%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO022-3 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:05:21 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of formulae : 34 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 186 ( 88 ~; 82 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 154 ( 138 !; 0 ?; 154 :)
% Comments :
%------------------------------------------------------------------------------
tff(equidistant_type,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(v_type,type,
v: $i ).
tff(u_type,type,
u: $i ).
tff(x_type,type,
x: $i ).
tff(w_type,type,
w: $i ).
tff(z_type,type,
z: $i ).
tff(y_type,type,
y: $i ).
tff(1,plain,
( equidistant(u,v,w,x)
<=> equidistant(u,v,w,x) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
equidistant(u,v,w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_w_to_x) ).
tff(3,plain,
equidistant(u,v,w,x),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,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(5,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)],[4]) ).
tff(6,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(7,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
tff(8,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
| ~ 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) )
| ~ equidistant(u,v,w,x)
| equidistant(w,x,u,v) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
| ~ equidistant(u,v,w,x)
| equidistant(w,x,u,v) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
| ~ equidistant(u,v,w,x)
| equidistant(w,x,u,v) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
equidistant(w,x,u,v),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( ~ equidistant(u,v,y,z)
<=> ~ equidistant(u,v,y,z) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
~ equidistant(u,v,y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitivity) ).
tff(17,plain,
~ equidistant(u,v,y,z),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( equidistant(w,x,y,z)
<=> equidistant(w,x,y,z) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
equidistant(w,x,y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_to_x_equals_y_to_z) ).
tff(20,plain,
equidistant(w,x,y,z),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
refl(( ( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) )
<=> ( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
trans(monotonicity(rewrite(( ( ~ equidistant(X,Y,Z,V)
| ~ equidistant(X,Y,V2,W) )
<=> ( ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ) )),
( ( ~ equidistant(X,Y,Z,V)
| ~ equidistant(X,Y,V2,W)
| equidistant(Z,V,V2,W) )
<=> ( ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V)
| equidistant(Z,V,V2,W) ) )),
rewrite(( ( ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V)
| equidistant(Z,V,V2,W) )
<=> ( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ) )),
( ( ~ equidistant(X,Y,Z,V)
| ~ equidistant(X,Y,V2,W)
| equidistant(Z,V,V2,W) )
<=> ( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( ~ equidistant(X,Y,Z,V)
| ~ equidistant(X,Y,V2,W)
| equidistant(Z,V,V2,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( ~ equidistant(X,Y,Z,V)
| ~ equidistant(X,Y,V2,W)
| equidistant(Z,V,V2,W) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
tff(27,plain,
! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) )
| equidistant(u,v,y,z)
| ~ equidistant(w,x,y,z)
| ~ equidistant(w,x,u,v) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) )
| equidistant(u,v,y,z)
| ~ equidistant(w,x,y,z)
| ~ equidistant(w,x,u,v) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) )
| equidistant(u,v,y,z)
| ~ equidistant(w,x,y,z)
| ~ equidistant(w,x,u,v) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,X: $i,V2: $i] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) )
| equidistant(u,v,y,z)
| ~ equidistant(w,x,y,z)
| ~ equidistant(w,x,u,v) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
$false,
inference(unit_resolution,[status(thm)],[33,30,20,17,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO022-3 : TPTP v9.0.0. Released v1.0.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.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 14:07:04 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Unsatisfiable
% 0.11/0.37 % SZS output start Proof
% See solution above
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------