%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO055-3 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:05:27 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 27 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 9 ~; 2 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 60 ( 54 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
tff(equidistant_type,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(v_type,type,
v: $i ).
tff(u_type,type,
u: $i ).
tff(extension_type,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(reflection_type,type,
reflection: ( $i * $i ) > $i ).
tff(1,plain,
^ [V: $i,U: $i] :
refl(( ( reflection(U,V) = extension(U,V,U,V) )
<=> ( reflection(U,V) = extension(U,V,U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) )
<=> ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) )
<=> ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-2.ax',reflection) ).
tff(5,plain,
! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) )
| ( reflection(u,v) = extension(u,v,u,v) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
reflection(u,v) = extension(u,v,u,v),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
extension(u,v,u,v) = reflection(u,v),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( equidistant(v,extension(u,v,u,v),u,v)
<=> equidistant(v,reflection(u,v),u,v) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( equidistant(v,reflection(u,v),u,v)
<=> equidistant(v,extension(u,v,u,v),u,v) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( ~ equidistant(v,reflection(u,v),u,v)
<=> ~ equidistant(v,extension(u,v,u,v),u,v) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ~ equidistant(v,reflection(u,v),u,v)
<=> ~ equidistant(v,reflection(u,v),u,v) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
~ equidistant(v,reflection(u,v),u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equidistance) ).
tff(16,plain,
~ equidistant(v,reflection(u,v),u,v),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ equidistant(v,extension(u,v,u,v),u,v),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
^ [W: $i,V: $i,Y: $i,X: $i] :
refl(( equidistant(Y,extension(X,Y,W,V),W,V)
<=> equidistant(Y,extension(X,Y,W,V),W,V) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V)
<=> ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V)
<=> ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
tff(22,plain,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V)
| equidistant(v,extension(u,v,u,v),u,v) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
equidistant(v,extension(u,v,u,v),u,v),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
$false,
inference(unit_resolution,[status(thm)],[26,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : GEO055-3 : TPTP v9.0.0. Released v1.0.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 14:12:09 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% See solution above
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------