TSTP Solution File: GEO029-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO029-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 : Fri Sep 16 20:34:23 EDT 2022
% Result : Unsatisfiable 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 37
% Syntax : Number of formulae : 75 ( 26 unt; 5 typ; 0 def)
% Number of atoms : 375 ( 68 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 514 ( 234 ~; 244 |; 0 &)
% ( 36 <=>; 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 : 11 ( 3 >; 8 *; 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 : 334 ( 302 !; 0 ?; 334 :)
% 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/sandbox/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/sandbox/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,Y: $i,X: $i] :
refl(
( between(X,Y,extension(X,Y,W,V))
<=> between(X,Y,extension(X,Y,W,V)) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V))
<=> ! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V)) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V))
<=> ! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
tff(25,plain,
! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V)),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V)),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V)),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V))
| between(u,v,extension(u,v,v,u)) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
between(u,v,extension(u,v,v,u)),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ ! [W: $i,V: $i,Y: $i,X: $i] : between(X,Y,extension(X,Y,W,V))
| between(u,v,extension(u,v,u,v)) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
between(u,v,extension(u,v,u,v)),
inference(unit_resolution,[status(thm)],[30,27]) ).
tff(32,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(33,axiom,
extension(u,v,u,v) != extension(u,v,v,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equal_extensions) ).
tff(34,plain,
extension(u,v,u,v) != extension(u,v,v,u),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ( u != v )
<=> ( u != v ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
tff(37,plain,
u != v,
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,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(39,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)],[38]) ).
tff(40,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(41,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(42,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)],[41]) ).
tff(43,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/sandbox/benchmark/theBenchmark.p',d9) ).
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) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,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)],[44,40]) ).
tff(46,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)],[45]) ).
tff(47,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)],[46,39]) ).
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) )
| ( 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(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) )
| ( 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(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) )
| ( 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)],[49,48]) ).
tff(51,plain,
~ equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u)),
inference(unit_resolution,[status(thm)],[50,47,37,34,31,29]) ).
tff(52,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(53,plain,
equidistant(v,extension(u,v,u,v),u,v),
inference(unit_resolution,[status(thm)],[52,7]) ).
tff(54,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(55,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)],[54]) ).
tff(56,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(57,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(58,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)],[57]) ).
tff(59,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/sandbox/benchmark/theBenchmark.p',d5) ).
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) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,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)],[60,56]) ).
tff(62,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)],[61]) ).
tff(63,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)],[62,55]) ).
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) )
| 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(65,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(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) )
| 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)],[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) )
| 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)],[66,64]) ).
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(u,v,v,extension(u,v,v,u))
| ~ equidistant(v,extension(u,v,u,v),u,v) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,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)],[68,67]) ).
tff(70,plain,
$false,
inference(unit_resolution,[status(thm)],[69,63,53,51,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO029-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n021.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 : Wed Aug 31 04:41:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.18/0.39 % SZS status Unsatisfiable
% 0.18/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------