%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO078-6 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 : Tue Sep 29 09:53:30 AM UTC 2026
% Result : Satisfiable 0.17s 0.48s
% Output : FiniteModel 0.17s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
tff('declare_$i1',type,
'fmb_$i_1': $i ).
tff('declare_$i2',type,
'fmb_$i_2': $i ).
tff('declare_$i3',type,
'fmb_$i_3': $i ).
tff('declare_$i4',type,
'fmb_$i_4': $i ).
tff('finite_domain_$i',axiom,
! [X: $i] :
( ( X = 'fmb_$i_1' )
| ( X = 'fmb_$i_2' )
| ( X = 'fmb_$i_3' )
| ( X = 'fmb_$i_4' ) ) ).
tff('distinct_domain_$i',axiom,
( ( 'fmb_$i_1' != 'fmb_$i_2' )
& ( 'fmb_$i_1' != 'fmb_$i_3' )
& ( 'fmb_$i_1' != 'fmb_$i_4' )
& ( 'fmb_$i_2' != 'fmb_$i_3' )
& ( 'fmb_$i_2' != 'fmb_$i_4' )
& ( 'fmb_$i_3' != 'fmb_$i_4' ) ) ).
tff(declare_at_least_one_line,type,
at_least_one_line: $i ).
tff(at_least_one_line_definition,axiom,
at_least_one_line = 'fmb_$i_1' ).
tff(declare_a_plane,type,
a_plane: $i ).
tff(a_plane_definition,axiom,
a_plane = 'fmb_$i_1' ).
tff(declare_line_from_to,type,
line_from_to: ( $i * $i ) > $i ).
tff(function_line_from_to,axiom,
( ( line_from_to('fmb_$i_1','fmb_$i_1') = 'fmb_$i_2' )
& ( line_from_to('fmb_$i_1','fmb_$i_2') = 'fmb_$i_4' )
& ( line_from_to('fmb_$i_1','fmb_$i_3') = 'fmb_$i_4' )
& ( line_from_to('fmb_$i_1','fmb_$i_4') = 'fmb_$i_3' )
& ( line_from_to('fmb_$i_2','fmb_$i_1') = 'fmb_$i_4' )
& ( line_from_to('fmb_$i_2','fmb_$i_2') = 'fmb_$i_3' )
& ( line_from_to('fmb_$i_2','fmb_$i_3') = 'fmb_$i_4' )
& ( line_from_to('fmb_$i_2','fmb_$i_4') = 'fmb_$i_1' )
& ( line_from_to('fmb_$i_3','fmb_$i_1') = 'fmb_$i_4' )
& ( line_from_to('fmb_$i_3','fmb_$i_2') = 'fmb_$i_4' )
& ( line_from_to('fmb_$i_3','fmb_$i_3') = 'fmb_$i_4' )
& ( line_from_to('fmb_$i_3','fmb_$i_4') = 'fmb_$i_2' )
& ( line_from_to('fmb_$i_4','fmb_$i_1') = 'fmb_$i_3' )
& ( line_from_to('fmb_$i_4','fmb_$i_2') = 'fmb_$i_1' )
& ( line_from_to('fmb_$i_4','fmb_$i_3') = 'fmb_$i_2' )
& ( line_from_to('fmb_$i_4','fmb_$i_4') = 'fmb_$i_4' ) ) ).
tff(declare_point_1_on_line,type,
point_1_on_line: $i > $i ).
tff(function_point_1_on_line,axiom,
( ( point_1_on_line('fmb_$i_1') = 'fmb_$i_2' )
& ( point_1_on_line('fmb_$i_2') = 'fmb_$i_3' )
& ( point_1_on_line('fmb_$i_3') = 'fmb_$i_4' )
& ( point_1_on_line('fmb_$i_4') = 'fmb_$i_2' ) ) ).
tff(declare_point_2_on_line,type,
point_2_on_line: $i > $i ).
tff(function_point_2_on_line,axiom,
( ( point_2_on_line('fmb_$i_1') = 'fmb_$i_4' )
& ( point_2_on_line('fmb_$i_2') = 'fmb_$i_4' )
& ( point_2_on_line('fmb_$i_3') = 'fmb_$i_1' )
& ( point_2_on_line('fmb_$i_4') = 'fmb_$i_1' ) ) ).
tff(declare_a_point_not_on_line,type,
a_point_not_on_line: $i > $i ).
tff(function_a_point_not_on_line,axiom,
( ( a_point_not_on_line('fmb_$i_1') = 'fmb_$i_1' )
& ( a_point_not_on_line('fmb_$i_2') = 'fmb_$i_2' )
& ( a_point_not_on_line('fmb_$i_3') = 'fmb_$i_2' )
& ( a_point_not_on_line('fmb_$i_4') = 'fmb_$i_4' ) ) ).
tff(declare_a_point_on_plane,type,
a_point_on_plane: $i > $i ).
tff(function_a_point_on_plane,axiom,
( ( a_point_on_plane('fmb_$i_1') = 'fmb_$i_3' )
& ( a_point_on_plane('fmb_$i_2') = 'fmb_$i_4' )
& ( a_point_on_plane('fmb_$i_3') = 'fmb_$i_4' )
& ( a_point_on_plane('fmb_$i_4') = 'fmb_$i_4' ) ) ).
tff(declare_a_point_not_on_plane,type,
a_point_not_on_plane: $i > $i ).
tff(function_a_point_not_on_plane,axiom,
( ( a_point_not_on_plane('fmb_$i_1') = 'fmb_$i_4' )
& ( a_point_not_on_plane('fmb_$i_2') = 'fmb_$i_1' )
& ( a_point_not_on_plane('fmb_$i_3') = 'fmb_$i_2' )
& ( a_point_not_on_plane('fmb_$i_4') = 'fmb_$i_3' ) ) ).
tff(declare_plane_for_points,type,
plane_for_points: ( $i * $i * $i ) > $i ).
tff(function_plane_for_points,axiom,
( ( plane_for_points('fmb_$i_1','fmb_$i_1','fmb_$i_1') = 'fmb_$i_2' )
& ( plane_for_points('fmb_$i_1','fmb_$i_1','fmb_$i_2') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_1','fmb_$i_1','fmb_$i_3') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_1','fmb_$i_1','fmb_$i_4') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_1','fmb_$i_2','fmb_$i_1') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_1','fmb_$i_2','fmb_$i_2') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_1','fmb_$i_2','fmb_$i_3') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_1','fmb_$i_2','fmb_$i_4') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_1','fmb_$i_3','fmb_$i_1') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_1','fmb_$i_3','fmb_$i_2') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_1','fmb_$i_3','fmb_$i_3') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_1','fmb_$i_3','fmb_$i_4') = 'fmb_$i_3' )
& ( plane_for_points('fmb_$i_1','fmb_$i_4','fmb_$i_1') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_1','fmb_$i_4','fmb_$i_2') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_1','fmb_$i_4','fmb_$i_3') = 'fmb_$i_3' )
& ( plane_for_points('fmb_$i_1','fmb_$i_4','fmb_$i_4') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_2','fmb_$i_1','fmb_$i_1') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_2','fmb_$i_1','fmb_$i_2') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_2','fmb_$i_1','fmb_$i_3') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_2','fmb_$i_1','fmb_$i_4') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_2','fmb_$i_2','fmb_$i_1') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_2','fmb_$i_2','fmb_$i_2') = 'fmb_$i_3' )
& ( plane_for_points('fmb_$i_2','fmb_$i_2','fmb_$i_3') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_2','fmb_$i_2','fmb_$i_4') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_2','fmb_$i_3','fmb_$i_1') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_2','fmb_$i_3','fmb_$i_2') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_2','fmb_$i_3','fmb_$i_3') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_2','fmb_$i_3','fmb_$i_4') = 'fmb_$i_2' )
& ( plane_for_points('fmb_$i_2','fmb_$i_4','fmb_$i_1') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_2','fmb_$i_4','fmb_$i_2') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_2','fmb_$i_4','fmb_$i_3') = 'fmb_$i_2' )
& ( plane_for_points('fmb_$i_2','fmb_$i_4','fmb_$i_4') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_3','fmb_$i_1','fmb_$i_1') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_3','fmb_$i_1','fmb_$i_2') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_3','fmb_$i_1','fmb_$i_3') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_3','fmb_$i_1','fmb_$i_4') = 'fmb_$i_3' )
& ( plane_for_points('fmb_$i_3','fmb_$i_2','fmb_$i_1') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_3','fmb_$i_2','fmb_$i_2') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_3','fmb_$i_2','fmb_$i_3') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_3','fmb_$i_2','fmb_$i_4') = 'fmb_$i_2' )
& ( plane_for_points('fmb_$i_3','fmb_$i_3','fmb_$i_1') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_3','fmb_$i_3','fmb_$i_2') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_3','fmb_$i_3','fmb_$i_3') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_3','fmb_$i_3','fmb_$i_4') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_3','fmb_$i_4','fmb_$i_1') = 'fmb_$i_3' )
& ( plane_for_points('fmb_$i_3','fmb_$i_4','fmb_$i_2') = 'fmb_$i_2' )
& ( plane_for_points('fmb_$i_3','fmb_$i_4','fmb_$i_3') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_3','fmb_$i_4','fmb_$i_4') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_4','fmb_$i_1','fmb_$i_1') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_4','fmb_$i_1','fmb_$i_2') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_4','fmb_$i_1','fmb_$i_3') = 'fmb_$i_3' )
& ( plane_for_points('fmb_$i_4','fmb_$i_1','fmb_$i_4') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_4','fmb_$i_2','fmb_$i_1') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_4','fmb_$i_2','fmb_$i_2') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_4','fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( plane_for_points('fmb_$i_4','fmb_$i_2','fmb_$i_4') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_4','fmb_$i_3','fmb_$i_1') = 'fmb_$i_3' )
& ( plane_for_points('fmb_$i_4','fmb_$i_3','fmb_$i_2') = 'fmb_$i_2' )
& ( plane_for_points('fmb_$i_4','fmb_$i_3','fmb_$i_3') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_4','fmb_$i_3','fmb_$i_4') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_4','fmb_$i_4','fmb_$i_1') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_4','fmb_$i_4','fmb_$i_2') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_4','fmb_$i_4','fmb_$i_3') = 'fmb_$i_4' )
& ( plane_for_points('fmb_$i_4','fmb_$i_4','fmb_$i_4') = 'fmb_$i_4' ) ) ).
tff(declare_common_point_on_planes,type,
common_point_on_planes: ( $i * $i * $i ) > $i ).
tff(function_common_point_on_planes,axiom,
( ( common_point_on_planes('fmb_$i_1','fmb_$i_1','fmb_$i_1') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_1','fmb_$i_1','fmb_$i_2') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_1','fmb_$i_1','fmb_$i_3') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_1','fmb_$i_1','fmb_$i_4') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_1','fmb_$i_2','fmb_$i_1') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_1','fmb_$i_2','fmb_$i_2') = 'fmb_$i_3' )
& ( common_point_on_planes('fmb_$i_1','fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( common_point_on_planes('fmb_$i_1','fmb_$i_2','fmb_$i_4') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_1','fmb_$i_3','fmb_$i_1') = 'fmb_$i_3' )
& ( common_point_on_planes('fmb_$i_1','fmb_$i_3','fmb_$i_2') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_1','fmb_$i_3','fmb_$i_3') = 'fmb_$i_1' )
& ( common_point_on_planes('fmb_$i_1','fmb_$i_3','fmb_$i_4') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_1','fmb_$i_4','fmb_$i_1') = 'fmb_$i_2' )
& ( common_point_on_planes('fmb_$i_1','fmb_$i_4','fmb_$i_2') = 'fmb_$i_1' )
& ( common_point_on_planes('fmb_$i_1','fmb_$i_4','fmb_$i_3') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_1','fmb_$i_4','fmb_$i_4') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_2','fmb_$i_1','fmb_$i_1') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_2','fmb_$i_1','fmb_$i_2') = 'fmb_$i_3' )
& ( common_point_on_planes('fmb_$i_2','fmb_$i_1','fmb_$i_3') = 'fmb_$i_2' )
& ( common_point_on_planes('fmb_$i_2','fmb_$i_1','fmb_$i_4') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_2','fmb_$i_2','fmb_$i_1') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_2','fmb_$i_2','fmb_$i_2') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_2','fmb_$i_2','fmb_$i_3') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_2','fmb_$i_2','fmb_$i_4') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_2','fmb_$i_3','fmb_$i_1') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_2','fmb_$i_3','fmb_$i_2') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_2','fmb_$i_3','fmb_$i_3') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_2','fmb_$i_3','fmb_$i_4') = 'fmb_$i_3' )
& ( common_point_on_planes('fmb_$i_2','fmb_$i_4','fmb_$i_1') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_2','fmb_$i_4','fmb_$i_2') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_2','fmb_$i_4','fmb_$i_3') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_2','fmb_$i_4','fmb_$i_4') = 'fmb_$i_2' )
& ( common_point_on_planes('fmb_$i_3','fmb_$i_1','fmb_$i_1') = 'fmb_$i_3' )
& ( common_point_on_planes('fmb_$i_3','fmb_$i_1','fmb_$i_2') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_3','fmb_$i_1','fmb_$i_3') = 'fmb_$i_1' )
& ( common_point_on_planes('fmb_$i_3','fmb_$i_1','fmb_$i_4') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_3','fmb_$i_2','fmb_$i_1') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_3','fmb_$i_2','fmb_$i_2') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_3','fmb_$i_2','fmb_$i_3') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_3','fmb_$i_2','fmb_$i_4') = 'fmb_$i_3' )
& ( common_point_on_planes('fmb_$i_3','fmb_$i_3','fmb_$i_1') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_3','fmb_$i_3','fmb_$i_2') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_3','fmb_$i_3','fmb_$i_3') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_3','fmb_$i_3','fmb_$i_4') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_3','fmb_$i_4','fmb_$i_1') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_3','fmb_$i_4','fmb_$i_2') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_3','fmb_$i_4','fmb_$i_3') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_3','fmb_$i_4','fmb_$i_4') = 'fmb_$i_1' )
& ( common_point_on_planes('fmb_$i_4','fmb_$i_1','fmb_$i_1') = 'fmb_$i_2' )
& ( common_point_on_planes('fmb_$i_4','fmb_$i_1','fmb_$i_2') = 'fmb_$i_1' )
& ( common_point_on_planes('fmb_$i_4','fmb_$i_1','fmb_$i_3') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_4','fmb_$i_1','fmb_$i_4') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_4','fmb_$i_2','fmb_$i_1') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_4','fmb_$i_2','fmb_$i_2') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_4','fmb_$i_2','fmb_$i_3') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_4','fmb_$i_2','fmb_$i_4') = 'fmb_$i_2' )
& ( common_point_on_planes('fmb_$i_4','fmb_$i_3','fmb_$i_1') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_4','fmb_$i_3','fmb_$i_2') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_4','fmb_$i_3','fmb_$i_3') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_4','fmb_$i_3','fmb_$i_4') = 'fmb_$i_1' )
& ( common_point_on_planes('fmb_$i_4','fmb_$i_4','fmb_$i_1') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_4','fmb_$i_4','fmb_$i_2') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_4','fmb_$i_4','fmb_$i_3') = 'fmb_$i_4' )
& ( common_point_on_planes('fmb_$i_4','fmb_$i_4','fmb_$i_4') = 'fmb_$i_4' ) ) ).
tff(declare_line_through_3_points,type,
line_through_3_points: ( $i * $i * $i ) > $i ).
tff(function_line_through_3_points,axiom,
( ( line_through_3_points('fmb_$i_1','fmb_$i_1','fmb_$i_1') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_1','fmb_$i_1','fmb_$i_2') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_1','fmb_$i_1','fmb_$i_3') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_1','fmb_$i_1','fmb_$i_4') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_1','fmb_$i_2','fmb_$i_1') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_1','fmb_$i_2','fmb_$i_2') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_1','fmb_$i_2','fmb_$i_3') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_1','fmb_$i_2','fmb_$i_4') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_1','fmb_$i_3','fmb_$i_1') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_1','fmb_$i_3','fmb_$i_2') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_1','fmb_$i_3','fmb_$i_3') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_1','fmb_$i_3','fmb_$i_4') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_1','fmb_$i_4','fmb_$i_1') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_1','fmb_$i_4','fmb_$i_2') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_1','fmb_$i_4','fmb_$i_3') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_1','fmb_$i_4','fmb_$i_4') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_2','fmb_$i_1','fmb_$i_1') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_2','fmb_$i_1','fmb_$i_2') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_2','fmb_$i_1','fmb_$i_3') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_2','fmb_$i_1','fmb_$i_4') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_2','fmb_$i_2','fmb_$i_1') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_2','fmb_$i_2','fmb_$i_2') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_2','fmb_$i_2','fmb_$i_3') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_2','fmb_$i_2','fmb_$i_4') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_2','fmb_$i_3','fmb_$i_1') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_2','fmb_$i_3','fmb_$i_2') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_2','fmb_$i_3','fmb_$i_3') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_2','fmb_$i_3','fmb_$i_4') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_2','fmb_$i_4','fmb_$i_1') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_2','fmb_$i_4','fmb_$i_2') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_2','fmb_$i_4','fmb_$i_3') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_2','fmb_$i_4','fmb_$i_4') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_3','fmb_$i_1','fmb_$i_1') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_3','fmb_$i_1','fmb_$i_2') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_3','fmb_$i_1','fmb_$i_3') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_3','fmb_$i_1','fmb_$i_4') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_3','fmb_$i_2','fmb_$i_1') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_3','fmb_$i_2','fmb_$i_2') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_3','fmb_$i_2','fmb_$i_3') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_3','fmb_$i_2','fmb_$i_4') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_3','fmb_$i_3','fmb_$i_1') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_3','fmb_$i_3','fmb_$i_2') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_3','fmb_$i_3','fmb_$i_3') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_3','fmb_$i_3','fmb_$i_4') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_3','fmb_$i_4','fmb_$i_1') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_3','fmb_$i_4','fmb_$i_2') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_3','fmb_$i_4','fmb_$i_3') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_3','fmb_$i_4','fmb_$i_4') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_4','fmb_$i_1','fmb_$i_1') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_4','fmb_$i_1','fmb_$i_2') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_4','fmb_$i_1','fmb_$i_3') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_4','fmb_$i_1','fmb_$i_4') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_4','fmb_$i_2','fmb_$i_1') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_4','fmb_$i_2','fmb_$i_2') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_4','fmb_$i_2','fmb_$i_3') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_4','fmb_$i_2','fmb_$i_4') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_4','fmb_$i_3','fmb_$i_1') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_4','fmb_$i_3','fmb_$i_2') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_4','fmb_$i_3','fmb_$i_3') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_4','fmb_$i_3','fmb_$i_4') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_4','fmb_$i_4','fmb_$i_1') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_4','fmb_$i_4','fmb_$i_2') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_4','fmb_$i_4','fmb_$i_3') = 'fmb_$i_4' )
& ( line_through_3_points('fmb_$i_4','fmb_$i_4','fmb_$i_4') = 'fmb_$i_4' ) ) ).
tff(declare_point_on_line,type,
point_on_line: ( $i * $i ) > $o ).
tff(predicate_point_on_line,axiom,
( ~ point_on_line('fmb_$i_1','fmb_$i_1')
& ~ point_on_line('fmb_$i_1','fmb_$i_2')
& point_on_line('fmb_$i_1','fmb_$i_3')
& point_on_line('fmb_$i_1','fmb_$i_4')
& point_on_line('fmb_$i_2','fmb_$i_1')
& ~ point_on_line('fmb_$i_2','fmb_$i_2')
& ~ point_on_line('fmb_$i_2','fmb_$i_3')
& point_on_line('fmb_$i_2','fmb_$i_4')
& ~ point_on_line('fmb_$i_3','fmb_$i_1')
& point_on_line('fmb_$i_3','fmb_$i_2')
& ~ point_on_line('fmb_$i_3','fmb_$i_3')
& point_on_line('fmb_$i_3','fmb_$i_4')
& point_on_line('fmb_$i_4','fmb_$i_1')
& point_on_line('fmb_$i_4','fmb_$i_2')
& point_on_line('fmb_$i_4','fmb_$i_3')
& ~ point_on_line('fmb_$i_4','fmb_$i_4') ) ).
tff(declare_point,type,
point: $i > $o ).
tff(predicate_point,axiom,
( point('fmb_$i_1')
& point('fmb_$i_2')
& point('fmb_$i_3')
& point('fmb_$i_4') ) ).
tff(declare_line,type,
line: $i > $o ).
tff(predicate_line,axiom,
( line('fmb_$i_1')
& line('fmb_$i_2')
& line('fmb_$i_3')
& line('fmb_$i_4') ) ).
tff(declare_plane,type,
plane: $i > $o ).
tff(predicate_plane,axiom,
( plane('fmb_$i_1')
& plane('fmb_$i_2')
& plane('fmb_$i_3')
& plane('fmb_$i_4') ) ).
tff(declare_point_on_plane,type,
point_on_plane: ( $i * $i ) > $o ).
tff(predicate_point_on_plane,axiom,
( point_on_plane('fmb_$i_1','fmb_$i_1')
& ~ point_on_plane('fmb_$i_1','fmb_$i_2')
& point_on_plane('fmb_$i_1','fmb_$i_3')
& point_on_plane('fmb_$i_1','fmb_$i_4')
& point_on_plane('fmb_$i_2','fmb_$i_1')
& point_on_plane('fmb_$i_2','fmb_$i_2')
& ~ point_on_plane('fmb_$i_2','fmb_$i_3')
& point_on_plane('fmb_$i_2','fmb_$i_4')
& point_on_plane('fmb_$i_3','fmb_$i_1')
& point_on_plane('fmb_$i_3','fmb_$i_2')
& point_on_plane('fmb_$i_3','fmb_$i_3')
& ~ point_on_plane('fmb_$i_3','fmb_$i_4')
& ~ point_on_plane('fmb_$i_4','fmb_$i_1')
& point_on_plane('fmb_$i_4','fmb_$i_2')
& point_on_plane('fmb_$i_4','fmb_$i_3')
& point_on_plane('fmb_$i_4','fmb_$i_4') ) ).
tff(declare_collinear,type,
collinear: ( $i * $i * $i ) > $o ).
tff(predicate_collinear,axiom,
( collinear('fmb_$i_1','fmb_$i_1','fmb_$i_1')
& collinear('fmb_$i_1','fmb_$i_1','fmb_$i_2')
& collinear('fmb_$i_1','fmb_$i_1','fmb_$i_3')
& collinear('fmb_$i_1','fmb_$i_1','fmb_$i_4')
& collinear('fmb_$i_1','fmb_$i_2','fmb_$i_1')
& collinear('fmb_$i_1','fmb_$i_2','fmb_$i_2')
& collinear('fmb_$i_1','fmb_$i_2','fmb_$i_3')
& ~ collinear('fmb_$i_1','fmb_$i_2','fmb_$i_4')
& collinear('fmb_$i_1','fmb_$i_3','fmb_$i_1')
& collinear('fmb_$i_1','fmb_$i_3','fmb_$i_2')
& collinear('fmb_$i_1','fmb_$i_3','fmb_$i_3')
& ~ collinear('fmb_$i_1','fmb_$i_3','fmb_$i_4')
& collinear('fmb_$i_1','fmb_$i_4','fmb_$i_1')
& ~ collinear('fmb_$i_1','fmb_$i_4','fmb_$i_2')
& ~ collinear('fmb_$i_1','fmb_$i_4','fmb_$i_3')
& collinear('fmb_$i_1','fmb_$i_4','fmb_$i_4')
& collinear('fmb_$i_2','fmb_$i_1','fmb_$i_1')
& collinear('fmb_$i_2','fmb_$i_1','fmb_$i_2')
& collinear('fmb_$i_2','fmb_$i_1','fmb_$i_3')
& ~ collinear('fmb_$i_2','fmb_$i_1','fmb_$i_4')
& collinear('fmb_$i_2','fmb_$i_2','fmb_$i_1')
& collinear('fmb_$i_2','fmb_$i_2','fmb_$i_2')
& collinear('fmb_$i_2','fmb_$i_2','fmb_$i_3')
& collinear('fmb_$i_2','fmb_$i_2','fmb_$i_4')
& collinear('fmb_$i_2','fmb_$i_3','fmb_$i_1')
& collinear('fmb_$i_2','fmb_$i_3','fmb_$i_2')
& collinear('fmb_$i_2','fmb_$i_3','fmb_$i_3')
& ~ collinear('fmb_$i_2','fmb_$i_3','fmb_$i_4')
& ~ collinear('fmb_$i_2','fmb_$i_4','fmb_$i_1')
& collinear('fmb_$i_2','fmb_$i_4','fmb_$i_2')
& ~ collinear('fmb_$i_2','fmb_$i_4','fmb_$i_3')
& collinear('fmb_$i_2','fmb_$i_4','fmb_$i_4')
& collinear('fmb_$i_3','fmb_$i_1','fmb_$i_1')
& collinear('fmb_$i_3','fmb_$i_1','fmb_$i_2')
& collinear('fmb_$i_3','fmb_$i_1','fmb_$i_3')
& ~ collinear('fmb_$i_3','fmb_$i_1','fmb_$i_4')
& collinear('fmb_$i_3','fmb_$i_2','fmb_$i_1')
& collinear('fmb_$i_3','fmb_$i_2','fmb_$i_2')
& collinear('fmb_$i_3','fmb_$i_2','fmb_$i_3')
& ~ collinear('fmb_$i_3','fmb_$i_2','fmb_$i_4')
& collinear('fmb_$i_3','fmb_$i_3','fmb_$i_1')
& collinear('fmb_$i_3','fmb_$i_3','fmb_$i_2')
& collinear('fmb_$i_3','fmb_$i_3','fmb_$i_3')
& collinear('fmb_$i_3','fmb_$i_3','fmb_$i_4')
& ~ collinear('fmb_$i_3','fmb_$i_4','fmb_$i_1')
& ~ collinear('fmb_$i_3','fmb_$i_4','fmb_$i_2')
& collinear('fmb_$i_3','fmb_$i_4','fmb_$i_3')
& collinear('fmb_$i_3','fmb_$i_4','fmb_$i_4')
& collinear('fmb_$i_4','fmb_$i_1','fmb_$i_1')
& ~ collinear('fmb_$i_4','fmb_$i_1','fmb_$i_2')
& ~ collinear('fmb_$i_4','fmb_$i_1','fmb_$i_3')
& collinear('fmb_$i_4','fmb_$i_1','fmb_$i_4')
& ~ collinear('fmb_$i_4','fmb_$i_2','fmb_$i_1')
& collinear('fmb_$i_4','fmb_$i_2','fmb_$i_2')
& ~ collinear('fmb_$i_4','fmb_$i_2','fmb_$i_3')
& collinear('fmb_$i_4','fmb_$i_2','fmb_$i_4')
& ~ collinear('fmb_$i_4','fmb_$i_3','fmb_$i_1')
& ~ collinear('fmb_$i_4','fmb_$i_3','fmb_$i_2')
& collinear('fmb_$i_4','fmb_$i_3','fmb_$i_3')
& collinear('fmb_$i_4','fmb_$i_3','fmb_$i_4')
& collinear('fmb_$i_4','fmb_$i_4','fmb_$i_1')
& collinear('fmb_$i_4','fmb_$i_4','fmb_$i_2')
& collinear('fmb_$i_4','fmb_$i_4','fmb_$i_3')
& collinear('fmb_$i_4','fmb_$i_4','fmb_$i_4') ) ).
tff(declare_line_on_plane,type,
line_on_plane: ( $i * $i ) > $o ).
tff(predicate_line_on_plane,axiom,
( line_on_plane('fmb_$i_1','fmb_$i_1')
& line_on_plane('fmb_$i_1','fmb_$i_2')
& line_on_plane('fmb_$i_1','fmb_$i_3')
& line_on_plane('fmb_$i_1','fmb_$i_4')
& line_on_plane('fmb_$i_2','fmb_$i_1')
& line_on_plane('fmb_$i_2','fmb_$i_2')
& line_on_plane('fmb_$i_2','fmb_$i_3')
& line_on_plane('fmb_$i_2','fmb_$i_4')
& line_on_plane('fmb_$i_3','fmb_$i_1')
& line_on_plane('fmb_$i_3','fmb_$i_2')
& line_on_plane('fmb_$i_3','fmb_$i_3')
& line_on_plane('fmb_$i_3','fmb_$i_4')
& line_on_plane('fmb_$i_4','fmb_$i_1')
& line_on_plane('fmb_$i_4','fmb_$i_2')
& line_on_plane('fmb_$i_4','fmb_$i_3')
& line_on_plane('fmb_$i_4','fmb_$i_4') ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO078-6 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 06:55:35 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.48 % (3192521)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (3192528)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3960195117:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (3192527)% WARNING: option uhcvi not known.
% 0.17/0.48 % (3192526)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2628299839_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (3192527)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1408602649:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (3192530)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1002460796:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (3192529)dis+10_1_sil=32000:sp=arity:random_seed=2945233279:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (3192531)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=482216038:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (3192532)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1642282459:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % TRYING [2]
% 0.17/0.48 % TRYING [3]
% 0.17/0.48 % TRYING [4]
% 0.17/0.48 % Finite Model Found!
% 0.17/0.48 % SZS status Satisfiable for theBenchmark
% 0.17/0.48 % (3192526) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3192521-3192526"...
% 0.17/0.48 % (3192526)...printing done.
% 0.17/0.48 % SZS output start FiniteModel for theBenchmark
% See solution above
% 0.17/0.48 % (3192526)------------------------------
% 0.17/0.48 % (3192526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (3192526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (3192526)CaDiCaL version: 2.1.3
% 0.17/0.48 % (3192526)Termination reason: Satisfiable
% 0.17/0.48 % (3192526)Time elapsed: 0.016 s
% 0.17/0.48 % (3192526)Peak memory usage: 12 MB
% 0.17/0.48 % (3192526)Instructions burned: 33 (million)
% 0.17/0.48 % (3192521)Success in time 0.053 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------