%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO027-3 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 28
% Syntax : Number of formulae : 59 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 331 ( 91 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 444 ( 195 ~; 215 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 23 ( 23 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 : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 249 ( 229 !; 0 ?; 249 :)
% Comments :
%------------------------------------------------------------------------------
tff(equidistant_type,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(extension_type,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(w_type,type,
w: $i ).
tff(v_type,type,
v: $i ).
tff(u_type,type,
u: $i ).
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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(5,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(6,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)],[5,4]) ).
tff(7,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(8,plain,
! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X)),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X)),
inference(modus_ponens,[status(thm)],[8,3]) ).
tff(10,plain,
! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X)),
inference(skolemize,[status(sab)],[9]) ).
tff(11,plain,
! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X)),
inference(modus_ponens,[status(thm)],[10,2]) ).
tff(12,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] : between(U,V,extension(U,V,W,X))
| between(u,v,extension(u,v,v,w)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
between(u,v,extension(u,v,v,w)),
inference(unit_resolution,[status(thm)],[12,11]) ).
tff(14,plain,
( ( w != extension(u,v,v,w) )
<=> ( w != extension(u,v,v,w) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
w != extension(u,v,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_w_is_an_extension) ).
tff(16,plain,
w != extension(u,v,v,w),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( u != v )
<=> ( u != v ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_not_v) ).
tff(19,plain,
u != v,
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( between(u,v,w)
<=> between(u,v,w) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
tff(22,plain,
between(u,v,w),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,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(24,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)],[23]) ).
tff(25,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(26,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(27,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)],[26]) ).
tff(28,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(29,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)],[28,27]) ).
tff(30,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)],[29,25]) ).
tff(31,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)],[30]) ).
tff(32,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)],[31,24]) ).
tff(33,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 )
| ( w = extension(u,v,v,w) )
| ~ between(u,v,w)
| ~ between(u,v,extension(u,v,v,w))
| ~ equidistant(v,w,v,extension(u,v,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) )
| ( u = v )
| ( w = extension(u,v,v,w) )
| ~ between(u,v,w)
| ~ between(u,v,extension(u,v,v,w))
| ~ equidistant(v,w,v,extension(u,v,v,w)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ( ( u = v )
| ( w = extension(u,v,v,w) )
| ~ equidistant(v,w,v,extension(u,v,v,w))
| ~ between(u,v,extension(u,v,v,w))
| ~ between(u,v,w) )
<=> ( ( u = v )
| ( w = extension(u,v,v,w) )
| ~ between(u,v,w)
| ~ between(u,v,extension(u,v,v,w))
| ~ equidistant(v,w,v,extension(u,v,v,w)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,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 )
| ( w = extension(u,v,v,w) )
| ~ equidistant(v,w,v,extension(u,v,v,w))
| ~ between(u,v,extension(u,v,v,w))
| ~ 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) )
| ( u = v )
| ( w = extension(u,v,v,w) )
| ~ between(u,v,w)
| ~ between(u,v,extension(u,v,v,w))
| ~ equidistant(v,w,v,extension(u,v,v,w)) ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,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 )
| ( w = extension(u,v,v,w) )
| ~ equidistant(v,w,v,extension(u,v,v,w))
| ~ between(u,v,extension(u,v,v,w))
| ~ 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) )
| ( u = v )
| ( w = extension(u,v,v,w) )
| ~ between(u,v,w)
| ~ between(u,v,extension(u,v,v,w))
| ~ equidistant(v,w,v,extension(u,v,v,w)) ) ),
inference(transitivity,[status(thm)],[35,33]) ).
tff(37,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 )
| ( w = extension(u,v,v,w) )
| ~ equidistant(v,w,v,extension(u,v,v,w))
| ~ between(u,v,extension(u,v,v,w))
| ~ between(u,v,w) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,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 )
| ( w = extension(u,v,v,w) )
| ~ between(u,v,w)
| ~ between(u,v,extension(u,v,v,w))
| ~ equidistant(v,w,v,extension(u,v,v,w)) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
~ equidistant(v,w,v,extension(u,v,v,w)),
inference(unit_resolution,[status(thm)],[38,32,22,19,16,13]) ).
tff(40,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(41,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)],[40]) ).
tff(42,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(43,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(44,plain,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( ~ ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V)
| equidistant(v,extension(u,v,v,w),v,w) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
equidistant(v,extension(u,v,v,w),v,w),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,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(50,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)],[49]) ).
tff(51,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(52,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(53,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
| ~ equidistant(v,extension(u,v,v,w),v,w)
| equidistant(v,w,v,extension(u,v,v,w)) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
| ~ equidistant(v,extension(u,v,v,w),v,w)
| equidistant(v,w,v,extension(u,v,v,w)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
| ~ equidistant(v,extension(u,v,v,w),v,w)
| equidistant(v,w,v,extension(u,v,v,w)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) )
| ~ equidistant(v,extension(u,v,v,w),v,w)
| equidistant(v,w,v,extension(u,v,v,w)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
$false,
inference(unit_resolution,[status(thm)],[58,55,48,39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO027-3 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:10:03 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% See solution above
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------