%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO009-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:05:18 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 39
% Syntax : Number of formulae : 106 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 416 ( 125 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 470 ( 184 ~; 234 |; 0 &)
% ( 52 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 276 ( 255 !; 0 ?; 276 :)
% Comments :
%------------------------------------------------------------------------------
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(insertion_type,type,
insertion: ( $i * $i * $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(a_type,type,
a: $i ).
tff(e_type,type,
e: $i ).
tff(d_type,type,
d: $i ).
tff(extension_type,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(lower_dimension_point_2_type,type,
lower_dimension_point_2: $i ).
tff(lower_dimension_point_1_type,type,
lower_dimension_point_1: $i ).
tff(1,plain,
( between(a,c,e)
<=> between(a,c,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
between(a,c,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_between_a_and_e) ).
tff(3,plain,
between(a,c,e),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
<=> ( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i3) ).
tff(8,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(a,c,e)
| ( c = insertion(a,e,a,c) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(a,c,e)
| ( c = insertion(a,e,a,c) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(a,c,e)
| ( c = insertion(a,e,a,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(a,c,e)
| ( c = insertion(a,e,a,c) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c = insertion(a,e,a,c),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
insertion(a,e,a,c) = c,
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( between(a,d,e)
<=> between(a,d,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
between(a,d,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_between_a_and_e) ).
tff(18,plain,
between(a,d,e),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(a,d,e)
| ( d = insertion(a,e,a,d) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(a,d,e)
| ( d = insertion(a,e,a,d) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(a,d,e)
| ( d = insertion(a,e,a,d) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( V = insertion(U,W,U,V) ) )
| ~ between(a,d,e)
| ( d = insertion(a,e,a,d) ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
d = insertion(a,e,a,d),
inference(unit_resolution,[status(thm)],[21,10,18]) ).
tff(23,plain,
insertion(a,e,a,d) = d,
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( between(a,insertion(a,e,a,d),insertion(a,e,a,c))
<=> between(a,d,c) ),
inference(monotonicity,[status(thm)],[23,15]) ).
tff(25,plain,
( between(a,d,c)
<=> between(a,insertion(a,e,a,d),insertion(a,e,a,c)) ),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
( ~ between(a,d,c)
<=> ~ between(a,insertion(a,e,a,d),insertion(a,e,a,c)) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( ~ between(a,d,c)
<=> ~ between(a,d,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
~ between(a,d,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_between_a_and_c) ).
tff(29,plain,
~ between(a,d,c),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
~ between(a,insertion(a,e,a,d),insertion(a,e,a,c)),
inference(modus_ponens,[status(thm)],[29,26]) ).
tff(31,plain,
( between(a,insertion(a,e,a,c),insertion(a,e,a,d))
<=> between(a,c,d) ),
inference(monotonicity,[status(thm)],[15,23]) ).
tff(32,plain,
( between(a,c,d)
<=> between(a,insertion(a,e,a,c),insertion(a,e,a,d)) ),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( ~ between(a,c,d)
<=> ~ between(a,insertion(a,e,a,c),insertion(a,e,a,d)) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ~ between(a,c,d)
<=> ~ between(a,c,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
~ between(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_not_between_a_and_d) ).
tff(36,plain,
~ between(a,c,d),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
~ between(a,insertion(a,e,a,c),insertion(a,e,a,d)),
inference(modus_ponens,[status(thm)],[36,33]) ).
tff(38,plain,
^ [V: $i,W1: $i,U: $i,U1: $i] :
refl(( ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) )
<=> ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) )
<=> ! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) )
<=> ! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-3.ax',insertion) ).
tff(42,plain,
! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) )
| ( insertion(a,e,a,insertion(a,e,a,d)) = extension(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,a,insertion(a,e,a,d)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
insertion(a,e,a,insertion(a,e,a,d)) = extension(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,a,insertion(a,e,a,d)),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
insertion(a,e,a,insertion(a,e,a,d)) = insertion(a,e,a,d),
inference(monotonicity,[status(thm)],[23]) ).
tff(48,plain,
insertion(a,e,a,d) = insertion(a,e,a,insertion(a,e,a,d)),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
insertion(a,e,a,d) = extension(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,a,insertion(a,e,a,d)),
inference(transitivity,[status(thm)],[48,46]) ).
tff(50,plain,
( between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,d))
<=> between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,extension(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,a,insertion(a,e,a,d))) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,extension(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,a,insertion(a,e,a,d)))
<=> between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,d)) ),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( between(U,V,extension(U,V,W,X))
<=> between(U,V,extension(U,V,W,X)) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X))
<=> ! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X)) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X))
<=> ! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X)) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X))
<=> ! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X)) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(56,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ( Y != extension(U,V,W,X) )
| between(U,V,Y) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X)) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(57,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ( Y != extension(U,V,W,X) )
| between(U,V,Y) )
<=> ! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X)) ),
inference(transitivity,[status(thm)],[56,55]) ).
tff(58,axiom,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ( Y != extension(U,V,W,X) )
| between(U,V,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b0) ).
tff(59,plain,
! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X)),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X)),
inference(modus_ponens,[status(thm)],[59,54]) ).
tff(61,plain,
! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X)),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X)),
inference(modus_ponens,[status(thm)],[61,53]) ).
tff(63,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X))
| between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,extension(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,a,insertion(a,e,a,d))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,extension(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,a,insertion(a,e,a,d))),
inference(unit_resolution,[status(thm)],[63,62]) ).
tff(65,plain,
between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,d)),
inference(modus_ponens,[status(thm)],[64,51]) ).
tff(66,plain,
( ( extension(e,a,lower_dimension_point_1,lower_dimension_point_2) = a )
<=> ( a = extension(e,a,lower_dimension_point_1,lower_dimension_point_2) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(67,plain,
( ( a = extension(e,a,lower_dimension_point_1,lower_dimension_point_2) )
<=> ( extension(e,a,lower_dimension_point_1,lower_dimension_point_2) = a ) ),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
( ( a != extension(e,a,lower_dimension_point_1,lower_dimension_point_2) )
<=> ( extension(e,a,lower_dimension_point_1,lower_dimension_point_2) != a ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
^ [V: $i,U: $i] :
refl(( ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) )
<=> ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) )
<=> ! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) )
<=> ! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,axiom,
! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_1) ).
tff(73,plain,
! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
( ~ ! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) )
| ( a != extension(e,a,lower_dimension_point_1,lower_dimension_point_2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
a != extension(e,a,lower_dimension_point_1,lower_dimension_point_2),
inference(unit_resolution,[status(thm)],[76,75]) ).
tff(78,plain,
extension(e,a,lower_dimension_point_1,lower_dimension_point_2) != a,
inference(modus_ponens,[status(thm)],[77,68]) ).
tff(79,plain,
( ~ ! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) )
| ( insertion(a,e,a,insertion(a,e,a,c)) = extension(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,a,insertion(a,e,a,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
insertion(a,e,a,insertion(a,e,a,c)) = extension(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,a,insertion(a,e,a,c)),
inference(unit_resolution,[status(thm)],[79,44]) ).
tff(81,plain,
insertion(a,e,a,insertion(a,e,a,c)) = insertion(a,e,a,c),
inference(monotonicity,[status(thm)],[15]) ).
tff(82,plain,
insertion(a,e,a,c) = insertion(a,e,a,insertion(a,e,a,c)),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
insertion(a,e,a,c) = extension(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,a,insertion(a,e,a,c)),
inference(transitivity,[status(thm)],[82,80]) ).
tff(84,plain,
( between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,c))
<=> between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,extension(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,a,insertion(a,e,a,c))) ),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,extension(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,a,insertion(a,e,a,c)))
<=> between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,c)) ),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X))
| between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,extension(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,a,insertion(a,e,a,c))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,extension(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,a,insertion(a,e,a,c))),
inference(unit_resolution,[status(thm)],[86,62]) ).
tff(88,plain,
between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,c)),
inference(modus_ponens,[status(thm)],[87,85]) ).
tff(89,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ between(U,V,W)
| ~ between(U,V,X) )
<=> ( ~ between(U,V,X)
| ~ between(U,V,W) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V ) )
<=> ( ~ between(U,V,X)
| ~ between(U,V,W)
| ( U = V ) ) )),
rewrite(( ( ~ between(U,V,X)
| ~ between(U,V,W)
| ( U = V ) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V ) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V )
| between(V,W,X) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X) ) )),
rewrite(( ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V )
| between(V,W,X) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V )
| between(V,W,X)
| between(V,X,W) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ) )),
rewrite(( ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V )
| between(V,W,X)
| between(V,X,W) )
<=> ( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ) )),
inference(bind,[status(th)],[]) ).
tff(93,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V )
| between(V,W,X)
| between(V,X,W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ between(U,V,X)
| ( U = V )
| between(V,W,X)
| between(V,X,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b13) ).
tff(95,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
| ( extension(e,a,lower_dimension_point_1,lower_dimension_point_2) = a )
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,c))
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,d))
| between(a,insertion(a,e,a,c),insertion(a,e,a,d))
| between(a,insertion(a,e,a,d),insertion(a,e,a,c)) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
| ( extension(e,a,lower_dimension_point_1,lower_dimension_point_2) = a )
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,c))
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,d))
| between(a,insertion(a,e,a,c),insertion(a,e,a,d))
| between(a,insertion(a,e,a,d),insertion(a,e,a,c)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
( ( ( extension(e,a,lower_dimension_point_1,lower_dimension_point_2) = a )
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,d))
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,c))
| between(a,insertion(a,e,a,c),insertion(a,e,a,d))
| between(a,insertion(a,e,a,d),insertion(a,e,a,c)) )
<=> ( ( extension(e,a,lower_dimension_point_1,lower_dimension_point_2) = a )
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,c))
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,d))
| between(a,insertion(a,e,a,c),insertion(a,e,a,d))
| between(a,insertion(a,e,a,d),insertion(a,e,a,c)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
| ( extension(e,a,lower_dimension_point_1,lower_dimension_point_2) = a )
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,d))
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,c))
| between(a,insertion(a,e,a,c),insertion(a,e,a,d))
| between(a,insertion(a,e,a,d),insertion(a,e,a,c)) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
| ( extension(e,a,lower_dimension_point_1,lower_dimension_point_2) = a )
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,c))
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,d))
| between(a,insertion(a,e,a,c),insertion(a,e,a,d))
| between(a,insertion(a,e,a,d),insertion(a,e,a,c)) ) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
| ( extension(e,a,lower_dimension_point_1,lower_dimension_point_2) = a )
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,d))
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,c))
| between(a,insertion(a,e,a,c),insertion(a,e,a,d))
| between(a,insertion(a,e,a,d),insertion(a,e,a,c)) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
| ( extension(e,a,lower_dimension_point_1,lower_dimension_point_2) = a )
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,c))
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,d))
| between(a,insertion(a,e,a,c),insertion(a,e,a,d))
| between(a,insertion(a,e,a,d),insertion(a,e,a,c)) ) ),
inference(transitivity,[status(thm)],[101,99]) ).
tff(103,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
| ( extension(e,a,lower_dimension_point_1,lower_dimension_point_2) = a )
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,d))
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,c))
| between(a,insertion(a,e,a,c),insertion(a,e,a,d))
| between(a,insertion(a,e,a,d),insertion(a,e,a,c)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ between(U,V,X)
| ~ between(U,V,W)
| between(V,W,X)
| between(V,X,W) )
| ( extension(e,a,lower_dimension_point_1,lower_dimension_point_2) = a )
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,c))
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,d))
| between(a,insertion(a,e,a,c),insertion(a,e,a,d))
| between(a,insertion(a,e,a,d),insertion(a,e,a,c)) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
( ( extension(e,a,lower_dimension_point_1,lower_dimension_point_2) = a )
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,c))
| ~ between(extension(e,a,lower_dimension_point_1,lower_dimension_point_2),a,insertion(a,e,a,d))
| between(a,insertion(a,e,a,c),insertion(a,e,a,d))
| between(a,insertion(a,e,a,d),insertion(a,e,a,c)) ),
inference(unit_resolution,[status(thm)],[104,98]) ).
tff(106,plain,
$false,
inference(unit_resolution,[status(thm)],[105,88,78,65,37,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO009-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 14:02:24 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41 % SZS output start Proof
% See solution above
% 0.21/0.44 % E exiting
%------------------------------------------------------------------------------