%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO063-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:05:29 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 26
% Syntax : Number of formulae : 63 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 169 ( 99 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 176 ( 75 ~; 76 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-4 aty)
% Number of variables : 218 ( 196 !; 0 ?; 218 :)
% Comments :
%------------------------------------------------------------------------------
tff(extension_type,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(x_type,type,
x: $i ).
tff(w_type,type,
w: $i ).
tff(u_type,type,
u: $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(v_type,type,
v: $i ).
tff(z_type,type,
z: $i ).
tff(y_type,type,
y: $i ).
tff(insertion_type,type,
insertion: ( $i * $i * $i * $i ) > $i ).
tff(equidistant_type,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(1,plain,
( ( insertion(u,v,y,z) = insertion(u,v,w,x) )
<=> ( insertion(u,v,w,x) = insertion(u,v,y,z) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,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(3,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)],[2]) ).
tff(4,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(5,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(6,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)],[5,4]) ).
tff(7,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)],[6]) ).
tff(8,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)],[7,3]) ).
tff(9,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(u,v,w,x) = extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,w,x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(10,plain,
insertion(u,v,w,x) = extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,w,x),
inference(unit_resolution,[status(thm)],[9,8]) ).
tff(11,plain,
extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,w,x) = insertion(u,v,w,x),
inference(symmetry,[status(thm)],[10]) ).
tff(12,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(u,v,y,z) = extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,y,z) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
insertion(u,v,y,z) = extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,y,z),
inference(unit_resolution,[status(thm)],[12,8]) ).
tff(14,plain,
extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,y,z) = insertion(u,v,y,z),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
( ( extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,y,z) = extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,w,x) )
<=> ( insertion(u,v,y,z) = insertion(u,v,w,x) ) ),
inference(monotonicity,[status(thm)],[14,11]) ).
tff(16,plain,
( ( extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,y,z) = extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,w,x) )
<=> ( insertion(u,v,w,x) = insertion(u,v,y,z) ) ),
inference(transitivity,[status(thm)],[15,1]) ).
tff(17,plain,
( ( insertion(u,v,w,x) = insertion(u,v,y,z) )
<=> ( extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,y,z) = extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,w,x) ) ),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( ( insertion(u,v,w,x) != insertion(u,v,y,z) )
<=> ( extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,y,z) != extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,w,x) ) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( ( insertion(u,v,w,x) != insertion(u,v,y,z) )
<=> ( insertion(u,v,w,x) != insertion(u,v,y,z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
insertion(u,v,w,x) != insertion(u,v,y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equality_of_insertions) ).
tff(21,plain,
insertion(u,v,w,x) != insertion(u,v,y,z),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,y,z) != extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,w,x),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
( ( u = extension(v,u,lower_dimension_point_1,lower_dimension_point_2) )
<=> ( extension(v,u,lower_dimension_point_1,lower_dimension_point_2) = u ) ),
inference(commutativity,[status(thm)],[]) ).
tff(24,plain,
( ( u != extension(v,u,lower_dimension_point_1,lower_dimension_point_2) )
<=> ( extension(v,u,lower_dimension_point_1,lower_dimension_point_2) != u ) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,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(26,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)],[25]) ).
tff(27,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(28,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(29,plain,
! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ~ ! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) )
| ( u != extension(v,u,lower_dimension_point_1,lower_dimension_point_2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
u != extension(v,u,lower_dimension_point_1,lower_dimension_point_2),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
extension(v,u,lower_dimension_point_1,lower_dimension_point_2) != u,
inference(modus_ponens,[status(thm)],[33,24]) ).
tff(35,plain,
( equidistant(w,x,y,z)
<=> equidistant(w,x,y,z) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
equidistant(w,x,y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_to_x_equals_y_to_z) ).
tff(37,plain,
equidistant(w,x,y,z),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
<=> ( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
tff(42,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
| ~ equidistant(w,x,y,z)
| equidistant(y,z,w,x) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
| ~ equidistant(w,x,y,z)
| equidistant(y,z,w,x) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
| ~ equidistant(w,x,y,z)
| equidistant(y,z,w,x) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
| ~ equidistant(w,x,y,z)
| equidistant(y,z,w,x) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
equidistant(y,z,w,x),
inference(unit_resolution,[status(thm)],[47,44,37]) ).
tff(49,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(( ( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) )
<=> ( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
rewrite(( ( ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) )
| ( U = V ) )
<=> ( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) )
| ( U = V ) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) )
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_2) ).
tff(55,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) )
| ( extension(v,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ~ equidistant(y,z,w,x)
| ( extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,y,z) = extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,w,x) ) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) )
| ( extension(v,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ~ equidistant(y,z,w,x)
| ( extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,y,z) = extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,w,x) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) )
| ( extension(v,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ~ equidistant(y,z,w,x)
| ( extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,y,z) = extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,w,x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( U = V )
| ~ equidistant(W,X,Y,Z)
| ( extension(U,V,W,X) = extension(U,V,Y,Z) ) )
| ( extension(v,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ~ equidistant(y,z,w,x)
| ( extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,y,z) = extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,w,x) ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
( ( extension(v,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ( extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,y,z) = extension(extension(v,u,lower_dimension_point_1,lower_dimension_point_2),u,w,x) ) ),
inference(unit_resolution,[status(thm)],[61,58,48]) ).
tff(63,plain,
$false,
inference(unit_resolution,[status(thm)],[62,34,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO063-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 14:12:08 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.39 % SZS status Unsatisfiable
% 0.18/0.39 % SZS output start Proof
% See solution above
% 0.18/0.40 % E exiting
%------------------------------------------------------------------------------