TSTP Solution File: GEO068-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO068-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 20:34:39 EDT 2022
% Result : Unsatisfiable 0.18s 0.42s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 68
% Syntax : Number of formulae : 136 ( 30 unt; 9 typ; 0 def)
% Number of atoms : 812 ( 0 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 1196 ( 538 ~; 596 |; 0 &)
% ( 62 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 27 ( 27 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 3 >; 7 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 525 ( 491 !; 0 ?; 525 :)
% Comments :
%------------------------------------------------------------------------------
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(u_type,type,
u: $i ).
tff(w_type,type,
w: $i ).
tff(v_type,type,
v: $i ).
tff(u1_type,type,
u1: $i ).
tff(w1_type,type,
w1: $i ).
tff(v1_type,type,
v1: $i ).
tff(colinear_type,type,
colinear: ( $i * $i * $i ) > $o ).
tff(equidistant_type,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(1,plain,
( ~ colinear(u1,v1,w1)
<=> ~ colinear(u1,v1,w1) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ colinear(u1,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_u1v1w1_colinear) ).
tff(3,plain,
~ colinear(u1,v1,w1),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ between(Y,Z,X)
| colinear(X,Y,Z) )
<=> ( ~ between(Y,Z,X)
| colinear(X,Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ between(Y,Z,X)
| colinear(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ between(Y,Z,X)
| colinear(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ between(Y,Z,X)
| colinear(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ between(Y,Z,X)
| colinear(X,Y,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ between(Y,Z,X)
| colinear(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity2) ).
tff(8,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ between(Y,Z,X)
| colinear(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ between(Y,Z,X)
| colinear(X,Y,Z) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ between(Y,Z,X)
| colinear(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ between(Y,Z,X)
| colinear(X,Y,Z) )
| ~ between(v1,w1,u1)
| colinear(u1,v1,w1) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ between(Y,Z,X)
| colinear(X,Y,Z) )
| ~ between(v1,w1,u1)
| colinear(u1,v1,w1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ between(Y,Z,X)
| colinear(X,Y,Z) )
| ~ between(v1,w1,u1)
| colinear(u1,v1,w1) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ between(Y,Z,X)
| colinear(X,Y,Z) )
| ~ between(v1,w1,u1)
| colinear(u1,v1,w1) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ between(v1,w1,u1),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( equidistant(u,w,u1,w1)
<=> equidistant(u,w,u1,w1) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
equidistant(u,w,u1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_w_equals_u1_to_w1) ).
tff(17,plain,
equidistant(u,w,u1,w1),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,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(19,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)],[18]) ).
tff(20,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(21,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_2) ).
tff(22,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
| ~ equidistant(u,w,u1,w1)
| equidistant(w,u,w1,u1) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
| ~ equidistant(u,w,u1,w1)
| equidistant(w,u,w1,u1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
| ~ equidistant(u,w,u1,w1)
| equidistant(w,u,w1,u1) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
| ~ equidistant(u,w,u1,w1)
| equidistant(w,u,w1,u1) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
equidistant(w,u,w1,u1),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
( equidistant(u,v,u1,v1)
<=> equidistant(u,v,u1,v1) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_u1_to_v1) ).
tff(31,plain,
equidistant(u,v,u1,v1),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,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(33,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(34,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)],[33,32]) ).
tff(35,plain,
equidistant(v,u,v1,u1),
inference(unit_resolution,[status(thm)],[34,24,31]) ).
tff(36,plain,
( equidistant(v,w,v1,w1)
<=> equidistant(v,w,v1,w1) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
equidistant(v,w,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_to_w_equals_v1_to_w1) ).
tff(38,plain,
equidistant(v,w,v1,w1),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
^ [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
refl(
( ( 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)
| ~ equidistant(U,W,U1,W1) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) )
<=> ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) )
<=> ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,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)
| ~ equidistant(U,W,U1,W1) )
<=> ( ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) ) )),
( ( ~ equidistant(U,V,U1,V1)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,W,U1,W1)
| ~ between(U,V,W) )
<=> ( ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1)
| ~ between(U,V,W) ) )),
rewrite(
( ( ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1)
| ~ between(U,V,W) )
<=> ( ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) ) )),
( ( ~ equidistant(U,V,U1,V1)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,W,U1,W1)
| ~ between(U,V,W) )
<=> ( ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) ) )),
( ( ~ equidistant(U,V,U1,V1)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,W,U1,W1)
| ~ between(U,V,W)
| 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) ) )),
rewrite(
( ( ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1)
| between(U1,V1,W1) )
<=> ( 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,V,U1,V1)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,W,U1,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,W,U1,W1) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( ~ equidistant(U,V,U1,V1)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,W,U1,W1)
| ~ between(U,V,W)
| between(U1,V1,W1) )
<=> ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( ~ equidistant(U,V,U1,V1)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,W,U1,W1)
| ~ between(U,V,W)
| between(U1,V1,W1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b11) ).
tff(45,plain,
! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
( ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) )
| ~ equidistant(v,w,v1,w1)
| between(v1,w1,u1)
| ~ equidistant(v,u,v1,u1)
| ~ equidistant(w,u,w1,u1)
| ~ between(v,w,u) )
<=> ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) )
| ~ equidistant(v,w,v1,w1)
| between(v1,w1,u1)
| ~ equidistant(v,u,v1,u1)
| ~ equidistant(w,u,w1,u1)
| ~ between(v,w,u) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ( between(v1,w1,u1)
| ~ between(v,w,u)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(v,w,v1,w1)
| ~ equidistant(v,u,v1,u1) )
<=> ( ~ equidistant(v,w,v1,w1)
| between(v1,w1,u1)
| ~ equidistant(v,u,v1,u1)
| ~ equidistant(w,u,w1,u1)
| ~ between(v,w,u) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) )
| between(v1,w1,u1)
| ~ between(v,w,u)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(v,w,v1,w1)
| ~ equidistant(v,u,v1,u1) )
<=> ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) )
| ~ equidistant(v,w,v1,w1)
| between(v1,w1,u1)
| ~ equidistant(v,u,v1,u1)
| ~ equidistant(w,u,w1,u1)
| ~ between(v,w,u) ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) )
| between(v1,w1,u1)
| ~ between(v,w,u)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(v,w,v1,w1)
| ~ equidistant(v,u,v1,u1) )
<=> ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) )
| ~ equidistant(v,w,v1,w1)
| between(v1,w1,u1)
| ~ equidistant(v,u,v1,u1)
| ~ equidistant(w,u,w1,u1)
| ~ between(v,w,u) ) ),
inference(transitivity,[status(thm)],[51,49]) ).
tff(53,plain,
( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) )
| between(v1,w1,u1)
| ~ between(v,w,u)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(v,w,v1,w1)
| ~ equidistant(v,u,v1,u1) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) )
| ~ equidistant(v,w,v1,w1)
| between(v1,w1,u1)
| ~ equidistant(v,u,v1,u1)
| ~ equidistant(w,u,w1,u1)
| ~ between(v,w,u) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
~ between(v,w,u),
inference(unit_resolution,[status(thm)],[54,48,38,35,28,14]) ).
tff(56,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ between(Z,X,Y)
| colinear(X,Y,Z) )
<=> ( ~ between(Z,X,Y)
| colinear(X,Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(57,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ between(Z,X,Y)
| colinear(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ between(Z,X,Y)
| colinear(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ between(Z,X,Y)
| colinear(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ between(Z,X,Y)
| colinear(X,Y,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ between(Z,X,Y)
| colinear(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity3) ).
tff(60,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ between(Z,X,Y)
| colinear(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ between(Z,X,Y)
| colinear(X,Y,Z) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ between(Z,X,Y)
| colinear(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ between(Z,X,Y)
| colinear(X,Y,Z) )
| ~ between(w1,u1,v1)
| colinear(u1,v1,w1) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ between(Z,X,Y)
| colinear(X,Y,Z) )
| ~ between(w1,u1,v1)
| colinear(u1,v1,w1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ between(Z,X,Y)
| colinear(X,Y,Z) )
| ~ between(w1,u1,v1)
| colinear(u1,v1,w1) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ between(Z,X,Y)
| colinear(X,Y,Z) )
| ~ between(w1,u1,v1)
| colinear(u1,v1,w1) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
~ between(w1,u1,v1),
inference(unit_resolution,[status(thm)],[65,62,3]) ).
tff(67,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(68,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(69,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)],[68,67]) ).
tff(70,plain,
equidistant(w,v,w1,v1),
inference(unit_resolution,[status(thm)],[69,24,38]) ).
tff(71,plain,
( ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( 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,v,u1,v1)
| between(w1,u1,v1)
| ~ equidistant(w,v,w1,v1)
| ~ equidistant(w,u,w1,u1)
| ~ between(w,u,v) )
<=> ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( 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,v,u1,v1)
| between(w1,u1,v1)
| ~ equidistant(w,v,w1,v1)
| ~ equidistant(w,u,w1,u1)
| ~ between(w,u,v) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( between(w1,u1,v1)
| ~ between(w,u,v)
| ~ equidistant(u,v,u1,v1)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1) )
<=> ( ~ equidistant(u,v,u1,v1)
| between(w1,u1,v1)
| ~ equidistant(w,v,w1,v1)
| ~ equidistant(w,u,w1,u1)
| ~ between(w,u,v) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) )
| between(w1,u1,v1)
| ~ between(w,u,v)
| ~ equidistant(u,v,u1,v1)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1) )
<=> ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( 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,v,u1,v1)
| between(w1,u1,v1)
| ~ equidistant(w,v,w1,v1)
| ~ equidistant(w,u,w1,u1)
| ~ between(w,u,v) ) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) )
| between(w1,u1,v1)
| ~ between(w,u,v)
| ~ equidistant(u,v,u1,v1)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1) )
<=> ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( 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,v,u1,v1)
| between(w1,u1,v1)
| ~ equidistant(w,v,w1,v1)
| ~ equidistant(w,u,w1,u1)
| ~ between(w,u,v) ) ),
inference(transitivity,[status(thm)],[73,71]) ).
tff(75,plain,
( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1) )
| between(w1,u1,v1)
| ~ between(w,u,v)
| ~ equidistant(u,v,u1,v1)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(w,v,w1,v1) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( 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,v,u1,v1)
| between(w1,u1,v1)
| ~ equidistant(w,v,w1,v1)
| ~ equidistant(w,u,w1,u1)
| ~ between(w,u,v) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
~ between(w,u,v),
inference(unit_resolution,[status(thm)],[76,48,31,70,28,66]) ).
tff(78,plain,
( colinear(u,v,w)
<=> colinear(u,v,w) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
colinear(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uvw_colinear) ).
tff(80,plain,
colinear(u,v,w),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ colinear(U,V,W)
| colinear(W,U,V) )
<=> ( ~ colinear(U,V,W)
| colinear(W,U,V) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,axiom,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_4) ).
tff(85,plain,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) )
| ~ colinear(u,v,w)
| colinear(w,u,v) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) )
| ~ colinear(u,v,w)
| colinear(w,u,v) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) )
| ~ colinear(u,v,w)
| colinear(w,u,v) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,U,V) )
| ~ colinear(u,v,w)
| colinear(w,u,v) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
colinear(w,u,v),
inference(unit_resolution,[status(thm)],[90,87,80]) ).
tff(92,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ between(X,Y,Z)
| colinear(X,Y,Z) )
<=> ( ~ between(X,Y,Z)
| colinear(X,Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ between(X,Y,Z)
| colinear(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ between(X,Y,Z)
| colinear(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ between(X,Y,Z)
| colinear(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ between(X,Y,Z)
| colinear(X,Y,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ between(X,Y,Z)
| colinear(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity1) ).
tff(96,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ between(X,Y,Z)
| colinear(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ between(X,Y,Z)
| colinear(X,Y,Z) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ between(X,Y,Z)
| colinear(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[97,93]) ).
tff(99,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ between(X,Y,Z)
| colinear(X,Y,Z) )
| ~ between(u1,v1,w1)
| colinear(u1,v1,w1) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ between(X,Y,Z)
| colinear(X,Y,Z) )
| ~ between(u1,v1,w1)
| colinear(u1,v1,w1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ between(X,Y,Z)
| colinear(X,Y,Z) )
| ~ between(u1,v1,w1)
| colinear(u1,v1,w1) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ between(X,Y,Z)
| colinear(X,Y,Z) )
| ~ between(u1,v1,w1)
| colinear(u1,v1,w1) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
~ between(u1,v1,w1),
inference(unit_resolution,[status(thm)],[101,98,3]) ).
tff(103,plain,
( ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( 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,v,u1,v1)
| between(u1,v1,w1)
| ~ between(u,v,w)
| ~ equidistant(v,w,v1,w1)
| ~ equidistant(u,w,u1,w1) )
<=> ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( 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,v,u1,v1)
| between(u1,v1,w1)
| ~ between(u,v,w)
| ~ equidistant(v,w,v1,w1)
| ~ equidistant(u,w,u1,w1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ( 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,v,u1,v1)
| between(u1,v1,w1)
| ~ between(u,v,w)
| ~ equidistant(v,w,v1,w1)
| ~ equidistant(u,w,u1,w1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( 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)
| ~ equidistant(u,w,u1,w1) )
<=> ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( 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,v,u1,v1)
| between(u1,v1,w1)
| ~ between(u,v,w)
| ~ equidistant(v,w,v1,w1)
| ~ equidistant(u,w,u1,w1) ) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( 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)
| ~ equidistant(u,w,u1,w1) )
<=> ( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( 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,v,u1,v1)
| between(u1,v1,w1)
| ~ between(u,v,w)
| ~ equidistant(v,w,v1,w1)
| ~ equidistant(u,w,u1,w1) ) ),
inference(transitivity,[status(thm)],[105,103]) ).
tff(107,plain,
( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( 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)
| ~ equidistant(u,w,u1,w1) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
( ~ ! [W: $i,V: $i,V1: $i,W1: $i,U: $i,U1: $i] :
( 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,v,u1,v1)
| between(u1,v1,w1)
| ~ between(u,v,w)
| ~ equidistant(v,w,v1,w1)
| ~ equidistant(u,w,u1,w1) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
( between(u1,v1,w1)
| ~ between(u,v,w) ),
inference(unit_resolution,[status(thm)],[108,48,31,38,17]) ).
tff(110,plain,
~ between(u,v,w),
inference(unit_resolution,[status(thm)],[109,102]) ).
tff(111,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
<=> ( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(112,plain,
( ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,plain,
( ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ colinear(X,Y,Z)
| between(X,Y,Z)
| between(Y,Z,X) )
<=> ( between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) )),
( ( ~ colinear(X,Y,Z)
| between(X,Y,Z)
| between(Y,Z,X)
| between(Z,X,Y) )
<=> ( between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z)
| between(Z,X,Y) ) )),
rewrite(
( ( between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z)
| between(Z,X,Y) )
<=> ( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) )),
( ( ~ colinear(X,Y,Z)
| between(X,Y,Z)
| between(Y,Z,X)
| between(Z,X,Y) )
<=> ( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(115,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ colinear(X,Y,Z)
| between(X,Y,Z)
| between(Y,Z,X)
| between(Z,X,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ colinear(X,Y,Z)
| between(X,Y,Z)
| between(Y,Z,X)
| between(Z,X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity4) ).
tff(117,plain,
! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[117,113]) ).
tff(119,plain,
! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
inference(skolemize,[status(sab)],[118]) ).
tff(120,plain,
! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[119,112]) ).
tff(121,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(u,v,w)
| between(w,u,v)
| between(v,w,u)
| ~ colinear(w,u,v) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(u,v,w)
| between(w,u,v)
| between(v,w,u)
| ~ colinear(w,u,v) ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
( ( between(v,w,u)
| between(u,v,w)
| between(w,u,v)
| ~ colinear(w,u,v) )
<=> ( between(u,v,w)
| between(w,u,v)
| between(v,w,u)
| ~ colinear(w,u,v) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(v,w,u)
| between(u,v,w)
| between(w,u,v)
| ~ colinear(w,u,v) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(u,v,w)
| between(w,u,v)
| between(v,w,u)
| ~ colinear(w,u,v) ) ),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(v,w,u)
| between(u,v,w)
| between(w,u,v)
| ~ colinear(w,u,v) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(u,v,w)
| between(w,u,v)
| between(v,w,u)
| ~ colinear(w,u,v) ) ),
inference(transitivity,[status(thm)],[123,121]) ).
tff(125,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(v,w,u)
| between(u,v,w)
| between(w,u,v)
| ~ colinear(w,u,v) ),
inference(quant_inst,[status(thm)],]) ).
tff(126,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(u,v,w)
| between(w,u,v)
| between(v,w,u)
| ~ colinear(w,u,v) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
$false,
inference(unit_resolution,[status(thm)],[126,120,110,91,77,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO068-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n008.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 05:12:40 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.
% 0.18/0.42 % SZS status Unsatisfiable
% 0.18/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------