thm)],[159]) ).
thf(52,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/sandbox/benchmark/theBenchmark.p',d9) ).
thf(192,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)],[52]) ).
thf(10,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_1) ).
thf(92,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',d8) ).
thf(224,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)],[70]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',d10_2) ).
thf(188,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)],[50]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( A @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
thf(141,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)],[30]) ).
thf(249,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) )
!= ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[74,116]) ).
thf(250,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) )
!= ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ) ),
inference(simp,[status(thm)],[249]) ).
thf(253,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ reflection ) )
!= lower_dimension_point_1 )
| ( B != lower_dimension_point_3 )
| ( A != lower_dimension_point_2 ) ),
inference(simp,[status(thm)],[250]) ).
thf(256,plain,
( ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ reflection ) )
!= lower_dimension_point_1 ),
inference(simp,[status(thm)],[253]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ reflection ) @ reflection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r6) ).
thf(124,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ reflection ) @ reflection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1,negated_conjecture,
~ ( w1 @ ( v1 @ ( w @ ( v @ equidistant ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_to_w_equals_v1_to_w1) ).
thf(72,plain,
~ ( w1 @ ( v1 @ ( w @ ( v @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(73,plain,
~ ( w1 @ ( v1 @ ( w @ ( v @ equidistant ) ) ) ),
inference(polarity_switch,[status(thm)],[72]) ).
thf(25,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(128,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)],[25]) ).
thf(15,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(105,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)],[15]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( D @ ( B @ ( A @ between ) ) )
| ~ ( D @ ( C @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b7) ).
thf(161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( D @ ( B @ ( A @ between ) ) )
| ~ ( D @ ( C @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
thf(180,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)],[46]) ).
thf(33,axiom,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ between ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2) ).
thf(149,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_2) ).
thf(204,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)],[58]) ).
thf(51,axiom,
w1 @ ( v1 @ ( u1 @ between ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_between_u1_and_w1) ).
thf(191,plain,
w1 @ ( v1 @ ( u1 @ between ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(316,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ between ) ) )
!= ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ) )
| ~ $true
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,116]) ).
thf(317,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ between ) ) )
!= ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(simp,[status(thm)],[316]) ).
thf(318,plain,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_3 @ ( lower_dimension_point_1 @ between ) ) ),
inference(pattern_uni,[status(thm)],[317:[bind(A,$thf( lower_dimension_point_1 )),bind(B,$thf( lower_dimension_point_3 )),bind(C,$thf( lower_dimension_point_2 ))]]) ).
thf(385,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) )
!= ( lower_dimension_point_2 @ ( lower_dimension_point_3 @ ( lower_dimension_point_1 @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[74,318]) ).
thf(386,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) )
!= ( lower_dimension_point_2 @ ( lower_dimension_point_3 @ ( lower_dimension_point_1 @ between ) ) ) ),
inference(simp,[status(thm)],[385]) ).
thf(400,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ reflection ) )
!= lower_dimension_point_2 )
| ( B != lower_dimension_point_3 )
| ( A != lower_dimension_point_1 ) ),
inference(simp,[status(thm)],[386]) ).
thf(402,plain,
( ( lower_dimension_point_3 @ ( lower_dimension_point_1 @ reflection ) )
!= lower_dimension_point_2 ),
inference(simp,[status(thm)],[400]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A = B )
| ~ ( B @ ( C @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_2) ).
thf(144,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)],[31]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ between ) ) )
| ( A != C )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b1) ).
thf(86,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)],[8]) ).
thf(42,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(172,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)],[42]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ between ) ) )
| ~ ( D @ ( C @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b9) ).
thf(113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ between ) ) )
| ~ ( D @ ( C @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_5) ).
thf(219,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)],[66]) ).
thf(313,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ between ) ) )
!= ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ) )
| ~ $true
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,132]) ).
thf(314,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ between ) ) )
!= ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(simp,[status(thm)],[313]) ).
thf(315,plain,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_1 @ ( lower_dimension_point_2 @ between ) ) ),
inference(pattern_uni,[status(thm)],[314:[bind(A,$thf( lower_dimension_point_2 )),bind(B,$thf( lower_dimension_point_1 )),bind(C,$thf( lower_dimension_point_3 ))]]) ).
thf(361,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) )
!= ( lower_dimension_point_3 @ ( lower_dimension_point_1 @ ( lower_dimension_point_2 @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[74,315]) ).
thf(362,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) )
!= ( lower_dimension_point_3 @ ( lower_dimension_point_1 @ ( lower_dimension_point_2 @ between ) ) ) ),
inference(simp,[status(thm)],[361]) ).
thf(372,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ reflection ) )
!= lower_dimension_point_3 )
| ( B != lower_dimension_point_1 )
| ( A != lower_dimension_point_2 ) ),
inference(simp,[status(thm)],[362]) ).
thf(377,plain,
( ( lower_dimension_point_1 @ ( lower_dimension_point_2 @ reflection ) )
!= lower_dimension_point_3 ),
inference(simp,[status(thm)],[372]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ between ) ) )
| ~ ( D @ ( C @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b4) ).
thf(98,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)],[12]) ).
thf(61,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(208,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)],[61]) ).
thf(139,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(polarity_switch,[status(thm)],[138]) ).
thf(140,plain,
lower_dimension_point_3 != lower_dimension_point_2,
inference(lifteq,[status(thm)],[139]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( D @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_4) ).
thf(213,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)],[63]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( C @ ( B @ ( B @ ( A @ extension ) ) ) ) )
| ( A = B )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_1) ).
thf(155,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)],[36]) ).
thf(54,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( D @ ( G @ ( B @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( C @ between ) ) )
| ~ ( E @ ( B @ ( A @ between ) ) )
| ~ ( H @ ( F @ ( G @ ( E @ equidistant ) ) ) )
| ~ ( H @ ( C @ ( G @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( C @ ( E @ ( A @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12) ).
thf(198,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( D @ ( G @ ( B @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( C @ between ) ) )
| ~ ( E @ ( B @ ( A @ between ) ) )
| ~ ( H @ ( F @ ( G @ ( E @ equidistant ) ) ) )
| ~ ( H @ ( C @ ( G @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( C @ ( E @ ( A @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(69,axiom,
! [B: $i,A: $i] : ( B @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
thf(223,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(304,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ between ) ) )
!= ( E @ ( D @ ( C @ between ) ) ) )
| ( C @ ( D @ ( E @ between ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[149,77]) ).
thf(305,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ between ) ) )
!= ( E @ ( D @ ( C @ between ) ) ) )
| ( C @ ( D @ ( E @ between ) ) ) ),
inference(simp,[status(thm)],[304]) ).
thf(306,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ between ) ) ),
inference(pattern_uni,[status(thm)],[305:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( D @ ( C @ ( A @ between ) ) )
| ~ ( D @ ( C @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b6) ).
thf(135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( D @ ( C @ ( A @ between ) ) )
| ~ ( D @ ( C @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(71,axiom,
w1 @ ( u1 @ ( w @ ( u @ equidistant ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_w_equals_u1_to_w1) ).
thf(226,plain,
w1 @ ( u1 @ ( w @ ( u @ equidistant ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(6,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(80,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)],[6]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ reflection ) ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3_1) ).
thf(150,plain,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ reflection ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( B @ ( C @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b3) ).
thf(95,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)],[11]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ between ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3) ).
thf(75,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(325,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ between ) ) )
!= ( E @ ( D @ ( C @ between ) ) ) )
| ( C @ ( D @ ( E @ between ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[75,77]) ).
thf(326,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ between ) ) )
!= ( E @ ( D @ ( C @ between ) ) ) )
| ( C @ ( D @ ( E @ between ) ) ) ),
inference(simp,[status(thm)],[325]) ).
thf(327,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ between ) ) ),
inference(pattern_uni,[status(thm)],[326:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B )),bind(E,$thf( B ))]]) ).
thf(260,plain,
( ( ( w1 @ ( u1 @ ( w @ ( u @ equidistant ) ) ) )
!= ( w1 @ ( v1 @ ( w @ ( v @ equidistant ) ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[226,73]) ).
thf(261,plain,
( ( w1 @ ( u1 @ ( w @ ( u @ equidistant ) ) ) )
!= ( w1 @ ( v1 @ ( w @ ( v @ equidistant ) ) ) ) ),
inference(simp,[status(thm)],[260]) ).
thf(262,plain,
( ( w1 != w1 )
| ( u1 != v1 )
| ( w != w )
| ( u != v ) ),
inference(simp,[status(thm)],[261]) ).
thf(263,plain,
( ( u1 != v1 )
| ( u != v ) ),
inference(simp,[status(thm)],[262]) ).
thf(44,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7) ).
thf(177,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3) ).
thf(182,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)],[47]) ).
thf(35,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(154,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)],[35]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_1) ).
thf(175,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)],[43]) ).
thf(41,axiom,
! [B: $i,A: $i] : ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_3) ).
thf(171,plain,
! [B: $i,A: $i] : ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(118,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(polarity_switch,[status(thm)],[117]) ).
thf(119,plain,
lower_dimension_point_3 != lower_dimension_point_1,
inference(lifteq,[status(thm)],[118]) ).
thf(231,plain,
( ( ( w @ ( v @ ( u @ between ) ) )
!= ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[187,116]) ).
thf(232,plain,
( ( w @ ( v @ ( u @ between ) ) )
!= ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(235,plain,
( ( lower_dimension_point_1 != w )
| ( lower_dimension_point_3 != v )
| ( u != lower_dimension_point_2 ) ),
inference(simp,[status(thm)],[232]) ).
thf(60,axiom,
v1 @ ( u1 @ ( v @ ( u @ equidistant ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_u1_to_v1) ).
thf(207,plain,
v1 @ ( u1 @ ( v @ ( u @ equidistant ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(81,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)],[80]) ).
thf(82,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)],[81]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A = B )
| ~ ( C @ ( A @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_1) ).
thf(168,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)],[40]) ).
thf(62,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(210,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)],[62]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ reflection ) )
= ( B @ ( A @ ( B @ ( A @ extension ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflection) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ reflection ) )
= ( B @ ( A @ ( B @ ( A @ extension ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ ( B @ extension ) ) ) )
= A ),
inference(lifteq,[status(thm)],[78]) ).
thf(53,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(195,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(93,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(polarity_switch,[status(thm)],[92]) ).
thf(94,plain,
lower_dimension_point_2 != lower_dimension_point_1,
inference(lifteq,[status(thm)],[93]) ).
thf(55,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(200,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(45,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(178,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)],[45]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ between ) ) )
| ~ ( D @ ( C @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b5) ).
thf(90,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ between ) ) )
| ~ ( D @ ( C @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(245,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) )
!= ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[74,121]) ).
thf(246,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) )
!= ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ) ),
inference(simp,[status(thm)],[245]) ).
thf(251,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ reflection ) )
!= lower_dimension_point_3 )
| ( B != lower_dimension_point_2 )
| ( A != lower_dimension_point_1 ) ),
inference(simp,[status(thm)],[246]) ).
thf(254,plain,
( ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ reflection ) )
!= lower_dimension_point_3 ),
inference(simp,[status(thm)],[251]) ).
thf(22,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( B @ ( A @ ( C @ ( E @ ( D @ ( F @ ( A @ inner_pasch ) ) ) ) @ ( E @ inner_pasch ) ) ) ) @ ( B @ between ) ) )
| ( C @ ( C @ ( B @ ( A @ ( C @ ( E @ ( D @ ( F @ ( A @ inner_pasch ) ) ) ) @ ( E @ inner_pasch ) ) ) ) @ ( F @ between ) ) )
| ~ ( D @ ( F @ ( A @ between ) ) )
| ~ ( C @ ( E @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b10) ).
thf(122,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( B @ ( A @ ( C @ ( E @ ( D @ ( F @ ( A @ inner_pasch ) ) ) ) @ ( E @ inner_pasch ) ) ) ) @ ( B @ between ) ) )
| ( C @ ( C @ ( B @ ( A @ ( C @ ( E @ ( D @ ( F @ ( A @ inner_pasch ) ) ) ) @ ( E @ inner_pasch ) ) ) ) @ ( F @ between ) ) )
| ~ ( D @ ( F @ ( A @ between ) ) )
| ~ ( C @ ( E @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A
!= ( A @ ( B @ reflection ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r4) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A
!= ( A @ ( B @ reflection ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(307,plain,
! [C: $i,B: $i,A: $i] :
( ( ( w1 @ ( v1 @ ( u1 @ between ) ) )
!= ( C @ ( B @ ( A @ between ) ) ) )
| ( A @ ( B @ ( C @ between ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[191,77]) ).
thf(308,plain,
! [C: $i,B: $i,A: $i] :
( ( ( w1 @ ( v1 @ ( u1 @ between ) ) )
!= ( C @ ( B @ ( A @ between ) ) ) )
| ( A @ ( B @ ( C @ between ) ) ) ),
inference(simp,[status(thm)],[307]) ).
thf(309,plain,
u1 @ ( v1 @ ( w1 @ between ) ),
inference(pattern_uni,[status(thm)],[308:[bind(A,$thf( u1 )),bind(B,$thf( v1 )),bind(C,$thf( w1 ))]]) ).
thf(64,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(215,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)],[64]) ).
thf(68,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(222,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)],[68]) ).
thf(25299,plain,
$false,
inference(e,[status(thm)],[78,255,203,138,101,234,115,217,120,184,110,164,121,147,280,221,132,133,116,206,312,74,233,117,201,102,160,192,92,224,188,141,256,124,77,73,128,105,161,180,149,204,191,402,144,86,187,172,113,219,377,76,318,98,208,140,213,155,198,223,306,135,226,80,150,95,327,263,177,182,154,72,175,158,171,75,119,235,207,82,315,168,210,107,126,79,195,94,131,200,178,90,254,122,83,309,215,222,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO032-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % 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
% 0.05/0.36 % Computer : n012.cluster.edu
% 0.05/0.36 % Model : x86_64 x86_64
% 0.05/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.36 % Memory : 8046.5625MB
% 0.05/0.36 % OS : Linux 6.8.0-71-generic
% 0.05/0.36 % CPULimit : 300
% 0.05/0.36 % WCLimit : 300
% 0.05/0.36 % DateTime : Fri Sep 25 12:34:05 UTC 2026
% 0.05/0.36 % CPUTime :
% 0.05/0.36 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
% 0.45/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.83/1.03 % [INFO] Parsing done (130ms).
% 0.83/1.03 % [INFO] Running in sequential loop mode.
% 1.20/1.23 % [INFO] eprover registered as external prover.
% 1.20/1.23 % [INFO] Scanning for conjecture ...
% 1.20/1.28 % [INFO] Found a conjecture (or negated_conjecture) and 70 axioms. Running axiom selection ...
% 1.41/1.32 % [INFO] Axiom selection finished. Selected 70 axioms (removed 0 axioms).
% 1.41/1.37 % [INFO] Problem is propositional (TPTP CNF).
% 1.41/1.38 % [INFO] Type checking passed.
% 1.41/1.38 % [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 ...
% 31.74/6.95 % External prover 'e' found a proof!
% 31.74/6.95 % [INFO] Killing All external provers ...
% 31.74/6.96 % Time passed: 6443ms (effective reasoning time: 5918ms)
% 31.74/6.96 % Axioms used in derivation (70): e3_2, d3, reflexivity_for_equidistance, r5, outer_five_segment, v1_between_u1_and_w1, d8, euclid3, d5, continuity1, e2_2, lower_dimension1, d4_4, b2, continuity2, b10, b3, r2_1, d4_5, transitivity_for_equidistance, e1, u_to_v_equals_u1_to_v1, b7, d9, r6, inner_pasch2, b4, lower_dimension2, t3, reflection, b1, r2_2, b8, u_to_w_equals_u1_to_w1, d12, identity_for_betweeness, r3_2, b0, upper_dimension, t2, b5, euclid1, d7, d10_2, r4, e2_3, segment_construction2, d2, d10_3, e3_1, d4_2, d4_1, lower_dimension3, t6_2, b9, b6, inner_pasch1, e3_3, r3_1, segment_construction1, euclid2, d10_1, e2_1, d1, t1, d11, identity_for_equidistance, d4_3, v_between_u_and_w, t6_1
% 31.74/6.96 % No. of inferences in proof: 213
% 31.74/6.96 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 6443 ms resp. 5918 ms w/o parsing
% 31.74/7.00 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 31.74/7.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------