%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO033-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:05:23 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 42
% Syntax : Number of formulae : 86 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 735 ( 0 equ)
% Maximal formula atoms : 28 ( 8 avg)
% Number of connectives : 1195 ( 588 ~; 554 |; 0 &)
% ( 53 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 42 ( 42 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 413 ( 378 !; 0 ?; 413 :)
% Comments :
%------------------------------------------------------------------------------
tff(equidistant_type,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(u1_type,type,
u1: $i ).
tff(w1_type,type,
w1: $i ).
tff(u_type,type,
u: $i ).
tff(w_type,type,
w: $i ).
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(v_type,type,
v: $i ).
tff(v1_type,type,
v1: $i ).
tff(x1_type,type,
x1: $i ).
tff(x_type,type,
x: $i ).
tff(1,plain,
( between(u,v,w)
<=> between(u,v,w) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
tff(3,plain,
between(u,v,w),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ between(U,V,W)
| between(W,V,U) )
<=> ( ~ between(U,V,W)
| between(W,V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
tff(8,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,v,w)
| between(w,v,u) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,v,w)
| between(w,v,u) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,v,w)
| between(w,v,u) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,v,w)
| between(w,v,u) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
between(w,v,u),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( between(u1,v1,w1)
<=> between(u1,v1,w1) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
between(u1,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_between_u1_and_w1) ).
tff(17,plain,
between(u1,v1,w1),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u1,v1,w1)
| between(w1,v1,u1) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u1,v1,w1)
| between(w1,v1,u1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u1,v1,w1)
| between(w1,v1,u1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u1,v1,w1)
| between(w1,v1,u1) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
between(w1,v1,u1),
inference(unit_resolution,[status(thm)],[20,10,17]) ).
tff(22,plain,
( equidistant(v,w,v1,w1)
<=> equidistant(v,w,v1,w1) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
equidistant(v,w,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_to_w_equals_v1_to_w1) ).
tff(24,plain,
equidistant(v,w,v1,w1),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
<=> ( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_2) ).
tff(29,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
| ~ equidistant(v,w,v1,w1)
| equidistant(w,v,w1,v1) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
| ~ equidistant(v,w,v1,w1)
| equidistant(w,v,w1,v1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
| ~ equidistant(v,w,v1,w1)
| equidistant(w,v,w1,v1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
| ~ equidistant(v,w,v1,w1)
| equidistant(w,v,w1,v1) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
equidistant(w,v,w1,v1),
inference(unit_resolution,[status(thm)],[34,31,24]) ).
tff(36,plain,
( ~ equidistant(v,x,v1,x1)
<=> ~ equidistant(v,x,v1,x1) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
~ equidistant(v,x,v1,x1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v_to_x_equals_v1_to_x1) ).
tff(38,plain,
~ equidistant(v,x,v1,x1),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( equidistant(w,x,w1,x1)
<=> equidistant(w,x,w1,x1) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
equidistant(w,x,w1,x1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_to_x_equals_w1_to_x1) ).
tff(41,plain,
equidistant(w,x,w1,x1),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( equidistant(u,x,u1,x1)
<=> equidistant(u,x,u1,x1) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
equidistant(u,x,u1,x1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_x_equals_u1_to_x1) ).
tff(44,plain,
equidistant(u,x,u1,x1),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
^ [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
refl(( ( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) )
<=> ( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ) )),
inference(bind,[status(th)],[]) ).
tff(46,plain,
( ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) )
<=> ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) )
<=> ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
^ [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,X,U1,X1) )
<=> ( ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ) )),
( ( ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(W,X,W1,X1) )
<=> ( ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(W,X,W1,X1) ) )),
rewrite(( ( ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(W,X,W1,X1) )
<=> ( ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ) )),
( ( ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(W,X,W1,X1) )
<=> ( ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ) )),
( ( ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(W,X,W1,X1)
| ~ between(U,V,W) )
<=> ( ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ between(U,V,W) ) )),
rewrite(( ( ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ between(U,V,W) )
<=> ( ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ) )),
( ( ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(W,X,W1,X1)
| ~ between(U,V,W) )
<=> ( ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ) )),
( ( ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(W,X,W1,X1)
| ~ between(U,V,W)
| ~ between(U1,V1,W1) )
<=> ( ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ between(U1,V1,W1) ) )),
rewrite(( ( ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ between(U1,V1,W1) )
<=> ( ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ) )),
( ( ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(W,X,W1,X1)
| ~ between(U,V,W)
| ~ between(U1,V1,W1) )
<=> ( ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ) )),
( ( ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(W,X,W1,X1)
| ~ between(U,V,W)
| ~ between(U1,V1,W1)
| equidistant(V,X,V1,X1) )
<=> ( ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1)
| equidistant(V,X,V1,X1) ) )),
rewrite(( ( ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1)
| equidistant(V,X,V1,X1) )
<=> ( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ) )),
( ( ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(W,X,W1,X1)
| ~ between(U,V,W)
| ~ between(U1,V1,W1)
| equidistant(V,X,V1,X1) )
<=> ( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ) )),
inference(bind,[status(th)],[]) ).
tff(49,plain,
( ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(W,X,W1,X1)
| ~ between(U,V,W)
| ~ between(U1,V1,W1)
| equidistant(V,X,V1,X1) )
<=> ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,axiom,
! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(W,X,W1,X1)
| ~ between(U,V,W)
| ~ between(U1,V1,W1)
| equidistant(V,X,V1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12) ).
tff(51,plain,
! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ),
inference(modus_ponens,[status(thm)],[53,46]) ).
tff(55,plain,
( ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) )
| equidistant(v,x,v1,x1)
| ~ equidistant(u,x,u1,x1)
| ~ equidistant(w,x,w1,x1)
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1) )
<=> ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) )
| equidistant(v,x,v1,x1)
| ~ equidistant(u,x,u1,x1)
| ~ equidistant(w,x,w1,x1)
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
( ( equidistant(v,x,v1,x1)
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| ~ equidistant(u,x,u1,x1)
| ~ equidistant(w,x,w1,x1)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1) )
<=> ( equidistant(v,x,v1,x1)
| ~ equidistant(u,x,u1,x1)
| ~ equidistant(w,x,w1,x1)
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) )
| equidistant(v,x,v1,x1)
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| ~ equidistant(u,x,u1,x1)
| ~ equidistant(w,x,w1,x1)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1) )
<=> ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) )
| equidistant(v,x,v1,x1)
| ~ equidistant(u,x,u1,x1)
| ~ equidistant(w,x,w1,x1)
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1) ) ),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) )
| equidistant(v,x,v1,x1)
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| ~ equidistant(u,x,u1,x1)
| ~ equidistant(w,x,w1,x1)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1) )
<=> ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) )
| equidistant(v,x,v1,x1)
| ~ equidistant(u,x,u1,x1)
| ~ equidistant(w,x,w1,x1)
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1) ) ),
inference(transitivity,[status(thm)],[57,55]) ).
tff(59,plain,
( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) )
| equidistant(v,x,v1,x1)
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| ~ equidistant(u,x,u1,x1)
| ~ equidistant(w,x,w1,x1)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,X: $i,U1: $i,X1: $i] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) )
| equidistant(v,x,v1,x1)
| ~ equidistant(u,x,u1,x1)
| ~ equidistant(w,x,w1,x1)
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ~ between(w1,v1,u1)
| ~ between(w,v,u)
| ~ equidistant(w,u,w1,u1) ),
inference(unit_resolution,[status(thm)],[60,54,44,41,38,35]) ).
tff(62,plain,
~ equidistant(w,u,w1,u1),
inference(unit_resolution,[status(thm)],[61,21,14]) ).
tff(63,plain,
( equidistant(u,v,u1,v1)
<=> equidistant(u,v,u1,v1) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,axiom,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_u1_to_v1) ).
tff(65,plain,
equidistant(u,v,u1,v1),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
| ~ equidistant(u,v,u1,v1)
| equidistant(v,u,v1,u1) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
| ~ equidistant(u,v,u1,v1)
| equidistant(v,u,v1,u1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
| ~ equidistant(u,v,u1,v1)
| equidistant(v,u,v1,u1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
| ~ equidistant(u,v,u1,v1)
| equidistant(v,u,v1,u1) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
equidistant(v,u,v1,u1),
inference(unit_resolution,[status(thm)],[68,31,65]) ).
tff(70,plain,
^ [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
refl(( ( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) )
<=> ( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ) )),
inference(bind,[status(th)],[]) ).
tff(71,plain,
( ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) )
<=> ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) )
<=> ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
^ [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ equidistant(U,V,U1,V1)
| ~ equidistant(V,W,V1,W1)
| ~ between(U,V,W) )
<=> ( ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ) )),
( ( ~ equidistant(U,V,U1,V1)
| ~ equidistant(V,W,V1,W1)
| ~ between(U,V,W)
| ~ between(U1,V1,W1) )
<=> ( ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ between(U1,V1,W1) ) )),
rewrite(( ( ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ between(U1,V1,W1) )
<=> ( ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ) )),
( ( ~ equidistant(U,V,U1,V1)
| ~ equidistant(V,W,V1,W1)
| ~ between(U,V,W)
| ~ between(U1,V1,W1) )
<=> ( ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ) )),
( ( ~ equidistant(U,V,U1,V1)
| ~ equidistant(V,W,V1,W1)
| ~ between(U,V,W)
| ~ between(U1,V1,W1)
| equidistant(U,W,U1,W1) )
<=> ( ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| equidistant(U,W,U1,W1) ) )),
rewrite(( ( ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| equidistant(U,W,U1,W1) )
<=> ( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ) )),
( ( ~ equidistant(U,V,U1,V1)
| ~ equidistant(V,W,V1,W1)
| ~ between(U,V,W)
| ~ between(U1,V1,W1)
| equidistant(U,W,U1,W1) )
<=> ( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ) )),
inference(bind,[status(th)],[]) ).
tff(74,plain,
( ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( ~ equidistant(U,V,U1,V1)
| ~ equidistant(V,W,V1,W1)
| ~ between(U,V,W)
| ~ between(U1,V1,W1)
| equidistant(U,W,U1,W1) )
<=> ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,axiom,
! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( ~ equidistant(U,V,U1,V1)
| ~ equidistant(V,W,V1,W1)
| ~ between(U,V,W)
| ~ between(U1,V1,W1)
| equidistant(U,W,U1,W1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8) ).
tff(76,plain,
! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ),
inference(modus_ponens,[status(thm)],[78,71]) ).
tff(80,plain,
( ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) )
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1)
| ~ equidistant(v,u,v1,u1) )
<=> ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) )
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1)
| ~ equidistant(v,u,v1,u1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
( ( equidistant(w,u,w1,u1)
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| ~ equidistant(v,u,v1,u1)
| ~ equidistant(w,v,w1,v1) )
<=> ( ~ between(w1,v1,u1)
| ~ between(w,v,u)
| equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1)
| ~ equidistant(v,u,v1,u1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
( ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) )
| equidistant(w,u,w1,u1)
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| ~ equidistant(v,u,v1,u1)
| ~ equidistant(w,v,w1,v1) )
<=> ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) )
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1)
| ~ equidistant(v,u,v1,u1) ) ),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
( ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) )
| equidistant(w,u,w1,u1)
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| ~ equidistant(v,u,v1,u1)
| ~ equidistant(w,v,w1,v1) )
<=> ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) )
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1)
| ~ equidistant(v,u,v1,u1) ) ),
inference(transitivity,[status(thm)],[82,80]) ).
tff(84,plain,
( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) )
| equidistant(w,u,w1,u1)
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| ~ equidistant(v,u,v1,u1)
| ~ equidistant(w,v,w1,v1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) )
| ~ between(w1,v1,u1)
| ~ between(w,v,u)
| equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1)
| ~ equidistant(v,u,v1,u1) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
$false,
inference(unit_resolution,[status(thm)],[85,79,69,35,21,14,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO033-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 14:06:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% See solution above
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------