TSTP Solution File: GEO069-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO069-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 41
% Syntax : Number of formulae : 86 ( 21 unt; 5 typ; 0 def)
% Number of atoms : 443 ( 69 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 604 ( 258 ~; 308 |; 0 &)
% ( 38 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 1 >; 2 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 246 ( 232 !; 0 ?; 246 :)
% Comments :
%------------------------------------------------------------------------------
tff(colinear_type,type,
colinear: ( $i * $i * $i ) > $o ).
tff(u_type,type,
u: $i ).
tff(w_type,type,
w: $i ).
tff(v_type,type,
v: $i ).
tff(x_type,type,
x: $i ).
tff(1,plain,
( colinear(x,v,u)
<=> colinear(x,v,u) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
colinear(x,v,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xvu_colinear) ).
tff(3,plain,
colinear(x,v,u),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ colinear(U,V,W)
| colinear(W,V,U) )
<=> ( ~ colinear(U,V,W)
| colinear(W,V,U) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_1) ).
tff(8,plain,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) )
| ~ colinear(x,v,u)
| colinear(u,v,x) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) )
| ~ colinear(x,v,u)
| colinear(u,v,x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) )
| ~ colinear(x,v,u)
| colinear(u,v,x) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) )
| ~ colinear(x,v,u)
| colinear(u,v,x) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
colinear(u,v,x),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( colinear(w,v,u)
<=> colinear(w,v,u) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
colinear(w,v,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wvu_colinear) ).
tff(17,plain,
colinear(w,v,u),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) )
| ~ colinear(w,v,u)
| colinear(u,v,w) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) )
| ~ colinear(w,v,u)
| colinear(u,v,w) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) )
| ~ colinear(w,v,u)
| colinear(u,v,w) ),
inference(quant_inst,[status(thm)],]) ).
tff(20,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) )
| ~ colinear(w,v,u)
| colinear(u,v,w) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
colinear(u,v,w),
inference(unit_resolution,[status(thm)],[20,10,17]) ).
tff(22,plain,
( ( u != v )
<=> ( u != v ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_not_v) ).
tff(24,plain,
u != v,
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
<=> ( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ colinear(U,V,W)
| ~ colinear(U,V,X) )
<=> ( ~ colinear(U,V,X)
| ~ colinear(U,V,W) ) )),
( ( ~ colinear(U,V,W)
| ~ colinear(U,V,X)
| colinear(V,W,X) )
<=> ( ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ) )),
rewrite(
( ( ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
<=> ( ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ) )),
( ( ~ colinear(U,V,W)
| ~ colinear(U,V,X)
| colinear(V,W,X) )
<=> ( ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ) )),
( ( ~ colinear(U,V,W)
| ~ colinear(U,V,X)
| colinear(V,W,X)
| ( U = V ) )
<=> ( ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X)
| ( U = V ) ) )),
rewrite(
( ( ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X)
| ( U = V ) )
<=> ( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ) )),
( ( ~ colinear(U,V,W)
| ~ colinear(U,V,X)
| colinear(V,W,X)
| ( U = V ) )
<=> ( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ colinear(U,V,W)
| ~ colinear(U,V,X)
| colinear(V,W,X)
| ( U = V ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ colinear(U,V,W)
| ~ colinear(U,V,X)
| colinear(V,W,X)
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_2) ).
tff(31,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) ),
inference(modus_ponens,[status(thm)],[33,26]) ).
tff(35,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( u = v )
| ~ colinear(u,v,w)
| ~ colinear(u,v,x)
| colinear(v,w,x) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( u = v )
| ~ colinear(u,v,w)
| ~ colinear(u,v,x)
| colinear(v,w,x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( ( u = v )
| ~ colinear(u,v,x)
| ~ colinear(u,v,w)
| colinear(v,w,x) )
<=> ( ( u = v )
| ~ colinear(u,v,w)
| ~ colinear(u,v,x)
| colinear(v,w,x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( u = v )
| ~ colinear(u,v,x)
| ~ colinear(u,v,w)
| colinear(v,w,x) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( u = v )
| ~ colinear(u,v,w)
| ~ colinear(u,v,x)
| colinear(v,w,x) ) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( u = v )
| ~ colinear(u,v,x)
| ~ colinear(u,v,w)
| colinear(v,w,x) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( u = v )
| ~ colinear(u,v,w)
| ~ colinear(u,v,x)
| colinear(v,w,x) ) ),
inference(transitivity,[status(thm)],[37,35]) ).
tff(39,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( u = v )
| ~ colinear(u,v,x)
| ~ colinear(u,v,w)
| colinear(v,w,x) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( u = v )
| ~ colinear(u,v,w)
| ~ colinear(u,v,x)
| colinear(v,w,x) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
colinear(v,w,x),
inference(unit_resolution,[status(thm)],[40,34,24,21,14]) ).
tff(42,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) )
| ~ colinear(v,w,x)
| colinear(x,w,v) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) )
| ~ colinear(v,w,x)
| colinear(x,w,v) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) )
| ~ colinear(v,w,x)
| colinear(x,w,v) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(W,V,U) )
| ~ colinear(v,w,x)
| colinear(x,w,v) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
colinear(x,w,v),
inference(unit_resolution,[status(thm)],[44,10,41]) ).
tff(46,plain,
( ( ~ colinear(x,w,u)
| ~ colinear(x,w,v) )
<=> ( ~ colinear(x,w,u)
| ~ colinear(x,w,v) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
( ~ colinear(x,w,u)
| ~ colinear(x,w,v) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_xwu_and_xwv_colinear) ).
tff(48,plain,
( ~ colinear(x,w,u)
| ~ colinear(x,w,v) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
~ colinear(x,w,u),
inference(unit_resolution,[status(thm)],[48,45]) ).
tff(50,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( u = v )
| ~ colinear(u,v,w)
| ~ colinear(u,v,x)
| colinear(v,x,w) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( u = v )
| ~ colinear(u,v,w)
| ~ colinear(u,v,x)
| colinear(v,x,w) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( u = v )
| ~ colinear(u,v,w)
| ~ colinear(u,v,x)
| colinear(v,x,w) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( u = v )
| ~ colinear(u,v,w)
| ~ colinear(u,v,x)
| colinear(v,x,w) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
colinear(v,x,w),
inference(unit_resolution,[status(thm)],[52,34,24,21,14]) ).
tff(54,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ colinear(U,V,W)
| colinear(V,U,W) )
<=> ( ~ colinear(U,V,W)
| colinear(V,U,W) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,axiom,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_5) ).
tff(58,plain,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) )
| ~ colinear(x,v,u)
| colinear(v,x,u) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) )
| ~ colinear(x,v,u)
| colinear(v,x,u) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) )
| ~ colinear(x,v,u)
| colinear(v,x,u) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) )
| ~ colinear(x,v,u)
| colinear(v,x,u) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
colinear(v,x,u),
inference(unit_resolution,[status(thm)],[63,60,3]) ).
tff(65,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| colinear(x,w,u)
| ( v = x )
| ~ colinear(v,x,u)
| ~ colinear(v,x,w) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| colinear(x,w,u)
| ( v = x )
| ~ colinear(v,x,u)
| ~ colinear(v,x,w) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ( ( v = x )
| ~ colinear(v,x,u)
| ~ colinear(v,x,w)
| colinear(x,w,u) )
<=> ( colinear(x,w,u)
| ( v = x )
| ~ colinear(v,x,u)
| ~ colinear(v,x,w) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( v = x )
| ~ colinear(v,x,u)
| ~ colinear(v,x,w)
| colinear(x,w,u) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| colinear(x,w,u)
| ( v = x )
| ~ colinear(v,x,u)
| ~ colinear(v,x,w) ) ),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( v = x )
| ~ colinear(v,x,u)
| ~ colinear(v,x,w)
| colinear(x,w,u) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| colinear(x,w,u)
| ( v = x )
| ~ colinear(v,x,u)
| ~ colinear(v,x,w) ) ),
inference(transitivity,[status(thm)],[67,65]) ).
tff(69,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| ( v = x )
| ~ colinear(v,x,u)
| ~ colinear(v,x,w)
| colinear(x,w,u) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ( U = V )
| ~ colinear(U,V,X)
| ~ colinear(U,V,W)
| colinear(V,W,X) )
| colinear(x,w,u)
| ( v = x )
| ~ colinear(v,x,u)
| ~ colinear(v,x,w) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
( colinear(x,w,u)
| ( v = x ) ),
inference(unit_resolution,[status(thm)],[70,34,64,53]) ).
tff(72,plain,
v = x,
inference(unit_resolution,[status(thm)],[71,49]) ).
tff(73,plain,
( colinear(v,w,u)
<=> colinear(x,w,u) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( colinear(x,w,u)
<=> colinear(v,w,u) ),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
( ~ colinear(x,w,u)
<=> ~ colinear(v,w,u) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
~ colinear(v,w,u),
inference(modus_ponens,[status(thm)],[49,75]) ).
tff(77,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) )
| ~ colinear(w,v,u)
| colinear(v,w,u) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) )
| ~ colinear(w,v,u)
| colinear(v,w,u) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) )
| ~ colinear(w,v,u)
| colinear(v,w,u) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ colinear(U,V,W)
| colinear(V,U,W) )
| ~ colinear(w,v,u)
| colinear(v,w,u) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
colinear(v,w,u),
inference(unit_resolution,[status(thm)],[79,60,17]) ).
tff(81,plain,
$false,
inference(unit_resolution,[status(thm)],[80,76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO069-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 05:24:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------