%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO029-3 : 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 05:05:22 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 34
% Syntax : Number of formulae : 74 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 385 ( 71 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 523 ( 237 ~; 247 |; 0 &)
% ( 39 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 25 ( 25 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-4 aty)
% Number of variables : 367 ( 335 !; 0 ?; 367 :)
% Comments :
%------------------------------------------------------------------------------
tff(equidistant_type,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(extension_type,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(u_type,type,
u: $i ).
tff(v_type,type,
v: $i ).
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,axiom,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
tff(5,plain,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V)
| equidistant(v,extension(u,v,v,u),v,u) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
equidistant(v,extension(u,v,v,u),v,u),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ~ equidistant(U,V,W,X)
| equidistant(X,W,U,V) )
<=> ( ~ equidistant(U,V,W,X)
| equidistant(X,W,U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,U,V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,U,V) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,U,V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,U,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_4) ).
tff(14,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,U,V) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,U,V) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,U,V) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,U,V) )
| ~ equidistant(v,extension(u,v,v,u),v,u)
| equidistant(u,v,v,extension(u,v,v,u)) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,U,V) )
| ~ equidistant(v,extension(u,v,v,u),v,u)
| equidistant(u,v,v,extension(u,v,v,u)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,U,V) )
| ~ equidistant(v,extension(u,v,v,u),v,u)
| equidistant(u,v,v,extension(u,v,v,u)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(X,W,U,V) )
| ~ equidistant(v,extension(u,v,v,u),v,u)
| equidistant(u,v,v,extension(u,v,v,u)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
equidistant(u,v,v,extension(u,v,v,u)),
inference(unit_resolution,[status(thm)],[19,16,9]) ).
tff(21,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(22,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)],[21]) ).
tff(23,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(24,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(25,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(26,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)],[25,24]) ).
tff(27,axiom,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ( Y != extension(U,V,W,X) )
| between(U,V,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b0) ).
tff(28,plain,
! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X)),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X)),
inference(modus_ponens,[status(thm)],[28,23]) ).
tff(30,plain,
! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X)),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X)),
inference(modus_ponens,[status(thm)],[30,22]) ).
tff(32,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X))
| between(u,v,extension(u,v,v,u)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
between(u,v,extension(u,v,v,u)),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X))
| between(u,v,extension(u,v,u,v)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
between(u,v,extension(u,v,u,v)),
inference(unit_resolution,[status(thm)],[34,31]) ).
tff(36,plain,
( ( extension(u,v,u,v) != extension(u,v,v,u) )
<=> ( extension(u,v,u,v) != extension(u,v,v,u) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
extension(u,v,u,v) != extension(u,v,v,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equal_extensions) ).
tff(38,plain,
extension(u,v,u,v) != extension(u,v,v,u),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( ( u != v )
<=> ( u != v ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_not_v) ).
tff(41,plain,
u != v,
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ( U = V )
| ( W = X )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) )
<=> ( ( U = V )
| ( W = X )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ( W = X )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ( W = X )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ( W = X )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ( W = X )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,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)
| ~ equidistant(V,W,V,X) )
<=> ( ~ between(U,V,X)
| ~ between(U,V,W)
| ~ equidistant(V,W,V,X) ) )),
rewrite(( ( ~ between(U,V,X)
| ~ between(U,V,W)
| ~ equidistant(V,W,V,X) )
<=> ( ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ~ equidistant(V,W,V,X) )
<=> ( ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ~ equidistant(V,W,V,X)
| ( U = V ) )
<=> ( ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W)
| ( U = V ) ) )),
rewrite(( ( ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W)
| ( U = V ) )
<=> ( ( U = V )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ~ equidistant(V,W,V,X)
| ( U = V ) )
<=> ( ( U = V )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ~ equidistant(V,W,V,X)
| ( U = V )
| ( W = X ) )
<=> ( ( U = V )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W)
| ( W = X ) ) )),
rewrite(( ( ( U = V )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W)
| ( W = X ) )
<=> ( ( U = V )
| ( W = X )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ) )),
( ( ~ between(U,V,W)
| ~ between(U,V,X)
| ~ equidistant(V,W,V,X)
| ( U = V )
| ( W = X ) )
<=> ( ( U = V )
| ( W = X )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ) )),
inference(bind,[status(th)],[]) ).
tff(46,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ between(U,V,X)
| ~ equidistant(V,W,V,X)
| ( U = V )
| ( W = X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ( W = X )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ between(U,V,X)
| ~ equidistant(V,W,V,X)
| ( U = V )
| ( W = X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9) ).
tff(48,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ( W = X )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ( W = X )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ( W = X )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ( W = X )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ),
inference(modus_ponens,[status(thm)],[50,43]) ).
tff(52,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ( W = X )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) )
| ( u = v )
| ( extension(u,v,u,v) = extension(u,v,v,u) )
| ~ equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u))
| ~ between(u,v,extension(u,v,v,u))
| ~ between(u,v,extension(u,v,u,v)) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ( W = X )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) )
| ( u = v )
| ( extension(u,v,u,v) = extension(u,v,v,u) )
| ~ equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u))
| ~ between(u,v,extension(u,v,v,u))
| ~ between(u,v,extension(u,v,u,v)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ( W = X )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) )
| ( u = v )
| ( extension(u,v,u,v) = extension(u,v,v,u) )
| ~ equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u))
| ~ between(u,v,extension(u,v,v,u))
| ~ between(u,v,extension(u,v,u,v)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ( W = X )
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) )
| ( u = v )
| ( extension(u,v,u,v) = extension(u,v,v,u) )
| ~ equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u))
| ~ between(u,v,extension(u,v,v,u))
| ~ between(u,v,extension(u,v,u,v)) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
~ equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u)),
inference(unit_resolution,[status(thm)],[54,51,41,38,35,33]) ).
tff(56,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(57,plain,
equidistant(v,extension(u,v,u,v),u,v),
inference(unit_resolution,[status(thm)],[56,7]) ).
tff(58,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(( ( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) )
<=> ( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
rewrite(( ( ~ equidistant(U,V,W,X)
| ~ equidistant(W,X,Y,Z)
| equidistant(U,V,Y,Z) )
<=> ( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) ) )),
inference(bind,[status(th)],[]) ).
tff(62,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| ~ equidistant(W,X,Y,Z)
| equidistant(U,V,Y,Z) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| ~ equidistant(W,X,Y,Z)
| equidistant(U,V,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5) ).
tff(64,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) )
| equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u))
| ~ equidistant(v,extension(u,v,u,v),u,v)
| ~ equidistant(u,v,v,extension(u,v,v,u)) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) )
| equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u))
| ~ equidistant(v,extension(u,v,u,v),u,v)
| ~ equidistant(u,v,v,extension(u,v,v,u)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ( equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u))
| ~ equidistant(u,v,v,extension(u,v,v,u))
| ~ equidistant(v,extension(u,v,u,v),u,v) )
<=> ( equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u))
| ~ equidistant(v,extension(u,v,u,v),u,v)
| ~ equidistant(u,v,v,extension(u,v,v,u)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) )
| equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u))
| ~ equidistant(u,v,v,extension(u,v,v,u))
| ~ equidistant(v,extension(u,v,u,v),u,v) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) )
| equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u))
| ~ equidistant(v,extension(u,v,u,v),u,v)
| ~ equidistant(u,v,v,extension(u,v,v,u)) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) )
| equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u))
| ~ equidistant(u,v,v,extension(u,v,v,u))
| ~ equidistant(v,extension(u,v,u,v),u,v) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) )
| equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u))
| ~ equidistant(v,extension(u,v,u,v),u,v)
| ~ equidistant(u,v,v,extension(u,v,v,u)) ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) )
| equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u))
| ~ equidistant(u,v,v,extension(u,v,v,u))
| ~ equidistant(v,extension(u,v,u,v),u,v) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) )
| equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u))
| ~ equidistant(v,extension(u,v,u,v),u,v)
| ~ equidistant(u,v,v,extension(u,v,v,u)) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
$false,
inference(unit_resolution,[status(thm)],[73,67,57,55,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO029-3 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n007.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 14:07:19 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
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------